Chemical Decomposition of Silanes for the Production of Solar Grade Silicon

UNIVERSIDAD POLITÉCNICA DE MADRID

ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE TELECOMUNICACIÓN

TESIS DOCTORAL

CHEMICAL DECOMPOSITION OF SILANES FOR THE PRODUCTION OF SOLAR GRADE SILICON

Gonzalo del Coso Sánchez Ingeniero Industrial 2010

UNIVERSIDAD POLITÉCNICA DE MADRID

Instituto de Energía Solar

Departamento de Electrónica Física

Escuela Técnica Superior de Ingenieros de Telecomunicación

TESIS DOCTORAL

DESCOMPOSICIÓN QUÍMICA DE SILANOS PARA LA OBTENCIÓN DE SILICIO DE CALIDAD SOLAR

AUTOR: Gonzalo del Coso Sánchez Ingeniero Industrial DIRECTORES: Antonio Luque López Doctor Ingeniero de Telecomunicación Carlos del Cañizo Nadal Doctor Ingeniero de Telecomunicación

2010

Tribunal nombrado por el Magfco. Y Excmo. Sr. Rector de la Universidad Politécnica de Madrid.

PRESIDENTE:

VOCALES:

SECRETARIO:

SUPLENTES:

Realizado el acto de defensa y lectura de la Tesis en Madrid, el día ___ de _____ de 200__ .

Calificación:

EL PRESIDENTE LOS VOCALES

EL SECRETARIO

A Dacil, mi vida. A Garo´e,mi cachito.

No te quedes inm´ovil al borde del camino no congeles el j´ubilo no quieras con desgana no te salves ahora ni nunca no te salves no te llenes de calma

no reserves del mundo sóloun rincóntranquilo no dejes caer los párpados pesados como juicios

no te quedes sin labios no te duermas sin sue˜no no te pienses sin sangre no te juzgues sin tiempo

pero si pese a todo no puedes evitarlo y congelas el j´ubilo y quieres con desgana

y te salvas ahora y te llenas de calma y reservas del mundo sóloun rincóntranquilo y dejas caer los párpados pesados como juicios y te secas sin labios y te duermes sin sueño y te piensas sin sangre y te juzgas sin tiempo y te quedas inmóvil al borde del camino y te salvas entonces no te quedes conmigo.

No te salves MARIO BENEDETTI

Agradecimientos

Yo hoy no ser´ıalo que soy, ni estar´ıadonde estoy, sin ti, Dacil. Eres el sol que ilumina mi vida. Y lo peor de todo, es que no sési lo sabes. Me has protegido y apoyado durante todo este proceso, y seguramente he tratado másy mejor a la tesis que a ti. Estoy en deuda contigo, Dacil. Te agradezco enormemente que seas mi hogar y mi felicidad. Y que me aguantes. Durante la tesis me has acompañadoen estancias y congresos: hemos perdido dinero en Las Vegas (de acuerdo, lo perd´ıyo), hemos pasado fr´ıoen Yosemite (también por mi culpa) y por poco somos comidos por los osos. Hemos visitado mecas del cine, universidades de pel´ıcula,fiordos y demás.Dicen que la tesis es dura, pero a tu lado todo ha sido muy sencillo. De mi hija, Garoé,he aprendido mucho en este añoy pico de vida que tiene. La lección másimportante: ten paciencia, papá.A la vida hay que ponerle una sonrisa e ilusión.La quiero mucho másde lo que puedo expresar. A mi madre y a mi padre les agradezco lo mucho que me han enseñadode la vida. Hicieron cosas hace 30 añosque no se generalizaránen Españahasta dentro de 40. As´ı son ellos, un modelo para nosotros sus hijos. A Carlos, el director de mi tesis, siempre lo recordarécon extraordinario cariño.Ha sacado lo mejor de m´ıhasta el últimod´ıa. Yo siempre he pensado que tiene madera de gestor. Es una buena persona, justo, inteligente y leal. Te deseo lo mejor, Carlos, y espero que sigamos en contacto. A Luque, sin élyo no hubiera venido al IES, ni hubiera cre´ıdotanto, ni me hubiera esforzado tanto. A su lado yo no encuentro el desaliento. A todo el IES, y aqu´ıtermino. He pasado los cinco añosmásbonitos de mi vida. Me voy y no quiero regodearme. Me voy y me llevo a todos en mi corazón.

RESUMEN

Esta Tesis Doctoral se centra en la reduccióndel coste y del consumo de energ´ıadurante el proceso de producciónde silicio ultrapuro, el tambiénllamado polisilicio. Estas reducciones ayudan a la tecnolog´ıa fotovoltaica basada en silicio a alcanzar dos de sus principales objetivos para establecerse como una tecnolog´ıa viable: bajos costes de produccióny bajos tiempos de recuperaciónde la energ´ıa. Se ha definido una tecnolog´ıafotovoltaica, basada en silicio cristalino, y se han presentado sus costes de producción. Este análisispermite estimar el impacto de la reducción de costes de la materia prima, el polisilicio, en el producto final, el modulo fotovoltaico. También,mediante dicho análisisse ha podido estudiar el impacto sobre el coste del módulo de las dos principales v´ıaspara producir polisilicio: la v´ıaqu´ımica,con altos costes y altas calidades, y la v´ıametalúrgica, con menores costes y menores calidades. Este ejercicio de análisismuestra que la calidad de la materia prima (evaluada como la eficiencia de célula)es un inductor de coste muy importante. Como consequencia, esta Tesis Doctoral se centra en la v´ıaqu´ımica,capaz de producir polisilicio de mayor calidad, proponiendo alternativas y mejoras en el proceso para disminuir los costes de produccióny el consumo energético. El análisisteóricodel depósitode polisilicio en un reactor de depósitoqu´ımicoen fase vapor (CVD), presentado en esta memoria, comprende: (a) el estudio de las condiciones óptimasde depósitomediante la teor´ıa fluido-mecánica; (b) el estudio de la radiación térmicade las varillas calientes de silicio por medio de la teor´ıade transferencia de calor por radiación;y (c) el estudio del calentamiento eléctricode las varillas de silicio mediante la teor´ıaelectromagnética. Se ha presentado un modelo fluido-mecániconovedoso que propone expresiones anal´ıti- cas para la tasa de crecimento de polisilicio sobre las varillas de silicio y para las pérdidas energéticaspor convección.La condiciones óptimasde depósito,basadas en el criterio de minimizacióndel consumo energético,se han obtenido del modelo. La transferencia de calor por radiacióndentro del reactor CVD se ha analizado en detalle para tres configuraciones que son estado del arte: 36 varillas organizadas en 3 anillos, 48 varillas organizadas en 4 anillos y 60 varillas organizadas en 4 anillos. Se han propuesto alternativas para disminuir las pérdidasenergéticaspor radiación:aumentar la capacidad de los reactores, mejorar la reflectividad de la pared del reactor e introducir escudos térmicosdentro del reactor. Resumen

Un inductor importante para la reduccióndel consumo energéticoes el diámetro máximode la varilla cuando se para el proceso. La principal limitaciónpara aumentar dicho diámetromáximoes el riesgo de que se funda el centro de la varilla. El modelo para el calentamiento eléctricode las varillas, presentado en esta memoria, permite conocer el perfil de temperatura dentro de la varilla de silicio, deduciendo el diámetrode varilla l´ımite, en el cual el centro de la varilla se funde. Se han propuesto en esta Tesis Doctoral dos alternativas para incrementar el diámetromáximomediante la homogenizacióndel perfil de temperaturas: incrementar la reflectividad de la pared, introducir escudos térmicosy utilizar fuentes de corriente de alta frecuencia para calentar las varillas de silicio. Se ha propuesto un proceso de depósticocompleto, basado en las aproximaciones teóricaspresentadas en esta Tesis y caracterizado por el bajo consumo energético. Se han detallado las condiciones de depósitoy las condiciones eléctricas,tensióny corriente, para calentar las varillas en un reactor CVD de 36 varillas. El análisisteóricose ha equilibrado con trabajo experimental, usando tanto triclorosilano como silano como gases precursores. El trabajo experimental ha mostrado las di- ficultades para trabajar en la condiciones óptimasde trabajo, ya que pueden originarse dendritas. Tambiénel caráctercorrosivo del triclorosilano se ha puesto de manifiesto durante la operaciónde reactor de depósito a escala de laboratorio, diseñado, desarrollado y construido en el Instituto de Energ´ıaSolar.

ii ABSTRACT

This Doctoral Thesis comprises research on the reduction of cost and energy consumption of the production of ultrapurified silicon, so-called polysilicon. These respective reductions are essential to achieving two wider objectives for silicon based photovoltaic technology: low production cost and low energy payback time. A crystalline silicon photovoltaic module technology is defined and its production costs are presented. This allows cost and energy reduction measures to be compared and valued with regard to their impact on the final product. It further permits a cost-per-kilowatt comparison of the two main polysilicon production routes: the chemical route, with high quality and high cost; and the metallurgical route, with lower quality and lower cost. This costing exercise shows the quality of polysilicon (evaluated as the cell efficiency) to be an important driver for module cost-per-kilowatt reduction. Consequently, the presented research focuses on the high-quality chemical route. The presented theoretical analysis of polysilicon deposition in a CVD reactor consists in: (a) the study of the optimum deposition conditions by means of fluid mechanical theory; (b) the study of the thermal radiation of the hot silicon rods by means of thermal radiation heat transfer theory; and (c) the study of the electric heating of the silicon rod by means of electromagnetic theory. A novel fluid mechanical model is presented that proposes analytical expressions for the growth rate of polysilicon onto the silicon rods and for the energy loss by convection. The optimum deposition conditions, which reduce energy consumption, are derived from the model. The thermal radiation heat transfer within the CVD reactor is studied in detail for three state-of-the-art configurations: 36 rods arranged in 3 rings, 48 rods arranged in 3 rings and 60 rods arranged in 4 rings. Alternatives are presented regarding the reduction of the radiant energy loss during the polysilicon deposition: enlarge the reactor capacities, enhance the wall reflectivity and introduce thermal shields within the reactor vessel. An important factor affecting overall energy consumption is the maximum rod diameter reached at the end of the process. The main limitation for increasing this maximum diameter is the risk of melting the rod core. The temperature profile within the silicon rod resulting from electrical heating is modelled, and the limiting diameter at which the core begins to melt is calculated. Two alternatives are proposed for increasing the maximum Abstract

diameter by reducing the non-homogeneous temperature profile: increasing the wall reflectivity/introducing thermal shields, and use of a high-frequency current source to heat the rods. Based on the presented theoretical study, a complete deposition process is proposed that is characterised by low energy consumption. The deposition conditions and the electrical conditions (current and voltage) for heating rods in a 36 rods CVD reactor are detailed. Finally, polysilicon deposition has been studied experimentally, and the practicability of the calculated optimum conditions has been tested. Silicon rods have been grown in the laboratory scale deposition reactor, designed, developed and constructed, in part by the author, at the Instituto de Energ´ıaSolar, using trichlorosilane and silane as prescursor gases. The experiments show the difficulty in working under the optimum conditions: undesirable dendritic growth was observed, and the trichlorosilane was seen to corrode the reactor. Further experimental study is required in the future to fully understand the polysilicon deposition process in a CVD reactor.

iv Contents

List of Figures ix

List of Symbols xix

1 Introduction 1 1.1 Silicon for photovoltaics applications ...... 3 1.1.1 Simplifying the chlorosilane route ...... 4 1.1.2 Metallurgical route ...... 5 1.1.3 Others ...... 6 1.2 Quality and cost ...... 6 1.3 Centesil, R&D on polysilicon production ...... 7 1.4 The thesis ...... 8

2 The inﬂuence of silicon feedstock on the photovoltaic module manufacturing cost 9 2.1 Introduction ...... 9 2.2 Establishing a reference technology ...... 11 2.2.1 Basepower reference technology ...... 12 2.3 Potential for cost savings ...... 12 2.3.1 Advanced Basepower technology ...... 15 2.4 The impact of silicon feedstock ...... 16 2.5 Results ...... 20 2.5.1 Impact of feedstock cost, silicon utilisation and cell eﬃciency . . . . 20 2.5.2 New feedstock sources ...... 24 2.6 Proposal of future technologies ...... 26 2.6.1 Cost structure of the future technologies ...... 26 2.6.2 Impact of new feedstock sources ...... 30 2.7 Conclusions ...... 31

v Contents

3 Model of chemical vapour deposition of polysilicon by trichlorosilane decomposition 33 3.1 Introduction ...... 33 3.2 Conservation equations ...... 36 3.2.1 Conservation of Mass ...... 37 3.2.2 Conservation of Individual Species Mass ...... 37 3.2.3 Conservation of Linear Momentum ...... 39 3.2.4 Conservation of Energy ...... 39 3.3 The properties of gases ...... 40 3.3.1 Binary diffusion coefficient ...... 40 3.3.2 Thermal diffusion factor ...... 41 3.3.3 Viscosity ...... 41 3.3.4 Thermal conductivity ...... 41 3.4 Deposition model ...... 42 3.4.1 Velocity profile ...... 43 3.4.2 Heat transfer ...... 44 3.4.3 Mass transport of species ...... 45 3.5 Results of the model ...... 49 3.5.1 Effect of the gas flow ...... 50 3.5.2 Effect of the gas composition ...... 52 3.5.3 Effect of the pressure and the rod surface temperature ...... 53 3.5.4 Effect of the rod diameter ...... 56 3.6 Discussion of results ...... 60 3.7 Conclusions ...... 65

4 Radiative energy loss in the polysilicon CVD reactor 67 4.1 Introduction ...... 67 4.2 Rod arrangement within the CVD deposition reactor ...... 68 4.2.1 Rod arrangement in concentric rings ...... 69 4.3 Radiation exchange between the polysilicon rods and the reactor wall . . . 72 4.3.1 Geometric conﬁguration factors ...... 73 4.3.2 Hottel’s crossed-string method ...... 75 4.3.3 Governing equations ...... 79 4.3.4 Properties of the materials ...... 83 4.4 Reactor conﬁgurations ...... 86 4.4.1 36 rods arranged in three rings ...... 87 vi Contents

4.4.2 48 rods arranged in three rings ...... 91 4.4.3 60 rods arranged in four rings ...... 94 4.5 Discussion ...... 98 4.5.1 Influence of the reactor configurations ...... 98 4.5.2 Influence of the thermal shields ...... 99 4.5.3 Influence of the wall properties ...... 103 4.6 Conclusions ...... 105

5 Electric heating of the polysilicon rods in the CVD reactor 107 5.1 Introduction ...... 107 5.2 Silicon rod resistance ...... 109 5.3 Model for the radial temperature profile in the silicon rods ...... 113 5.3.1 Vibration model of the silicon rod ...... 115 5.4 Results of the model ...... 116 5.4.1 Effect of the radiation conditions ...... 116 5.4.2 Effect of the high frequency current sources ...... 119 5.5 Discussion of results ...... 122 5.6 Current-Voltage curves in the CVD reactor ...... 126 5.6.1 Current-Voltage curves during the preheating of the silicon rods . . 126 5.6.2 Current-Voltage curves during operation ...... 128 5.7 Conclusions ...... 131

6 Experimental approach 133 6.1 Introduction ...... 133 6.2 Lawrence Berkeley National Laboratory ...... 133 6.2.1 Description of the system ...... 134 6.2.2 Experimental ...... 136 6.2.3 Quality analysis by means of LA-ICP-MS ...... 139 6.3 Instituto de Energ´ıaSolar ...... 145 6.3.1 Description of the system ...... 145 6.3.2 Measurement of the rod surface temperature ...... 148 6.3.3 Experimental ...... 150 6.3.4 Summary of experiments ...... 159 6.4 Conclusions ...... 160

7 Conclusions and future works 163 7.1 Conclusions ...... 164

vii Contents

7.2 Future works ...... 167

A Derivation of the solutions for the conservation equations 169 A.1 Temperature distribution ...... 169

A.2 Mass fraction distribution: growth limited by H2 ...... 170

A.3 Mass fraction distribution: growth limited by HSiCl3 after limitation change 171

Bibliography 173

viii List of Figures

1.1 Thousand tons per year of silicon production. Estimates taken from [Rogol, 2010]...... 1 1.2 Electronic and solar shares of silicon consumption. Estimates taken from [Meyers, 2009a]...... 2 1.3 Routes towards the production of ’Solar Silicon’...... 4 1.4 Cost break down for Polysilicon. Estimates from [Mozer and Fath, 2006]. . 5

2.1 Cost structure of Basepower technology. (a) Breakdown by process step −1 and by cost category, in e·Wp . (b) Cost breakdown in percent, with indications of the basic approaches that should be followed for cost reduction. 14 2.2 Cost structure of Advanced Basepower technology. (a) Breakdown by pro- −1 cess step and by cost category, in e·Wp . (b) Cost breakdown in percent. . 18 2.3 Explanation of the ”Fully-integrated cost” concept, using silicon growth as

an example. Throughout the production chain the yield losses (Yj) are 0 accumulated and therefore the ingot growth cost increases. Ci is the cost for the ingot growth process disregarding any yield loss...... 20 2.4 Module cost dependence on encapsulated cell efficiency for Advanced Base- power technology. Advanced Basepower absolute parameters: encapsulated −1 cell efficiency, 15.8%, total cost, 1.15 e·Wp ...... 21 2.5 Iso-cost curves for Advanced Basepower technology regarding encapsulated cell efficiency and feedstock cost. Advanced Basepower absolute parameters: encapsulated cell efficiency, 15.8%, feedstock cost, 20 e·kg−1...... 22 2.6 Iso-cost curves for Advanced Basepower technology regarding ingot growth

fraction (fig) and feedstock cost. Advanced Basepower absolute parameters: −1 fig, 93%, feedstock cost, 20 e·kg ...... 23 2.7 Iso-cost curves for Advanced Basepower technology regarding feedstock process yield and feedstock cost. Advanced Basepower absolute parameters: feedstock process yield, 100%, feedstock cost, 20 e·kg−1...... 23

ix List of Figures

2.8 Iso-cost curves for Advanced Basepower technology regarding slicing pitch and feedstock cost. Advanced Basepower absolute parameters: slicing pitch, 350 µm, feedstock cost, 20 e·kg−1 ...... 24

2.9 Sketches of the cell structures and module assemblies proposed in the future technologies. (a) Sketches of the cell structures. Top left: Advanced Basepower; top right: front and rear contacted Multistar and Superslice; bottom left: all-rear-contacted MultistaR and SuperslicE. (b) Sketches of the assembly approaches for the front to rear contacted cells (left) and the all rear contacted cells (right)...... 27

3.1 Polysilicon deposition reactor. In this particular case, there are 24 rods arranged in two concentric rings. Source: STR group...... 35

3.2 System geometry. Top and side view ...... 42

3.3 Growth rate (−) and deposition efficiency (−−) for different total gas flow

rates, from Re = 1-2300. Gas molar composition: xH2 = 0.9. All other parameters are set as presented in table 3.1...... 50

3.4 Power loss by convection (−) and energy loss by convection per kg of polysilicon produced (−−) for diﬀerent total gas ﬂow rates, from Re = 1-2300. Gas

molar composition: xH2 = 0.9. All other parameters are set as presented in table 3.1...... 51

3.5 Growth rate (−) and deposition eﬃciency (−−) for diﬀerent inlet gas compositions. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1...... 52

3.6 Power loss by convection (−) and energy loss by convection per kg of polysilicon produced (−−) for diﬀerent inlet gas compositions. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1...... 53

3.7 Inlet gas compositions, expressed as the hydrogen molar fraction, that achieve the maximum growth rate for diﬀerent rod surface temperatures and reactor pressures. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1...... 54

3.8 Maximum growth rate, expressed in µm·min−1, dependence on the reactor pressure and rod surface temperature. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1...... 55 x List of Figures

3.9 Dependence of the total energy consumption, considering convection and radiation, on the rod surface temperature. Re = 2300 at the inlet, the reactor pressure is p = 6 atm and the inlet gas compositions are those presented in ﬁgure 3.7. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. All other parameters are set as presented in table 3.1. . 55

3.10 Dependence of the total energy consumption, considering convection and radiation, on the pressure within the reactor vessel. Re = 2300 at the inlet, the rod surface temperature is 1150 ◦C and the inlet gas compositions are those presented in ﬁgure 3.7. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. All other parameters are set as presented in table 3.1...... 56

3.11 Maximum growth rate, expressed in µm·min−1, dependence on the rod surface temperature and the rod diameter. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. All other parameters are set as presented in table 3.1...... 57

3.12 Inlet gas compositions, expressed as the hydrogen molar fraction, that achieve the maximum growth rates presented in ﬁgure 3.11. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. All other parameters are set as presented in table 3.1...... 58

3.13 Power loss by convection, expressed in kW, dependence on the rod surface temperature and the rod diameter. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. The inlet gas compositions are presented in ﬁgure 3.12. All other parameters are set as presented in table 3.1...... 58

3.14 Inlet gas flows, expressed in kmol·h−1, that achieve the maximum growth rates presented in figure 3.11. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. The inlet gas compositions are presented in figure 3.12. All other parameters are set as presented in table 3.1...... 59

3.15 Variation of the rod surface temperature that minimises the total energy consumption, considering convection and radiation, with rod diameter. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. All other parameters are set as presented in table 3.1...... 60

xi List of Figures

3.16 Inlet gas composition, expressed as the hydrogen molar fraction, throughout the deposition process. The pressure in the reactor vessel is p = 6 atm, and ◦ the rod surface temperature is Ts = 1050 C. All other parameters are set as presented in table 3.1...... 62 3.17 Inlet gas ﬂow, expressed in kmol·h−1, that yields a deposition eﬃciency of 10% throughout the deposition process. The pressure in the reactor vessel ◦ is p = 6 atm, and the rod surface temperature is Ts = 1050 C. A 36 rod CVD reactor is considered. All other parameters are set as presented in table 3.1...... 62 3.18 Growth rate, expressed in µm·min−1, throughout the deposition process. The pressure in the reactor vessel is p = 6 atm, and the rod surface tem- ◦ perature is Ts = 1050 C. All other parameters are set as presented in table 3.1...... 63 3.19 Energy consumption, expressed in kWh·kg−1, throughout the deposition process. Radiation loss and convection loss are considered. The pressure in

the reactor vessel is p = 6 atm, and the rod surface temperature is Ts = 1050 ◦C. A 36 rod CVD reactor is considered. All other parameters are set as presented in table 3.1...... 63

4.1 Undesirable rod arrangements. (a) There is no space for polysilicon growth or gas circulation. (b) The rods do not occupy the reactor uniformly . . . . 69 4.2 Hexagonal rod arrangement...... 70 4.3 Ring of rods...... 71 4.4 Distance between rings. Two control spaces in ring two are tangential to one control space in ring one...... 72

4.5 Rate of incoming and outgoing radiant energy per unit area of Ak...... 74 4.6 Radiative transfer between differential areas...... 75 4.7 Hottel’s crossed-string method for evaluating geometric configuration factors. 76 4.8 Configuration factor between two cylinders of equal radius...... 77 4.9 Comparison of the exact and approximated method for evaluating the geometric configuration factor. The distance between cylinder centres is four times their radius. (a) Geometric configuration factors for infinitely long cylinders and finite length cylinders. (b) Difference in the calculated values of the geometric configuration factor, relative to the value for finite length cylinders. F ∞ is for the configuration factor calculated by Hottel’s method and F l is the configuration factor calculated by reference Jull [1982]. . . . . 78 xii List of Figures

4.10 The polysilicon rods, at a known and constant temperature are surrounded by thermal shields, whose temperatures depend on the radiation transfer in the system. The reactor wall encloses the system at a known and constant temperature...... 81 4.11 Spectral emissivity of n-type silicon, doping concentration 2.94 · 1014 cm−3. From reference [Ravindra et al., 2001]...... 84 4.12 Spectral reflectivity of alumina and aluminium nitride. Measured by Dr. Ignacio Tob´ıasduring the Ph.D. thesis of Rodr´ıguezSan Segundo [2007]. . 85 4.13 Total hemispherical reflectivity of inconel 718. From reference Greene et al. [2000]...... 86 4.14 CVD reactor with 36 rods arranged in 3 rings, the control space diameter is 25 cm. Typical capacity: 200 t/year. Inner ring diameter: 50 cm, middle ring diameter: 96.5 cm, outer ring diameter: 143 cm, wall diameter: 229 cm. The rods are labelled counter-clockwise...... 87 4.15 Geometric configuration factor from rod 1 to the wall in a 36 rod CVD

reactor. drod is the silicon rod diameter and the control space diameter is d = 25 cm...... 88 4.16 Power radiated by the silicon rods and absorbed by the reactor wall in the 36 rod CVD reactor presented in figure 4.14, for different rod diameters. . 89 4.17 Power radiated by one rod in each ring (inner, middle and outer rings) to the wall in the 36 rod CVD reactor presented in figure 4.14...... 89 4.18 Power radiated by the silicon rods and absorbed by the reactor wall in the 36 rod CVD reactor with one thermal shield, for different rod diameters. . 90 4.19 Temperature of the thermal shield for different rod diameters in the 36 rod CVD reactor...... 90 4.20 CVD reactor with 48 rods arranged in 3 rings, the control space diameter is 25 cm. Typical capacity: 300 t/year. Inner ring diameter: 81 cm, middle ring diameter: 129 cm, outer ring diameter: 175 cm, wall diameter: 260 cm. The rods are labelled counter-clockwise...... 91 4.21 Geometric configuration factor from rod 1 to the wall in a 48 rod CVD

reactor. drod is the silicon rod diameter and the control space diameter is d = 25 cm...... 92 4.22 Power radiated by the silicon rods and absorbed by the reactor wall in the 48 rod CVD reactor presented in figure 4.20, for different rod diameters. . 92 4.23 Power radiated by the characteristic rods of every ring (inner, middle and outer) to the wall in the 48 rod CVD reactor presented in figure 4.20. . . . 93

xiii List of Figures

4.24 Power radiated by the silicon rods and absorbed by the reactor wall in the 48 rod CVD reactor with one thermal shield, for diﬀerent rod diameters. . 93

4.25 Temperature of the thermal shield for diﬀerent rod diameters in the 48 rod CVD reactor...... 94

4.26 CVD reactor with 60 rods arranged in 4 rings, the control space diameter is 25 cm. Typical capacity: 400 t/year. Inner ring diameter: 50 cm, second ring diameter: 96.5 cm, third ring diameter: 143 cm, outer ring diameter: 191.5 cm, wall diameter: 276.5 cm. The rods are labelled counter-clockwise. 95

4.27 Geometric conﬁguration factor from rod 1 to the wall in a 60 rod CVD

reactor. drod is the silicon rod diameter and the control space diameter is d = 25 cm...... 95

4.28 Power radiated by the silicon rods and absorbed by the reactor wall in the 60 rod CVD reactor presented in ﬁgure 4.26, for diﬀerent rod diameters. . 96

4.29 Power radiated by the characteristic rods of every ring (inner, second, third and outer) to the wall in the 60 rod CVD reactor presented in ﬁgure 4.26. . 96

4.30 Power radiated by the silicon rods and absorbed by the reactor wall in the 60 rod CVD reactor with one thermal shield, for diﬀerent rod diameters. . 97

4.31 Temperature of the thermal shield for diﬀerent rod diameters in the 60 rod CVD reactor...... 97

4.32 Average power emitted per rod and absorbed by the reactor wall for diﬀerent reactor conﬁgurations...... 98

4.33 Dependence of the energy radiated per kilogram of polysilicon produced on the average growth rate throughout the deposition process, for the three reactor conﬁgurations considered...... 99

4.34 Power absorbed by the wall for diﬀerent arrangements of thermal shields in a 36 rods reactor. Diﬀerent rod diameters are considered. (a) Power absorbed by the wall without thermal shields and with one thermal shield in a 36 rods reactor. (b) Power absorbed by the wall with one, two and three thermal shields in a 36 rod reactor...... 100

4.35 Temperatures of the thermal shields for diﬀerent arrangements of thermal shields in a 36 rod reactor. (a) One shield. (b) Two shields...... 101

4.36 Dependence of the energy radiated per kilogram of polysilicon produced on the average growth rate throughout the deposition process, considering the 36 rod reactor without thermal shields and with one thermal shield. . . . . 102 xiv List of Figures

4.37 Dependence of the energy radiated per kilogram of polysilicon produced on the thermal shield emissivity. Only one shield considered in a 36 rod reactor. The average polysilicon growth rate is 7 µm·min−1...... 102 4.38 Shield emissivity dependence of the temperature of the thermal shield and the layer thickness of polysilicon deposited on it. Only one shield considered in a 36 rod reactor. (a) Dependence of the temperature of the thermal shield on the thermal shield emissivity. (b) Estimation of the polysilicon growth over the thermal shield...... 103 4.39 Power radiated by the silicon rods and absorbed by the reactor wall in a 36 rod CVD reactor for diﬀerent wall emissivities...... 104 4.40 Energy radiated per kilogram of polysilicon produced in a 36 rod CVD reactor for diﬀerent values of the wall emissivity. The average polysilicon growth rate is 7 µm·min−1...... 104

5.1 Electron and hole mobilities in n-type silicon, ρ =200 mΩcm at room temperature...... 111 5.2 Carrier concentration of electrons and holes, n and p, in n-type silicon (ρ

=200 mΩcm at room temperature) and intrinsic carrier concentration, ni. . 112 5.3 Resistance for n-type slim rods for two doping levels: 200 and 40 mΩcm at room temperature. Rod length: 4 m, rod diameter: 1 cm...... 112 5.4 Temperature profile within silicon rods located in the inner ring, middle ring and outer ring of a 36 rod CVD reactor. The rod diameter is 14 cm ◦ and the rod surface temperature is Ts=1050 C...... 117 5.5 Temperature profile within the silicon rod as a function of reactor wall emissivity. The rod has a diameter of 14 cm and is located in the outer ring ◦ of a 36 rod CVD reactor. The rod surface temperature is Ts=1050 C. . . . 117 5.6 Temperature difference between the rod centre and the rod surface as a

function of the wall emissivity. The rod surface temperature is Ts=1050 ◦C, the rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor...... 118 5.7 RMS current needed to set the rod surface temperature at 1050 ◦C as a function of the wall emissivity. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor...... 118 5.8 Temperature proﬁle within the silicon rod for diﬀerent current frequencies. The rod has a diameter of 14 cm and is located in the outer ring of a 36 ◦ rod CVD reactor. The rod surface temperature is Ts=1050 C...... 119

xv List of Figures

5.9 RMS current density profile within silicon rod for different current frequencies. Current density profiles generate temperature profiles presented in figure 5.8. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor...... 120 5.10 Temperature difference between the centre and the surface of the rod as a function of frequency considering the outer ring (−), the middle ring (−−), and the inner ring (·−) in a 36 rod CVD reactor. The rod surface ◦ temperature is Ts=1050 C and the rod diameter is 14 cm...... 121 5.11 RMS current needed to set the rod surface temperature at 1050 ◦C as a function of frequency. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor...... 121 5.12 Energy consumption throughout the deposition process for different maximum rod diameters, from 14 to 20 cm. A 36 rod CVD reactor is considered, and the average polysilicon growth rate is 7 µm·min−1...... 123 5.13 Maximum surface temperature that can be reached before the core melts as a function of rod diameter. The U-rod is located in the outer ring of a 36 rod CVD reactor. The wall emissivity is 0.5...... 123 5.14 Maximum Current that can be reached before the core melts as a function of rod diameter. The U-rod is located in the outer ring of a 36 rod CVD reactor. The wall emissivity is 0.5...... 124 5.15 Dependence on the reactor wall emissivity of the maximum rod surface temperature that can be reached before melting the rod core. The rod is located in the outer ring of a 36 rod CVD reactor, and its diameter is 20 cm.125 5.16 Voltage (−) and current (−−) applied to a silicon U-rod to maintain different rod temperatures. The U-rod is located in the outer ring of a 36 rod CVD reactor. U-rod length: 4m, U-rod diameter: 0.7 cm, n-type silicon, room resistivity: 200 mΩ·cm. Reactor under vacuum...... 127 5.17 Ignition temperature (−) and peak voltage (−−) of a silicon U-rod for different doping levels: from highly doped n-type silicon (0.1 Ω·cm) to intrinsic material (105 Ω·cm). U-rod length: 4m, U-rod diameter: 0.7 cm. Reactor under vacuum. Reactor wall at 100 ◦C...... 128 5.18 Voltage (−) and current (−−) throughout the process for a U-rod located in the outer ring. U-rod length: 4 m. The deposition process takes place in the 36 rod CVD reactor presented in chapter 4 (section 4.4.1 without thermal shield). The deposition conditions are presented in table 3.2. . . . . 129 xvi List of Figures

5.19 Voltage (−) and current (−−) throughout the process for a U-rod located in the middle ring. U-rod length: 4 m. The deposition process takes place in the 36 rod CVD reactor presented in chapter 4 (section 4.4.1 without thermal shield). The deposition conditions are presented in table 3.2. . . . . 130 5.20 Voltage (−) and current (−−) throughout the process for a U-rod located in the inner ring. U-rod length: 4 m. The deposition process takes place in the 36 rod CVD reactor presented in chapter 4 (section 4.4.1 without thermal shield). The deposition conditions are presented in table 3.2. . . . . 130

6.1 Laboratory-scale deposition reactor. Electronic Materials Program, Mate- rials Science Division, LBNL. From Ager et al. [2005]...... 135 6.2 Laboratory-scale recirculating system. Electronic Materials Program, Ma- terials Science Division, LBNL. From Ager et al. [2005]...... 136 6.3 Laboratory-scale deposition reactor. Electronic Materials Program, Mate- rials Science Division, LBNL. Picture taken during my research stay at the LBNL, October, 2007...... 137 6.4 Diagram of the experiment for producing polysilicon, under steady-state

conditions. MS: silane, SiH4, H2: hydrogen, H2...... 138 6.5 Polysilicon rod grown in the laboratory-scale deposition reactor during my research stay at the Materials Science Division, LBNL. November, 2007. . 139 6.6 Set-up of a laser ablation system, using ICP-MS and ICP-AES detection. ICP-MS detection is employed at the Laser Spectroscopy & Applied Ma- terials Group, Environmental Energy Technologies Division, LBNL. From reference Russo et al. [2002]...... 141 6.7 Polysilicon sample after laser ablation...... 142 6.8 Image of the ablated zone acquired by a white light interferometry microscope. The acronym IES (Instituto de Energ´ıaSolar) is written in 0.5 mm. 142 6.9 ICP-MS intensity for silicon. Detection of silicon in the polysilicon sample. 143 6.10 ICP-MS for B, Mg, Al, P, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo and Sn (considering different masses). The intensity when the laser is on is compared to the intensity when the laser is off...... 143 6.11 ICP-MS for the four elements detected in the analysis of the polysilicon sample: (a) Mg, (b) Ti , (c) Cu, and (c) Zn...... 144 6.12 Polysilicon deposition reactor. Instituto de Energ´ıa Solar, Universidad Politécnicade Madrid...... 146

xvii List of Figures

6.13 Laboratory-scale complete system. Instituto de Energ´ıaSolar, Universidad Polit´ecnicade Madrid...... 147 6.14 Picture of the laboratory-scale deposition system. Instituto de Energ´ıaSo- lar, Universidad Polit´ecnicade Madrid...... 147 6.15 Circuit diagram of the laboratory scale reactor power supply...... 148 6.16 Calibration of the two-colour pyrometer. Determination of the ratio of emissivities. The average ratio is 0.9305...... 151 6.17 Experiment 1: rod after polysilicon deposition...... 152 6.18 Experiment 1: detailed view of the rod after polysilicon deposition...... 153 6.19 Experiment 2: a detailed view of the rod after polysilicon deposition. . . . . 154 6.20 Experiment 3: detailed view of the rod after polysilicon deposition...... 155 6.21 Experiment 4: a detailed view of the rod after polysilicon deposition. . . . . 156 6.22 Experiment 5: a detailed view of the rod after polysilicon deposition. . . . . 158 6.23 Experiment 6: a detailed view of the rod after polysilicon deposition. . . . . 159

xviii List of Symbols

αT thermal diﬀusion factor, dimensionless

∆TTs − T0,K

κ thermal conductivity of the gas mixture, W m−1 K−1

µ viscosity of the gas mixture, kg m−1 s−1

νi molar stoichiometry coeﬃent of species i in chemical reaction (3.36)

ωi mass fraction of species i

ρ density of the gas mixture, kg m−3

A0 property A at inlet conditions

As property A on the rod surface

−1 −1 Cp heat capacity at constant pressure, J kg K

Di binary diﬀusion coeﬃcient of species i, see DH2 , Dtcs and Dhcl

Deq equivalent diameter, 2 (ro − ri), m

2 −1 Dh2 binary diﬀusion coeﬃcient of H2 in HSiCl3, m s

2 −1 Dhcl binary diﬀusion coeﬃcient of HCl in H2, m s

−3 dSi density of solid silicon, kg m

2 −1 Dtcs binary diﬀusion coeﬃcient of HSiCl3 in H2, m s

F1→2 Geometric conﬁguration factor from area A1 to A2 fig ingot growth fraction g gravity acceleration, m s−2

xix List of symbols

h convection coeﬃcient, W m−2 K−1

J0 ﬁrst kind bessel function of order zero k overall reaction rate constant, m4 mol−1 s−1

−1 kr decomposition rate constant, m s

−1 kad chemisorption rate constant, m s

L reactor length, m

−1 Mi molecular weight of species i, kg mol

−1 Msi molecular weight of silicon, kg mol p pressure, Pa r radial component, m

−2 −1 Ri mass rate of consumption or generation of species i on the rod surface, kg m s ri rod radius, inner radius, m ro outer radius, m

−1 Re Reynolds number ρvDeqµ , dimensionless

T temperature, K

TCS trichlorosilane, HSiCl3

−1 vg polysilicon growth rate, µm min

−1 vr radial component of the gas velocity, m s

−1 vz axial component of the gas velocity, m s

Y0 second kind bessel function of order zero zl changing limitation point, m

[i] mole concentration of species i on the rod surface, mol·m−3

Wp watt-peak

xx Chapter 1

Introduction

The market for ultrapurified silicon, typically referred to as ’polysilicon’, which was traditionally devoted to microelectronics, is currently subject to profound changes due to the expansion of the photovoltaic (PV) industry. In 2009, a total amount of 80,000 t of polysilicon was consumed by the solar industry vs 20,000 t by the semiconductor industry [Rogol, 2010], and the share of polysilicon used for solar will certainly increase in the medium and long terms [Meyers, 2009a], as the perspectives of growth for the PV industry are very solid [Luque, 2001]. The estimates for worldwide silicon production in the following years can be consulted in figure 1.1, and the electronic and solar industry shares of silicon consumption are depicted in figure 1.2.

Figure 1.1: Thousand tons per year of silicon production. Estimates taken from [Rogol, 2010].

The consequence is that while in 2000 virtually only 6 companies supplied all polysilicon

1 Chapter 1. Introduction

Figure 1.2: Electronic and solar shares of silicon consumption. Estimates taken from [Meyers, 2009a]. consumed worldwide (Hemlock, Wacker, REC, MEMC, Tokuyama, and Mitsubishi), this concentration no longer makes sense, since even for a medium size PV company producing 100 MWp/a, it is worth having their own silicon feedstock factory, in the range of 1000 t/a. The reliance of PV companies on polysilicon has put them in a complex situation in recent years, as traditional suppliers were not prepared to attend to their quickly growing demands. That produced a scenario of scarcity of polysilicon, which made prices climb to the level of hundreds of dollars per kg, shrank the capacity expansions already planned by a great number of PV companies, and jeopardized those which were not able to secure their polysilicon feedstock. Traditional polysilicon suppliers reacted by expanding production, and a number of newcomers tried to enter the market, acquiring the technology by themselves or even exploring the viability of new sources of purified silicon [Meyers, 2009b]. The scenario has abruptly changed due to the economic crisis, the financial restrictions and the modified regulations of some PV regional markets such as Spain. In 2009 the PV companies grew at a much lower rate than expected, so that many requests for polysilicon have been cancelled or postponed, making polysilicon prices fall quickly, strengthening the position of the established companies, as they have optimised cost structures and proven technologies, and putting pressure to the new entrants that have to compete with them. But this situation of overcapacity is temporary, because PV annual productions in the range of tens of GW are foreseen in some years. The demand for polysilicon will be much

2 1.1. Silicon for photovoltaics applications

higher, and new capacity will have to be implemented. Issues such as material quality, energy consumption in the fabrication process and cost structure of the product will then return to the foreground. The CENTESIL initiative is being developed in this exciting market, as a new private- public partnership venture promoting a pilot plant for polysilicon production, in an advanced state of construction. CENTESIL aims at allowing photovoltaic companies worldwide to consult an independent research centre to help them to establish their own polysilicon plant. In the following section the diﬀerent routes followed to purify silicon are described, paying attention to the key aspects for PV applications.

1.1 Silicon for photovoltaics applications

Metallurgical silicon is the raw material for polysilicon production. It is produced by carbothermic reduction of quartz at high temperature (approximately 2000◦C) in an electrical arc furnace. The liquid silicon produced is refined in a laddle, poured into a mould where it solidifies, and crushed. 98-99% pure silicon is obtained in a process that consumes around 10 kWh/kg. Annual world production is in the range of 1.500.000 tonnes per year, of which only a small fraction (≤10%) is devoted to the semiconductor and photovoltaic industries. Further purification in these cases is required, for which a three step process known as the ’Siemens process’ is traditionally performed: metallurgical silicon reacts with hydrogen chloride or silicon tetrachloride (SiCl4) in a fluidized bed reactor to synthesize a volatile silicon hydride, trichlorosilane, which can be fractionally distilled in a number of columns, then deposited as solid silicon by Chemical Vapor Deposition (CVD) on slim seed rods heated by the Joule effect. Purities in the range of 99.9999999% are within reach, but at the cost of high energy consumption (in the range of 100-150 kWh/kg) and low efficiency deposition (for each mole of Si converted to polysilicon in the CVD reactor, 3 to 4 moles are converted to SiCl4) [Ceccaroli and Lohne, 2003]. For PV applications, the level of silicon purification is not as critical as for microelectronics, allowing process simplifications that can lead to cost reductions. Several processes exist for developing a product that can be called ’solar silicon’ or ’solar grade silicon’. They are classified in figure 1.3, and are briefly described below. Most correspond to routes explored in the 70s-80s [Dietl, 1987; McCormick, 1985], which achieved different levels of development but in general did not reach industrial production due to funding cuttings and market conditions.

3 Chapter 1. Introduction

Figure 1.3: Routes towards the production of ’Solar Silicon’.

1.1.1 Simplifying the chlorosilane route

An alternative for simplifying the traditional route is to replace trichlorosilane with monosilane, which has advantages in the deposition step because deposition temperatures are lower (800◦C instead of 1100◦C) and productivities can be higher. This process was proposed in the early 80s and industrially exploited, ﬁrst for the semiconductor industry, and more recently for the solar industry [Bye, 2006]. The drawback is the need for additional steps for redistribution and separation, as monosilane is produced from triclorosilane, and the need to recycle the chlorosilanes not converted in the redistribution steps.

Given that the electricity consumption during the silicon deposition in the CVD reactor is responsible for a big part of the cost of the technology [Mozer and Fath, 2006] (see ﬁgure 1.4), another approach is to replace the silicon seed rods by small silicon particles which are continually fed into a ﬂuidized bed reactor. The energy consumption using these reactors can be decreased sevenfold. Because it is a continuous process and not batch-type, the productivity is increased, and the need for crushing the deposited silicon is avoided. However, there are some challenges to using these silicon granules in the following crystallization step that should be addressed.

A combination of silane and ﬂuidized bed deposition has been in production since the 90s [Ceccaroli and Lohne, 2003], and the use of trichlorosilane is being evaluated as an alternative [Weidhaus et al., 2005]. When using silane, the main disadvantages are silicon powder formation and the porous morphology of the polysilicon produced. The other

4 1.1. Silicon for photovoltaics applications

Figure 1.4: Cost break down for Polysilicon. Estimates from [Mozer and Fath, 2006]. alternative, the utilisation of trichlorosilane, is characterised by difficulty of heating, lack of powder formation, and better morphology of the granules obtained [Kim et al., 2010]. A different approach called Vapor to Liquid Deposition involves injecting trichlorosilane at a very high temperature into a graphite tube where it first liquefies in droplets and then solidifies in granules. The process is continuous, the energy consumption is reduced and the productivity is increased; however, carbon is incorporated to the silicon in great quantities [Oda, 2004]. A concept based on the decomposition of silane into silicon powder in a free- space reactor also aims at reaching high productivity and low energy consumption [Muller et al., 2009]. In general, the ’chlorosilane route’ or ’chemical route’ technologies reach high levels of purity. The question they must answer is whether they do so at a lower cost than the conventional approach.

1.1.2 Metallurgical route

The metallurgical route refers to processes that avoid the conversion of metallurgical silicon into a volatile compound, decreasing to a great extent the energy consumption in the deposition step. The metallurgical silicon is upgraded through a combination of steps suited to the different impurities. For example, directional solidification takes advantage of the high liquid-solid segregation coefficient of metallic impurities; leaching eliminates metallic silicides in the grain boundaries; slagging, gas blowing, evaporation and plasma torching reduces the concentration of boron and/or phosphorus; etc. [Flamant et al., 2006; Rousseau et al., 2007; Yuge et al., 2001].

5 Chapter 1. Introduction

The purity usually reached with these processes is much lower than that of the chlorosilane route, but that doesn’t necessarily mean that the material cannot be used for solar cells. In fact, by introducing some changes to the crystallisation and solar cell processing steps, similar solar cell eﬃciencies have been achieved with this lower quality material as have been achieved with semiconductor grade material [Peter et al., 2008]. Another issue that ’metallurgical route’ technologies must address is the process yield, as a fraction of the material may not reach the required quality. It should be noted that in general these technologies are more sensitive to the initial quality of the metallurgical silicon.

1.1.3 Others

A direct carbothermic reduction from selected quartzes and carbons has also been investi- gated, with the philosophy of avoiding not only the chlorosilanes but also the metallurgical intermediate step [Kvande, 2010]. Steps to reduce carbon content need be incorporated. Until now the achieved silicon quality has been low. Other ideas are also proposed from time to time, followed for some time because of their potential, but abandoned or ’frozen’ due to poor results or lack of funding, and sometimes revisited after a while. Examples include using silicon tetraﬂuoride, a by-product of the fer- tiliser industry, as a volatile compound [McCormick, 1985]; performing an aluminothermic reduction of silicon [Mukashev et al., 2009] or transferring silicon electrolytically through a KF:LiF:SiK2F6 electrolite [Carleton et al., 1983].

1.2 Quality and cost

Although quality requirements for PV applications are ’relaxed’ as compared to those of microelectronics, they are still very demanding. There is an open debate about what are the acceptable contamination levels within the purified silicon feedstock to specify the material as solar silicon. Researches at the Instituto de Energ´ıa Solar (IES) have calculated the acceptable contamination levels of different characteristic impurities for each fabrication step of a typical industrial process, from feedstock to solar cell [del Cañizoet al., 2005; Hofstetter et al., 2009]. Their results show that the acceptable contamination level in solar cells depends on the form in which the polysilicon is crystallised, and on the particular impurity in question (for example the acceptable level for Fe is almost two orders of magnitude higher than for Cr). This analysis can be complemented with the effect of the dopant levels, which can be allowed in higher concentrations in solar grade polysilicon than in electronic grade

6 1.3. Centesil, R&D on polysilicon production

polysilicon [Dubois et al., 2008]. For PV applications, a general specification of purity (99.999% or 99,99999%, for example) is not, therefore, informative enough, and a more detailed specification should be made. Also, the purification methods should take this into account, developing dedicated steps for specific impurities, if necessary. As there is a trade-off between process cost and material quality, a threshold for low cost routes should be established to preserve a certain quality level. To this end, the author has carried out a cost analysis, presented in chapter 2, where the impact of new silicon feedstock materials on the total module cost is quantified by describing new materials in terms of production cost (e/kg) and quality (evaluated as cell efficiency) [del Coso et al., 2010b]. An important conclusion is extracted from this analysis: high cell efficiency is a key driver for module cost reduction, and the increase of the feedstock cost can be easily compensated by high efficiencies. That is why the initiative CENTESIL, which is presented in the following paragraph, is aligned with the production of highly purified polysilicon for high efficiency solar cells via the chlorosilane route.

1.3 Centesil, R&D on polysilicon production

The Centro de Tecnolog´ıadel Silicio Solar, CENTESIL, was founded in 2006 as a private- public partnership venture owned by the Universidad Politécnicade Madrid (29.5% of the shares), the Universidad Complutense de Madrid (19.5%), and three companies (Isofotón, DC Wafers and TécnicasReunidas, each with 17%). CENTESIL is currently building a 50 t/a pilot plant for silicon purification following the chlorosilane route. Although a classical modernized technological path has been selected as a first choice, the purpose is also to develop new processes that have the potential to reduce the cost effectively. The development contains four areas of activity: (1) synthesis of chlorosilanes, with silicon tetrachloride, a process by-product, as the main source of chlorine; (2) trichlorosilane purification based on fractional distillation, but with additional processes when necessary to remove lifetime-killing impurities; (3) development of routes to reduce the energy consumption of the chemical vapor deposition and (4) recycling of the by-products for optimal use and sustainability. Additionally, the project includes facilities for monocrystalline growth and wafering, and also the solar cell processing line of the Instituto de Energ´ıaSolar, so that it will benefit from an integrated approach, from feedstock to solar cell.

7 Chapter 1. Introduction

The plant is located in a technological park in Getafe, a town to the south of Madrid, where a 2500 m2 building has been purpose built.

1.4 The thesis

This work presented in this thesis falls within the third area of activity: the development of routes to reduce energy consumption during the polysilicon deposition. The thesis profoundly analyses the different aspects of the polysilicon deposition process: (a) the fluid mechanical and chemical conditions in which the polysilicon is deposited [del Coso et al., 2008], (b) the radiation conditions during the process [del Coso et al., 2010a], and (c) the electrical heating of the silicon rods [del Coso et al., 2007]. Based on the knowledge obtained from this study, improvements are proposed to reduce energy consumption. Theoretical analysis is balanced with the experimental work, carried out at two different locations and periods of time: at the University of California, Berkeley, in 2007, and at the IES facilities in 2010. The thesis is structured as follows: In chapter 2, a cost analysis is presented of the crystalline silicon PV module. The impact of different feedstock materials on the module cost is studied. In chapter 3, the novel fluid mechanical model for polysilicon deposition developed by the author is described. The results of the model are studied, and better conditions are proposed for depositing hyper-pure silicon with minimum energy consumption. In chapter 4, the radiative energy loss in the CVD reactor is studied. Alternatives are explored for reducing energy consumption, such as enlarging the reactor capacities, enhancing the wall reflectivity and introducing thermal shields. In chapter 5, the electric heating of the silicon rods is analyzed. Alternatives are proposed to increase the maximum rod diameter before stopping the deposition process: a key issue for reducing energy consumption in the CVD reactor. In chapter 6, the experimental part of the thesis project is presented. Both the work carried out at the University of California, Berkeley, and at the IES are described in detail. Finally, in chapter 7, conclusions are made and future work is proposed.

8 Chapter 2

The inﬂuence of silicon feedstock on the photovoltaic module manufacturing cost

2.1 Introduction

Photovoltaic (PV) solar energy has been presented as an alternative source of electricity since it began to be developed in the 1950s and has received particular attention since the oil crises of the 1970s. So far, manufacturing costs and prices of PV modules and systems have fallen by more than an order of magnitude. Additionally, it has been possible to improve impressively the performance and overall reliability of PV systems. This, in combination with successful market incentives in a growing number of countries, has enabled an enormous expansion of the PV market in the last decade, with annual growth rates in the range of 40-50% [Hirshman et al., 2007]. Although PV electricity cannot yet compete directly with electricity from conventional sources on the level of wholesale or retail prices, it is already competitive during peak power times, usually in the middle of the day [Greenpeace and EPIA, 2007]. According to a recent study by the European PV Technology Platform, it will reach ”grid parity” with retail prices in Southern Europe before 2015 and in most of Europe by 2020, if the tendency of cost decrease is maintained [European Photovoltaic Technology Platform, 2007]. The PV market is so far largely based on crystalline silicon wafer (c-Si) technology, which has a share of around 90%, and still has a huge potential for further cost reduction, provided technology improvements and innovations continue to be implemented. This was the main aim of CrystalClear (CC), a European Integrated Project carried out in the 6th Framework Programme, which started in 2004 and ﬁnished in mid-2009. CrystalClear

9 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

gathered expertise from 9 private manufacturers, 3 universities and 4 research centres, aiming primarily at ”research, development, and integration of innovative manufacturing technologies that allow solar modules to be produced at a cost of 1 e per watt-peak (Wp) in next generation plants”. This chapter reports on the work performed within CrystalClear to analyze the manufacturing cost of c-Si PV modules, revealing the key aspects that influence cost savings regarding the silicon feedstock. This analysis uncovers the issues that solar grade silicon (SoG-Si) feedstock research must address to effectively reduce PV cost. Environmental aspects, which are not dealt with in this chapter, can be consulted in the literature [Alsema and de Wild-scholten, 2007; Fthenakis and Alsema, 2006]. A simple classification of SoG-Si sources, as already mentioned in the previous chapter, distinguishes two main approaches: the ”chemical route” [Ceccaroli and Lohne, 2003], which is supposed to yield silicon that is relatively similar to conventional polysilicon for semiconductor applications, and the ”metallurgical route” [de Wild-Scholten et al., 2008], which has a higher potential for production cost reduction, but a larger uncertainty regarding the feedstock quality [Flynn et al., 2008] and processing yield [Hesse et al., 2007]. The efforts of the metallurgical route research are mainly directed toward the removal of impurities [Schei, 1998], the understanding of how the remaining impurities affect the solar cell [Macdonald et al., 2009], and the enhancement of solar cell performance [Kaes et al., 2006]. The chemical route research is mainly focused on minimizing production cost by reducing energy consumption [Hesse et al., 2008], enlarging the reactor sizes, improving the gas recirculation system and increasing the annual capacity of polysilicon plants [Keck, 2009]. The question tackled in this chapter is how and to what extent both approaches can reduce the module manufacturing cost. First, the steps taken to define a reference technology are described, and its cost breakdown shown. This technology corresponds to the state-of-the-art at the end of 2005, with production levels in the range of 30-50 MWp/a. Second, some modifications are made to the manufacturing chain of the reference technology to reduce its manufacturing cost. This defines an advanced reference technology which represents the technology of today, produced in high throughput plants (300-500 MWp/a). Third, the impact of different SoG-Si feedstock alternatives on this advanced technology is discussed. Some authors have analyzed the SoG-Si production processes indepen- dently from the manufacturing chain. For instance, the energy consumption during SoG-Si production and its processing cost have been studied by Odden et al. [2008] and Hesse et al. [2008], showing the importance of developing less energy-intensive processes, which lead to reduction of processing cost and greenhouse gas (GHG) emissions. Nevertheless, it

10 2.2. Establishing a reference technology

is crucial to analyze the entire manufacturing chain, and not only the feedstock manufacturing step, to understand the requirements that the SoG-Si feedstock should accomplish to reduce the PV module cost.

Finally, four more technologies, which are representative of the alternative options currently being considered in c-Si R&D, are presented. These cover different crystalline silicon technology families, different cell processes and different module assembly schemes. The impact of silicon feedstock on these future technologies is analyzed.

2.2 Establishing a reference technology

Industrial partners involved in the CrystalClear project have provided data on the cost structure of their PV technology. Data corresponds to direct manufacturing costs at the end of 2005, and covers silicon crystallisation, wafering, cell fabrication and module assembly. Data from diﬀerent partners are extrapolated to similar production levels in the range of 30-50 MWp/a. Note that we always refer to cost and not price. This will help make the analysis independent of external and temporary factors inﬂuencing PV price, such as the recent shortage of high-purity silicon.

Nine diﬀerent European manufacturers have participated. Depending on their company structure and business, some of them have contributed to the whole chain from crystallisation to module assembly, while others covered some or one of the steps. In some cases, technologies are quite similar (such as wafering techniques and module assembly), but in others they are not (for instance, growth of multicrystalline or monocrystalline silicon crystals or cell processing).

Production costs have been distributed in the following categories: equipment (with ten years for depreciation), labour, materials, yield losses and fixed costs. Energy and maintenance costs are included in equipment, and consumables in materials. For cells and modules the cost breakdown has been given for the different process steps into which they can be divided. An aggregated figure, in e·kg−1, is estimated for silicon feedstock cost. After collection, the data has been averaged. The total cost of the PV module resulting −1 from the benchmark exercise is in the range 2.0-2.3 e·Wp . This range relates to different technologies used, not to variation from manufacturer to manufacturer. The resulting manufacturing cost is within the range of other published data on manufacturing costs of PV producers [Song and Rogol, 2008], considering that our figures correspond to cost by the end of year 2005.

11 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

2.2.1 Basepower reference technology

This reference cost helps to define a representative technology, for which the most relevant parameters have been quantified. This baseline technology is hereafter called Basepower, its main characteristics are summarised in table 2.1. The cost breakdown is shown in figure −1 2.1. It corresponds to a Si usage of 9.1 g·Wp . As shown in Figure 2.1(b), analysis of the cost structure suggests research which must be undertaken to reduce the module manufacturing cost; for instance, the following goals should be pursued [European Photovoltaic Technology Platform, 2007; Rohatgi, 2003]: a) Reduction of silicon consumption per Wp, or reduction of silicon cost per kg, or both, by applying new solar grade silicon feedstocks, improving ingot growth, increasing the number of wafers per ingot and diminishing or completely avoiding sawing losses (including silicon ribbon growth and the development of so-called thin-film wafer equivalents, i.e., a thin high-quality crystalline silicon layer on a low cost substrate); b) High-throughput, high-efficiency cell processing, including implementing effective front and back surface passivation on thin wafers; c) High throughput, high total-area efficiency and low-cost module manufacturing, which can be achieved by applying rear interconnection schemes for thin wafers and easy module assembly, and new interconnection and encapsulation materials and methods.

2.3 Potential for cost savings

The reference technology, Basepower, is based on 2005 technology and on plant capacities around 30-50 MWp/a. A thorough revision of this technology has been carried out, modifying its characteristics to represent high throughput plants (300-500 MWp/a) producing in 2011. This revision has been made introducing some new assumptions, reﬁning the cost breakdown of particular steps, or benchmarking with other cost studies disseminated within the PV community. The updated version of Basepower technology resulting from this revision is named Advanced Basepower technology.

As explained, Basepower ﬁgures refer to a 30-50 MWp/a factory: the typical size of PV plants in 2005-2006. A cost study was performed in the late 1990s, evaluating the feasibility of a 500 MWp/a c-Si module manufacturing plant and the potential cost savings [Bruton, 1997]. Such a size was out of reach ten years ago, but because of the growth of the PV industry, 500 MWp/a -1 GWp/a plants will surely be a reality in the short to medium term [Kreutzmann and Schmela, 2008], making the analysis of additional cost savings due to large scale production relevant.

12 2.3. Potential for cost savings

Table 2.1: Description and main parameters of the reference technology Basepower.

Overall technology Basepower name Feedstock Electronic grade polysilicon at 40 e·kg−1 Crystallization Ingot casting Good Si in/Si out per batch: 75% Recycled Si per batcha: 20% Ingot yield: 95% Wafering Wafer size: 156x156 mm2 Wafer thickness: 220 µm Kerf loss: 200 µm Wafer yield: 92% Cell processing Front and rear sreen-printed electrodes Aluminium back-surface field (Al BSF) Cell efficiency: 15% Cell yield: 93% Module assembly Front-to-rear interconnection, soldering foil lamination, framing Cell efficiency in the moduleb: 14.5% Module yield: 97% a The recycled silicon per batch is the reused scrap silicon from a crystallization step used in the subsequent run, expressed as a percentage of the ingot. b Cell efficiency of the module takes into account the loss in output power due to cell interconnection and encapsulation.

An analysis of cost reductions in thin-film photovoltaics due to very large scale integrated manufacturing has been performed recently by Hewlett Packard [Keshner and Arya, 2004]. Although these findings cannot be directly applied to crystalline silicon photovoltaics due to differences in technology, some of the assumptions can be adapted to our case. In the aforementioned study, the total cost reduction for thin-film photovoltaics due to economies of scale is more than 70%, mainly because of the reduction in complexity and in installation and module manufacturing costs. We have assumed quite modest economies of scale for wafer-based photovoltaics compared to thin-film photovoltaics (roughly 30% less), since installation and module manufacturing are more complex for wafer-based technologies. Our calculations are therefore considered to give an upper limit of costs for very large scale manufacturing. This is complemented by input from the industrial partners in CrystalClear, who have shared their qualitative and quantitative estimtates associated to expansion to the GWp scale through a questionanaire. The following considerations have been made to facilitate the quantification of cost savings:

13 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

(a)

(b)

Figure 2.1: Cost structure of Basepower technology. (a) Breakdown by process step and by cost category, −1 in e·Wp . (b) Cost breakdown in percent, with indications of the basic approaches that should be followed for cost reduction.

• The 500 MWp/a -1 GWp/a factory will comprise the whole production chain from ingot production to module manufacturing. Silicon feedstock is assumed to be produced elsewhere. This approach will beneﬁt from reduced handling, shared infras- tructure and improved quality control.

• Following the arguments of reference Keshner and Arya [2004], using a large number of systems similar to the ones used in the fabrication lines of today results in cost

14 2.3. Potential for cost savings

reduction. Most of the cost is in the engineering to design and develop the process for the system, once the system is working well the cost of replicating the system is much lower.

• Reductions in labour due to further automation.

• Due to the volume considered, some materials and consumables may be produced on site, reducing substantially their cost by eliminating distributors, wholesalers, retailers and manufacturers with their transportation, handling and marketing costs, and their proﬁt margins. For example, the analysis of reference Keshner and Arya [2004] argues that building a dedicated on-line glass production plant can make cost fall to 20% of current values. We propose applying a similar philosophy to include subplants for crucible production and for screen printing pastes, although with a smaller cost reduction.

• The prices of the rest of the materials and consumables, not produced on-site, decrease due to the increased size of purchases that results from enlarging the size of the plant.

• Yield increase due to reduction in transportation and handling and improvement in equipment.

• Regarding ﬁxed costs, some of them will increase with increased volume production (those related to footprint, sales department etc.), and others (those related to administrative services, the R&D department etc.) will not change signiﬁcantly

as compared to the 30 MWp/a plant. We foresee an important cost reduction in

relative terms (per Wp).

The estimated reduction for the diﬀerent process steps and categories is shown in table

2.2, expressed as a percentage of the cost ﬁgures for volume productions of 30-50 MWp/a.

2.3.1 Advanced Basepower technology

The Advanced Basepower represents the standard technology of today’s plants: relatively thick wafers, front-and-rear contacted solar cells with full Al BSFs and conventional encapsulation. It is important to note that current technology evolution is by no means spontaneous; on the contrary, it is the result of many eﬀorts to solve a number of technological problems: the processing of thinner wafers, the optimisation of screenprinted metallisation schemes or the improvements in cell interconnection, to mention just a few. The cost reduction in Si feedstock is also included, as it is expected from the profound

15 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

Table 2.2: Reduction in % of the Advanced Basepower cost ﬁgures because of large scale production.

Ingot Wafer Cell Module Equipment -30% -30% -30% -30% Labour -40% -40% -40% -40% Materials and Crucible -40% Pastes -40% -20% -20% consumables Rest -20% Rest -20% Fixed cost -50% -50% -50% -50%

changes that the silicon feedstock market is experiencing, with a big expansion of production capacity from traditional polysilicon producers, the entry of a number of newcomers and the development of alternative puriﬁcation routes [Flynn and Bradford, 2006]. The Advanced Basepower technology is described in table 2.3. Taking into account the technology update and the large scale estimates, the cost ﬁgures for the Advanced Basepower are calculated according to the following procedure:

• Taking the cost results for Basepower technology (30-50 MWp/a), shown in Figure 2.1(a), as a reference.

• Implementing the changes in the technology to update it (180 µm thick wafer instead of 220 µm, 15.8% encapsulated cell eﬃciency instead of 14.5%, etc.)

• Scaling those numbers according to the ”large scale estimates” (300-500 MWp/a) presented in table 2.2.

−1 The Advanced Basepower technology cost is 1.15 e·Wp and the silicon utilisation is −1 6.5 g·Wp . The cost distribution is shown in Figure 2.2.

2.4 The impact of silicon feedstock

The impact of SoG-Si feedstock on the module cost involves not only to the feedstock production cost but also the utilisation and quality of the SoG-Si material. Thus, analysis of the inﬂuence of the SoG-Si feedstock materials requires analysis of the entire manufacturing chain, from the feedstock to the PV module. In this section, we analyze the eﬀect on the total module cost of the following variables (assumed to be independent): the feedstock cost, the yield of the feedstock production process, the material loss in ingot growth, the wafer thickness and the kerf loss (hereafter

16 2.4. The impact of silicon feedstock

Table 2.3: Description and main parameters of the Advanced Basepower technology.

Overall technology Advanced Basepower name Feedstock Solar grade polysilicon at 20 e·kg−1 Crystallization Ingot casting Good Si in/Si out per batch: 75% Recycled Si per batch: 20% Ingot yield: 95% Wafering Wafer size: 156x156 mm2 Wafer thickness: 180 µm Kerf loss: 170 µm Wafer yield: 92% Cell processing Front and rear sreen-printed electrodes Aluminium back-surface field (Al BSF) Cell efficiency: 16.3% Cell yield: 93% Module assembly Front-to-rear interconnection, soldering foil lamination, framing Cell efficiency in the module: 15.8% Module yield: 97%

the sum of the wafer thickness and the kerf loss will be referred to as the ’slicing pitch’), and the cell efficiency. With the exception of the slicing pitch, they have been chosen because the Si feedstock can have a clear impact on them. The slicing pitch is important as a parameter because it partly determines the silicon utilisation. Effects of variations in yield caused by alternative Si feedstock are not discussed in this work to reduce the number of variables to handle, thus the yields of every process except feedstock production are considered constant. The impact of new silicon feedstock materials on the module cost is quantified by describing the new materials in terms of cost (e·kg−1) and quality (relative cell efficiency: ratio of the cell efficiency with a new material to that achieved with the conventional material). The impact of silicon utilisation is also analysed, considering that the amount of silicon feedstock consumed to produce one Wp of module power is determined by the expression (2.1),

g dSi · (wt + k) 1 = · Q (2.1) Wp η · Gstc fig · j Yj

−3 where dSi is the solid silicon density expressed in g·m , wt is the wafer thickness expressed in m, k is the kerf loss expressed in m, η the cell eﬃciency and Gstc is the solar −2 irradiance under standard test conditions (1000 W·m ). Yj is the yield of technological

17 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

(a)

(b)

Figure 2.2: Cost structure of Advanced Basepower technology. (a) Breakdown by process step and by cost −1 category, in e·Wp . (b) Cost breakdown in percent.

step j, covering the whole production chain, from SoG-Si feedstock production to module assembly (Yf for feedstock, Yi for ingot growth, Yw for wafering, Yc for cell processing, and Ym for module assembly). The ingot growth fraction, fig, is the ratio of silicon output to silicon input in the ingot growth (recycled silicon is not considered part of the silicon input). Silicon utilisation therefore depends on the losses in ingot growth, the slicing pitch, the cell eﬃciency and the yield of every technological step.

Considering a certain technology, alternative Si feedstock and eﬃciency of utilisation

18 2.4. The impact of silicon feedstock

−1 will impact upon its module total cost (in terms of e·Wp ) according to the equation (2.2),

1 (wt + k)rel e 1 (wt + k)rel Ctotal = A · · · + B · · (fig)rel · (Yf )rel ηrel kg (fig)rel ηrel (w + k) 1 +C · t rel + D · (2.2) ηrel ηrel in which the subscript rel denotes a relative ratio (relative to the parameter’s value when using a conventional feedstock) and the constants A,B,C, and D are derived for the considered technology as follows

g −3 A = · 10 ,B = Ci,C = Cw,D = Cc + Cm. (2.3) Wp

−1 Cj is the fully-integrated processing cost (in e·Wp ) of the corresponding process step.

Cj includes the yield losses in the subsequent technological steps. For instance, as can be seen in Figure 2.3, the fully-integrated cost of ingot growth includes the accumulated yield losses during ingot growing, wafering, cell processing and module assembly. To produce an −1 ingot has a certain cost (e·Wp ), and this cost increases if the power produced per ingot diminishes due not only to ingots being (partly) out of specification, but also to broken wafers, wrongly processed cells or modules being out of specification. A useful concept to aid analysis of the influence of the variables in equation (2.2) on the total cost is the ”sensitivity”. The sensitivity of a quantity Q to changes in a parameter P is defined as follows

∂Q/Q SQ = (2.4) P ∂P/P The sensitivities to the main parameters involved in the cost calculations are determined by the following expressions

Ctotal Sη = −1 C + C + C + C SCtotal = +1 − i w c m CF m Ctotal

Ctotal Ci + Cw + Cc + Cm SY = −1 + (2.5) f Ctotal C + C + C SCtotal = −1 + w c m fig Ctotal C + C SCtotal = +1 − c m wt+k Ctotal −1 CF m is the feedstock cost expressed in e·kg .

19 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

Figure 2.3: Explanation of the ”Fully-integrated cost” concept, using silicon growth as an example.

Throughout the production chain the yield losses (Yj ) are accumulated and therefore the ingot growth 0 cost increases. Ci is the cost for the ingot growth process disregarding any yield loss.

Table 2.4: Advanced Basepower parameters for the cost calculations regarding the influence of feedstock cost, efficiency of silicon utilisation and cell efficiency.

3 −1 A (x10 ) B C D Total cost ( e·Wp ) Advanced 6.5 0.068 0.125 0.822 1.15 Basepower

2.5 Results

2.5.1 Impact of feedstock cost, silicon utilisation and cell eﬃciency

The Advanced Basepower technology is considered for analysis of the impact of SoG-Si feedstock on the PV module cost. The parameters that describes this technology in terms of equation (2.2) are summarized in table 2.4. The impact of the variables presented in section 2.4 on the total module cost can be analyzed by modifying the variable in question while the others remain constant. As an example, the dependence of module cost on cell eﬃciency is presented in Figure 2.4. It can be seen that a cell eﬃciency reduction from 15.8% to 14.2% (a relative reduction of 10%) increases the module cost by 11%. A similar treatment of the dependence of total

20 2.5. Results

Figure 2.4: Module cost dependence on encapsulated cell efficiency for Advanced Basepower technology. −1 Advanced Basepower absolute parameters: encapsulated cell efficiency, 15.8%, total cost, 1.15 e·Wp . cost on feedstock cost demonstrates that if the feedstock cost were 0 e·kg−1, the module cost would decrease by 11%. Nevertheless, an alternative feedstock might change the cell efficiency, the feedstock yield or the ingot growth fraction (fig). Thus, analysis of the impact on module cost regarding a combination of variables is recommended. Iso-cost curves, showing variable combinations for which the total module cost is constant, can be deduced from the cost calculations. Regarding Advanced Basepower technology, iso-cost curves are presented in Figure 2.5 (for feedstock cost vs encapsulated cell efficiency), Figure 2.6 (for feedstock cost vs fig), and Figure 2.7 (for feedstock cost vs feedstock process yield). The iso-cost curve for feedstock cost vs slicing pitch is presented in Figure 2.8, analyzing the importance of slicing pitch as a cost driver of the module cost. It can be deduced from Figure 2.5 how sensitive the Advanced Basepower technology is to increases in the feedstock cost. Starting from 20 e·kg−1 and relative efficiency 1, if the feedstock cost increases to 30 e·kg−1 (a 50% increase), increasing efficiency by a relative 6% neutralises the cost increase, and the module cost remains constant. Likewise, if the efficiency decreases a relative 10%, the feedstock cost must decrease to 2 e·kg−1 (90% down) to keep the module cost constant. Concerning the ingot growth step, the fraction of the incoming silicon that is crystallised into usable silicon might vary when using different feedstock material. The effect of the combination of feedstock cost and ingot growth fraction, fig, is shown in Figure 2.6.

21 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

Figure 2.5: Iso-cost curves for Advanced Basepower technology regarding encapsulated cell eﬃciency and feedstock cost. Advanced Basepower absolute parameters: encapsulated cell eﬃciency, 15.8%, feedstock cost, 20 e·kg−1.

Starting from 20 e·kg−1 and relative ingot fraction 1, if the feedstock cost decreases to 10 e·kg−1 (a 50% reduction) the ingot growth fraction could be relaxed by a relative 31% whilst maintaining a constant module cost. In the iso-cost curve presented in Figure 2.7 the module remains constant for a constant ratio of feedstock cost to feedstock yield, as expected from equation (2.2). Thus, starting from 20 e·kg−1 and a relative feedstock production yield 1, if the feedstock cost decreases to 10 e·kg−1 (a 50% reduction) the feedstock yield could be relaxed by a relative 50% whilst maintaining a constant module cost. Similar reasoning can be applied to the iso-cost curves presented in Figure 2.8, where cell efficiency and feedstock yield are kept constant, and slicing pitch and feedstock cost are modified. From the starting situation of 20 e·kg−1 and relative slicing pitch 1, if the feedstock cost increases to 30 e·kg−1 (a 50% increase), reducing the slicing pitch by a relative 16% neutralises the cost increase, and the module cost remains constant. Likewise, if the slicing pitch increases a relative 10%, the feedstock cost should decrease to 15 e·kg−1 (a 25% reduction) to keep the module cost constant. Sensitivity factors, detailed in table 2.5, also provide valuable information. It can be seen that the highest absolute sensitivity is exhibited by the efficiency, followed by the slicing pitch, the ingot growth fraction, and finally, the feedstock cost and feedstock yield. The efficiency sensitivity is ten times the feedstock cost sensitivity, the slicing pitch sensitivity 3 times the feedstock cost sensitivity, and the ingot growth fraction sensitivity 1.5

22 2.5. Results

Figure 2.6: Iso-cost curves for Advanced Basepower technology regarding ingot growth fraction (fig) and −1 feedstock cost. Advanced Basepower absolute parameters: fig, 93%, feedstock cost, 20 e·kg .

Figure 2.7: Iso-cost curves for Advanced Basepower technology regarding feedstock process yield and feedstock cost. Advanced Basepower absolute parameters: feedstock process yield, 100%, feedstock cost, 20 e·kg−1.

23 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

Figure 2.8: Iso-cost curves for Advanced Basepower technology regarding slicing pitch and feedstock cost. Advanced Basepower absolute parameters: slicing pitch, 350 µm, feedstock cost, 20 e·kg−1 times the feedstock cost sensitivity. The sensitivity factors show the importance of every parameter as a mathematically independent variable. It has to be understood, however, that the difficulty of varying the slicing pitch or the feedstock cost by, for instance, relative 10% is completely different from varying the cell efficiency, the ingot growth fraction or the process yields by a relative 10%.

Table 2.5: Advanced Basepower sensitivity factors to changes in the total module cost of: feedstock cost, slicing pitch, cell eﬃciency, ratio of output silicon to input silicon in ingot growth process and feedstock process yield.

C C C C S total S total SCtotal S total S total CF m wt+k η fig Yf Advanced 0.11 0.28 -1 -0.17 -0.11 Basepower

2.5.2 New feedstock sources

In the past, the PV industry consumed semiconductor-grade silicon, characterized by high quality and high production cost. Currently, the industry demands speciﬁc silicon (solar grade silicon) for solar applications, with the required quality and the lowest possible production cost. The uncertain trade-oﬀ between quality and cost that is acceptable for the industry is the scope of this section.

24 2.5. Results

Table 2.6: Maximum relative variation of eﬃciency, feedstock yield or ingot growth fraction allowed for UMG-Si feedstock (10 e·kg−1) to be more cost eﬀective than Near SeG-Si feedstock (30 e·kg−1). The Advanced Basepower technology is considered.

Relative Relative feedstock Relative ingot-growth eﬃciency (%) yield (%) fraction (%) Advanced -10.8 -66.7 -49.5 Basepower

In this work two limits have been estimated for feedstock manufacturing cost: the upper limit is 30 e·kg−1 [Keck, 2009; Rogol, 2008], corresponding to near-semiconductor- grade silicon (Near SeG-Si), and the lower limit is 10 e·kg−1 [Flynn et al., 2008; Song, 2009], corresponding to upgraded metallurgical-grade silicon (UMG-Si). Since the quality of Near SeG-Si is very good, its utilisation as feedstock material is supposed to yield a relative efficiency of 1, a relative feedstock yield of 1, and a relative ingot growth fraction of 1. Since the cost of UMG-Si is lower, the use of this material could be more cost effective on the module level despite the reduction in feedstock quality or in efficiency of silicon utilisation. This UMG-Si cost advantage can be lost under unfavourable combinations of efficiency, feedstock yield, and ingot growth fraction during module manufacturing. Therefore, the maximum variation of efficiency, feedstock yield or ingot growth fraction allowed for UMG-Si feedstock (10 e·kg−1) to be more cost effective than Near SeG-Si feedstock (30 e·kg−1) has been calculated and detailed in table 2.6, where the Advanced Basepower technology is considered.

Regarding absolute values, starting from Near SeG-Si utilisation and an encapsulated cell eﬃciency of 15.8%, a feedstock yield 1 and an ingot growth fraction 93.0%, the cost advantage of UMG-Si will be lost if the encapsulated cell eﬃciency is lower than 14.1%, the feedstock yield is lower than 33% or the ingot growth fraction is lower than 50%.

The feedstock yield and ingot growth fraction variations do not introduce strong limitations for UMG-Si users, according to table 2.6, since the minimum values acceptable are probably not diﬃcult to reach. On the other hand, UMG-Si users must be careful with the cell eﬃciency, avoiding reductions above 1.7% (absolute) by means of, for instance, bulk quality enhancement or defect engineering [Pickett and Buonassisi, 2008].

25 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

2.6 Proposal of future technologies

Four technology scenarios have been considered, combining options for the different steps of the production chain that are known or expected to be effective in terms of cost, man- ufacturability or efficiency. The combinations were selected to represent different crystalline silicon technology families (cast multicrystalline silicon, Czochralski-grown (Cz) single crystal silicon), and also to cover a range of potentials for cost reduction. They are related to the R&D lines being followed within CrystalClear, so that the assumptions related to each of the alternatives and to the prospects of implementation are largely based on the expertise of the CrystalClear partners. These four technologies are briefly described in the following tables, and some drawings at the cell and module level are also given in Figure 2.9 to highlight the main innovations they include. They have been given names to facilitate easy identification. Multistar (table 2.7) is an advanced multicrystalline-silicon based module with a medium technology risk profile [Choulat et al., 2007], which can be implemented at the industrial level with a high probability of success in the near future. A modified version of Multistar (table 2.8) features a Metallisation Wrap-Through (MWT) design [Kerschaver et al., 1998; Romijn et al., 2008], enabling an all-rear interconnection scheme in the PV module [Kerschaver and Beaucarne, 2006]. Superslice (table 2.9) implements a high efficiency cell structure on very thin monocrystalline silicon [Hofmann et al., 2008; Schultz et al., 2006], and has a medium risk profile for industrialisation in the near future. There is also a modified version of Superslice (table 2.10), based on an Emitter Wrap-Through (EWT) design [Kress et al., 1999] which allows for all-rear interconnection, and is categorised as having medium-to- high technology risk: it needs a few more years of research and particularly development to be ready for industrial implementation with a production performance equalling that of more conventional technologies. It is noted that the use of all-rear interconnection schemes (in 2 of the 4 technologies) is consistent with the need for high efficiencies and considered attractive or even necessary for high-yield module manufacturing using very thin cells.

2.6.1 Cost structure of the future technologies

The cost modelling of the future technologies has been performed by describing cost in terms of the impact of technological improvements, with respect to the Advanced Base- power technology. The cost of technological steps not included in the Advanced Basepower technology, such as hole drilling or laser ﬁring, have been estimated by extrapolating data from pilot plant scale production to industrial production.

26 2.6. Proposal of future technologies

(a)

(b)

Figure 2.9: Sketches of the cell structures and module assemblies proposed in the future technologies. (a) Sketches of the cell structures. Top left: Advanced Basepower; top right: front and rear contacted Multistar and Superslice; bottom left: all-rear-contacted MultistaR and SuperslicE. (b) Sketches of the assembly approaches for the front to rear contacted cells (left) and the all rear contacted cells (right).

Table 2.7: Description and main parameters of roadmap scenario Multistar.

Overall technology Multistar name Feedstock Solar grade polysilicon at 20 e·kg−1 Crystallization Ingot casting Good Si in/Si out per batch: 80% Recycled Si per batch: 17% Ingot yield: 95% Wafering Wafer thickness: 120 µm Kerf loss: 140 µm Wafer yield: 90% Cell processing Front and rear sreen-printed electrodes Passivated rear side Cell yield: 96% Cell eﬃciency: 17% Module assembly Front-to-rear, low stress interconnects, foil lamination, frameless Module yield: 98% Cell eﬃciency in the module: 16.7%

27 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

Table 2.8: Description and main parameters of roadmap scenario MultistaR (modiﬁed Multistar).

Overall technology MultistaR (modified version name of Multistar) Feedstock Solar grade polysilicon at 20 e·kg−1 Crystallization Ingot casting Good Si in/Si out per batch: 80% Recycled Si per batch: 17% Ingot yield: 95% Wafering Wafer thickness: 120 µm Kerf loss: 140 µm Wafer yield: 90% Cell processing Metallised-Wrap-Through design, Passivated rear side Cell yield: 96% Cell efficiency: 17% Module assembly All rear low-stress interconnects, conductive pattern integrated at the back sheet, foil lamination, frameless Module yield: 98% Cell efficiency in the module: 17%

Table 2.9: Description and main parameters of roadmap scenario Superslice.

Overall technology Superslice name Feedstock Near semiconductor grade polysilicon at 30 e·kg−1 Crystallization Cz monocrystalline Good Si in/Si out per batch: 80% Recycled Si per batch: 17% Ingot yield: 95% Wafering Wafer thickness: 120 µm Kerf loss: 140 µm Wafer yield: 92% Cell processing Rear side passivated with dielectric stack, laser fired local rear contacts Cell yield: 96% Cell efficiency: 19% Module assembly Front-to-rear, low-stress interconnects, foil lamination, frameless Module yield: 98% Cell efficiency in the module: 18.7%

28 2.6. Proposal of future technologies

Table 2.10: Description and main parameters of roadmap scenario SuperslicE (modiﬁed version of Super- slice).

Overall technology SuperslicE (modified version name of Superslice) Feedstock Near semiconductor grade polysilicon at 30 e·kg−1 Crystallization Cz monocrystalline Good Si in/Si out per batch: 80% Recycled Si per batch: 17% Ingot yield: 95% Wafering Wafer thickness: 120 µm Kerf loss: 140 µm Wafer yield: 92% Cell processing Emitter-Wrap-Through design Cell yield: 95% Cell efficiency: 18.5% Module assembly All rear low-stress interconnects, conductive pattern integrated at the back sheet, foil lamination, frameless Module yield: 98% Cell efficiency in the module: 18.5%

Since the information provided by the research groups and their partners is based on laboratory experience and current insights it contains inherent uncertainties. Also, the costs related to the use of new materials may be diﬀerent than currently foreseen. In general, we have used conservative estimates in all cases where clear uncertainties exist, meaning that our cost calculations give upper values. Therefore, the results presented in this chapter should only be regarded as indicative.

The cost breakdown of the alternative scenarios is shown in table 2.11. It should be −1 noted that the module manufacturing cost of 1 e·Wp is within reach considering the technology improvements proposed in the diﬀerent alternatives, when they are manufactured in large scale plants.

It should also be taken into account that because the generation cost of solar electricity is determined by the system price (i.e., the sum of the module price and Balance-of-System- −1 price), the optimum solar module is not necessarily the cheapest module (in e·Wp ). Modules with a higher efficiency and somewhat higher price may lead to a lower turn-key system price because of lower area-related Balance-of-System costs. Although this issue is beyond the analysis being reported, it is an additional argument supporting the interest in defining different routes for crystalline silicon PV technology.

29 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

Table 2.11: Cost breakdown of the future technologies and Advanced Basepower. The production levels are 300-500 MWp/a .

Advanced −1 e·Wp Multistar MultistaR Superslice SuperslicE Basepower Feedstock 0.10 0.07 0.07 0.10 0.10 Ingot growth 0.07 0.05 0.05 0.10 0.10 Wafering 0.13 0.09 0.09 0.08 0.08 Cell 0.30 0.33 0.34 0.33 0.37 Module 0.54 0.47 0.51 0.42 0.48 −1 Total (e·Wp ) 1.15 1.00 1.06 1.03 1.13 −1 g·Wp 6.5 4.5 4.4 3.9 4.0

2.6.2 Impact of new feedstock sources

The impact of diﬀerent feedstock sources on the four presented technologies can also be analyzed. To carry out this analysis, the parameters that describe each technology in terms of equation (2.2) are presented in table 2.12.

Table 2.12: Parameters for the cost calculations regarding the influence of feedstock cost, efficiency of silicon utilisation and cell efficiency.

3 −1 A (x10 ) B C D Total cost ( e·Wp ) Multistar 4.5 0.046 0.088 0.779 1.00 MultistaR 4.4 0.045 0.086 0.844 1.06 Superslice 3.9 0.102 0.077 0.737 1.03 SuperslicE 4.0 0.104 0.078 0.830 1.13

Iso-cost curves, similar to those presented in section 2.5, can be drawn for the future technologies. Comparing the future technologies with Advanced Basepower, SuperslicE is the least sensitive technology to feedstock cost increases, followed by Superslice, MultistaR, Multistar and, ﬁnally, Advanced Basepower. The technologies with higher ratio of total −1 −1 cost (e·Wp ) to silicon utilisation (g·Wp ) are less sensitive to feedstock variations since the feedstock processing cost forms a smaller part of the total cost. The sensitivity factors for these technologies are detailed in table 2.13. Again, for any of the technologies, the most sensitive variable is the eﬃciency, followed by slicing pitch, ingot growth fraction, feedstock cost and feedstock yield.

30 2.7. Conclusions

Table 2.13: Sensitivity factors to changes in the total module cost of feedstock cost, slicing pitch, cell eﬃciency, ratio of output silicon to input silicon in ingot growth process and feedstock process yield.

C C C C S total S total SCtotal S total S total CF m wt+k η fig Yf Multistar 0.09 0.22 -1 -0.14 -0.09 MultistaR 0.08 0.21 -1 -0.12 -0.08 Superslice 0.11 0.29 -1 -0.21 -0.11 SuperslicE 0.11 0.27 -1 -0.20 -0.11

Table 2.14: Maximum relative variation of eﬃciency, feedstock yield or ingot growth fraction allowed for UMG-Si feedstock (10 e·kg−1) to be more cost eﬀective than Near SeG-Si feedstock (30 e·kg−1).

Relative Relative feedstock Relative ingot-growth eﬃciency (%) yield (%) fraction (%) Multistar -8.5 -66.7 -49.5 MultistaR -7.9 -66.7 -49.5 Superslice -7.5 -66.7 -35.6 SuperslicE -7.0 -66.7 -35.6

Regarding the utilisation of different SoG-Si feedstock, table 2.14 summarizes the maximum variation of efficiency, feedstock yield or ingot growth fraction allowed for UMG-Si users to produce more cost effective modules than Near SeG-Si users.

2.7 Conclusions

Direct manufacturing costs for crystalline silicon PV modules have been calculated for the whole production chain, taking into account equipment, labour, material, yield losses and fixed cost contributions. Data provided by PV manufacturing companies have shown costs −1 in the range of 2.0-2.3 e·Wp at the end of 2005, for a 30-50 MWp/a level production. The cost figures show that due to the combined effects of technology development and economies of scale the direct manufacturing costs of crystalline silicon PV modules can −1 be brought down to 1.15 e·Wp . By comparing the total cost figures for Basepower (the 2005 reference technology) with the Advanced Basepower (the 2009 reference technology produced in large scale plants) it becomes clear that the reduction obtained through tech-

31 Chapter 2. The inﬂuence of silicon feedstock on the PV module cost

−1 nology development is roughly 0.5 e·Wp , while economies of scale subtract a further 0.5 −1 e·Wp . Although we have separated the effects of technology development and economies of scale in the cost calculations, they are actually quite closely interlinked. The reason for this is that many of the manufacturing processes and design concepts used for the future technologies have been especially selected to enable or facilitate high-throughput (large scale) production at high yield. Regarding the impact of SoG-Si feedstock on the technology scenarios, the figures show that if the cell efficiency can be maintained, then the variation of feedstock processing cost, from Near SeG-Si to UMG-Si, changes the total manufacturing cost of c-Si modules by between 11% and 7%. The greatest change is for the Advanced Basepower technology, and the lowest for the future technologies. However, the cost advantage of low-cost feedstock utilisation is completely lost if cell efficiency is reduced, due to quality degradation, by an absolute 1.7% for the Advanced Basepower module technology or by an absolute 1.3% for the future technologies. It is also concluded that the variations of feedstock yield and variations of ingot-growth fraction only weakly affect to low-cost feedstock users since the minimum values accepted are well within reach. Our research efforts, resulting from the importance of the cell efficiency on the module cost, are directed toward reducing the cost of the SoG-Si production process without endangering the quality of the material produced. To this end, the potential for cost reduction of the chemical route is explored in this thesis, aiming at reducing the cost of high quality SoG-Si feedstock material. Energy consumption is the main cost driver in the chemical route, since this polysilicon production process is highly energy intensive. Regarding the polysilicon deposition, the energy consumption can be reduced by increasing the polysilicon production per unit time and by lowering the power loss. Increasing the polysilicon productivity requires understanding of the effect of the process variables: the pressure, the rod temperature, the gas composition, etc. on the deposition process. The deposition model presented in the following chapter helps to identify the best conditions for increasing the polysilicon productivity and allows better understanding of the process. The power loss will be analyzed in further chapters.

32 Chapter 3

Model of chemical vapour deposition of polysilicon by trichlorosilane decomposition

3.1 Introduction

The chemical route for the production of polysilicon consists of three steps, as already explained. The ﬁrst is the synthesis of a volatile silicon hydride from metallurgical grade silicon (MG-Si). The second is the puriﬁcation of the synthesised silicon hydride. The third consists in decomposition of the silicon hydride into hyperpure silicon, referred to as polysilicon. The silicon hydride most commonly used in the industry is trichlorosilane (TCS,

HSiCl3). The synthesis of trichlorosilane is carried out in a ﬂuidized bed reactor, where a chloride gas (HCl or SiCl4) reacts with MG-Si. The products are silicon hydrides

(Hx−4SiClx, x=0,...,4) and gases containing the impurities extracted from the MG-Si. Production of trichlorosilane is maximised by choosing favourable reactor conditions. For instance, when MG-Si reacts with HCl at 300 ◦C and atmospheric pressure, trichlorosilane ◦ can account for 85% of end products; whereas when MG-Si reacts with SiCl4 at 500 C and 35 atm, the amount of trichlorosilane in the exhaust gas is less than 30% [M´endez, 2009]. In the next step, the chemical compounds resulting from the synthesis are separated by distillation. Trichlorosilane is puriﬁed and supplied to the decomposition step, the remaining silicon hydrides are somewhat recycled into the system, and the impurities are removed [Rogers, 1990]. The last step consists in reducing trichlorosilane and hydrogen to polysilicon in a chemical vapour deposition (CVD) reactor [Bugl et al., 1982]. Silane is also used in the industry as the precursor gas instead of trichlorosilane. In this

33 Chapter 3. Model of CVD of polysilicon by TCS decomposition

case, the silane is produced by several intermediate catalytic rearrangement steps using the synthesised trichlorosilane as the raw material [Hunt, 1990]. Then, the silane is puriﬁed by distillation and introduced into the CVD reactor, where it is reduced [Hashimoto et al., 1990]. These three steps (synthesis, distillation and decomposition) are strongly interlinked. Reducing the energy consumption of the overall process requires understanding each step and their interactions. It should be noted that more than 60% of the energy used in producing polysilicon is consumed in the decomposition process [Mozer and Fath, 2006; Odden et al., 2008]. The polysilicon CVD reactor, also called a Siemens reactor, consists of a gas-tight chamber where several high-purity silicon slim rods are heated by an electric current ﬂowing through them. Polysilicon is deposited on the seed rods through the thermal decomposition of trichlorosilane in a hydrogen environment. Figure 3.1 shows a diagram of a polysilicon deposition reactor. In this diagram there are 24 rods arranged in two concentric rings. Currently, this kind of reactor can have 36 rods (arranged in three concentric rings), 48 rods (arranged in three concentric rings) or even 60 rods (arranged in four concentric rings). There are to two main paths to reduce the energy consumed during the decomposition, per kg of polysilicon produced:

• Reducing the power loss.

• Increasing the polysilicon productivity (kg·h−1), i.e. increasing the polysilicon growth rate.

The power consumed in the CVD reactor has three contributions: power loss through convection, power loss through radiation and the power consumed in the chemical decomposition of TCS. The heated gasses convect power through the exhaust or exchange their heat with the reactor cold wall. The radiated power is emitted by the polysilicon rods toward the reactor cold wall. The power consumed in the chemical decomposition of TCS, compared to the other two contributions, can be disregarded. The total power, the sum of these three contributions, is supplied to the silicon rods as electric power. This chapter studies power loss by convection in the CVD reactor. The influence of the deposition conditions is analysed and power loss minimisation is sought. The study of power loss by radiation is presented in chapter 4. The polysilicon productivity depends on the gas flow and therefore the fluid-mechanical regime has to be analyzed profoundly to achieve optimum flow conditions. Also, the rate of decomposition of trichlorosilane in hydrogen into polysilicon is highly influenced by

34 3.1. Introduction

Figure 3.1: Polysilicon deposition reactor. In this particular case, there are 24 rods arranged in two concentric rings. Source: STR group.

temperature [Habuka et al., 1996]. At low temperatures the decomposition rate is limited by the reaction rate. Under these conditions, the reaction rate is low and therefore the concentration of species on the rod surface is similar to that at the entrance of the reactor. Otherwise, at high temperatures the decomposition rate is limited by the transport of mass. In this case, the reaction rate is high and the concentration of chemically active species on the rod surface is close to zero. This latter regime is more interesting for the polysilicon deposition because the decomposition rate is higher.

The transport limited decomposition process has been modelled in the literature [Ev- ersteijn, 1974] in the limit of inﬁnite reaction rate, k → ∞. This is equivalent to stating that the concentration of chemically active species on the rod surface is equal to zero (allowing treatment of inﬁnite deposition rates to be avoided). The decomposition process limited by the reaction rate has been modelled in the literature [Faller and Hurrle, 1999] under the assumption that the concentration of species on the hot surface equals that at the entrance of the reactor. Neither approach considers both limitation regimes. Conse- quently, some authors carried out complete modelling, considering both limitation regions,

35 Chapter 3. Model of CVD of polysilicon by TCS decomposition

taking the reaction rate constant to have a finite value and calculating the composition of species at the hot surface. Reference Habuka et al. [1996] presents a complete model for the epitaxial growth of a silicon layer from trichlorosilane decomposition onto a hot wafer substrate. Reference Hashimoto et al. [1990] deals with a complete model for the growth of polysilicon by silane decomposition onto a hot silicon rod. This chapter presents an original complete model, not previously reported in the literature, for the growth of polysilicon from trichlorosilane decomposition onto a hot silicon rod. Analytical solutions for the deposition rate of polysilicon are presented, based on splitting the second-order reaction rate into two systems of first-order reaction rates. These solutions describe both decomposition regimes: reaction limited and transport limited. The decomposition model relies on the well-known conservation equations [Stokes, 1880], presented in the following subsection. The properties of the gas mixture (trichlorosilane, hydrogen and by-products) are calculated. The model is then derived and the results presented. The influence of the deposition conditions on the growth rate and the power loss is studied. The impact of the following variables on the process is analysed in detail: the gas flow, the gas composition, the pressure within the reactor vessel, the rod surface temperature and the rod diameter. Finally, during the discussion of the results, a deposition process is proposed for a 36 rods CVD reactor. The deposition conditions are defined, and the process is simulated with the presented model.

3.2 Conservation equations

The conservation principles ensure that for any ﬂuid, in any state of motion, the following quantities are balanced:

• Mass: the total mass of the ﬂuid; the individual chemical species mass (e.g., HSiCl3,

H2, etc); the individual chemical element mass (e.g., Si, Cl, H, etc.).

• Momentum: the total linear momentum (a vector); the total angular momentum (also a vector).

• Energy: the total energy; the kinetic energy (mechanical).

• Entropy: the total entropy.

These conservation principles apply not only to any ﬂuid, but to any region of space. Thus, considering a control volume (CV) of arbitrary size and shape, and its control surface (CS), the conservation equations are expressed as follows at each instant [Rosner, 2000]

36 3.2. Conservation equations

Net outflow rate Rate of quantity Net inflow rate of Net source of quantity by accumulation in + = quantity by diffu- + of quantity convection across CV sion across CS within CV CS where quantity stands for mass, momentum, energy or entropy. The conservation equations used to understand and analyze the chemical decomposition of trichlorosilane are detailed in the following paragraphs.

3.2.1 Conservation of Mass

The total mass per unit volume is the density of the gas mixture, ρ. This quantity is balanced by taking into account that the total mass of the mixture can only be trans- ported by convection, not by diﬀusion, and that it cannot be created. Within a CV the conservation equation is, in its integral form

∂ Z Z ρdV + ρv · ndS = 0 (3.1) ∂t CV CS where v: fluid velocity and n: CS normal vector. Applying the divergence theorem1 and taking the limit as the CV tends to zero (in which the fluid is treated as a continuum), equation (3.1) yields the differential form of the Conservation of Mass equation

∂ρ + div (ρv) = 0 (3.2) ∂t

The ﬂuid density is calculated according to the equation of state for an ideal gas

pM ρ = m (3.3) RT

Mm being the molar mass of the gas mixture, R the universal gas constant and p, T the pressure and temperature respectively.

3.2.2 Conservation of Individual Species Mass

The density of each chemical species in the mixture is ρi = ρωi, where ωi stands for the mass fraction of species i. The convective flow of species i in the gas is ρiv, and it usually does not fit with the total flow of this substance, ρivi. Flux difference is considered to be 00 000 outflow rate across CV by diffusion, ji = ρivi − ρiv. Definingr ˙i to be the net rate of Z Z 1 ρv · ndS = div (ρv) dV CS CV

37 Chapter 3. Model of CVD of polysilicon by TCS decomposition

production of species i in mass per unit volume per unit time, the conservation equation in its integral form is Z Z Z Z ∂ 00 000 ρidV + ρiv · ndS = − ji · ndS + r˙i dV (3.4) ∂t CV CS CS CV A diﬀerential equation can be obtained following the same reasoning used for equation (3.2), yielding

∂ρ i + div (ρ v) = −div j00 +r ˙000 (3.5) ∂t i i i

This equation can be modiﬁed using equation (3.2) and the deﬁnition of ρi, leading to the following expression

∂ω ρ i + v · grad (ω ) = −div j00 +r ˙000 (3.6) ∂t i i i

00 The mass diffusion vector, ji , has four contributions, making up the generalized Fick law [Bird et al., 2002]: the concentration diffusion term (Fick’s first law), the pressure diffusion term (containing the pressure gradient), the forced diffusion term (containing the external forces) and the thermal diffusion term (the so-called Soret effect). Nevertheless, if the pressure inside the reactor is assumed to be constant and external forces, for instance gravity, are assumed to have the same effect over all species, both terms can be neglected and diffusion flow can be calculated using the following expression

00 ji = ρDi [(−gradωi) + αTωiωc (−grad(ln T ))] (3.7) where the left-hand term in parenthesis represents the normal Fickian diffusion and the right-hand represents the Soret effect. ωc is the mass fraction of carrier gas, H2 in the case of the CVD reactor; αT is the thermal diffusion factor; and Di the effective diffusion coefficient, which can be set equal to the binary diffusion coefficient if a low-density gas is considered (diluted gas in a carrier gas). As a result of the Soret effect, the species with the larger molecular weight in binary mixtures usually goes to the colder region [Bird et al., 2002; Holstein, 1988]. Finally, the Conservation of Individual Species Mass equation is

∂ω ρ i + v · grad (ω ) = div (ρD [(gradω ) + α ω ω (grad(ln T ))]) +r ˙000 (3.8) ∂t i i i T i c i

The molar mass of the gas mixture can be calculated from the following expression

!−1 ω M = X i (3.9) m M i i where Mi is molar weight of species i.

38 3.2. Conservation equations

3.2.3 Conservation of Linear Momentum

The linear momentum of the mixture of gases per unit volume is ρv. Thus, the conservation equation of this property is, in its integral form ∂ Z Z Z Z ρvdV + ρvv · ndS = [Π] · ndS + ρgdV (3.10) ∂t CV CS CS CV [Π] is a local stress operator over the CS and g is the gravity vector. The differential formula can again be obtained ∂ (ρv) + div (ρvv) = div ([Π]) + ρg (3.11) ∂t The stress operator can be split into a pressure component and a viscous stress component, τ , associated with fluid motion. Then, [Π] = [τ ] − p [I], where p is the pressure and [I] is the identity matrix [Rosner, 2000]. The viscous stress matrix is defined as

h i 2 [τ ] = µ gradv + (gradv)t + k − µ div(v)[I] . (3.12) 3 where µ is the viscosity of the mixture and k the dilatational viscosity of the mixture. In most cases the k coeﬃcient is neglected [Bird et al., 2002]. Taking equation (3.2) into account and introducing the diﬀerent terms into the equation, the Conservation of Linear Momentum equation is derived from equation (3.11), ∂v ρ + vgradv = ρg − gradp + ∂t h i 2 div µ gradv + (gradv)t − µ · div(v)[I] (3.13) 3

3.2.4 Conservation of Energy

Regarding the energy in a flow system, two properties can be balanced. Firstly, the total energy, leading to the Conservation of energy equation. The total energy is the addition of kinetic and internal energy. The kinetic energy is the energy associated with the observable motion of a fluid, which is 1/2ρv2 ≡ 1/2ρ(v · v). The internal energy is that considered in the first law of thermodynamics. Secondly, the kinetic energy can also be balanced (taking the dot product of 1/2 ·v with the equation (3.11)) leading to the equation of change for kinetic energy. These equations are detailed in [Bird et al., 2002]. The most useful form of the conservation of energy equation is that which includes temperature dependence. To obtain such an equation, the equation of change for kinetic energy is subtracted from the conservation of energy equation. The following equation is obtained ∂ (ρCpT ) ∂lnρ dp + div (ρCpT v) = div (κ · gradT ) − (3.14) ∂t ∂lnT p dt

39 Chapter 3. Model of CVD of polysilicon by TCS decomposition

where Cp is the speciﬁc heat of the gas, T is temperature, κ the thermal conductivity of the mixture of gases and - ∂lnρ dp is the rate of heat generation by compression. In this ∂lnT p dt equation the rate of heat generation by viscous dissipation has been neglected. Note that dp is the total, not partial, derivative, and that for an ideal gas, ∂lnρ = −1. dt ∂lnT p Finally, using equation (3.2) and assuming Cp to be constant [Masi et al., 2003], the equation of change for temperature is derived from equation (3.14), ∂T dp ρC + v · gradT = div (κgradT ) + (3.15) p ∂t dt

3.3 The properties of gases

3.3.1 Binary diﬀusion coeﬃcient

Considering a binary mixture of non-polar gases a and b, the mass diﬀusivity Dab can be predicted to within about 5% by kinetic theory using the following formula [Bird et al., 2002] s 3 1 1 1 Dab = 0.0018583 · T + · 2 (3.16) Ma Mb p · σabΩDab 2 −1 −1 ˚ the units are: Dab [cm s ], T [K], Mi [gmol ], p [atm], σab [A], ΩDab [dimensionless].

ΩDab is the ”collision integral” for diﬀusion, σab the ”characteristic diameter” for diﬀusion,

Ma the molar mass of species a and Mb the molar mass of species b.

In order to obtain the values of ΩDab and σab for a speciﬁc binary mixture some quantities should be introduced: σ is the characteristic diameter of the molecules of a gas, often called the collision diameter, and is the characteristic energy of a gas. σab is calculated as follows σ + σ √ σ = a b = · (3.17) ab 2 ab a b

Data corresponding to or σ are tabulated for some gases [Rosner, 2000], such as H2 and HCl. Where data cannot be found, it can be approximated by the following expressions

/k = 0.77Tc σ = 2.44 (Tc/pc) (3.18) where k is the Boltzmann constant, and c denotes critical properties. Here /k and T are in units of K, σ in A,˚ pc in atm. Based on the equations presented above, a value of Ωab can be calculated as follows 1.06036 0.19300 1.03587 1.76474 Ω = + + + (3.19) ab τ 0.15610 exp (0.47635 · τ) exp (1.52996 · τ) exp (3.89411 · τ)

(1,1) being τ = kT/ab. This collision integral for diﬀusion corresponds to Ωab presented in reference Neufeld et al. [1972].

40 3.3. The properties of gases

3.3.2 Thermal diﬀusion factor

The thermal diﬀusion factor αT for a binary gas mixture consisting of a carrier gas of molecular weight Mb, in which a gas with molecular weight Ma is diluted, can be obtained from the following equation [Holstein, 1988]

√ (1,2) (1,1) ! 5 2 σ 2 6Ω − 5Ω 3M α = ab ab ab 1 − b (3.20) T (2,2) 8 σb 2Ma Ωb where Ω’s are transport collision integrals presented in reference Neufeld et al. [1972]. The ˚ (j,k) −1 units are: αT [dimensionless], σi [A], Ωi [dimensionless], Mi [gmol ].

3.3.3 Viscosity

The viscosity of a pure monatomic gas of molecular weight M may be written as √ −5 MT µ = 2.6693 · 10 · 2 (3.21) σ Ωµ

−1 −1 −1 the units are: µ [gcm s ], M [gmol ], T [K], σ [A],˚ Ωµ [dimensionless]. Ωµ is the ”collision integral” for viscosity. This parameter can be calculated according to the formula presented in reference Bird et al. [2002],

1.16145 0.52487 2.16178 Ω = + + (3.22) µ τ 0.14874 exp (0.77320 · τ) exp (2.43787 · τ) where τ = kT/. Quantities and σ are presented in equation (3.18). This collision integral for diﬀusion corresponds to Ω(2,2) presented in reference Neufeld et al. [1972]. Finally, the calculation of the viscosity of a gas mixture is made using the semi- empirical Wilke approximation,

N x µ µ = X α α (3.23) mix P x Φ α=1 β β αβ where the dimensionless quantities Φαβ are

 2 !(−1/2) !1/2 1/4 1 Mα µα Mβ Φαβ = √ 1 + 1 +  (3.24) 8 Mβ µβ Mα

3.3.4 Thermal conductivity

The thermal conductivity of a pure monatomic gas of molecular weight M and viscosity µ may be written as [Bird et al., 2002]

15 R κ = µ (3.25) 4 M

41 Chapter 3. Model of CVD of polysilicon by TCS decomposition

Figure 3.2: System geometry. Top and side view the units are κ [Wm−1K−1], R (the universal gas constant [Jmol−1K−1], M [kgmol−1] and µ [kgm−1s−1]. The calculation of the thermal conductivity of a gas mixture is carried out using the semi-empirical Mason-Saxena approximation,

N x κ κ = X α α (3.26) mix P x Φ α=1 β β αβ where the dimensionless quantities Φαβ are identical to those appearing in the viscosity equation, presented in (3.24).

3.4 Deposition model

As a result of the symmetries within the reactor, see Figure 3.1, there is a closed and adiabatic boundary between each pair of neighbouring rods, i.e. neither mass nor heat can pass through. The shape of this boundary depends on the arrangement of the rods in the reactor (hexagonal, circular, etc.). A cylindrical adiabatic boundary is considered in this work for simplicity. Thus, a hollow cylinder deﬁnes the system geometry, shown in

figure 3.2. The inner radius, ri, defines a surface that corresponds to the polysilicon rod and the outer radius, ro, defines the closed and adiabatic boundary that corresponds to the equidistant space between neighboring rods. The height of the cylinder is L. The transport phenomena and the surface reactions have to be taken into account

42 3.4. Deposition model

when discussing the silicon growth rate. The concentrations of chemical species at the rod surface set, among other variables, the growth rate and differ from those at the entrance to the reactor; therefore, they should be calculated by analysing the transport phenomena. Some assumptions are made to assist in the solution of the conservation equations [Ager et al., 2005; Hashimoto et al., 1990]: no axial diffusion of the discussed properties, steady and laminar flow, ideal gas law, the gas properties are independent of the mass fraction of the species, the thermal diffusion is negligible, and the pressure is set as constant. A steady-state condition has been considered because although deposition takes place and changes the geometry, the mass fraction and temperature profile reach a steady state faster than this occurs. Cylindrical coordinates, coaxial with the reactor and with z=0 at the base, are chosen to solve the equations.

3.4.1 Velocity proﬁle

The velocity proﬁle of the gas mixture across the reactor is calculated by means of the conservation of mass equation and the conservation of linear momentum equation in axial direction,

∂ 1 ∂ (ρv ) + (rρv ) = 0 (3.27) ∂z z r ∂r r ∂v ∂v ∂p 1 ∂ ∂v 4 ∂2v ρ v z + v z = − + µ r z + µ z − ρg (3.28) r ∂r z ∂z ∂z r ∂r ∂r 3 ∂z2

It should be noted that p has not yet been set as a constant. The equation of change for temperature and the conservation of individual species mass equation are also required to obtain the velocity profile since both determine the temperature and spatial coordinate dependence of ρ. Despite that, the reasoning presented below is focused on the two displayed equations because it is based in the Heaton et al. [1964] analytical solution of these equations for incompressible fluids and their calculated hydrodynamic entry length. Some conclusions can be derived from this analysis even though, in our study, the fluid properties are not constant with temperature and the fluid is compressible: the lower the viscosity of the fluid the larger the entry length. The gas mixture actually has a lower viscosity than the incompressible fluids presented in the aforementioned study [Heaton et al., 1964] and thus a longer entry length. By setting the reactor length lower than the entry length the boundary layer would be thin and not fully developed, and therefore the radial component of the gas velocity can be ignored because it only exists within this thin layer. The warming of the gas mixture also has to be taken into account: the gas closer to the rod heats up, consequently its density decreases and its velocity increases. The increase

43 Chapter 3. Model of CVD of polysilicon by TCS decomposition

in velocity in that region makes the boundary layer where the radial component has to be considered even smaller. Thus, it can be stated that the radial velocity and the boundary layer can be ignored.

After ignoring vr the equations can be solved separately. Equation (3.27) yields

∂ (ρv ) = 0 (3.29) ∂z z

The boundary condition is vz|z=0 = v0 and the solution to this equation, ρ0 being the density of the gas at the entrance of the reactor, is

ρ0 T (r, z) vz = v0 · ⇐⇒ vz(r, z) = v0 · (3.30) ρ T0

Note that the value of this solution at the rod surface is not zero because of the assumption that the boundary layer is suﬃciently small to be ignored. In the boundary layer the velocity components go from a certain value at the border of the layer to zero on the surface, but taking the limit as the layer thickness approaches zero the value of the axial velocity at the surface is not zero.

3.4.2 Heat transfer

Some aspects, such us the maximum temperature permitted to avoid the gas phase reactions or the optimization between power loss and growth rate in the reactor, demand that the temperature distribution be obtained in the gas mixture. This temperature distribution is obtained using the equation of change for temperature,

∂T 1 ∂ ∂T ρC v = κ · r (3.31) p z ∂z r ∂r ∂r

The boundary conditions for T are: (i) the temperature of the gas on the surface of the rod is Ts,(ii) adiabatic condition at ro, and (iii) constant and known temperature distribution at the reactor entrance, T0. The solution of equation (3.31), which is derived in appendix A.1, is

! ∞ θ2 κz ∆T (r, z) = ∆T · X A · exp − n χ (r) (3.32) 0 n ρ v C n n=0 0 0 p where ∆T (r, z) = T (r, z) − Ts. The convection is the heat transfer mechanism that takes place in a ﬂuid because of the heat conduction and the energy transport as consequence of the ﬂuid motion. The power loss due to warming of the gas, transferred by convection, can be analyzed by means of Newton’s law of cooling: P = h · (Ts − T0) · 2πriL, where the

44 3.4. Deposition model

convection coeﬃcient, h, is introduced. On the other hand, the power loss, according to the model, is

Z L ∂∆T P = κ |ri · 2πri · dz (3.33) 0 ∂r Thus, " !# κ ∞ θ2 κL ρ v C h = X A · 1 − exp − n · 0 0 p [J (θ r ) − α · Y (θ r )] (3.34) L n ρ v C θ κ 1 n i n 1 n i n=0 0 0 p n

From eqs. (3.32) and (3.34) the dependences of thermal variables on the parameters that deﬁne the ﬂuid regime can be derived.

3.4.3 Mass transport of species

The growth of silicon in the seed rod can be either limited by chemical reactions or by mass transport. At low temperatures the reaction rate is low and an excess of HSiCl3 is located in this region because few HSiCl3 molecules are converted into silicon. Therefore, the silicon growth is limited by the reaction. When the temperature rises the reaction rate increases and there is a lack of HSiCl3 on the surface because there are no HSiCl3 molecules left to be converted into silicon. In this situation, the silicon growth is limited by mass transport. In the model presented below both limitations can be analysed. The only chemical reaction considered is the silicon deposition, although some gas phase reactions may appear, promoted by high temperatures in the gas phase; for instance the conversion of HSiCl3 into SiCl4 [Ceccaroli and Lohne, 2003] or the homogeneous nucleation of condensed silicon. The latter can be disregarded in the case of HSiCl3 and ◦ Ts ' 1100 C [Herrick and Woodruﬀ, 1984]. The HSiCl3 conversion into SiCl4 can also be disregarded since the growth rate is limited in a wide range of gas compositions by the hydrogen concentration at the rod surface, as explained later. The conservation of individual species mass equation for species i is

∂w 1 ∂ ∂w ρv i = ρD · r i (3.35) z ∂z r ∂r i ∂r

The following silicon deposition overall reaction has been considered [Habuka et al., 1996]

HSiCl3 + H2 → Si + 3HCl (3.36)

The incorporation of silicon atoms into the crystal lattice in polysilicon is supposed to be that of the single-crystalline silicon, because the growth rate does not vary considerably with diﬀerent crystal orientations [Faller and Hurrle, 1999]. The reaction is assumed to

45 Chapter 3. Model of CVD of polysilicon by TCS decomposition

be a second-order reaction and the rate of mass consumption or generation of species i on the surface is expressed as

−2 −1 Ri = νiMik[HSiCl3][H2] (kg m s ) (3.37) where k is the overall reaction rate constant, νi the stoichiometry coefficients of the compounds involved (-1 for HSiCl3 and H2 and 3 for HCl) and [i] the mole concentration of species i on the surface expressed in [mol·m−3]. A boundary condition will set this rate of mass consumption or generation equal to the diffusion flow driven by the concentration. The overall reaction constant is analysed in reference Habuka et al. [1996] and depends on the rate of HSiCl3 chemisorption on the surface, kad, and the rate of decomposition into

Si, kr. It can be expressed as

1 [HSiCl ] [H ] = 3 + 2 (3.38) k kr kad

Both rate constants obey Arrhenius’s law and can be expressed at atmospheric pressure as

6 5 kad(T ) = 2.72 · 10 exp −1.72 · 10 /RT (3.39) 3 5 kr(T ) = 5.63 · 10 exp −1.80 · 10 /RT (3.40)

In order to aid in the solution of the system, two extreme situations have been considered,

[HSiCl3] [H2] 1. > ⇒ k[HSiCl3][H2] ' kr · [H2] ⇒ growth limited by H2 kr kad

[HSiCl3] [H2] 2. < ⇒ k[HSiCl3][H2] ' kad · [HSiCl3] ⇒ growth limited by HSiCl3 kr kad

This approach, based on the different orders of magnitude of both constants, allows a second-order reaction CVD system to be converted into a first-order reaction system, which can be solved analytically. The limitation changes along the silicon rod when concentration of HSiCl3 and H2 at the surface fulfils the following expression, where ρs is the density of the mixture at the rod surface,

[HSiCl3] [H2] ρswtcs ρswh2 kr Mtcs = ⇔ = ⇔ wtcs = · · wh2 (3.41) kr kad Mtcskr Mh2 kad kad Mh2

Growth limited by H2

At the entrance of the reactor the mass fraction of species is constant along the radius, and only HSiCl3 and H2 exist because the HCl has not yet been generated. It can then

46 3.4. Deposition model

be stated, taking into account that wtcs0 = 1 − wh20 , that the deposition process begins limited by H2 when 1 w ≤ (3.42) h20 k M 1 + r · tcs kad Mh2 The system that has to be solved is the corresponding partial derivative equation (3.35) for each compound: trichlorosilane, hydrogen and hydrogen chloride respectively, and the following boundary conditions: (i) mass fraction at the entrance: known and constant,

(ii) closed boundary at ro and (iii) the diﬀusion ﬂow driven by the concentration is equal to the rate of mass consumption or generation at ri.

When the growth rate is limited by H2, the boundary conditions for the mass transport equation are as follows

wi|z=0 = wi0 (3.43) ∂w i | = 0 (3.44) ∂r ro ∂wi 1 ρ0Di0 |ri = −νiMiρskr (Ts) wh2 |ri (3.45) ∂r Mh2 i = HSiCl3, H2, HCl

Equation (3.35) for hydrogen leads to the following solution (see Appendix A.2 for derivation) ! ∞ θ2 D z w (r, z) = w · X A · exp − n h20 β (r) (3.46) h2 h20 n v n n=0 0

Note that, resulting from the mass fraction deﬁnition in the case of whcl and resulting from the equations system,

Mtcs wtcs − wtcs0 = (wh2 − wh20 ) ∀ r, z Mh2 (3.47)

whcl = 1 − wtcs − wh2 ∀ r, z

The growth rate is derived from (3.37) considering that the growth is limited by H2, 7 6 · 10 Msi −1 vg (z) = · · ρskr(Ts)wh2 (ri, z)(µm · min ) (3.48) dSi Mh2 −3 where dSi is the density of solid silicon expressed in kg·m . The mass fraction of HSiCl3 and H2 diminishes along the rod length whereas the HCl mass fraction increases. Even though the growth is limited by H2 the situation changes when wtcs and wh2 on the rod surface meets equation (3.41). Taking equation (3.47) into account, the value of wh2 on the rod surface when the limitation changes is M 1 + tcs · w − 1 M h20 w (r , z ) = w = h2 (3.49) h2 i l h2lim M k tcs · 1 − r Mh2 kad

47 Chapter 3. Model of CVD of polysilicon by TCS decomposition

The height of the rod where the limitation changes is zl, i.e, wh2 (ri, zl) = wh2lim = w . h2zl

Limitation change

The reaction rate after the limitation change is governed by the HSiCl3 chemisorption on the surface. This situation has to be considered when the system started limited by H2, i.e. when equation (3.42) is fulﬁlled and wh2lim ≥ 0. Then, it is considered that when

Mh2 1 ≤ wh20 ≤ (3.50) M + M kr Mtcs h2 tcs 1 + · kad Mh2

The boundary conditions must change because the growth is now limited by HSiCl3. The new conditions that deﬁne the system are as follows

wi|z=zl = wizl (3.51) ∂w i | = 0 (3.52) ∂r ro ∂wi 1 ρ0Di0 |ri = −νiMiρskad (Ts) wtcs|ri (3.53) ∂r Mtcs i = HSiCl3, H2, HCl

The equation for HSiCl3 is solved and its mass fraction is obtained by means of the following summation (see Appendix A.3 for derivation) ! ∞ η2D (z − z ) w (r, z) = X B · exp − n tcs0 l δ (r) ∀z > z (3.54) tcs n v n l n=0 0

Again, as a result of the mass fraction deﬁnition in the case of whcl and of the system of equations, it is derived that

Mh2 wh2 − wh20 = (wtcs − wtcs0 ) ∀r, ∀z > zl Mtcs (3.55)

whcl = 1 − wh2 − wtcs ∀r, ∀z > zl

The growth rate is expressed as

7 6 · 10 Msi −1 vg (z) = · · ρskad(Ts)wtcs (ri, z) ∀z > zl (µm · min ) (3.56) dSi Mtcs

Growth limited by HSiCl3

In this situation the growth process begins limited by HSiCl3, i.e., 1 w > (3.57) h20 k M 1 + r · tcs kad Mh2

48 3.5. Results of the model

The solution of this system is similar to that presented in equations (3.46)-(3.48) taking into account that kad has to be used instead of kr and wtcs plays the role of wh2 and vice versa. In this case wh20 < wh2lim and the evolution of wh2 never reaches the changing limitation value. It can then be assured that the growth remains limited by HSiCl3 and does not change to being limited by H2. The three expressions derived in this section for the growth rate allow calculation of the growth uniformity along the silicon rod and the eﬃciency of deposition, deﬁned as the ratio of silicon introduced into the reactor per unit time to the silicon deposited per unit time. The growth uniformity can be calculated by comparing the growth rate at the bottom and at the top of the rod.

3.5 Results of the model

The results of the model are now presented, showing the influence on the polysilicon production process of the deposition conditions: gas flow, inlet gas composition, pressure, and rod temperature. The gas flow is determined by means of the dimensionless Reynolds number, Re, at the reactor entrance. Re is defined as follows,

ρvD Re = eq (3.58) µ

ρ being the gas density, v the gas velocity, Deq the equivalent diameter and µ the gas viscosity. The greater the gas flow rate, the greater the Reynolds number. The gas flow rate is expressed using the following units: slm, standard litres per minute, and kmol·h−1, kilomoles per hour. The inlet gas in the CVD reactor is composed of trichlorosilane and hydrogen exclusively. The inlet gas composition can therefore be defined by its hydrogen molar fraction

(xH2 ), understanding that its trichlorosilane molar fraction is xtcs = 1 − xH2 . It is important to analyse the optimum inlet gas composition for growing polysilicon, since a bad choice of inlet gas composition can produce a very slow polysilicon growth rate, and therefore a very high energy consumption. The pressure within the reactor chamber and the rod surface temperature have a strong inﬂuence on the deposition process. The presented analysis allows these parameters to be set for optimum operation of the CVD reactor. Finally, the evolution of the process with the rod diameter is studied. The rods thicken during the process. Thus, the analysis of the variation of the process with the rod diameter shows how the deposition process changes when it evolves with time.

49 Chapter 3. Model of CVD of polysilicon by TCS decomposition

The general parameters for the calculations presented in this chapter are depicted in table 3.1.

Table 3.1: Reference parameters for the calculations presented in this chapter. The geometry of the system is presented in ﬁgure 3.2

◦ T0 300 C L 2 m ◦ Ts 1150 C r0 12.5 cm

p 1 atm ri 1 cm

3.5.1 Eﬀect of the gas ﬂow

The evolution of the deposition features is calculated for a fixed gas composition (xH2 = 0.9) over a range of gas flow rates corresponding to Re = 1-2300, which is the range for which flow is considered laminar. This analysis is detailed in figures 3.3 and 3.4. The trends shown in these figures are similar for any set of inlet parameters: gas composition, pressure, system dimensions, inlet gas temperature and rod surface temperature.

Figure 3.3: Growth rate (−) and deposition efficiency (−−) for different total gas flow rates, from Re =

1-2300. Gas molar composition: xH2 = 0.9. All other parameters are set as presented in table 3.1.

Figure 3.3 shows high deposition efficiencies when the gas flow is low. This is because, in this case, the rate of silicon introduced into the reactor per unit time is low and can therefore be consumed throughout the entire length of the reactor yielding high deposition efficiencies. However, low gas flow generates a smooth mass fraction profile for trichlorosi-

50 3.5. Results of the model

Figure 3.4: Power loss by convection (−) and energy loss by convection per kg of polysilicon produced

(−−) for different total gas flow rates, from Re = 1-2300. Gas molar composition: xH2 = 0.9. All other parameters are set as presented in table 3.1. lane and hydrogen yielding low growth rates because of the low diffusion of mass toward the silicon rod surface. A flat region is found for the growth rate when increasing the gas flow, where the growth rate evolves smoothly while the deposition efficiency continuously decreases and the power loss continuously increases, as seen in figure 3.4. The flow regime determined by Re = 2300 gives the maximum growth rate and the minimum deposition efficiency for a given gas composition. The ratio of energy loss by convection to mass of polysilicon produced is also depicted in figure 3.4. It is calculated from the following expression, where dSi is the silicon density, expressed in kg·m−3, and the power loss by convection (P) is expressed in kW,

Power loss P −1 E = = −5 (kWh · kg ) (3.59) Mass rate 2πri · L · vg · dSi · 6 · 10 It can be seen that there is a minimum in the energy loss evolution. At the left of this minimum the power loss and the growth rate are low, yielding a high energy loss. Otherwise, at the right of this minimum, the power loss and the growth rate are high, yielding again a high energy loss. The minimum is therefore located between the low mass rate region and the high power loss region. In this particular case, the minimum is found when the gas flow per rod is 0.1 kmol·h−1 (40 slm) and the growth rate is around 5 µm·min−1. The gas flow can be chosen according to several criteria: high growth rate, high deposition efficiency, low power loss or low energy consumption. According to this work, if the

51 Chapter 3. Model of CVD of polysilicon by TCS decomposition

low energy consumption criterion is followed: (a) the production cost is lower because the energy consumption is optimised, (b) the deposition eﬃciency is intermediate and the recirculation system has medium size, and (c) the power consumption is optimised, reducing the power requirements.

3.5.2 Eﬀect of the gas composition

As presented above, the maximum growth rate is achieved when Re = 2300 for a given gas composition. In this section the variation of this maximum growth rate with the gas composition at the reactor inlet is studied. The evolution of the maximum growth rate is presented in figure 3.5. Starting from xH2 = 1, the growth rate increases on diminishing the H2 molar fraction up to a certain value, in this particular case xH2 = 0.91 (the molar ratio H2:HSiCl3 is 10), it then decreases due to the hydrogen limitation. This maximum depends on the system dimensions, the surface temperature, the temperature of the inlet gas and the pressure within the reactor vessel. The efficiency reaches a maximum at a slightly different H2 molar fraction, as seen in figure 3.5.

Figure 3.5: Growth rate (−) and deposition eﬃciency (−−) for diﬀerent inlet gas compositions. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1.

The evolution of the power loss per rod and the energy loss when Re=2300 is presented in ﬁgure 3.6. It is found that there is a wide range of inlet gas compositions for which the energy loss can be considered constant. Analysing this range in detail it can be seen that at the left-hand side, both the growth rate and the power loss are low. At the right-hand

52 3.5. Results of the model

Figure 3.6: Power loss by convection (−) and energy loss by convection per kg of polysilicon produced (−−) for diﬀerent inlet gas compositions. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1. side of the range, the growth rate and the power loss are both greater than the values in the left-hand side. Therefore, the expression presented in equation (3.59) provides similar values within this range. This ﬂat range is important because, theoretically, there is a wide range of good conditions for growing polysilicon.

3.5.3 Eﬀect of the pressure and the rod surface temperature

There is an inlet gas composition, as already presented, that allows the maximum growth rate to be reached. In this section the changes of this composition and the maximum growth rate with the pressure and the rod surface temperature are studied. The inlet gas compositions where the maximum growth rates are reached, for different surface temperatures and pressures, are presented in figure 3.7. It is shown that the optimum hydrogen molar fraction decreases when increasing the pressure and the rod surface temperature. When the pressure rises the reactant concentration increases, the hydrogen limitation being more difficult to reach. When the rod surface temperature increases, the reaction constants, kad and kr, change in a manner different from one another [Habuka et al., 1996]. As a consequence, the hydrogen limitation is reached at a lower hydrogen molar fraction. The maximum growth rate for different surface temperatures and pressures is presented in figure 3.8. It is seen that the rod surface temperature and the pressure within the reactor

53 Chapter 3. Model of CVD of polysilicon by TCS decomposition

Figure 3.7: Inlet gas compositions, expressed as the hydrogen molar fraction, that achieve the maximum growth rate for diﬀerent rod surface temperatures and reactor pressures. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1. vessel have a strong impact on the growth rate. A good combination of both increases the growth rate sixfold. When the rod surface temperature is raised, the kinetic of the silicon deposition is faster because the reactor constants, presented in the previous section, have an exponential dependence on this parameter [Habuka et al., 1996]. When the pressure in the reactor vessel is raised, the growth rate increases because the concentration of reactant species (hydrogen and trichlorosilane) is greater.

Comparing both parameters, the influence on the growth rate of the temperature is greater than the influence of the pressure. Also, the impact of both on the growth rate is somewhat different. The growth rate increases faster in the low pressure regime than in the high pressure regime. However, considering the rod temperature, the growth rate increases slower in the low temperature regime than in high temperature regime.

Focusing on the target of high growth rates, the previously presented data indicates that the pressure and the rod temperature should be increased as much as possible. The reactor vessel could work, for instance, at 100-150 atm and the rod surface temperature could be close to the silicon melting point (1410 ◦C). However, the analysis of the energy consumption shows that the pressure and rod temperature should be set carefully, and not increased as much as possible.

The impact of the rod temperature on the energy consumption, expressed in kWh·kg−1, is analysed in ﬁgure 3.9. The energy consumption presented in this ﬁgure has two compo-

54 3.5. Results of the model

Figure 3.8: Maximum growth rate, expressed in µm·min−1, dependence on the reactor pressure and rod surface temperature. Re = 2300 at the inlet. All other parameters are set as presented in table 3.1.

Figure 3.9: Dependence of the total energy consumption, considering convection and radiation, on the rod surface temperature. Re = 2300 at the inlet, the reactor pressure is p = 6 atm and the inlet gas compositions are those presented in ﬁgure 3.7. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. All other parameters are set as presented in table 3.1.

nents: the convection component, estimated by the model, and the radiation component, explained and calculated in the following chapter. There is a minimum in the energy consumption, at around 1200 ◦C, which is not close to the silicon melting point. When

55 Chapter 3. Model of CVD of polysilicon by TCS decomposition

the temperature is higher than this value, the radiation loss increases dramatically while the growth rate increases more slowly, leading to higher energy consumption. When the temperature is lower, the radiation loss decreases but, in this case, it is the growth rate which decreases dramatically, leading again to higher energy consumption.

Figure 3.10: Dependence of the total energy consumption, considering convection and radiation, on the pressure within the reactor vessel. Re = 2300 at the inlet, the rod surface temperature is 1150 ◦C and the inlet gas compositions are those presented in ﬁgure 3.7. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. All other parameters are set as presented in table 3.1.

The impact of the pressure within the reactor vessel on the energy consumption, expressed in kWh·kg−1, is analysed in ﬁgure 3.10. Again, the convection and radiation are taken into account in the energy consumption. It can be seen that the energy consumption decreases monotonically with increasing pressure. However, above a pressure of 6 atm, the decrease in the energy consumption is unremarkable, and therefore increasing the pressure above this value is not justiﬁed.

3.5.4 Eﬀect of the rod diameter

It is important to analyse the change of the deposition process with the rod diameter because the rods thicken throughout the process. Therefore, analysing the effect of the rod diameter is necessary to understand the evolution of the deposition conditions with time. First, the variation of the maximum growth rate when increasing the rod diameter is studied. The maximum growth rate is presented in figure 3.11 for different rod diameters

56 3.5. Results of the model

and rod surface temperatures, considering a constant pressure within the reactor vessel of p = 6 atm. It can be observed that if the surface temperature remains constant, the growth rate changes throughout the deposition process as the rod diameter increases. This variation is greater at high temperatures than at low temperatures. The reason is found in the diffusion of reactant molecules toward the surface, because the diffusion flow of molecules is greater when the rod is thin. At high rod surface temperatures the growth is clearly limited by the transport of molecules toward the surface, and the variation of the growth rate with the rod diameter is bigger.

Figure 3.11: Maximum growth rate, expressed in µm·min−1, dependence on the rod surface temperature and the rod diameter. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. All other parameters are set as presented in table 3.1.

The inlet gas composition that achieves these maximum growth rates is presented as a function of rod diameter and temperature in figure 3.12. Again, it is shown that the inlet gas composition should be modified slightly during the process to achieve the greatest growth rates. However, if the inlet gas composition were set constant during the process, the growth rate would not change remarkably. The higher the rod diameter the higher the rod surface area. This obvious statement helps it be understood that power loss by convection, which depends on the rod surface, increases as the process evolves. Not only the power loss, but also the gas flow depends on the rod diameter, because enlarging the rod surface means that the reactant gases have a greater area on which to react. Greater gas flow should therefore be used if maintaining the growth rate is intended.

57 Chapter 3. Model of CVD of polysilicon by TCS decomposition

Figure 3.12: Inlet gas compositions, expressed as the hydrogen molar fraction, that achieve the maximum growth rates presented in ﬁgure 3.11. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. All other parameters are set as presented in table 3.1.

Figure 3.13: Power loss by convection, expressed in kW, dependence on the rod surface temperature and the rod diameter. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. The inlet gas compositions are presented in ﬁgure 3.12. All other parameters are set as presented in table 3.1.

The evolution of the power loss by convection, in the whole CVD reactor, throughout the deposition process is shown in ﬁgure 3.13, where a constant reactor pressure is considered. The power loss by convection increases almost linearly with the rod diameter, but

58 3.5. Results of the model

Figure 3.14: Inlet gas flows, expressed in kmol·h−1, that achieve the maximum growth rates presented in figure 3.11. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. The inlet gas compositions are presented in figure 3.12. All other parameters are set as presented in table 3.1.

it is almost constant with respect to the rod surface temperature. This is due to the inlet gas composition: when raising the surface temperature, the trichlorosilane molar fraction of the gas composition increases, i.e. the gas mixture is enriched as seen in figure 3.12. When the gas mixture is enriched, its specific heat decreases, and the mixture cools the rod less efficiently. Enriching the gas mixture and increasing the rod temperature have opposite effects on the power loss; when balanced the power loss by convection remains constant.

The inlet gas flows that achieve maximum growth rates are presented in figure 3.14. It is shown that at low rod temperatures the inlet gas flows are greater. In this low temperature regime, the flow does not have a noteworthy variation when increasing the rod diameter. In the high temperature regime, the gas flow should be slightly modified during operation of the reactor. First, in the middle of the process the gas flow should be reduced. Then, after a certain rod diameter is reached, it should be increased again.

Another important issue that has to be analysed is the variation of the optimum rod surface temperature, presented in figure 3.9 for ri = 1 cm, as the rod diameter increases. This is presented in figure 3.15. It can be seen that the optimum rod surface temperature decreases throughout the process. This is because, as seen in figure 3.11, the growth rate variation with the surface temperature is greater when the rod diameter is low.

59 Chapter 3. Model of CVD of polysilicon by TCS decomposition

Figure 3.15: Variation of the rod surface temperature that minimises the total energy consumption, considering convection and radiation, with rod diameter. Re = 2300 at the inlet and the reactor pressure is p = 6 atm. The CVD reactor considered is a 36 rod reactor arranged in 3 rings. All other parameters are set as presented in table 3.1.

3.6 Discussion of results

The target of the deposition process is to produce high-purity silicon with minimum energy consumption. Thus, the rod surface temperature, the pressure in the reactor chamber, the gas flow and the inlet gas composition should be chosen to achieve this target. Some of these deposition conditions should be modified throughout the process, seeking the best conditions as the process evolves with time and the rods thicken. As seen in figure 3.10, the operation pressure should be around 6 atm. Increasing the pressure above this value is not justified, as already mentioned, because there is no noteworthy improvement in the energy consumption. Nevertheless, the difference between operation pressures of 1 atm and 6 atm is remarkable, and the energy consumption is more than halved if the pressure is set to 6 atm. Similarly, when the rods thicken the pressure should not be modified; this deposition condition should be maintained throughout the process. The rod surface temperature has a strong influence on the low energy consumption target. Theoretically, the greater the temperature the greater the growth rate. However, as seen in figure 3.9, the rod surface temperature should be set within the range 1150- 1200 ◦C to achieve the lowest energy consumption, considering convection and radiation losses. This is because the ratio of energy consumption to silicon produced at very high

60 3.6. Discussion of results

rod surface temperature is high due to high energy loss, and this ratio is also high at low surface temperature due to a low mass production rate. Throughout the deposition process, the optimum deposition temperature decreases as presented in figure 3.15, but never drops below 1140 ◦C. An important issue not dealt with in this chapter is whether this temperature range is attainable. There is a limitation caused by the risk, that increases when the rod thickens, of reaching the melting point at the core of the silicon rods. In chapter 5 the temperature distribution inside the silicon rod is analysed, and the maximum surface temperature allowed during the process is presented. However, as a general trend, the rod surface temperature should be as close as possible to the optimum temperature, in order to minimise the energy consumption. Analysing figure 3.9, it can be seen that if the surface temperature is set to 1000 ◦C instead of the optimum temperature, the energy consumption is doubled. This model cannot estimate or evaluate the dendritic growth of polysilicon, the so- called “pop-corn” [Ceccaroli and Lohne, 2003]. According to reference Rogers [1990], this undesirable growth may occur if the surface temperature is above 1100 ◦C. Some experiments carried out in this thesis produced dendritic growth at temperatures even lower than 1100 ◦C at atmospheric pressure (see chapter 6). This phenomena forces to stop the process. The theoretical optimum deposition temperature cannot be reached for two reasons: the melting of the silicon rod core when the rod diameter is high, and the formation of dendrites during the polysilicon growth. To avoid these drawbacks, the rod surface temperature can be set to 1050 ◦C. This surface temperature should be maintained throughout the process. The optimum inlet gas composition, presented in figure 3.16, is calculated for a selected pressure of 6 atm, and a rod surface temperature of 1050 ◦C. The hydrogen molar fraction should be in the range of 0.75-0.9 and therefore the trichlorosilane molar fraction should be around 0.1-0.25. At the begining of the process, the optimum inlet gas mixture has a hydrogen to trichlorosilane ratio of H2:TCS'7. At the end of the process, the relative content of trichlorosilane in the optimum gas mixture increases, leading to a hydrogen to trichlorosilane ratio of H2:TCS'4. Seeking a trade-off between the growth rate and the deposition efficiency, the inlet gas flow throughout the deposition process is calculated. Gas flows that ensure a deposition efficiency of 10% are chosen, and shown in figure 3.17. This deposition efficiency is selected because it can be achieved with an intermediate gas flow that produces a high growth rate and low energy consumption, when considering convection and radiation. It can be seen

61 Chapter 3. Model of CVD of polysilicon by TCS decomposition

Figure 3.16: Inlet gas composition, expressed as the hydrogen molar fraction, throughout the deposition ◦ process. The pressure in the reactor vessel is p = 6 atm, and the rod surface temperature is Ts = 1050 C. All other parameters are set as presented in table 3.1.

Figure 3.17: Inlet gas flow, expressed in kmol·h−1, that yields a deposition efficiency of 10% throughout the deposition process. The pressure in the reactor vessel is p = 6 atm, and the rod surface temperature is ◦ Ts = 1050 C. A 36 rod CVD reactor is considered. All other parameters are set as presented in table 3.1. that the total inlet gas flow increases when the rods thicken. The values shown in this figure correspond to a 36 rod CVD reactor. The deposition process, considering the deposition conditions presented above, is cal-

62 3.6. Discussion of results

Figure 3.18: Growth rate, expressed in µm·min−1, throughout the deposition process. The pressure in the ◦ reactor vessel is p = 6 atm, and the rod surface temperature is Ts = 1050 C. All other parameters are set as presented in table 3.1.

Figure 3.19: Energy consumption, expressed in kWh·kg−1, throughout the deposition process. Radiation loss and convection loss are considered. The pressure in the reactor vessel is p = 6 atm, and the rod ◦ surface temperature is Ts = 1050 C. A 36 rod CVD reactor is considered. All other parameters are set as presented in table 3.1. culated with the model presented in this chapter. The results are presented in ﬁgure 3.18, where the growth rate in the process is shown, and ﬁgure 3.19, where the energy consumption, considering radiation loss and convection loss, is depicted. The growth

63 Chapter 3. Model of CVD of polysilicon by TCS decomposition

rates throughout the process are in the range of 9.5-12 µm·min−1, the mean value is 10 µm·min−1. The energy consumption is higher when the rods are thin. This is due to the mass production rate and the radiative transfer between the rods and the reactor wall. A thinner rod leads to a lower mass production rate than a thicker rod, because the surface area where the deposition takes place is lower. The radiative transfer from the rods to the reactor wall is not blocked by other rods when the rods are thin. However, when the rods thicken, some blockage takes place and the power loss decreases, as will be explained in the following chapter. Therefore, the process uses the energy more eﬃciently when the rods are thick. As a consequence, the maximum diameter of the silicon rods in the CVD reactor must be increased to diminish the energy consumption of the process per kg of polysilicon produced. The deposition process discussed and presented in this section is summarised in tables 3.2 and 3.3. The deposition conditions and the results of the simulations are presented in the former table. The general results of the process are outlined in the latter table.

Table 3.2: Proposed process parameters for polysilicon deposition in a 36 rod CVD reactor. The deposition conditions proposed are: the inlet gas ﬂows, the reactor pressure and the rod surface temperature. The resulting growth rate and the energy consumption are presented. The energy consumption includes radiation loss and convection loss.

Rod diameter Time TCS ﬂow H2 ﬂow Pressure Ts vg E cm h kmol·h−1 kmol·h−1 atm ◦C µm·min−1 kWh·kg−1 1.0 7.1 1.28 9.79 6 1050 11.79 70.59 2.0 15.0 1.61 8.63 6 1050 10.52 66.30 3.0 23.4 1.96 8.90 6 1050 9.94 61.25 4.0 32.0 2.33 9.62 6 1050 9.66 56.01 5.0 40.7 2.72 10.57 6 1050 9.56 51.00 6.0 49.4 3.12 11.68 6 1050 9.56 46.45 7.0 58.1 3.54 12.93 6 1050 9.62 42.37 8.0 66.7 3.98 14.31 6 1050 9.74 38.75 9.0 75.1 4.44 15.82 6 1050 9.88 35.55 10.0 83.4 4.92 17.47 6 1050 10.06 32.78 11.0 91.5 5.41 19.26 6 1050 10.25 30.40 12.0 99.5 5.92 21.21 6 1050 10.46 28.35 13.0 107.3 6.45 23.33 6 1050 10.68 26.58 14.0 114.9 7.00 25.67 6 1050 10.91 25.07

64 3.7. Conclusions

Table 3.3: Global results of the process presented in table 3.2. Time / h 115 Silicon produced / kg 2570 Growth rate / µm·min−1 10.15 Polysilicon productivity / kg·h−1 22.3 Energy consumption / kWh·kg−1 47.3 TCS inlet / kmol 447

H2 inlet / kmol 1705

3.7 Conclusions

A model for the decomposition of trichlorosilane in a polysilicon deposition reactor is presented. Regarding the inﬂuence of the deposition process on the temperature, two regions are distinguished: the region limited by the reaction, where the process is limited by the chemical reaction rate; and the region limited by the transport of mass, where the process is limited by the transport of chemical species towards the hot surface. The model derived in this chapter describes the deposition process in both regimes. Therefore, it predicts the polysilicon growth under a wide range of temperatures and species concentrations. Considering the deposition reaction, the model is based on splitting the second-order reactor rate of the trichlorosilane decomposition [Habuka et al., 1996] into two systems of ﬁrst-order reaction rates, which can be solved analytically. This approach has not before been presented in the literature. Thus, two situations are considered: one where the polysilicon growth is governed by the rate of chemisorption of HSiCl3 molecules on the surface, that is, it is governed by the HSiCl3 concentration at the rod surface; and one where the growth process is governed by the rate of decomposition of the chemisorpted

HSiCl3 molecules into polysilicon, that is, it is governed by the H2 concentration at the rod surface. Analytical expressions for the growth rate of polysilicon onto the silicon rods are derived, regarding the composition of the gas mixture (HSiCl3 and H2) at the inlet, the gas flow, the pressure within the reactor and the rod surface temperature. These expressions provide an estimation for the growth rate for any rod radii and for any distance along the rod length. The growth uniformity and the efficiency of deposition are then easily calculated. The effect of the deposition conditions is studied and presented. Regarding the gas flow, the greater the gas flow the higher the polysilicon growth rate. Also, increasing the gas flow decreases the deposition efficiency (silicon conversion) and increases the power

65 Chapter 3. Model of CVD of polysilicon by TCS decomposition

loss by convection. There is an intermediate gas flow where energy loss by convection reaches a minimum. There is an optimum gas composition where a maximum growth rate can be found. However, analysing the deposition process as the inlet gas composition is modified, it is seen that there is a wide range where the energy loss by convection can be considered constant. The trichlorosilane molar fraction in the optimum gas composition increases when the pressure or the rod surface temperature increases. The rod temperature and the reactor pressure are very influential conditions in the deposition process. However, comparing the two, the rod surface temperature has a stronger influence on the process than the pressure. When increasing the pressure, the growth rate increases and the energy consumption decreases. An optimum pressure can be found at 6 atm, since increasing the pressure above this value does not produce a noteworthy variation in the energy consumption. Therefore, increasing the reactor pressure above 6 atm is not justified. Regarding the rod surface temperature, it is seen that there is an optimum deposition temperature that leads to minimum energy consumption. This temperature is between 1100-1200 ◦C, depending on the deposition conditions. The effect of the rod radius on the deposition process is also presented, showing the variation of the optimum deposition conditions throughout the process. Based on this analysis, a polysilicon deposition process is proposed and summarised in tables 3.2 and 3.3. This model does not study and estimate the dentritic growth of polysilicon, the so- called ’pop-corn’, during the deposition process under certain undesirable growing conditions. This important topic should be considered as future work, its effects introduced into the model. The deposition conditions are analysed in detail, and the power loss by convection estimated. In the next chapter the power loss by radiation, due to radiative transfer between the hot polysilicon rods and the cold reactor wall, is studied in detail. Again, some proposals will be made for diminishing the radiation related energy consumption.

66 Chapter 4

Radiative energy loss in the polysilicon CVD reactor

4.1 Introduction

This chapter deals with the radiation loss in the CVD reactor, analysing how the hot polysilicon rods radiate heat toward the reactor wall, and how this energy loss can be minimised. Two paths can be followed to reduce the radiation loss:

• Increasing the number of rods within the reactor vessel. Before the 1970’s the CVD reactor was made of quartz or metal and there was only one rod per reactor, as presented in references Schweickert et al. [1957], Gutsche [1962] and Reuschel and Kersting [1962]. With such a conﬁguration, the power radiated by this unique rod was exchanged with the surroundings and lost. The utilization of metal instead of quartz reduced the radiation loss, since part of this radiation was reﬂected toward the rod, and also allowed operation higher pressures. Nevertheless, the utilization of metal could introduce impurities in the polysilicon growth. For that reason the reactor metal wall was and still is water cooled. After the 1970’s the amount of rods within the reactor vessel increased and the reactor wall was always made of metal. When increasing the number of rods, part of the radiation from one rod does not leave the reactor, since it can be absorbed by another rod.

• Introducing a high reflectivity reactor wall and/or thermal shields. Increasing the reflectivity of the reactor wall by making it of silver or silver-plated steel, as presented in reference Köpplet al. [1979], reduces the amount of radiation energy absorbed by the wall. However, care must be taken to avoid the contamination of the polysilicon produced. Also thermal shields can be used to reduce the radiation loss [Siegel

67 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

and Howell, 1972]. These shields are placed between the rods and the reactor cold wall, and their behaviour is analysed in this chapter. The shields are made of a ceramic material such as aluminium nitride (AlN), with relatively high reﬂectivity and resistance to the gases in the reactor.

The temperature of the rods is roughly 1100 ◦C and the reactor wall is cold. Some questions arise: are all the rods radiating in the same manner?, to what degree does a rod in the inner ring radiate differently to a rod in the outer ring?, how much power is required to maintain the temperature of all rods at 1100 ◦C in the water-cooled CVD reactor?, how and to what extent can this power be reduced? An energy balance is required to answer these questions, this is performed in this chapter. The influence of the number of rods on the radiation loss is analysed, and also the influence of the wall reflectivity and the thermal shields.

4.2 Rod arrangement within the CVD deposition reactor

As has been mentioned in other parts of this work, a CVD deposition reactor consists of a chamber where several high-purity silicon slim rods are heated by the Joule effect, and the polysilicon is deposited onto these seed rods, thickening them. Typically, the rods are made of two vertical parts, parallel to one another so that their free ends do not touch, and a silicon rod bridge that connects these ends. The rods have a U-inverted shape. For clarity, two terms are defined that will be used hereafter in this chapter: the term rod will denote the vertical part, and U-rod the U-shaped combination of rods. There are multiple options for arranging the silicon rods within the reactor vessel. However, as seen in figure 4.1, there are some common sense limitations:

1. The rods cannot be in contact with one another (without space between their surfaces). There are two reasons: the rods are thickening during the process, and the reactant gases must be able to arrive at the rod surfaces.

2. The rods should occupy the reactor uniformly.

Each rod will have a free-space around it, referred to as control space that allows it to grow, and allows the gases to reach its surface. The shape of this control space is, for simplicity, a cylinder surrounding the rod. For instance, if the maximum diameter of a silicon rod at the end of the process is 15 cm, a control space diameter of 25 cm is sensible. The diﬀerent control spaces will be arranged uniformly within the reactor vessel. The beehive hexagonal structure, shown in ﬁgure 4.2 and often seen in nature, allows the control spaces to be arranged with maximum compactness. Nevertheless, if this structure is used,

68 4.2. Rod arrangement within the CVD deposition reactor

(a) (b)

Figure 4.1: Undesirable rod arrangements. (a) There is no space for polysilicon growth or gas circulation. (b) The rods do not occupy the reactor uniformly rods in the same ring have different conditions: some rods are closer to the water-cooled wall than others. Thus, the quantity of heat given up to the surroundings is different for each rod. It is good practice to have the same current flowing to every rod, to make sure that the temperature at the surface is the same. To this end, some rods (typically six) are connected in series, and the temperature is monitored in just one rod surface. However, if the rods have different cooling conditions, the same current does not lead to the same temperature, resulting in the need to monitor the temperature in all rods. A more desirable option is a radially symmetrical structure, which leads to similar conditions for each rod in a ring, and requires that less surface temperatures be monitored. The considered structure, therefore, is radially symmetric and consists of rods arranged in concentric rings.

4.2.1 Rod arrangement in concentric rings

In this structure, the control spaces of all rods are arranged in concentric rings. The number of rings can be specific to a particular reactor. When designing a reactor, it is desirable to obtain the highest achievable compactness. By doing so, the wall surface area, and thereby the power loss, is minimised. In such a structure, all the control spaces in one ring are tangential to one another, as show in figure 4.3. In each ring, the following expression is fulfilled,

π −1 R = r · sin (4.1) N

69 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.2: Hexagonal rod arrangement.

N being the number of rods in the ring, r the radius of the control space, and R the distance from the centre of the ring to the centre of each rod. The next step is to define the distance between rings. It can be arbitrarily fixed, but we have chosen that two control spaces in the i + 1 ring be tangential to one control space in the ith ring, as seen in figure 4.4. By doing so, the compactness achieved in the CVD reactor is increased. With this configuration, the number of rods in the i+1 ring with respect to the number of rods in the ith level is π N = (4.2) i+1 √ −1/2 2 arcsin (Ni/π + 3) + 1

The value obtained with this expression must be rounded to have an integer number of rods in the i + 1 ring. Once the rod arrangement in concentric rings is understood, the next step consists in deﬁning a rod arrangement for a given total number of rods. Consider 36 rods: the ﬁrst approach is to arrange the 36 rods in one ring. The distance from the centre of the ring to the centre of each rod would be: 12.74 · r. Seeking higher compactness, another arrangement can be proposed: two rings. In this case, N1 would be the number of rods in the inner ring and N2 the number of rods in the outer ring, where

N2 is related to N1 according to equation (4.2). Then,

Ntotal = 36 = N1 + N2(N1) (4.3)

The solution for this equation is: N1 = 15 and N2 = 21, i.e, there are 15 rods in the inner ring and 21 rods in the outer ring. The outer ring radius is 7.50·r, according to expression

70 4.2. Rod arrangement within the CVD deposition reactor

Figure 4.3: Ring of rods.

(4.1). There is another even more compact conﬁguration: three rings. In this case, the equation that should be solved is

Ntotal = 36 = N1 + N2(N1) + N3(N2) (4.4)

The solution for this equation is N1 = 6, N2 = 12 and N3 = 18, i.e. there are six rods in the inner ring, 12 rods in the middle ring and 18 rods in the outer ring. Again, according to expression (4.1), the outer ring is separated from the centre of the concentric rings by 5.76 · r. The question is what the limit for the number of rings is. To answer this, four rings are considered. With four rings, the equation to be solved is

Ntotal = 36 = N1 + N2(N1) + N3(N2) + N4(N3) (4.5)

There is no solution for this equation, and therefore 36 rods cannot be arranged in more than three concentric rings. The same reasoning has been carried for different total numbers of rods, summarized in table 4.1. The analysis of this table shows that some configurations have an odd number of rods in a ring. That means that one vertical part of a U-rod is in one ring, and the other vertical part is in other ring. This can be a problem because there are different cooling conditions from one ring to the other, but the same current is flowing through the U-rod. Therefore, configurations with an odd number of rods in a ring should be avoided. From the configurations presented, those analysed in this work are: 36 rods in three rings, 48 rods in three rings and 60 rods in four rings.

71 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.4: Distance between rings. Two control spaces in ring two are tangential to one control space in ring one.

4.3 Radiation exchange between the polysilicon rods and the reactor wall

The thermal radiation transfer within the CVD reactor is analysed in this section. The thermal radiation is that detected as heat or light, in an intermediate wavelength range of 10−1 to 103 µm. The system consists of polysilicon rods, a reactor wall and, in some cases, thermal shields. All the surfaces are considered to be diffuse and grey. Diffuse means that the radiant intensity leaving the surface does not depend on the direction. Grey means that part of the incident energy on a surface is reflected. The diffuse-grey approximation assumes that the radiant intensity directly emitted and reflected at each surface is uniform over all directions. The reflected and emitted energies can then be combined into a single diffuse energy flux leaving the surface. The introduction of several quantities helps understanding of the thermal radiation exchange between finite diffuse-grey areas. These quantities, presented below, are drawn in figure 4.5.

• Irradiance (G): rate of incoming radiant energy per unit area, in W·m−2.

• Directly emitted energy ﬂux (E): rate of directly emitted energy per unit area, in W·m−2. The expression is derived following the theory of grey surfaces. is the

emissivity of the surface, Eb the energy ﬂux emitted by a black body per unit area,

72 4.3. Radiation exchange between the polysilicon rods and the reactor wall

Table 4.1: Diﬀerent reactor conﬁgurations. Note that two rods make one U-rod.

#Rods Ring 1 Ring 2 Ring 3 Ring 4 18 6 12 0 0 24 9 15 0 0 36 15 21 0 0 36 6 12 18 0 48 10 16 22 0 48 3 9 15 21 60 14 20 26 0 60 6 12 18 24

σ the Stefan-Boltzmann constant and T the temperature of the surface,

4 E = · Eb = · σ · T (4.6)

• Radiosity (J): rate of outgoing radiant energy per unit area, in W·m−2. It has two components: the directly emitted energy flux and the reflected energy flux. ρ is the reflectivity of the surface,

J = E + ρ · G = · σ · T 4 + ρ · G (4.7)

To carry out the energy balance between the different surfaces (rods, wall and shields) it is necessary to evaluate the fraction of the energy flux leaving a surface (J) that arrives at the other surface. This fraction is referred to as the geometric configuration factor. As its name suggests, it only depends on geometric aspects. In the following paragraphs the configuration factor is introduced, and its calculation derived.

4.3.1 Geometric conﬁguration factors

To introduce the geometric configuration factors, first we analyse the radiative transfer from a diffuse differential area element to another diffuse differential area element. The system presented in figure 4.6 is considered. There are two differential area elements, dA1 and dA2, arbitrarily oriented. Their normals are at angles θ1 and θ2 to the straight line of length S which connects them.

The total energy per unit time leaving dA1 and incident on dA2 is

2 d Qd1→d2 = J1/π · dA1 · cos θ1 · dω1 (4.8)

73 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.5: Rate of incoming and outgoing radiant energy per unit area of Ak.

This energy differential is second order since there are two differentials involved, dA1 and dω1. dA1 cos θ1 is the projected area of dA1 normal to the line between dA1 and dA2. dω1 is the solid angle subtended by dA2 at dA1, it is related to the projected area of dA2 and the distance between the differential elements, and is expressed as

dA · cos θ dω = 2 2 (4.9) 1 S2

Substituting the expression for the solid angle into equation (4.8),

J · dA · cos θ · dA · cos θ d2Q = 1 1 1 2 2 (4.10) d1→d2 π · S2

The geometric configuration factor is defined as the fraction of energy leaving diffuse surface element dA1 that arrives at element dA2. It is expressed as

2 J1 · cos θ1 · cos θ2 · dA1 · dA2/(π · S ) cos θ1 · cos θ2 dFd1→d2 = = 2 dA2 (4.11) J1 · dA1 π · S where J1 · dA1 is the total diﬀuse energy leaving dA1 within the entire hemispherical solid angle over dA1. The geometric conﬁguration factor can also be expressed as follows, showing its dependence on the solid angle subtended by dA2 at dA1 and on its orientation with respect to dA1.

cos θ · dω dF = 1 1 (4.12) d1→d2 π

When two ﬁnite areas are considered, such as two silicon rods, the geometric conﬁg- uration factor from A1 to A2 can be obtained by careful integration of equation (4.11),

74 4.3. Radiation exchange between the polysilicon rods and the reactor wall

Figure 4.6: Radiative transfer between diﬀerential areas. yielding Z Z 2 J1 · cos θ1 · cos θ2/(π · S ) · dA2 · dA1 A1 A2 F1→2 = = J1 · A1 1 Z Z cos θ1 · cos θ2 = · 2 · dA2 · dA1 (4.13) A1 A1 A2 π · S

If the same derivation is done for the geometric conﬁguration factor from A2 to A1, the reciprocity relation for two ﬁnite areas is found,

A1 · F1→2 = A2 · F2→1 (4.14)

There are different mathematical techniques for evaluating the geometric configuration factors that can be consulted in reference Siegel and Howell [1972]. The complexity for evaluating the integral presented in equation (4.13) is strong, particularly if the surfaces are not regular or if there is some radiant blockage by other surfaces. However, some assumptions can be made to facilitate its calculation. The author has calculated the configuration factor for the silicon rods assuming that they are infinitely long. In the following paragraph the method used is presented, it is called Hottel’s crossed-string method.

4.3.2 Hottel’s crossed-string method

This is a geometric method for evaluating the configuration factors. This method assumes that all surfaces extend infinitely along one coordinate. When considering the silicon rods, the assumption is that the rods are infinitely long. When the aspect ratio, the ratio of length to radius, of the silicon rod is high enough, this assumption can be valid. If the

75 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.7: Hottel’s crossed-string method for evaluating geometric conﬁguration factors. aspect ratio is not so high, this assumption can provide less accurate but also valuable conﬁguration factors.

Consider the evaluation of the configuration factor from finite area A1 to finite area A2 when some blockage of radiant transfer occurs because of surfaces A3 and A4. The cross section of this typical configuration is presented in figure 4.7. This situation is analogous to what happens in a CVD reactor: a rod is radiating toward the wall and its radiation is blocked by other rods.

In ﬁgure 4.7, area A1 is concave (it may not be) but it can be seen that every string: agf, abc, fed, ad and fc, is either planar or convex. Applying Hottel’s crossed-string method [Siegel and Howell, 1972] results in

Acf + Aad − Aabc − Adef F1→2 = (4.15) 2 · A1

Because all surfaces extend infinitely along one coordinate, in a two-dimensional geometry, the configuration factor is one-half the total quantity formed by the sum of the lengths of the crossed strings connecting the outer edges of A1 and A2 minus the sum of the lengths of the uncrossed strings, divided by the length of area A1. The silicon rods in CVD reactors are not infinite, so we should estimate the error when the configuration factors are calculated using this method. For a rather simple configuration, two cylinders of equal radius and equal finite length, the geometric configuration factor has been evaluated using the infinitely long approach, presented in this section, and an exact approach presented by Jull [1982]. The comparison, presented below, shows the range of rod aspect ratios where the infinite length approximation can be applied.

76 4.3. Radiation exchange between the polysilicon rods and the reactor wall

Figure 4.8: Conﬁguration factor between two cylinders of equal radius.

Evaluation of the error when using Hottel’s crossed-string method

First, the configuration factor is evaluated considering that the rod length is infinite. In figure 4.8 two infinitely long cylindrical surfaces of equal radius R are separated by a minimum distance D. The length of crossed string abcde is denoted as Lc and the length of uncrossed string ef as Lu. The derivation of F1→2 yields

2 · Lc − 2 · Lu 2 · Lc − 2 · Lu F1→2 = = (4.16) 2 · L1 4 · πR

Lu = D + 2R. Lc is twice the length of cde, Lc = 2 · (Lcd + Lde). The segments Lcd and Lde are

" #1/2 D 2 L = + R − R2 (4.17) cd 2 R L = R · ϕ = R · sin−1 (4.18) de D/2 + R

Finally, deﬁning X = 1 + D/2R,

1 1/2 1 F = · X2 − 1 + sin−1 − X (4.19) 1→2 π X

The next step is to calculate the configuration factor considering that the rod has finite length l. The reader should consult Jull [1982] for the mathematical formula that governs the configuration factor in this case. The system considered for the comparison consists of two cylinders of equal radius, whose centres are separated by four times their radius, and different aspect ratios ranging from 1 to 100. The configuration factors calculated are depicted in figure 4.9(a) and the

77 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

(a)

(b)

Figure 4.9: Comparison of the exact and approximated method for evaluating the geometric configuration factor. The distance between cylinder centres is four times their radius. (a) Geometric configuration factors for infinitely long cylinders and finite length cylinders. (b) Difference in the calculated values of the geometric configuration factor, relative to the value for finite length cylinders. F ∞ is for the configuration factor calculated by Hottel’s method and F l is the configuration factor calculated by reference Jull [1982].

78 4.3. Radiation exchange between the polysilicon rods and the reactor wall

differences between the configuration factors calculated by both methods are presented in figure 4.9(b). The range of rod aspect ratios where Hottel’s crossed-string method can be applied is deduced from figure 4.9(b). For aspect ratios greater than 20, the variation of the configuration factor is below 8%. The rod length is 2 metres. At the beginning of the deposition process, the rod radius is around 0.5 cm, corresponding to an aspect ratio of 400. At the end of the process, the rod radius can reach around 8 cm, corresponding to an aspect ratio of 25. The differences in the evaluation of the configuration factors are then around 6% at the end of the process and around 2% at the beginning. These variations in the evaluation of the configuration factors are acceptable for the calculation of the radiative transfer between the silicon rods and the reactor wall. Moreover, the evaluation of finite length configuration factors with radiant transfer blockage is very complicated, and requires computational simulation. Therefore, the first approach in this work is to analyse the radiation within the reactor vessel taking into account the configuration factors obtained by Hottel’s method. As demonstrated, the error in the evaluation of the configuration factors is lower than 6%.

4.3.3 Governing equations

The governing equations for the thermal radiation transfer within the reactor vessel are presented in this section. First, the system consisting of polysilicon rods and a reactor wall is considered. Later, the governing equations for the system considering polysilicon rods, thermal shields and a reactor wall are derived.

Polysilicon rods and reactor wall

The system considered has n surfaces: the reactor wall, at a cold and known temperature, and n-1 silicon rods, at a hot and known temperature. For the ith surface area Ai the following relation is fulﬁlled

Ji = Ei + ρi · Gi = i · Ebi + (1 − i) · Gi (4.20) where ρi = 1 − αi = 1 − i for opaque grey surfaces. ρi, αi, and i are the reﬂectivity, 4 absortivity and emissivity of the ith surface respectively. As mentioned before, Ebi = σ·Ti .

From this relation the irradiance, Gi, can be derived

1 Gi = · (Ji − i · Ebi ) (4.21) 1 − i

The net thermal radiation heat exchanged by the ith surface is the balance between

79 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

the outgoing energy ﬂux: the radiosity, and the incoming energy ﬂux: the irradiance,

qi = Ai · (Ji − Gi) (4.22)

Substituting equation (4.21) into equation (4.22),

i qi = Ai · · (Ebi − Ji) (4.23) 1 − i The irradiance received by the ith surface is radiated by the other surfaces in the system. The irradiance integrated along the whole surface (Ai · Gi) can therefore be expressed as the sum of the radiosities (Aj ·Jj) of all surfaces, weighted by the conﬁguration factors. Hence, from equation (4.22),

n n X X qi = Ai · Ji − Aj · Fj→i · Jj = Ai · Ji − Ai · Fi→j · Jj (4.24) j=1 j=1 where the reciprocity relation of the conﬁguration factors has been used. The system of equations is obtained by combining the equations (4.23) and (4.24) and rearranging the resultant expression,

1 n A · · J − X A · F · J = A · i · E i = 1, . . . , n (4.25) i 1 − i i i→j j i 1 − bi i j=1 i

The unknowns of the problem are Ji for i = 1, . . . , n. The values for Ebi are known since the temperature of the rods and the wall is constant and known. The solution for this system of equations provides the values for Ji. These values, when substituted in equation (4.23) lead to the net radiation heat exchanged by each surface, qi. Summarizing, the system of equations is

[A] · [J] = [B] where

A(i, j) = −Ai · Fi→j i 6= j i, j = 1, . . . , n 1 A(i, i) = Ai · − Ai · Fi→i i = 1, . . . , n 1 − i i B(i) = Ai · · Ebi i = 1, . . . , n 1 − i

Polysilicon rods, thermal shields and reactor wall

In this case, the system considered is diﬀerent. It has n surfaces: the reactor wall, at a cold and known temperature, m-1 silicon rods, at a hot and known temperature and (n − m) thermal shields at unknown temperatures. It is assumed that the shields transfer heat only by radiation; conduction and convection mechanisms are neglected. That means, for

80 4.3. Radiation exchange between the polysilicon rods and the reactor wall

instance, that even though the thermal shields stand on the chamber baseplate they are not transferring heat by conduction to this baseplate. The system is depicted in ﬁgure 4.10. During the derivation of the governing equations, the following subscripts will denote the components of the system:

• 1 . . . m − 1: polysilicon rods,

• m . . . n − 1: thermal shields,

• n: reactor wall.

Figure 4.10: The polysilicon rods, at a known and constant temperature are surrounded by thermal shields, whose temperatures depend on the radiation transfer in the system. The reactor wall encloses the system at a known and constant temperature.

The thermal shields are cylinders surrounding the polysilicon rods, between them and the reactor wall. They are made of a material with high reﬂectivity. The objective is to reduce the thermal loss, but a secondary eﬀect is that the shields can reach high temperatures. If the temperature is high, some polysilicon can deposit on the shields. It is therefore important to evaluate the power loss reduction achieved with these shields, and the temperature that these devices reach. Analyses for evaluating both are presented below. The derivation begins with the heat balance for every rod, that is, for every component between i = 1 . . . m − 1. The heat balance equation is the same as that for the previous

81 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

case: equation (4.25). The expression is repeated here for clarity, 1 m A · · J − X A · F · J = A · i · E i = 1, . . . , m − 1 (4.26) i 1 − i i i→j j i 1 − bi i j=1 i 4 where the value of Ebi = σTi is known because the temperature of the polysilicon rods,

Ti, is constant and known. It should be noted that the radiosities of elements m + 1 to n are not included because the rods do not see these elements, and vice versa. For the ﬁrst thermal shield (element m), the same equation is used. But in this case the temperature of the shield is unknown. Therefore, when rearranging the expression, the following equation is found 1 m A · · J − X A · F · J − A · m · σ · T 4 = 0 (4.27) m 1 − m m m→j j m 1 − m m j=1 m it should be noted that Jm is the radiosity of the inner surface of element m, that is, the surface of the thermal shield facing the polysilicon rods. The heat balance for every thermal shield should be derived. Nevertheless, if steady state is considered, the same thermal heat q passes through the entire series of shields. Note that the shields are not transferring heat either by convection or conduction. This radiant heat transfer, q, between two thermal shields, considered as two inﬁnitely long cylinders [Siegel and Howell, 1972] can be expressed as follows

4 4 q · (1/(Ai · i) + 1/Ai+1(1/i+1 − 1)) = σ Ti+1 − Ti i = m, . . . , n − 1 (4.28)

After adding the equation (4.28) for every value of i, dividing by the resulting factor multiplying q on the left-hand side, and rearranging, the following expression is obtained σ T 4 − T 4 σ T 4 − T 4 q = n m = n m (4.29) n−1 X γ 1/(Am · s) + 1/An · (1/n − 1) + (2/s − 1) · 1/Ai i=m+1 Where γ stands for the large denominator. It is considered that all the thermal shields have the same emissivity, s, and the wall emissivity is n. This thermal heat, q, cannot be evaluated directly because the value of Tm, the temperature of the ﬁrst thermal shield, is unknown. The heat exchanged by the ﬁrst thermal shield is q. It can also be evaluated using equation (4.23),

s 4 qm = Am · · σTm − Jm (4.30) 1 − s The last equation for solving the system is obtained by combining equations (4.30) and (4.29) and rearranging the resultant expression s 1 4 s Ebn Am · + · σTm − Am · · Jm = (4.31) 1 − s γ 1 − s γ

82 4.3. Radiation exchange between the polysilicon rods and the reactor wall

The system of equations consists of equations (4.26), (4.27), and (4.31), where the unknowns are: Ji for i = 1, . . . , m and Tm. The values of Tj for j = m + 1, . . . , n − 1 are also unknowns, and are not directly obtained from these equations. To evaluate their values, equations (4.28) and (4.29) are applied after solving the system. Summarizing, the system of equations is

[A] · [X] = [B] where

A(i, j) = −Ai · Fi→j i 6= j i, j = 1, . . . , m 1 A(i, i) = Ai · − Ai · Fi→i i = 1, . . . , m 1 − i A(i, m + 1) = 0 i = 1, . . . , m − 1 s A(m, m + 1) = −An · · σ 1 − s A(m + 1, j) = 0 j = 1, . . . , m − 1 s A(m + 1, m) = −An · 1 − s s 1 A(m + 1, m + 1) = Am · + · σ 1 − s γ

X(i) = Ji i = 1, . . . , m 4 X(m + 1) = Tm

i B(i) = Ai · · Ebi i = 1, . . . , m − 1 1 − i B(m) = 0 E B(m + 1) = bn γ

4.3.4 Properties of the materials

The CVD reactor system is presented and the equations that allow evaluation of the radiation heat balance between the different components derived. However, solving the equations requires that the properties of the different materials involved be known. The emissivities of the rods, the reactor wall and the thermal shields have to be defined. First, the silicon rod emissivity is analysed. The emissivity of silicon depends on the temperature and the doping concentration, and varies with the wavelength of the emitted radiation. In figure 4.11 the spectral emissivity of n-type silicon at doping concentration of 2.94 · 1014 cm−3 is shown, extracted from [Ravindra et al., 2001]. The analysis carried out in the previous section does not take into account the spectral distribution of the emissive power. The value of the emissivity used should be valid for

83 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.11: Spectral emissivity of n-type silicon, doping concentration 2.94 · 1014 cm−3. From reference [Ravindra et al., 2001]. all wavelengths. If a spectral distribution is considered, the directly emitted energy flux, instead of being defined as E(T ) = σT 4, should be defined using Planck’s law:

2πC1 E(λ0,T ) = (λ0,T ) · 5 (4.32) λ0 (exp(C2/λ0T ) − 1) being C1 and C2 constants that can be consulted in [Siegel and Howell, 1972].

Only when the emissivity, (λ0,T ), is wavelength invariant does the integration of equation (4.32) yield E(T ) = σT 4. As seen in ﬁgure 4.11, the value of emissivity is not constant below 873 K, so the analysis leads to inaccurate solutions when the rods are below this temperature. However, during deposition, the rods have a temperature around 1300 K. At such a temperature, the emissivity can be roughly considered constant for every wavelength. Therefore, during the analysis carried out in this chapter the emissivity of the silicon rods is considered to be = 0.7.

The thermal shields can be made of different materials, among others: alumina (Al2O3), aluminium nitride (AlN), nickel, tantalum or gold. These materials have relatively low emissivity, and therefore high reflectivity. Using these materials, the radiant heat that the shields send back to the rods is high. The introduction of nickel, tantalum or gold can be dangerous for the polysilicon, since some contamination can take place. Alumina is a stable component, but the introduction of oxygen in the reactor vessel must be avoided. Aluminium nitride (AlN) is a good candidate since the emissivity is relatively high, it is stable and no impurities are introduced. In figure 4.12 the reflectivity (ρ = 1 − ) of alumina and aluminium nitride are presented. These measurements were carried out by Dr. Ignacio Tob´ıas,in the framework of the Ph.D. thesis of Rodr´ıguezSan Segundo [2007].

84 4.3. Radiation exchange between the polysilicon rods and the reactor wall

Figure 4.12: Spectral reﬂectivity of alumina and aluminium nitride. Measured by Dr. Ignacio Tob´ıas during the Ph.D. thesis of Rodr´ıguezSan Segundo [2007].

For the calculations carried out in further sections, aluminium nitride is chosen as the thermal shield. The emissivity estimated for this material is = 0.45, combining the information shown in ﬁgure 4.12 for all the wavelengths presented. This emissivity is higher that the emissivity observed for the alumina ( = 0.30). Therefore, the results will be more conservative.

The reactor wall can be made of stainless steel, hastelloy R or inconel R . These are different alloys, typically used in the industry, that provide good resistance to high temperatures and corrosive gases. On the one hand, inconel is a good candidate because it is better than stainless steel, regarding the resistance to corrosive gases, and it is cheaper than hastelloy. The hemispherical emissivity of inconel 718 is analysed in [Greene et al., 2000], and is shown in figure 4.13. As seen in this figure, there is a strong dependence on temperature. The temperature of the water-cooled wall is around 100 ◦C at the inner surface. At this temperature the emissivity is around 0.3, but if some deposition takes place or the temperature increases this emissivity can be higher. On the other hand, the stainless steel (for instance 316) is a well know material that it has an emissivity of 0.7. If this material is used, making the reactor vessel cheaper, the wall can be polished to decrease the emissivity. For that reason, if inconel or stainless steel is used, a sensible value for the emissivity of the wall is = 0.5.

85 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.13: Total hemispherical reﬂectivity of inconel 718. From reference Greene et al. [2000].

Table 4.2: General parameters for the calculation of the radiation exchange in the CVD reactor.

Emissivity of the rods 0.7 Temperature of the rods 1150 ◦C Emissivity of the shields 0.45 Temperature of the wall 100 ◦C Emissivity of the wall 0.5 Control space diameter 25 cm Rod length 2 m

4.4 Reactor conﬁgurations

In this section some reactor configurations are analysed in detail, with and without thermal shields. The governing equations are solved and the solutions presented. The first configuration considered is 36 rods arranged in three rings. This configuration has a typical capacity of 200 t/year of polysilicon. The next configuration studied is 48 rods arranged in three concentric rings, whose capacity is around 300 t/year. The last configuration analysed is 60 rods in four concentric rings, with a capacity of around 400 t/year.

There are some general parameters, used in the calculations of every reactor conﬁgu- ration, that are summarized in table 4.2. The wall diameter for every conﬁguration is 85 cm larger than the outer concentric ring. That means that the wall is placed 30 cm from the end of the control spaces in the outer ring.

86 4.4. Reactor conﬁgurations

4.4.1 36 rods arranged in three rings

The conﬁguration studied is presented in ﬁgure 4.14. The rods are numbered from 1 to 36. In the diagram only rods 1, 7 and 19 are labelled, the rest are labelled counter-clockwise.

Figure 4.14: CVD reactor with 36 rods arranged in 3 rings, the control space diameter is 25 cm. Typical capacity: 200 t/year. Inner ring diameter: 50 cm, middle ring diameter: 96.5 cm, outer ring diameter: 143 cm, wall diameter: 229 cm. The rods are labelled counter-clockwise.

For this configuration the radiation of rods 1, 7 and 19 is analysed in detail. The geometric configuration factors have been calculated using Hottel’s crossed-string method, presented in the previous section. The configuration factor from rod 1 to the reactor wall is presented in figure 4.15. To evaluate the configuration factor from any rod to the wall it should be noted that the sum of all configuration factors from a certain rod to the rest of the elements of the system must be 1.

It can be seen that when the diameter of the rod is small, for instance drod = 0.1·d = 2.5 cm, the geometric configuration factor is F1→wall = 0.76, that is, 76% the of energy radiated by rod 1 is reaching the wall. When the rods thicken, the radiation from rod 1 has more difficulty in reaching the wall. For instance, if the diameter is large, drod = 0.8·d = 20 cm the configuration factor is F1→wall = 0.01, that means that only 1% of the energy radiated by rod 1 reaches the wall. The heat balance in the system is carried out considering first the polysilicon rods and

87 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.15: Geometric conﬁguration factor from rod 1 to the wall in a 36 rod CVD reactor. drod is the silicon rod diameter and the control space diameter is d = 25 cm. the wall, with the data presented in table 4.2 and the equations presented in section 4.3.3; and second, considering the polysilicon rods, the thermal shields and the wall.

Polysilicon rods and reactor wall

The heat balance provides the results presented in figures 4.16 and 4.17. The power radiated by the silicon rods and absorbed by the wall for different rod diameters is shown in figure 4.16. The power given by rods 1, 7 and 19 to the wall are shown in figure 4.17. The power given by the rest of the rods to the wall can be inferred from this data since every rod in the reactor behaves identically to one of these rods.

The total radiative power absorbed by the reactor wall increases at the beginning of the process almost linearly with the rod diameter, as seen in ﬁgure 4.16. The thin rods do not block the radiant energy coming from other rods. When the rods thicken, blockage between silicon rods takes place and therefore the power increases more slowly. At diameters greater than 6 cm, the power absorbed by the wall is not increasing linearly with the rod diameter.

This power evolution can also be seen in ﬁgure 4.17 where the power emitted by rods 1, and 7 have a maximums at radii of around 8 cm, and then decrease because the rest of the rods are blocking their radiation. At the end of the process, these rods are emitting less than at the beginning, because they are surrounded by other rods at their temperature, and they do not see the wall.

88 4.4. Reactor conﬁgurations

Figure 4.16: Power radiated by the silicon rods and absorbed by the reactor wall in the 36 rod CVD reactor presented in ﬁgure 4.14, for diﬀerent rod diameters.

Figure 4.17: Power radiated by one rod in each ring (inner, middle and outer rings) to the wall in the 36 rod CVD reactor presented in ﬁgure 4.14.

Polysilicon rods, thermal shields and reactor wall

The system studied is that shown in figure 4.14, but with one thermal shield located between the silicon rods and the reactor wall. The thermal shield is a cylinder placed between the wall and the outer ring and has a diameter of 199 cm. The power radiated by the silicon rods that is absorbed by the reactor wall is shown in figure 4.18. It can be seen that the power absorbed by the wall is more than a half of the power absorbed without a thermal shield. The temperature of the shield is presented in figure 4.19. It can be seen that at the

89 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.18: Power radiated by the silicon rods and absorbed by the reactor wall in the 36 rod CVD reactor with one thermal shield, for diﬀerent rod diameters.

Figure 4.19: Temperature of the thermal shield for diﬀerent rod diameters in the 36 rod CVD reactor. beginning of the process, the temperature is very high, around 830 ◦C, and at the end of the process this temperature increases even more, reaching 940 ◦C. It is necessary to evaluate whether at such temperatures the silicon deposits on the wall. Some rough estimates can be made using the silicon deposition constants presented in expressions (3.39)-(3.40): the rate of polysilicon deposition onto the wall is around 6.5% of the deposition rate at the rods, considering that the silicon rod temperature is 1150 ◦C and the shield temperature is around 930 ◦C. The surface of the rods, where the deposition takes place, at the beginning of the process (a diameter of 1 cm) is 2.2 m2 and at the end of the process (roughly a diameter of 15 cm) is 34 m2; therefore, an average of 18 m3 can be considered. The

90 4.4. Reactor conﬁgurations

surface of the thermal shield, where deposition may take place, is 12.5 m2. Combining the deposition rate diﬀerence and the diﬀerence in the surfaces of the rods (on average) and shields, it can be deduced that the silicon deposited in the shield is around 4.5% of the silicon deposited in the rods. If the silicon deposited on the rods is around 3 t, on the thermal shield the material deposited is 134 kg, which means a thickness of 4.6 mm of silicon grown over the thermal shield.

4.4.2 48 rods arranged in three rings

The conﬁguration studied is presented in ﬁgure 4.20. The rods are numbered from 1 to 48. In the drawing only rods 1, 11 and 27 are labelled, the rest are labelled counter-clockwise.

Figure 4.20: CVD reactor with 48 rods arranged in 3 rings, the control space diameter is 25 cm. Typical capacity: 300 t/year. Inner ring diameter: 81 cm, middle ring diameter: 129 cm, outer ring diameter: 175 cm, wall diameter: 260 cm. The rods are labelled counter-clockwise.

For this configuration the radiation of rods 1, 11 and 27 is analysed in detail. The configuration factor from rod 1 to the reactor wall is presented in figure 4.21. It is very similar to that presented in figure 4.15, corresponding to the 36 rod reactor. This makes sense since both configurations have three rings and the blockage to the radiation emitted by the inner ring is similar.

91 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.21: Geometric conﬁguration factor from rod 1 to the wall in a 48 rod CVD reactor. drod is the silicon rod diameter and the control space diameter is d = 25 cm.

Polysilicon rods and reactor wall

The heat balance results are presented in figures 4.22 and 4.23. The power absorbed by the wall, seen in figure 4.22, is slightly higher than the power absorbed by the 36 rod reactor because the wall surface is greater and there are more rods radiating. Similar reasoning as presented for the 36 rod reactor can be applied to explain the curves presented in figure 4.23, where the radiation of the inner and middle ring rods approaches zero at the end of the process.

Figure 4.22: Power radiated by the silicon rods and absorbed by the reactor wall in the 48 rod CVD reactor presented in ﬁgure 4.20, for diﬀerent rod diameters.

92 4.4. Reactor conﬁgurations

Figure 4.23: Power radiated by the characteristic rods of every ring (inner, middle and outer) to the wall in the 48 rod CVD reactor presented in ﬁgure 4.20.

Polysilicon rods, thermal shields and reactor wall

The system studied is that shown in ﬁgure 4.20, but with one thermal shield located between the silicon rods and the reactor wall. The thermal shield is a cylinder placed between the wall and the outer ring and has a diameter of 230 cm. The power radiated by the silicon rods that is absorbed by the reactor wall is shown in ﬁgure 4.24. It can be seen that the power absorbed by the wall is around one third of the power absorbed without a thermal shield.

Figure 4.24: Power radiated by the silicon rods and absorbed by the reactor wall in the 48 rod CVD reactor with one thermal shield, for diﬀerent rod diameters.

The temperature of the shield is presented in ﬁgure 4.25. Both the power absorbed by

93 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.25: Temperature of the thermal shield for diﬀerent rod diameters in the 48 rod CVD reactor. the wall and the temperature of the shield are very similar to the 36 rod reactor. Again, it is necessary to evaluate the amount of silicon deposited on the wall. Following similar reasoning as before, if the silicon deposited in the rods is around 4 t, in the thermal shield the material deposited is 180 kg, which means a thickness of 5.4 mm of silicon grown over the thermal shield.

4.4.3 60 rods arranged in four rings

The configuration studied is presented in figure 4.26. The rods are numbered from 1 to 60. In the diagram only rods 1, 7 ,19 and 37 are labelled, the rest are labelled counter- clockwise. For this configuration, the radiation of rods 1, 7 ,19 and 37 is analysed in detail. The configuration factor from rod number 1 to the reactor wall is presented in figure 4.27. This geometric configuration factor is lower than the factors presented for the 36 and 48 rod reactors because with four rings the radiation from rod 1, placed in the inner ring, has more difficulty in reaching the wall.

Polysilicon rods and reactor wall

The heat balance results are presented in figures 4.28 and 4.29. The power absorbed by the wall, seen in figure 4.28, is higher than the power absorbed by the 36 and 48 rod reactors because, again, the wall surface is greater and there are more rods radiating. Similar reasoning as presented previousely can be applied to explain the curves presented in figure

94 4.4. Reactor conﬁgurations

Figure 4.26: CVD reactor with 60 rods arranged in 4 rings, the control space diameter is 25 cm. Typical capacity: 400 t/year. Inner ring diameter: 50 cm, second ring diameter: 96.5 cm, third ring diameter: 143 cm, outer ring diameter: 191.5 cm, wall diameter: 276.5 cm. The rods are labelled counter-clockwise.

Figure 4.27: Geometric conﬁguration factor from rod 1 to the wall in a 60 rod CVD reactor. drod is the silicon rod diameter and the control space diameter is d = 25 cm.

4.29. The radiation reching the wall from the inner, second and third rings approaches zero at the end of the process because of blockage from the outer ring.

95 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.28: Power radiated by the silicon rods and absorbed by the reactor wall in the 60 rod CVD reactor presented in ﬁgure 4.26, for diﬀerent rod diameters.

Figure 4.29: Power radiated by the characteristic rods of every ring (inner, second, third and outer) to the wall in the 60 rod CVD reactor presented in ﬁgure 4.26.

Polysilicon rods, thermal shields and reactor wall

The system studied is that shown in figure 4.26, but with one thermal shield located between the silicon rods and the reactor wall. The thermal shield is, again, a cylinder placed between the wall and the outer ring, with diameter of 246.5 cm. In figure 4.30 the power radiated by the silicon rods that it is absorbed by the reactor wall is shown. As in the 48 rod configuration, it can be seen that the power absorbed by the wall is around one third of the power absorbed without a thermal shield. The temperature of the shield is presented in figure 4.31. Both the power absorbed by

96 4.4. Reactor conﬁgurations

Figure 4.30: Power radiated by the silicon rods and absorbed by the reactor wall in the 60 rod CVD reactor with one thermal shield, for diﬀerent rod diameters.

Figure 4.31: Temperature of the thermal shield for diﬀerent rod diameters in the 60 rod CVD reactor.

the wall and the temperature of the shield are slightly greater than the values obtained for the other conﬁgurations considered.

The evaluation of the amount of silicon deposited on the wall is carried out as before. In this case, the estimated layer of silicon grown over the shield has a thickness of 5.7 mm.

97 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

4.5 Discussion

4.5.1 Inﬂuence of the reactor conﬁgurations

We have seen in figures 4.16, 4.22 and 4.28 the total power absorbed by the reactor wall for the different CVD reactor configurations. However, in order to compare the different rod arrangement, the average power per rod is more useful. For the three configurations considered, the average power emitted per rod is depicted in figure 4.32. It can be seen that the power required to keep a rod at the deposition temperature in the 48 rod reactor is 10% lower than the power required in the 36 rod reactor, and the power required in the 60 rod reactor is 20% lower.

Figure 4.32: Average power emitted per rod and absorbed by the reactor wall for diﬀerent reactor conﬁg- urations.

The power absorbed by the wall is an important parameter to estimate the necessary power supply and to evaluate the power loss in a CVD reactor. However, the energy consumed per kilogram of polysilicon produced is more important. The analysis carried out allows estimation of the energy radiated for different reactors. Since the energy depends on the polysilicon growth rate, the energy radiated is presented in figure 4.33 for different average growth rates throughout the deposition process and for the three reactor configurations considered. According to the model, the variation of the energy radiated when enlarging the reactor size from 36 to 48 rods is 10% for all growth rates and the variation when enlarging from 36 to 60 rods is 20%. Considering an average growth rate of 7 µm·min−1, the energy radiated for the three configurations are presented in table 4.3. The growth rate of 7 µm·min−1 is a conservative

98 4.5. Discussion

Figure 4.33: Dependence of the energy radiated per kilogram of polysilicon produced on the average growth rate throughout the deposition process, for the three reactor conﬁgurations considered. value, as presented in previous chapter, and therefore the energies presented in this table may be lower.

Table 4.3: Energy radiated per kilogram of polysilicon produced, in kWh·kg−1, for the diﬀerent CVD reactors considered when the average growth rate is 7 µm·min−1. The process ﬁnishes when the rod diameter is 15 cm.

36 Rods / 3 rings 48 Rods / 3 rings 60 Rods / 4 rings E (kWh·kg−1) 56 50 45

Some rough estimations can be made considering the economical savings due to the energy reduction when enlarging from 36 rods to 60 rods. Consider a 5.000 t/year factory of polysilicon and an energy price of 8 ce/kWh. Enlarging the reactors from 36 rods to 60 rods would save 11 kWh·kg−1, and therefore the annual savings would be 4.4 million e per year.

4.5.2 Inﬂuence of the thermal shields

The advantage of using thermal shields has already been presented: the power absorbed by the wall reduces by two thirds, as seen in ﬁgure 4.34(a). The introduction of more thermal shields is presented in ﬁgure 4.34(b). It can be seen that there is no noteworthy reduction in the power loss when introducing two shields instead of one, and that the behaviour of the system with two shields and three shields is equal, since the respective lines on the

99 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

graph overlap. Also, when more than one shield is considered, the temperature of the inner shield does not change remarkably as seen in ﬁgure 4.35.

(a)

(b)

Figure 4.34: Power absorbed by the wall for diﬀerent arrangements of thermal shields in a 36 rods reactor. Diﬀerent rod diameters are considered. (a) Power absorbed by the wall without thermal shields and with one thermal shield in a 36 rods reactor. (b) Power absorbed by the wall with one, two and three thermal shields in a 36 rod reactor.

The energy radiated by the rods and absorbed by the wall is drastically reduced when one thermal shield is used instead of none, as seen in ﬁgure 4.36. The energy radiated is halved when a thermal shield is used. The emissivity of the thermal shields is an important parameter to analyse. The reduction of the shield emissivity reduces the energy absorbed by the reactor wall because

100 4.5. Discussion

(a)

(b)

Figure 4.35: Temperatures of the thermal shields for different arrangements of thermal shields in a 36 rod reactor. (a) One shield. (b) Two shields. more energy radiated by the rods is sent back to them, as seen in figure 4.37. The energy absorbed by the wall is reduced remarkably when the emissivity decreases. If the shield emissivity were as low as = 0.3 radiated the energy would be as low as 13 kWh·kg−1 in a 36 rods CVD reactor with one thermal shield. It is also important to know if there is a noteworthy variation of the temperature of the thermal shield when reducing the shield emissivity, since a lower temperature would lead to a lower amount of silicon deposited on this device. The temperature of the thermal shield and the amount of silicon deposited in the shield is depicted in figure 4.38. The change of the temperature of the shield with the shield emissivity is negligible and the

101 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

Figure 4.36: Dependence of the energy radiated per kilogram of polysilicon produced on the average growth rate throughout the deposition process, considering the 36 rod reactor without thermal shields and with one thermal shield.

Figure 4.37: Dependence of the energy radiated per kilogram of polysilicon produced on the thermal shield emissivity. Only one shield considered in a 36 rod reactor. The average polysilicon growth rate is 7 µm·min−1. average temperature is always around 930 ◦C. The amount of silicon deposited in the shield is estimated taking this temperature into account. It can be seen that the layer of silicon grown over the shield is more or less constant and cannot be drastically reduced by modifying the shield emissivity. Again some rough estimations can be made regarding the savings of introducing thermal shields. Consider a 5000 t/year plant of polysilicon, with 36 rod CVD reactors. If a thermal shield is introduced in every reactor, with an emissivity of 0.45, the savings would

102 4.5. Discussion

(a)

(b)

Figure 4.38: Shield emissivity dependence of the temperature of the thermal shield and the layer thickness of polysilicon deposited on it. Only one shield considered in a 36 rod reactor. (a) Dependence of the temperature of the thermal shield on the thermal shield emissivity. (b) Estimation of the polysilicon growth over the thermal shield. be, according to ﬁgure 4.36 around 20 kWh·kg−1. This would lead to annual savings of 8 million e per year.

4.5.3 Inﬂuence of the wall properties

The wall emissivity has a strong inﬂuence on the radiative power loss. When the emissivity increases, the reﬂectivity of the wall decreases and the power absorbed increases, as seen

103 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

in ﬁgure 4.39. It is shown that if the emissivity of the wall reaches = 0.7 the radiated power at the end of the process is around 400 kW higher than for = 0.5.

Figure 4.39: Power radiated by the silicon rods and absorbed by the reactor wall in a 36 rod CVD reactor for diﬀerent wall emissivities.

Figure 4.40: Energy radiated per kilogram of polysilicon produced in a 36 rod CVD reactor for diﬀerent values of the wall emissivity. The average polysilicon growth rate is 7 µm·min−1.

The energy radiated has a noteworthy variation for different values of the wall emissivity. The energy radiated per kilogram of polysilicon is calculated, considering a growth rate of 7 µm·min−1, and depicted in figure 4.40 for different values of the wall emissivity. The energy radiated if the wall emissivity is 0.9 (very bad material) is more than double the energy radiated if the wall emissivity is 0.3 (very good material). Considering a 5000 t/year polysilicon plant with 36 rod CVD reactors. If the wall

104 4.6. Conclusions

emissivity is improved, from 0.5 to 0.3, the savings would be around 17 kWh·kg−1. This means annual savings of 6.8 million e per year.

4.6 Conclusions

In this chapter the governing equations for the radiation exchange within the CVD reactor have been presented. Three reactor configurations are presented in detail: 36 rods arranged in 3 concentric rings, 48 rods arranged in three concentric rings and 60 rods arranged in four rings. The power radiated by a characteristic rod in each ring is calculated. It is shown that the power emitted by the rods placed in the inner rings that reaches the outer wall reduces strongly as the rods thicken. The effect of enlarging the reactor capacity is analysed. The energy radiated by the rods is reduced by 20% when comparing the 60 rod CVD reactor to the 36 rod CVD reactor. This is a reduction of around 11 kWh per kg of polysilicon produced. Translated to cost savings, considering an energy cost of 8 ce/kg, the cost reduction is around 0.88 e per kg of polysilicon produced. In a 5000 t/year polysilicon plant the savings would be up to 4.4 million e/year. The impact of thermal shields has also been analysed. This option has the greatest potential for cost savings, since the energy savings are around 20 kWh per kg of polysilicon produced. Nevertheless, the temperature that these devices reach allows polysilicon to be deposited on them. It is estimated that a layer of 4 mm would be grown on the shields. The energy savings would mean a cost reduction of around 1.6 e per kg of polysilicon produced. In a 5000 t/year plant the savings would be 8 million e/year. A careful economical assessment is required to decide if this is a real cost reduction, because the thermal shields are expensive devices and they should be removed from the reactor when the silicon deposition is high. After 3-10 runs the shields should be cleaned or recycled. The degree of influence of the wall emissivity lies between the other two factors already presented. If the wall emissivity is improved, by selecting better materials or by surface treatment, the energy savings are around 17 kWh per kg of polysilicon produced. Which would be a cost saving of around 1.36 e per kg of polysilicon produced. In high production plants the savings would be around 6.8 million e/year. The total savings in the polysilicon production, summing all contributions, can be up to 3.84 e per kg of polysilicon produced.

105 Chapter 4. Radiative energy loss in the polysilicon CVD reactor

106 Chapter 5

Electric heating of the polysilicon rods in the CVD reactor

5.1 Introduction

The power losses in the CVD reactor have been studied in the previous chapters, analysing the two main components: power loss by convection and power loss by radiation. The total power loss is supplied to the system by means of an electric current flowing through the silicon rods that heats them up to the deposition temperature, and maintains them at this temperature while the rods thicken. Some proposals have already been presented aiming at reducing energy consumption. First, establishing the optimum deposition conditions, and operating as close to them as possible, looking for a trade-off between the power loss and the mass production rate in the deposition process. Second, to design the reactor focusing on diminishing the power loss by radiation: enlarging the reactor capacities, introducing thermal shields or even enhancing the optical properties of the reactor wall. In this chapter, a new proposal for diminishing the energy consumption is presented: increasing the maximum rod diameter. The deposition process uses energy more efficiently when the rod diameter is high. This has two causes: first, part of the radiation is blocked when the diameter is high, as presented in the previous chapter; and second, the net deposition surface increases tremendously. When the rod diameter is above 10 cm, the power loss rises slowly while the mass production rate increases notably, yielding low energy consumption per kg of silicon produced. The comparison of the process at the beginning (rod diameter: 1 cm) and at the end (for instance, rod diameter: 14 cm) shows that the mass production rate increases by 1400% and the energy consumption is reduced fivefold.

107 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

Thus, the increase in the rod diameter throughout process reduces the energy consumption per kg of silicon produced, resulting in a more energy eﬃcient process. The question is: what is the limitation for the maximum rod diameter? The limitation is found in the risk of melting the rod core. This undesirable situation must be avoided because it is dangerous for the rod itself, for the production and for the reactor.

The electric current flowing through the rod generates a non-homogeneous temperature profile within the rod, which can melt it. This is mainly because: (a) the inner part of the carrier rod is thermally insulated by the outer region or ”skin”, becoming progressively hotter relative to it; and (b) the silicon electric conductivity increases with temperature, so when the centre of the rod becomes hotter the conductivity increases in that region. As a result, even more current flows and more heat is created.

Two ways are proposed in this chapter to increase the maximum rod diameter. One is based on reducing the power lost by the rods by enhancing the wall optical properties. The other is based on utilisation of high frequency current sources to heat the rods.

The former makes the temperature profile more homogeneous because the cooling of the rods is lower, as will be explained later. The latter reduces the non-homogeneous temperature profile because high frequency current produces the well-known skin effect. This effect is observed in a conductor material at low frequencies (∼ 50 Hz): alternating current flowing through a conductor produces the migration of most of the current density to the outer region. In a semiconductor the skin effect does not work exactly as in a conductor because the electric conductivity is higher in the inner region since it is always hotter. However, it can be expected that when the silicon rod is heated by a high frequency current it will experience two opposed effects: the higher temperature on the centre will cause more current density to flow through the inner region; but on the other hand, the high frequency current would push current density to the outer region. At a certain frequency, detailed in the following sections, these two effects are not balanced and the current density migrates to the outer region, reducing the temperature in the centre of the rod.

The electrical resistivity of the silicon rod is presented first in this chapter, because it is a very important parameter when heating the rods by Joule effect. The derived resistivity is used to estimate the radial temperature profile of the silicon rods. The model for estimating the temperature profile is presented later, showing the most relevant results and discussing them. Finally, the current and voltage requirements during the deposition process are presented, showing the strong variation of both throughout the process.

108 5.2. Silicon rod resistance

5.2 Silicon rod resistance

The resistance of a silicon rod at a constant temperature can be calculated as 1 L R = · (5.1) σ S taking the conductivity, σ, the length, L, and the cross section area of the rod, S into account. The conductivity dependence on the temperature and the doping concentration can be estimated according to semiconductor theory as follows [Grove, 1967; Pierret, 1982; Ruiz et al., 1982]

σ(T,Na,Nd) = e · [µh(T,Na,Nd) · p(T,Na,Nd) + µe(T,Na,Nd) · n(T,Na,Nd)] (5.2) in which e is the electron charge, µh the hole mobility, µe the electron mobility, and n and p the electron and hole concentrations respectively. The carrier mobilities have been studied in the literature [Arora et al., 1982; Caughey and Thomas, 1967] and some expressions can be used to estimate them. For the calculations presented in this section the following expression is used, where the required parameters are shown in table 5.1,

T β1 (µ − µ ) T β2 µ(T,N ,N ) = µ + max min · (5.3) a d min T β4 300K α·( 300K ) 300K Na+Nd 1 + T β3 NREF ·( 300K )

Table 5.1: Parameters for the calculation of the electron and hole mobilities. From PC1D software.

Parameter Electrons Holes Units 2 −1 −1 µmax 1417 470 cm ·V ·s 2 −1 −1 µmin 60 37.4 cm ·V ·s −3 NREF 9.64E+16 2.82E+17 cm α 0.664 0.642 -

β1 -0.57 -0.57 -

β2 -2.33 -2.23 -

β3 2.4 2.4 -

β4 -0.146 -0.146 -

The carrier concentration, n and p, are calculated by means of the mass action law and the charge neutrality relationship,

2 np = ni (5.4) + − p + Nd = n + Na (5.5)

109 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

+ ni is the intrinsic concentration, Nd is the number of ionised (positively charged) donor − sites and Na is the number of ionised (negatively charged) acceptor sites. Above room temperature, practically every donor or acceptor site is ionised, so the carrier concentration is, " #(1/2) N − N N − N 2 n = d a + d a + n2 (5.6) 2 2 i " #(1/2) n2 N − N N − N 2 p = i = a d + a d + n2 (5.7) n 2 2 i The temperature dependence of carrier concentration is explicitly shown through the def- inition of ni, Eg (T ) n = pM · M · exp − (5.8) i c v 2kT ∗ 3/2 15 mn 3/2 Mc = 4.82 · 10 · · T (5.9) m0 ∗ !3/2 15 mp 3/2 Mv = 4.82 · 10 · · T (5.10) m0 in which Mc is the effective density of conduction band states, Mc is the effective density of −3 valence band states, both expressed in cm , Eg is the band gap energy, k the Boltzmann ∗ ∗ constant, T the temperature, m0 the mass of a rest electron, and mn, mp the effective ∗ ∗ masses of electrons and holes at 300K respectively. The values of mn, mp are shown in table 5.2. The variation of Eg with temperature can be estimated according to the equation presented below [Alex et al., 1996; Hull, 1999], T 2 E = E0 − α · (5.11) g g T + β 0 −4 −1 Eg = 1.1692 eV, α = 4.9 · 10 eV · K , β = 655 K

Table 5.2: Eﬀective mass of electrons and holes. From [Pierret, 1982].

∗ ∗ mn/m0 mp/m0 1.18 0.81

The carrier mobilities, carrier concentrations and resistity calculated from this theoretical model are presented in ﬁgures 5.1, 5.2, and 5.3 respectively, over a range of temperatures from room temperature to the silicon melting point (∼1414◦C), for n-type silicon with a resistivity of ρ = 200 mΩcm at room temperature. The combined eﬀect of the carrier concentrations and the carrier mobilities determines the evolution of the resistivity,

110 5.2. Silicon rod resistance

and therefore of the resistance, with temperature. It can be observed that below 450◦C the electron mobility decreases notably while the majority carrier concentration, n in this case, remains constant and equals Nd. As a result, the resistivity increases fourfold from room temperature to 450 ◦C. Above 450◦C the mobilities change steadily whereas the carrier concentrations strongly increase as a consequence of the huge thermal generation of electron-hole pairs, producing a important reduction in resistivity. Thus, the evolution of the resistance with the temperature has two diﬀerent regions: at the left of the resistance peak the slope is positive and at the right the slope is negative.

Figure 5.1: Electron and hole mobilities in n-type silicon, ρ =200 mΩcm at room temperature.

The negative slope above the peak forces the use of a current source instead of a voltage source when heating in this region. This is because the power supplied to the rod, P = V 2 · R−1, increases with the temperature if a constant voltage is applied. Thus, a temperature equilibrium will never be reached and the silicon rod will melt. A constant current flowing through the rod leads to a decreasing power supply as the temperature rises, P = I2 · R, and therefore an equilibrium will be reached at a certain temperature; the silicon rod will not melt (if the current is moderate). The resistance of two different silicon slim rods is analysed and presented in figure 5.3. The rods are 4 meters long and 1cm in diameter, they are n-type and their resistivities 17 are 40 and 200 mΩcm at room temperature (these values correspond to Nd = 3.2 · 10 16 −3 and Nd = 3.3 · 10 cm respectively). It can be seen that the rod with greater resistivity at room temperature displays a resistance maximum at lower values, because the initial doping is lower and the rod becomes ’intrinsic’ earlier, as seen in figure 5.2. However, the

111 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

Figure 5.2: Carrier concentration of electrons and holes, n and p, in n-type silicon (ρ =200 mΩcm at room temperature) and intrinsic carrier concentration, ni.

Figure 5.3: Resistance for n-type slim rods for two doping levels: 200 and 40 mΩcm at room temperature. Rod length: 4 m, rod diameter: 1 cm. peak is smaller for the highly doped rod and therefore the voltage required to heat it from room temperature to deposition temperature is lower. Nevertheless, a thick rod does not have a constant temperature along the radius. It is important to estimate the variation of the temperature along the radius in order to avoid melting of the rod and to estimate the current and voltage requirements to maintain the

112 5.3. Model for the radial temperature proﬁle in the silicon rods

rods at the desired temperature. To this end, a model is presented in the next section that serves to estimate the temperature proﬁle within the silicon rods.

5.3 Model for the radial temperature proﬁle in the silicon rods

Let’s start by considering a cylindrical silicon rod, vertically oriented, with an arbitrary radius R. A time-harmonic electrical current passes through the Si rod. Because of the symmetry of the problem, far from the bottom and top edges, the current density J ﬂows exclusively in the z-direction, and there is no θ or z dependence (J = J (r)·uz ). Note that in the last formula J is complex, the real current density being j (r, t) = Re J (r) · eiωt, √ where i denotes −1 and ω is the current angular frequency. The electric ﬁeld, E, that generates this current density has the same direction as J, according to J = σ · E . Thus

E = E (r) · uz, E being complex. Heat is generated inside the semiconductor by the Joule effect, giving a radial dependent temperature distribution T (r). The electric conductivity σ has a strong temperature dependence, so that there is also a non-uniform radial conductivity, which causes a modifi- cation of the current density inside the rod. The analytical expression for σ(T ) is presented in section 5.2. Application of maxwell’s equations inside the semiconductor lead to the following Helmholtz equation for the electric field,

∇2E + κ2E = 0 (5.12)

2 2 where κ = µω − iωµσ (T (r)) , where µ = µ0 is the magnetic permeability of silicon and

= 11.9·0 the dielectric permeability of silicon. A steady state is considered and therefore the time dependence of temperature has been neglected. This is a valid assumption because the temperature evolves much more slowely than the electric ﬁeld. It should be noted that the current density J does not satisfy (5.12) because of the temperature dependence -and therefore radial dependence- of σ. Regarding the heat transfer within the semiconductor, the following equation is fulﬁlled under steady state conditions [Chapman, 1984],

∇ (k · ∇T ) + q = 0 (5.13) where k is the thermal conductivity of Si, and q the heat generation per unit volume, deﬁned as q (T, r) = |J(r)|2/(2 · σ(T )) . Steady state conditions are also considered in this case. Although deposition takes place and changes the geometry, heat conduction sets a temperature proﬁle much faster.

113 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

The dependence of k on temperature and its derivative, k0, can be obtained by linear interpolation of tabulated data (from -73 ◦C to 1408 ◦C) presented in [Hull, 1999]. Taking the symmetries in the problem into account, (5.12) and (5.13) yields,

d2E 1 dE + + κ2E = 0 (5.14) dr2 r dr

! d2T 1 dT k0(T ) dT 2 σ(T )|E(r)|2 + + + = 0 (5.15) dr2 r dr k(T ) dr 2 · k(T ) with boundary conditions for (5.14) being dE = 0 on r = 0, (5.16) dr √ Z 2 · Itot + 0 · i = σ · E dΩ, (5.17) Ω and for (5.15) being dT = 0 on r = 0, (5.18) dr dT −k = p + p + p on r = R, (5.19) dr convection radiation reaction where Ω is rod’s circular section. Itot in Eq. (5.17) is the rms current through the rod. (5.19) states that inner heat, transferred to the surface by conduction, is dissipated from the surface by convection, radiation and endothermic reaction.

The power loss by convection per unit surface area is pconvection, and is calculated using the model presented in chapter 3. The power loss by radiation per unit surface area is pradiation, and is calculated in chapter 4. Finally, preaction is the power consumed by the chemical reaction per unit surface area and is calculated in the following paragraph. As presented previously, the deposition reaction that takes place on the rod surface is assumed to be

SiHCl3 + H2 ↔ Si + 3HCl (5.20)

The power dissipated on the chemical reaction per unit surface area is

preaction = ∆Hr · dSi · vg (5.21) where ∆Hr is the reaction enthalpy, dSi is the solid silicon density and vg is the silicon growth rate expressed in the appropriate units. ∆Hr is calculated by means of equation

Z Ts 0 ∆Hr(Ts) = ∆Hr + ∆Cp dT (5.22) T0 where superscript 0 denotes standard conditions (0 ◦C, 1 atm) and ∆ denotes the diﬀerence between the quantity in question for the product and for the reactants, with appropriate

114 5.3. Model for the radial temperature proﬁle in the silicon rods

stoichiometric weighting. A typical value for the power consumed in the deposition might −2 be: preaction = 2600 W·m . A vibrational model of the silicon rod is also presented because a high frequency current source can generate external forces acting on the rod. If the frequency of these forces (either axial or transverse) is close to any of the natural frequencies of the rod, the vibrations can break it. The study of the silicon rod’s natural frequencies is presented below.

5.3.1 Vibration model of the silicon rod

Axial and transverse vibrations are modelled based on beam theory. The main assumptions considered for the analysis are: the axial direction is considerably larger than the radial direction, silicon is consider to be linearly elastic (Hookean), and the Poisson effect is neglected. When studying the transverse vibrations, i.e. the flexure of the silicon rod, it is assumed that the planes perpendicular to the neutral axis (the non-deformed axis) remain perpendicular after deformation, and that the angle of rotation is small. A Bernoulli based model has been considered for axial vibration [Han and Benaroya, 2000]. The differential equation of motion for this vibration is given by ∂2u ∂2u d · − M · = 0 (5.23) Si ∂t2 ∂z2 where u is the axial deflection, dSi the silicon density, z the axial coordinate, t time, and M the modulus of elasticity. The separation of variables method applied to equation (5.23) leads to the axial natural frequencies formula, by means of evaluation of the boundary conditions, s n M fa = · n = 1, 2, 3,... (5.24) 2L dSi where L is the rod length. According to this result, long rods have low axial natural frequencies. The Rayleigh beam model [Han et al., 1999] explains the transversal movement of the rod, and the differential equation of motion is given by ∂4v ∂4v ∂2v MI · − d I · + d Ω · = 0 (5.25) z ∂z4 Si z ∂2z∂t2 Si ∂t2 where v is the transversal deflection, Ω the cross-section area, and Iz the area moment of inertia of cross-section about the neutral axis. In the same way as for the case of axial natural frequencies the transverse natural frequencies can be obtained, although the derivation is more laborious. The following expression is used to calculate these frequencies, s 1 a4k2 M ft = · 2 2 · (5.26) 2π a k + 1 dSi

115 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

2 2 where k = Iz/Ω = R /4 for a circular rod section, R being the rod radius, and a is evaluated as the roots of the expression

(bL)2 − (aL)2) sin(aL) sinh(bL) − 2abL2 cos(aL) cosh(bL) + 2abL2 = 0 (5.27) where b = a·p1/(a2k2 + 1). It can be observed that natural transverse frequencies depend, among others, on the rod length, the rod radius and the cross-sectional shape. Note that if either the rod length increases or the rod radius decreases then the vibrational natural frequencies decrease.

5.4 Results of the model

The model presented in the previous section is solved numerically. To do so, both equations (5.14) and (5.15) are approximated by finite differences, using numerical derivatives. This provides a system of non-linear equations. The system is solved by numerical approaches such as Newton’s method or other non-linear methods that improve the convergence. The results presented below are focused on the radiation conditions and on the high frequency current sources as alternatives for reducing the non-homogeneous temperature profile within the silicon rods.

5.4.1 Eﬀect of the radiation conditions

The study of the effect of the radiation conditions on the rod temperature profile is divided into two parts. First, the influence of the location of the silicon rods within the reactor is studied. Then, the influence of the wall emissivity, i.e, the way the wall returns radiation to the rods, is analysed. The study begins by showing in figure 5.4 the temperature profile of silicon rods located in the inner ring, middle ring and outer ring in a 36 rod CVD reactor during the deposition ◦ process. The rod surface temperature is Ts=1050 C and the rod diameter is 14 cm. It can be seen that the temperature profile is more homogeneous in the inner and middle rings than in the outer ring. The temperature difference between the centre and the surface of an outer ring rod is twice the difference of an inner ring rod. The rods located ◦ in the inner and middle ring are surrounded by other rods at Ts=1050 C, and therefore the cooling of the rods is reduced. As long as cooling is low, the surface temperature will tend to be closer to that at the centre. The rods located in the outer ring have higher temperature in the centre and the risk of reaching the melting point is greater in this case. Obviously, locating rods in the outer ring cannot be avoided. Another solution can be implemented to increase the temperature homogeneity within the rods: enhancing

116 5.4. Results of the model

Figure 5.4: Temperature profile within silicon rods located in the inner ring, middle ring and outer ring of ◦ a 36 rod CVD reactor. The rod diameter is 14 cm and the rod surface temperature is Ts=1050 C. the behaviour of the reactor wall. An appropriate surface treatment in the reactor wall decreases the emissivity of the surface, increasing the radiation power reflected by the wall. By doing so, the temperature profile within the rods becomes flatter, as seen in figure 5.5.

Figure 5.5: Temperature proﬁle within the silicon rod as a function of reactor wall emissivity. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor. The rod surface temperature ◦ is Ts=1050 C.

117 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

Figure 5.6: Temperature diﬀerence between the rod centre and the rod surface as a function of the wall ◦ emissivity. The rod surface temperature is Ts=1050 C, the rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor.

The temperature difference between the centre and the surface of the silicon rods increases with the wall emissivity, as presented in figure 5.6. Reducing the emissivity of the reactor wall from 0.8 to 0.4 with any surface treatment reduces the non-homogeneous temperature profile in the silicon rods by 40%.

Figure 5.7: RMS current needed to set the rod surface temperature at 1050 ◦C as a function of the wall emissivity. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor.

118 5.4. Results of the model

A smoother temperature profile requires less current to set the operation temperature at the rod surface, as seen in figure 5.7. Considering a constant surface temperature, when the wall emissivity decreases, a flatter temperature profile is obtained. Lower temperatures along the rod are then found, resulting in a lower conductivity in the rod. Lower conductivity leads to less current generating the same heat by the Joule effect. Not only is less current needed to reach the operation temperature but also less power is required because when the wall emissivity decreases, the radiation loss decreases as well.

5.4.2 Eﬀect of the high frequency current sources

Another way to increase the homogeneity of the temperature profile in the silicon rods is presented: the utilisation of high frequency current sources. In the CVD reactor, the rods heated by a high frequency current source will experience two opposed effects: the higher temperature at the centre will cause more current density to flow through the inner region; on the other hand, the high frequency current will push current density to the outer region. This effect is studied in detail in the following paragraphs. In Fig. 5.8 some temperature profiles within the silicon rod are presented, showing the dependency on the current frequency. In Fig. 5.9 the current densities that generate these temperature profiles are shown.

Figure 5.8: Temperature proﬁle within the silicon rod for diﬀerent current frequencies. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor. The rod surface temperature ◦ is Ts=1050 C.

At low frequencies, more current density tends to ﬂow through the hotter centre than

119 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

Figure 5.9: RMS current density profile within silicon rod for different current frequencies. Current density profiles generate temperature profiles presented in figure 5.8. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor.

through the surface. When frequency increases, current density is pushed to the outer region of the semiconductor rod due to the skin effect; therefore, heat generation in the inner region decreases. Thus, temperature profile close to the centre becomes flatter as frequency rises. It can be seen that around 10 kHz the skin effect begins to be noticed.

Precise information about the importance of this effect is given in Fig. 5.10, that shows the difference between the temperature at the centre and at the surface as a function of ◦ frequency when the rod surface temperature is Ts=1050 C. Three curves are presented, one for each ring in a 36 rod CVD reactor. It can be seen that for the outer ring there is a bigger difference between the rod centre and its surface. The reason is, as mentioned before, that the temperature profile within the rods placed in the inner and middle ring are more homogeneous because they are surrounded by other rods. It can be appreciated in figure 5.10 that the first part of the curve (0-100 kHz) decreases sharply with frequency; at 100 kHz the temperature difference has already been reduced by 80%. For higher frequencies the slope is quite small, and there is no noteworthy improvement in temperature uniformity by going beyond 200 kHz.

A high frequency current source not only generates ﬂatter temperature proﬁles, it also requires less electric current to set the required operation temperature at the rod surface, that is, lower current is required to generate the power needed to set the operation

120 5.4. Results of the model

Figure 5.10: Temperature diﬀerence between the centre and the surface of the rod as a function of frequency considering the outer ring (−), the middle ring (−−), and the inner ring (·−) in a 36 rod CVD reactor. ◦ The rod surface temperature is Ts=1050 C and the rod diameter is 14 cm.

Figure 5.11: RMS current needed to set the rod surface temperature at 1050 ◦C as a function of frequency. The rod has a diameter of 14 cm and is located in the outer ring of a 36 rod CVD reactor. temperature. This is conﬁrmed by Figure 5.11, in which the rms current needed to obtain a surface temperature of 1050 ◦C is presented. It has to be noted that even though less current is required when the frequency rises, the power needed remains constant, and therefore the voltage requirements increase. The

121 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

reason is that the power loss in the CVD reactor does not change with the frequency: the radiation and the convection losses are the same independent of the frequency used.

5.5 Discussion of results

The temperature within the silicon rods is not homogeneous, as derived from the model presented in this chapter. There is a temperature difference between the centre and surface of the rods that has to be controlled to finish the deposition process successfully. The deposition process finishes, according to a conservative approach established in the industry, when the rod diameter is around 14 cm. According to the study presented in the previous section, at the end of the process, choosing 1050 ◦C as the rod surface temperature, the centre temperature is around 1120 ◦C in the outer ring. This non- homogeneous temperature profile seems to be acceptable, and the silicon centre certainly does not melt. Nevertheless, it is crucial to increase the maximum rod diameter aiming at decreasing the energy consumption during the polysilicon deposition. The maximum rod diameter considered in this work is 20 cm, this stems from the reactor design: the distance between rods is 25 cm and it is considered that at least 5 cm are needed between rods to allow the gases to flow. Figure 5.12 presents the variation of the energy consumption with maximum rod diameter, considering a 36 rod CVD reactor and an average polysilicon growth rate of 7 µm·min−1. It can be seen that the difference in the energy consumption when stopping the process at 14 cm diameter compared to finishing at 20 cm is 13 kWh·kg−1. This reduction is similar to the reduction caused by enlarging the reactor capacity from 36 to 60 rods. It is clearly desirable therefore to increase the maximum rod diameter to 20 cm. It is also crucial to increase the rod surface temperature during the deposition process seeking the optimum surface temperature presented in chapter 3. By doing so, the energy consumption is also diminished and the process optimised. The target being to increase the maximum rod diameter and the rod surface temperature, it is necessary to analyse at what point the rod core melts. The melting point of solid silicon is between 1408-1414 ◦C [Hull, 1999], however it is considered in this work that the rod’s core melts if the rod centre temperature is higher than 1350 ◦C. The maximum surface temperature that the rod can reach before melting is presented in figure 5.13, for a wide range of rod diameters, from 1 to 20 cm. For the calculation, one rod in the outer ring of a 36 rod CVD reactor is considered, without thermal shields and with a wall emissivity of 0.5. The current at which the rod melts is presented in figure 5.14 for the same range

122 5.5. Discussion of results

Figure 5.12: Energy consumption throughout the deposition process for diﬀerent maximum rod diameters, from 14 to 20 cm. A 36 rod CVD reactor is considered, and the average polysilicon growth rate is 7 µm·min−1. of rod diameters, showing that around 6200 A of rms current will melt a rod of 20 cm diameter.

Figure 5.13: Maximum surface temperature that can be reached before the core melts as a function of rod diameter. The U-rod is located in the outer ring of a 36 rod CVD reactor. The wall emissivity is 0.5.

The values presented for the maximum rod surface temperature and for the maximum current correspond to a rod in the outer ring. Therefore, for the rods located in the inner

123 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

Figure 5.14: Maximum Current that can be reached before the core melts as a function of rod diameter. The U-rod is located in the outer ring of a 36 rod CVD reactor. The wall emissivity is 0.5. and middle ring these values would not melt the rod core because, as seen in figure 5.4, the temperature profile is more homogeneous in these rods. It is observed that, theoretically, the maximum rod surface temperature is always higher than the optimum surface temperature, presented in figure 3.15. In other words, the risk of melting the rod is low when operating at the optimum temperature. Earlier in this memory, two limitations to operating at the optimum surface temperature were outlined: the risk of melting the rod and the undesirable dendritic growth that happens above 1100 ◦C. The analysis carried out in this chapter shows that the risk of melting is low when working below 1100 ◦C, and therefore the rod diameter can be increased during the process up to 20 cm. The emissivity of the reactor wall has a strong influence on the risk of melting the rod, so it must be understood that figure 5.13 relates to a reactor wall emissivity of 0.5. Thus, if the wall emissivity has a different value the maximum temperature before melting will change. The maximum rod surface temperature for a thick rod (20 cm of diameter) considering different values of the wall emissivity is presented in figure 5.15. It is shown that a high wall emissivity leads to a maximum surface temperature below 1200 ◦C. This temperature can be around 1150 ◦C if the wall emissivity is considerably bad, such as = 0.85. However, it can be seen that the values calculated for the maximum temperatures are never below the optimum temperature, presented in figure 3.15. Therefore, in this case, the risk of melting the rod is not a limitation which requires the

124 5.5. Discussion of results

Figure 5.15: Dependence on the reactor wall emissivity of the maximum rod surface temperature that can be reached before melting the rod core. The rod is located in the outer ring of a 36 rod CVD reactor, and its diameter is 20 cm. process be stopped before a rod diameter of 20 cm is reached. Nevertheless, it should be noted that the maximum temperature before melting varies more than 150 ◦C depending on the wall emissivity.

The utilisation of high frequency current sources is also studied in this chapter, showing that it is only necessary for heating rods in the outer ring because the improvement on the temperature proﬁle in the rest of the rods does not justify the utilisation of this more complex current source. It is shown that the frequency should be around 100 kHz to achieve maximum homogeneity in the temperature proﬁle.

Nevertheless, high frequency current sources may generate external forces acting on the rod that, if close to any of the natural frequencies, can break it. The calculation of natural frequencies has been performed considering: L = 2 m, ri = 1 cm and rod temperature Ts = 1050 ◦C. The lower natural frequency deserves special attention, because it imposes a threshold for the frequency of the external forces. If that threshold is exceeded, the rod can vibrate, due to external forces, under resonance conditions and it can be damaged.

The lower natural frequencies calculated are: fa = 1980 Hz and ft = 190 Hz. Based on these low values it can be stated that the vibrations in the polysilicon rod can aﬀect its stability, advising against this kind of current source as a solution.

By enlarging the reactor capacities, the cooling of the rods is reduced. Thus, the temperature proﬁle of the rods is ﬂatter in the 48 and 60 rod reactors. Consequently, the

125 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

data presented in this section is conservative when considering larger reactors. In other words, the risk of melting the rods will be lower and the rod diameter could be more easily increased in a larger reactor.

5.6 Current-Voltage curves in the CVD reactor

The silicon rods are resistive loads heated by passing current through them. The shape and the temperature of the rods vary considerably throughout the process due to changes in resistance. In the following paragraphs the current and voltage requirements for the diﬀerent steps of the process are presented.

5.6.1 Current-Voltage curves during the preheating of the silicon rods

The preheating of the silicon rods is the first step of the polysilicon deposition process; the temperature of the rods is increased from room temperature to the deposition temperature. In this step, electric power is supplied to the rods, heating them by the Joule effect. The main difficulty is the temperature dependence of the silicon resistivity. The evolution of the resistance with the temperature reaches a maximum, depending on the doping levels, and this maximum may impose a big voltage when supplying power. During the preheating it is supposed that the reactor is under vacuum; therefore, the power supplied to the silicon rods either heats them up or is transferred by radiation to the reactor wall. The current and voltage requirements are studied when the steady-state is reached and the rod temperature does not rise further. The power balance for a certain rod temperature is carried out as follows  V · I = Pradiation (T )  ⇒ V = V (T )& I = I (T ) (5.28) V = I · R (T ) 

Pradiation being the power transferred by radiation from the rods to the reactor wall, as presented in chapter 4, and R (T ) the rod resistance presented in equation (5.1). Because the rod diameter is small, around 0.7 cm, it is considered that the temperature is constant along the radius. The current and voltage values from room to deposition temperature are presented in figure 5.16. It is shown that, for instance, to heat the rod up to 770 ◦C, a current of 10 A is needed. In this case, when the current starts flowing, the rod temperature will rise until reaching a steady state of 770 ◦C. The voltage applied to the rod in the steady-state would be 360 V, as shown in the figure. While the voltage and the current remains constant at 360 V and 10 A respectively, the temperature will remain at 770 ◦C. To increase the rod temperature from this value the current must rise.

126 5.6. Current-Voltage curves in the CVD reactor

Figure 5.16: Voltage (−) and current (−−) applied to a silicon U-rod to maintain diﬀerent rod temperatures. The U-rod is located in the outer ring of a 36 rod CVD reactor. U-rod length: 4m, U-rod diameter: 0.7 cm, n-type silicon, room resistivity: 200 mΩ·cm. Reactor under vacuum.

As seen in figure 5.16 there is a peak in the voltage curve. The position of this peak with respect to the temperature depends on the doping level. The voltage at the peak depends on the doping level and the rod length and diameter. The temperature at which the peak is reached is called the Ignition Temperature. The ignition temperature and the peak voltage are presented in figure 5.17 for different doping levels: from highly doped n-type silicon rods (0.1 Ω·cm) to intrinsic material (105 Ω·cm). Similar results are found when studying p-type silicon instead of n-type. It can be seen that for intrinsic silicon rods the peak voltage increases tremendously (to around 5000 V for the U-rods considered in the analysis) and the ignition temperature decreases to 120 ◦C, the reactor wall temperature being 100 ◦C. It is not possible to heat the rod electrically to the deposition temperature if the power source cannot supply the peak voltage. When the rods are considerably doped (1 Ω·cm or lower) the peak voltage is 1000 V. This can be delivered by the commercial power supplies used during the deposition. However, when the rods are intrinsic the peak power is very high and other solutions should be considered for preheating the rods:

• Medium voltage power supply. This solution consists in the utilisation of two different power supplies: one during the preheating of the rods, suitable for reaching around 8000 V and low currents; and another, conventional power supply, during the deposition, which is suitable for providing high current and moderate voltage.

127 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

Figure 5.17: Ignition temperature (−) and peak voltage (−−) of a silicon U-rod for diﬀerent doping levels: from highly doped n-type silicon (0.1 Ω·cm) to intrinsic material (105 Ω·cm). U-rod length: 4m, U-rod diameter: 0.7 cm. Reactor under vacuum. Reactor wall at 100 ◦C.

• Radiation ﬁnger. This solution consists in the utilisation of a removable radiation ﬁnger, introduced into the chamber at the beginning of the preheating, that heats the rods up to around 400 ◦C. It is later removed and the conventional power supply heats the rods up to the deposition temperature.

• Hot gases. This solution consists in the utilisation of hot inert gases to heat the rods up to 400 ◦C. The conventional power supply then heats the rods up to the deposition temperature.

5.6.2 Current-Voltage curves during operation

During the deposition process, the voltage requirements are not as demanding as during the preheating step because the rod temperature remains at a constant high temperature (around 1050 ◦C). Conversely, the current requirements are very demanding because the rods thicken, forcing the current to be increased notably to maintain the deposition temperature at the rod surface. The values of the current and voltage presented below have been calculated considering a conventional current frequency (50 Hz) and using the model presented in section 5.3. The current and voltage variation throughout the process are, along with the deposition conditions, the required information for operating the CVD reactor and producing polysilicon. The curves are presented for the U-rods located in the outer ring, middle ring and inner

128 5.6. Current-Voltage curves in the CVD reactor

ring of a 36 rod CVD reactor in figures 5.18, 5.19 and 5.20 respectively. The deposition process takes place in the 36 rod CVD reactor presented in chapter 4 (section 4.4.1 without thermal shield), and the deposition conditions are presented in table 3.2. The process continues until a rod diameter of 20 cm is reached. It should be noted that the current and voltage at the beginning of the process are slightly different than the values presented in figure 5.16 for 1050 ◦C. This is because the reactor is not under vacuum and hence convection loss is also accounted for.

Figure 5.18: Voltage (−) and current (−−) throughout the process for a U-rod located in the outer ring. U-rod length: 4 m. The deposition process takes place in the 36 rod CVD reactor presented in chapter 4 (section 4.4.1 without thermal shield). The deposition conditions are presented in table 3.2.

It can be observed that the voltage profile is very similar for all U-rods in the reactor. The power loss is different for each ring, as is previously discussed. The rod resistance is different for each ring because the radial temperature profile is different. The effect of the variation of the power loss and the resistance for each ring serve to counteract one another yielding, by chance, very similar voltage curves for all rings. The voltage is around 240 V at the beginning of the process. When the process evolves, the rods thicken and the voltage decreases. The voltage is around 15 V when the rod radius reaches 20 cm and the process finishes. The current profiles for U-rods in different rings are distinct. The power loss in the inner and middle ring is lower than in the outer ring, and consequently the current in those rings is lower throughout the process. At the end of the process the current in the outer ring is twice the current in the inner ring.

129 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

Figure 5.19: Voltage (−) and current (−−) throughout the process for a U-rod located in the middle ring. U-rod length: 4 m. The deposition process takes place in the 36 rod CVD reactor presented in chapter 4 (section 4.4.1 without thermal shield). The deposition conditions are presented in table 3.2.

Figure 5.20: Voltage (−) and current (−−) throughout the process for a U-rod located in the inner ring. U-rod length: 4 m. The deposition process takes place in the 36 rod CVD reactor presented in chapter 4 (section 4.4.1 without thermal shield). The deposition conditions are presented in table 3.2.

The current is, for the three rings considered, around 46 A at the beginning of the process (diameter: 0.7 cm). At the end of the process (diameter: 20 cm) the current for

130 5.7. Conclusions

the outer ring rods is around 4200 A, the current for the middle ring is around 2600 A and the current for the inner ring is 2200 A.

5.7 Conclusions

An estimation for the electrical resistance of the silicon rod is presented in this chapter. The combined effect of the carrier concentrations and the carrier mobilities determines the evolution of the resistance with temperature. As the temperature is increased from room temperature, the strong reduction in the mobilities leads to a steady increase in the resistance until a peak is reached at what is defined the ignition temperature. Above this temperature, the thermal generation of carriers causes the resistance to decrease steadily. The negative slope of the resistance does not allow the utilisation of voltage sources to heat the rods above the ignition temperature. Since the deposition temperature is always above the ignition temperature the rods must be heated by means of current sources, not voltage sources, during the deposition phase. The radial temperature profile within the silicon rods has been studied. It is concluded that the rods located in the outer ring have the greatest temperature variation along the radius, it being more than double that of the rest of rods. This is because the power given off to the surroundings is higher for the outer ring, since they are adjacent to the cold wall whereas the others are surrounded by hot rods. Two alternatives are presented to reduce the non-homogeneous temperature profile in the silicon rods: (1) reduce the power loss by enhancing the wall emissivity, and (2) use a high frequency current source for heating the rods. The first alternative increases homogeneity by decreasing the cooling of the silicon rods. This not only reduces the risk of melting the rod but also requires less power to maintain the deposition temperature. The second alternative is only worthwhile for use in the outer ring; its impact on the rest of the rings its not sufficient for its justification. The frequency of the current source should be around 100 kHz, above this value there is no noteworthy improvement in the temperature profile. This alternative requires less current, but the same power, for heating the rods. This is because the power loss, and therefore the power supplied, is independent of the current frequency. A vibrational analysis has been carried out to ascertain if the external forces generated by this current source can break the rods. Based on this study, it is concluded that the vibrations caused in a polysilicon rod can affect its stability. Use of a high frequency current source is therefore inadvisable. The maximum temperature that may be reached by the rod surface has been studied. This maximum temperature, when studying a 36 rod reactor with a wall emissivity of

131 Chapter 5. Electric heating of the polysilicon rods in the CVD reactor

0.5 and a 50 Hz current source, is always above the optimum temperature, presented in figure 3.15, considering rod diameters from 1 to 20 cm. In this case, it does not therefore introduce a limitation for stopping the process before a rod diameter of 20 cm is reached. It has to be noted that if the wall has a higher emissivity the maximum temperature decreases, and depending on the wall emissivity its value may vary by more that 150 ◦C. Theoretically, the maximum temperature is always above the optimum temperature, regardless of the wall emissivity. Hence, the maximum rod diameter can be increased up to 20 cm. It has been calculated that the reduction of energy consumption as a consequence of stopping the process at 20cm instead of 14cm is 13 kWh·kg−1. This reduction is similar to the reduction by enlarging the reactor capacity from 36 to 60 rods. Translated to cost savings, considering an energy cost of 8 ce/kg, the cost reduction is around 1.04 e per kg of polysilicon produced. In a 5000 t/year polysilicon plant the savings would be up to 5.2 million e/year. The current and voltage curves for the different steps of the process have been presented. During the preheating of the rods the maximum voltage required and the ignition temperature are presented for different doping levels: from highly doped rods to intrinsic rods. When the doping level is reduced the maximum voltage increases and the ignition temperature decreases. The ignition temperature of highly doped rods is around 400 ◦C and the maximum voltage is around 600 V (considering U-rods 4 m in length with a diameter of 0.7 cm). For intrinsic U-rods, the ignition temperature is around 120 ◦C and the maximum voltage is around 5000 V. It is important to note that if the power supply does not reach the maximum voltage, the rods cannot be heated electrically above the ignition temperature. The evolution of the current and voltage requirements during the process are also presented. It is shown that the current increases notably, because the rods thicken, while the voltage maintains moderate values.

132 Chapter 6

Experimental approach

6.1 Introduction

The theoretical work carried out in this thesis is focused on the industrial-scale CVD reactors: optimum deposition conditions, minimum radiative loss, optimum electrical heating, etc. The reader may understand that it is very diﬃcult to develop experimental work in such reactors, since polysilicon plants worldwide are committed to full-time production. When fully operational, the CENTESIL pilot plant will provide a means for experimental testing in a full-scale polysilicon reactor under industrial conditions. Until such time, experiments must be carried out in a smaller laboratory reactor, under slightly diﬀerent operation conditions. In this thesis, the experimental work is made up of two parts, this chapter is divided into two sections accordingly:

• LBNL, Berkeley, California: during my research stay at the Lawrence Berkeley Na- tional Laboratory (USA), in 2007, experiments were carried out in producing polysilicon. This comprised three months work.

• Instituto de Energ´ıaSolar (IES), Madrid: the author has been heavily involved in the development and construction of a laboratory scale reactor at the IES. Experiments have been carried out in 2010, providing valuable information.

6.2 Lawrence Berkeley National Laboratory

J.W. Ager III and collaborators (Electronic Materials Program, Materials Science Division, LBNL) produced isotopically enriched silicon, that is, single crystals of silicon enriched in one of its three stable isotopes: 28Si, 29Si, and 30Si. This work is reported in reference Ager et al. [2005]. Polysilicon was ﬁrst synthesised, using the so-called Komatsu process, by the

133 Chapter 6. Experimental approach

decomposition of isotopically enriched silane (SiH4). Single crystals were then grown by the ﬂoat-zone (FZ) technique.

The production of isotopic silane began with the enrichment of SiF4 gas at the Elec- trochemical Plant, Zelenogorsk, Russia. Then, SiF4 was converted to SiH4 by Voltaix, Inc. (NJ, USA). The following precursor gases were then used for producing polysilicon: 28 29 30 SiH4, SiH4, and SiH4. The composition of silicon found in nature is (in atom %): 92.2% of 28Si, 4.7% of 29Si, and 3.10% of 30Si. The isotopically enriched crystals reported were: 28Si (99.9% of this isotope in the crystal), 29Si (91.7% of this isotope in the crystal), and 30Si (89.8% of this isotope in the crystal). These high purity crystals were produced to study the properties of the stable isotopes of silicon. Measurements of the thermal conductivity show that it is enhanced in the range of 10-15% when the crystal is isotopically enriched [Ager et al., 2005]. This can be of interest to manufacturers of integrated circuits because the transport of heat away from the electronic device is improved. The aim of my research in the Lawrence Berkeley National Laboratory was to study and operate the laboratory scale deposition reactor, to produce polysilicon (28Si) and to analyse the purity of the material grown.

6.2.1 Description of the system

The laboratory-scale deposition reactor is detailed in figure 6.1. It is a one rod reactor where in which a mixture of silane and hydrogen flows upwards around the rod, depositing polysilicon. The reactor design is based on a one-pass flow reactor presented previously by Hashimoto et al. [1990]. As shown in figure 6.1, the reactor is a double-tube reactor: the inner tube is made of quartz and the outer tube is made of polycarbonate (lexan R ). The cooling system consists of water flowing upwards in between these two tubes. The rod is heated by passing current through it. Both electrodes are water-cooled and suitable for high-current. The initial rod is made of graphite in order to make the heating of the rod easier because the resistance of a graphite rod does not change as strongly as the resistance of a silicon rod. The upper electrode contact is designed to have some axial freedom of movement to compensate for the thermal expansion of the rod: a Ga-Sn eutectic solution is used to form a sliding contact with low electrical resistance. The process gas is a dilute mixture of silane in hydrogen, which flows from bottom to top around the rod inside the inner tube. The rod temperature is measured with a one-colour optical pyrometer. The recirculating system is presented in figure 6.2. The recirculating system is designed to perform a conversion with an efficiency above 95% and minimal generation of

134 6.2. Lawrence Berkeley National Laboratory

Figure 6.1: Laboratory-scale deposition reactor. Electronic Materials Program, Materials Science Division, LBNL. From Ager et al. [2005].

Si particles from homogeneous nucleation of the precursor [Herrick and Woodruff, 1984]. To this end, a relatively dilute concentration of silane is used, in the range of 0.25-2%, with hydrogen as the carrier gas. The gas mixture is recirculated through the reactor at 15 slm. The decomposition occurs at a rod temperature of 700-750 ◦C. These deposition conditions are different from the industrial silane process, which operates at 800 ◦C with silane concentrations in the range of 1.5-5% [Ager et al., 2005]. The motivation for these variations in the deposition conditions is to diminish homogeneous nucleation and to increase silicon conversion by means of recirculation. The system has two mass flow controllers at the gas inlet, one for silane with a maxi-

135 Chapter 6. Experimental approach

Figure 6.2: Laboratory-scale recirculating system. Electronic Materials Program, Materials Science Divi- sion, LBNL. From Ager et al. [2005]. mum flow of 100 sccm (standard cm3 per minute) and the other for hydrogen. Afterwards, there is a pressure gauge that ensures the pressure in the system does not exceed 1.3 atm. A particle filter, fabricated from porous 316 stainless steel, is placed after the reactor to eliminate particles from the system. The exhaust of the system follows and consists of a ballast volume and a 500 sccm mass flow controller. Finally, the recirculating loop is closed by the recirculation pump. A picture of the reactor is presented in figure 6.3. More pictures and information about the deposition reactor can be found in reference Ager et al. [2004].

6.2.2 Experimental

During my research stay at the Material Science Division, one experiment was carried out in the polysilicon reactor. This experiment was done using a recipe that had been developed in-house. It is described in the following paragraphs. First, a graphite rod of 15 cm length and a diameter of 0.3 cm is introduced into the reactor. Then, the start up of the system is carried out. It comprises mainly the preparation of the process loop and the calibration of the rod temperature with the combination of the optical pyrometer and a photodiode. The preparation of the process loop consists in making a vacuum in the system and identifying any possible leakages. To carry out the calibration of the rod temperature, the reactor is cooled and current is applied to the graphite rod. Typically, 730 ◦C is attained at a current of 44 A; at this point the voltage in the photodiode is registered. This reference voltage in the photodiode must be corrected

136 6.2. Lawrence Berkeley National Laboratory

Figure 6.3: Laboratory-scale deposition reactor. Electronic Materials Program, Materials Science Division, LBNL. Picture taken during my research stay at the LBNL, October, 2007. during the process because when the deposition takes place, the photodiode reading falls to 75% of its original value due to the lower emissivity of silicon compared to graphite. Once the start up is accomplished, the operation starts.

The operation begins by turning on the recirculation and the exhaust pumps. The process loop is then filled with ultra-high-purity hydrogen. The pressure is set at approximately 1.2 atm and the recirculation mass flow controller is set to 15 slm. Silane is then introduced into the process loop: the mass flow controller of silane is set to 10 sccm, and the exhaust flow is set to around 19.7 sccm. These values for the silane inlet flow and exhaust flow maintain a constant pressure of 1.2 atm inside the system.

The chemical reaction that takes place in the CVD reactor is consider to be [Hashimoto et al., 1990]

SiH4 → Si + 2H2 (6.1)

A diagram of the experiment is presented in ﬁgure 6.4 under steady-state conditions (when the pressure during the operation is constant).

137 Chapter 6. Experimental approach

Figure 6.4: Diagram of the experiment for producing polysilicon, under steady-state conditions. MS: silane,

SiH4, H2: hydrogen, H2.

During the ﬁrst stage of the experiment,

[MS]inlet = 10 sccm [H2] = 0 sccm inlet (6.2) [MS]exh + [H2]exh = 19.7 sccm

[MS]recir + [H2]recir = 15000 sccm The solution of the balance shown in figure 6.4, based on the conditions presented in equations (6.2), provides the following information for the beginning of the process: the molar fraction of silane in the process loop is 1.5%, the conversion per pass in the CVD reactor is η = 4%, the global conversion in the process loop is ηtotal = 97%, and the −1 growth rate is around vg = 4.1 µm·min . The value of the growth rate matches the value estimated in reference Hashimoto et al. [1990]. Throughout the process, as the rod thickens, the silane flow at the inlet is increased linearly with the rod radius, which is estimated with the growth rate. The exhaust gas flow rate is also modified; it is nominally twice the silane feed rate. If the pressure in the loop drops for any reason (for instance, a possible gas chromatograph sampling), fresh hydrogen is added to increase it. The deposition time is 17-18 h; in this time a rod with a diameter of 12 mm and a mass of 35 g is grown. The average deposition rate is 4 µm·min−1. The initial rod, made of graphite, is removed from the grown polysilicon by a combination of drilling and lapping.

Then, etching with a 1:10 mixture of HF and HNO3 is carried out to remove mechanical damage and residual impurities. The polysilicon rod produced in the experiment is shown in figure 6.5. The figure shows the starter graphite rod (at both ends), the polysilicon deposited and the drill after removing the graphite. This experiment used silane as precursor gas instead of trichlorosilane, and therefore few conclusions can be extracted regarding the chemical aspects of the deposition. How- ever, it was the first growth of polysilicon undergone as a part of this thesis, and therefore

138 6.2. Lawrence Berkeley National Laboratory

Figure 6.5: Polysilicon rod grown in the laboratory-scale deposition reactor during my research stay at the Materials Science Division, LBNL. November, 2007. was very useful for understanding how these kind of systems work, the way a silicon rod is heated and the way it grows. Once the polysilicon rod was grown, the next step was to analyse the quality of the material produced. Among the different techniques available to test the quality of the material, the LA-ICP-MS (Laser Ablation Inductively Coupled Plasma Mass Spectrometry) technique was used. This is only a first approach to quality analysis, an important field and the subject of much effort in the scientific community.

6.2.3 Quality analysis by means of LA-ICP-MS

Polysilicon is the raw material for producing the crystalline silicon wafers that are used for processing solar cells. The quality of the material in these three steps (polysilicon, wafer and solar cell) can be analysed by different sampling techniques, some of which are summarised in table 6.1. These techniques have a variety of functions and limitations, while some measure the carbon or oxygen content, others measure the metallic impurity content; while some require a crystalline structure others can be applied to bulk material; etc. Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) [Günther, 2002; Günther et al., 2000; Russo et al., 2002, 2004], is a direct solid sampling technique that mainly consists in: (a) a laser ablation of a certain volume of the solid sample, producing particles in vapour phase, (b) these particles are introduced into a inductively coupled

139 Chapter 6. Experimental approach

Table 6.1: Diﬀerent techniques for analysing the quality of polysilicon, crystalline silicon wafers and silicon solar cells.

Glow Discharge Mass Spectrometry, GDMS [Becker, 2007] Secondary Ion Mass Spectrometry, SIMS [Becker, 2007] Polysilicon X-ray Fluorescence Microscopy, XRF [Cullity and Stock, 2001] Inductively Coupled Plasma Mass Spectrometry, ICP-MS [Becker, 2007] ICP Atomic Emission Spectrometry, ICP-AES [Becker, 2007] Fourier Transform Infrared Spectroscopy, FTIR [Schroder, 2006] Deep Level Transient Spectroscopy, DLTS [Schroder, 2006] Micro-Wave Photo Conductance Decay, µW-PCD [Schroder, 2006] Wafer Quasi Steady State PhotoConductance, QSSPC [Schroder, 2006] Photoluminiscence, PL [Schroder, 2006] 4-points probe [Schroder, 2006] I-V curve, dark & illuminated [Nelson, 2003] Solar Cell Quantum Eﬃciency, Q.E. [Nelson, 2003] Ligh beam induced current, LBIC [Schroder, 2006]

plasma torch producing ions that correspond to the constituents of the sample, and (c) the ions are analysed in the mass spectrometer. A schematic of a laser ablation system can be seen in ﬁgure 6.6.

A short-pulsed high-power laser beam is directed onto the surface of a sample in an air-tight ablation cell. As a result of the interaction of the laser with the sample, a ﬁnite volume of the solid sample is converted into its vapour phase constituents. The chamber is ﬂushed with an inert gas (argon or helium) that transports the ablated material to the inductively coupled plasma (ICP) torch. The ions generated in the ICP are introduced in a mass spectrometer, typically a quadrupole mass analyser, and detected.

The main advantages of this technique are the direct characterisation of solids, the easy sample preparation and the rapid measurement. It is becoming a dominant technology for both qualitative and quantitative analysis. The drawback of this technique is the lack of reference materials for calibration and the so-called elemental fractionation. The fractionation, a result of the diﬀerent mass removal of the constituents of the sample, leads to a situation in which the ablated mass composition is not the same as the actual sample composition. Therefore, the composition of the mass analysed is not representative of the bulk sample. The lack of reference materials and the fractionation limit accurate quantitative analysis.

The detection limits can be consulted in [G¨unther, 2002] where it can be seen, for instance, that some elements such as Li or Pb can be detected if their concentration is

140 6.2. Lawrence Berkeley National Laboratory

Figure 6.6: Set-up of a laser ablation system, using ICP-MS and ICP-AES detection. ICP-MS detection is employed at the Laser Spectroscopy & Applied Materials Group, Environmental Energy Technologies Division, LBNL. From reference Russo et al. [2002]. higher than 1015 cm−3 and the concentration of Cu to be detected is 1016 cm−3. This is not the concentration in the sample but the concentration in the ablated mass.

The characterisation of the polysilicon sample took place at the facilities of the Laser Spectroscopy & Applied Materials Group, LBNL, in November, 2007, and was conducted by Dr. Jhanis González. An unprepared polysilicon sample of 0.5 cm2 was introduced into the ablation cell. Some measurements were carried out that involved ablating the sample in different positions, as seen in figure 6.7. The focused laser beam permits spatial characterisation in this kind of solid samples, since different zones can be ablated. However, in this particular case the sample was ablated several times in order to have a batch of experiments and results, not for carrying out a spatial characterisation of the material.

In ﬁgure 6.8 the ablated zone is observed by means of a white light interferometry microscope. It is observed that the crater produced by the laser beam is around 20 µm in depth and the shape of the ablation can be arbitrary, in this case, the acronym IES was written.

Analysis was made to seek the presence of the following elements in the polysilicon sample: B, Mg, Al, P, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo and Sn. It was not possible

141 Chapter 6. Experimental approach

Figure 6.7: Polysilicon sample after laser ablation.

Figure 6.8: Image of the ablated zone acquired by a white light interferometry microscope. The acronym IES (Instituto de Energ´ıaSolar) is written in 0.5 mm. to scan for two important elements: carbon and oxygen. A LA-ICP-MS measurement takes around 160 seconds, as seen in figure 6.9 where the detection of silicon by the mass spectrometer is depicted. It can be seen that for the first 30-40 seconds the laser is off, and there is a DC level in the intensity signal. After this time, the laser is on for around 80 seconds and the intensity signal increases strongly because it is detecting the silicon in the sample. For the last 30-40 seconds the laser is off and the intensity signal decreases.

The ICP-MS intensity for all the aforementioned elements was analysed, comparing the intensity signal when the laser is on and off (DC signal). This comparison, for all the elements studied, is shown in figure 6.10. The criterion chosen to confirm that an element is detected is that the signal when the laser is on is at least 3 times the signal when the laser is off. Following this criterion, the following elements were detected in our polysilicon sample: Mg (mass 24), Ti (masses 47 and 48), Cu (masses 63 and 65) and Zn (masses 64

142 6.2. Lawrence Berkeley National Laboratory

Figure 6.9: ICP-MS intensity for silicon. Detection of silicon in the polysilicon sample. and 66). The ICP-MS results for these elements are presented in ﬁgure 6.11 and table 6.2.

Figure 6.10: ICP-MS for B, Mg, Al, P, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo and Sn (considering diﬀerent masses). The intensity when the laser is on is compared to the intensity when the laser is oﬀ.

Comparing all the elements detected, excluding Si, the ICP-MS intensity for Ti is the greatest, followed by Cu and Mg and ﬁnally Zn. However, the only conclusion that can be extracted is that these elements are in the polysilicon sample. There was no a

143 Chapter 6. Experimental approach

(a) (b)

Figure 6.11: ICP-MS for the four elements detected in the analysis of the polysilicon sample: (a) Mg, (b) Ti , (c) Cu, and (c) Zn.

Table 6.2: ICP-MS results for the elements detected in the analysis of the polysilicon sample. Element Mass Intensity laser on / Intensity laser oﬀ Intensity / counts s−1 Mg 24 13 0.8·103 Si 29 126 3·106 Ti 48 23 4.4·103 Cu 63 13 2.4·103 Zn 64 4 1.2·103

calibrated polysilicon sample, with a known impurity content, from which a quantitative analysis could be carried out. As a consequence of this and the fractionation, it cannot be concluded that the content of Ti in the sample is greater than that of Cu, Mg or Zn.

144 6.3. Instituto de Energ´ıaSolar

6.3 Instituto de Energ´ıaSolar

The experiment at the LBNL was carried out using silane as precursor gas. With the aim of carrying out experiments using trichlorosilane, a deposition system was designed and constructed at the IES facilities. Advantage was of the knowledge and skills acquired in a previous project presented in [Rodr´ıguezSan Segundo, 2007]. Some equipment from this previous system was also used. A laboratory scale reactor provides valuable information for understanding and opti- mising the operation of an industrial scale deposition reactor. First and foremost, it allows easy testing of diﬀerent deposition conditions: rod temperatures, pressures, gas compositions, etc. The cost testing in an industrial reactor is very high (in terms of direct cost and opportunity cost). There are two ways to reduce this cost: simulate the system and/or test it in a laboratory scale reactor.

6.3.1 Description of the system

The polysilicon deposition reactor was designed and constructed in the first half of 2008. During the second half of this year, the system was built up, introducing the pumps, mass flow controllers, gas cabinet, connections to the reactor, sensors, etc. The main difficulty was finding a trichlorosilane supplier. This gas is commonly used in the semiconductor and solar industry, but the gas supplier companies in Spain would not deliver quantities as little as 10-20 kg of this gas for research purposes. Consequently, it was not possible to introduce trichlorosilane into the deposition chamber until the end of 2009. The polysilicon deposition reactor is presented in figure 6.12. It is bigger than the reactor operated at the LBNL: the height is around 70 cm and the diameter of the reactor vessel 20 cm. As shown in the figure, the reactor is a double tube reactor; the inner tube is made of stainless steel and the outer tube is made of PMMA (Polymethyl methacrylate). The cooling system consists of water flowing upwards between these two tubes and in both the upper and lower plates. The rod is vertically oriented in the inner tube. The electric feedthroughs are located in the upper and lower plates. The upper electrode contact has some axial freedom of movement to compensate for thermal expansion of the rod: a Ga-In eutectic solution is used to form a sliding contact with low electrical resistance. The gas mixture (trichlorosilane and hydrogen) flows upwards surrounding the rod. Before the exhaust, there is a heat exchanger to reduce the gas temperature. The complete system is presented in figure 6.13. It is a non-recirculating system because the outlet gas composition contains SiCl4 and HCl in notable proportions. In order to reuse the outlet gas, a recirculating system similar to the industrial one is required:

145 Chapter 6. Experimental approach

Figure 6.12: Polysilicon deposition reactor. Instituto de Energ´ıaSolar, Universidad Polit´ecnicade Madrid.

distillation columns, SiCl4 hydrogenation, etc. In a laboratory this kind of recirculation system is impractical. The fresh TCS, which is a liquid stored in a 10 kg bottle, is evaporated before entering the system. The hydrogen is stored in four bottles of 8000 standard litres each. Two mass flow controllers govern the amount of TCS and H2 entering the reactor. The gas mixture introduced into the reactor flows upwards around the silicon rod. A particle filter is located after the reactor in order to eliminate possible particle formation during deposition. Finally, the exhaust pump blows the gas mixture to the scrubber for neutralisation. A picture of the system is presented in figure 6.14. There are different sensors measuring the temperature and pressure at different points of the reactor vessel. The pressure under vacuum conditions is measured by the Maxigauge TPG256A sensor, and the pressure in the reactor vessel during operation is governed by the MKS651 controller. The temperature of the gases in the reactor is measured by a K-type

146 6.3. Instituto de Energ´ıaSolar

Figure 6.13: Laboratory-scale complete system. Instituto de Energ´ıaSolar, Universidad Polit´ecnicade Madrid.

Figure 6.14: Picture of the laboratory-scale deposition system. Instituto de Energ´ıaSolar, Universidad Polit´ecnicade Madrid. thermocouple. The rod temperature is monitored by a two-colour radiation thermometer, also called a two-colour pyrometer (Omega R iR2P).

A LabView R application was developed to control the system. It acquires data from

147 Chapter 6. Experimental approach

the thermocouples, the pressure sensors, and the two-colour pyrometer, displaying on the operator screen the temperature of the gas mixture at diﬀerent points of the system, the pressure within the reactor vessel and the rod surface temperature. The application also governs the mass ﬂow controllers, and therefore the operator introduces the value of the

TCS and H2 flow rate directly on the PC. The power supply used for heating the silicon rod was manufactured ad hoc by AEG Power Solutions. It consists on a power controller (Thyro-P family), a trifasic transformer and a rectifier to supply DC current to the silicon rod. The circuit diagram is presented in figure 6.15. It can supply up to 200 V and 150 A.

Figure 6.15: Circuit diagram of the laboratory scale reactor power supply.

6.3.2 Measurement of the rod surface temperature

The temperature measurement of the rod is non-contacted and uses a radiation pyrometer. Radiation pyrometers can be classiﬁed as follows:

• Broadband radiation pyrometers

• Narrow band radiation pyrometers

• Ratio radiation pyrometers

Broadband radiation pyrometer

This pyrometer measures a signiﬁcant fraction of the thermal radiation emitted by the object. It is dependent on the total emissivity of the surface being measured. When

148 6.3. Instituto de Energ´ıaSolar

measuring with this device, the path to the object must be unobstructed: no water vapour, dust or smoke can be present in the atmosphere because the resultant attenuation leads to a weak signal. There are two main difficulties for utilisation of this pyrometer in our polysilicon reactor: (1) the emissivity of the rod surface must be known, and (2) energy absorbing gases are found in the reactor vessel and silicon is deposited on the window during the deposition process. The emissivity of the rod surface varies with the temperature, as seen in figure 4.11, so the pyrometer must be calibrated each time the object temperature changes. This is impractical during operation. Also, the value of the emissivity must be substituted by the apparent emissivity [Sparrow et al., 1962], which takes the radiation reflected by the object surface into the account. The value of the apparent emissivity changes throughout the process, which makes a precise calibration of the pyrometer even more difficult. Since the path to the object is obstructed and the emissivity is unknown, these devices are not appropriate for measurement of the rod temperature.

Narrow band radiation pyrometer

This pyrometer measures the thermal radiation emitted by the object over a narrow range of wavelengths. It can also be referred to as single colour pyrometer. These devices use ﬁlters to restrict response to a selected wavelength. The basic equation for understanding the operation of this pyrometer is the spectral distribution for the radiated energy by the object (Planck’s radiation law):

2πC1 E(λ, T ) = (λ, T ) · 5 (6.3) λ (exp(C2/λT ) − 1)

C1 and C2 being constants that can be consulted in [Siegel and Howell, 1972]. When considering one particular wavelength, this expression is a function of the temperature and of the emissivity at this wavelength, so the temperature of an object could be measured if the (apparent) emissivity were known. The problem is, again, the variation of the apparent emissivity with temperature, and the variation of the apparent emissivity throughout the process. Since the value of the apparent emissivity is again diﬃcult to measure, this kind of pyrometer should not be used to measure the rod temperature.

Ratio radiation pyrometer

This pyrometer measures the radiated energy of an object in two narrow wavelength bands, and calculates the ratio of the two energies, which is a function of the temperature of the object. It can also be referred to as a two-colour pyrometer. Any parameter which aﬀects the amount of energy in each band by an equal proportion has no eﬀect on the temperature

149 Chapter 6. Experimental approach

indication. This measuring technique may reduce or completely eliminate error in the measurement caused by changes in emissivity, surface ﬁnish, and energy absorbing materials, such as vapour in the reaction chamber or silicon deposited on the reactor window. The ratio of the two energies is:

5 E(λ1,T ) (λ1,T ) λ2 (exp(C2/λ2T ) − 1) (λ1,T ) = · 5 = · f(T ) (6.4) E(λ2,T ) (λ2,T ) λ1 (exp(C2/λ1T ) − 1) (λ2,T ) For grey body materials, the emissivity is wavelength independent at all temperatures.

Therefore the ratio (λ1,T )/(λ2,T ) is constant and is equal to 1. As a consequence, the energy ratio presented in equation (6.4) depends exclusively on the temperature, and not on the variation of emissivity. Therefore, although the emissivity varies with temperature and the radiated energy is obstructed by intermediate absorbing materials, the pyrometer provides an accurate measurement. If the material is not a grey body, the emissivity depends on the wavelength but the variation of emissivity with temperature can be considered wavelength independent. The ratio of emissivities, (λ1,T )/(λ2,T ), can therefore be considered constant. This ratio must be determined experimentally because it depends on the material (silicon in this case), on its surface preparation and on the intermediate absorbing materials between the object and the pyrometer. Thus, the two-colour pyrometer needs to be calibrated. As already mentioned, the temperature of the silicon rod in the laboratory scale deposition reactor is measured with a two-colour pyrometer. The calibration of this pyrometer was carried out in a diffusion furnace where the temperature is stable and known. The diffusion furnace is typically used for creating the emitter region of solar cells. A silicon rod was introduced into the furnace. It was assumed that after a certain time the temperature of the rod and the temperature of the furnace would reach equilibrium. The temperature of the rod was measured by the two-colour pyrometer through a safire window and the value of the ratio of emissivities was modified until the temperature measured by the pyrometer matched the temperature of the furnace. The furnace temperature was changed from 550 ◦C to 1100 ◦C in order to determine the ratio at different temperatures. The data obtained during the calibration is presented in figure 6.16. The average ratio is 0.9305; this value was introduced as the slope parameter of the two-colour pyrometer.

6.3.3 Experimental

Several experiments were carried out in the deposition reactor in which the gas ﬂow and the rod surface temperature were varied. These are detailed in the following paragraphs. They are ordered sequentially as they were carried out. The most convenient gas ﬂow rates, and TCS molar fraction were chosen according to the results presented in chapter

150 6.3. Instituto de Energ´ıaSolar

Figure 6.16: Calibration of the two-colour pyrometer. Determination of the ratio of emissivities. The average ratio is 0.9305.

3. The silicon rods were provided by the Leibniz Institute for Crystal Growth (IKZ). All the rods have similar characteristics: the length is 560 mm, the diameter is in the range 6-8.5 mm and the resistivity is around 100 mΩcm. Industrial scale reactors operate at pressures around 6 atm, as derived in chapter 3. However, the pressure in the laboratory scale reactor cannot exceed 0.8 atm because the over-pressure valve in the system breaks at slightly below 1 atm.

Experiment 1

The laboratory reactor is a one rod reactor. The main characteristics of the seed rod used in this experiment are presented in table 6.3.

Table 6.3: Experiment 1: initial rod characteristics. Rod diameter / mm Rod length / mm Mass / g 7.0 560 49.8

The growth conditions for this ﬁrst experiment were quite conservative; the aim was to produce polysilicon and test the reactor. The growth conditions are depicted in table 6.4. The rod surface temperature was set to 1000 ◦C to avoid the dendritic growth. The results of the experiment are summarised in table 6.5. Sixty-four grams of polysilicon were grown in 24 hours. The diameter of the rod grew by around 4 mm in this time,

151 Chapter 6. Experimental approach

Table 6.4: Experiment 1: growth conditions.

Ts p H2 ﬂow rate TCS ﬂow rate TCS molar fraction time ◦C atm slm slm % h 1000 0.8 15 0.3 2 24.10

and the average growth rate was 1.3 µm·min−1. From the total amount of TCS introduced into the deposition chamber, 11.8% of the molecules were deposited onto the silicon rod. The estimated values for the growth rate and the silicon conversion are also presented, showing that the model provided good estimates for both. A picture of the rod after the polysilicon deposition is presented in ﬁgure 6.17. A more detailed picture of the rod surface is presented in ﬁgure 6.18.

Table 6.5: Experiment 1: comparison of experimental results and values predicted by the model presented in chapter 3.

Final rod Final vg Silicon Model vg Model silicon diameter / mm mass / g µm·min−1 conversion / % µm·min−1 conversion / % 10.8 114 1.3 11.8 1.2 9.6

Figure 6.17: Experiment 1: rod after polysilicon deposition.

Experiment 2

In this experiment the rod surface temperature was increased up to 1150 ◦C. The TCS ﬂow rate was also increased to 0.625 slm, raising the TCS molar fraction to 4%. Precise information about the rod used in this experiment is presented in table 6.6. The growth conditions are presented in table 6.7. The rod temperature was 1150 ◦C and the TCS molar fraction was 4%. The deposition time was 6.25 hours. After this time the rod broke due to dendritic growth.

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Figure 6.18: Experiment 1: detailed view of the rod after polysilicon deposition.

Table 6.6: Experiment 2: initial rod characteristics. Rod diameter / mm Rod length / mm Mass / g 6.1 560 38.6

Table 6.7: Experiment 2: growth conditions.

Ts p H2 ﬂow rate TCS ﬂow rate TCS molar fraction time ◦C atm slm slm % h 1150 0.8 15 0.625 4 6.25

The results of the experiment are summarised in table 6.8. The growth rate is 2.22 µm·min−1; although it should be noted that this is the quotient of the total mass grown and the deposition time, and therefore corresponds to the apparent growth rate in a smooth surface without dendritic growth. The growth was dominated by dendritic formation, as seen in figure 6.19, the deposition being promoted in preferred directions and forming pyramids with spaces between them. It is difficult to determine the growth rate in the dendrites, but it is certainly higher than the apparent growth rate. The low value of the silicon conversion can be explained by the dendritic growth. At a certain point of the deposition process, when the dendrites are formed, the TCS molecules have more difficulty in decomposing, and the silicon conversion is lower than predicted. There are two causes: the temperature of the pyramids is lower than the deposition temperature, because no current is flowing through them; and the reacting gases cannot easily reach the inner part of such an uneven surface.

The electric current was heavily concentrated within the rod core because of the non-

153 Chapter 6. Experimental approach

Table 6.8: Experiment 2: comparison of experimental results and values predicted by the model presented in chapter 3.

Final rod Final vg Silicon Model vg Model silicon diameter / mm mass / g µm·min−1 conversion / % µm·min−1 conversion / % 7.8 60.7 2.2 7.6 3.7 13.6

homegeneous growth, causing the rod to melt. In general, under dendritic growth conditions the deposition process must be stopped and the rod replaced.

Figure 6.19: Experiment 2: a detailed view of the rod after polysilicon deposition.

Experiment 3

In this experiment a high rod surface temperature of 1150 ◦C was maintained, and the amount of TCS entering the reactor was reduced. The aim was to analyse the dendritic formation during the polysilicon deposition, ﬁnding out the inﬂuence of the rod surface temperature and of the TCS concentration on the appearance of the dendritic growth. The initial characteristics of the rod are presented in table 6.9.

Table 6.9: Experiment 3: initial rod characteristics. Rod diameter / mm Rod length / mm Mass / g 6.3 560 40.5

The deposition conditions are presented in table 6.10. The pressure was set to 0.8 atm as mentioned before, and the TCS ﬂow rate was reduced to 0.3 slm, the TCS molar fraction being 2%. The temperature of the rod was maintained at 1150 ◦C. The deposition process took around 3.5 hours and was stopped because of dendritic formation. The results of the experiment are summarised in table 6.11. The apparent growth rate

154 6.3. Instituto de Energ´ıaSolar

Table 6.10: Experiment 3: growth conditions.

Ts p H2 ﬂow rate TCS ﬂow rate TCS molar fraction time ◦C atm slm slm % h 1150 0.8 15 0.3 2 3.42

was 2.7 µm·min−1 and the silicon conversion 19.1 %. The dendritic formation can be seen in ﬁgure 6.20.

Table 6.11: Experiment 3: results of the experiment and predicted values from the model presented in chapter 3.

Final rod Final vg Silicon Model vg Model silicon diameter / mm mass / g µm·min−1 conversion / % µm·min−1 conversion / % 7.4 55.1 2.7 19.0 1.8 13.9

In this experiment the dendrites are not as big as in the previous experiment, and consequently the silicon conversion and growth rate are both higher. The model predicts lower growth rate and lower silicon conversion. This is because the model does not consider dendritic growth.

Figure 6.20: Experiment 3: detailed view of the rod after polysilicon deposition.

Experiment 4

In this experiment the rod surface temperature was reduced to 1050 ◦C, with the aim of reducing the dendritic formation. The initial characteristics of the rod are presented in table 6.12. The growth conditions are presented in table 6.13. The main diﬀerence to the previously described experiment is the variation of the rod surface temperature. This experi-

155 Chapter 6. Experimental approach

Table 6.12: Experiment 4: initial rod characteristics. Rod diameter / mm Rod length / mm Mass / g 7.0 560 50.5

ment took more time: 11 hours. At the end of the experiment some dendritic formation was detected, and the experiment consequently stopped.

Table 6.13: Experiment 4: growth conditions.

Ts p H2 ﬂow rate TCS ﬂow rate TCS molar fraction time ◦C atm slm slm % h 1050 0.8 15 0.3 2 11.00

The results are presented in table 6.14. 40 g of polysilicon was grown, and no dendritic growth was detected until the very end. This can be seen in figure 6.21. The apparent growth rate was 2.6 µm·min−1, which differs from the estimated value of 1.7 µm·min−1. The silicon conversion, around 21.9%, is also very different to the value estimated by the model.

Table 6.14: Experiment 4: comparison of experimental results and values predicted by the model presented in chapter 3.

Final rod Final vg Silicon Model vg Model silicon diameter / mm mass / g µm·min−1 conversion / % µm·min−1 conversion / % 9.5 90.6 2.6 21.9 1.7 13.3

Figure 6.21: Experiment 4: a detailed view of the rod after polysilicon deposition.

156 6.3. Instituto de Energ´ıaSolar

Experiment 5

In this experiment more the rod surface temperature was reduced further to 1025 ◦C. The objective was to reduce or even avoid dendritic formation. The initial characteristics of the rod are presented in table 6.15.

Table 6.15: Experiment 5: initial rod characteristics. Rod diameter / mm Rod length / mm Mass / g 7.4 560 56.7

The only deposition condition which diﬀers from those of the previous experiment, presented in table 6.16, is the rod surface temperature, which was reduced to 1025 ◦C.

The TCS molar fraction at the inlet is 2% and the TCS and H2 ﬂow rates are 0.3 and 15 slm respectively. The deposition time was 7.7 hours, and the process ﬁnished when some dendritic formation was detected.

Table 6.16: Experiment 5: growth conditions.

Ts p H2 ﬂow rate TCS ﬂow rate TCS molar fraction time ◦C atm slm slm % h 1025 0.8 15 0.3 2 7.7

The results are summarised in table 6.17. A picture of the rod after the deposition process is shown in ﬁgure 6.22. At this temperature, dendritic formation also takes place; however, it can be seen that there are some lines along the silicon rod where the deposition is homogeneous with very localised dendrites, and other lines where the dendrites are strongly formed. This is because at this temperature an intermediate situation is found between the dendritic formation presented in experiment 4, which is very homogeneous along the surface, and the non-dendritic formation presented in experiment 1.

Table 6.17: Experiment 5: comparison of experimental results and values predicted by the model presented in chapter 3.

Final rod Final vg Silicon Model vg Model silicon diameter / mm mass / g µm·min−1 conversion / % µm·min−1 conversion / % 9.5 90.4 2.3 19.5 1.6 12.4

157 Chapter 6. Experimental approach

Figure 6.22: Experiment 5: a detailed view of the rod after polysilicon deposition.

Experiment 6

The previous experiments show that the temperature has a strong influence on dendritic formation. More experiments could be made reducing further the temperature. However, this has already been done, experiment 1 was made under the same conditions as experiment 5, but with a lower surface temperature, 1000 ◦C. It can be seen in the description of experiment 1 that no dendritic formation was noticed. This experiment seeks to find out if the molar fraction of TCS has any influence on dendritic formation; that is, if the dendrites can be avoided by lowering the TCS molar fraction. To answer this question, a molar fraction of 1% was chosen. The initial characteristics of the rod are presented in table 6.18.

Table 6.18: Experiment 6: initial rod characteristics. Rod diameter / mm Rod length / mm Mass / g 7.4 560 55.8

The growth conditions are presented in table 6.19. They are slightly diﬀerent from the growth conditions presented for the previous experiments. The rod temperature is, again, 1025 ◦C and the principal change is the reduction of the TCS molar fraction from 2% to

1%. The TCS and H2 flow rates are 0.23 and 22.5 slm respectively. The deposition time was 8.2 hours, and the process finished when some dendritic formation was detected. The results of this experiments are presented in table 6.20. The rod after the deposition process is shown in figure 6.23. It can be seen that the dendritic formation was not avoided by reducing the TCS molar fraction to 1%, but the growth rate was affected, having been reduced by 40% compared to experiment 5. Again, some lines along the rod can be seen where the dendritic formation is not as strong.

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Table 6.19: Experiment 6: growth conditions.

Ts p H2 ﬂow rate TCS ﬂow rate TCS molar fraction time ◦C atm slm slm % h 1025 0.8 22.5 0.23 1 8.2

Table 6.20: Experiment 6: comparison of experimental results and values predicted by the model presented in chapter 3.

Final rod Final vg Silicon Model vg Model silicon diameter / mm mass / g µm·min−1 conversion / % µm·min−1 conversion / % 8.9 79.5 1.5 16.7 1.0 9.6

Figure 6.23: Experiment 6: a detailed view of the rod after polysilicon deposition.

6.3.4 Summary of experiments

Six experiments were successfully carried out in which polysilicon was produced with or without dendrites. These are summarized in table 6.21. There were also some unsuccessful experiments performed at the laboratory: the silicon rods melted in several experiments when we started working with the system; the trichlorosilane mass flow controller failed in some experiments and had to be changed; etc. Trichlorosilane is a difficult gas to work with and handle. As mentioned, one mass flow controller broke because the trichlorosilane liquefied, and needed to be substituted by another mass flow controller suitable to work at 80 ◦C. The exhaust and vacuum pumps required notable maintenance, and in some cases professional cleaning was required to eliminate the oxidation formed. The scrubber filled up after each 10 kg of trichlorosilane used, which meant around 90 hours of processing. It was therefore very challenging to grow polysilicon from trichlorosilane decomposition in the laboratory. Dendritic growth took place in five experiments out of six, the main deposition param-

159 Chapter 6. Experimental approach

P PP PP TCS PP 1% 2% 3% PP Rod T PPP 1150 ◦C Experiment 3a Experiment 2a 1050 ◦C Experiment 4a 1025 ◦C Experiment 6a Experiment 5a 1000 ◦C Experiment 1

aDendritic growth observed.

Table 6.21: Map of the experiments at the IES deposition reactor.

eter changed being the temperature. Above 1000 ◦C the dendrites do not allow proper growth of polysilicon and the experiments in this temperature regime were stopped pre- maturely. The model predicted the growth rate well in the first experiment, where no dendrites were formed. The rest of experiments were characterised by the dendritic growth and under such conditions the model predicted values far from those measured. Further experiments are required to extract adequate conclusions, to analyse for instance the effect of the pressure or the effect of the gas composition at the inlet on the dendrites formation.

6.4 Conclusions

The experimental work presented in this chapter comprises two parts: the experiments carried out at the LBNL, and the experiments carried out at the IES. At the LBNL, polysilicon was grown through silane decomposition and the purity of the material produced was analysed by LA-ICP-MS. Producing polysilicon through silane decomposition is more eﬃcient, at the laboratory level, than through trichlorosilane decomposition, since almost every silane molecule can be converted to polysilicon (the overall deposition eﬃciency can be up to 97%). The LA-ICP-MS technique was used to analyse the purity of the material, showing that Mg, Ti, Cu and Zn were found in the polysilicon sample. The lack of a reference material prevents any conclusion regarding the amount of these impurities in the polysilicon to be inferred. An important future work is make this measurement quantitatively using a reference material. At the Instituto de Energ´ıaSolar we have designed and developed a one-rod deposition reactor. The experiments carried out were based on the decomposition of trichlorosilane.

160 6.4. Conclusions

Dendritic growth appeared in five experiments, in which the temperature was above 1000 ◦C. In one experiment, at 1000 ◦C, the polysilicon growth was very good and the surface of the rod after the deposition process was uniform. Further experiments are needed to evaluate what influences the dendritic growth. It is sensible to identify the rod temperature as an important parameter influencing this phenomena, but more work is needed to know if the composition of the gas at the inlet or the pressure within the reactor have any influence. The system at the IES is not a closed loop, and consequently the overall deposition efficiency cannot be as high as when working with silane in a closed loop. The overall deposition efficiency in our system was never above 20%, compared with values around 97% for silane in a closed loop. The experimental work developed in this thesis is a first step for producing polysilicon, and valuable information has been obtained; not only scientific knowledge but also technical skills for working with this kind of system, based on trichlorosilane decomposition.

161 Chapter 6. Experimental approach

162 Chapter 7

Conclusions and future works

This Doctoral Thesis comprises research on the reduction of cost and energy consumption of the production of ultrapuriﬁed silicon, so-called polysilicon. These respective reductions are essential to achieving two wider objectives for silicon based photovoltaic technology: low production cost and low energy payback time.

A crystalline silicon photovoltaic module technology is defined and its production costs are presented. This allows cost and energy reduction measures to be compared and valued with regard to their impact on the final product. It further permits a cost-per-kilowatt comparison of the two main polysilicon production routes: the chemical route, with high quality and high cost; and the metallurgical route, with lower quality and lower cost. This costing exercise shows the quality of polysilicon (evaluated as the cell efficiency) to be an important driver for module cost-per-kilowatt reduction. Consequently, the presented research focuses on the high-quality chemical route.

The presented theoretical analysis of polysilicon deposition in a CVD reactor consists in: (a) the study of the optimum deposition conditions by means of ﬂuid mechanical theory; (b) the study of the thermal radiation of the hot silicon rods by means of thermal radiation heat transfer theory; and (c) the study of the electric heating of the silicon rod by means of electromagnetic theory.

A novel ﬂuid mechanical model is presented that proposes analytical expressions for the growth rate of polysilicon onto the silicon rods and for the energy loss by convection. The optimum deposition conditions, which reduce energy consumption, are derived from the model.

The thermal radiation heat transfer within the CVD reactor is studied in detail for three state-of-the-art conﬁgurations: 36 rods arranged in 3 rings, 48 rods arranged in 3 rings and 60 rods arranged in 4 rings. Alternatives are presented regarding the reduction

163 Chapter 7. Conclusions and future works

of the radiant energy loss during the polysilicon deposition: enlarge the reactor capacities, enhance the wall reflectivity and introduce thermal shields within the reactor vessel. An important factor affecting overall energy consumption is the maximum rod diameter reached at the end of the process. The main limitation for increasing this maximum diameter is the risk of melting the rod core. The temperature profile within the silicon rod resulting from electrical heating is modelled, and the limiting diameter at which the core begins to melt is calculated. Two alternatives are proposed for increasing the maximum diameter by reducing the non-homogeneous temperature profile: increasing the wall reflectivity/introducing thermal shields, and use of a high-frequency current source to heat the rods. Based on the presented theoretical study, a complete deposition process is proposed that is characterised by low energy consumption. The deposition conditions and the electrical conditions (current and voltage) for heating rods in a 36 rods CVD reactor are detailed. Finally, polysilicon deposition has been studied experimentally, and the practicability of the calculated optimum conditions has been tested. Silicon rods have been grown in the laboratory scale deposition reactor, designed, developed and constructed, in part by the author, at the Instituto de Energ´ıaSolar, using trichlorosilane and silane as prescursor gases. The experiments show the difficulty in working under the optimum conditions: undesirable dendritic growth was observed, and the trichlorosilane was seen to corrode the reactor. Further experimental study is required in the future to fully understand the polysilicon deposition process in a CVD reactor.

7.1 Conclusions

The principal conclusions of this Doctoral Thesis are summarised in the following paragraphs.

1. Data provided by photovoltaic manufacturing companies has shown costs to be in −1 the range of 2.0-2.3 e·Wp by the end of 2005, for 30-50 MWp/year level production. The combined eﬀects of technology development and economies of scale bring the direct manufacturing costs of crystalline silicon photovoltaic modules down to 1.15 −1 e·Wp . By comparing the total cost ﬁgures for Basepower (the 2005 reference technology) with Advanced Basepower (the 2009 reference technology produced in large scale plants), it is concluded that the reduction obtained by technology development −1 −1 is roughly 0.5 e·Wp , while economies of scale subtract a further 0.5 e·Wp .

2. Regarding the impact of alternative feedstock on the Advanced Basepower module

164 7.1. Conclusions

cost, the author concludes that if the cell efficiency can be maintained at 15.8%, the variation of feedstock processing cost - from near semiconductor grade silicon to upgraded metallurgical grade silicon - reduces the total manufacturing cost of crystalline silicon modules by 11%. However, the cost advantage of low-cost feedstock utilisation is completely lost if cell efficiency is below 14.1% (a relative drop of 11%), due to quality degradation. It is also concluded that variations of feedstock yield and variations of ingot-growth fraction only weakly affect low-cost feedstock users, since the minimum values required to be cost competitive are well within reach.

3. The rod temperature and the reactor pressure are very inﬂuential factors in the polysilicon deposition process in a CVD reactor. However, comparing the two, the rod surface temperature has a stronger inﬂuence on the process than the pressure. Regarding the rod surface temperature, it is concluded that there is an optimum deposition temperature betweeen 1100-1200 ◦C, depending on the rod radius. The optimum deposition temperature may not be reached because of dendritic growth, but as a general trend, the deposition temperature should be as close as possible to the optimum. Considering the pressure, it is also concluded that an optimum pressure is found at 6 atm, since increasing the pressure above this value does not produce a noteworthy variation on the energy consumption. Both optimum pressure and optimum temperature are based on the low energy consumption criterion.

4. The deposition conditions vary during the process as the rods thicken. With the objective of reducing energy consumption, a polysilicon deposition process is proposed in which the deposition conditions throughout the complete process are deﬁned. The rod temperature is set to 1050 ◦C and the pressure to 6 atm. The hydrogen molar fraction is in the range 0.78-0.88; 0.88 at the beginning of the process and 0.78 at the end. The gas mixture ﬂow rate is varied almost linearly with the rod radius, the starting value is 10 kmol·h−1 and the value at the end of the process is 33 kmol·h−1. The deposition time is 115 hours, and 2570 kg of polysilicon are produced. The silicon conversion (trichlorosilane to polysilicon) is 10%. The average growth rate is 10 µm·min−1 and the energy consumption is 47 kWh·kg−1.

5. The eﬀect of enlarging the reactor capacity is quantiﬁed. The energy radiated by the rods is reduced by 10% when comparing the 48 rod CVD reactor to the 36 rod CVD reactor, and by 20% when comparing the 60 rod reactor to the 36 rod reactor. This latter case corresponds to a reduction of around 11 kWh per kg of polysilicon produced. Translated to cost savings, considering an energy cost of 8 ce/kg, the

165 Chapter 7. Conclusions and future works

reduction of cost is around 0.88 e per kg of polysilicon produced. In a 5000 t/year polysilicon plant this corresponds to savings of up to 4.4 million e/year.

6. The impact of introducing thermal shields within the CVD reactor is also quantiﬁed. This option has a great potential for cost savings, since the energy savings are around 20 kWh per kg of polysilicon produced. Nevertheless, the temperature that these devices reach allows polysilicon to be deposited over them. It is estimated that a layer of 4 mm would be grown over the shields. The energy savings would mean a cost reduction of around 1.6 e per kg of polysilicon produced. In a 5000 t/year plant the savings would be 8 million e/year.

7. The inﬂuence of the wall emissivity is also studied. It is concluded that if the wall emissivity were improved from 0.5 to 0.3, by selecting better materials or by any surface treatment, the energy savings would be around 17 kWh per kg of polysilicon produced. This means cost savings of around 1.36 e per kg of polysilicon produced. In a 5000 t/year polysilicon plant the savings would be around 6.8 million e/year.

8. Theoretically, the limiting surface temperature before rod melting is always, inde- pendently of the wall emissivity, above the optimum temperature, considering rod diameters from 1 to 20 cm. Melting the rod core does not therefore introduce a limitation for stopping the process. It is thus concluded that the maximum rod diameter can be increased up to 20 cm. The resultant reduction in energy consumption is 13 kWh·kg−1 compared to stopping the process at 14 cm. This reduction is similar to that of enlarging the reactor capacity from 36 to 60 rods. Translated to cost savings, the reduction is around 1.04 e per kg of polysilicon produced. In a 5000 t/year polysilicon plant the savings would be up to 5.2 million e/year.

9. The utilisation of a high frequency current source to heat the silicon rods is beneficial when used in the outer ring, however, its impact on the rest of the rings is very low. The frequency of the current source should be around 100 kHz; above this value there is no noteworthy improvement in the temperature profile. This alternative requires less current for heating the rods but the same power. High frequency current sources lead to vibrations in the silicon rod. Vibrational analysis shows that this affects the rod stability. The use of high frequency current sources is not therefore advisable.

10. A laboratory scale deposition reactor has been designed, developed and constructed at the Instituto de Energ´ıa Solar. Polysilicon has been produced in this reactor under favourable conditions.

166 7.2. Future works

7.2 Future works

Proposed future work is summarised as follows, Dendritic formation

• This phenomena has to be carefully studied; the physical and chemical aspects of dendritic growth must be understood. Special attention should be paid to its dependence on the crystallographic orientation of the polysilicon rod

CVD model

• Once dendritic formation is understood, the model should be reﬁned to provide accurate estimation of this phenomenon under given conditions

Radiation

• The model can be improved by introducing exact conﬁguration factors instead approximated ones

• The radiation model should be tested using the 36 rod CVD reactor at CENTESIL

• Diﬀerent materials should be tested for use in the wall and/or thermal shield, and the optimum materials chosen

Electric heating

• The maximum rod diameter of 20 cm should be achieved experimentally

• When increasing the maximum rod diameter, the ﬁrst parts of the U-rod that melt are its corners. This problem should be addressed. Its impact on the maximum rod diameter should be studied and solutions proposed

Experimental

• More experiments must be carried out to validate the deposition model

• The eﬀect of the pressure, temperature, gas ﬂow and gas composition on the formation of dendrites should be analysed

• Enough polysilicon should be produced at the lab-scale reactor to grow a single- crystal; wafers could then be cut and solar cells processed.

• A reference material should be chosen for carrying out a quantitative analysis using the LA-ICP-MS technique

• Other techniques for evaluating the quality of the material should be explored

167 Chapter 7. Conclusions and future works

168 Appendix A

Derivation of the solutions for the conservation equations

A.1 Temperature distribution

The equation of change for temperature is used to obtain the temperature distribution

∂T 1 ∂ ∂T ρC v = κ · r (A.1-1) p z ∂z r ∂r ∂r

In this equation the variation of thermal conductivity with temperature can be ignored according to the following reasoning [Bird et al., 2002; Neufeld et al., 1972]

0.5+0.14874 0.64874  T T κ ' κ0 · = κ0 ·  T0 T0    dκ 1 0.64874−1 ≤ κ (A.1-2) dκ κ0 T dT T ' ·  0 dT T0 T0    where T0 is the gas temperature at the entrance of the reactor, whose value is ﬁxed at

T0 = 773K. It is shown that the thermal conductivity is about 773 times greater than its derivative, and therefore the latter can be ignored in the equation and the former can be outside the derivative. According to equations (3.30) and (A.1-2), the equation (A.1-1) can be expressed as

∂∆T 1 ∂ ∂∆T ρ C v = κ · r (A.1-3) 0 p 0 ∂z r ∂r ∂r where ∆T (r, z) = T (r, z) − Ts. The separation of variables method applied to eq. (A.1-3) leads to ! θ2κz ∆T (r, z) = exp − (AJ0 (θr) + BY0 (θr)) (A.1-4) ρ0v0Cp

169 Appendix A. Derivation of the solutions for the conservation equations

J0 and Y0 are the ﬁrst and second kind bessel functions of order zero, respectively. The boundary conditions for ∆T are: (i) the temperature of the gas on the rod surface is Ts,

∆T (ri, z) = 0, (ii) adiabatic condition in ro, ∂∆T/∂r(ro, z) = 0 and (iii) constant and known temperature distribution at the reactor entrance, ∆T (r, 0) = ∆T0. Conditions (i) and (ii) yield a relation that θ has to fulﬁll to be part of the solution of the problem

J0 (θri) Y1 (θro) − J1 (θro) Y0 (θri) = 0 (A.1-5)

The set of solutions of this equation is {θn}. Condition (iii) leads to the solution by means of the following summatory ! ∞ θ2 κz ∆T (r, z) = ∆T · X A · exp − n χ (r) (A.1-6) 0 n ρ v C n n=0 0 0 p

An are the coeﬃcient corresponding to the orthogonal function χn, calculated following the Sturm-Liouville conditions, and κ the thermal conductivity at Tm = (Ts − T0)/2. J0 (θnri) χn(r) = J0 (θnr) − Y0 (θnr) = (J0 (θnr) − αn · Y0 (θnr)) (A.1-7) Y0 (θnri) Z ro ri rχn(r)dr − [J1(θnri) − αn · Y1(θnri)] ri θn An = Z ro = (A.1-8) 2 1 h 2 2 2 i rχn(r)dr · ro · χn(ro) − ri (J1(θnri) − αn · Y1(θnri)) ri 2

A.2 Mass fraction distribution: growth limited by H2

The conservation of individual species mass equation for species i is ∂w 1 ∂ ∂w ρv i = ρD · r i (A.2-1) z ∂z r ∂r i ∂r

It is assumed that the ρDi dependence on temperature is negligible according to the following reasoning [Bird et al., 2002; Neufeld et al., 1972]

0.6561  T ρDi ' ρ0Di0 ·  T0     d (ρDi) 1 0.6561−1 ≤ ρDi (A.2-2) dρDi ρ0Di0 T dT T ' ·  0 dT T0 T0   

Then, taking into account equations (3.30) and (A.2-2), the partial derivative equation yields v ∂w 1 ∂ ∂w 0 i = r i (A.2-3) Di0 ∂z r ∂r ∂r

It has to be noted that Di0 stands for the binary diﬀusion coeﬃcient at the inlet temperature between HSiCl3 and H2 in the case of i=HSiCl3,H2 and between HCl and H2 in the case of i=HCl.

170 A.3. Mass fraction distribution: growth limited by HSiCl3 after limitation change

The equation system is solved for hydrogen, with its boundary conditions shown in equations (3.43)-(3.45): (i) mass fraction at the entrance: known and constant, (ii) closed boundary at ro and (iii) the diffusion flux driven by the concentration is equal to the rate of mass consumption or generation at ri. The separation of variables method applied to equation (A.2-3) leads to the following solution ! ∞ θ2 D z w (r, z) = w · X A · exp − n h20 β (r) (A.2-4) h2 h20 n v n n=0 0 where {θn} is the set of solutions of equation (A.2-5) and An are the coefficient corresponding to the orthogonal functions βn, calculated following the Sturm-Liouville conditions.

ρskr ρskr Y0(θri) + θY1(θri) J1(θro) − J0(θri) + θJ1(θri) Y1(θro) = 0 (A.2-5) ρ0Dh20 ρ0Dh20 J1 (θnro) βn(r) = J0 (θnr) − Y0 (θnr) = (J0 (θnr) − γn · Y0 (θnr)) (A.2-6) Y1 (θnro) r − i [J (θ r ) − γ · Y (θ r )] θ 1 n i n 1 n i A = n (A.2-7) n 1 h i · r2 · β (r )2 − r2 · β (r )2 − r2 (J (θ r ) − γ · Y (θ r )) 2 o n o i n i i 1 n i n 1 n i

A.3 Mass fraction distribution: growth limited by HSiCl3 after limitation change

The equation solved is (A.2-3). The limitation is considered to change in zl, i.e, wh2 (ri, zl) = w = w . The boundary conditions, presented in equations (3.51)-(3.53), are: (i) h2lim h2zl the mass fraction at the limitation point, zl, is known, (ii) closed boundary at ro and (iii) the diﬀusion ﬂux driven by the concentration is equal to the rate of mass consumption or generation at ri.

The equation for HSiCl3 is solved and its mass fraction is obtained by means of the following summatory

! ∞ η2D (z − z ) w (r, z) = X B · exp − n tcs0 l δ (r) ∀z > z (A.3-1) tcs n v n l n=0 0 where {ηn} is the set of solutions to equation (A.3-2) and Bn are the coeﬃcient corresponding to the orthogonal functions δn.

ρskad ρskad Y0(ηri) + ηY1(ηri) J1(ηro) − J0(ηri) + ηJ1(ηri) Y1(ηro) = 0(A.3-2) ρ0Dtcs0 ρ0Dtcs0 J1 (ηnro) δn(r) = J0 (ηnr) − Y0 (ηnr) = (J0 (ηnr) − γn · Y0 (ηnr))(A.3-3) Y1 (ηnro)

171 Appendix A. Derivation of the solutions for the conservation equations

The method for obtaining Bn is the same as for obtaining An, but there is one more integral involved that should be known,

r Z o 1 ρs rβm(r)δn(r)dr = − 2 2 · · (kad − kr) · riβm(ri)δn(ri) ∀n, m (A.3-4) ri θm − ηn ρ0Dtcs0

172 Bibliography

J. Ager, J. Beeman, W. Hansen, and E. Haller. Design, construction, and operation of a laboratory scale reactor for the production of high-purity, isotopically enriched bulk silicon. Technical report, Lawrence Berkeley National Laboratory, 2004.

J. Ager, J. Beeman, W. Hansen, E. Haller, I. Sharp, C.Liao, A.Yang, M. Thewalt, and H. Riemann. High purity, isotopically enriched bulk silicon. Journal of the Electrochem- ical Society, 152:448–451, 2005.

V. Alex, S. Finkbeiner, and J. Weber. Temperature dependence of the indirect energy gap in crystalline silicon. Journal of Applied Physics, 79(9):6943–6946, 1996.

E. Alsema and M. de Wild-scholten. Reduction of the environmental impacts in crystalline silicon module manufacturing. In 22nd European Photovoltaic Solar Energy Conference and Exhibition, pages 829–836, Milan, 2007.

N. Arora, J. Hauser, and D. Roulston. Electron and hole mobilities in silicon as a function of concentration and temperature. IEEE Transaction on Electron devices, 29:292–295, 1982.

J. S. Becker. Inorganic Mass Spectrometry: Principles and Applications. Wiley, 2007.

R. B. Bird, W. E. Steward, and E. N. Lightfoot. Transport Phenomena. John Wiley & Sons, Inc., 2002.

T. M. Bruton. A study of the manufacture at 500 mwp p.a. of crystalline silicon photovoltaic modules. In 14th European Photovoltaic Solar Energy Conference, pages 11–16, Barcelona, 1997.

E. Bugl, R. Griesshammer, H. Lorenz, H. Hamster, and F. K¨oppl.Method for the deposition of pure semiconductor material. Patent US4311545, 1982.

G. Bye. Renewable energy corporation. In 3rd Solar Silicon Conference, 2006.

173 Bibliography

K. Carleton, J. Olson, and A. Kibbler. Electrochemical nucleation and growth of silicon in molten ﬂuorides. Journal of the electrochemical society, 130(4):782–786, 1983.

D. Caughey and R. Thomas. Carrier mobilities in silicon empirically related to doping and ﬁeld. In Proceedings of the IEEE, 1967.

B. Ceccaroli and O. Lohne. Handbook of Photovoltaic Science and Engineering, chapter Solar Grade Silicon Feedstock, pages 153–205. John Wiley & Sons, 2003.

A. J. Chapman. Heat Transfer. MacMillan, 1984.

P. Choulat, G. Agostinelli, Y. Ma, F. Duerinckx, and G. Beaucarne. Above 17silicon substrate. In 22nd European Photovoltaic Solar Energy Conference and Exhibition, pages 1011–1015, Milan, 2007.

B. Cullity and S. Stock. Elements of X-Ray Diﬀraction. Addison-Wesley Publishing company, 2001.

M. de Wild-Scholten, R. Glockner, J. O. Odden, G. Halvorsen, and R. Tronstad. Environ- mental life cycle assessment of the elkem solar metallurgical process route to solar grade silicon with focus on energy consumption and greenhouse gas emissions. In Silicon for the chemical and solar industry IX, pages 235–241, 2008.

C. del Ca˜nizo,A. Luque, J. Bull´on,A. Miranda, J. M´ınguez, H. Riemann, and N. Abrosi- mov. Integral procedure for the fabrication of solar cells on solar silicon. In 20st European Photovoltaic Solar Energy Conference, 2005.

G. del Coso, I. Tob´ıas,C. del Ca˜nizo,and A. Luque. Temperature homogeneity of polysilicon rods in a siemens reactor. Journal of Crystal Growth, 299:165–170, 2007.

G. del Coso, C. del Ca˜nizo,and A. Luque. Chemical vapor deposition model of polysilicon in a trichlorosilane and hydrogen system. Journal of the Electrochemical Society, 155: D485–D491, 2008.

G. del Coso, C. del Ca˜nizo, and A. Luque. Radiative energy loss in a polysilicon cvd reactor. Solar Energy Materials and Solar Cells, submitted, 2010a.

G. del Coso, C. del Ca˜nizo,and W. Sinke. The impact of silicon feedstock on the PV module cost. Solar Energy Materials and Solar Cells, 94(2):345–349, 2010b.

J. Dietl. Silicon processing for photovoltaics II, chapter Metallurgical ways of silicon melt- stock processing, pages 285–351. Elsevier science, 1987.

174 Bibliography

S. Dubois, N. Enjalbert, and J. P. Garandet. Slow down of the light-induced-degradation in compensated solar-grade multicrystalline silicon. Applied physics letters, 93(10), 2008.

European Photovoltaic Technology Platform. A strategic research agenda for photovoltaic solar energy technology. Technical Report ISBN 978-92-79-05523-2, 2007.

F. Eversteijn. Chemical-reaction engineering in the semiconductor industry. Philips research reports, 26:45–66, 1974.

F. Faller and A. Hurrle. High-temperature cvd for crystalline-silicon thin-ﬁlm solar cells. IEEE Transactions on electron devices, 46:2048–2054, 1999.

G. Flamant, V. Kurtcuoglu, J. Murray, and A. Steinfeld. Puriﬁcation of metallurgical grade silicon by a solar process. Solar Energy Materials and Solar Cells, 90(14):2099 – 2106, 2006.

H. Flynn and T. Bradford. Polysilicon supply, demand, & implications for the pv industry. Technical report, Prometheus Institute for Sustainable Development, 2006.

H. Flynn, M. Meyers, and M. Rogol. Is mr. homan losing sleep yet? Photon International, 6:144–145, 2008.

V. Fthenakis and E. Alsema. Photovoltaics energy payback times, greenhouse gas emissions and external costs: 2004-early 2005 status. Prog Photovolt: Res. Appl., (14): 275–280, 2006.

G. A. Greene, C. C. Finfrock, and T. F. Irvine. Total hemispherical emissivity of oxidized Inconel 718 in the temperature range 300-1000 ◦C. Experimental Thermal and Fluid Science, 22(3-4):145 – 153, 2000.

Greenpeace and EPIA. Solar generation iv 2007 - solar electricity for over one billion people and two million jobs by 2020. Technical report, 2007.

S. Grove. Physics and Technology of Semiconductor Devices. Wiley, 1967.

D. G¨unther. Laser-ablation inductively-coupled plasma mass spectrometry. Analytical and Bioanalytical Chemistry, 372:31–32, 2002.

D. G¨unther, I. Horn, and B. Hattendorf. Recent trends and developments in laser ablation- icp-mass spectrometry. Fresenius’ Journal of Analytical Chemistry, 368:4–14, 2000.

H. Gutsche. Method for producing highest-purity silicon for electric semiconductor devices. Patent US3042494, 1962.

175 Bibliography

H. Habuka, T. Nagoya, M. Mayusumi, M. Katayama, M. Shimada, and K. Okuyama.

Model on transport phenomena and epitaxial growth of silicon thin ﬁlm in SiHCl3-H2 system under atmospheric pressure. Journal of Crystal Growth, 169:61–72, 1996.

S. Han and H. Benaroya. Non-linear coupled transverse and axial vibration of a compliant structure, part 1: formulation and free vibration. Journal of Sound and Vibration, 237: 837–873, 2000.

S. Han, H. Benaroya, and T. Wei. Dynamics of transversely vibrating beams using four engineering theories. Journal of sound and vibration, 225(5):935–988, 1999.

K. Hashimoto, K. Miura, T. Masuda, M. Toma, H. Sawai, and M. Kawase. Growth kinetics of polycrystalline silicon from silane by thermal chemical vapor deposition method. Journal of the Electrochemical Society, 137:1000–1007, 1990.

H. Heaton, W. C. Reynolds, and W. Kays. Heat transfer in annular passages: simultaneous development of velocity and temperature ﬁelds in laminar ﬂow. Int. J. Heat Mass Transfer, 7:763–781, 1964.

C. Herrick and D. Woodruﬀ. The homogeneus nucleation of condensed silicon in the gaseous si-h-cl system. Journal of the Electrochemical Society, 131:2419–2422, 1984.

K. Hesse, E. Schindlbeck, and H.-C. Freiheit. An overview on silicon feedstock. In 23rd European Photovoltaic Solar Energy Conference and Exhibition, pages 61–67, 2007.

K. Hesse, E. Schindlbeck, and H.-C. Freiheit. Challenges of solar silicon production. In Silicon for the chemical and solar industry IX, pages 61–67, 2008.

W. Hirshman, G. Hering, and M. Schmela. Gigawatts - the measure of things to come. Photon International, 3:136–166, 2007.

M. Hofmann, D. Erath, L. Gautero, J. Nekarda, A. Grohe, D. Biro, J. Rentsch, and B. Bitnar. Industrial type cz silicon solar cells with screen-printed ﬁne line front contacts and passivated rear contacted by laser ﬁring. In 23rd European Photovoltaic Solar Energy Conference and Exhibition, Valencia, 2008.

J. Hofstetter, J. F. Leli`evre,C. del Ca˜nizo,and A. Luque. Acceptable contamination levels in solar grade silicon: From feedstock to solar cell. Materials Science and Engineering: B, 159-160:299–304, 2009.

W. L. Holstein. Thermal diﬀusion in metal-organic chemical vapor deposition. Journal of the Electrochemical Society, 135:1788–1793, 1988.

176 Bibliography

R. Hull, editor. Properties of Crystalline Silicon. Inspec, 1999.

L. Hunt. Handbook of semiconductor silicon technology, chapter Silicon precursors: their manufacture and properties, pages 1–32. Noyes Publications, 1990.

N. Jull. View factors in radiation between two parallel oriented cylinders of ﬁnite length. Journal of Heat Transfer, 104:384–388, 1982.

M. Kaes, G. Hahn, K. Peter, and E. Enebakk. Over 18feedstock from a metallurgical process route. In Conference Record of the 2006 IEEE 4th World Confer- ence on Photovoltaic Energy Conversion, volume 1, pages 873–878, May 2006. doi: 10.1109/WCPEC.2006.279596.

D. Keck. Polysilicon production costs. In The Seventh Solar Silicon Conference, 2009.

E. V. Kerschaver and G. Beaucarne. Back contact solar cells: a review. Prog Photovolt: Res. Appl., (14):107–123, 2006.

E. V. Kerschaver, R. Einhaus, J. Szlufcik, J. Nijs, and R. Mertens. A novel silicon solar cell structure with both external polarity contacts. In 2nd World Conf. and Exhib. Photovoltaic Solar Energy Conversion, pages 1479–1482, 1998.

M. Keshner and R. Arya. Study of potential cost reductions resulting from super-large- scale manufacturing of pv modules. Technical Report NREL/SR-250-36846, 2004.

H. Y. Kim, K. Yoon, Y. Park, and W. Choi. Preparation of polysilicon granules with a new ﬂuidized bed deposition process. In Silicon for the chemical and solar industry X, pages 259–260, 2010.

F. K¨oppl,H. Hamster, R. Griesshammer, and H. Lorenz. Process for the deposition of pure semiconductor material. Patent US4179530, 1979.

A. Kress, R. K¨uhn,P. Fath, G. Willeke, and E. Bucher. Low-cost back contact silicon solar cells. IEEE Trans. Electron. Devices, 46(10):2000–2004, 1999.

A. Kreutzmann and M. Schmela. Emancipation from subsidy programs. Photon Interna- tional, 12:84–92, 2008.

R. Kvande. Solar cells manufactured from silicon made by the solsilc process. In Silicon for the chemical and solar industry X, pages 191–202, 2010.

A. Luque. Photovoltaic market and costs forecast based on a demand elasticiety model. Progress in photovoltaics: research and applications, 9:303–312, 2001.

177 Bibliography

D. Macdonald, F. Rougieux, A. Cuevas, B. Lim, J. Schmidt, M. Di Sabatino, and L. J. Geerligs. Light-induced boron-oxygen defect generation in compensated p-type czochralski silicon. Journal of Applied Physics, 105(9):7, 2009.

M. Masi, M. D. Stanislao, and A. Veneroni. Fluid-dynamics during vapor epitaxy and modeling. Progress in Crystal Growth and Characterization of Materials, 47:239–270, 2003.

J. McCormick. Silicon processing for photovoltaics I, chapter Polycrystalline silicon technology requirements for photovoltaic applications, pages 2–47. Elsevier science, 1985.

L. P. M´endez. Sintesis de clorosilanos para la industria fotovoltaica. PhD thesis, Univer- sidad Complutense de Madrid - Facultad de ciencias quimicas, 2009.

M. Meyers. Incumbents face the future. Photon International, 7:100, 2009a.

M. Meyers. Taking stock. Photon International, 8:82, 2009b.

A. Mozer and P. Fath. Design criteria for polysilicon factories. In 3rd Solar Silicon Conference, 2006.

B. N. Mukashev, K. A. Abdullin, M. F. Tamendarov, T. S. Turmagambetov, B. A. Beketov, M. R. Page, and D. M. Kline. A metallurgical route to produce upgraded silicon and monosilane. Solar energy materials and solar cells, 93(10):1785–1791, 2009.

A. Muller, R. Sonnenschein, T. Sill, A. Golz, C. Beyer, J. Piotraschke, D. B. D. Kaden and, and S. Stute. The sunsil-process: The most energy-eﬃcient process to produce solar grade silicon. In 24th European Photovoltaic Solar Energy Conference and Exhibition, pages 61–67, 2009.

J. Nelson. The physics of solar cells. Imperial College Press, 2003.

P. D. Neufeld, A. Janzen, and R. Aziz. Empirical equation to calculate 16 of the transport collision integrals for the leonard-jones potential. The Journal of Chemical Physics, 57: 1100–1102, 1972.

H. Oda. Solar grade silicon from tokuyama. In 1st Solar Silicon Conference, 2004.

J. O. Odden, G. Halvorsen, H. Rong, and R. Glockner. Comparison of the energy consumption in diﬀerent production processes for the solar grade silicon. In Silicon for the chemical and solar industry IX, pages 75–89, 2008.

178 Bibliography

K. Peter, R. Kopecek, A. Soiland, and E. Enebakk. Future potential for sog-si feedstock from the metallurgical process route. In 23rd European Photovoltaic Solar Energy Con- ference and Exhibition, Valencia, 2008.

M. D. Pickett and T. Buonassisi. Iron point defect reduction in multicrystalline silicon solar cells. Applied physics letters, 92:122–103, 2008.

R. Pierret. Modular Series on solid state devices: Volume I Semiconductor Fundamentals. Addison-Wesley Publishing company, second edition, 1982.

N. Ravindra, B. Sopori, O. Gokce, S. Cheng, A. Shenoy, L. Jin, S. Abedrabbo, W. Chen, and Y. Zhang. Emissivity measurements and modeling of silicon-related materials: An overview. International Journal of Thermophysics, 22:1593–1611, 2001.

K. Reuschel and A. Kersting. Method for producing hyperpure silicon. Patent US3057690, 1962.

H.-J. Rodr´ıguezSan Segundo. Desarrollo de un reactor epitaxial de alta capacidad de produccion para la fabricaciónde célulassolares. PhD thesis, Universidad Politécnica de Madrid - Escuela TécnicaSuperior de Ingenieros de Telecomunicación,2007.

L. Rogers. Handbook of semiconductor silicon technology, chapter Polysilicon preparation, pages 33–94. Noyes Publications, 1990.

M. Rogol. Have fundamentals collapsed for si? In The Sixth Solar Silicon Conference, 2008.

M. Rogol. Silicon 2010: two sports with one name. In 8th Solar Silicon Conference, 2010.

A. Rohatgi. Road to cost-eﬀective crystalline silicon photovoltaics. In 3rd World Confer- ence on Phofovoltaic Energy Conversion, 2003. Carpeta1/Seccion5.

I. Romijn, A. Mewe, M. Lamers, E. Kossen, E. Bende, and A. Weeber. An overview of mwt cells and evolution to the aspira concept: a new integrated mc-si cell and module design for the high-eﬃciencies. In 23rd European Photovoltaic Solar Energy Conference and Exhibition, Valencia, 2008.

D. E. Rosner. Transport Processes in Chemically Reacting Flow Systems. Dover Publica- tions, 2000.

S. Rousseau, M. Benmansour, D. Morvan, and J. Amouroux. Puriﬁcation of MG silicon by thermal plasma process coupled to DC bias of the liquid bath. Solar energy materials and solar cells, 91(20):1906–1915, 2007.

179 Bibliography

J. Ruiz, G. Aparicio, and G. Sala. F´ısica de dispositivos electr´onicos. Servicio de Publica- ciones ETSIT-UPM, ﬁrst edition, 1982.

R. Russo, X. Mao, H. Liu, J. Gonz´alez,and S. S. Mao. Laser ablation in analytical chemistry - a review. Talanta, 57:425–451, 2002.

R. E. Russo, X. L. Mao, C. Liu, and J. Gonzalez. Laser assisted plasma spectrochemistry: laser ablation. Journal of Analytical Atomic Spectrometry, 19:1084–1089, 2004.

A. Schei. Method for reﬁning of silicon. Patent US5788945, 1998.

D. K. Schroder. Semiconductor Material and Device Characterization. Wiley-Interscience, 2006.

O. Schultz, S. Glunz, W. Warta, R. Preu, A. Grohe, M. Köber, G. Willeke, R. Russel, J. Fernández,C. Morilla, B. R, and I. Vincueria. High-efficiency solar cells with laser- grooved buried contact front and laser-fired rear for industrial production. In 21st Eu- ropean Photovoltaic Solar Energy Conference and Exhibition, pages 826–829, Dresden, 2006.

H. Schweickert, K. Reuschel, and H. Gutsche. Production of high-purity semiconductor materials for electrical purposes. Patent US3011877, 1957.

R. Siegel and J. R. Howell. Thermal radiation heat transfer. Mc Graw Hill, 1972.

J. Song. Back to cost: from $500 to $40. In The Seventh Solar Silicon Conference, 2009.

J. Song and M. Rogol. Reﬁning benchmarks and forecasts. Photon International, 1:84–98, 2008.

E. Sparrow, L. Albers, and E. Eckert. Thermal radiation characteristics of cylindrical enclosures. Journal of heat transfer, pages 72–81, 1962.

G. G. Stokes. Mathematical and physical papers, volume 1. Cambridge University press, 1880.

D. Weidhaus, E. Schindlbeck, K. Hesse, and E. Dornberger. Pilot production of granular polysilicon from trichlorosilane using a ﬂuidized bed-type reactor. In 20th European Photovoltaic Solar Energy Conference, 2005.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani. Puriﬁcation of metallurgical-grade silicon up to solar grade. Progress in photovoltaics, 9(3):203–209, 2001.

180 Publications related to the thesis

Patents

[P1]. C. Ca˜nizo, G. del Coso, A. Luque, H. Rodr´ıguez,I. Tob´ıas,J.C. Zamorano (a.o.), “Reactor de Dep´ısitode silicio de gran pureza para aplicaciones fotovoltaicas”, in process.

[P2]. C. Cañizo, G. del Coso, A. Luque, J.C. Zamorano (a.o.), “Escudo térmicopara reactores de producciónde silicio”, in process.

Journal Publications

[J1]. G. del Coso, C. Ca˜nizo,and A. Luque, “Radiative energy loss in a polysilicon CVD reactor”, Solar energy materials and solar cells, Submitted, 2010.

[J2]. G. del Coso, C. Ca˜nizo,and W.C. Sinke, “The impact of silicon feedstock on the PV module cost”, Solar energy materials and solar cells, vol 94, pp. 345-349, 2010.

[J3]. C. Ca˜nizo, G. del Coso, and W.C. Sinke, “Crystalline silicon solar module technology: towards the 1 Euro per watt peak goal”, Progress in Photovoltaics: Reseach and Applications, vol 17, pp. 199-209, 2009.

[J4]. G. del Coso, C. Ca˜nizo,and A. Luque, “Chemical vapor deposition model of polysilicon in a trichlorosilane and hydrogen system”, Journal of the Electrochemical Soci- ety, vol. 155 (6), pp. D485-D491, 2008.

[J5]. G. del Coso, I. Tob´ıas, C. Ca˜nizo,and A. Luque, “Temperature homogeneity of polysilicon rods in a siemens reactor”, Journal of Crystal Growth, vol. 299, pp. 165-170, 2007.

181 Publications

Conference Publications

[C1]. G. del Coso, C. Ca˜nizo,and A. Luque, “Disclosing the polysilicon deposition process”, Proc. of 25 th European Photovoltaic Solar Energy Conference, Valencia, Spain, 2010.

[C2]. G. del Coso, C. Ca˜nizo,and A. Luque, “How to diminish the radiation loss in a Siemens-type Reactor”, Proc. of Silicon for the Chemical and Solar Industry X, Alesund - Geiranger, Norway, 2010.

[C3]. G. del Coso, M.T. Sánchez, M. González,J.C. Zamorano, C. Cañizo,and A. Luque, “Polysilicon deposition by trichlorosilane decomposition”, Proc. of 24 th European Photovoltaic Solar Energy Conference, Hamburg, Germany, 2009.

[C4]. G. del Coso, C. Ca˜nizo, and W.C. Sinke, “Inﬂuence of feedstock on c-Si module cost”, Proc. of 24 th European Photovoltaic Solar Energy Conference, Hamburg, Germany, 2009.

[C5]. G. del Coso, J.C. Zamorano, C. del Ca˜nizo, J.F. Leli`evre, J. Hofstetter and A. Luque, “Solar Grade Silicon production through trichlorosilane decomposition”, Proc. of 7 th Spanish conference on electron devices, Santiago de Compostela, Spain, 2009.

[C6]. W.C. Sinke, C. Ca˜nizo,and G. del Coso, “1 Euro per watt-peak advanced crystalline silicon modules: the CrystalClear integrated project”, Proc. of 23 rd European Photovoltaic Solar Energy Conference, pp. 3700-3705, Valencia, Spain, 2008.

[C7]. G. del Coso, J.F. Leli`evre,J.C. Zamorano, C. Ca˜nizo,and A. Luque, “Validation of a chemical vapor deposition model for polysilicon by a lab reactor”, Proc. of Silicon for the Chemical and Solar Industry IX, Oslo, Norway, June 23-26, 2008.

[C8]. G. del Coso, H.J. Rodr´ıguez,I. Tob´ıas,C. Ca˜nizo,and A. Luque, “Approach to silicon CVD reactor modelling”, Proc. of 22 nd European Photovoltaic Solar Energy Conference, pp. 1082-1085, Milano, Italy, 2007.

[C9]. G. del Coso, I. Tob´ıas,C. Ca˜nizo,and A. Luque, “Increase on Siemens Reactor Throughput by Tailoring Temperature Proﬁle of Polysilicon Rods”, Proc. of 6 th Spanish conference on electron devices, San Lorenzo de El Escorial, Spain, 2007.

[C10]. W.C. Sinke, G. del Coso, and C. Ca˜nizo,“Crystalline silicon PV technology roadmapping in the crystalclear integrated project”, Proc. of 21 st European Photo- voltaic Solar Energy Conference, pp. 3213-3216, Dresden, Germany, 2006.

182 Publications

Invited Talks

[T1]. G. del Coso, “Silicon Puriﬁcation for Solar Cells”, E.E. Haller Group Seminar Series, Fall 2007, Material Science Division, LBNL, Berkeley, USA. October 2007.

183