Control of Oxygen Impurities in a Continuous-Feeding Czochralski-Silicon Crystal Growth by the Double-Crucible Method

Article Control of Oxygen Impurities in a Continuous-Feeding Czochralski-Silicon Crystal Growth by the Double-Crucible Method

Wenhan Zhao, Jiancheng Li and Lijun Liu *

Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (W.Z.); [email protected] (J.L.) * Correspondence: [email protected]; Tel.: +86-29-82663443

Abstract: The continuous-feeding Czochralski method is a cost-effective method to grow single silicon crystals. An inner crucible is used to prevent the un-melted silicon feedstock from transferring to the melt-crystal interface in this method. A series of global simulations were carried out to investigate the impact of the inner crucible on the oxygen impurity distributions at the melt-crystal interface. The results indicate that, the inner crucible plays a more important role in affecting the O concentration at the melt-crystal interface than the outer crucible. It can prevent the oxygen impurities from being transported from the outer crucible wall effectively. Meanwhile, it also introduces as a new source of oxygen impurity in the melt, likely resulting in a high oxygen concentration zone under the melt-crystal interface. We proposed to enlarge the inner crucible diameter so that the oxygen concentration at the melt-crystal interface can be controlled at low levels.

Citation: Zhao, W.; Li, J.; Liu, L. Keywords: computer simulation; impurities; continuous-feeding Czochralski method; heat transfer; Control of Oxygen Impurities in a double crucible technique Continuous-Feeding Czochralski- Silicon Crystal Growth by the Double-Crucible Method. Crystals 2021, 11, 264. https://doi.org/ 1. Introduction 10.3390/cryst11030264 The continuous-feeding Czochralski method (CCZ) is an effective method to produce Academic Editor: Evgeniy single crystals, especially for crystalline silicon (Si) [1,2]. Compared with the standard N. Mokhov Czochralski (CZ) method, it has many advantages. For example, since silicon melt can be replenished continuously during a CCZ crystal growth process, the melt volume can Received: 29 January 2021 remain limited and unchanged in the crucible so that the melt flow becomes stable and Accepted: 24 February 2021 the unsteady kinetics of the melt will be suppressed. In addition, continuous recharging Published: 8 March 2021 of the melt allows for stable control of dopant [3], impurities, and resistivity distribution in a growing crystal, which helps to improve the crystal quality [4,5]. Therefore, it is Publisher’s Note: MDPI stays neutral a very promising technology to produce high-quality crystals at a low cost. However, with regard to jurisdictional claims in the CCZ grown crystal exhibits special defects, which are considered to be related to the published maps and institutional affil- relatively high hydrogen content of the recharged Si granules [6]. These defects lead to iations. serious challenges in the application of CCZ single crystals of silicon in electronic devices. Fortunately, with respect to the solar application, they are considered unlikely to have an adverse effect on solar cell performance [7]. In recent years, with a strong demand for producing n-type crystals for high-efficiency solar cells, the CCZ method has become very Copyright: © 2021 by the authors. promising [8–10]. It is predicted that the CCZ method will make significant gains in the Licensee MDPI, Basel, Switzerland. market share over conventional CZ in the next 3–5 years [11]. This article is an open access article The growth of crystalline silicon is invariably accompanied by impurities transport, distributed under the terms and such as oxygen (O), carbon (C), and other related products, from reactions [12]. Special conditions of the Creative Commons attention has been paid to, and, therefore, many researches [13–22] have been contributed, Attribution (CC BY) license (https:// the control O concentration in the melt and growing crystals. In the growth process of creativecommons.org/licenses/by/ some conventional methods, it affects the formation of micro-defects in the growing crystal 4.0/).

Crystals 2021, 11, 264. https://doi.org/10.3390/cryst11030264 https://www.mdpi.com/journal/crystals Crystals 2021, 11, x FOR PEER REVIEW 2 of 10

some conventional methods, it affects the formation of micro-defects in the growing crystal in a complex manner [13]. In the CCZ process, to prevent the unmelted silicon feedstock from transferring to the melt-crystal (m-c) interface, an inner quartz crucible is usually placed on the bottom of the outer quartz crucible [23]. Since O impurities are dis- Crystals 2021, 11, 264 solved from the quartz crucible wall, a new source of O impurity is thus introduced.2 of 9 Therefore, it is important to investigate the impact of the inner crucible on the O distributions in the melt, especially at the m-c interface, because O impurities will enter the crystal throughin a complex the m manner-c interface. [13]. If In the the initial CCZ O process, concentration to prevent of n the-type unmelted CCZ wafers silicon is feedstocktoo high, thefrom solar transferring cell efficiency to the will melt-crystal be reduced (m-c) [24] interface,. Previous an research inner quartz indicates crucible that isthe usually inner crucibleplaced onis the main bottom reason of the for outer this quartzphenomenon, crucible and [23 ].the Since O concentration O impurities at are the dissolved m-c in- terfacefrom the will quartz increase crucible in the wall, double a new-crucible source ofCCZ O impuritymethod [25] is thus. Providin introduced.g an electromag- Therefore, it neticis important stirring toof investigatethe melt is thean effective impact of way the to inner decrease crucible the on O theconcentration O distributions at the in m the-c interfacemelt, especially [26]. However, at the m-c theinterface, complexity because of the Ocrystal impurities growth will systems enter and the crystalthe cost through will be increasedthe m-c interface. by this method. If the initial O concentration of n-type CCZ wafers is too high, the solar cell efficiencyThis study will aim bes to reduced find an effective [24]. Previous way to research reduce the indicates O concentration that the inner by the crucible double is- cruciblethe main CCZ reason method. for this The phenomenon, impact of the and inner the crucible O concentration was investigated at the m-c by interfaceglobal simu- will lationsincrease, including in the double-crucible coupled O and CCZ C transport, method [which25]. Providing have been an widely electromagnetic used to study stirring the Oof distributions the melt is an in effectivea crystal waygrowth to decreaseprocess [16,20,27 the O concentration–33]. The influence at the mechanism m-c interface of [the26]. innerHowever, crucible the on complexity the O concentration of the crystal in the growth melt systemswas analyzed. and the Based cost willon this be increasedresearch, an by effectivethis method. method to decrease the O distribution in the double-crucible CCZ method was proposed.This study aims to find an effective way to reduce the O concentration by the double- crucible CCZ method. The impact of the inner crucible was investigated by global simu- 2.lations, Problem including Description coupled and O M andathematical C transport, Models which have been widely used to study the 2.1.O distributions Furnace Configuration in a crystal growth process [16,20,27–33]. The influence mechanism of the inner crucible on the O concentration in the melt was analyzed. Based on this research, an effectiveA schematic method diagram to decrease of the CCZ the Ofurnace distribution for industrial in the double-cruciblemanufacture is given CCZ methodin Figurewas proposed. 1. The diameter of the crystal was 200 mm. The crystal length was 600 mm. The inner and outer crucible diameters were 300 mm and 540 mm, respectively. To prevent the2.Problem un-melted Description silicon feedstock and Mathematical from transferring Models to the m-c interface, an inner quartz cru- cible2.1. Furnacewas placed Configuration on the bottom of the outer quartz crucible. The main dimensions of the CCZ furnaceA schematic are listed diagram in Table of the1. CCZ furnace for industrial manufacture is given in FigureIn 1our. The investigation, diameter of we the compare crystal wasd the 200 case mm. of Thethe conventional crystal length CZ was method 600 mm. with The a singleinner andcrucible outer (the crucible single diameters-crucible case) were and 300 the mm proposed and 540 mm,CCZ respectively.method with To two prevent crucibles the (theun-melted double silicon-crucible feedstock case). For from the transferring single-crucible to the case, m-c interface,the crystal an and inner crucible quartz rotation crucible rateswas placedwere set on as the 12bottom rpm and of − the6 rpm, outer respectively. quartz crucible. For the The double main- dimensionscrucible case, of the the rota- CCZ tionfurnace rates are of listedcrystal in and Table crucible1. were set as 12 rpm and −4 rpm, respectively.

1：Crystal 2：Melt 3：Inner crucible 4：Outer crucible 5：Heat shields 1 5 3 2 Windows of the inner crucible

FigureFigure 1. 1. SchematicSchematic diagram diagram of of the the continuous continuous-feeding-feeding Czochralski Czochralski method method (CCZ (CCZ)) furnace furnace with with doubledouble crucibles. crucibles.

Table 1. The dimensions of the continuous-feeding Czochralski method (CCZ) furnace.

Diameter of Inner Diameter of Outer Crystal Diameter (mm) Crystal Length (mm) Crucible (mm) Crucible (mm) 200 600 300 540 Crystals 2021, 11, x FOR PEER REVIEW 3 of 10

Crystals 2021, 11, 264 Table 1. The dimensions of the continuous-feeding Czochralski method (CCZ) furnace. 3 of 9 Crystal Diameter Crystal Length Diameter of Inner Crucible Diameter of Outer Crucible (mm) (mm) (mm) (mm) In200 our investigation,600 we compared the case300 of the conventional CZ540 method with a single crucible (the single-crucible case) and the proposed CCZ method with two crucibles 2.2.(the Numerical double-crucible Modeling case). For the single-crucible case, the crystal and crucible rotation ratesA were series set of as global 12 rpm simulations and −6 rpm, were respectively. carried out For in the this double-crucible study. An in case,-house the software rotation (CGeMoS)rates of crystal which and has crucible been developed were set asand 12 used rpm in and our− researches4 rpm, respectively. [16,27,28,34–36] for more than 18 years (see http://cgsolar.xjtu.edu.cn/, accessed on 29 January 2021), was applied in our2.2. investigation. Numerical Modeling A grid independence test was carried out for our simulations, and the total gridA series number of global was about simulations 60,000. The were latent carried heat out released in this at study. the m An-c interface in-house was software taken into(CGeMoS) account. which A dynamic has been meshing developed technique and used was in employed our researches to get [16 the,27 m,28-c,34 interface–36] for posi- more tionthan that 18 years coincides (see http://cgsolar.xjtu.edu.cn/with the isotherm of 1685 K., accessed on 29 January 2021), was applied in ourFor investigation. O calculation, A a grid well independence-developed global test wasmodel carried of coupled out for O our and simulations, C transport and in thethe whole total grid furnace number was was employed about 60,000. to study The the latent impurities heat released transportation at the m-c in interface the furnace was [29,30]taken into. For account. the governing A dynamic equations meshing and technique boundary was conditions employed of tothe get O theand m-c C transport interface modelposition, please that coincides refer to [ with30]. The the isothermglobal model of 1685 has K. been validated in previous researches [16,18]For. O calculation, a well-developed global model of coupled O and C transport in the whole furnace was employed to study the impurities transportation in the furnace [29,30]. 3.For The the Effect governing of Inner equations Crucible and on boundarythe O Distributions conditions in of M theelt O and C transport model, 3.1.please Comparison refer to [of30 O]. TheDistributions global model in the has Melt been between validated Single in-C previousrucible and researches Double-Crucible [16,18 ]. C3.ases The Effect of Inner Crucible on the O Distributions in Melt 3.1. ComparisonSince the O of is O dissolved Distributions from in the the quartz Melt between crucible Single-Crucible wall, an extra and O Double-Cruciblesource is introduced Cases when an inner crucible is placed in the outer crucible. This may lead to the increase in O Since the O is dissolved from the quartz crucible wall, an extra O source is introduced concentration in the melt. However, it is the O concentration at the m-c interface that af- when an inner crucible is placed in the outer crucible. This may lead to the increase in O fectsconcentration the O concentration in the melt. in However, the growing it is the crystal. O concentration Therefore, atwe the need m-ced interface to investigate that affects the impactthe O concentration of the inner crucible in the growing on the O crystal. concentration Therefore, at wethe neededm-c interface. to investigate For this the purpose, impact weof thefirst inner carried crucible out a on series the Oof concentrationsimulations to at compare the m-c interface.the O concentration For this purpose, at the wem-c ﬁrst in- terfacecarried between out a series the case of simulations with a single to-crucible compare and the the O concentrationcase with a double at the-crucible. m-c interface betweenTemperature the case withdistributions a single-crucible in the silicon and the melt case using with the a double-crucible. single-crucible and double- crucibleTemperature methods are distributions shown in Figure in the 2. silicon It was melt found using that the the single-crucible highest melt temperature and double- increasecrucibled methods by about are 14 shownK in the in double Figure-crucible2. It was case. found This that is thebecause highest that melt the temperaturethermal con- ductivityincreased of by the about inner 14 quartz K in thecrucible double-crucible is much smaller case. than This that is because of the silicon that the melt. thermal The introductionconductivity of the innerinner quartzcrucible crucible in the ismelt much makes smaller the thanheat thattransferred of the silicon more melt. difficult The fromintroduction the outer of crucible the inner to crucible the m-c ininterface the melt, and makes more the oxygen heat transferred is released more from difﬁcult the crucible from wallthe outer with cruciblea higher totemperature. the m-c interface, and more oxygen is released from the crucible wall with a higher temperature.

(a) single-crucible case (b) double-crucible case

Figure 2. Temperature distributions (K) in the melt: (a) the case with the conventional single-crucible method, (b) the case with the double-crucible method.

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Figure 2. Temperature distributions (K) in the melt: (a) the case with the conventional single-crucible method, (b) the case with the double-crucible method.

The stream function and O concentration in the melt in the single-crucible and double-crucible cases are shown in Figure 3. The O distribution patterns in the melt were similar to the melt flow patterns, which indicates that the O transportation is affected by the melt flow remarkably. For the single-crucible case, there were two vortexes in the melt, which were driven by thermal buoyancy, as shown in the left part of Figure 3a. Oxygen impurities dissolved from the crucible bottom wall were transported to the crucible side- Crystals 2021, 11, 264wall by the melt flow, resulting in a high O concentration near the crucible sidewall. Then, 4 of 9 with the interaction between the outer and inner vortexes, oxygen impurities were transported to the m-c interface by the inner vortex. A low O concentration zone was, therefore, located right under the m-c interface. Compared with the high O concentration near the crucible wall, O concentrationThe stream function under andthe mO- concentrationc interface decrease in the meltd byin about the single-crucible 60%. Obvi- and double- ously, the flowcrucible patterns cases in the are single shown-crucible in Figure case3. Theare Obeneficial distribution to reduce patterns the inO theconcen- melt were similar tration at the mto-c the interface. melt flow While patterns, for the which double indicates-crucible that case the, as O shown transportation in Figure is3b, affected high by the melt O concentrationflow zones remarkably. were observed For the near single-crucible both the inner case, and there outer were crucible two vortexes walls. inJust the melt, which like the singlewere-crucible driven case, by thermal O impurities buoyancy, dissolved as shown from in the the left outer part crucible of Figure wall3a. Oxygenwere impurities transported bydissolved the melt fromflow from the crucible the crucible bottom bottom wall wereto the transported crucible sidewall. to the crucibleMelt with sidewall by the a high O concentrationmelt flow, resultingnear the outer in a high crucible O concentration wall was blocked near the by crucible the inner sidewall. crucible, Then, with the which is helpfulinteraction to decrease between the O the concentration outer and inner at the vortexes, m-c interface. oxygen However, impurities melt were with transported to the a high O concentrationm-c interface near by the the inner inner wall vortex. of the A lowinner O crucible concentration can be zone transported was, therefore, to the located right under the m-c interface. Compared with the high O concentration near the crucible wall, O m-c interface directly by the vortex inside the inner crucible, which may lead to the in- concentration under the m-c interface decreased by about 60%. Obviously, the flow patterns crease in O concentration at the m-c interface. Compared with the single-crucible case, O in the single-crucible case are beneficial to reduce the O concentration at the m-c interface. concentration under the m-c interface increased from 15 ppma to 19 ppma, which indi- While for the double-crucible case, as shown in Figure3b, high O concentration zones were cates that the O concentration at the m-c interface will increase in the CCZ crystal growth observed near both the inner and outer crucible walls. Just like the single-crucible case, O process with double crucibles. This result agrees well with the research reported in [25]. impurities dissolved from the outer crucible wall were transported by the melt flow from To clarify if this is a general conclusion for the CCZ method with double-crucible, we the crucible bottom to the crucible sidewall. Melt with a high O concentration near the compared the O distributions at the crucible walls, as shown in Figure 4, for both cases outer crucible wall was blocked by the inner crucible, which is helpful to decrease the O with a single crucible and with double crucibles, which act as the origins of oxygen impu- concentration at the m-c interface. However, melt with a high O concentration near the rities. From the results shown in Figure 4, we can see that the oxygen concentration at the inner wall of the inner crucible can be transported to the m-c interface directly by the vortex outer crucible walls was higher and the oxygen concentration at the inner crucible walls inside the inner crucible, which may lead to the increase in O concentration at the m-c was lower in theinterface. double Compared-crucible case with than the single-cruciblethat in the single case, crucible O concentration case. Since under O impu- the m-c interface rities dissolveincreased from both from the 15inner ppma and to outer 19 ppma, crucible which walls, indicates it is essential that the to O make concentration clear at the m-c which crucibleinterface is the dominant will increase source in theof oxygen CCZ crystal impurities growth transported process with to doublethe m-c crucibles. inter- This result face. agrees well with the research reported in [25].

Crystals 2021, 11, x FOR PEER REVIEW 5 of 10

(a) single-crucible case

(b) double-crucible case

Figure 3. The streamFigure function 3. The stream(left) and function oxygen (left) concentration and oxygen (right, concentration ppma) in (right,the melt ppma): (a) the in the melt: (a) the case case with the conventional single-crucible method, (b) the case with the double-crucible method. with the conventional single-crucible method, (b) the case with the double-crucible method.

To clarify if this is a general conclusion for the CCZ method with double-crucible, we 42.0 compared the O distributions at the crucible walls, as shown in Figure4, for both cases with a single crucible and with double crucibles, which act as the origins of oxygen impurities. Single crucible 41.5 From the results shown in Figure4, we can see that the oxygen concentration at the outer Double crucibles

41.0 Outer crucible

p 40.5

c 40.0

39.5 Inner crucible

39.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Height / m Figure 4. The oxygen distribution (ppma) at crucible walls.

3.2. Study of the O Source at the Melt-Crystal Interface with Double-Crucible Method To make clear which crucible is the dominant source of oxygen impurities transported to the m-c interface in the double-crucible CCZ method, we investigated the impact of the inner crucible and the outer crucible, respectively, on the O concentration at the m- c interface. For the sake of convenience in our numerical investigation, we introduced a concept of a virtual coating layer that is of no thickness and no oxygen dissolution. For example, when the inner crucible walls are covered with the virtual coating layer, there is no oxygen dissolved into the melt from the inner crucible. Therefore, the outer crucible becomes the unique source of oxygen impurities. In Figure 5a, we show the O distribution in the melt for the case in which the outer crucible was covered by this virtual coating layer, which means that the inner crucible was the unique source of oxygen impurities in the melt. Compared with the results in Figure 3b, we found that the O concentration under the m-c interface only slightly decreased. Correspondingly, in Figure 5b, we show the O distribution in the melt for the case in which the inner crucible was covered by this virtual coating layer, which means that the outer crucible was the unique source of oxygen impurities in the melt. It is obviously found in this case that the O concentration under the m-c interface was remarkably reduced as compared to the results shown in Figures 3b and 5a. In Figure 6, we compared the impact of the inner crucible and outer crucible on the oxygen distribution at the m-c

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(b) double-crucible case crucible walls was higher and the oxygen concentration at the inner crucible walls was Figurelower in3. The the stream double-crucible function (left) case and than oxygen that concentration in the single (right, crucible ppma) case. in Sincethe melt O: impurities (a) the casedissolve with the from conventional both the inner single and-crucible outer method, crucible (b) walls, the case it with is essential the double to make-crucible clear method. which crucible is the dominant source of oxygen impurities transported to the m-c interface.

42.0

Single crucible 41.5 Double crucibles

41.0 Outer crucible

p 40.5

c 40.0

39.5 Inner crucible

39.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Height / m Figure 4. The oxygen distribution (ppma) at crucible walls.

3.2. Study of the O S Sourceource at the M Melt-Crystalelt-Crystal InterfaceInterface with Double-CrucibleDouble-Crucible MethodMethod TToo make make clear clear which which crucible crucible is the is the dominant dominant source source of oxygen of oxygen impurities impurities transported trans- portedto the m-cto the interface m-c interface in the in double-crucible the double-crucible CCZ CCZ method, method we, investigatedwe investigated the the impact impact of the inner crucible and the outer crucible, respectively, on the O concentration at the m-c of the inner crucible and the outer crucible, respectively, on the O concentration at the m- interface. For the sake of convenience in our numerical investigation, we introduced a c interface. For the sake of convenience in our numerical investigation, we introduced a concept of a virtual coating layer that is of no thickness and no oxygen dissolution. For concept of a virtual coating layer that is of no thickness and no oxygen dissolution. For example, when the inner crucible walls are covered with the virtual coating layer, there is example, when the inner crucible walls are covered with the virtual coating layer, there is no oxygen dissolved into the melt from the inner crucible. Therefore, the outer crucible no oxygen dissolved into the melt from the inner crucible. Therefore, the outer crucible becomes the unique source of oxygen impurities. becomes the unique source of oxygen impurities. In Figure5a, we show the O distribution in the melt for the case in which the outer In Figure 5a, we show the O distribution in the melt for the case in which the outer crucible was covered by this virtual coating layer, which means that the inner crucible crucible was covered by this virtual coating layer, which means that the inner crucible was the unique source of oxygen impurities in the melt. Compared with the results was the unique source of oxygen impurities in the melt. Compared with the results in in Figure3b, we found that the O concentration under the m-c interface only slightly Figuredecreased. 3b, we Correspondingly, found that the O in concentration Figure5b, we under show thethe Om- distributionc interface only in the slightly melt forde- creased.the case Correspondingly, in which the inner in crucibleFigure 5b was, we covered show the by O this distribution virtual coating in the layer,melt for which the casmeanse in thatwhich the the outer inner crucible crucible was was the covered unique by source this virtual of oxygen coating impurities layer, which in the means melt. thatIt is the obviously outer crucible found inwas this the case unique that source the O concentrationof oxygen impurities under thein the m-c melt. interface It is obvi- was ouslyremarkably found reduced in this case as compared that the O to concentration the results shown under in the Figures m-c 3interfaceb and5a. was In Figure remarkably6, we reducedcompared as thecompar impacted to of the the results inner crucible shown in and Figure outers 3b crucible and 5a. on In the Figure oxygen 6, we distribution compared theat the impact m-c interface.of the inner The crucible results and veriﬁed outer thatcrucible the inneron the crucible oxygen candistribution effectively at preventthe m-c the O impurities dissolved from the outer crucible walls from being transported to the m-c interface, but the inner crucible itself acts as the dominant source of O impurities transported to the m-c interface. Therefore, the design of the inner crucible and control of the melt ﬂow in the inner crucible are the key factors to reduce the O concentration at the m-c interface in the CCZ double-crucible method. Crystals 2021,, 11,, xx FORFOR PEERPEER REVIEWREVIEW 6 of 10

interface.interface. TheThe resultsresults verifverifiedied thatthat thethe innerinner cruciblecrucible cancan effectivelyeffectively preventprevent thethe OO impuri-impuri- tiesties dissolveddissolved fromfrom thethe outerouter cruciblecrucible wallswalls fromfrom beingbeing transportedtransported toto thethe mm--c interface, but the inner crucible itself acts as the dominant source of O impurities transported to the m--c interface.. Therefore,Therefore, thethe designdesign ofof thethe innerinner cruciblecrucible andand controlcontrol ofof thethe meltmelt flowflow inin the inner crucible are the key factors to reduce the O concentration at the m-c interface in Crystals 2021, 11, 264 the inner crucible are the key factors to reduce the O concentration at the m-c interface6 ofin 9 thethe CCZCCZ doubledouble--crucible method.

((a)) oxygenoxygen onlyonly fromfrom thethe innerinner cruciblecrucible wallswalls ((b)) oxygenoxygen onlyonly fromfrom thethe outerouter cruciblecrucible wallswalls

FigureFigure 5. 5. TheThe O O distribution distribution ( (ppma)ppma)) inin in thethe the meltmelt melt::: (( (aa))) therethere there isis is nono no oxygenoxygen oxygen dissolveddissolved dissolved intointo into thethe the meltmelt melt fromfrom from thethe the outerouter outer cruciblecrucible crucible andand and thethethe innerinner inner cruciblecrucible crucible isis is thethe the uniqueunique unique sourcesource source ofof of oxygenoxygen oxygen impurities,impurities, impurities, (( (bb))) therethere there isis is nono no oxygenoxygen oxygen dissolved dissolved into into the the melt melt from from the the inner inner cruciblecrucible and and the the outer outer crucible crucible is is the the unique unique source source of of oxygen oxygen impurities. impurities.

O ssourrccee:: iinneerr ccrrucciibllee O source: outer crucible 20 O source: outer crucible

a a 15

c 10 c 10

0 0..00 0..02 0..04 0..06 0..08 0..10 r // m

Figure 6. Impacts of the inner crucible and outer crucible on the oxygen distribution (ppma) at the Figure 6. ImpactsImpacts ofof thethe innerinner cruciblecrucible andand outerouter cruciblecrucible onon thethe oxygenoxygen distributiondistribution (ppma)(ppma) atat thethe mm-c--c interface. interface. 3.3. Approach to Decrease O Distributions at the m-c Interface by Double-Crucible Method 3.3. Approach to Decrease O Distributionsistributions atat thethe mm--c IInterface by Double--Crucible Method Based on our research, the inner crucible was the dominant source of oxygen impu- Based on our research, the inner crucible was the dominant source of oxygen impu- ritiesBas transporteded on our research, to the m-c the interface, inner crucible and the was melt the flow dominant inside the source inner of crucible oxygen playsimpu- a rities transported to the m-c interface, and the melt flow inside the inner crucible plays a ritieskey roletransported in transporting to the m the-c oxygeninterface dissolved, and the frommelt flow the crucible inside the walls inner to thecrucible m-c interface. plays a key role in transporting the oxygen dissolved from the crucible walls to the m-c interface. keyTherefore, role in transporting we proposed the an oxygen approach dissolved with a from larger the inner crucible crucible walls in to the the CCZ m-c method interface. to Therefore, we proposed an approach with a larger inner crucible in the CCZ method to Therefore,reduce the we oxygen proposed content an inapproach the growing with crystals.a larger Weinner carried crucible out in numerical the CCZ simulationsmethod to reduce the oxygen content in the growing crystals. We carried out numerical simulations reduceto verify the our oxygen proposed content approach. in the growing crystals. We carried out numerical simulations toto verifyverifyExcept ourour for proposedproposed the case approach.approach. with an inner crucible diameter of 300 mm, as we have investigated in detail, global simulations of the thermal field and oxygen transport in the whole furnace were carried out for two cases with larger inner crucible diameters of 360 mm and 420 mm, respectively. The melt flow pattern and oxygen distributions in the melt for the two cases are shown in Figure7. Comparing the results shown in Figures7 and3b, we can see that when the diameter of the inner crucible was enlarged, the melt flow patterns in the crucibles were similar. However, the O concentration in the melt between the two crucibles increased while it decreased inside the inner crucible. As a result, the O concentration at the m-c interface decreased accordingly, as shown in Figure8, where a comparison is shown Crystals 2021, 11, x FOR PEER REVIEW 7 of 10

Except for the case with an inner crucible diameter of 300 mm, as we have investigated in detail, global simulations of the thermal field and oxygen transport in the whole furnace were carried out for two cases with larger inner crucible diameters of 360 mm and 420 mm, respectively. The melt flow pattern and oxygen distributions in the melt for the two cases are shown in Figure 7. Comparing the results shown in Figures 7 and 3b, we can see that when the diameter of the inner crucible was enlarged, the melt flow patterns Crystals 2021, 11, 264 in the crucibles were similar. However, the O concentration in the melt between the two7 of 9 crucibles increased while it decreased inside the inner crucible. As a result, the O concentration at the m-c interface decreased accordingly, as shown in Figure 8, where a comparison is shown for O distributions at the m-c interface for cases with different inner crucible for O distributions at the m-c interface for cases with different inner crucible diameters diameters and the case with a single crucible. The oxygen concentration at the m-c inter- and the case with a single crucible. The oxygen concentration at the m-c interface in the face in the case with the inner crucible diameter of 420 mm was reduced by nearly 40% case with the inner crucible diameter of 420 mm was reduced by nearly 40% from about from20 ppma about to 20 about ppma 12 to ppma about when 12 ppma compared when compar to the caseed to with the thecase inner with crucible the inner diameter crucible of diameter300 mm, of and 300 reduced mm, and by reduced 25% from by 16 25% ppma from to about16 ppma 12 ppma to about when 12 compared ppma when to the com- case parofed conventional to the case of method conventional with a method single crucible. with a single This ﬁndingcrucible. is This exciting finding to us is becauseexciting itto is usvery because useful it tois reducevery useful the oxygen to reduce impurities the oxygen in the impurities silicon crystals in the grown silicon by crystals a CCZ grown method. byOur a CCZ proposed method. approach Our proposed is, therefore, approach veriﬁed is, therefore as effective., verified as effective.

(a) Inner crucible radius of 180 mm

Crystals 2021, 11, x FOR PEER REVIEW (b) Inner crucible radius of 210 mm 8 of 10

FigureFigure 7. 7.TheThe melt melt flow ﬂow patterns patterns (left) (left) and and O distributions O distributions (right, (right, ppma) ppma) in the in themelt melt:: (a) the (a) inner the inner cruciblecrucible radius radius is is180 180 mm, mm, (b ()b the) the inner inner crucible crucible radius radius is is210 210 mm. mm.

a 15

O 10

c Single crucible

Double crucibles, Rinner crucible=150 mm

5 Double crucibles, Rinner crucible=180 mm

Double crucibles, Rinner crucible=210 mm

0 0.00 0.02 0.04 0.06 0.08 0.10 r / m Figure 8.8. Comparison of O distributions (ppma) atat thethe m-cm-c interface.interface.

4. Conclusions In this research, a series of global simulations were carried out for a double-crucible CCZ furnace. The impact of the inner crucible on the O distribution at the m-c interface was investigated. On the one hand, the inner crucible can prevent the O impurities dissolved from the outer crucible from transporting to the m-c interface effectively. On the other hand, the inner crucible itself is the main source of O impurities transported to the m-c interface in the melt. We proposed an improved approach with a larger inner crucible diameter to reduce the O concentration at the m-c interface in a double-crucible CCZ method. The numerical investigation results verified the proposed approach as effective. The O concentration at the m-c interface can be reduced by 25% compared to the conventional CZ method with a single crucible.

Author Contributions: Conceptualization, L.L.; methodology, W.Z. and L.L.; validation, W.Z. and J.L.; formal analysis, W.Z. and L.L.; investigation, W.Z. and L.L.; writing—original draft preparation, W.Z.; writing—review and editing, W.Z., J.L., and L.L.; All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 51676154). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors gratefully thank the support of National Natural Science Founda- tion of China (Grant No. 51676154). Conflicts of Interest: The authors declare no conflict of interest.

Crystals 2021, 11, 264 8 of 9

4. Conclusions In this research, a series of global simulations were carried out for a double-crucible CCZ furnace. The impact of the inner crucible on the O distribution at the m-c interface was investigated. On the one hand, the inner crucible can prevent the O impurities dissolved from the outer crucible from transporting to the m-c interface effectively. On the other hand, the inner crucible itself is the main source of O impurities transported to the m-c interface in the melt. We proposed an improved approach with a larger inner crucible diameter to reduce the O concentration at the m-c interface in a double-crucible CCZ method. The numerical investigation results veriﬁed the proposed approach as effective. The O concentration at the m-c interface can be reduced by 25% compared to the conventional CZ method with a single crucible.

Author Contributions: Conceptualization, L.L.; methodology, W.Z. and L.L.; validation, W.Z. and J.L.; formal analysis, W.Z. and L.L.; investigation, W.Z. and L.L.; writing—original draft preparation, W.Z.; writing—review and editing, W.Z., J.L., and L.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 51676154). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors gratefully thank the support of National Natural Science Founda- tion of China (Grant No. 51676154). Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Kitashima, T.; Liu, L.; Kitamura, K.; Kakimoto, K. Numerical analysis of continuous charge of lithium niobate in a double-crucible Czochralski system using the accelerated crucible rotation technique. J. Cryst. Growth 2004, 266, 109–116. [CrossRef] 2. Kitashima, T.; Liu, L.; Kitamura, K.; Kakimoto, K. Effects of shape of an inner crucible on convection of lithium niobate melt in a double-crucible Czochralski process using the accelerated crucible rotation technique. J. Cryst. Growth 2004, 267, 574–582. [CrossRef] 3. Yoon, Y.; Yan, Y.; Ostrom, N.P.; Kim, J.; Rozgonyi, G. Deep level transient spectroscopy and minority carrier lifetime study on Ga-doped continuous Czochralski silicon. Appl. Phys. Lett. 2012, 101, 222107. [CrossRef] 4. Anselmo, A.; Koziol, J.; Prasad, V. Full-scale experiments on solid-pellets feed continuous Czochralski growth of silicon crystals. J. Cryst. Growth 1996, 163, 359–368. [CrossRef] 5. Ono, N.; Arai, Y.; Abe, K.; Sahira, K. A new technique for controlling the dopant concentration in the double-crucible method. J. Cryst. Growth 1994, 135, 359–364. [CrossRef] 6. Iino, E.; Takano, K.; Kimura, M.; Yamagisi, H. Cavities owing to hydrogen in Si single crystals grown by continuously charging CZ method. Mater. Sci. Eng. B 1996, 36, 146–149. [CrossRef] 7. Giannattasio, A. A simplified model to predict resistivity profiles in continuous-feeding Cz-silicon crystals. J. Cryst. Growth 2020, 542, 125686. [CrossRef] 8. Von Ammon, W. FZ and CZ crystal growth: Cost driving factors and new perspectives. Phys. Status Solidi A 2014, 211, 2461–2470. [CrossRef] 9. Xu, H. Characterization of n-type mono-crystalline silicon ingots produced by continuous Czochralski (Cz) Technology. Energy Procedia 2015, 77, 658–664. [CrossRef] 10. Xu, H.; Tian, X. Minority carrier lifetime of n-type mono-crystalline silicon produced by continuous Czochralski technology and its effect on hetero-junction solar cells. In Proceedings of the 6th International Conference on Crystalline Silicon Photovoltaics (SiliconPV), Chambéry, France, 7–10 March 2016; Ribeyron, P.J., Cuevas, A., Weeber, A., Ballif, C., Glunz, S., Poortmans, J., Brendel, R., Aberle, A., Sinton, R., Verlinden, P., et al., Eds.; Elsevir: Amsterdam, The Netherlands, 2016; Volume 92, pp. 708–714. 11. International Technology Roadmap for Photovoltaic (ITRPV). Results 2015, 7th ed.; ITRPV: Frankfurt, Germany, 2015. 12. Liaw, H.M. Oxygen and carbon in Czochralski-grown silicon. Microelectron. J. 1981, 12, 33–36. [CrossRef] 13. Kulkarni, M.S. Defect dynamics, in the presence of oxygen in growing Czochralski silicon crystals. J. Cryst. Growth 2007, 303, 438–448. [CrossRef] 14. Kesavan, V.; Srinivasan, M.; Ramasamy, P. Optimizing oxygen impurities using different heater design in the directional solidification of multi-crystalline silicon. Mater. Res. Express 2019, 6, 106323. [CrossRef] Crystals 2021, 11, 264 9 of 9

15. Shao, Y.; Li, Z.; Yu, Q.; Liu, L. Control of melt flow and oxygen distribution using traveling magnetic field during directional solidification of silicon ingots. Silicon 2020, 12, 2395–2404. [CrossRef] 16. Li, Z.; Liu, L.; Ma, W.; Kakimoto, K. Effects of argon flow on impurities transport in a directional solidification furnace for silicon solar cells. J. Cryst. Growth 2011, 318, 304–312. [CrossRef] 17. Teng, Y.-Y.; Chen, J.-C.; Huang, B.-S.; Chang, C.-H. Numerical simulation of impurity transport under the effect of a gas flow guidance device during the growth of multicrystalline silicon ingots by the directional solidification process. J. Cryst. Growth 2014, 385, 1–8. [CrossRef] 18. Gao, B.; Nakano, S.; Kakimoto, K. Global Simulation of Coupled Carbon and Oxygen Transport in a Unidirectional Solidification Furnace for Solar Cells. J. Electrochem. Soc. 2010, 157, H153–H159. [CrossRef] 19. Wang, H.; Liu, L.; Liu, X.; Li, Z. Control of Oxygen Transport in the Melt of a Czochralski-Silicon Crystal Growth. J. Enhanc. Heat Transf. 2012, 19, 505–514. [CrossRef] 20. Smirnov, A.D.; Kalaev, V.V. Development of oxygen transport model in Czochralski growth of silicon crystals. J. Cryst. Growth 2008, 310, 2970–2976. [CrossRef] 21. Liu, X.; Harada, H.; Miyamura, Y.; Han, X.-F.; Nakano, S.; Nishizawa, S.-I.; Kakimoto, K. Transient global modeling for the pulling process of Czochralski silicon crystal growth. II. Investigation on segregation of oxygen and carbon. J. Cryst. Growth 2020, 532, 125404. [CrossRef] 22. Teng, Y.-Y.; Chen, J.-C.; Lu, C.-W.; Huang, C.-C.; Wun, W.-T.; Chen, H.-I.; Chen, C.-Y.; Lan, W.-C. Numerical simulation of the effect of heater position on the oxygen concentration in the CZ silicon crystal growth process. Int. J. Photoenergy 2012, 2012, 395235. [CrossRef] 23. Jomaa, M.; M’Hamdi, M. Effect of crucible diameter on heat transfer and melt flow in continuous czochralski process for silicon crystal growth. In Proceedings of the 27th European Photovoltaic Solar Energy Conference and Exhibition, Frankfurt, Germany, 24–28 September 2012; pp. 1072–1075. 24. Binns, M.J.; Kearns, J.; Good, E.A. (Invited) Impact of oxygen-related defects on lifetime degradation in n-type CCZ/CZ mono-crystalline silicon during cell processing. ECS Trans. 2014, 60, 1233–1238. [CrossRef] 25. Ono, N.; Kida, M.; Arai, Y.; Sahira, K. A numerical study on oxygen transport in silicon melt in a double-crucible method. J. Cryst. Growth 1994, 137, 427–434. [CrossRef] 26. Ono, N.; Trapaga, G. A numerical study of the effects of electromagnetic stirring on the distributions of temperature and oxygen concentration in silicon double-crucible Czochralski processing. J. Electrochem. Soc. 1997, 144, 764–772. [CrossRef] 27. Liu, X.; Gao, B.; Kakimoto, K. Numerical investigation of carbon contamination during the melting process of Czochralski silicon crystal growth. J. Cryst. Growth 2015, 417, 58–64. [CrossRef] 28. Liu, X.; Gao, B.; Nakano, S.; Kakimoto, K. Numerical investigation of carbon and silicon carbide contamination during the melting process of the Czochralski silicon crystal growth. Cryst. Res. Technol. 2015, 50, 458–463. [CrossRef] 29. Matsuo, H.; Ganesh, R.B.; Nakano, S.; Liu, L.; Kangawa, Y.; Arafune, K.; Ohshita, Y.; Yamaguchi, M.; Kakimoto, K. Thermody- namical analysis of oxygen incorporation from a quartz crucible during solidification of multicrystalline silicon for solar cell. J. Cryst. Growth 2008, 310, 4666–4671. [CrossRef] 30. Vorob’ev, A.N.; Sid’ko, A.P.; Kalaev, V.V. Advanced chemical model for analysis of Cz and DS Si-crystal growth. J. Cryst. Growth 2014, 386, 226–234. [CrossRef] 31. Bornside, D.E.; Brown, R.A.; Fujiwara, T.; Fujiwara, H.; Kubo, T. The Effects of Gas-Phase Convection on Carbon Contamination of Czochralski-Grown Silicon. J. Electrochem. Soc. 1995, 142, 2790–2804. [CrossRef] 32. Chen, J.-C.; Chiang, P.-Y.; Chang, C.-H.; Teng, Y.-Y.; Huang, C.-C.; Chen, C.-H.; Liu, C.-C. Three-dimensional numerical simulation of flow, thermal and oxygen distributions for a Czochralski silicon growth with in a transverse magnetic field. J. Cryst. Growth 2014, 401, 813–819. [CrossRef] 33. Lan, C. Recent progress of crystal growth modeling and growth control. Chem. Eng. Sci. 2004, 59, 1437–1457. [CrossRef] 34. Liu, L.; Nakano, S.; Kakimoto, K. Investigation of oxygen distribution in electromagnetic CZ-Si melts with a transverse magnetic field using 3D global modeling. J. Cryst. Growth 2007, 299, 48–58. [CrossRef] 35. Liu, L.J.; Kakimoto, K.; Taishi, T.; Hoshikawa, K. Computational study of formation mechanism of impurity distribution in a silicon crystal during solidification. J. Cryst. Growth 2004, 265, 399–409. [CrossRef] 36. Zhao, W.; Liu, L. Control of heat transfer in continuous-feeding Czochralski-silicon crystal growth with a water-cooled jacket. J. Cryst. Growth 2017, 458, 31–36. [CrossRef]