MICROWAVE INDUCED REMOTE HYDROGEN PLASMA (MIRHP) PASSIVATION OF MULTICRYSTALLINE SILICON SOLAR CELLS
Dissertation
zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.) an der Universität Konstanz Fakultät für Physik
vorgelegt von
Markus Spiegel
Konstanz, Oktober 1998
Contents
1 Introduction 1 1.1 The energy problem - need for photovoltaics 1 1.2 The importance of multicrystalline silicon for the PV industry 1 1.3 Organization of this work 3
2 Multicrystalline silicon materials and laboratory cell processing 5 2.1 Introduction 5 2.2 Production of multicrystalline silicon 5 2.2.1 Block cast mc-Si 5 2.2.2 Ribbon cast mc-Si 6 2.3 Structural and electrical properties 6 2.4 Processing of laboratory solar cells 7 2.4.1 Cells with homogeneous emitter 7 2.4.2 Cells with selective emitter 8 2.4.3 Cell processing using RGS and EFG base material 8
3 Characterization of silicon wafers and cells 10 3.1 Introduction 10 3.2 Contactless measurement methods 10 3.2.1 Surface photovoltage method 10 3.2.2 Microwave-detected photoconductance decay technique (MW-PCD) 12 3.3 Measurements on solar cells 13 3.3.1 Dark I-V characteristics - the two-diode model 13 3.3.2 Illuminated I-V characteristics 13 3.3.3 LBIC 14 3.3.4 Spectral response 15 3.3.4.1 Measurement and determination of the internal quantum efficiency (IQE) 15 3.3.4.2 Influence of the bias light on the IQE 16 3.3.4.3 Influence of a high temperature step on the IQE of EFG solar cells 17 3.4 Theory on the internal quantum efficiency (IQE) 17 3.4.1 Introduction 17 3.4.2 Literature work 18 3.4.2.1 Contributions of emitter, space charge region and base to the IQE 18 3.4.2.2 Additional approximations for the base IQE 20 3.4.2.2.1 wb >> Lb 20 3.4.2.2.2 wb << Lb 20 3.4.3 The general problem with the approximated base IQEs 21 3.4.4 Own work 22 3.4.4.1 Approximations on the emitter and space charge region 22 II Contents
3.4.4.2 Direct way of deducing approximated IQEe+scr 23 3.4.4.3 Proof for 1/IQEtotal 1+1/(Lbα) ´near´ the space charge region 24 3.4.4.4 Comparison of the different approximated total IQEs 25 3.4.4.5 Validity region of eq. (3.23) 25 3.4.4.6 Theoretical and experimental accuracy 27 3.4.4.7 Consequences of eq. (3.23) 29 3.4.4.8 Influence of a weak surface texturization 30
4 Microwave induced remote hydrogen plasma (MIRHP) passivation 33 4.1 Introduction 33 4.2 The MIRHP device 34 4.3 Optimization of the MIRHP process 35 4.3.1 Procedure of the optimization 35 4.3.2 Optimization of the microwave power, gas flow and gas pressure 35 4.3.2.1 EMC base material 36 4.3.2.2 SOLAREX base material 37 4.3.3 Optimization of the diffusion temperature and process time 38 4.3.3.1 Cast silicon 38 4.3.3.2 Ribbon silicon 40 4.3.4 LBIC measurements 41 4.3.5 Summary of the optimal process parameters for the investigated materials 42 4.4 MIRHP of RGS solar cells 44 4.4.1 Introduction 44 4.4.2 Flat cells 44 4.4.2.1 Cell processing 44 4.4.2.2 IQE before H-passivation 45 4.4.2.3 Improvement of RGS cell performance due to MIRHP 46 4.4.3 V-grooved cells 47 4.4.3.1 Cell processing 47 4.4.3.2 Homogeneity of the RGS material, benefit from forming gas annealing 47 4.4.3.3 Benefit from the MIRHP applied before the DARC 49 4.4.3.3.1 I-V characteristics 49 4.4.3.3.2 IQE-measurements 50 4.4.3.4 The MIRHP applied after the DARC 51 4.4.4 Results on RGS cells 52 4.5 Results on multicrystalline PERL-cells 52 4.5.1 Introduction 52 4.5.2 Combining the MIRHP passivation with the PERL cell process 53 4.5.3 Influence of MIRHP and thermal annealing on PERL cells 53 4.5.4 Improvement of the IQE by the MIRHP 54 4.5.5 Illuminated I-V results 55 4.5.6 Conclusions 56 4.6 MIRHP of cells with homogeneous emitter 56 4.7 Summary of results 58
5 Diffusion and effusion of hydrogen in silicon 60 5.1 Introduction 60 5.2 Theoretical work on hydrogen diffusion 60 5.2.1 Free diffusion of hydrogen 60 5.2.2 Multiple trapping of hydrogen 61 Contents III
5.2.3 Methods for extracting diffusion parameters from H-depth data 62 5.2.3.1 The topt-method 63 5.2.3.2 The tconst-method 64 5.2.3.3 The Tconst-method 64 5.3 Experimental determination of hydrogen/deuterium in silicon 65 5.3.1 Introduction 65 5.3.2 Thermal effusion (TE) 65 5.3.3 Secondary ion mass spectroscopy (SIMS) 66 5.3.4 Discussion 67 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 67 5.4.1 Introduction 67 5.4.2 Two-layer model of the IQE 68 5.4.2.1 Exact calculation of the base IQE 68 5.4.2.2 Approximations of the base region 71 5.4.2.2.1 Thick second base region 71 5.4.2.2.2 High back side recombination velocity 72 5.4.2.3 The total IQE 73 5.4.2.4 Comparison of the approximated total IQEs 74 5.4.2.5 Theoretical and experimental accuracy 75 5.4.2.6 Summary of this section 76 5.4.3 Experiment 78 5.4.3.1 Fit of the two-layer model to experiment 78 5.4.3.2 Comparison of the two-layer model with PC-1D 79 5.4.3.3 Extraction of diffusion parameters for SOLAREX base material 80 5.4.3.4 Comparison of the diffusion constants of different mc-Si materials 81 5.5 Effusion experiments on solar cells 81 5.5.1 Introduction 81 5.5.2 Influence of H-effusion on the IQE 82 5.5.3 Influence of H-effusion on the illuminated and dark I-V parameters 83 5.6 Conclusions 85
6 The MIRHP process within an industrial cell production line 87 6.1 Introduction 87 6.2 Industrial solar cell production at Eurosolare and Solarex 87 6.3 MIRHP of screen-printed cells. 89 6.3.1 MIRHP after cell processing 89 6.3.2 MIRHP in industrial cell processes 90 6.3.2.1 MIRHP within the production line at Eurosolare 91 6.3.2.2 MIRHP within the production line at Solarex 92 6.3.3 Industrial importance of the MIRHP processes 93 6.4 PECVD SiN 94 6.5 Combination of PECVD SiN and MIRHP 95 6.6 Conclusions 96
7 Summary 97
8 References 99
9 Appendixes 105 9.1 Single-layer IQE 105
9.2 Single-layer IQE at α = 1/Lb 106 IV Contents
9.3 Single-layer IQE and weak surface texturization 107 9.4 Double-layer IQE 110
9.5 Double-layer IQE at α = 1/L1 and α = 1/L2 111 9.6 From the double-layer IQE back to the single-layer IQE 114 9.7 Double-layer IQE and weak surface texturization 115
10 List of abbreviations, symbols, figures and tables 117 10.1 List of abbreviations 117 10.2 List of symbols 118 10.3 List of figures 120 10.4 List of tables 121
11 List of Publications 123
12 Zusammenfassung 126
13 Danksagung 128 1 Introduction
1.1 The energy problem - need for photovoltaics Today, the main contribution to the world-wide used energy comes from fossil and nuclear resources. Because of the limitations of the oil, gas, coal and uranium resources and environmental problems such as the green house effect, acid rain and nuclear by-products most energy scenario studies predict a fundamental change in the world energy supply during the coming century [1, 2]. In these studies it is supposed that renewable energy systems, such as wind energy, photovoltaics, solar heating and biomass will become more important. These energy systems do not depend on resources, which are limited to our earth, but on the constant radiation - at least for the human horizon - of the sun. Among these renewable energies, the photovoltaic conversion of light energy into electricity is very promising. Photovoltaic (PV) systems are reliable, almost maintenance-free and do not cause polluting by-products. Additionally, photovoltaics is modular in the range from milliwatt to megawatt. Because of these advantages photovoltaics is one of the fastest growing markets during the last years as can be seen in the world photovoltaic cell and module shipments from 1980 to 1997 shown in Fig. 1.1. Despite these advantages, the installed world total PV power is still below the power output of one single nuclear power station. The relatively high costs of PV modules in the range of $3.5-4.5/Wp [3] are the reason for the small contribution of PV energy compared to the total electric energy consumption.
Fig. 1.1: Total world photovoltaic cell and 120 world photovoltaic cell 120 module shipment. The contribution of thin and module shipments film cells and modules is also shown for 100 100 comparison [4]. 80 80 total 60 60
40 40 thin films total power [MWp] 20 20
0 0 80 82 84 86 88 90 92 94 96 98 year
1.2 The importance of multicrystalline silicon for the PV industry The cost per Wp of a PV module can be reduced by either increasing the module efficiency or by decreasing the total module production costs. In the following the field of thin film solar cells made either from amorphous silicon or other semiconductor material is not considered, because their contribution to the total PV market has decreased during the last years as was also seen in Fig. 1.1. However, thin film cells might play an important role for cost reductions in the future. Bulk silicon solar cells based on crystalline 2 1 Introduction
(throughout this work this term is used for both mono- and multicrystalline) silicon still dominate the PV market with 87% market share as was seen in Fig. 1.1. During the last two decades the efficiency of small area laboratory solar cells, processed by sophisticated microelectronic techniques using high-quality FZ (Float Zone) silicon, has reached 24.4% [5]. This is not far away from the theoretical limit of 28.8% for a silicon cell under the global AM1.5 solar spectrum [6]. During the same period, the efficiency of the best commercially available modules, which are based on Cz (Czochralski) silicon, increased from 8% to 14 -16% [4]. With industrial processes the highest efficiencies on large area Cz silicon will not increase 20% [3], therefore not much can be gained by concentrating in cell efficiency improvements alone. During the last years it became clear that further considerable reductions in the costs per Wp can only be obtained by cost reductions in the PV module production. The total cost breakdown for five manufacturers of crystalline silicon PV modules into Si wafer, cell fabrication and module fabrication is shown in Fig. 1.2. Almost half of the total cost is due to the Si wafer which makes a further investigation of this factor interesting. The contribution of the Si wafer of 46% to the total cost can be further divided into the silicon feedstock (10%), the crystallization (18%) and the wafering (18%). The recent European APAS case study [7, 8] has shown that the cost contribution of the Si wafer will further increase in a very large scale (500 MWp/y) module fabrication. As a comparison the world total shipment of PV modules was 125 MWp in 1997 as seen in Fig. 1.1. In order to reduce the cost factor of the Si wafer, cell manufacturers started to use block casted multicrystalline silicon (mc-Si) instead of Cz silicon material. Today about half of the crystalline PV modules are based on mc-Si. By using block casting for the crystallization of the silicon feedstock the expensive Czochralski crystallization process, which increases the cost of Si from $80/kg to $370/kg is avoided [9]. Comparing the Cz crystallization with block casting, the material throughput can be increased and the energy consumption reduced. However with the block casting techniques two problems are still present, a too low throughput for decisive cost reductions in the crystallization process and the need for wafering which contributes to nearly 1/5 to the total PV module cost. The wafering also results in a material loss of around 50%. With the development of a broad variety of ribbon techniques, which are aiming at a direct deposition of the Si sheets it is proposed that in the near future the wafering is not necessary anymore and the throughput can be increased drastically [3]. The above mentioned European APAS case study has shown that with a market size of 500 MWp/year and under the assumption of realistic technical improvements in material production and cell processing the present price of $3.5 - 4.5/Wp will drastically fall down to $1.6/Wp for monocrystalline, $1.2/Wp for block casted multicrystalline and $0.95/Wp for EFG (edge-defined film-fed growth) ribbon silicon PV modules. Because of the higher potential for cost reductions, the contribution of mc-Si will further increase. The higher crystal defect densities and impurity concentrations of mc-Si compared to Cz silicon makes defect passivation techniques such as hydrogen passivation a key issue for high efficiencies on mc-Si solar cells. It is now generally accepted that the incorporation of atomic hydrogen into mc-Si neutralizes recombination centers for minority carriers, which otherwise would limit the performance of multicrystalline silicon solar cells [10]. By atomic hydrogen the influence of the trapping sites associated with defects is made electrically inactive. Atomic hydrogen is relatively mobile in silicon, even at low temperatures, and is particularly so along dislocations [11]. Several techniques exist for introducing atomic hydrogen in semiconductors, such as H-ion implantation, direct and remote H-plasma passivation and high temperature forming gas annealing [10]. In contrast to the first two techniques no surface damage is caused during the remote hydrogen passivation, which makes this technique also attractive to be applied after cell 1.3 Organization of this work 3 processing. In addition, the remote hydrogen process is also ideally suited for H-diffusion experiments, where a surface damage could influence the measurement result.
Si-feedstock module fabrication 10% crystallization 30% Si wafer 18% 46% cell fabrication wafering 24% 18%
Fig. 1.2: The total cost breakdown for five manufacturers of crystalline silicon PV modules into Si wafer, cell and module fabrication (left side). The contribution of the Si wafer can be further divided into the silicon feedstock (10%), the crystallization (18%) and the wafering (18%) [3].
1.3 Organization of this work The subject of this thesis is volume (bulk) passivation of multicrystalline silicon (mc-Si) solar cells by the means of atomic hydrogen. The microwave induced remote hydrogen plasma (MIRHP) technique is used to decrease the bulk recombination of silicon solar cells based on various multicrystalline silicon materials. Besides the effect of passivating defects by hydrogen, also hydrogen diffusion and effusion in solar cells are studied.
In chapter 2 the structural and electrical properties of the block and ribbon cast multicrystalline silicon materials under study are given. The cell processing sequences of small laboratory cells is described including the modifications necessary for the ribbon silicon materials of investigation.
The characterization methods for mc-Si wafers and cells used in this work are presented in chapter 3. A key parameter for the characterization of bulk recombination is the bulk minority carrier diffusion length Lb. By a fit on the cell’s internal quantum efficiency (IQE), which is obtained from a spectral response and reflectance measurement, Lb is determined using a newly derived approximated formulation of the total IQE including the emitter, space charge region and bulk of a cell.
The effectiveness of the MIRHP technique as a function of the passivation parameters for various mc-Si materials is presented in chapter 4. Differences between block and ribbon silicon concerning the optimum passivation temperature and time are investigated and the influence of the crystal defect concentration as well as the content of interstitial oxygen on the passivation parameters are discussed. The MIRHP process is also applied to high efficiency mc-Si PERL (passivated emitter, rear locally-diffused) cells.
The diffusion and effusion of atomic hydrogen in multicrystalline silicon is studied in chapter 5. To overcome the limitations of thermal effusion and secondary ion mass spectroscopy measurement techniques, a new non-destructive electrically sensitive method for the determination of the passivation depth of hydrogen in mc-Si cells is described. This method is based on a fit of the internal quantum efficiency of hydrogen passivated cells with a two-layer model of the IQE. Using this method, the activation energy for H-diffusion and the diffusion coefficient can be determined. A further insight of H-diffusion in different mc-Si materials is obtained by H-effusion experiments on hydrogen passivated cells. 4 1 Introduction
Finally in chapter 6 the MIRHP process is applied within industrial screen-printed cell processes at Eurosolare and Solarex and the industrial importance of the MIRHP process for bulk passivation is discussed. 2 Multicrystalline silicon materials and laboratory cell processing
2.1 Introduction
In the following two sections a short overview on the production and some structural as well as electrical properties of the block and ribbon cast mc-Si materials used in this work is given. Afterwards the standard cell processing of small laboratory cells is described.
2.2 Production of multicrystalline silicon 2.2.1 Block cast mc-Si The mc-Si materials used nowadays in PV industry are almost completely made by block casting techniques which all have in common that the polysilicon feedstock is liquified and afterwards recrystallized as a block. The block casting techniques differ in the method of liquefying the Si feedstock, the crystallization velocity, the orientation of the crystallites and the obtained material quality. A good overview on the different block casting techniques is given in [9, 12]. Most of the materials used in this work were processed using directional solidification or also called the Bridgman-Stockbarger method where a crucible is moved downward in a fixed temperature field (Eurosolare, Photowatt, Solarex). A planar solidification front is obtained by the SOPLIN (solidification by planar interface) process developed at Bayer [13]. The EMC (electromagnetic casting) process applied by Sumitomo Sitix differs from these conventional casting techniques by melting the Si feedstock in an induction melting crucible where a direct contact between the ingot and the crucible is avoided [14]. Table 2.1 lists some of the block casted mc-Si materials used in this work, the material supplier and the maximum efficiency reached up to date. Besides the current record by the group of M. A. Green of 19.8% on a PERL (passivated emitter, rear locally-diffused) cell based on EUROSIL material also the 18.6% on a cell based on HEM (heat exchange method) material processed by the group of A. Rohatgi are remarkable. High efficiencies are reached not only on these small 11 cm2 cells as for example the result of the FhG-ISE of 17.4% on a 55 cm2 EUROSIL cell shows.
2 material company ηmax / A [cm ] literature
BAYSIX SOPLIN (solidification by planar interface) Bayer 16.8% / 25 [15] [16] EMC (electromagnetic casting) Sumitomo Sitix 15.9% / 4 [17] [18] EUROSIL Eurosolare 19.8% / 1 [19]; 17.4% / 25 [15] [20] HEM (heat exchange method) Crystal Systems 18.6% / 1 [21] [22] SOLAREX Solarex 16.7% / 4.6 [23] [24, 25] POLIX* Photowatt 16.8% / 4 [26] [27] Table 2.1: The used block casted mc-Si materials, the material supplier and the maximum efficiency reached up to date are listed. *Not used in this work but cooperation planned in the near future. 6 2 Multicrystalline silicon materials and laboratory cell processing
2.2.2 Ribbon cast mc-Si There is hope that also the next step to ribbon cast mc-Si will further decrease the costs of PV materials and modules as in the case from the change from Cz-Si to block cast mc-Si. To avoid the material loss due to wafer slicing and to further decrease the base Si material costs intensive research activities have been directed into the development of ribbon casting techniques such as the EFG (edge-defined film-fed growth) process from ASE [28, 29], the String Ribbon process from Evergreen Solar [30], the dendritic web process from EBARA Solar [31], the spin-casting concept [32] as well as the RGS (ribbon growth on substrate) process from Bayer [33]. In 1994 ASE was the first company to put its crystallization technology into full scale manufacturing. At the end of 1998 the EFG-process will provide Si material for modules with a total power output of 11 MW/year with an additional increase planned for the near future to 20 MW/year [34, 35]. The EFG technique described in [29] consists on pulling a hollow octagon shaped mc-Si tube out of a Si melt. Finally the octagon is cut into 10 10 cm2 wafers using a high speed laser. Pilot lines for most of the above mentioned ribbon materials exist and production lines are planned in the near future by Evergreen Solar and EBARA Solar. A serious competitor to these ribbon materials is RGS, distinguished by a very fast production process which relies on the casting of a layer of molten silicon on a supporting substrate with the crystallization front lying nearly parallel to the plane of the ribbon. At the end of the process the wafer is automatically separated from the reusable substrate. With this production technique the costs for a Si wafer can be drastically reduced [33]. Because of the leading role of EFG for the present PV industry and the large opportunities of RGS within the ribbon materials to further reduce production costs I have focused in my work on these two ribbon materials. As a long term alternative to block and ribbon cast Si the development of thin film mc-Si solar cells on cheap foreign substrates [36, 37][38] or self supporting [39-41] has to be mentioned. However difficulties in the deposition of Si on cheap substrates such as glass for the former case and problems in the handling of thin wafers as in the later case have to be solved. Because of these problems only AstroPower with the Silicon-FilmTM process is planning to start with a nine megawatt per year capacity production line at the end of 1998 [38]. The process consists of producing continuous silicon sheets by depositing p-type doped silicon from a liquid solution on conductive ceramics, followed by emitter diffusion and standard screen-printing metallization.
2.3 Structural and electrical properties Differences of the used crystallization techniques result in a large variety of structural and electrical properties of the block and ribbon materials. Some of these properties for the mc-Si materials used in this work are shown in Table 2.2. Large grain diameters dgrain, low dislocation
-2 -3 -3 material dgrain [mm] ND [cm ][Oi] [cm ][Ci] [cm ] metals Lb [µm] BAYSIX <20 3105 [16] 1 - 61017 [16] < 31017 [16] 100 - 130 EUROSIL <20 low 0.9 - 71017 [20, 42] 81016 [42] 120 - 150 SOLAREX <10 104 - 106 [25] 0.3 - 1.21018 [25] - <100 EMC <5 106 - 108 [43] < 1016 [18, 42] 1-31016 [18, 44] 30 - 120 EFG * 104 - 108 [45] < 51016 [46] 1018 [45][47] Fe, Ti** [46] < 80 RGS 0.2 - 1 [48] 105 - 107 [48, 49] > 1018 [48] > 1018 [50] Fe, Ni, Cu*** [51] < 30
Table 2.2: Some of the structural properties (the average grain diameter dgrain, the dislocation density ND, the concentration of interstitial oxygen/carbon Oi/Ci and possible metal contamination) and the bulk minority carrier diffusion length Lb of the mc-Si materials used in this work are shown. Lb was determined by UKN with the SPV (surface photovoltage) method on chemically polished wafers. *long narrow crystallites, **measured with DLTS, ***measured with neutron activation analysis to approximately 1014 cm-3. 2.4 Processing of laboratory solar cells 7
densities ND and high bulk minority carrier diffusion lengths Lb are determined for BAYSIX, EUROSIL and SOLAREX. During the crystallization of these materials the ingot was in direct contact with the crucible, which is a source for oxygen, carbon and other impurities. Therefore these block casted materials have larger concentrations of interstitial oxygen/carbon Oi/Ci than EMC where during the crystallization the ingot is not in direct contact with the crucible. The economically necessary fast pulling velocity of the EMC process and the curved solid-liquid interface during crystallization result in smaller grains, considerably more dislocations with a higher density as in the case for the other block casted materials. For EMC the material quality is mainly determined by the dislocation density which results in a broad distribution of the bulk minority carrier diffusion lengths. For the ribbon materials in addition to the structural defects also metallic impurities determined by DLTS (deep level transient spectroscopy) considerably reduce Lb.
2.4 Processing of laboratory solar cells 2.4.1 Cells with homogeneous emitter For the processing of small 4 cm2 laboratory cells either a homogeneous or a selective emitter structure was used. The processing sequence for the homogeneous emitter cells is shown in Fig. 2.1. As starting material p-type doped mc-Si wafers were used. For the removal of the saw damaged layer that occurred during wafer slicing about 15 µm per side were etched using an acid solution (HF(50%):HNO3(65%):CH3COOH(99%) = 1:8:1). After applying an IMEC clean [52] the n+ emitter was formed by phosphorus diffusion at 820 °C. The phosphorus glass was etched with HF(5 v%) resulting in a sheet resistance of 90 Ω/. After a second IMEC clean a dry thermal oxide of approximately 11 nm was grown at 900°C to ensure a good surface passivation. With the evaporation of 2 µm aluminum on the back side followed by sintering for 30 min at 800°C the back side emitter is overcompensated resulting in a slight back surface field (BSF). During this step also gettering of metallic impurities was observed [53, 54]. After definition of the front contact with photolithography a sequence of Ti/Pd/Ag (50 nm/50 nm/3 µm) is evaporated. With a lift-off in acetone the metal remains only at the defined front grid region. Finally a 2 µm Al back contact is evaporated. For healing the E-gun damage of the front surface the cells were annealed in Ar/H2 at 380°C for 1 h.
homogeneous emitter solar cell process
surface defect etching
+ POCl 3 diffusion of n (820°C -> 90Ω /sqr) dry therm al oxidation
E-gun Al evaporation at back side A l sintering (A l-B SF)
photolithography at front side E-gun evaporation of Ti/Pd/Ag lift-off E-gun Al evaporation at back side
Fig. 2.1: Solar cell processing sequence of the homogeneous emitter solar cells used in this work. 8 2 Multicrystalline silicon materials and laboratory cell processing
2.4.2 Cells with selective emitter During my work on hydrogen passivation I found out that applying the MIRHP process after complete cell processing on cells with a lowly doped homogeneous emitter of 90 Ω/ can result in a degradation of cell performance especially of the fill factor FF and the open circuit voltage VOC [43]. This degradation effect will be further discussed in chapter 4.6. It was found that using a selective emitter cell structure with a highly doped emitter below the front grid and a lowly doped emitter between the fingers this degradation effect can be completely avoided resulting in improvements of all illuminated I-V parameters due to the MIRHP process [55]. As shown in Fig. 2.2 the selective emitter cell process consists on the following processing steps applied before carrying out the processing steps of the homogeneous emitter cell. As for the homogeneous emitter process the saw damage was removed, followed by an IMEC clean and the diffusion of a deep, highly doped emitter with sheet resistance of 20 Ω/. The front side was masked with a 50 nm thick silicon nitride (SiN) film deposited by PECVD (plasma enhanced chemical vapor deposition). The abbreviation SiN can not be interpreted as the stoichiometric composition which will be discussed in section 6.4. Using photolithography the region of the front grid is defined by a photoresist and the SiN underneath is protected. The non protected SiN is etched by buffered HF which does not attack the photoresist. After removing of the photoresist with an organic etching solution the emitter is removed with NaOH (5 v%). The SiN region of the front side is not attacked by the NaOH leaving the emitter only at the front grid region. Finally the SiN is etched by HF (10 v%). The cell processing is finished with the processing steps for the homogeneous emitter formation as shown on the right side of Fig. 2.2.
selective emitter solar cell process
surface defect etching ++ ++ ++ + n POCl 3 diffusion of n n POCl 3 diffusion of n (900°C -> 20 Ω /sqr) (820°C -> 90Ω /sqr) dry therm al oxidation
++ E-gun Al evaporation at back side n SiN-m asking on front side Al sintering (Al-BSF) ++ n photolithography on front side
photolithography at front side ++ n SiN-etching (HF) E-gun evaporation of Ti/Pd/Ag
removal of photoresist ++ lift-off n em itter etching (N aO H ) E-gun Al evaporation at back side
Fig. 2.2: Solar cell processing sequence of the selective emitter solar cells used in this work.
2.4.3 Cell processing using RGS and EFG base material The RGS sheets used in this study had a size of 7.5 11 cm2, a thickness varying between 250 and 350 µm and an average crystal grain diameter of approximately 0.5 mm. For a convenient cell processing each RGS sheet was cut in two 5 5 cm2 wafers. The solar cell processing started with a leveling of the uneven front surface of the RGS wafer with a planarisation blade mounted on a conventional silicon dicing saw to enable the usage of photolithography and to remove the segregation layer of about 25 µm on top of the wafer. Afterwards the saw damage 2.4 Processing of laboratory solar cells 9 and a carbon rich layer on the back surface has been taken away in a defect etching step. The further cell processing was analogous to the other materials shown in 2.4.1 and 2.4.2. For EFG it was found that photolithography can be applied without leveling the uneven wavy front surface, however the back surface had to be planarized analogous to the front side of the RGS wafer to ensure a good wafer fixation on a vacuum chuck when using the mask aligning step for the selective emitter process. 3 Characterization of silicon wafers and cells
3.1 Introduction The used measurement techniques for the characterization of multicrystalline wafers and cells will be presented in this chapter. Two contactless techniques, the surface voltage and the microwave-detected photoconductance technique have been used to characterize silicon wafers before cell processing and will be presented in the following section. The characterization of solar cells by dark/illuminated I-V, spectral response and light-beam-induced current measurements is described in section 3.3. From the theoretical side this chapter focuses on the interpretation of the internal quantum efficiency (IQE) determined by spectral response and reflection measurement. An intensive literature research has shown that the well known experimentally observed connection between the inverse of the IQE and the inverse of the absorption coefficient has not been theoretically consistent explained until now. In section 3.4 this gap in theory will be filled by deriving an approximated equation for the total IQE including the contributions of the emitter, space charge region and base of a cell. By this new approach a complete theoretical understanding of the experimentally observed linearity between the inverse of the IQE and the inverse of the absorption coefficient is given. Besides the theoretical understanding this approach also provides rules for selecting the fit range of the wavelength in which the bulk minority carrier diffusion length is obtained. Besides the importance of the new approach for extracting bulk diffusion lengths from experimentally obtained IQEs the new procedure is also used in section 5 for the derivation of the two-layer IQE, with which partly H-passivated cells can be simulated.
3.2 Contactless measurement methods 3.2.1 Surface photovoltage method During the last years contactless measurement techniques such as the surface photovoltage method have gained a great deal of attention in semiconductor industry for monitoring of bulk minority carrier diffusion lengths during various processing steps [56, 57]. The effect that the illumination of a semiconductor surface induces a voltage, the so called surface photovoltage (SPV), was first investigated by Garrett [58]. Electron-hole pairs generated by photons of energies larger than the semiconductor band gap energy are subjected to bulk and surface recombination as well as to diffusion along concentration gradients. From the redistribution of charges a change in the surface potential on the semiconductor surface and therefore a change of the bending of the energy bands arises. The SPV is usually defined as the change in surface barrier heights but can also be defined at low injection levels (the case for all measurement conditions at UKN) as the difference between the quasi-Fermi levels of electrons and holes under illumination. It was found that the SPV is a monotone function of excess carrier density which itself depends on the incident photon flux φph, the optical absorption coefficient α, the bulk minority carrier diffusion length Lb and some other parameters [59]. A 3.2 Contactless measurement methods 11 more detailed theory taking into account recombination in the surface space charge region as well as at surface states is found in [60] and experimental results on solar cells are given in [61]. For the constant SPV method where the wavelength λ of exciting light is increased and the photon flux is adjusted to get a constant SPV the following proportionality can be deduced from theory [59]:
φα∝+−1 phL b . (3.1)
-1 By plotting φph against α a straight line is obtained, which extrapolated in the negative region -1 -1 of the α axis, results in Lb as the intercept with the α axis. In the case of a properly set up measurement system the main source of error is due to uncertainties in the knowledge of the functional dependence of the absorption coefficient on the wavelength. Especially α(λ) of small grained mc-Si materials like RGS show deviations from the well known α(λ) of monocrystalline silicon [62]. The absorption coefficient was calculated from the measured transmission and reflection of a thin mechanically polished RGS wafer [43]. For the larger grained mc-Si materials of investigation α(λ)-data obtained from a specially thin BAYSIX wafer was used, because it was found that the measurement uncertainty in α(λ) accounts for more than the differences between the large grained mc-Si materials. A description of the measurement set up used in our lab can be found in [63, 64]. The SPV measurement was carried out by first increasing the wavelength from 850 nm to 1010 nm and then reducing it back to 850 nm. Fig. 3.1 shows the distribution of the bulk minority carrier diffusion lengths Lb on a 10 10 cm2 EMC wafer before and after HP (hydrogen passivation). Before HP a large variation of Lb between 35 and 124 µm with an average value of 74 µm and a standard deviation of 31 µm was observed. These values are in excellent agreement with the values of
Lb between 39 and 111 µm and an average Lb of 75 µm published by Sumitomo Sitix [18]. After the hydrogen passivation SPV measurements were carried out on selected positions. It is clearly seen in Fig. 3.1 that a large increase in Lb due to the HP is obtained with a better improvement for the poorer regions, leading to a tighter distribution of the Lb values with differences between the minimum and maximum Lb values of 89 µm before and 55 µm after hydrogen passivation. With an average value for Lb of 153 µm after the MIRHP process the diffusion length improves by a factor of 2 during the MIRHP process.
180 Measurement positions on 2 m before HP the 10 10 cm EMC wafer: 160 µ
55 55 after HP 140 1 2 3 4 5 120 g
m] 6 7 8 9 10 5 µ 100 [
b 11 12 13 14 15
m 5 L
80 µ 16 17 18 19 20
89 89 5 60 21 22 23 24 25 40 20 0 0 5 10 15 20 25 Position on the wafer
2 Fig. 3.1: Distribution of the bulk minority carrier diffusion length Lb on a 10 10 cm EMC wafer determined with the SPV method before and after hydrogen passivation. The HP results in a large increase of Lb with better improvement for the poorer regions. The measurement positions on the wafer are shown on the right side. 12 3 Characterization of silicon wafers and cells
3.2.2 Microwave-detected photoconductance decay technique (MW-PCD) With the MW-PCD (microwave-detected photoconductance decay) technique the effective minority carrier life time τeff, which depends on bulk and surface recombination, of a semiconductor can be measured. Most of the MW-PCD methods use for the generation of excess charge carriers a pulsed light source [65, 66] but also a quasi-steady state photoconductance method was established recently [67-69] which resembles the illumination conditions as in the case during the illuminated I-V measurement. For both methods the change in carrier concentration results in a change in the conductivity of the semiconductor which is determined by the reflection of microwaves. For the simplification of the following equations only the case of equal front and back surface recombination velocity named S is considered. Cases with different surface recombination velocities can be found in [70-73] and references given therein. The following approximations for τeff are given in literature for the cases of either large or small S [74]:
11 D =+π 2 b for S >> D /d ττ 2 b (3.2) eff b d and
11=+S ττ2 for S << Db/d (3.3) eff b d
with the bulk minority carrier life time τb, the bulk minority carrier diffusion coefficient Db and the semiconductor thickness d. A none-passivated silicon surface, which is only covered by a native oxide, results in values for 6 2 S in the order of 10 cm/s. Together with Db = 30 cm /s and a usual wafer thickness of 300 µm the assumption (S >> Db/d) made for eq. 3.2 is excellently fulfilled. However using eq. 3.2 for the determination of τb one also has to know Db. By successive wafer etching and MW-PCD -2 measurement the functional dependence of the inverse of τeff over d is obtained and by a linear fit τb and Db can be determined. However the etching is laborious and not always practicable for example in the case of process monitoring where τb has to be determined between several process steps. To avoid these disadvantages one passivates the semiconductor surfaces to reduce S below
Db/d and uses eq. 3.3 to obtain τb. For example a very low surface recombination velocity of 0.25 cm/s was obtained on a FZ silicon wafer (lightly doped at 150 Ωcm, <111> surface) after thermal oxidation followed by the dissolution of the oxide layer by hydrofluoric (HF) [75]. Using a remote PECVD (plasma enhanced chemical vapor deposition) silicon nitride recombination velocities below 10 cm/s were reached on FZ-Si [76]. But even if one assumes a more moderate S of 50 cm/s and d = 300 µm, the bulk lifetime τb can be approximated by τeff within an error of below 10% as long as τb is below 30 µs which corresponds to diffusion lengths below 300 µm. For most mc-Si materials τb is below this value. The MW-PCD measurements used in this work were carried out at Eurosolare and recently also at our lab using a MW-PCD device from Amecon [77]. At our lab the used wavelength was 904 nm which results in a light penetration depth of 30 µm. During the measurements the surface is passivated by an ethanol-iodine solution [78]. In the near future also a HF passivation cell will be used, therefore avoiding a wafer contamination by the ethanol-iodine solution [77]. 3.3 Measurements on solar cells 13
3.3 Measurements on solar cells 3.3.1 Dark I-V characteristics - the two-diode model The measurement of the dark I-V characteristics can provide important information about the recombination processes involved in a solar cell. The most widely used model for describing the voltage dependence of the dark current density JD is the two-diode equation [79-81]:
VRJV− () VRJV− () VRJV− () JV()= Jexp sD − 11 + J exp sD − + sD (3.4) D 01 ⋅ 02 ⋅ nV12th nVth Rsh
with the saturation current densities J01/2, the diode factors n1/2 of the first and second diode, the series resistance Rs, the shunt resistance Rsh and the thermal voltage Vth = kT/e = 25.7 mV at T = 25°C. Rs was added to include the voltage drop due to the resistance of the metallization grid, emitter and bulk as well as the metal silicon contact resistance. A voltage independent shunt is represented by Rsh. The values of the diode factors depend on the type of recombination. The strength of recombination is determined by the saturation current density. Generally a diode factor of 1 is assigned to the first diode which is theoretically due to the recombination current in the base and emitter [82]. Originally the second diode was added with a diode factor of 2 to include recombination in the scr (space charge region) due to localized traps within the energy gap [83]. This theory was expanded by [84] to extended crystal defects like GBs (grain boundaries) and dislocations. In [85] it was found theoretically that besides the effect of recombination in the scr also the shunting via dislocations bordering the scr shows a n2 = 2 dependence. Using two dimensional computer simulations an enhanced recombination activity in the scr was also found at grain boundaries passing vertically through the scr [86]. For this case a diode factor of 1.8 was calculated. There are also theoretical models explaining diode factors different from 1 and 2. Diode factors between 1.2 and 1.6 were found in dependence of the trap energy [87] and above 2 in the case of asymmetrical p-n junctions [88] which are common to Si solar cells. Experimentally it is often observed that the second diode factor is larger than 2. It is found that the front metal coverage, the surface structure and the emitter diffusion profile can have an influence on the second diode factor resulting in values up to 4.5 [89]. On some FZ-Si high efficiency cells also non ideal diode factors between 2 and 4 were observed, which are most probably due to recombination at the cell edges [90]. Throughout my work I used a fixed value of 1 for the first diode factor and took the second as fit parameter. In my earlier work [43] I have shown that due to hydrogen passivation of multicrystalline silicon solar cells high second diode factors can be reduced to more ideal values. On EMC cells it was shown that due to a MIRHP process n2 decreases from 3 to 2.3. This behavior is again observed for RGS cells (see chapter 4.4.4) where after H-passivation almost ideal diode factors of 2.05 were obtained.
3.3.2 Illuminated I-V characteristics From the illuminated I-V characteristics measured under standard test conditions (AM1.5 [91], 1000 W/m2, 25°C) the most important cell parameters, the cell efficiency η, the short circuit current density JSC, the open circuit voltage VOC and the fill factor FF can be extracted. A correlation between the dark and illuminated current characteristics can be made under the assumption of the superposition principle for solar cells [92, 93] which states that the current density of an illuminated solar cell JL(V) equals the short circuit current density subtracted by the dark current density:
()=− JVLSCD J J(). V (3.5) 14 3 Characterization of silicon wafers and cells
In this formulation according to [93] all currents were taken to be in the first I-V quadrant and JL(V) to be positive below VOC. There are several instances discussed in literature where it is shown that the superposition principle and therefore eq. (3.5) does not hold for solar cells (see references given in [94]). Among these high injection conditions and a high series resistance are the most important examples. However the laboratory cells processed at the UKN exhibited low series resistances of 30 - 60 mΩcm-2 and were measured at low injection conditions (AM1.5). Recently, with computer simulations it has been found that two further departures from eq. (3.5) exist, the first one only relevant for high efficiency cells where the recombination experiences a saturation behavior and the second one occurring at low forward-bias voltages affecting all cells to a varying degree [94]. However it was stated that the second departure only affects the behavior near the short circuit current point and therefore the validity of eq. (3.5) can be taken for granted at VOC. Because of the dominance of the first diode at large voltages, the open circuit voltage VOC can be calculated from eq. (3.4) and eq. (3.5) by neglecting the second diode [92], as well as Rs and Rsh [95]:
J VnV=⋅ ⋅ln SC +1 . OC1 th (3.6) J 01
3.3.3 LBIC LBIC (light-beam-induced current) measurements offer the possibility to separate intragrain and grain boundary recombination of mc-Si solar cells [96]. With this method minority carriers are generated locally in a solar cell by a light beam and the short circuit current is measured. With the short circuit current, a measure for the recombination in the illuminated area is obtained. The following LBIC measurements were carried out at FhG-ISE before and after a MIRHP process on one cell processed at our lab and based on EMC material. To compensate variations of the light source used for the carrier generation, the measured short circuit current is divided by the lamp voltage resulting in the LBIC mappings shown in Fig. 3.2. Due to the MIRHP process a clear increase in the LBIC signal (from dark to light) correlated to a decrease in the recombination of the grain boundaries is seen. Because of differences in the LBIC setup (relative sample position to the bias light beam) during the two measurement days an absolute comparison between the measurement before and after the MIRHP process and therefore an exact calibration of the LBIC signal is not possible 1. However from the comparison of the intragrain LBIC signal, which has to be after the MIRHP process at least as large as before the MIRHP process, it can be concluded that the measurements after the H-passivation have to be corrected to higher values, therefore showing an even further decrease in the grain boundary recombination. Since recently also LBIC measurements can be carried out at our lab and first results obtained on cells based on EFG and SOLAREX material before and after a MIRHP process are presented in section 4.3.4.
1 Private communication with Ralf Lüdemann. 3.3 Measurements on solar cells 15
relative LBIC signal
1.25 1.75 2.25 2.75 3.25
a): before MIRHP b): after MIRHP
Fig. 3.2: LBIC measurement results obtained on one cell based on EMC before (left side) and after (right side) a complete MIRHP process.
3.3.4 Spectral response 3.3.4.1 Measurement and determination of the internal quantum efficiency (IQE) Measuring the short circuit current as a function of the wavelength of monochromatic light impinging on a cell the cell’s spectral response (SR) is obtained. Because of the strong dependence of the light absorption coefficient on the light wavelength information of the recombination processes in the emitter, space charge region and the base as well as on the front and back surface of a cell is in principle possible. In the following a description of the measurement of the SR and how the internal quantum efficiency (IQE) is obtained from the SR and reflectance measurement is given. For the theory of the IQE of a solar cell the reader is referred to section 3.4. The spectral response measurement set-up is described in [97]. Light from a 100 W halogen lamp is collimated and modulated with 30 Hz by a chopper. The light passes through a grating monochromator, where a wavelength between 350 and 1200 nm is selected, and is directed to the cell. A white light source (bias light) is used to saturate traps and obtain similar conditions as for the illuminated I-V measurement. By the means of a lock-in amplifier the incremental response of the small alternating component of monochromatic light is filtered from the bias light. Dividing the measured cell current ISC(λ) by the light intensity Ilight(λ) determined with a calibrated cell gives the spectral response:
I ()λ ()λ = SC SR ()λ . (3.7) I light 16 3 Characterization of silicon wafers and cells
The internal quantum efficiency (IQE) is defined as the number of minority carriers contributing to the short circuit current divided by the number of photons entering the cell. Therefore the IQE includes the effects that a photon which enters the cell is absorbed and generates an electron-hole pair which is separated and collected at the contacts. From this definition the IQE is given by the SR and the external front surface reflectance R:
1 Ie()λ 1 hc IQE()λ = ⋅ SC = ⋅⋅SR()λ . ()− ()λ ⋅ ()λλ()()− ()λ λ (3.8) 1 R Ihclight 1 R e with the factor 1/(1-R(λ)) to exclude the influence of the front surface reflectance.
3.3.4.2 Influence of the bias light on the IQE To ensure a high measurement accuracy the intensity of the used bias light was restricted to 0.1 sun intensity. For higher bias light intensities the limit of the lock-in technique used at our lab was reached resulting in a low signal to noise ratio especially for small wavelengths, for which the intensity of the used halogen lamp was low. To investigate the influence of a bias light on the mc-Si material for all materials the SR was measured with and without the bias light. Fig. 3.3 shows the results of cells based on RGS and BAYSIX. As shown for the BAYSIX material and also for the other high quality block cast materials (EUROSIL, EMC) used in this work no changes or only minor ones in the IQE due to a bias light were observed. For the lower quality SOLAREX material the SR increased up to a bias light of 0.1 sun intensity. Also shown in Fig. 3.3 is a clear increase of the IQE due to a bias light for the RGS cell. Even a larger increase of the IQE due to a 0.1 sun bias light is obtained on the other ribbon material of investigation, namely EFG (see Fig. 3.4). Higher bias lights than 0.1 suns resulted only in small increases of the IQE for EFG and no further increases of the IQE of cells based on the other investigated materials.
1,0 Fig. 3.3: Internal quantum efficiencies of cells based on RGS and BAYSIX determined from SR 0,8 measurements with and without a bias light. For the bias light a halogen lamp was used resulting in 0,6 0.1 sun intensity.
IQE Si-material biaslight 0,4 RGS no yes 0,2 BAYSIX no yes 0,0 500 600 700 800 900 1000 1100 λ [nm] 1,0 Fig. 3.4: Influence of the bias light intensity on the internal quantum efficiency of a cell based on EFG. 0,8
0,6
IQE Si-material biaslight 0,4 EFG no 0.1 sun 0,2 0.2 sun 0.3 sun 0,0 500 600 700 800 900 1000 1100 λ [nm] 3.4 Theory on the internal quantum efficiency (IQE) 17
3.3.4.3 Influence of a high temperature step on the IQE of EFG solar cells High temperature loads during processing of mc-Si cells can be disadvantageous to the final material quality and especially to the base minority carrier diffusion length Lb. For the selective emitter cell process described in Fig. 2.2 the highest temperature load is caused during the first P-diffusion at 900°C. As seen in Fig. 3.5 using EFG as base material a considerable lower IQE, Lb, JSC and VOC are determined on cells with a selective emitter than with a homogeneous emitter. This proves that the high temperature load during the first P-diffusion of the selective emitter cell process is critical for processing of EFG cells. However, for the other mc-Si materials under study no deterioration of the cell performance is observed by comparing selective and homogeneous emitter cells. Comparing the structural and electrical material parameters of the EFG material with those of the other mc-Si materials especially the high carbon concentration of 1018 cm-3 [45, 47] and the presence of Fe and Ti [46] can be a cause for the special sensitivity of EFG to high temperature loads. Interestingly applying the MIRHP process on selective emitter solar cells based on EFG increases the IQE above the value for homogeneous emitter cells which is also seen in Fig. 3.5.
Fig. 3.5: IQEs of one EFG cell 1,0 with homogeneous emitter (short material: dotted line) and one with selective emitter (long dotted/closed line 0,8 EFG before/after MIRHP). Using a cell process with a homogeneous emitter a higher IQE is obtained 0,6 than with a selective emitter due to a deterioration of the EFG IQE material during the high 0,4 L b JSC VOC temperature load of the first emitter HP [ µm] [mAcm-2] [mV] P-diffusion. Applying a MIRHP 0,2 homogeneous no 95 19.6 544 process the deterioration is selective no 40 16.7 511 removed. The bulk diffusion selective yes 122 22.1 563 length L is obtained by a fit of the b 0,0 IQE with eq. (3.25) presented in 400 500 600 700 800 900 1000 1100 section 3.4.4. λ [nm]
3.4 Theory on the internal quantum efficiency (IQE) 3.4.1 Introduction The first calculations of the internal quantum efficiency (IQE) of the base of solar cells date back to the beginning of solar cell processing [98]. The first most detailed investigations of the influence of the emitter and the cell thickness to the IQE are given in [99-101]. However, the given formulas can only be used to calculate the contribution of the emitter or base separately, but not the total IQE with the contribution of the space charge region included. Actually several equations or approximations for the IQE derived up to date deal only with the contribution of the base [90, 102-105]. However, neglecting the contributions of the emitter and space charge region results in a theoretically inconsistent formulation of the IQE, which also leads to a wrong interpretation of SR-measurement data. Starting in section 3.4.2 from theoretical work on the IQE of the three regions the general problem is described in section 3.4.3. Applying moderate approximations on the emitter region, a formulation of the total IQE is derived in section 3.4.4. 18 3 Characterization of silicon wafers and cells
3.4.2 Literature work 3.4.2.1 Contributions of emitter, space charge region and base to the IQE For a simplified theoretical description all equations are formulated for cells with n-p junction, that means p-type base material with a n-type emitter, however by changing indices all conclusions are also valid for p-n junction cells. Fig. 3.6 shows a schematic representation of a standard flat cell. The cell of total thickness H can be described by a model of three regions, the emitter, the space charge region (scr) and the base of corresponding widths we, wscr and wb. The recombination in the emitter and base are described in terms of average diffusion lengths of minority carriers Le and Lb, respectively. No recombination is assumed in the scr. The recombination on the front and back surface is described by the recombination velocities Se and Sb. For a simplification of the following equations the author prefers to label the front and back side recombination velocities according to emitter and base.
Fig. 3.6: Sketch of a solar cell of total thickness H separated into the emitter of width we, a space charge region (scr) of width wscr and a base of width wb. The recombination in the emitter/base is described by the emitter/base minority carrier diffusion length Le/Lb. No recombination is assumed in the scr. The front/back surface recombination velocity at the emitter/base is given by Se/Sb.
The dependence of the total internal quantum efficiency on the light absorption coefficient α is obtained from the contributions of the three cell regions the emitter, the scr and the base:
αα=+ αα + IQEtotal() IQE e () IQE scr () IQE b (). (3.9)
Under the assumption of homogeneously doped regions and a thick cell compared to the light penetration depth (A3.1: H >> α-1) exact formulations of the IQEs of the three regions can be derived. The last assumption of relatively small light penetration depth ensures that internal back side reflection can be neglected resulting in an exponentially decreasing generation profile:
gx()=⋅⋅−α F()1 R ⋅ e−⋅α x with F the flux of photons onto the front cell surface and R the front surface reflectance. With the assumption of homogeneously doped regions and the approximation A3.1, the contributions of the regions to the IQE are given in the following. The structural and electrical parameters used in the equations are defined in Fig. 3.6. 3.4 Theory on the internal quantum efficiency (IQE) 19
IQE of the base:
It is shown in appendix 9.1 that with the assumption of a homogeneously doped base region and with the approximation A3.1 given above the base IQE can be calculated by [106]:
wb wb −⋅α w ⋅++−()α b sb cosh sinh Lsebb 1 αL −⋅α L L IQE ()α ≠= b ⋅−eLw α b b (3.10) b α 2 − b w w Lb ()Lb 1 ⋅+b b sb sinh cosh Lb Lb
⋅ = SLbb =+ with the reduced back surface recombination velocity sb and wwescr w. Db
IQE of the emitter:
For a homogeneously doped emitter an expression analogous to the base region is obtained [106]:
w w −⋅α w sLs+−α coshe + sinh e e e eee 1 αL Le Le −⋅α w IQE ()α ≠= e −⋅αLe e (3.11) e α 2 − w w e Le ()Le 1 e + e se sinh cosh Le Le
SL⋅ = ee with the reduced front surface recombination velocity se . De
IQE of the space charge region:
With the assumption that recombination in the space charge region can be neglected the IQE of the scr is given by the product of the two probabilities that a photon reaches the scr and is absorbed in the scr [106]:
−⋅ααww −⋅ α =−escr IQEscr () e()1. e (3.12)
IQE of base region at α = 1/Lb and of emitter region at α = 1/Le:
Note that the equation for the base IQE is not defined at α = 1/Lb. It is shown in appendix 9.2 that eq. (3.10) can be expanded continuously at α = 1/Lb because the left and right limit are equal:
wb w −⋅−() w −− 11sb b 1 L Lb L 1 α =⋅b ⋅− ⋅ b = lim IQEb () e 1 eIQE:()b . (3.13) α→ 2 wb wb L 1 Lb ⋅+ b sb sinh cosh Lb Lb
The same procedure can be applied for the IQE of the emitter at α = 1/Le. 20 3 Characterization of silicon wafers and cells
3.4.2.2 Additional approximations for the base IQE
3.4.2.2.1 wb >> Lb In the following the IQE of the base given in eq. (3.10) is simplified by the assumption of a thick base region relative to Lb (A3.2a: wb >> Lb). Dividing the fraction in brackets of eq. (3.10) by cosh(wb/Lb) results for the base IQE in:
−⋅α w e wb s ++⋅−⋅tanh b ()α Ls b bb () α ⋅ L −⋅α Lb cosh wL IQE ()α = b ⋅⋅⋅−eLw α bb b α ⋅−2 b w ()Lb 1 ⋅+b sb tanh 1 Lb
Aa32. −⋅α −()wL α ⋅ L sLsee++12()α ⋅ − ⋅wb ⋅⋅ bb ≈ b ⋅⋅⋅−eL−⋅α w α bbb α ⋅−2 b + ()Lb 1 sb 1 Aa32. α ⋅ L ≈ b ⋅⋅⋅−eL−⋅α w []α 1 α ⋅−2 b ()Lb 1 with the final result:
α ⋅ L α ≈ b ⋅ −⋅α w IQEb () α ⋅+e . (3.14) ()Lb 1
With the assumption of a large light penetration depth compared to the thickness of the emitter -1 and space charge region (A3.3: w = we + wscr << α ) eq. (3.14) reduces to the well known formula given for example in [102]:
α ⋅ L 1 1 α ≈ b =+1 (3.15) IQEb () α ⋅+ or αα⋅ Lb 1 IQEbb() L
3.4.2.2.2 wb << Lb
For the assumption of a base region thin with respect to Lb (A3.2b: wb << Lb), a large cell thickness compared to the light penetration depth (A3.1: H >> α-1) and approximation A3.3, an expression similar to eq. (3.15) was first proposed by Basore [104]:
1 =+ 1 αα1 ⋅ (3.16) IQEbeff() L with the effective base diffusion length:
⋅+wb sb tanh 1 = Lb LLeff b . (3.17) + wb sb tanh Lb 3.4 Theory on the internal quantum efficiency (IQE) 21
Because Leff equals Lb in the limit wb >> Lb it is assumed in [105] that eq. (3.16) together with Leff from eq. (3.17) is also valid for all values of Lb, but no mathematical prove was given.
3.4.3 The general problem with the approximated base IQEs To make the point about the general problem of using the approximated equations of the base IQEs deduced in the previous section to fit IQE-data, we will restrict ourselves to eq. (3.15). But the same arguments can also be applied by using equations (3.16)/(3.17) which were obtained by assuming wb << Lb. Additionally, for the following discussion the specific structural and electrical cell parameters from Table 3.1 are taken to calculate the IQEs of the different regions shown in Fig. 3.7. These parameters are also used for the IQE calculations throughout this chapter. Differences from these parameters are indicated in the graphs separately.
structural and electrical cell parameters region width of region diffusion coefficient diffusion length surface recombination velocity
2 emitter we = 0.5 µm De = 5 cm /s Le = 15 µm Se = 1E4 cm/s
scr wscr = 1.0 µm 2 base wb = 298.5 µm Db = 30 cm /s Lb = 100 µm Sb = 1E7 cm/s total H = 300 µm
Table 3.1: The structural and electrical parameters of the solar cells used in the following IQE calculations.
Fig. 3.7: Contributions of the 1,0 exact total IQE base (eq. (3.10)), emitter (eq. (3.11)) (eq. 3.9 with approximated bulk IQE and space charge region (eq. (3.12)) eq. 3.10-12) 0,8 (eq. 3.15) to the total IQE (eq. (3.9)). For the emitter IQE calculations the structural and base (eq. 3.10) electrical parameters given in 0,6 (eq. 3.11) Table 3.1 are taken. Additionally shown is the contribution of the base IQE 0,4 space charge region approximated by eq. (3.15). (eq. 3.12)
0,2
0,0 400 600 800 1000 λ [nm]
For the following argumentation we restrict on the cell parameters given in Table 3.1. However, in section 3.4.4.5 it is shown that this argumentation is also valid for nearly all cell designs.
For conventional 300 µm thick cells with Lb < 150 µm it is generally accepted that Lb can be obtained by a fit of eq. (3.15) to measured IQE-data in the wavelength range between 800 and 1000 nm according to light penetration depths α-1 between 12 µm and 150 µm [105, 107]. It is stated that another cell thickness H changes the upper value of the fit region in the way that the 22 3 Characterization of silicon wafers and cells
-1 maximum α is below H/2 and that Lb has also to be below H/2. However in the deduction of equation (3.15), the contribution of the emitter and space charge regions are completely neglected. The example Fig. 3.7 shows that the emitter and scr contribute considerably to the IQE for wavelengths up to 900 nm. In addition eq. (3.15) is only a good approximation of the contribution of the base for wavelengths above 900 nm. Astonishingly, the total IQE is approximated by eq. (3.15) relatively well for wavelengths down to 500 nm. However, it is rather by coincidence than by physics that the neglect of the emitter and space charge region is almost exactly compensated by the difference of the approximated and exact base IQE (eq. (3.15) and eq. (3.10)) [108]. From experiments it is shown that also for multicrystalline silicon solar cells eq. (3.15) can be applied to fit measured IQE-data when Lb is substituted by an effective diffusion length. There are two reasons why an effective diffusion length has to be used. The first reason follows from the inhomogeneity of Lb in mc-Si materials. The second reason follows from theoretical work on multicrystalline solar cells including the recombination at grain boundaries [103] and dislocations [109] resulting also in approximated base IQEs according to eq. (3.15) but with Lb substituted by an effective diffusion length, which is a function of the defect geometry, the recombination velocity at the defect and the intragrain diffusion length. Despite of the importance of eq. (3.15) for mono- and multicrystalline silicon solar cells, the author did not find in literature a theoretical justification why this equation can be used to fit the total IQE within a broad wavelength region as seen in Fig. 3.7. To explain why equation (3.15) can be used to fit measured IQEs within a broad wavelength region an analogous equation for the total IQE is derived in the following by taking the contributions of emitter and space charge region to the total IQE into account.
3.4.4 Own work 3.4.4.1 Approximations on the emitter and space charge region In the following using some assumptions on the emitter an approximated IQE of the emitter is 2 derived. By the assumptions of a good quality emitter region (A3.4: we << Le) , a moderate 2 3 condition on the light penetration depth (A3.5: (weα) << 1) and a good surface passivation 2 (A3.6: se = (SeLe)/De << Le/we) the IQE of the emitter (eq. (3.11)) can be simplified:
−⋅α w w sLes+⋅α −we coshe + sinh e α ⋅ ee e L Le Le −⋅α IQE ()α = e −⋅α Le ⋅ we e α ⋅−2 w w e ()Le 1 e + e se sinh cosh Le Le
+⋅α w w we ()+⋅αα − +e −⋅ ⋅ e + A34. −⋅α eseee Ls Lsee 1 α ⋅⋅ we L L ≈ Lee e e α ⋅−2 w ()Le 1 e + se 1 Le
2 2 Note that reasonable values for a diffused emitter are we = 0.5 µm, Le = 15 µm, De = 5 cm /s therefore satisfying the first 5 assumption A3.4 and with a medium surface passivation of Se << 10 cm/s also the third assumption A3.6. 3 Note that only the weak approximation A3.5 instead of the strong approximation weα << 1 is used (see also footnote 4 on p. 24). Using we = 0.5 µm instead of w = 1.5 µm in approximation A3.5 increases considerably the lower wavelength region down to 500 - 600 nm. 3.4 Theory on the internal quantum efficiency (IQE) 23
w A35. ()()1 +⋅ααws ⋅ +⋅ Ls − −e −⋅ ααsw ⋅ −⋅ L αα⋅⋅−⋅Lw()1 ee e eL ee e ≈ ee e α ⋅−2 w ()Le 1 e + se 1 Le 2 A35. 2 αα⋅⋅−⋅ww()1 ()α ⋅−L 1 α ⋅ w ()α ⋅−L 1 α ⋅ w = ee e ≈ e e = e . α ⋅−2 w α ⋅−2 w w ()Le 1 e + ()Le 1 e + e + se 1 se 11 se Le Le Le
Finally with approximation A3.6 the following equation is obtained:
A36. ≈⋅α IQEeew . (3.18)
Using approximation A3.5 the IQE of the space charge region can be written as:
A35. −⋅α ()ww + −⋅α αα≈−⋅−escr =−⋅− α w IQEscr() 11we e wee (3.19)
=+ with wwescr w.
Adding eq. (3.18) and eq. (3.19) gives for the IQE of the emitter and space charge region:
αα=+ α =−−⋅α w IQEe+ scr() IQE e () IQE scr () 1 e . (3.20)
In the following section this equation is also derived directly from the generation profile.
3.4.4.2 Direct way of deducing approximated IQEe+scr We have used the relatively long way from the exact IQE (eq. (3.11)) to the approximated IQEe eq. (3.18) to find out the exact formulations of the approximations on the emitter needed to obtain eq. (3.20). However eq. (3.20) can also be directly obtained from the generation profile if recombination on the front surface and in the emitter is negligible and therefore all within the emitter generated carriers contribute to the IQEe. In this case the contribution of the emitter is given by:
w e −⋅αα −⋅ =⋅α x =− we IQEe ∫ dx e1 e (3.21) 0
Adding this equation to the exact contribution of the scr results again in eq. (3.20). Until now the author has found no way to deduce eq. (3.21) from the exact IQE (3.11) by only using approximations A3.4 and A3.6. Eq. (3.21) could only be derived from eq. (3.11) with additional restrictions on the light penetration depth A3.5 or the emitter diffusion length which 24 3 Characterization of silicon wafers and cells are not always fulfilled. Nevertheless, approximation A3.5 leads to no restrictions in the following discussion.
3.4.4.3 Proof for 1/IQEtotal 1+1/(Lbα) ´near´ the space charge region Using the approximation for the contribution of the emitter and the space charge region (3.20) together with the approximated equation for the base eq. (3.14) the total IQE is given by:
α ⋅ α ⋅+−−⋅α w α =−−⋅ααw + Lb −⋅w = Leb 1 IQEtotal () 1 e α ⋅+e α ⋅+ . (3.22) Lb 1 Lb 1
Interestingly, exactly this equation was obtained for a Schottky-barrier solar cells when the contributions of the depletion region and base are summed [110]. We have now shown that this equation is also valid in the case of a cell with homogeneously diffused emitter. With another approximation (A3.7: (wα)2 << 1) equation (3.22) reduces to:
A37. α ⋅+()Lw w α ⋅ L IQE ()α ≈ b =+1 ⋅ b (3.23) total α ⋅+ α ⋅+. Lbb1 L Lb 1
For the discussion in the following section the inverse of eq. (3.23) is needed:
11 11 1 = ⋅+1 = + . (3.24) αα+ ⋅ + α ⋅+() IQEtotal() 1 w L b L b1 w L b Lwb
For a small emitter and space charge region compared to the base diffusion length (A3.8: w << Lb) equation (3.23) reduces to the following equations:
α ⋅ L 1 1 α ≈ b ≈+1 (3.25) IQEtotal () α ⋅+ or αα⋅ . Lb 1 IQEtotal() L b
Therefore the same functional dependence on α is obtained for the approximated total IQE and the approximated base IQE in eq. (3.15). The important difference of our new approach and 2 the one found in literature is that the approximations A3.7 ((wα) << 1) and A3.8 (w << Lb) needed for deriving eq. (3.25) are much weaker than approximation A3.3 (wα << 1) made for obtaining eq. (3.15). Additionally one gets into serious problems if eq. (3.25) is deduced directly from eq. (3.22) by using approximation A3.3. First, A3.3 suggests a good approximation only within a small wavelength region 4. Second, by applying approximation A3.3 on eq. (3.20) follows that the contribution of the emitter and scr to the IQE can be neglected. But the neglect of the emitter and scr are the main problem of all earlier derived equations of the IQE. Our new approach shows that the emitter and scr can not be neglected by the derivation of the total IQE.
4 Approximation A3.7 is the reason why eq. (3.25) can be used also ‘near’ the space charge region. With w = 1.5 µm and αw = 0.1 << 1 follows α-1 = 15 µm. The weaker approximation (αw)2 = 0.1 << 1 results in α-1 = 4.7 µm which increases the wavelength region from 830 nm down to 680 nm, therefore extending the region for a good approximation. 3.4 Theory on the internal quantum efficiency (IQE) 25
3.4.4.4 Comparison of the different approximated total IQEs The approximated total IQEs derived in this section and the exact total IQE are seen in Fig. 3.8. The improved accuracy of the IQE from eq. (3.22) and (3.23) is seen by comparing with the IQE from eq. (3.25) where the parameter w is neglected. The relative deviations of the approximated total IQEs from the exact total IQE are shown in Fig. 3.9. For equations (3.22) and (3.23) the relative deviation is between 0.2 - 0.4% within the wavelength region of 760 - 920 nm, whereas for eq. (3.25) the deviation is 1.0 - 1.2%. The calculations were carried out by assuming a shallow emitter with we = 0.5 µm, a good surface passivation with 4 Se = 10 cm/s and a small space charge region with wscr = 1 µm. In the case if any of these parameters is larger, the relative error by using eq. (3.25) increases.
Fig. 3.8: Comparison of the exact total IQE 1,0 with the approximations deduced in this total IQE chapter. The simple equations (3.22) and (3.23) result in a very good agreement with 0,9 the exact IQE, whereas a deviation is caused
when the parameter w is neglected in IQE eq. (3.25). Lb is 100 µm and the other cell 0,8 parameters are given in Table 3.1. eq. 3.9 with eq. 3.10-12 0,7 eq. 3.22 eq. 3.23 eq. 3.25 (or eq. 3.15) 500 600 700 800 900 1000 λ [nm]
Fig. 3.9: Relative deviations of the 7 relative deviation of approx. from exact total IQE approximated total IQEs from the exact total 6 IQE (0% - line). For equations (3.22) and eq. 3.22: 1-exp(-α*w)/(1+α*L ) 5 b (3.23) the relative deviation is smaller than 4 α α 1% within the wavelength region of 650 - eq. 3.23 : *(Lb+w)/(1+ *Lb) 960 nm, which corresponds to light 3 µ α α penetration depths of 3.5 - 75 m. No good 2 eq. 3.25 : *Lb/(1+ *Lb) 1% agreement is obtained by eq. (3.25). Lb is 1 µ 100 m and the other cell parameters are 0 0% given in Table 3.1. -1% relative deviation [%] -1 -2 500 600 700 800 900 1000 λ [nm]
3.4.4.5 Validity region of eq. (3.23) We have seen in the previous section that equation (3.23) as compared to eq. (3.25) increases considerably the accuracy of the calculation of the total IQE. In this section the influence of the front surface recombination velocity Se, the emitter width we and the space charge width wscr on the validity region of eq. (3.23) are investigated. Fig. 3.10 shows the exact IQEs of the emitter, scr, emitter + scr and total cell. The approximated total IQE given in eq. (3.23), which includes the contributions of emitter, scr and base, agrees very well with the exact total IQE down to λ = 600 nm. Comparing the approximated total IQE of eq. (3.23) with the approximated bulk IQE of eq. (3.15), which was 26 3 Characterization of silicon wafers and cells shown in Fig. 3.7, one sees that for wavelengths below 940 nm the newly derived total IQE agrees considerably better with the exact IQE. Additionally the approximations used for the emitter given in eq. (3.18) and of the scr given in eq. (3.19) are good for wavelengths down to 600 nm. The approximation of the combined contribution of emitter and scr can even be used for wavelengths down to 500 nm.
Fig. 3.10: Exact IQEs (lines) of the 1,0 emitter, scr, emitter + scr and total cell compared with the approximated 0,8 total IQE (eq. 3.23) IQEs (symbols) deduced in this chapter. lines: The equations (3.20) and (3.23) are good exact IQEs approximations down to 500 and 600 nm, 0,6 (eq. 3.9-12) emitter + scr (eq. 3.20) respectively. For the IQE calculations the symbols: structural and electrical parameters given IQE 0,4 approx. IQEs in Table 3.1 are taken. scr (eq. 3.19) emitter (eq. 3.18) 0,2
0,0 400 600 800 1000 λ [nm]
The influence of the space charge region width wscr, the front surface recombination velocity Se and the emitter width we on the exact IQEs of the emitter, scr, base and total cell are discussed in the following. The influence of the space charge region width wscr on the exact IQEs (lines) of the combined contribution of emitter and scr, the base and the total cell is shown in Fig. 3.11. The scr width has an considerable influence on the IQE of the scr and base, but nearly no influence on the total IQE. The reason for this is the assumption made in section 3.4.2.1 that recombination in the scr can be neglected. Because of the large bulk diffusion length of 100 µm used for the calculations compared to the small scr width, the total IQE depends only slightly on the value of wscr. Even for a small scr the IQE of the base approximates the total IQE only for λ 940 nm, which again proves the importance of our new approach.
Fig. 3.11: Influence of the space charge 1,0 approximated total IQE 0.5 µm region width wscr, which is given in the (eq. 3.23) w =1 µm figure, on the exact IQEs (lines) of the e total IQE 0,8 1.5 µm emitter + scr, base and total cell. The (eq. 3.9 with eq. 3.10-12) approximated total IQE (symbols) is only slightly influenced by wscr and is in good 0,6 emitter + scr agreement with the exact total IQEs (eq. 3.20) base (eq. 3.10)
down to λ = 600 nm. For all calculations IQE 4 0,4 we is 0.5 µm, Se is 10 cm/s and the other cell parameters are given in Table 3.1. 0,2
0,0 400 600 800 1000 λ [nm]
In Fig. 3.12 the influence of the front surface recombination velocity Se on the exact IQEs (lines) of the total cell and the combined contribution of emitter and scr is shown. For 4 Se = 10 cm/s the approximated total IQE (open circles) is in good agreement with the exact 3.4 Theory on the internal quantum efficiency (IQE) 27 total IQE down to λ = 600 nm. A lower front surface recombination velocity of 102 cm/s further extends the lower bound of the wavelength to 500 nm, whereas even for a completely 7 unpassivated front surface with Se = 10 cm/s the lower bound of the wavelength is 800 nm.
Fig. 3.12: Influence of the front surface 1,0 approximated total IQE 102cm/s recombination velocity Se which is given (eq. 3.23) S =104cm/s in the figure on the exact IQEs (lines) of e 0,8 total IQE the total cell and of the combined (eq. 3.9 with eq. 3.10-3.12) contribution of emitter and scr. For 4 Se≤10 cm/s the approximated 0,6 approx. emitter + scr
IQEs (symbols) of the total cell and of the 5 (eq. 3.20) 10 cm/s combined contribution of emitter and scr IQE 0,4 are in good agreement with the exact emitter + scr IQEs down to λ = 600 nm and 500 nm, (eq. 3.11 + 3.12) 0,2 respectively. The emitter width we is 7 lines: exact IQEs 0.5 µm, wscr is 1 µm and the other cell 10 cm/s symbols: approximated IQEs parameters are given in Table 3.1. 0,0 400 600 800 1000 λ [nm]
The influence of the emitter width we on the exact IQEs (lines) of the total cell, the base and the combined contribution of emitter and scr can be seen in Fig. 3.13. From this figure it can be concluded that for emitter widths between 0.5 and 1.5 µm lower bounds of the wavelength of 600 to 800 nm have to be used to ensure with eq. (3.23) a good approximation to the exact total IQE.
Fig. 3.13: Influence of the emitter width 1,0 approximated total IQE w =0.5 µm we given in the figure on the exact e total IQEs (eq. 3.23) IQEs (lines) of the emitter + scr, base and (eq. 3.9 with eq. 3.10-12) 0,8 total cell. For we 1.5 µm the approximated total IQEs (symbols) are in w [µm] good agreement with the exact total IQEs 0,6 scr base (eq. 3.10) λ 2 down to at least = 800 nm. For all 1.5 4 µ IQE calculations wscr is 0.5 m, Se is 10 cm/s 0,4 1 and the other cell parameters are given in Table 3.1. emitter + scr 0,2 (eq. 3.20)
0,0 400 600 800 1000 λ [nm]
In this section it was found that eq. (3.23) is in a very general sense a good approximation to 7 the total IQE of a cell. Even for completely unpassivated emitters with Se = 10 cm/s or deep emitters with we > 1 µm a good approximation is obtained down to λ = 800 nm, which is generally used for a fit on a measured IQE to obtain Lb. The accuracy of Lb when determined with a fit using equation (3.23) is discussed in the following section.
3.4.4.6 Theoretical and experimental accuracy Theoretical accuracy of the approximated equations
Using equations (3.9)-(3.10) the exact total internal quantum efficiency is calculated for two minority carrier diffusion lengths (L = 100 µm and L = 25 µm) and w = 2.5 µm. The other 28 3 Characterization of silicon wafers and cells parameters are given in Table 3.1. By fitting the calculated IQE-data with the approximated equations their theoretical accuracy can be estimated. Table 3.2 shows the fit results using the approximated equations eq. (3.25) for case A and eq. (3.23) for case B and C. The emitter and space charge region widths w was taken to be the accurate value 2.5 µm (case B) or was used as a second fit parameter (case C).
IQE from eq. (3.9)-(3.10) Lb = 100 µm, w = 1.5 µmLb = 25 µm, w = 1.5 µm
fit variables Lbfit [µm] wfit [µm] Lbfit [µm] wfit [µm]
case A: eq. (3.25) Lbfit 107 (+7%) - 30.1 (+20%) -
case B: eq. (3.23) Lbfit 97.5 (-2.5%) 2.5 (fixed) 24.6 (-1.6%) 2.5 (fixed)
case C: eq. (3.23) Lbfit, wfit 98.1 (-1.9%) 2.34 25.6 (+2.4%) 2.06
Table 3.2: The theoretical accuracy of the approximated IQEs (cases A-C) is obtained by a fit of the exact IQE. For the calculation of the exact IQEs the minority carrier diffusion lengths L = 100 µm and L = 25 µm were used. The other cell parameters are given in Table 3.1. The values given in brackets denote the relative deviation of Lbfit from the Lb used for the calculation of the exact IQE.. The fit region was taken to be λ = 800 - 960 nm corresponding to light penetration depths of 10 - 75 µm.
For both diffusion lengths the fit with eq. (3.23) under the assumption of w = 2.5 µm is much better than with eq. (3.25). Even if one does not know the actual width of the emitter and space charge region this parameter can be taken as an additional fit variable resulting for case C in nearly the same diffusion lengths as for case B.
Influence of the experimental accuracy
In the previous paragraph the IQE-data was assumed to be known exactly. In reality the IQE data is obtained by a measurement of the spectral response and front surface reflection of a solar cell (see chapter 3.3.4.1). The main uncertainty comes from the spectral response measurement itself which is between 2 - 3 % [97]. To examine the influence of this calibration uncertainty on the determination of Lb, an error IQE is defined by the exact IQE multiplied with a wavelength independent error factor ferror = 0.975 and 1.025 respectively corresponding to a plus/minus 2.5% deviation:
αα=⋅ IQEerror() IQE total () f error . (3.26)
Table 3.3 shows the results obtained by a fit of the error IQE to the approximated equations of cases A-C.
eq. (3.9)-(3.10) Lb = 100 µm, w = 2.5 µmLb = 25 µm, w = 2.5 µm
ferror 0.975 1.025 0.975 1.025
Lbfit [µm] wfit[µm] Lbfit [µm] wfit[µm] Lbfit [µm] wfit[µm] Lbfit [µm] wfit[µm] case A 97.5 (-13%) - 118 (18%) - 28.5 (14%) - -31.8 (27%) - case B 88.5 (-12%) 2.5 107 (7%) 2.5 23.1 (-8%) 2.5 -26.1 (4%) 2.5 case C 98.1 (-2%) -0.16 98.1 (-2%) 4.85 25.6 (2%) 1.37 25.6 (2%) 2.75
Table 3.3: The influence of the experimental accuracy on the fit results of the approximated IQEs (cases A-C) is obtained by a fit to the error IQE defined in (3.26). The values given in brackets denote the relative deviation of Lbfit from the Lb used for the calculation of the exact IQE. Cases A to C are the same as in Table 3.2. 3.4 Theory on the internal quantum efficiency (IQE) 29
Again, the fit with eq. (3.23) under the assumption of w = 2.5 µm is much better than with eq. (3.25). Comparing Table 3.3 with Table 3.2 shows that by a fit with variable wfit (case C) on the error IQE results in the same values for Lbfit as when the exact IQE is fitted. This follows directly from eq. (3.23) because w occurs only in the wavelength independent factor (1+w/L) and therefore completely compensates a wavelength independent error factor. If the error factor ferror is known, the ‘physical’ w can be calculated from wfit using the following equation:
w fit 1 w =+L −1 fit (3.27) f error f error which is obtained from eq. (3.23) and eq. (3.26).
3.4.4.7 Consequences of eq. (3.23) 1. The inverse of equation (3.23), equation (3.24), is a very interesting result because it explains why a fit of the form:
11 C 1 =+⋅=⋅+⋅CC C1 2 . αα12 1 α (3.28) IQEtotal () C1 results always in a coefficient C1 < 1 in contrast with eq. (3.15) were C1 = 1. In practice if one gets C1 1 it is generally assumed on the basis of eq. (3.15) that the calibration of the spectral response measurement was insufficient in the way that the SR-signal is simply shifted by a wavelength independent factor C1 and the inverse of the absolute IQE has to be 1/IQEabs = 1+1/(Lbα) with Lb = C1/C2 [107]. It is proven now that this generally accepted calibration procedure is wrong. One gets the right value for Lb but a wrong absolute IQE because C1 has to be always smaller than 1 and depends on Lb and w.
2. Comparing eq. (3.24) with eq. (3.28) one gets:
C 1 − C = 1 = 1 Lb and w . (3.29) C2 C2
With the last equation theoretically the value w can be obtained by a fit of the IQE-data.
Practically this is difficult because of the small w =1 - 2.5 µm compared to Lb > 80 µm for conventional multicrystalline silicon materials 5. However from a statistical point of view eq. (3.28) explains why from spectral response measurements carried out in our lab on solar cells with w/Lb smaller than the measurement accuracy more fits resulted in C1 < 1 than in C1 1.
3. Even if w is not known at all, using this parameter as an additional fit variable in eq. (3.23) improves the accuracy of Lb decisively as shown in section 3.4.4.6. It was also stated that using w as fit parameter the influence of an error in the calibration of the SR-measurement on the
5 For solar cells based on conventional multicrystalline silicon w/Lb is within the accuracy of the spectral response measurement of 2 - 3% [97] making it impossible to fit w accurately. For cells based on low quality mc-Si material Lb is much smaller and a fit of w from eq. (3.24) is possible as shown for SOLAREX cells in section 5.4.3. 30 3 Characterization of silicon wafers and cells
determination of Lb can be reduced. For the special case where incorrect IQE-data is due to a simple wavelength independent shift the complete error is `absorbed` by the additional fit parameter w.
4. As seen in Fig. 3.9 the fit region can be extended considerably in the small wavelength region. For eq. (3.23) a relative error compared to the exact IQE below 1% is obtained for λ = 640 - 960 nm according to α-1 = 3.3 - 75 µm. Using this fit region for a 300 µm thick cell instead of λ = 800 - 1000 nm proposed in literature [105] results in a considerably improved fit accuracy. Rules of thumb for the fit region as depending on the cell thickness, emitter width and front surface recombination velocity are given in the following. As discussed in section 3.4.4.5 the lower bound depends on the front surface recombination velocity Se and on the emitter width we. In the case of a completely unpassivated front surface or a deep emitter, λ = 800 nm should be used as the lower bound. In the case of a passivated 4 front surface with Se 10 cm/s the lower bound of λ should corresponded with a light -1 penetration depth α = 1.5we, which follows directly from Fig. 3.13. An analogous rule of thumb can be obtained for the upper bound of the wavelength, which should correspond for a cell of thickness H to a light penetration depth α-1 = H/4. That means for the interesting range of cell thicknesses between 100 µm and 500 µm that the upper bound for λ has to be between 880 and 990 nm.
5. For the deduction of the total IQE we have assumed until now the approximation used in section 3.4.2.2.1 (A3.2a: wb >> Lb). Instead of using this approximation the equations (3.22) - (3.25) can also be obtained by the approximation in section 3.4.2.2.2 (A3.2b: wb << Lb). In this case only Lb has to be substituted by Leff from eq. (3.17).
3.4.4.8 Influence of a weak surface texturization The weak surface texturization obtained during the NaOH-etch of the selective emitter process shown in Fig. 2.2 makes it necessary to formulate also the approximated total IQE of a weakly textured cell. We will show in this section that by using effective values for α, Lb and w the IQEs deduced in the previous sections can also be used for weakly textured cells. Therefore all equations deduced in this chapter and later in chapter 5 for the single- and double-layer IQEs can be used for the simulation of the selective emitter cells presented in this work if one keeps in mind that a fit results in effective values. For the following considerations we assume that the scale of the texture is small compared with the cell thickness but large compared with the emitter and space charge region. These assumptions are generally satisfied for chemically textured cells were the texture size is about 10 µm, which is small compared with conventional cell thicknesses of > 200 µm and large compared with the width of the emitter of 0.2 - 0.5 µm and space charge region of 1 - 2 µm. The procedure to obtain the total IQE of a textured cell from the total IQE of a flat cell is the same as described in literature for the base IQE [104, 105] but with the difference that again the contributions of the emitter and scr to the IQE are included. From the sketch of a solar cell with a weak surface texturization shown in Fig. 3.14 it is obvious that light passes with different angles relative to the emitter/scr and to the base. 3.4 Theory on the internal quantum efficiency (IQE) 31
Fig. 3.14: Sketch of a solar cell with a weak surface texturization. Light hits the surface with angle γ normal to the texture, passes the emitter and scr γ γ relative with an angle ϕ and succeeds relative to the base of the cell with angle ϑ. The cell thickness H is ϕ taken as the average value over the texture. The electrical model is taken from Fig. 3.6.
ϑ
The angle with which light passes the emitter and space charge region ϕ(λ) can be calculated from the facet angle of the texturization γ and from the refractive index of silicon nSi by Snell’s law:
sin()ϕ 1 sin()γ =→=ϕ arcsin (3.30) sin()γ nnSi Si
Fig. 3.15 shows the dependence of the refractive index of silicon nSi on the wavelength of light λ. Because we are only interested in approximations of the IQE for wavelengths λ > 600 nm were nSi depends only slightly on λ the refractive index nSi, ϕ and ϑ are taken as independent of λ. However if one is interested in the IQE at small wavelengths for which the emitter dominates the IQE, the functional dependence on the wavelength has to be taken into account for these parameters.
Fig. 3.15: The dependence of the Angle of texturization γ = 54.7 ° ϕ 13 13 [°] refractive index of silicon nSi on the wavelength of light λ results in a 12 12 considerable variation of the angle ϕ for 11 11 λ < 600 nm. For λ > 600 nm the 10 10 refractive index of silicon can be taken as 9 9 constant. 8 8 7 7 6 6 5 5 Si n 4 4 3 400 600 800 1000 λ [nm]
From Fig. 3.14 and eq. (3.30) the angle ϑ with which light passes the base is given by:
sin()γ ϑγϕγ== − = − arcsin . (3.31) nSi 32 3 Characterization of silicon wafers and cells
The generation profile can be directly obtained from Fig. 3.14 which is also shown in [111]:
α −⋅x α ()ϕ ⋅ Using this generation profile and assuming that the one-dimensional electrical model shown in Fig. 3.6 is a good approximation for the weakly textured cell, the contributions of the base and the emitter/scr to the IQE can be calculated. In appendix 9.3 it is shown that adding the IQEs from these three regions and applying some approximations leads to the following expression for the total IQE of a textured cell: αϑϕ⋅+[]Lwcos() cos() w cos()ϑ L ⋅αϑcos() IQE textured ()α = b =+1 ⋅ ⋅ b . (9.22) total ⋅+αϑ() ()ϕ ⋅+αϑ() Lbbcos 1 L cos Lb cos 1 A comparison of this equation with the exact total IQE (the sum of eq. (9.15) and (9.18) which is also deduced in appendix 9.3) for a flat (γ = 0°) and a textured (γ = 54.7°) cell is shown in Fig. 3.16. The angles ϕ and ϑ are calculated from γ by using eq. (3.30) and (3.31). With the approximated IQE a very good agreement with the exact IQE is obtained for λ > 700 nm. Fig. 3.16: Comparison of the exact total 1,0 IQE (lines) for a flat and a textured cell with the approximated IQE (symbols) 0,8 approximated total IQE deduced in this chapter. Using the (eq. 3.44) approximated IQEs a very good Facet angle agreement with the exact IQE is obtained 0,6 for λ > 700 nm. For the facet angle of the exact total IQE of texturization IQE (eq. 3.38 and 3.41) γ = 0 ° textured cell γ = 54.7° is used. The other 0,4 cell parameters are given in Table 3.1. γ = 54.7 ° 0,2 0,0 400 600 800 1000 λ [nm] 4 Microwave induced remote hydrogen plasma (MIRHP) passivation 4.1 Introduction As shown by SPV and LBIC measurements presented in the previous chapter, the bulk recombination of multicrystalline silicon materials and solar cells can be considerably decreased by the incorporation of atomic hydrogen. A large variety of techniques exists for the incorporation of atomic hydrogen in silicon [10]. Much work is published on hydrogen ion implantation [112-114] and direct hydrogen plasma processes [115-117]. For the latter the H-plasma is often excited in a small plate reactor using an rf-power generator. To avoid a surface damage during the hydrogenation process, remote plasma techniques as described for example in [118, 119] have been developed, where the H-plasma is separated from the place of H-diffusion into the sample. These remote plasma techniques were found to be ideally suited for H-diffusion studies, where a surface damage during hydrogenation could influence the measurement result. In 1988 the remote hydrogen plasma technique was further developed by C. Vinckier for kinetic studies of the gas-phase reactions of metal atoms [120]. Metal atoms in the gas phase were produced from metal compounds in the afterglow of a remote hydrogen plasma device using microwave power. In cooperation with C. Vinckier considerable improvements of the performance of mc-Si solar cells were obtained by H. Elgamel [44, 121]. It was also proposed that remote plasma hydrogenation can be used for passivation of electronic defects in amorphous silicon solar cells [122]. In 1994 we also started in our lab studying H-bulk passivation of multicrystalline silicon materials and solar cells with first results published in [43, 123]. The microwave induced remote hydrogen plasma device, or MIRHP device as we call it, is very similar to the ones described in [44, 120] and will be presented in section 4.2. Despite the importance of the MIRHP technique to boost the efficiency of multicrystalline silicon solar cells, there is not much work published on the effectiveness of the MIRHP process as a function of the passivation parameters: sample temperature, gas pressure, gas flow, microwave power and processing time. In section 4.3 the results of various optimization studies according to these process parameters using solar cells based on different mc-Si materials will be presented. Special attention was drawn in section 4.4 to cells based on RGS-material, including V-structuring of the front surface, forming gas annealing and double layer antireflection coating, which finally resulted in a record efficiency of 11.1%. By avoiding a surface damage during the MIRHP process, this technique can be applied to surface passivated cells making this technique also very attractive for improving mc-Si high efficiency PERL (passivated emitter, rear locally-diffused) cells. Promising results obtained in cooperation with J. Zhao from the group of M. A. Green are presented in section 4.5. Applying the MIRHP process on cells with homogeneous emitter after front contact metallization, a degeneration of the cell performance is often observed. This effect will be investigated in section 4.6 on the cell level. Because of this degeneration effect the 34 4 Microwave induced remote hydrogen plasma (MIRHP) passivation optimization of the MIRHP process is carried out only on cells with a selective emitter. Using a selective emitter no degeneration within the used MIRHP processing times was observed. 4.2 The MIRHP device A schematical view of the MIRHP (microwave induced remote hydrogen plasma) passivation device used in my work for defect passivation of multicrystalline silicon wafers and solar cells is shown in Fig. 4.1. To dissociate molecular hydrogen, microwave power is coupled through a cavity into a gas mixture consisting of 10% H2 and 90% He (purity 6N). Driven by a pump the atomic hydrogen diffuses into the heated samples, which are separated from the plasma by about 1 m. On the way to the samples the atomic hydrogen is kept from recombining by the presence of the helium atoms. The special H2/He gas concentration was taken because it was found that the amount of atomic hydrogen generated by the microwave power does not further increase if higher H2-concentrations are chosen [120]. Additionally, the low H2-concentration gas mixture is incombustible. The temperature was measured inside the tube at the place of the samples during the MIRHP process. The total gas pressure is determined by a hot wire manometer adjusted before the microwave cavity. To keep the contamination of the heated samples as low as possible, the reactor is swept with nitrogen (purity 5N) during the loading of the samples. With this set-up the following process parameters can be varied independently: sample temperature, gas pressure, gas flow, microwave power and processing time. The following modifications compared to an earlier MIRHP system used during the work for my master thesis [43] were carried out. By changing the tube geometry in the way that the excited gas has to flow along a 90° angle to the samples, the UV-radiation of the plasma is coupled out of the gas flow, therefore ensuring that no UV-surface damage can occur. Not coupling the UV-radiation out of the gas flow results in a serious damage of the front surface seen for example by EBIC-measurements and also by a degeneration of the cell fill factors during the MIRHP process [43, 123]. With the up-scaling of the reactor to a quartz tube diameter of 15 cm also large area industrial solar cells can be passivated. He/H2 temperature microwave control induced plasma quartz to manometer tube samples furnace to microwave- generator to pum p cavity loading of H2 O-cooling samples Fig. 4.1: Schematic diagram of the MIRHP (microwave induced remote hydrogen plasma) device for hydrogen passivation of silicon wafers and solar cells. On the right side the microwave generator (2.45 GHz, Mark III of company Schäfer GmbH) with maximum power output of 200 W is shown. To dissociate molecular hydrogen, the microwave power is coupled through a cavity into a gas mixture consisting of 10% H2 and 90% He. The atomic hydrogen, kept from recombining by the presence of the helium atoms, diffuses into the heated samples. 4.3 Optimization of the MIRHP process 35 4.3 Optimization of the MIRHP process 4.3.1 Procedure of the optimization For the optimization of the MIRHP passivation it is advantageous that this process can be applied to completed solar cells. With the use of the large number of existing cell characterization techniques which were partly presented in chapter 3, much information can be obtained about the passivation effect of hydrogen in mc-Si. By applying the MIRHP process several times with the other process parameters unchanged, a considerably smaller set of cells is needed for the optimization as if the MIRHP process would have been applied before the cell metallization. However using only small sets of cells, only cells with the same crystal structure can be compared. Even for the four 22 cm2 cells processed in our lab together on one 55 cm2 wafer, strong variations of the illuminated I-V parameters are observed. This is shown in Fig. 4.2 for example for the short circuit current density obtained from an optimization study of the Al-gettering process carried out by some of my colleagues [53]. By comparing only cells taken from the same position of the original wafers, the same optimization result is obtained than if the average values of the four cells per wafer are compared. On the other hand, mixing the positions of the cells on the wafers and comparing single cells can result in a wrong conclusion about the optimum temperature. To obtain on one hand maximum information about the result of one process condition, but on the other hand also to investigate a large set of process conditions including different mc-Si materials, for the following investigations only cells with the same crystal structure are compared. Fig. 4.2: Optimization results of Al-gettering on cells based on EUROSIL EUROSIL material. The four symbols represent the 22 2 four 22 cm cells cut after cell processing from one 55 cm2 wafer with ] the same crystal structure [53]. 2 21 [mA/cm sc J 20 ungettered 700 800 900 1000 1100 Al-gettering temperature [°C] To exclude any negative effect of the MIRHP process applied after front contact evaporation, the complete optimization of the MIRHP process in section 4.3 is carried out on cells with a selective emitter. The negative effect of the MIRHP on cells with homogeneous emitter is discussed in chapter 4.6. The aim of the first optimization study is to find the optimum microwave power, gas flow and gas pressure to maximize the concentration of atomic hydrogen at the position of the cells. Afterwards the more material depending MIRHP parameters passivation temperature and time are optimized for each material of investigation separately. 4.3.2 Optimization of the microwave power, gas flow and gas pressure In the following the influence of the process parameters, microwave power, gas flow and gas pressure which determine the concentration of atomic hydrogen at the place of the samples is 36 4 Microwave induced remote hydrogen plasma (MIRHP) passivation investigated. For the optimization of these process parameters cells were processed using EMC mc-Si material with a high defect density but low oxygen concentration as seen in Table 2.2 of section 2.3. The high defect density ensures that a large amount of atomic hydrogen is needed for the passivation, making this material attractive to optimize these process parameters. To be sensitive to the amount of hydrogen at the cell surface it is also necessary that hydrogen diffuses rapidly into the cell, which is ensured by the low oxygen concentration of the EMC material. As will be seen later, the optimal process parameters found are also sufficient for materials with lower defect densities such as EUROSIL and BAYSIX. To investigate as well the influence of these process parameters on the improvement of a material with a reduced H-diffusion, this optimization was also carried out on cells based on SOLAREX mc-Si material containing a large amount of oxygen of up to 1.21018 cm-3 [25]. 4.3.2.1 EMC base material Four different MIRHP processing conditions shown in Table 4.1 were applied to solar cells prepared from mc-Si EMC material. As a starting point for the temperature the value of 350°C was taken, which will be further discussed in section 4.3.5. For each process condition, the time of the MIRHP treatment was successively increased from 30 min to 2 h and the illuminated I-V characteristics measured. The influence of the different MIRHP process conditions on VOC and JSC can be seen in Fig. 4.3. The process H3 with the lowest gas pressure is clearly the best which appears to almost fully passivate EMC solar cells within 2h. Whereas for the first 30 min VOC increases rapidly for all process gas pressure [mbar] microwave power [W] gas flow [ml/min] H1 1 50 4 H2 1 150 12 H3 0.1 50 4 H4 10 50 4 Table 4.1: MIRHP processing conditions used for the optimization of cells based on EMC. A temperature of 350°C was taken and the passivation time for each solar cell was successively increased from 30 min up to 2 h. base material: 0,8 15 base material: EMC EMC ] 0,6 -2 10 before after 2h 0,4 [mV] before HP after 2h HP HP HP oc [mAcm V H1 563 579 sc H1 22.1 22.9 ∆ 5 J H2 562 575 ∆ 0,2 H2 21.9 22.7 H3 563 575 H3 22.0 22.8 H4 563 572 H4 22.1 22.7 0 0,0 0306090120 0 306090120 passivation time [min] passivation time [min] Fig. 4.3: Influence of the MIRHP process conditions shown in Table 4.1 on the increase of VOC (left side) and JSC (right side) of selective emitter solar cells using EMC as base Si-material. Before the MIRHP passivation all four cells have nearly identical VOC and JSC values, therefore proving the good homogeneity of our cell process. 4.3 Optimization of the MIRHP process 37 processing conditions, a saturation of JSC is reached faster for the process H3 than for the other processes. This is due to the lower gas pressure resulting in a higher amount of H-atoms at the position of the cells [123]. In agreement with this argumentation, the condition H4 with the highest gas pressure leads to the slowest increase in JSC. Gas pressures lower than 0.1 mbar can not be used because they resulted in an instability of the plasma. However, from theoretical considerations based on kinetic gas theory follows that the optimum gas pressure for the MIRHP passivation of mc-Si materials containing high defect densities is between 0.1 and 1 mbar [43]. By comparing the results of process H1 with H2, it can be seen that higher microwave powers and higher gas flows do not lead to a faster passivation of EMC material. Additionally, there is no negative effect on VOC by the use of the higher microwave power. The slightly smaller JSC of process H2 compared with H1 can not be explained by a damage due to the microwave power, because this damage should be first seen in VOC which is more sensitive to the surface than JSC. 4.3.2.2 SOLAREX base material We have seen from the optimization on EMC cells that increasing the microwave power from 50 to 150 W and the gas flow from 4 to 12 ml/min does not result in a better MIRHP process. To investigate if the efficiency of the MIRHP process can be improved for oxygen rich material by increasing the microwave power and gas flow, MIRHP processes on cells based on SOLAREX material were carried out. Assuming that there is no influence of the material on the optimum gas pressure of 0.1 mbar found for the EMC material, this pressure will also be used in the following study. The influence of the microwave power, gas flow and process time on the improvement of JSC can be seen in the left graph of Fig. 4.4. Comparing the two conditions of low gas flow (4 ml/min), JSC increases considerably slower by using a low microwave power of 50 W than by taking 150 W. The microwave power has also an influence on the shape of the JSC - t curves. A fast increase is seen for 150 W within the first 60 min which then results in a slow nearly linear increase during the following 4 h. Using 50 W, there is a non-linear increase observed during at least the first 2 h. Increasing in addition to the microwave power also the gas flow to 12 ml/min, no significant difference to the results obtained with 150 W and 4 ml/min can be seen. The observation that increasing the microwave power results in a faster passivation is also confirmed by the improvements of VOC of these cells shown in the right graph of Fig. 4.4. A MIRHP process for only 60 min results in a nearly saturated VOC. Again increasing the gas flow from 4 to 12 ml/min and keeping the microwave power constant at 150 W leads to no change. base material: SOLAREX 2,5 20 base material: 2,0 SOLAREX ] 15 -2 1,5 microwave gas flow [mV] 10 microwave gas flow oc [mAcm 1,0 power [W] [ml/min] power [W] [ml/min] V sc J 50 4 ∆ ∆ 50 4 5 0,5 150 4 150 4 150 12 150 12 0,0 0 0 60 120 180 240 300 0 60 120 180 240 300 passivation time [min] passivation time [min] Fig. 4.4: Increase in JSC (left side) and VOC (right side) of cells based on SOLAREX material as a function of process time for different combinations of gas flow and microwave power. A gas pressure of 0.1 mbar and a process temperature of 350°C was used. The dotted line is a guide to the eye. 38 4 Microwave induced remote hydrogen plasma (MIRHP) passivation It was stated previously that VOC is more sensitive to the emitter and space charge region than to the bulk, therefore explaining the large increases of VOC during the first 30 min for all process parameters. After the emitter/scr region is completely passivated, the further increase of VOC is due to the diffusion of hydrogen into the bulk. For the conditions of 50 W and 4 ml/min the H-diffusion in the bulk is slowed down either because not enough atomic hydrogen is available or the average energy of the H-atoms is too low. The last point is not very reasonable, since because of the large distance of 1 m between H-generation and sample position, the H-atoms should be in thermal equilibrium. It is more reasonable that the H-amount generated in the cavity increases with microwave power but if also the gas flow is increased, no more H-atoms are generated. With this follows that the gas flows used in our study provide sufficient H-molecules for the support of the plasma process. 4.3.3 Optimization of the diffusion temperature and process time The dynamics of the H-diffusion in mc-Si is influenced by the passivation temperature as well as by specific material properties such as crystal defect structure and oxygen concentration. Because of large differences in these properties between the materials of investigation, the temperature has to be optimized for each material separately. For a direct comparison of the results obtained on cells based on the different mc-Si materials, all other process parameters were kept constant at the following values: a gas pressure of 0.1 mbar, a gas flow of 4 ml/min and a microwave power of 150 W. It is seen later that there is a considerable difference in the optimum values of passivation temperature and time found between the cast silicon and ribbon silicon materials, which shows that these groups should be discussed in the following separately. 4.3.3.1 Cast silicon For the following investigation, the passivation temperature was varied between 275 and 425°C and the passivation time was successively increased up to 6 h. For a direct comparison between cells based on different materials the normalized values (VOC(t) - VOC)/(VOCHP - VOC) and (JSC(t) - JSC)/(JSCHP - JSC) are used in the following with VOC and JSC determined before the MIRHP process, VOC(t) and JSC(t) obtained after the MIRHP of time t and VOCHP and JSCHP measured after no further improvement during the MIRHP is observed. The influence of the passivation temperature and time on the normalized VOC and JSC values of cells based on BAYSIX and SOLAREX material are shown on the following side in Fig. 4.5. Note that the time scaling is different for the two materials showing that the H-diffusion in SOLAREX material is slower than in BAYSIX. The following results are obtained from these graphs in Fig. 4.5: • The absolute increases for VOC, also shown in the graphs, were higher when a MIRHP temperatures of 350 - 400°C for BAYSIX and of 375°C for SOLAREX was applied. For example, comparing two BAYSIX cells with the same crystal structure and the same VOC of 587 mV before the HP results in 602 mV with the HP applied at 350°C and in finally only 596 mV with the HP carried out at 425°C. On this cell with an additional MIRHP process at 350°C, a further increase in VOC of 4 mV was observed. The observation that the surface region, mainly correlated to VOC, is not completely passivated by applying the MIRHP at 425°C can be explained by the beginning of H-diffusion out of the cell. This results in a lower H-concentration and therefore in a reduced passivation in the near surface region. By effusion experiments presented in section 5.5 this observation will be further investigated. 4.3 Optimization of the MIRHP process 39 • During the first 60 min H-passivation the largest increases of the normalized JSC and VOC are obtained for a passivation temperature of 425°C. This proves that for this temperature the bulk is passivated fastest. • No large differences in the normalized VOC and JSC values are seen for the BAYSIX material when comparing these values for T = 350 - 400°C. For the SOLAREX material the normalized values of VOC and JSC increase in the order of the passivation temperature, resulting in a faster passivation for T = 400°C than for 350°C. However the best absolute increases in VOC and JSC for the SOLAREX cells were obtained at 375°C. • From these graphs it can be concluded, that the optimum passivation temperature for applying the MIRHP process on cells based on BAYSIX is 350 - 400°C with a passivation time of 120 min and on SOLAREX cells 375°C with 180 min. 1,0 1,0 0,8 T t ∆V 0,8 ∆ OC opt oc OC T topt Voc [°C] [min] [mV] [°C] [min] [mV] 0,6 275 >240 +16 0,6 275 >360 +21 350 120 +15 350 180-300 +20 0,4 375 120 +14 0,4 375 180 +28 400 120 +15 400 120 +11 normalized V normalized normalized V 0,2 material: 425 60 + 9 0,2 material: 425 90-120 +7 BAYSIX => Topt = 350 - 400°C SOLAREX => Topt = 375°C 0,0 0,0 0 30 60 90 120 150 0 60 120 180 240 300 passivation time [min] passivation time [min] 1,0 1,0 T t ∆J ∆ 0,8 opt sc 0,8 T t opt Jsc [°C] [min] [mAcm -2] -2 SC SC [°C] [min] [mAcm ] 0,6 275 >240 +1.0 0,6 275 >360 +2.4 350 120 +1.1 350 300 +2.3 0,4 375 120 +1.1 0,4 375 180 +3.2 400 120 +1.0 400 120 +2.6 normalized J 425 30 +0.8 J normalized 425 90-120 +2.7 0,2 material: 0,2 material: => T = 375°C BAYSIX => Topt = 350 - 400°C SOLAREX opt 0,0 0,0 0 30 60 90 120 150 0 60 120 180 240 300 passivation time [min] passivation time [min] Fig. 4.5: The influence of the passivation temperature and time on the normalized open circuit voltage (VOC(t) - VOC)/(VOCHP - VOC) (graphs above) and normalized short circuit current density (JSC(t) - JSC)/(JSCHP - JSC) (graphs below) of cells based on BAYSIX material (left side) and SOLAREX material (right side). VOC and JSC is determined before the MIRHP process, VOC(t) and JSC(t) after a MIRHP process of time t and VOCHP and JSCHP after no further improvement is observed. The passivation temperatures and optimum times are given in the graphs together with the absolute increase of ∆VOC and ∆JSC after complete MIRHP passivation. The following process parameters are kept constant: a gas pressure of 0.1 mbar, a gas flow of 4 ml/min and a microwave power of 150 W. The optimization results obtained on the other two cast silicon materials of investigation EUROSIL and EMC will be presented in Table 4.2 of section 4.3.5. 40 4 Microwave induced remote hydrogen plasma (MIRHP) passivation 4.3.3.2 Ribbon silicon The optimization results of cells based on the ribbon silicon materials EFG and RGS are presented next. For different MIRHP passivation temperatures and times, the increases of the open circuit voltage ∆VOC and the short circuit current density ∆JSC of solar cells based on these materials are shown in Fig. 4.6. From ∆JSC and ∆VOC it is seen that EFG (open symbols) can be fully passivated at a process temperature of 275°C within only 2 - 3 h and at 425°C even after 15 - 30 min. This is the fastest H-passivation observed on any of the investigated materials. RGS containing high concentrations of oxygen of 1018 cm-3 [48] behaves totally different to EFG with oxygen concentrations below 51016 cm-3 [46]. For the RGS cell (solid symbols), where the MIRHP process was applied at 275°C, a relatively small increase in JSC of 0.8 mAcm-2 is obtained after 5 h. Not shown in this graph is that an additional 1 h MIRHP process of this cell at 400°C resulted in a further improvement of 0.9 mAcm-2. For RGS cells there is no difference in the increase of the open circuit voltage for the passivation temperatures of 275°C and 350°C. Only if a temperature of 425°C is used, VOC increases faster and seems to saturate at shorter times. 4 40 ] 3 30 -2 2 20 [mV] T[°C] EFG RGS OC [mAcm V SC 425 ∆ J 1 10 ∆ 350 0 0 275 012345 012345 passivation time [h] passivation time [h] Fig. 4.6: The influence of the passivation temperature during the MIRHP process on the increase of the short circuit current density (left side) and the open circuit voltage (right side) of solar cells based on RGS and EFG silicon. The following process parameters are kept constant: a gas pressure of 0.1 mbar, a gas flow of 4 ml/min and a microwave power of 150 W. From the experiments with selective emitter cells follows for RGS, contrary to the other investigated mc-Si materials, that the optimum MIRHP temperature is considerably above 350°C. In addition as will be discussed in section 4.6 using RGS as base material, also cells with a homogeneous emitter can be used for applying the MIRHP process after front contact metallization. Therefore a further optimization in the higher temperature region between 375°C and 450°C was carried out using homogeneous emitter cells based on defect rich RGS material [124]. The influence of the MIRHP process on the increases of the illuminated I-V parameters are shown in Fig. 4.7. A nearly complete passivation can be obtained within 1 h at a passivation temperature of 450°C as seen in the increases of VOC and JSC,. Using lower temperatures considerably increases the optimum passivation time. Also seen is the effect that for lower temperatures even after several hours JSC and VOC slowly further increase. These very slow increases of the JSC and VOC curves were also observed on SOLAREX cells. From the LBIC measurements presented in the following section it can be concluded, that these slow increases are due to the regions where hydrogen diffusion is reduced, and therefore H-passivation takes longer. The observed decreases of FF and VOC in dependence of the MIRHP passivation temperature is due to the degeneration of the front contact and the 4.3 Optimization of the MIRHP process 41 diffusion of metal atoms from the front contact into the cell. As discussed in chapter 6.3 for industrial applications, it is beneficial to apply the MIRHP process before the front grid metallization. Applying the MIRHP on RGS cells before the cell metallization, not only JSC and VOC will increase fastest at T = 450°C but also the fill factor. Fig. 4.7: The influence of the 012345678910 MIRHP passivation temperature 80 (given in the graph) on the 60 absolute increases of JSC, VOC, FF [mV] and η of solar cells based on RGS oc 40 V using the homogeneous emitter ∆ 20 cell process described in 0 section 2.4.1. Due to the MIRHP ] 2 process The following process 4 parameters are kept constant: a gas pressure of 0.1 mbar, a gas [mA/cm 2 sc J flow of 4 ml/min and a microwave ∆ power of 150 W [124]. 0 6 ] abs 4 2 FF [% ∆ 0 ] 2 abs 450° C 425° C [% 1 ∆η 400° C 375° C 0 012345678910 MIRHP passivation time [h] 4.3.4 LBIC measurements Some information about the influence of the MIRHP process on the homogeneity of the electronic activity of mc-Si material can be obtained by LBIC measurements. Fig. 4.8 shows LBIC scans of two cells, one based on SOLAREX material and the other on EFG material. Comparing the LBIC signals of the SOLAREX cell before (Fig. 4.8a) and after (Fig. 4.8b) a MIRHP process, it is clearly seen that the intragrain recombination of the large grains on the right side of the cell is reduced due to the MIRHP process. Additionally the LBIC signal from the grain boundaries has increased during the MIRHP process. Different to the improvement of the large grained region, the LBIC signal of the left side of the cell including many small grains does not improve considerably. In this region the hydrogen diffusion seems to be limited by the high amount of crystal defects. Despite the average increase of the LBIC signal of 23%, the homogeneity of the electronic activity in the used SOLAREX material is not increased by the MIRHP process. The used passivation time of 90 min for the SOLAREX cell was considerably lower than the optimum for this material of 180 min found in section 4.3.3.1. In this section it was found that for cells based on SOLAREX material the short circuit current and the open circuit voltage increase rapidly during the first 1 h and slowly during the following 2 -3 h MIRHP. From the LBIC measurements follows that the first large increases in JSC and VOC are due to H-diffusion into large grained regions and the following small increases in JSC and VOC are mainly due to the improvement of the small grained regions. As also seen from the LBIC 42 4 Microwave induced remote hydrogen plasma (MIRHP) passivation scans intragrain diffusion is the most important diffusion channel for atomic hydrogen in mc-Si SOLAREX material. Different to SOLAREX, for EFG material all regions clearly improve due to the MIRHP process, which is seen by comparing the LBIC scans of the EFG cell determined before (Fig. 4.8c) and after (Fig. 4.8d) a MIRHP process. Due to the MIRHP process some of the grain boundaries can not be seen on the LBIC scan anymore, which means that they are completely passivated. For the EFG cell the average LBIC signal increases by 57%. a): SOLAREX cell before MIRHP b): same SOLAREX cell as in a) after MIRHP c): same EFG cell before MIRHP d): same EFG cell as in c) after MIRHP Fig. 4.8: LBIC measurement results obtained on one cells based on SOLAREX (above) and on one cell based on EFG (below) before (left side) and after (right side) a MIRHP process. The following parameters are used for the MIRHP process: a passivation temperature of 375°C, a passivation time of 90 min, a gas pressure of 0.1 mbar, a gas flow of 4 ml/min and a microwave power of 150 W. 4.3.5 Summary of the optimal process parameters for the investigated materials In the following a short summary of the optimal process parameters for the investigated materials is given. Table 4.2 shows the optimum MIRHP process temperatures and times together with the relative increases in cell efficiency for the materials of investigation. The other process parameters are the following: a gas pressure of 0.1 mbar, a microwave power of 150 W and a gas flow of 4 ml/min. Comparing the cast-Si materials, the shortest passivation times are needed for the high quality large grained mc-Si materials EUROSIL and BAYSIX. The high defect densities in EMC result in a slightly longer optimum process time. The longest process time is needed for SOLAREX material due to the high oxygen concentration, which slows down the H-diffusion in this material. Comparing these materials it can be concluded that the lower the material 4.3 Optimization of the MIRHP process 43 quality the larger the improvement in cell efficiency by a MIRHP process. The increases in relative cell efficiency for the cast silicon materials are between 2 and 15%. Very large differences in the optimum passivation parameters were obtained between the two ribbon Si materials of investigation EFG and RGS. EFG with very low oxygen concentrations can be completely passivated within 30 min at 350°C. Even if the temperature is reduced to 275°C, the passivation is completed after 2 - 3 h. For optimum passivation of RGS cells both temperature and time have to be considerably increased. The increases in relative cell efficiency for both materials are up to 30%, therefore proving the importance of the MIRHP process for improving the quality of ribbon materials. cast silicon ribbon silicon EUROSIL BAYSIX EMC SOLAREX EFG RGS Topt [°C] 350 350-400 350-375 375 (350) 350 (425) 425 (450*) topt [min] 90 120 120 - 150 180 (300) 30 (15) 210 (60*) ∆ηrel [%] 2 - 7 5 - 8 6 - 9 7 - 15 21 - 31 15 - 30 Table 4.2: The optimum MIRHP process temperature and time are shown together with the relative increases in cell efficiency for the materials of investigation, using the selective emitter cell process described in section 2.4.2. The other process parameters are the following: a gas pressure of 0.1 mbar, a microwave power of 150 W and a gas flow of 4 ml/min. *For RGS a further decrease in topt to 60 min can be obtained by H-passivation at 450°C as seen in Fig. 4.7 for defect rich homogeneous emitter RGS cells. The illuminated I-V parameters of the best selective emitter solar cells based on the materials under study after a MIRHP process but without an ARC (antireflection coating) can be seen in Table 4.3. The figures in brackets denote the calculated JSC and η values, using an estimated average reflectance of 5% of an ideal double layer ARC. cast silicon ribbon silicon EUROSIL BAYSIX EMC SOLAREX EFG RGS** -2 JSC [mAcm ] 25.6 (34.7) 23.4 (34.0) 25.2 (33.5) 21.6* (30.1) 25.3 (34.3) 22.4 (30.4) VOC [mV] 623 615 589 591 571 510 FF [%] 76.3 77.2 77.4 75.5 74.2 61.7 η [%] 12.1 (16.4) 11.1 (16.1) 11.5 (15.3) 9.7 (13.5) 10.7 (14.5) 7.1 (9.6) Table 4.3: Illuminated I-V parameters of the best 4 cm2 solar cells with selective emitter after MIRHP and without ARC. The figures in brackets denote the calculated JSC and η values, using an estimated average reflection of 5% of an ideal double layer ARC. *Reduced JSC supposed due to high defect density and oxygen concentration. **Better cell parameters for RGS are obtained on V-grooved cells presented in section 4.4.3. Because of the importance of the passivation temperature to further reduce the passivation time some notes on this subject follow next. An optimum temperature of 350°C was also proposed for hydrogen passivation of polycrystalline silicon thin films [125]. Carrying out ESR (electron spin resonance) measurements it was found that the spin density, which is a measure of the amount of dangling Si-bonds, is lowest at a passivation temperature of 350°C. It was also found by SIMS (secondary ion mass spectroscopy) measurements that at the higher passivation temperature of 450°C hydrogen diffuses faster into the silicon films, but the H-concentration in the surface region is lower than for passivation at 350°C, explaining the higher value of the spin density when 450°C is used. The observation that a fast bulk passivation can be obtained by using higher temperatures is an important point for industrial 44 4 Microwave induced remote hydrogen plasma (MIRHP) passivation application of the MIRHP process. Using a short high temperature step for bulk passivation followed by a short low temperature process for surface passivation, the total MIRHP process time can be considerably reduced for example for BAYSIX material from 2h to 30 - 60 min, as can be concluded from Fig. 4.5. 4.4 MIRHP of RGS solar cells 4.4.1 Introduction Compared to the other mc-Si materials of investigation, only few literature can be found about the properties of RGS material [33, 48, 50, 126, 127] and about RGS cell processing [49, 123, 124, 127-130]. Therefore we have focused at UKN on RGS cell processing since 1994. In the following a short historic overview of cell efficiency of RGS cells is given. Based on a 30 µm thick epitaxially grown silicon layer on highly doped RGS, an efficiency of 10.4% was reported [128]. In contrast to this result the efficiency remained well below 10% for a long time with RGS sheets as active solar cell material. The efficiency of `active` RGS solar cells is supposed to be limited by the interaction of high oxygen and carbon concentrations above 1018 cm-3 [48, 50] and a variety of crystal defects (dislocations in the range of 105 - 107 cm-2, grain boundaries with average grain diameter between 0.2 - 1 mm, point defects,...) [48]. In additional with neutron activation analysis Fe, Ni and Cu were determined with concentrations of approximately 1014 cm-3 [51]. In 1997, for the first time the milestone of 10% efficiency on an `active` RGS solar cell has been achieved in our laboratory due to improved RGS base material quality [48] and due to mechanical V-structuring of the front surface and aluminum-gettering [127]. Applying the MIRHP to RGS solar cells resulted in a further record of 11.1% cell efficiency and 538 mV open circuit voltage [49, 129]. On flat RGS cells with a selective emitter interesting IQE-measurement results have been obtained before and after a MIRHP process, which are shown in section 4.4.2. The benefit of the MIRHP process depending on the different cell processes is studied in section 4.4.3, including mechanically V-structuring of the front surface, PECVD (plasma enhanced chemical vapor deposition) SiN/SiO2 double layer antireflection coating and forming gas annealing. A special mark is put on the homogeneity of cells processed from same and also from different RGS sheets. 4.4.2 Flat cells 4.4.2.1 Cell processing Cells with selective emitter were processed as described in section 2.4.2. For the investigation of the reproducibility of the RGS crystallization process, four 2 2 cm2 solar cells were processed on two 5 5 cm2 wafers labeled in the following as R15 and R16, which were cut from two different RGS sheets. The sheets were grown in different batches but without changing the crystallization process parameters. The cells were labeled according to their -2 RGS-wafer JSC [mAcm ] VOC [mV] FF [%] η [%] R15 20.5 - 21.2 478 - 481 58 - 61 5.8 - 6.0 R16 15.0 - 16.1 485 - 487 59 - 66 4.3 - 5.2 Table 4.4: Range of the illuminated I-V parameters of the four cells processed on the wafers R15 and R16. No MIRHP process and no ARC was applied. 4.4 MIRHP of RGS solar cells 45 positions on the wafer as a, b, c and d. The range of the illuminated I-V parameters of cells processed on the wafers R15 and R16 are shown in the Table 4.4. The observed large differences in especially the short circuit current density show that further work has do be done on the reproducibility of the crystallization process. Currently it is discussed if the differences in the cell parameters are caused by different impurity concentrations in the two RGS sheets [51]. Despite the variation between the two sheets, the cells processed on the same sheet do not vary to a larger extent in the illuminated I-V parameters than cells processed on most of the other mc-Si materials. For example four 2 2 cm2 cells processed on one 5 5 cm2 EUROSOLARE wafer exhibit also a variation in -2 JSC of 1 mAcm , as was shown in Fig. 4.2. In the following the cells R15b and R16b are further investigated. The other cells were used in section 4.3.3 for the optimization of the MIRHP process. 4.4.2.2 IQE before H-passivation Fig. 4.9 shows the internal quantum efficiency and the I-V measurement results of two cells R15b and R16b before applying the MIRHP process. Cell R15b has a considerably higher IQE and short circuit current density JSC but a lower fill factor FF and slightly lower open circuit voltage VOC than cell R16b. A correlation between low VOC, low FF and high JSC or vice versa is often observed on RGS cells, however not understood yet. Interestingly, the unpassivated cell R15b can be well simulated with PC-1D [131] in the long wavelength region but not at all in the short wavelength region. Furthermore the base minority carrier diffusion length Lb of 85 µm determined in the long wavelength region seems to be far too large for RGS, where usually Lb < 30 µm is reported [129] and is not consistent with the low VOC. With the observation that the IQE for cell R15b is high below 500 nm, where the emitter dominates the IQE, and relatively high above 950 nm, where the base dominates the IQE it can be argued that for cell R15 the deviation between 500 - 950 nm is most probably due to some effect in the space charge region, causing a decrease of the IQE. As shown in Fig. 3.7 of chapter 3, the contribution of the scr is of the order of the deviation in the measured and simulated IQE of cell R15b. A moderate fit is obtained with PC-1D on the IQE of the non-passivated cell R16b, resulting in Lb = 7.5 µm, which is consistent with the measured VOC, JSC and FF. From this consistency and the better agreement of the measured and simulated IQE of cell 16b, it seems that this cell behaves more like a cell based on conventional silicon. However carrying out the MIRHP process on both cells, we will see in the following section that both cells behave similarly. Fig. 4.9: The internal quantum efficiency 1,0 and the illuminated I-V parameters of L = 85 µm solar cells R15b and R16b based on RGS b 0,8 simulation material. Simulation results with two different PC-1D [131] are also given in the figure. with PC-1D RGS materials PC-1D is a quasi-one-dimensional 0,6 L = 7.5 µm finite-element computer program b especially invented for the simulation of IQE solar cells. 0,4 meassurement: η V OC JSC FF -2 0,2 cell [mV] [mAcm ] [%] [%] R15b 481 20.6 60.9 6.01 R16b 487 16.0 66.1 5.17 0,0 500 600 700 800 900 1000 1100 λ [nm] 46 4 Microwave induced remote hydrogen plasma (MIRHP) passivation It was also proposed that VOC might be reduced for RGS cells because of a shunting mechanism through the space charge region (scr) caused by conducting microdefects such as FeSi2 precipitates penetrating the space charge region [50]. Support for this model comes from the previously mentioned observation that high concentrations of Fe, Ni and Cu are present in RGS silicon [51]. However, this model can not explain the relatively high value of the short circuit current density and of the IQE for wavelengths above 950 nm of cell R15b. By C. Häßler and H.-U. Höfs [51] another model is suggested to explain the effect of high short circuit currents and low open circuit voltages. Due to intrinsic doping of grain boundaries caused by segregation of oxygen or other impurities, the emitter area could be increased, therefore resulting even for low bulk diffusion lengths in high short circuit currents and IQEs. In this concept shunts through the doped grain boundaries might be the cause for the low open circuit voltages and fill factors. With two-dimensional computer simulations, which take into account the crystal structure as well as doping effects of the grain boundaries, the deviation of the measured IQE from theory will be further investigated by G. Hahn. 4.4.2.3 Improvement of RGS cell performance due to MIRHP Applying the MIRHP process, the IQEs of both cells improve mainly in the medium wavelength region between 500 and 950 nm as seen in Fig. 4.10. After a complete MIRHP passivation process, both experimental IQE curves are fitted much better with PC-1D than before hydrogenation. By comparing the measured IQE of the non-passivated cell R16b with the PC-1D simulation, for Lb = 20 µm one sees that also for the IQE of cell R16b a medium wavelength region exists which can not be simulated with PC-1D. Due to the MIRHP process for both cells all illuminated I-V parameters increase, resulting in final cell efficiencies without ARC of 6.85% and 6.94% for R15b and R16b, respectively. Assuming that the intrinsic doping effect of grain boundaries mentioned in the previous section exists, the observed increases of the IQE for the small wavelength region might be explainable by the diffusion of hydrogen only a few microns deep into the cell. 1,0 1,0 µ Lb= 85 m L = 20 µm simulation b simulation 0,8 0,8 with PC-1D µ with PC-1D Lb= 7.5 m 0,6 meassurement results 0,6 of cell R16b: meassurement results of cell R15b: IQE η IQE t V J FF η t HP VOC JSC FF HP OC SC 0,4 0,4 -2 [min] [mV][mAcm-2][%] [%] [min] [mV] [mAcm ] [%] [%] 0 487 16.0 66.1 5.17 0 481 20.6 60.9 6.01 0,2 30 518 17.7 68.5 6.28 0,2 30 499 21.3 61.8 6.56 150 527 18.6 68.3 6.68 150 506 22.0 61.9 6.88 315 532 18.6 69.3 6.85 315 508 22.0 62.3 6.94 0,0 0,0 500 600 700 800 900 1000 1100 500 600 700 800 900 1000 1100 λ [nm] λ [nm] Fig. 4.10: Influence of the MIRHP passivation time on the internal quantum efficiency (IQE) and the illuminated I-V parameters of the same RGS cells R16b (left side) and R15b (right side) as in Fig. 4.9. Simulation results with PC-1D are also given in the graphs. The MIRHP process parameters are the following: a passivation temperature of 350°C, a gas pressure of 0.1 mbar, a microwave power of 150 W and a gas flow of 4 ml/min. It was mentioned in section 3.3.1 that from dark current measurements information about the recombination in the emitter, scr and bulk can be obtained. As shown in Fig. 4.11, the dark current density JD decreases for cell R16b for all voltages, which is consistent with the improvements of the illuminated I-V parameters and IQE-curves presented in the previous 4.4 MIRHP of RGS solar cells 47 section. In agreement with the lower VOC and FF of cell R15b, their dark current density is higher than the one of cell R16b. Astonishingly, on cell R15b after a MIRHP process no change for negative voltages, corresponding to a shunt resistance, or of the second diode current, corresponding to recombination in the scr, is observed. Only for larger voltages a slight decrease in JD is seen, which represents a reduction in emitter or/and bulk recombination. Fig. 4.11: Influence of the MIRHP passivation on the dark -2 I-V characteristics of the same cells as 10 shown in Fig. 4.9. -4 ] 10 -2 Cell t [min] -6 HP [Acm 10 D R15b 0 J R15b 315 10-8 R16b 0 R16b 315 -0,2 0,0 0,2 0,4 0,6 voltage [V] 4.4.3 V-grooved cells 4.4.3.1 Cell processing V-grooving of the front surface of solar cells is a very promising technique for reducing reflection losses and increasing the light path within silicon [132, 133]. V-grooving together with a single layer ARC is supposed to boost up cell efficiency by 0.5 - 1% absolute, when compared to flat cells with the same ARC. Especially for small grained mc-Si such as RGS, where alkaline etching results only in minor reductions in the reflection, V-grooving is one of the most promising techniques for industrial applications [134]. To avoid additional photolithography steps, V-grooved cells with a homogeneous instead of a selective emitter were processed. Contrary to some of the other materials of investigation, where a degeneration of the cell performance was observed, when the MIRHP process was applied on homogeneous emitter cells after the front contact metallization on RGS, no degeneration was observed even after 4 hours MIRHP processing at 375°C, as was seen in Fig. 4.7. The homogeneous emitter cells were processed according to chapter 2.4.1 with an additional processing step for the front surface texturization. The front surface was mechanically textured by using a beveled saw blade leading to a V-groove like pattern with a groove depth and pitch of about 60 µm. After cell separation and characterization including illuminated and dark I-V, spectral response and reflectance measurements, some cells were submitted to a MIRHP passivation and a SiN/SiO2 double layer antireflection coating (DARC) deposited by the PECVD (plasma enhanced chemical vapor deposition) technique. In order to maintain consistency in the material quality as discussed in chapter 4.4.2.2 and to exclude possible variations due to the solar cell processing, four solar cells with an area of 4 cm2, referred to hereafter as A, B, C and D, were processed together on one 25 cm2 RGS wafer. 4.4.3.2 Homogeneity of the RGS material, benefit from forming gas annealing Table 4.5 shows the illuminated and dark I-V parameters of the four RGS cells after a short (30 min) and an additional long (3 h) FGA (forming gas annealing) step at 380°C. It is believed 48 4 Microwave induced remote hydrogen plasma (MIRHP) passivation that the short annealing is sufficient for healing the surface damage caused by the e-gun evaporation of the front contact, whereas improvements of the I-V parameters during the long annealing are mainly due to the passivation of defects within the surface region of the RGS cells. The very good correspondence of the illuminated I-V parameters of all four RGS solar cells demonstrates the good homogeneity of the RGS wafer used. The nearly identical improvements of these cells due to the second long FGA suggests the same passivation mechanism for all cells and therefore a rather homogeneous distribution of the passivated crystal defects. The dark I-V parameters were obtained by fitting the dark current JD to the theoretical two-diode model given in eq. (3.4). Cell Anneal Illuminated I-V parameters Fit of the dark I-V curve eq. (3.6) -2 -2 VOC [mV] JSC [mAcm ] FF [%] η [%] J01 [pAcm ] Rsh [kΩ] VOC [mV] A 30 min 510 22.3 72.3 8.23 44 3.7 515 B “ 505 21.9 71.8 7.94 51 5.3 511 C “ 508 22.1 71.1 7.97 38 0.8 519 D “ 509 22.7 71.5 8.25 44 2.0 516 A 3 h 513 (+3) 22.9 (+0.6) 72.2 (-0.1) 8.48 (+0.25) 39 6.2 519 B “ 508 (+3) 22.5(+0.6) 72.3 (+0.5) 8.29 (+0.35) 38 12.0 519 C “ 511 (+3) 22.7 (+0.6) 72.2 (+1.1) 8.27 (+0.30) - - - D “ 511 (+2) 22.9 (+0.2) 72.2 (+0.7) 8.44 (+0.19) 39 2.8 519 Table 4.5: Effect of the duration of a FGA (forming gas annealing) step at 380°C on the illuminated (25°C, 1000 Wcm-2, AM1.5 standard terrestrial spectrum) I-V parameters of the four investigated RGS solar cells. The saturation current density J01 and the shunt resistance Rsh were obtained by a fit of the dark I-V data with a two-diode model choosing n1 = 1. The very good correspondence of the illuminated I-V parameters of all four RGS solar cells shows the excellent homogeneity of the RGS material. The figures in brackets denote the absolute increase due to the second FGA step. In the last column the calculated VOC from equation (3.6) is outlined, which is in good agreement with the measured VOC. A fixed n1 of 1 leads to very good fits with nearly equal J01 and similar n2 (2.13 - 2.27 before and 1.96 - 2.19 after the second FGA) for all four cells further confirming the excellent homogeneity of the RGS material. In contrast to these nearly ideal diode factors of 1 for n1 and 2 for n2, RGS solar cells processed in the past in our laboratory had high diode factors (n2 of up to 10) and more inhomogeneous illuminated I-V parameters. The large variations in the shunt resistance Rsh between 0.8 and 12 kΩ before MIRHP passivation have no influence on VOC - as indicated by the fact that the lowest open circuit voltage is measured on the cell with the highest shunt resistance. If VOC depends on the shunt resistance, the cell with the highest shunt resistance should have the highest VOC. After applying the MIRHP process, all four cells have almost identical fill factors, which also do not depend on the shunt resistance. Because of the dominance of the first diode for voltages between 350 mV and 550 mV, as seen in the dark current characteristics in Fig. 4.12, the open circuit voltage VOC can be calculated from equation (3.6) by neglecting the second diode as well as Rs and Rsh. As shown in Table 4.5 the measured VOC of the cells A, B, C and D corresponds very well with the calculated VOC with relative deviations of below 2.2%. Equation (3.6) could not be applied to RGS solar cells processed in the past in our laboratory due to their highly non ideal diode factors and to the fact that at VOC both diodes contributed substantially to the dark current density. 4.4 MIRHP of RGS solar cells 49 4.4.3.3 Benefit from the MIRHP applied before the DARC 4.4.3.3.1 I-V characteristics On cell D a MIRHP process was applied before the deposition of a PECVD SiN/SiO2 double layer antireflection coating (DARC), resulting in absolute improvements in VOC of 27 mV, JSC of 2.8 mAcm-2, FF of 2.4% and cell efficiency η of 1.86% due to the MIRHP alone (see Table 4.6). After the deposition of the DARC, high values for VOC of 538 mV and for η of 11.1% have been reached on this RGS solar cell. The optimal process time for the MIRHP was found to be 2 h, whereas most of the improvements for all illuminated I-V parameters occur within the first hour. Also seen are the improvements in the illuminated I-V characteristics due to the second long FGA step mentioned above. Cell Processing Illuminated I-V parameters Fit of the dark I-V curve -2 -2 VOC [mV] JSC [mAcm ] FF [%] η [%] J01 [pAcm ] n2 A 30 min anneal 510 22.3 72.3 8.23 44 2.25 3 h anneal 513 22.9 72.2 8.48 39 2.19 DARC 517 27.1 71.2 9.95 32 2.19 D 30 min anneal 509 22.7 71.5 8.25 44 2.27 3 h anneal 511 22.9 72.2 8.44 39 2.03 2 h MIRHP 538 (+27) 25.7 (+2.8) 74.6 (+2.4) 10.30 (+1.86) 14 2.05 DARC 538* 28.5* 72.4* 11.1* 14 2.17 Table 4.6: Dark and illuminated I-V parameters of cells A and D after different processing steps. *Independently certified measurement at the FhG-ISE at Freiburg, Germany (8/97). The MIRHP process parameters were the following: passivation temperature of 350°C, a gas pressure of 0.2 mbar, a microwave power of 50 W and a gas flow of 4 ml/min. The illuminated I-V characteristics of cell A without MIRHP passivation is included in Table 4.6, showing the impact of the MIRHP in combination with a PECVD SiN/SiO2 DARC. Comparing cell A with cell D after the deposition of the DARC, the MIRHP leads to absolute -2 improvements in VOC of 21 mV, JSC of 1.4 mAcm , FF of 1.2% and η of 1.15%. These increases in VOC and JSC are lower than the ones observed during the MIRHP process applied on cell D, which is due to a PECVD passivation effect discussed in the next section. The positive influence of the MIRHP process on the solar cell performance can also be seen by comparing the measured dark current density JD of cell D after different processing steps as shown in Fig. 4.12. A large decrease in JD is seen for voltages above 260 mV after the MIRHP as compared to the measurement after the second forming gas annealing. A reduction in the dark current density for small voltages below 400 mV – this is below the voltage at the maximum power point VMMP of 431 mV – could be observed after the second forming gas annealing in comparison to JD after the first short anneal. A comparison of the non MIRHP treated cell A with cell D after the MIRHP step shows the superiority of the latter in the voltage region of 190 to 600 mV, which is the important region determining VOC as well as VMMP. Below 190 mV cell A has a lower JD because of the higher shunt resistance of 6.3 kΩ compared to 2.7 kΩ of cell D. Both shunt resistances have no considerable influence on the fill factor. The higher series resistance of cell A of 220 mΩ compared to 130 mΩ of cell D, which can also be seen in the shift of the JD curve to higher voltages, reduces the fill factor of cell A. 50 4 Microwave induced remote hydrogen plasma (MIRHP) passivation Fig. 4.12: Dark I-V charact- -1 cell D: eristics of cell D after 10 different processing steps and anneal 1 (380 °C / 30 min) of cell A after the deposition anneal 2 (380 °C / 3 h) 10-2 of the PECVD SiN/SiO2 MIRHP and DARC (SiO2/SiN) higher Rs double layer antireflection ] -2 of cell A coating. 10-3 cell A: DARC (SiO2/SiN) / no MIRHP lower J of cell D [Acm 01 D J due to MIRHP 10-4 10-5 higher Rsh of cell A 10-6 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 voltage [V] 4.4.3.3.2 IQE-measurements In the previous section it was stated that the MIRHP process applied to cell D results in larger increases of VOC and JSC than when the MIRHP passivated and SiN/SiO2 coated cell D is compared with the non MIRHP passivated cell A. This can be explained by the passivation of SiO2 / emitter interface states due to the diffusion of hydrogen from the hydrogen rich SiN layer into the cell. It is well known that SiN PEVCD films contain large amounts of hydrogen of up to 20% atom percent [135]. Because of the sufficient H-passivation of cell D, the improvements of the illuminated I-V parameters are only due to the reduction of the reflectance, whereas the none MIRHP treated cell A improves also because of the PECVD passivation effect. This argumentation can be proven by the calculation of the different contributions to JSC from internal quantum efficiency and reflectance measurements, as shown in Fig. 4.13. Fig. 4.13: IQE data of cells A 100 and D after different cell A: µ processing steps. The figures before DARC (9 m) after DARC (11 µm) in brackets denote the base 80 no surface damage cell D: minority carrier diffusion µ by MIRHP before MIRHP (9 m) lengths determined by after MIRHP (22 µm) two-dimensional simulations. µ 60 -2 after DARC (22 m) The measured reflectances of loss of 0.26 mAcm due to cell D before and after the surface damage by PECVD and absorption in SiN-film deposition of the PECVD 40 SiN/SiO2 antireflection coat- [%] IQE R, ing are included. The aver- aged reflectance between 20 360 - 1040 nm was 15.9% before and 4.6% after the reflectance of cell D deposition of the DARC. 0 400 500 600 700 800 900 1000 1100 1200 λ [nm] 4.4 MIRHP of RGS solar cells 51 The contribution of the passivation effect of the PECVD to the total short current density increase is given by the following equation: ∆ =⋅()λλλλλ − () ⋅−() ⋅() JeIQEIQESC∫ () after before()1 R after Fd (4.33) with IQEbefore/after being the internal quantum efficiencies before and after depositing the DARC, Rafter the reflectance after depositing the ARC and F(λ) the photon flux per wavelength interval. With an analogous equation: ∆ =⋅()λλλλλ ⋅ () − () ⋅() JeIQERSC∫ before() before R after Fd (4.34) with Rbefore representing the reflectance before depositing the ARC, the increase of JSC due to the reduction of the reflectance can be derived. According to these equations, the reduction of -2 the reflectance of cell A leads to an increase in JSC of 3 mAcm and the passivation effect of -2 -2 1 mAcm , which together agrees very well with the increase in JSC of 4.2 mAcm as determined by the I-V measurement (see Table 4.6). For cell D eq. (4.34) gives an increase of -2 JSC of 3.2 mAcm due to the reduced reflectance and equation (4.33) leads to no improvement -2 of JSC but a slight decrease of 0.07 mAcm . The difference between the increase in JSC of 2.8 mAcm-2 as determined by the I-V measurement (see Table 4.6) and the above calculated 3.2 mAcm-2 can be explained by the measurement uncertainty in the spectral response measurement of 2 - 3%. From the IQEs in Fig. 4.13. a plasma damage within the surface region - corresponding to wavelengths below 500 nm - due to a non-optimized direct PECVD process can be derived. Using ellipsometric measurements it was shown that current losses due to absorption within the SiN film are negligible compared to the plasma damage. The damage by direct PECVD is discussed in detail in literature [136]. Recently JSC and VOC decay measurements have shown that this damage can be further minimized [137] by increasing the deposition temperature. With equation (4.33) one gets in the surface region for cell D a decrease of JSC of 0.23 mAcm-2, which is only 0.8% of the total short circuit current density for this cell. Because of the PECVD surface damage, VOC does not increase but is unchanged at 538 mV during the deposition of the DARC, as can be seen in Table 4.6. The expected increase of VOC due to the increase of JSC can be calculated with equation (3.6) to be 3 mV or equal to 0.6% relative. With the prevention of reductions in the fill factor by a thicker front metal grid, the cell D could have at least a FF of 74.6% after the ARC deposition. Taking these possible improvements into account, an increase in the cell efficiency by 0.4% absolute is feasible on RGS by further optimizing the solar cell process. 4.4.3.4 The MIRHP applied after the DARC On cell B the MIRHP process was applied after the deposition of a PECVD SiN/SiO2 DARC. The changes in the illuminated I-V parameters of cell B after different processing steps are shown in Fig. 4.14, including the results of cell D as a reference. The large increases of all illuminated I-V parameters of cell D after a one hour MIRHP duration with only slight increases during the second hour contrasts with the results of cell B. Even after a 4 h MIRHP process only slight absolute increases in VOC of 1 mV, FF of 0.2% and η of 0.1% could be observed without changing JSC. This shows that the atomic hydrogen does not diffuse through the PECVD SiN/SiO2 DARC. 52 4 Microwave induced remote hydrogen plasma (MIRHP) passivation 540 29 +1.7 +0 28 +2.8 J 530 27 SC [mAcm +0.1 26 [mV] +25.7 OC 520 25 -2 V +2.7 24 ] 510 23 cell D cell B +0.8 11,0 74 +0.3 -2.2 +0.1 10,5 +2.1 η 10,0 [%] 73 +1.8 9,5 FF [%] 72 9,0 8,5 3h 1h 2h 4h 3h 1h 2h 4h anneal MIRHP MIRHP DARC MIRHP anneal MIRHP MIRHP DARC MIRHP Fig. 4.14: Change of the illuminated I-V parameters of cell D and cell B after different processing steps. On cell B the MIRHP was applied after the deposition of the DARC, whereas on cell D the MIRHP treatment was performed prior to the DARC. 4.4.4 Results on RGS cells The microwave induced remote hydrogen plasma (MIRHP) technique was found to be very effective in enhancing the performance of RGS (ribbon growth on substrate) silicon solar cells. The MIRHP alone resulted in absolute improvements in the open circuit voltage of 27 mV, in the short circuit current density of 2.8 mAcm-2 and in the cell efficiency of 1.9%, leading to an open circuit voltage of 538 mV and an efficiency of 11.1% confirmed at FhG-ISE, Freiburg. These are the highest reported values so far for this low cost material. The base minority carrier diffusion length improved from 9 µm to 22 µm after MIRHP passivation. The excellent homogeneity of the RGS sheets has been demonstrated by the good correspondence of the illuminated and dark current voltage characteristics as well as the internal quantum efficiency of solar cells processed on one RGS wafer. 4.5 Results on multicrystalline PERL-cells 4.5.1 Introduction In recent years the quality of various multicrystalline silicon materials has considerably improved. To point out the potential of mc-Si silicon for cell processing some groups have focused on applying high efficiency cell processing sequences, originally developed for FZ-Si material, on high quality mc-Si materials. With HEM (heat exchanger method) mc-Si material a solar cell of 18.6% (11 cm2 area) has been achieved by a process including Al-gettering and back surface passivation [21]. Using the PERL (passivated emitter, rear locally-diffused) cell structure [138, 139], an efficiency of 18.2% was reported on a 11 cm2 cell based also on HEM material [140]. Finally, combining the PERL process with a honeycomb textured front surface resulted in the recent 19.8% efficiency record on a 11 cm2 EUROSIL mc-Si material [19]. 4.5 Results on multicrystalline PERL-cells 53 In the following sections it is shown that the MIRHP process is ideally suited for improving the bulk of high efficiency mc-Si PERL cells based on EUROSIL material. The implementation of the MIRHP process into the PERL cell process is described in section 4.5.2. It is shown in section 4.5.3 that an additional annealing step applied after a complete MIRHP process results in further improvements of the cell performance. Internal quantum efficiency and illuminated I-V measurements presented in section 4.5.4 and 4.5.5 clearly prove that the minority carrier recombination in the cell bulk is reduced by the MIRHP process. 4.5.2 Combining the MIRHP passivation with the PERL cell process The solar cells for the following investigations were processed at the UNSW by applying the PERL processing sequence on EUROSIL mc-Si material [138, 140]. The important processes for the evaluation of the MIRHP study are the following: the creation of an honeycomb etched well structure [19] on the front surface with photolithography and the growth of a 10 nm thin thermal oxide for front surface passivation. To ensure that atomic hydrogen diffuses into the cell during the MIRHP process, no antireflection coating was used. For the same reason no thick better passivating thermal oxide can be applied. Due to the honeycomb structure of the front surface an average front surface reflectance of 26 - 28% was measured between 350 - 1100 nm on the cells. The reflection can be reduced after the MIRHP process with a double layer antireflection coating as in the case of the original PERL process. The following investigations were carried out on one 4 inch wafer WD6-1 consisting of 24 small 11 cm2 and 6 large 22 cm2 PERL cells. We decided not to separate the cells to avoid recombination of minority carriers at the cell edges which can considerably decrease the cell performance of small area high efficiency cells [90]. For a separated cell its edges may also be improved by a MIRHP process, which makes it difficult to obtain from measurements the improvement of the cell bulk. Additionally, difficulties in further cell processing at UNSW, such as ARC coating and additional annealing processes would arise if the wafer is separated into smaller pieces. On this wafer the MIRHP process is applied and on all cells the illuminated I-V characteristics as well as on some cells the IQE measured after 15 min, 60 min and 120 min MIRHP passivation time. It was found and will be discussed in the following that in addition to the MIRHP process an additional annealing step has to be applied for maximum improvements of the illuminated I-V parameters. 4.5.3 Influence of MIRHP and thermal annealing on PERL cells For one cell the illuminated I-V results after these processes are shown in Table 4.7. After 60 min MIRHP no further improvement of the illuminated I-V parameters is seen. However, if an additional H2/He annealing step is applied, VOC and JSC further improve. The additional improvement due to the annealing is also seen on most of the other PERL cells. Because no improvement due to annealing after the MIRHP process was observed on cells processed at our lab, it is supposed that during the MIRHP process the very high quality front surface passivation of the PERL cells is slightly damaged. This can be explained by the enhanced recombination rate of atomic hydrogen to molecular hydrogen in the presence of a surface [141]. This recombination reaction is highly exothermic resulting in a release per H2-molecule of 4.5 eV which is enough to generate defects in the passivating oxide and at the interface of the oxide and the silicon. During the annealing some atomic hydrogen from the base diffuses back to the surface and heals the slight damage. Investigations in the future will deal with the reduction of the slight surface damage by decreasing the amount of atomic hydrogen at the sample surface. It was shown in an earlier study [123] that the plasma power can be reduced from the used 50 W to 20 W without increasing the passivation time, therefore keeping room for further decreasing the amount of 54 4 Microwave induced remote hydrogen plasma (MIRHP) passivation atomic hydrogen. In the case that a surface damage is unavoidable during the MIRHP process, it has to be shown if the additional annealing step completely heals the damage. Process Illuminated I-V parameters -2 VOC [mV] JSC [mAcm ] FF [%] η [%] before MIRHP 599 26.9 79.1 12.7 after 15 min MIRHP 604 26.9 80.2 13.0 after 60 min MIRHP 607 27.3 80.4 13.3 after 120 min MIRHP 606 27.3 80.4 13.3 after 60 min annealing 609 27.9 80.0 13.6 after 120 min annealing 609 27.9 79.9 13.6 measured at UNSW 608 27.5* 80.2 13.4 Table 4.7: Influence of MIRHP and annealing (380°C, H2/He) processes on the illuminated I-V parameters of one 22 cm2 PERL cell. The MIRHP process parameters were the following: a passivation temperature of 350°C, gas pressure of 0.1 mbar, a microwave power of 50 W and a gas flow of 4 ml/min. The last row shows the results of the I-V measurement carried out at the UNSW. *Slight differences in JSC between measurement at UKN and UNSW due to the use of a peripheral shading mask for the I-V measurement at the UNSW. 4.5.4 Improvement of the IQE by the MIRHP For all PERL honeycomb cells the IQE of the long wavelength region has considerably improved due to the MIRHP process. This is for example shown in Fig. 4.15 for the worst and best 22 cm2 PERL cell processed together on the wafer under investigation. Also seen in this figure are the improvements in the effective bulk minority carrier diffusion length Leff determined by eq. (3.16) as well as the improvements of JSC and VOC. The worst cell increases -2 by 1.5 mAcm / 6 mV and Leff from 259 to 433 µm, whereas the best cell improves by -2 1.1 mAcm / 4 mV and Leff from 377 to 482 µm. In the low wavelength region a small decrease in the IQE is observed, which is in agreement with the previously mentioned slight surface damage. From these measurements follows that the distribution width of cell parameters can be reduced by the MIRHP process. Additionally, even the best mc-Si PERL cells can be improved with a MIRHP process. 100 100 cell WD6-1-1A 80 cell WD6-1-1B 80 MIRHP L J V MIRHP L J V eff SC OC eff SC OC µ[m] [mAcm-2] [mV] 60 [ µm] [mAcm-2] [mV] 60 no 377 27.6 613 no 259 26.1 596 yes 482 28.7 617 40 yes 433 27.6 602 40 IQE, R R [%] IQE, IQE, R [%] 20 Reflectance 20 Reflectance 0 0 500 600 700 800 900 1000 1100 500 600 700 800 900 1000 1100 λ [nm] λ [nm] Fig. 4.15: Improvement of the IQE of two 22 cm2 mc-Si PERL cells due to a MIRHP passivation process. Both cells were processed on the same wafer. The effective bulk minority carrier diffusion length Leff according to eq. (3.16) as well as JSC and VOC are also shown in the figure. For these cells an average front surface reflectance of 27% was obtained in the range of λ =350 -1100 nm. The MIRHP process parameters were the following: a passivation temperature of 350°C, a passivation time of 2 h, a gas pressure of 0.1 mbar, a microwave power of 50 W and a gas flow of 4 ml/min. After the MIRHP an annealing step at 380°C over 2 h was carried out to further increase JSC and VOC. 4.5 Results on multicrystalline PERL-cells 55 4.5.5 Illuminated I-V results The short circuit current density and the open circuit voltage after the MIRHP process and their increases due to a MIRHP process of the cells processed together on the 4 inch wafer are shown in Fig. 4.16. The values for JSC and VOC also include a 2 h annealing step described in section 4.5.3. The crosses indicate cells with damaged front surface grid, which are not used 2 for this study. JSC of all cells and apart from two 11 cm cells also VOC increase due to the MIRHP process. For most cells it is valid that the higher the final JSC and VOC the lower was their increase due to the MIRHP. The observed inhomogeneity of especially VOC from the right to the left wafer side might be due to the fact that the orientation of the wafer was parallel to the gas flow during the MIRHP process. In the case of an induced slight surface damage as discussed in the previous section the right wafer side, which was nearer to the gas flow, could be damaged more strongly than the left wafer side. After we have proven that the MIRHP process generally improves mc-Si PERL cells, further investigations are under way to investigate the observed inhomogeneities as well as the in section 4.5.3 mentioned possible damage of the front surface passivation during the MIRHP process. The illuminated I-V parameters of the best 11 cm2 and 22 cm2 PERL cells after MIRHP -2 passivation are shown in Table 4.8. After hydrogen passivation JSC of 29.3 mAcm -2 (28.7 mAcm ), VOC of 624 mV (617 mV), FF of 80.2% (80.0%) and η of 14.7% (14.2%) was obtained on the best 11 cm2 (22 cm2) cell. The front surface reflectance on these cells was with 26-28% (averaged over 350 - 1100 nm) relatively high due to the fact that no antireflection coating was applied on the front surface. Assuming an average reflectance of 5%, which is reasonable for a double layer antireflection coating, efficiencies of 19% on the best 11 cm2 cell and 18.5% on the best 22 cm2 cell are feasible. short circuit current density [mAcm-2] open circuit voltage [mV] 28.7 27.6 617 602 +1.1 +1.5 +4 +6 X 27.5 27.7 28.4 X 608 607 613 +1.1 +1.1 +1.0 +11 +11 +2 26.1 29.3 29.2 26.4 27.8 28.0 27.5 X 603 624 620 593 613 619 609 X +2.4 +0.7 +0.7 +2.1 +1.6 +0.5 +0.2 +10 +5 +5 +16 +10 +1 +1 27.0 28.0 28.1 27.2 28.1 27.8 602 616 618 609 611 609 X X X X +2.1 +1.1 +0.7 +1.1 +0.4 +0.8 +12 +9 +5 +8 +3 +2 26.8 27.5 27.5 27.7 603 610 614 607 +1.5 +1.0 +0.8 +1.4 +10 +8 +6 +9 27.2 27.6 28.6 29.1 602 605 611 610 +3.0 +2.5 +1.7 +1.9 +4 +3 -2 +0 2 2 Fig. 4.16: JSC (left side) and VOC (right side) after MIRHP passivation of 11 cm and 22 cm PERL cells processed on the same 4 inch wafer labeled WD6-1. Additionally, the increases of JSC and VOC due to the MIRHP process are shown in the figures. Also included in these increases is an annealing step at 380°C over 2 h applied after the MIRHP process. The crosses indicate cells with damaged front surface grid, which are not used for this study. The MIRHP process parameters were the following: a passivation temperature of 350°C, a passivation time of 2 h, a gas pressure of 0.1 mbar, a microwave power of 50 W and a gas flow of 4 ml/min. 56 4 Microwave induced remote hydrogen plasma (MIRHP) passivation Cell Area Illuminated I-V parameters 2 -2 [cm ] VOC [mV] JSC [mAcm ] FF [%] η [%] WD6-1-1A 22 617 28.7 80.0 14.2 WD6-1-3B 11 624 29.3 80.2 14.7 Table 4.8: The illuminated I-V parameters of the best 11 cm2 and 22 cm2 multicrystalline PERL cells after MIRHP passivation. No ARC was applied on the cells with a honeycomb textured front surface, which resulted in an average reflectance of about 27 % between 350 and 1100 nm. 4.5.6 Conclusions It was shown that the MIRHP process is ideally suited for improving the bulk minority carrier diffusion length of high efficiency mc-Si cells. It was found beneficial for the illuminated I-V parameters to apply after the complete MIRHP process an additional 1 h annealing process at 380°C. On cells with a honeycomb textured surface on the front side but without antireflection -2 -2 coating, the MIRHP process leads to average increases in JSC of +1.3 mAcm (+1.1 mAcm ) 2 2 and VOC of +6 mV (+8 mV) on 11 cm (22 cm ) cells. After hydrogen passivation JSC of -2 -2 29.3 mAcm (28.7 mAcm ), VOC of 624 mV (617 mV), FF of 80.2% (80.0%) and η of 14.7% (14.2%) was obtained on the best 11 cm2 (22 cm2) cell. Due to the inverted pyramids the front surface reflectance on these cells was with 26 -28% (averaged over 350 - 1100 nm) relatively high. These results suggest that applying the MIRHP process on mc-Si PERL cells followed by an ideal double layer ARC the 20% efficiency milestone can be reached in the near future. 4.6 MIRHP of cells with homogeneous emitter As mentioned in chapter 2.4.2 it was found that applying the MIRHP process on completed solar cells with a lowly doped homogeneous emitter of 90 Ω/ results in a degeneration of the fill factor FF and open circuit voltage VOC. This in the following called degeneration effect was first published in [43, 123] and verified in later studies [53, 55, 124]. In addition Elgamel, who worked much on MIRHP of selective emitter solar cells at IMEC, also stated that he has observed a degeneration of the illuminated I-V parameters during MIRHP processing of cells with a homogeneous emitter 6. However using a selective emitter cell structure, processed according to section 2.4.2, with high doping underneath the front grid and low doping between the fingers this degeneration was not observed, but an increase of all illuminated I-V cell parameters [44, 55]. To investigate the degeneration effect, experiments on the solar cell level were performed resulting in the following observations (O1-O3): O1: No decrease in FF and VOC was observed on cells with a lowly doped homogeneous emitter based on various mc-Si materials during FGA (forming gas annealing) over 5 h at 350°C carried out in the MIRHP reactor without microwave injection. However, using homogeneous emitter cells from the same batch with the same crystal structure, a decrease in FF and VOC was observed after 30 min - 2h MIRHP at 350°C [55]. O2: Using cells with a highly doped homogeneous emitter of 26 Ω/ or a selective emitter, no degeneration but an improvement of all illuminated I-V cell parameters is observed during a MIRHP process [55]. 6 Private statement at the 2nd WCPEC at Vienna, 1998. 4.6 MIRHP of cells with homogeneous emitter 57 O3: The degeneration effect depends on the mc-Si base material used for cell processing. For example, on cells based on EFG [55] the degeneration of FF and VOC was found to be considerable faster than on RGS, where the degeneration effect was observed only after several hours MIRHP processing [124]. Seeing no degeneration effect during a FGA process over 5 h it can be concluded from observation O1 that the degeneration effect is assisted by the large amount of atomic hydrogen produced during the MIRHP process. With observation O2 it is clear that the degeneration effect of homogeneous emitter cells is caused at the regions where the front grid directly contacts the lowly doped emitter. EFG and RGS differ in crystal structure and content of interstitial oxygen. In section 4.3.3.2 it was found that the diffusion of atomic hydrogen is much faster for EFG than for RGS material due to the lower oxygen content of the EFG material. Under the obvious assumption that for fast diffusers in silicon such as titanium the diffusion coefficient is further increased in EFG it can be argued from observation O3 that Ti from the front contact, which is in direct contact with the emitter, enters the cell and causes a shunt through the space charge region. From observation O1 it can be concluded that the shunting of the scr is considerably enhanced during a MIRHP process at 350°C compared to the same process without plasma. It is therefore suggested that the energetic release of 4.5 eV during the recombination of atomic hydrogen to molecular hydrogen [141] supports the diffusion of Ti along crystal defects into the emitter and space charge region of the cell. This is a reasonable assumption, because a reduction in FF and VOC is also observed during simple annealing processes at temperatures above 450°C [142]. From this follows that the MIRHP process simply reduces the critical temperature, where the diffusion of titanium starts. As obtained from secondary ion mass spectroscopy measurements shown in Fig. 5.2 of section 5.3.3, the near surface region of a MIRHP passivated sample contains H-concentrations up to 51018 cm-3. Because of the considerably lower defect densities of the used mc-Si material it can be assumed that most of the hydrogen in the near surface region exists in molecular form. Support for the assumption that the space charge region is shunted is given by carrying out dark I-V measurements on cells before and after a MIRHP processes. To ensure that the degeneration effect is not due to the cell processing at UKN but to the fact that the MIRHP process is applied after the metallization, also cells processed at FhG-ISE were taken. In Fig. 4.17 the influence of the MIRHP process on the dark circuit current density JD for one cell processed at UKN (left side) and the other at FhG-ISE (right side) is shown. For voltages below 0.3 - 0.4 V there is a clear increase in Jd caused by the decrease of the shunt resistance Rsh, which is given in the figure. Rsh was determined by a fit to the two-diode model given in eq. (3.4). As the MIRHP process time succeeds, the critical voltage, defined as the intersection of the dark current characteristics of the passivated with the non-passivated cell, increases. With the critical voltages approaching the voltage at the maximum power point VMPP, at first the fill factor starts to decrease followed by the open circuit voltage and finally the short circuit current. This is also the sequence with which the degeneration of these parameters is experimentally observed on cells based on EFG, EMC and EUROSIL [55] as well as on RGS [124]. Using a selective emitter structure on all investigated mc-Si materials, no increase of Jd and decrease of Rsh was observed during a 5 h MIRHP process. Above these processing times there will most probably start a degeneration in FF and VOC, however these passivation times are much longer than those necessary for complete bulk passivation as shown in section 4.3.5. 58 4 Microwave induced remote hydrogen plasma (MIRHP) passivation 0,1 0,1 material: BAYSIX material: EMC 0,01 homogeneous emitter 0,01 homogeneous emitter no thermal oxidation thermal oxidation 0.40 V 1E-3 ] ] 1E-3 -2 -2 0.34 V R = 0.9 kΩ 1E-4 1E-4 sh 1.5 kΩ 0.33 V Rsh = [Acm [Acm 0.28 V Ω D D 1E-5 5 k 1E-5 J J Ω 3.4 k 0 min MIRHP 1E-6 14 kΩ 0 min MIRHP 1E-6 30 min MIRHP 60 kΩ 30 min MIRHP 1E-7 1E-7 60 min MIRHP 60 min MIRHP 1E-8 1E-8 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 voltage [V] voltage [V] Fig. 4.17: Dark current density JD as a function of the voltage for one cell processed at UKN (left side) and the other at FhG-ISE (right side) measured before and after a 30 / 60 min MIRHP process. Due to the MIRHP process, a clear increase of JD for negative and small positive voltages is observed, which can be explained within the two-diode model given in eq. (3.4) as a decrease of the shunt resistance Rsh through the space charge region. 4.7 Summary of results The effectiveness of the MIRHP (microwave induced remote hydrogen plasma) technique as a function of the process parameters sample temperature, gas pressure, gas flow, microwave power and processing time was investigated. For oxygen rich materials such as RGS and SOLAREX, it is found that the H-diffusion is reduced. By applying higher passivation temperatures and microwave powers, the passivation times of these materials can be considerably reduced. For further reductions of the passivation time, a two step passivation process including a short high temperature step at 425 - 450°C or above for good bulk passivation followed by a short low temperature step at 350°C for good passivation of the surface region is suggested. For EFG containing low oxygen concentrations a very fast passivation during only 30 min at 350°C or 15 min at 425°C is observed. It is found that the MIRHP passivation is very effective in improving various multicrystalline silicon cells, resulting in relative increases of the cell efficiency of 2 - 15% when cast silicon and 15 - 31% when ribbon silicon is used as base material. For the first time efficiencies above 11% for solar cells (4 cm2) based on Bayer RGS (ribbon growth on substrate) crystalline silicon have been demonstrated including mechanical V-structuring of the front surface, MIRHP passivation and PECVD SiN/SiO2 double layer antireflection coating. MIRHP alone resulted in absolute improvements in the open circuit voltage of 27 mV, in the short circuit current density of 2.8 mAcm-2 and in the cell efficiency of -2 1.9% leading to VOC of 538 mV, JSC of 28.5 mAcm and η of 11.1%. Due to the MIRHP process an improvement of the base minority carrier diffusion length from 9 µm to 22 µm was observed. The excellent homogeneity of RGS sheets has been demonstrated by the good correspondence of the illuminated and dark current measurements as well as the internal quantum efficiencies of cells processed together on one RGS wafer. It was shown that the MIRHP process is ideally suited for improving the bulk minority carrier diffusion length even for high efficiency mc-Si cells. Applying the MIRHP process on 11 cm2 (22 cm2) PERL cells based on EUROSIL material without antireflection coating led to -2 -2 average increases in JSC of +1.3 mAcm (+1.1 mAcm ) and VOC of +6 mV (+8 mV). After hydrogen passivation a voltage of 624 mV, a short circuit current density of 29.3 mAcm-2 and an efficiency of 14.7% was obtained on one 11 cm2 cell. All cells under investigation exhibit a high front surface reflectance of 26 - 28% (averaged over 350 - 1100 nm) due to the fact that no antireflection coating but only a honeycomb texturization of the front surface [19], was applied. These results suggest that applying the MIRHP process on mc-Si PERL cells with a 4.7 Summary of results 59 honeycomb textured surface [19], the 20% efficiency milestone will be reached in the near future. Finally the often observed degeneration of the fill factor and open circuit voltage during a MIRHP process on cells with homogeneous emitter after front contact metallization was investigated on the cell level. No degeneration of VOC and FF was observed during forming gas annealing or when a highly doped homogeneous or selective emitter was used. From these observations it can be concluded, that the high amount of atomic hydrogen during the MIRHP process plays a major role in the degeneration effect. It is suggested that the energetic release of 4.5 eV during the recombination of atomic hydrogen to molecular hydrogen supports the diffusion of titanium from the front grid along crystal defects into the emitter and space charge region of cells. 5 Diffusion and effusion of hydrogen in silicon 5.1 Introduction In the following chapter the MIRHP technique for the passivation of multicrystalline silicon solar cells is presented. Besides the effect of passivating dangling Si-bonds the MIRHP technique can also be used for the study of H-diffusion processes in mc-Si silicon. In section 5.2 some of the theoretical work on H-diffusion in silicon is given. In mc-Si it is assumed that atomic hydrogen mainly diffuses along crystal defects and traps, which results in the so-called trap-assisted H-diffusion. Three methods for extracting the activation energy for diffusion and the diffusion coefficient from H-passivation depths data are given. The H-passivation depth d is defined as the depth to which atomic hydrogen diffuses with a concentration with which all H-sensitive traps can be passivated. The two most commonly used methods to determine hydrogen in silicon are thermal effusion and secondary ion mass spectroscopy measurements, which will be discussed in section 5.3. It is found that both techniques can not be used to obtain the H-passivation depth, which is most important in mc-Si solar cell research. To fill this gap, a new non-destructive electrically sensitive method based on internal quantum efficiency measurements is presented in section 5.4. Using the theoretical work of the total IQE presented in section 3.4.4, several approximated formulations of the total IQE of a cell with two base regions 1 and 2, which differ in their minority carrier diffusion length L1 and L2 are derived. Using the so called two-layer IQE to fit measured IQEs the H-passivation depth, which corresponds to the width of the passivated base region 1, as well as the diffusion lengths L1 and L2 of both regions are obtained. A summary on this theoretical work is given in section 5.4.2.6. To experimentally verify this method, the two-layer IQE is used in section 5.4.3 to obtain from cells based on SOLAREX material after various MIRHP passivations the H-passivation depth in dependence of the passivation time and temperature. From this H-passivation depth data, the activation energy for diffusion and the diffusion coefficient is calculated by applying the evaluation methods presented in section 5.2. It is found that for SOLAREX material the square root law between H-passivation depth and passivation time is satisfied within the uncertainty of the IQE measurement and evaluation method. Finally in section 5.5 effusion experiments are presented, where hydrogen is diffused during an annealing process out of H-passivated cells. Carrying out IQE and I-V measurements before and after annealing, it is found that the temperature where the effusion of atomic hydrogen from the cell base starts, is strongly material depended. 5.2 Theoretical work on hydrogen diffusion 5.2.1 Free diffusion of hydrogen To gain an insight into H-diffusion processes in silicon, the case of free diffusion of atomic hydrogen as described for example in [10, 143] is presented in the following. In this case, the 5.2 Theoretical work on hydrogen diffusion 61 concentration gradient of hydrogen is the driving force for diffusion and the hydrogen concentration [H] obeys Fick`s second diffusion law [10]: ∂ ∂ 2 []HD=⋅ []H (5.1) ∂t ∂x 2 with the diffusion coefficient D. Assuming, as it is the case during the MIRHP process, a constant H-concentration source [H]0 on the sample surface (x = 0) and initially none of the hydrogen inside the semiconductor: []== [] [] Hxt=≥00,, H 0 and H xt >= 00 0 (5.2) the H-concentration profile for t > 0 is given by [10]: x []HHerfc=⋅ [] (5.3) xt, 0 2 Dt⋅ with the complementary error function erfc. With SIMS measurements, described in section 5.3.3, of hydrogen passivated defect free Cz and FZ silicon samples this functional behavior of the hydrogen concentration is often observed [10]. The spatial scaling leads to the commonly used expression for the mean square diffusion distance: xDtorxDt22=⋅42 ⋅ =⋅ . (5.4) The influence of the temperature on D depends on the dominating diffusion process. At room temperature and especially at the MIRHP process temperatures only non-quantum diffusion has to be considered which is thermally-activated of the form [10]: E A DD=⋅exp − (5.5) 0 kT⋅ with the diffusion constant D0 and the activation energy EA. 5.2.2 Multiple trapping of hydrogen In multicrystalline silicon a variety of impurities and defects are present which can influence the diffusion of hydrogen. For the case of trap-assisted H-diffusion, where H-atoms can be captured and released at traps X, the following reaction mechanism has to be studied [10, 143]: K E →X − X [][]HX+ [ HX⋅ ] with KDRHX= 4π (), and Be=⋅ν kT ← X XX (5.6) BX with [X] the trap concentration, [HX] the concentration of the hydrogen-trap complex which is assumed to be immobile, KX the reaction coefficient, R(H,X) the capture radius for the reaction, BX the dissociation coefficient, νX the vibrational frequency for dissociation and EX the binding energy of the HX complex. For the following discussion it is assumed that the 62 5 Diffusion and effusion of hydrogen in silicon dissociation of the HX complex is negligible, which is also discussed in the footnote on page 67: [][]+→K⋅X [ ] = π () (5.7) HX HX with KDRHXX 4 ,. The kinetics of eq. (5.7) is described by the following diffusion equations: ∂ ∂ 2 ∂ []HD=⋅[]HKHX − [][] ⋅ and [][][]HX⋅= K H ⋅ X. (5.8) ∂t ∂x 2 X ∂t X Until now there exists no analytical solution for these coupled differential equations, therefore we restrict on the case where the steady-state regime can be assumed [10]: ∂ ∂ 2 []H = 0 and therefore D ⋅=⋅⋅[]HK [][] HX. (5.9) ∂t ∂x 2 X The solution of this differential equation is given by [10]: K []HH=⋅−⋅ []exp()α x with απ=⋅⋅4,RH() X ⋅[] X =X ⋅[]X .(5.10) x 0 H H D There are some references which show that this exponential decay of the hydrogen (deuterium) concentration can be observed in multicrystalline silicon even for the non-steady state case [10, 42, 144]. This exponential behavior is totally different to the error function solution in the case of free Fickian diffusion, suggesting that the diffusion of H in multicrystalline silicon is also different from that in Cz and FZ silicon. Because there is no analytical solution for the non-steady state case found, an expression between the mean diffusion distance and the diffusion time for trap-assisted diffusion is not derived from theory yet. Therefore the relation between the mean diffusion distance and the diffusion time for defect rich material such as mc-Si is postulated in the following in analogy to the case of Fickian diffusion: 2 =⋅ ⋅β xD2 Ctt . (5.11) 0.5-β with an exponent β which might differ from 0.5 and Ct = 1 s to ensure that the diffusion coefficient D has the dimension cm2s-1 as defined in eq. (5.4). Equation (5.11) with β 0.5 is discussed in literature for the case of diffusion in a fractal lattice [145]. An exponent β of 0.5 is then a measure how good H-diffusion can be described by one, two or three-dimensional diffusion models, whereas other values of β occur for diffusion in a fractal lattice. The reduced dimension of a fractal lattice reduces the number of free sides and therefore hinders the diffusion process causing a smaller exponent β. It is mentioned in [10] that H-diffusion along defects such as dislocations can also be described by diffusion through a fractal lattice. We will therefore investigate in section 5.4.3 how good H-diffusion can be described by an exponent β of 0.5 for multicrystalline silicon material with high defect density. 5.2.3 Methods for extracting diffusion parameters from H-depth data For the following calculations it is important to define for a given H-concentration profile [H]x a corresponding hydrogen depth d. For example for free diffusion, d can be defined according to eq. (5.4) by the mean square diffusion distance: 5.2 Theoretical work on hydrogen diffusion 63 dx= 2 . (5.12) If one is interested in the depth to which hydrogen passivates defects, this definition can not be used because this definition implies with eq. (5.3) that the H-concentration at depth d is equal to 0.157 times the H-concentration at the sample surface or in mathematical language erfc(1) = 0.157 [146]. As we will see in section 5.3.1, from SIMS (secondary ion mass spectroscopy) measurements follows that the H-concentration at this depth is much larger than the defect concentrations in all mc-Si materials under investigation. The actual depth to which the material is completely passivated, or as we call it the passivation depth, is therefore much deeper. Because we are mainly interested in the passivation effect in mc-Si material we will set in the following considerations the depth d equal to the passivation depth. How the passivation depth can be experimentally obtained from spectral response measurements of solar cells is described in chapter 5.4. If one is interested in the diffusion parameters D, D0 and EA of eq. (5.4) and (5.5), the dependence of d from the diffusion temperature and time has to be considered, which we will name in the following the depth data d(t, T). The diffusion coefficient D is originally defined in eq. (5.1) for free diffusion with a complementary error function solution for the H-concentration profile. We will use D in a more general and empirical sense without restriction on the H-concentration profile. Three methods will be presented in the following sections for the extraction of the diffusion parameters D, D0 and EA from passivation depth data. These three methods will be applied in chapter 5.4.3 to extract these diffusion parameters for one mc-Si material with high defect density. For some equations the logarithm has to be taken, therefore the following equations are made dimensionless by normalizing all parameters according to the dimensions [cm], [s] and [eV]. With this normalization, Ct becomes 1 and can be canceled in eq. (5.11). 5.2.3.1 The topt-method For this method, the passivation of similar solar cells is carried out using different hydrogenation temperatures until no further improvement of the short circuit current can be measured. Therefore the minority carrier diffusion length of the passivated region L1 can be used as a lower bound for the passivation depth d of the hydrogen. The thickness of the cell H can be taken as an upper bound for d. The relation between the passivation temperature and the optimal passivation time is then given by eq. (5.5) and (5.11): β d E ()t = ⋅ exp A opt ⋅ ⋅⋅ (5.13) 2 D0 2 kT or 1 d 1 E 1 ln()t =⋅ ln +⋅A =+⋅CD . opt ββ ⋅ ⋅ MM11()⋅ (5.14) 2 D0 2 kT kT e Note that because of the normalization according to dimension [s] mentioned above this equation is without dimension. With eq. (5.14) the diffusion constant D0 is obtained from the intercept CM1 and the activation energy EA is obtained from the slope DM1: 2 d −⋅⋅β D =⋅e2 CM1 and E =⋅2β D . (5.15) 0 4 AM1 64 5 Diffusion and effusion of hydrogen in silicon These equations can be used as a first estimate for the diffusion parameters. But for a more accurate investigation of the diffusion parameters the following two methods should be used. Additionally with this method β has to be known to calculate D0 and EA. 5.2.3.2 The tconst-method For this method the penetration depth of the hydrogen has to be determined on similar samples for different temperatures but with a constant passivation time, which has to be considerably smaller than the optimal passivation time used for the topt-method. The relation between the passivation depth and the passivation temperature is then again given by eq. (5.5) and (5.11): β E =⋅() ⋅ ⋅ − A dt2 const Dexp (5.16) 0 2 ⋅⋅kT or β E 1 ln()dDt=⋅ ln()2 ⋅ −A =+⋅CD . 022const 2 ⋅⋅kT MM()kT⋅ e (5.17) As for the topt-method D0 and EA can be calculated from CM2 and DM2, respectively: 1 ⋅ D = ⋅=−⋅e2 CM 2 and E2 D . 0 ⋅ 2β AM2 (5.18) 4 tconst The advantage of this method is that β has not to be known to calculate EA. Additionally, the determination of d by for example the method proposed in chapter 5.4 is more accurate than estimating d with lower and upper limit as done at the topt-method. 5.2.3.3 The Tconst-method As for the tconst-method the passivation depth d has to be determined, but in this case in dependence of the passivation time. For this method only one sample is needed, on which the passivation depth is successively measured during several H-passivation processes. For the evaluation only eq. (5.11) has to be used: β dDt=⋅2 ⋅ (5.19) or ()=⋅ +⋅=β () + ⋅ () lndDtCDt ln()2 lnMM33 ln . (5.20) The diffusion coefficient D and the exponent β are obtained from CM3 and DM1, respectively: 1 ⋅ D=⋅ e2 CM 3 andβ = D . (5.21) 4 M 3 Compared to the other two methods, this is the only method to determine β. Using the value for β together with the results from the other two methods, the diffusion constant D0 and the activation energy EA can be determined. 5.3 Experimental determination of hydrogen/deuterium in silicon 65 In the following section the two most commonly used methods for the determination of hydrogen in silicon are discussed. Because of the limitations of these methods for obtaining the depth data d(T, t), a new method using spectral response measurements of mc-Si solar cells is suggested in section 5.4. For examples of the three methods derived in this section for extracting diffusion parameters the reader is referred to section 5.3.4. 5.3 Experimental determination of hydrogen/deuterium in silicon 5.3.1 Introduction The two most commonly used methods to determine hydrogen in silicon are the TE (thermal effusion) and the SIMS (secondary ion mass spectroscopy) technique which will be presented in the following sections. 5.3.2 Thermal effusion (TE) For the TE technique described for example in [147], a hydrogen passivated sample is heated either in a closed or in an open vacuum system using a constant temperature ramp. In the case of the closed system, the effusion rate behaves as the time derivative of the partial hydrogen pressure, provided that the readsorption of hydrogen at the sample and the adsoption of hydrogen at the walls is negligible. In the case of an open system, a constant pumping speed ensures that the partial hydrogen pressure is a measure of the hydrogen effusion rate. In general, a mass analyzer is used for the determination of the partial pressure. To prevent measurement errors by adsorbed water in the samples and in the vacuum system, the hydrogen is substituted by deuterium, an isotope which duplicates hydrogen chemically with differences in the binding energies between Si-D and Si-H of less than 1% [147]. Because of the mass difference between deuterium and hydrogen, the diffusion constant, defined in eq. (5.1), is reduced by a factor of 2 for deuterium [10]. Measurement results of the thermal effusion technique applied on direct rf (radio frequnecy) deuterium plasma passivated Eurosolare Si-material are shown in Fig. 5.1 [44]. From this figureit is clear that the diffusion of deuterium becomes important only for temperatures above 350°C. The two peaks at 500 and 800 - 900°C are supposed to be due to two distinct deuterium diffusion mechanisms. The peak at the lower temperature belongs to the effusion of atomic deuterium and the peak with the higher temperature from the effusion of molecular deuterium. By defined wet etching of a front layer from the substrate prior to the TE measurement, some information can be extracted about the position of the deuterium in the sample. By comparing the TE signal of the etched sample with the non etched sample, it is found that for rf-deuterium Fig. 5.1: Relative rate of deuterium effusion determined from the measurement current of a mass analyzer as a function of the sample temperature for two rf-deuterium plasma passivated Eurosolare Si-material samples. For one sample, a 3 µm thick layer was etched prior to the H-effusion [44]. 66 5 Diffusion and effusion of hydrogen in silicon plasma passivated samples most of the deuterium is within the first 3 µm. The enhanced diffusion of hydrogen in the near surface region is due to the high density of defects generated by the rf-plasma process. However the defined wet etching is difficult to apply and for a depth profile, several samples with identical defect structure are needed. Furthermore the TE method provides no information about the binding and the position of the deuterium atoms - within the grain boundaries or intragrain defects - inside the mc-Si substrates. 5.3.3 Secondary ion mass spectroscopy (SIMS) Another method for the direct determination of deuterium concentration profiles of passivated sample is the SIMS technique [148, 149]. During a successive ion bombardment of the sample, surface deuterium ions are sputtered and measured with a mass analyzer. With the SIMS method some of the disadvantages of the TE method can be avoided. In dependence of the depth, absolute deuterium concentrations can be determined by measuring the depth of the sputtered crater and assuming a constant sputtering rate. Positioning the sputtering ion beam entirely inside the grain, the intragrain diffusion of deuterium can be studied. Despite the above mentioned advantages of the SIMS method, there is also a serious problem because the defect concentrations of various mc-Si materials are lower than the SIMS measurement limit for deuterium of around 1015 cm-3. After applying two different D-plasma passivation techniques - the direct rf (radio frequnecy) plasma and the microwave induced remote (MIR) plasma - on mc-Si samples, very different deuterium depth profiles were obtained by SIMS measurements shown in Fig. 5.2 [121]. The different D-concentrations within the surface region of the samples can be explained by the direct exposure of the samples to the plasma in the case of the rf-plasma, causing high defect densities in the near surface region, whereas for the MIR-plasma the samples are not in contact with the plasma. Using the rf-technique, most of the deuterium is trapped at defects or formed into immobile D-molecules near the surface, which hinders the further diffusion of D-atoms into the sample bulk. Therefore, the higher D-penetration depth caused by the MIR-technique can be explained by the avoidance of a surface damage and the high dissociation yield of deuterium molecules into atoms. The higher D2-dissociation yield of the MIR- compared to the rf-technique is due to the higher frequency of the former leading to a higher free mean diffusion length and therefore a higher mean energy of the electrons in the plasma, until they collide with hydrogen molecules. From the SIMS profiles shown in Fig. 5.2, a diffusion coefficient D of 1.1210-11 cm2/sec was calculated for EMC by the authors [42]. In my opinion this value is too small because from this value with eq. (5.4) after 1 h passivation, a penetration depth of only 2 µm results. Much higher values of D around 10-9 cm2/sec for mc-Si materials are given in literature [11] which are also in agreement with the values obtained in this work (see chapter 5.4.3). The inaccurate value for D is probably due to the assumption that the Fig. 5.2: Intragrain deuterium SIMS profiles after exposing electromagnetic cold crucible (EMC) casted p-type mc-Si wafers to a MIR and rf deuterim plasma treatment [121]. 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 67 exponential scaling factor αΗ in eq. (5.10) behaves as the square root of the diffusion time, e.g. -1/2 7 αΗ = (Dt) . For the non-Fickian, most probably trap-assisted diffusion in mc-Si, this behavior is theoretically not proven yet (see chapter 5.2.2). 5.3.4 Discussion Despite the possibility to determine deuterium (hydrogen) directly with TE and SIMS, these techniques provide no information on the actual D/H-passivation depth and the improvement of the recombination parameters e.g. the minority carrier diffusion lengths of solar cell materials and cells. The D/H-concentration at the actual passivation depth is usually smaller than the detection limit of the SIMS technique. Furthermore both methods are destructive, therefore they prevent the possibility to observe the effectiveness of the H-passivation with succeeding passivation time. From these considerations it can be concluded that an additional non-destructive electrically sensitive method for the determination of the passivation activity and passivation depth of the incorporated hydrogen is needed to fill this gap. This new method will be described in the following chapter. 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 5.4.1 Introduction In this section we will propose a new method for extracting passivation depths from spectral response measurements of not completely H-passivated cells. For the derivation of the internal quantum efficiency of this problem, the theoretical background from earlier research is helpful and presented in the following. Soon after the first calculations of internal quantum efficiencies of solar cells were published (see references given in chapter 3.4), expressions for the IQE were derived including electrostatic drift fields and the separation of the base (emitter) into two base (emitter) regions with different minority carrier diffusion lengths and mobilities [150]. The separation of a cell into two base regions can be seen in Fig. 5.3. These expressions were helpful for the simulation of a radiation damage in the upper base region of space cells caused by particle bombardment and for the reduction of this damage by the use of drift fields in the base region. Different to the base it was found that drift fields in the emitter do not improve the cell performance. For terrestrial cells the only known case where drift fields play a role is when a heavily doped layer at the back surface of the cell with the same type of doping as the base exists. With the so called back-surface field (BSF), minority carriers are shielded from the back contact. However the influence of a BSF is usually not directly described by the internal field at the back side region but by introducing a reduced effective back surface recombination velocity [151, 152]. Apart from the remaining interest in space cells, not much attention was paid to the two-layer IQEs during the following three decades until the importance of two-layer IQEs gained again attention for the simulation of cells consisting of thin layer silicon films deposited on cheap silicon substrates. Depending on the performance of these cells, carrier injection into and carrier generation within the substrate has to be taken into account for IQE simulations, making it necessary to describe the substrate as a second base layer [153]. Using the same electrical model as derived in [150], a recently published equation for the two-layer base IQE 7 This time dependency of αH was first published by [143] but no prove was given. I suppose the authors obtained this dependency by defining the time parameter as the inverse product of KX and [X], t := 1/(KX[X]). The larger KX and [X] the faster is the trap-assisted diffusion of H. This definition results with eq. (5.10) in the proposed time dependence of αH However, this procedure has been critically questioned, because assuming trap-assisted diffusion the dissociation of the HX complex can not be neglected as was done by deriving eq. (5.10). Otherwise only free Fickian diffusion occurs in steady-state conditions, which are assumed in the derivation of eq. (5.10). 68 5 Diffusion and effusion of hydrogen in silicon includes also weak surface texturization and internal rear and internal front side reflection for the calculation of the generation profile [111]. Using the work in [150] as starting point for our work, approximated expressions of the contribution of the base are derived. Following the same procedure as in chapter 3.4, we will derive an approximation for the total IQE by including the contributions of the emitter and space charge region. Using the newly derived total IQE of a cell with a high diffusion length L1 in the first base region and a lower diffusion length L2 in the second base region, a not completely H-passivated cell can be simulated. The depth d where both base regions contact is then obtained by a fit of the derived total IQE on the measured IQE. 5.4.2 Two-layer model of the IQE 5.4.2.1 Exact calculation of the base IQE In the following, the derivation of the two-layer bulk IQE according to [150] is presented. A sketch of a cell consisting of two base regions is shown in Fig. 5.3. We restrict ourselves to the case where the two base regions 1 and 2 need only to differ in their base minority carrier τ =⋅τ lifetimes 1/2 or according to LD12//b 12 in their base diffusion lengths L1/2. For the latter application of the derived equations to H-passivated mc-Si cells it has to be kept in mind that the H-passivation must not change the diffusion constant Db. Apart from the small grained RGS material this is due for all mc-Si materials under investigation. 0 Fig. 5.3: Sketch of a solar cell with two base em itter and regions 1,2 of different minority carrier diffusion space charge region lengths L1,2. The other parameters are the depth of the w emitter and space charge region w, the cell thickness H, the depth were regions 1 and 2 contact d and the base region 1 back surface recombination velocity Sb. with L 1 d base region 2 with L 2 H S b x Following the same procedure as in appendix 9.1, the starting point for the derivation of the base IQE of this cell is the differential equation of the excess minority carrier density. To cancel all parameters which do not enter the final formula of the IQE, a reduced minority carrier density is defined analogous to appendix 9.1 in both bulk regions separately. Assuming a thick cell compared to the light penetration depth (A5.1: H >> α-1 ) results in the following ∆ ′ differential equation for the reduced minority carrier density ni for both regions i = 1,2: 2 ≤≤ dnx∆∆′()nx′ () −⋅α 1 for w x d ii− =−ex and i = 22 <≤ (5.22) dx Li 2 for d x H with the diffusion length Li of region i, the width of the emitter and space charge region w, the depth d were both regions contact and the light absorption coefficient α. The general solution of this differential equation within the two regions is given by: 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 69 2 x x L −⋅α ∆nx′=⋅() Acosh +⋅B sinh + i ⋅=ex with i 12 , (5.23) ii L i L −⋅()α 2 i i 1 Li with four constants A1/2 and B1/2 which have to be determined by the following four boundary conditions. For x = w and x = H the same boundary conditions as in the case of the single-layer model have to be used: ∆ ′ = nw1() 0 (5.24) and dn∆∆′ () x nH′ ( ) SL⋅ 2 =− ⋅ 2 = b 2 s2 with s2 (5.25) dx xH= L2 Db with the back surface recombination velocity Sb and the reduced back surface recombination velocity s2. For x = d, where both regions contact, the reduced excess minority carrier concentration has to be continuous to insure equilibrium state conditions: ∆∆′ = ′ nd12() n () d (5.26) and continuously differentiable to avoid a loss current at the contact area: dn∆∆′() x dn′ () x 12= . (5.27) dx xd==dx xd Note that for α = 1/L1 or α = 1/L2 eq. (5.23) is not defined. We will come back to this point later. The IQE of this double-layer model is obtained from ∆n’ in the same way as for the single-layer cell shown in appendix 9.1, resulting in the simple expression: dn∆ ′(, xα ) αα== ⋅ 1 IQEb () (5.28) dx xw= As shown in appendix 9.1, coefficient A1 is calculated in dependence of B1 by inserting boundary condition (5.24) into (5.23). From this the IQE is obtained in dependence of the coefficient B1: αα()+ 111()tanh w B IQE ()α = ⋅+e −⋅α w 1 (5.29) b α 2 − ()⋅ 1 1 cosh wL11 with w1 = w/L1 and α1 = αL1. In the following the hyperbolic sine, cosine and tangent functions are abbreviated by sh, ch and th, respectively. The explicit calculation of B1 using the boundary conditions (5.25)-(5.27) is shown in appendix 9.4, resulting in eq. (9.28) for B1. Inserting this expression into eq. (5.29) results in: 70 5 Diffusion and effusion of hydrogen in silicon α −⋅α C CC+ IQE= 1 ⋅⋅+−− ew α th() w 1 23 (5.30) b α 2 − 11 1 1 C4 C4 with the coefficients C1 to C4 introduced to shorten the mathematical formulations of the IQE in the following discussion: 1 L L =⋅−⋅+⋅⋅ ()() 2 () +⋅ () +2 ⋅() C1 ()th H22 d ch d 1 s 2 sh d12 s ch d 1 sh d1 ch w1 L1 L1 2 []th()() H−⋅−⋅+− d1 αα s s =− L2 ⋅ 22 2222⋅ −⋅α ()dw − C2 1 e L2 ()1 − α 2 1 2 (5.31) ()−⋅⋅−αα2 2 () 1 1 Ls2 22 −⋅α () − C = ⋅ e Hw 3 −⋅⋅α 2 2 () − ()1 2 LchHd1 22 =−⋅+−+⋅−⋅+⋅−() ( )L2 () ( ) C4 sh d112 w[] s th H 22 d ch d11 w[]1. s 2 th H 22 d L1 with the newly defined parameters α2 = αL2, H2 = H/L2, d1 = d/L1 and d2 = d/L2. Using the addition theorems for the hyperbolic sine and cosine functions on the fraction C1/C4 and including the hyperbolic tangent of eq. (5.30) results in the following simplified expression: α −⋅α CC+ IQE= 1 ⋅⋅−− ew α C 23 (5.32) b α 2 − 15 1 1 C4 with sthHd+−()L 222+⋅2 th() d − w 1+⋅sthHd() − L 11 = 2221 C5 . (5.33) sthHd+−()L th() d−⋅ w 222+ 2 11+⋅() − 1 sthHd222L1 Summing up the coefficients leads to: α −⋅α CC+ IQE= 1 ⋅⋅− ew []α C with CC=+23 b α 2 − 16 65 (5.34) 1 1 C4 with the coefficients C2 to C4 defined in eq. (5.31) and C5 given in eq. (5.33). Besides that eq.(5.34) is not defined at α = 1/L1, from coefficients C2 and C3 it is seen that eq. (5.34) is also not defined at α = 1/L2. In appendix 9.5 it is shown that for both values the left and right limit of eq. (5.34) are finite and equal, respectively. Therefore eq. (5.34) can be expanded continuously at these two positions, resulting in a physical solution within the whole absorption region. 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 71 5.4.2.2 Approximations of the base region The rather complicate equation (5.34) can be considerably simplified by assuming either a region 2 thick compared to the diffusion length L2 within this region (A5.2a: H - d >> L2 or equal to H2 - d2 >> 1) or a large back surface recombination velocity Sb (A5.2b: Sb >> Db/L2 or equal to s2 >> 1). In approximation A5.2b the value s2 is the reduced back surface recombination velocity, which appears in the second boundary condition (eq. (5.25)). For cells with a full metal back contact, approximation A5.2b is always satisfied. If backside recombination, as for example in the case of point contact cells, plays a role, approximation A5.2a has to be used considering also the restrictions on the parameters d and L2, which will be discussed in appendix 9.6. 5.4.2.2.1 Thick second base region With the assumption of a thick second base region (A5.2a: H2 - d2 >> 1), the hyperbolic cosine and tangent functions can be expanded into a Taylor series, yielding the following approximations: 1 − thHd()−≈1 andchHde () −≈Hd22. (5.35) 22 222 With these approximations the coefficient C6 of eq. (5.34) can be considerably simplified: −−α() 2 −−α()dw ()1 −⋅⋅−⋅αα2 Lse2 ()Hw L2 e 1 2 22 L2 − 1 + 1 +−th() d w 2 − 11 L ()1 + α ()1105−⋅⋅+⋅⋅α 2 Ls2 (). eHd22 = L1 + 1 2 2 1 2 C61H . (5.36) ()−+L2 ()−+⋅L2 () − th d11 w sh d11 w ch d11 w L1 L1 At α = 1/L2 the last term has a pole, which could make it necessary to keep this term. However, we restrict in the following ourselves to the region outside the pole, where the last term can be neglected because of the small factors exp[-α(H - w)] due to approximation A5.1 and exp[-(H2 - d2)] due to A5.2a. Canceling the last term results in: −⋅α () − L L2 e dw cosh()dw−+2 sinh()dw −+ 2 −1 11L 11 L2 ()1 + α = 1 1 2 C62H (5.37) ()−+⋅L2 () − sinhdw11 cosh dw11 L1 (outside the region of the pole α = 1/L2). In appendix 9.5 it is shown that this expression for C6H2 is also obtained by calculating the left and right limit of the exact base IQE (eq. (5.34)). It is shown that the left and right limit are equal. Carrying out the approximation A5.2a on the limit results in the same coefficient as given by eq. (5.37). The point is that the term including the exponent of (H -w) is canceled due to approximation A5.2a alone, without any further assumptions on the pole region. One also obtains this result when approximation A5.2a is introduced directly in the fourth boundary condition. In the limit H → , eq. (5.27) results with eq. (9.25) in the simple connection between the coefficients of the second base region A2 = -B2. After some further calculations eq. (5.37) is obtained. The reason why s2 does not appear in eq. (5.37), which was 72 5 Diffusion and effusion of hydrogen in silicon derived by only assuming H - d >> L2, is the same as in the case of the base single-layer IQE (see section 3.4.2.2.1), where with approximation H >> Lb the reduced back surface recombination velocity sb was canceled. For L2 = L1, the coefficient C6H2 becomes 1 as for the single-layer model. 5.4.2.2.2 High back side recombination velocity With the assumption of a large back surface recombination velocity Sb (A5.2b: Sb >> Db/L2 or equal to s2 >> 1), the coefficient C6 of eq. (5.34) can be approximated to: − α 2 2 −−α()Hw L ()12th L −−α() 1 L e ch112+⋅2 sh th + 2 2 −1e dw − 2 − α 2 − αα2 2 − 2 2 2 2 L1 ()1 2 L1 ()1 2 L1 ch C = 61s L (5.38) sh112+⋅⋅2 ch th L1 with th2 = th(H2 - d2), ch2 = ch(H2 - d2), ch1 = ch(d1 - w1) and sh1 = sh(d1 - w1). For C6s1 the last and the middle term become infinite at α = 1/L2. In appendix 9.5 it is shown that the sum of both terms result in a finite value at α = 1/L2, making it necessary to use inside the pole region both terms. Outside the pole region, with approximation A5.1 the last term becomes negligible compared to the first term: − α 2 L ()12th L −−α() ch112+⋅2 sh th + 2 2 −1e dw − α 2 2 L1 ()1 2 L1 C = (5.39) 62s L sh112+⋅⋅2 ch th L1 (outside the region of the pole α = 1/L2). When d becomes large compared to the light penetration depth (d >> α-1) also the second term can be neglected resulting in a wavelength independent coefficient: L dw− Hd− 1 +⋅2 th ⋅ th L11L L 2 C = . (5.40) 63s − L − dw+2 ⋅ Hd th th L1 L12L Eq. (5.38) is also obtained by introducing approximation A5.2b directly in the fourth boundary condition. For infinite s2 the reduced excess minority carrier concentration has to be zero at the back side to insure that its derivation does not become infinity, which would correspond to a ∆ ′ = non-physically infinite loss current. With the modified fourth boundary condition nH2()0 , the functional dependence of the coefficients A2 and B2 on each other is the same as for the coefficients A1 and B1, as is seen by comparing eq. (9.7) in appendix 9.1 with eq. (9.25) in appendix 9.4. After some further calculations eq. (5.40) is obtained. For d = H and H -w >> L1 or L2 = L1 and H -w >> L1, the coefficient C6s3 becomes 1 as for the single-layer model. 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 73 5.4.2.3 The total IQE In the following, an approximated equation for the total IQE of the two-layer model is derived using the base IQE equation (5.34) together with any one of the derived expressions for the coefficient C6. In analogy to the derivation of the total IQE of the single-layer model, the approximated equation eq. (3.20) is used for the emitter and the space charge region, resulting in the total IQE: −⋅ααα −⋅ IQE=−1 eww + 1 ⋅⋅− e[]α C total α 2 − 16 1 1 1 −⋅αα −⋅ −⋅ α = ⋅−−−⋅+⋅[]αα2 11()2 eeCeww α2 −⋅⋅ α w (5.41) α 2 − 1 1 1 16 1 1 1 −⋅αα −⋅ = ⋅−+−⋅⋅[]αα2 1 eCeww α 2 − 1 16 1 1 By using the approximation of an emitter and space charge region small compared to the light penetration depths (A5.3: (αw)2 << 1), the total IQE can be written as: A53. 1 IQE ≈ ⋅−⋅−⋅⋅−⋅[]αα2 wC α()1 α w total α 2 − 1 1 16 1 (5.42) α = 1 ⋅⋅+⋅[]α ()()1 wC − C + w α 2 − 11661 1 1 with the equality αw = α1w1 used in the last line. For C6 = 1 eq. (5.42) reduces to eq. (3.23) in chapter 3.4. With the additional assumption of an emitter and space charge region small compared to the base diffusion length of region 1 (A5.4: w1 << 1), eq. (5.42) can be simplified to: α IQE= 1 ⋅−[]α C total α 2 − 16 (5.43) 1 1 As in the case of the single-layer model, also the stronger approximation (wα) << 1 could be used instead of the two approximations A5.3 and A5.4 to derive eq. (5.43). However using approximation (wα) << 1, the contribution of emitter and space charge region are completely canceled, therefore this approximation can only be applied as long as the IQE is determined by the base alone. For smaller wavelengths where the contribution of the emitter and scr has to be accounted for the procedure proposed in this work is unavoidable. Note that approximation A5.4 is not carried out on C6 to keep the exponential dependency of w. For completeness, the total IQE in the case of approximation A5.2a, A5.3 and A5.4 is given in 74 5 Diffusion and effusion of hydrogen in silicon the following, inclusive the limit value at α = 1/L1, which is derived by continually expanding the approximated IQE at α = 1/L1: α = IQEtotal (, L12 , L ,, d w ) 2 −⋅α () − dw− L dw− L e dw ch + 2 sh +− 2 1 2 ()+⋅α α ⋅ L L1 L11L L1 1 L2 1 1 ⋅⋅−α L :α ≠ 2 1 − − ()α ⋅−L 1 dw L2 dw L1 1 sh + ch L1 L11L − (5.44) ⋅ () − dw L dw− 2 LL21 L 2 −1 ⋅ + − 2 ⋅ e L1 + L11L 1 ()LL L1 1 + 1 12 α = 1 : 2 2 dw− L dw− L sh + 2 ch 1 L1 L11L It has to be mentioned that expanding the approximated IQE of eq. (5.43) at the poles α = 1/L1 and α = 1/L2 gives the right result as discussed in the following, but is mathematical inconsistent. The coefficient C6H2 of eq. (5.37) was only derived for α ≠ 1/L1 and outside the pole region of α = 1/L2. The mathematically consistent way to obtain the limit of the IQE at the poles α = 1/L1 and α = 1/L2 is shown in appendix 9.5, where at first the exact IQE is expanded continually at these poles. Carrying out the approximations A5.2a, A5.3 and A5.4 on the IQE at these two places leads to the same values as defined in eq. (5.44). The same procedure can be carried out using approximation A5.2b instead of approximation A5.2a, therefore proving that all approximated base IQEs derived in the previous chapter can be expanded continuously at their undefined places α = 1/L1 and α = 1/L2. 5.4.2.4 Comparison of the approximated total IQEs Fig. 5.4 shows the comparison of the exact total IQE with the approximations deduced in the previous section for a 300 µm thick cell with two base regions with diffusion lengths L1 = 100 µm and L2 = 25 µm. The exact total IQE is calculated by adding the contribution of the base with eq. (5.34), of the emitter with eq. (3.11) and the space charge region with eq. (3.12) of section 3.4.2.1. The emitter and base regions are supposed to be homogeneously doped. No recombination within the space charge region is assumed. With the coefficient C6H2 approximated from eq. (5.37), the equations (5.42) and (5.43) result in a very good agreement with the exact IQE down to λ = 750 nm, whereas a deviation is caused when the parameter w is partly neglected in eq. (5.44). Different to equations (5.42) and (5.43), the parameter w enters eq. (5.44) only through the coefficient C6H2 from eq. (5.37). The influence of the width d of the first base region on the IQE is shown in Fig. 5.5. 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 75 Fig. 5.4: Comparison of the exact 1,0 Influence of approximations total IQE with the approximations deduced in this chapter. The on total IQE equations (5.41) and (5.42) result in a 0,8 very good agreement with the exact λ IQE down to = 750 nm, whereas a 0,6 deviation is caused when IQEtotal approximations IQEb(eq.5.34) approximation A5.4 is used to derive + exact exact C6 IQE 0,4 eq. (5.44). For the calculation the eq. 5.41 A5.2a C6H2 (eq.5.37) following parameters were taken: eq. 5.42 A5.2a + 5.3 C6H2 (eq.5.37) 4 µ eq. 5.44 A5.2a + 5.3 + 5.4 C (eq.5.37) Sb = 10 cm/s, L1 = 100 m, L2 = 0,2 6H2 25 µm and d = 50 µm. The other cell + parameters are given in Table 3.1. emitter/scr by eq. 3.11/12 400 600 800 1000 λ [nm] Fig. 5.5: Influence of d on the internal 1,0 quantum efficiency approximated by L = 100 µm (eq. 3.23) equation (5.42). For the calculation, b 4 0,8 Sb = 10 cm/s was taken. The other cell parameters are given in Table 3.1. 0,6 L = 25 µm (eq. 3.23) d[µm] = 150 b 100 50 IQE 0,4 25 L = 100 µm, L = 25 µm 0,2 1 2 approx. eq. 5.42 800 850 900 950 1000 λ [nm] 5.4.2.5 Theoretical and experimental accuracy The accuracy of determining the passivation depth d from a SR-measurement depends on the accuracy of the SR-measurement and on the accuracy of the approximated double-layer IQE equation used for the fit procedure. As seen in Fig. 5.4 of chapter 5.4.2.3, eq. (5.42) provides a very good agreement with the exact IQE for wavelengths down to 800 nm, therefore the accuracy of determining d from a fit using this equation is further investigated in the following. The input data is calculated with the exact IQE using eq. (3.11) for the emitter, eq. (3.12) for the space charge region and eq. (5.34) for the base. Note that using these equations to calculate the exact total IQE, the following investigation does not take into account the case of a non-homogeneously doped emitter. The approximation of a homogeneously doped emitter is reasonable, because the doping profile has only an influence on the internal quantum efficiency for wavelengths smaller than the fit region used in the following. This can be proven by IQE simulations with the computer program PC-1D. To investigate additionally the influence of a wavelength independent error factor, the input data is multiplied by a factor of 0.975 and 1.025, respectively. These error factors correspond to measurement errors of 2.5%. For the diffusion lengths used for the fit either the exact input values were taken or deviations of 10%. The fit results are shown in Table 5.1. Using the accurate values for the diffusion lengths and assuming exact input data, a fit with eq. (5.42) 76 5 Diffusion and effusion of hydrogen in silicon results in only 1 - 2% deviation of d. With inaccurate input data of 2.5% deviation, the error in d increases to approximately 10% for the smaller d = 50 µm and 20% for the larger d = 150 µm. About the same errors in d are obtained when incorrect diffusion lengths with both having an error of 10% are taken. In general L2 (L1) is obtained by a fit on the IQE of the not passivated (completely passivated) cell resulting in errors in the range of 10% if the conventional eq. (3.15) is used [108]. This error can be reduced by using eq. (3.23) instead as shown in chapter 3.4. The effect that the error in d is smaller for d = 50 µm than for d = 150 µm is due to the fact that for d lying between the two diffusion lengths, a small change in d can change the IQE considerably as seen also in Fig. 5.5. Conclusively it can be assumed that the proposed method of determining a passivation depth d from SR-measurements results in errors up to 20% of d. input parameter: L1 = 100 µm, L2 = 25 µm dinput = 50 µm dinput = 150 µm error factor L1 used for fit L2 used for fit dfit [µm] dfit [µm] 0.975 100 25 44 (-12%) 125 (-17%) 1 100 25 49 (-2%) 149 (-1%) 1.025 100 25 55 (+10%) 178 (+19%) 1 110 27.5 44 (-12%) 130 (-13%) 1 90 22.5 54 (+8%) 183 (+22%) Table 5.1: The accuracy of determining d is estimated by several fits of eq. (5.42) on the exact IQE. For the calculation of the exact IQEs, the minority carrier diffusion lengths L1 = 100 µm, L2 = 25 µm and two different depths d were used. The error factor given in the first row corresponds to a calibration error described in the text. The other cell parameters are given in Table 3.1. The values given in brackets denote to the relative deviation of dfit from d used for the calculation of the input data. The fit region was taken to be λ = 800 - 1000 nm corresponding to light penetration depths of 10 - 156 µm. 5.4.2.6 Summary of this section In the following a summary of the two-base-layer internal quantum efficiencies derived in the previous sections is given. As starting point the homogeneously doped base was separated into two base regions 1 and 2, which differ in their minority carrier diffusion length L1 and L2, respectively, as seen in Fig. 5.3 in section 5.4.2. The width of base region 1 was defined as d - w, with w the total width of the emitter and space charge region and d the depth where both base regions contact. With total cell thickness H, the width of region 2 is H - d. Assuming a thick cell compared to the light penetration depth (A5.1: H >> α-1), the contribution of the base to the internal quantum efficiency was calculated according to the procedure given in [150]. From this formulation of the exact base IQE, as we call it in the following, different approximated base IQEs were derived. The exact as well as the approximated base IQEs can be calculated by eq. (5.34) with different coefficients C6. Generally C6 is dependent on the absorption coefficient. A summary of the assumptions made and the derived coefficients C6 are given in Table 5.2. The base IQE derived under the assumption of A5.1 and A5.2b (Sb >> Db/L2) is also given in [150], but the approximated IQE using A5.2a (H - d >> L2) is presented here for the first time. The approximation A5.2a is ideally suited for the application of the calculation of the IQE of not completely H-passivated cells. In this context L2 refers to the unpassivated region and is lower than L1 of the H-passivated first base region. As long as the H-passivation depth d is not too deep, approximation A5.2a is satisfied. Note that with this approximation the back surface recombination velocity is canceled in the IQE. The reason for this is the same as for the 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 77 single-layer base IQE, where it was shown in section 3.4.2.2 that the approximation A3.2a (wb =H - w >> Lb) also cancels the back surface recombination velocity. approximations equation for A5.1 A5.2a A5.2b C6 of eq. (5.34) -1 -1 H >> α H - d >> L2 Sb >> Db/L2 d >> α yes (5.31) and (5.33) yes yes (5.37) yes yes (5.39) yes yes yes (5.40) Table 5.2: Equations for the approximated coefficient C6 used in eq. (5.34) for the calculation of the approximated base IQE for the two-layer model. As shown in section 3.4.3, the contribution of the emitter and the space charge region must not be neglected for wavelengths below 900 nm. With the assumption that recombination in the space charge region can be neglected and assuming a homogeneously doped emitter region, the same procedure as in section 3.4.4 was used to derive approximated formulations for the total IQE of the two-layer model. These approximated total IQEs are presented here for the first time. For the approximations A3.4 to A3.6 on the emitter, the reader is referred to section 3.4.4. These approximations resulted in eq. (3.20) for the contribution of the emitter and space charge region to the total IQE. Using this formulation, the total IQE for the two-layer model can be calculated with eq. (5.41). A summary of the derived approximated total IQEs together with the assumptions made is given in Table 5.3. For the coefficient C6 any of the equations given in Table 5.2 can be used taking into account the made assumptions. approximations equation for A5.3 A5.4 the total IQE 2 (αw) << 1 w << L1 (5.41) yes (5.42) yes yes (5.43) Table 5.3: Equations for the approximated total IQE of the two-layer model. For the coefficient C6 any of the equations given in Table 5.2 can be used taking into account the made assumptions. It was found in section 5.4.2.4 that equation (5.42) together with C6 from eq. (5.37) results in a very good agreement with the IQE calculated using the exact formulations for the IQEs of the emitter, space charge region and base given in eq. (3.11), (3.12) and (5.34), respectively. Equation (5.43) together with C6 from eq. (5.37) results in a deviation. The proposed method for obtaining the H-passivation depth d of a not completely H-passivated cell is the following. Measure the spectral response of one cell before any H-passivation, after a not complete H-passivation and after a complete H-passivation. Calculate the internal quantum efficiency from the spectral response and reflectance for all three cases. The reflectance not influenced by the MIRHP passivation has only to be measured once. The diffusion length L2 (L1) is determined by a fit with eq. (3.23) on the non-passivated (completely passivated) cell. Using these two diffusion lengths for the two base regions of the two-layer IQE, a fit with for example eq.(5.42) and (5.37) results in the H-passivation depth d. 78 5 Diffusion and effusion of hydrogen in silicon Using eq. (5.42) and (5.37), the combined error of determining d was estimated for a special choice of L1 and L2 to be below 20%. Other values of L1 and L2 might change the error in d, which will be investigated in future work by applying a sensitivity analysis. Another error comes from the assumption of a step function for the diffusion length which is in reality a continuous transition from L1 to L2. Using three or more layers for the simulation of the IQE with PC-1D, the influence of the transition region will be investigated in further work. Because of the large fit region between 800 and 1000 nm, which corresponds to light penetration depths between 12 and 156 µm, the influence of the transition region is supposed small compared to the influence of the uncertainties in the determination of L1 and L2. Finally I want to point out that intensive work was also focused on the two places α = 1/L1 and 1/L2 where the base IQE given in eq. (5.30) and (5.31) is not defined. It was shown in appendix 9.5 that the exact base and total IQE as well as their approximations presented in the previous sections can be continuously expanded at these two places. This prove was needed to show that the approximated IQEs can also be used ‘near’ α = 1/L1 and 1/L2. 5.4.3 Experiment 5.4.3.1 Fit of the two-layer model to experiment By assuming that the bulk of an incompletely H-passivated cell can be described by a region 1 with high minority carrier diffusion length L1 and a region 2 with L2 < L1, eq. (5.42) can be used to extract a H-passivation depth d from IQE data. To experimentally verify the new method, IQEs of cells made from SOLAREX mc-Si material have been measured before the MIRHP process and after several MIRHP process steps. For cell processing the selective emitter structure described in chapter 2.4.2 was used. The cell thicknesses are 240 - 250 µm. In Fig. 5.6 is the influence of several MIRHP processes on the measured IQE of one cell together with fit results shown. L2 of the unpassivated and L1 of the fully passivated cell were obtained, as well as w by a fit with eq. (3.23). Using these values for the diffusion lengths of the two regions in eq. (5.42), d is obtained by a fit on the measured IQE of the incompletely passivated cell. For a more detailed view see Fig. 5.7, where the IQE is shown as a function of 1,0 experimental.: fit+: experimental: fit++: For a more detailed view 0,8 0 h 0.5 h 0,8 see figure on the right. 6 h 1 h 2 h 0,6 experimental: fit with eq. 3.23: 0 h L =30 µm; w=1.3 µm 0,6 2 IQE IQE 6 h L =80 µm; w=1.5 µm 0,4 1 fit with eq. 5.42: 0,2 0.5 h d-w=22.8 µm 0,4 lines: measured IQE 1 h d-w=34.9 µm symbols: fit with one+/two++-layer model µ 2 h d-w=53.2 m using eq. 3.23+ / 5.42++ 0,0 500 600 700 800 900 1000 1100 20 30 40 50 60 70 λ [nm] light penetration depth [µm] Fig. 5.6: IQEs of one cell based on SOLAREX Fig. 5.7: A detailed view of Fig. 5.6 with the IQE as material as a function of the wavelength before the a function of the mean light penetration depth. The MIRHP process and after several MIRHP processes. shown data range corresponds to wavelengths The MIRHP process temperature was 275°C during between 800 and 960 nm. the first 2 h and 350°C during the following 4 h to ensure a complete passivation. Also shown are the simulated IQE curves calculated from eq. (5.42) and the obtained fit parameter d - w. L1, L2 and w are obtained by a fit of the IQE of the completely passivated (non-passivated) cell on eq. (3.23). 5.4 A new approach to determine the passivation depth of hydrogen in solar cells 79 the mean penetration depth of the light, which is equal to the inverse of the absorption coefficient. It is clearly seen in both figures that with eq. (5.42) an excellent fit of measured IQEs can be obtained. The influence of the MIRHP temperature on the passivation depth d is discussed next. In addition to the MIRHP processes at T = 275°C, the MIRHP was applied also at 350°C and 425°C using two further SOLAREX cells with the same crystal structure as the first one. Table 5.4 shows the fit parameter d as a function of the MIRHP temperature and time. Using the high temperature of 425°C, a fast diffusion is observed within the first 15 min. After 30 min, the same passivation depth for the cell passivated at 350°C is obtained. The observation that after 30 min H-passivation at 350°C the passivation depths is lower as when using 425°C corresponds to the measurements of the short circuit current density shown in Fig. 4.5 of section 4.3.3.1. In this chapter it was proposed that the optimum passivation temperature for SOLAREX cells is 375°C for optimum bulk and surface passivation. In chapter 5.4.3.3 this d(T,t)-data will be used for the extraction of diffusion parameters. passivation time t [min] 15 30 60 120 passivation 275 14.2 24.1 36.2 54.5 temperature 350 - 57.3 - - T [°C] 425 58.5 78.5 - - Table 5.4: Dependence of the fit parameter d (bold numbers) obtained by the step model of the IQE given in eq. (5.42) on the MIRHP passivation temperature T and time t of SOLAREX cells. No measurement of the IQE was carried out for the vacant boxes. 5.4.3.2 Comparison of the two-layer model with PC-1D The accuracy of the proposed method for determining passivation depths by SR-measurements is further proven by comparing fit results with simulation results using the quasi-one-dimensional finite-element program PC-1D [104, 131]. Fig. 5.8 shows the same measured IQEs as in Fig. 5.6 together with PC-1D simulation results. Compared to a fit with eq. (3.23) on the nonpassivated and completely passivated cell shown in Fig. 5.6, only small differences in the diffusion lengths L2 and L1 were obtained by using PC-1D. Choosing for the PC-1D simulation two base regions with width d and H - d results in a good agreement with the measured IQE obtained after 2 h MIRHP, when the same depth d is taken as before by Fig. 5.8: Same measured IQEs as shown 1,0 in Fig. 5.6 together with simulation results using PC-1D. Compared to a fit with eq. (3.23) on the non-passivated and 0,8 completely passivated cell shown in Fig. 5.6, only small differences in the 0,6 diffusion lengths L2 and L1 were obtained by using PC-1D. Choosing two base IQE 0,4 regions for the PC-1D simulation results experimental: simulation with PC1D: in a good agreement with the measured t HP IQE obtained after 2 h MIRHP, when the 0 h L =27 µm 0,2 2 µ same depth d is taken as before 3 h L1=75 m µ µ µ determined with a fit using eq. (5.42). 2 h d=54.5 m, L1=75 m, L2=27 m 0,0 500 600 700 800 900 1000 1100 λ [nm] 80 5 Diffusion and effusion of hydrogen in silicon using eq. (5.42). For consistency, the diffusion lengths L1 and L2 obtained by a PC-1D simulation using only one region are used. These values are slightly lower than obtained by a fit with eq. (3.23). 5.4.3.3 Extraction of diffusion parameters for SOLAREX base material In Fig. 5.9 and Fig. 5.10 the results for the topt- and Tconst-method are shown, which are described in chapter 5.2.3. For the topt-method, the lower bound of the passivation depth was set equal to the minority carrier diffusion length of the totally passivated cell (L = 80 µm) and for the upper bound the cell thickness was used (H = 250 µm). For the Tconst-method the passivation depth d was taken from Table 5.4. 400 60 topt-method 50 Tconst-method (T=275°C) β = 1 300 D =0.604 eV +/- 0.038 eV ( = 2βE ) m] 2 h M1 A µ 40 CM1=-1.496 +/- 0.678 β DM3 = 0.589 +/- 0.0001 ( = ) β = 0.5 200 1 h 30 CM3 = -10.440 +/- 0.0078 [min] opt 30 min t 20 with β=0.5 100 µ 2 d=80 m => D0=7.1E-5 cm /s 80 passivation depth d [ µ 2 15 min 2 d=250 m => D0=7.0E-4 cm /s => D(275°C) = 2.1E-10 cm /s 60 10 16,5 17,0 17,5 18,0 18,5 19,0 20 30 60 100 e/(kT) [1/eV] t [min] Fig. 5.9: According to eq. (5.14) of the topt-method a Fig. 5.10: According to eq. (5.20) of the linearity between the logarithm of the optimum Tconst-method a linearity between the logarithm of the passivation time and the inverse of the passivation passivation depth and the passivation time is seen for temperature is seen. passivation times between 30 min and 2 h. For 15 min a small deviation is observed. Because of a lack of data and of cells with the same crystal structure the tconst-method eq. (5.17) was only applied using the two measurement results for a MIRHP temperature of 275°C and 350°C with equal passivation times of 30 min. The logarithmic plotting of the passivation depth, again determined by the IQE-step model proposed in chapter 5.4.2, against the inverse temperature leads to a linear dependency with slope DM2 = -0.340 eV and intercept CM2 = 1.168. With the assumption of β = 0.5, this results with eq. (5.18) in a diffusion -3 2 coefficient D0 = 1.410 cm /s and EA = 0.68 eV. Both values are higher than those ones determined by method 1. Using the values of D0 and EA determined with method 2 results in diffusion constants of D = 8.310-10 cm2/s and 4.410-9 cm2/s for T = 275 C and 350 C, respectively. The value for D at T = 275°C and 350°C is between the values determined by method 1. Compared to method 3, the diffusion coefficient is by a factor of 4 larger when method 2 is used. However, uncertainties in D of order 1 are common for diffusion experiments [10]. The determined diffusion constants are within the values for mc-Si given in literature [11, 154], varying for temperatures in the range of 300 to 400°C between 10-10 cm2/s -8 2 and 10 cm /s. Also the values for EA are between the generally measured values for mc-Si between 0.5 and 1 eV [10]. Table 5.5 shows a summary of the results obtained from the three methods. The exponent β of eq. (5.21) determined by method 3 is nearly 0.5. From Fig. 5.10 it is seen that a fit on the depth data with β = 0.5 results only in a small deviation, whereas no acceptable fit is obtained for example by β = 1. Taking these points together with an assumed uncertainty of d of 20%, it can be concluded that the t -law is valid for the diffusion of atomic hydrogen 5.5 Effusion experiments on solar cells 81 method nr. of exponent activation energy diffusion coeff. diffusion constant D [1E-9 cm2/s] 2 points β EA [eV] D0 [cm /s] T = 275°C T = 350°C topt 4 1/2* 0.60 7.1E-5 - 7.0E-4 0.21 - 2.0 0.92 - 9.1 tconst 2 1/2* 0.68 1.4E-3 0.83 4.4 Tconst 3 0.589 - - 0.21 - Table 5.5: Results of the diffusion parameters of SOLAREX material obtained by the methods proposed in chapter 5.2.3. *Theoretically assumed, not obtained from experiment. in multicrystalline SOLAREX silicon material. However because of the different H-concentration profiles in mc-Si and defect free silicon mentioned above, it remains still an open question how equation (5.4) can be theoretically derived for mc-Si where for example trap-assisted H-diffusion occurres. 5.4.3.4 Comparison of the diffusion constants of different mc-Si materials Until now only the diffusion of hydrogen in SOLAREX material was investigated. Additional diffusion experiments were carried out on cells made on BAYSIX, EMC and EFG. The results of the diffusion parameters for these materials are shown in Table 5.6. Comparing the diffusion constants of SOLAREX and BAYSIX, it is seen that high oxygen concentrations of the SOLAREX material reduce the H-diffusion. The fastest H-diffusion is observed on EFG material with low oxygen concentration. However, high dislocation densities can reduce the H-diffusion of material containing low oxygen concentrations as in the case of EMC. material SOLAREX EMC BAYSIX EFG L after HP [µm] 80 150 190 120 H [µm] 250 330 325 200 1 topt [min]* 300 150 120 30 Dmin [cm2/s]*2 9.010-10 6.310-9 1.310-8 2.010-8 Dmax [cm2/s]*3 9.110-9 2.510-8 3.710-8 5.610-8 -2 4 6 6 8 5 4 8 ND [cm ]10 - 10 10 - 10 310 10 - 10 -3 18 16 17 16 [Oi] [cm ] 0.3 - 1.210 <10 1 - 610 <510 Table 5.6: The influence of base mc-Si material on the diffusion constant D for T = 350°C is shown. The 1 min/max optimum passivation times topt* were taken from Table 4.2. D was determined by using eq. (5.15) with d = L*2 or H*3. 5.5 Effusion experiments on solar cells 5.5.1 Introduction Deuterium and hydrogen can exist in many bonded states in mc-Si. By using conventional thermal effusion or SIMS measurements described in chapter 5.3, also the deuterium/hydrogen which does not change the electrical material properties, for example molecular deuterium/hydrogen, is detected. It is difficult or even impossible to get from these measurement techniques information about the part of deuterium/hydrogen which contributes to the deactivation of electronically active defects in semiconductors. On the other hand in the broad field of hydrogen passivation of solar cells, one is mainly interested in the part of 82 5 Diffusion and effusion of hydrogen in silicon hydrogen which contributes to the electrical material properties. To obtain additional information about hydrogen diffusion and passivation, a variety of different electrically sensitive thermal effusion measurements can be found in literature [147, 155, 156]. In my work the diffusion of hydrogen out of H-passivated solar cells is done by annealing the cells in a vacuum system consisting of a quartz tube and a vacuum pump, which holds a constant pressure of 10 µbar. With IQE and I-V measurements carried out on these cells before and after various annealing processes, changes in the cell performance due to movements of the part of hydrogen which contributes to the passivation effect are investigated. To avoid a degradation in especially the fill factor and open circuit voltage of cells during the effusion experiments at temperatures up to 475°C, solar cells with a selective emitter structure were used. 5.5.2 Influence of H-effusion on the IQE The diffusion of hydrogen out of the surface and base of solar cells is studied by H-effusion experiments of fully passivated cells. The change of the internal quantum efficiency for wavelengths above 800 nm can be taken as a measure for the change of the hydrogen content contributing to the passivation effect in the base. Fig. 5.11 shows the IQEs for solar cells based on EFG, EMC and SOLAREX material before and after the diffusion of hydrogen during MIRHP processes (open symbols) at 350°C into the base and after successive annealing step (lines) for 15 min at various temperatures. After the last annealing step, the cells were again MIRHP passivated resulting in the same or even slightly higher IQEs as after the MIRHP processes carried out before the effusion experiment. Additionally, no decrease in the illuminated I-V parameters is observed between the measurements of the MIRHP before annealing and the MIRHP after annealing, which clearly proves that during the annealing processes the cells were not damaged, for example by shunting of the front grid through the space charge region. A clear influence of the material on the temperature where the H-diffusion out of the cell starts can be seen in this figure. The H-effusion starts for EFG below 375°C, for EMC at 450 - 475°C and for SOLAREX above 475°C. These differences in temperatures correspond also with the different diffusion coefficients as shown in Table 5.6, and with the different optimum passivation times of these materials as seen in Table 4.2 of chapter 0. It is seen from Table 4.2 that the H-diffusion is fastest in EFG and slowest in SOLAREX. The minimum energy, where the effusion of hydrogen starts can be estimated from the obtained temperatures for EFG below 56 meV, for EMC to 62 - 65 meV and for SOLAREX above 65 meV. It is remarkable that for SOLAREX material H diffuses into the bulk during a MIRHP process at 275°C (see Fig. 5.6) but the diffusion out of the bulk starts at a much higher temperature. From these two observations it can be concluded that either the energy for diffusion of hydrogen is lower than the energy needed to dissociate a hydrogen-trap complex or that the MIRHP process transfers additional non thermal energy to the hydrogen atoms. However, the hydrogen atoms are in thermal equilibrium because of the large distance of 1 m between the place of H-generation and H-diffusion into the cell. For the used process pressures of 0.1 -1 mbar, the mean free path of hydrogen atoms is only a few millimeters. It is more reasonable that the differences between H-diffusion into the bulk for T 275°C and out of the bulk for T > 475°C are due to a trap-assisted diffusion of H atoms along shallow traps. The largest contribution to the passivation effect comes from the passivation of deep traps, where the hydrogen atoms are strongly bound. Within this physical picture, the higher effusion temperature is needed to dissociate the trapped hydrogen. Because of the used macroscopic spectral response measurement with a lateral resolution of 1 mm it is not possible to obtain from these measurements a further insight into the influence of 5.5 Effusion experiments on solar cells 83 crystal defect structure and impurity content on the H-effusion process. However, by using a local IQE measurement system, which is currently under construction in our lab, a resolution of 50 µm will be possible [77]. The observation, that for the EFG cell the IQE decreases due to the last annealing step at 475°C below the value measured before any MIRHP process, is explained in the following section. 1,0 annealing 0 min HP 0 min HP annealing 0 min HP (15 min, 475°C) 375°C 30 min HP 30 min H 30 min H 400°C 120 min HP 180 min HP 180 min HP 0,8 425°C HP after annealing HP after annealing HP after annealing IQE 450°C annealing 0,6 475°C (15 min, 450°C) annealing 0,4 (15 min, 475°C) 0,2 EFG EMC Solarex 0,0 900 1000 1100 900 1000 1100 900 1000 1100 λ [nm] Fig. 5.11: The internal quantum efficiency for solar cells based on EFG, EMC and SOLAREX Si material measured before and after various H-diffusion (MIRHP at 350°C) and H-effusion (15 min annealing) processes. The MIRHP process time and the annealing temperatures are given in the figure. After the last annealing process, the cells were again MIRHP passivated, resulting in the same or even slightly higher IQEs than after the first passivations. 5.5.3 Influence of H-effusion on the illuminated and dark I-V parameters Further insight into the H-diffusion and passivation can be obtained by illuminated and dark I-V measurements. The change in the short circuit current densities JSC can be a measure for the H-diffusion out of the bulk, whereas the H-diffusion out of the surface is given by the change in the open circuit voltages VOC, which is more sensitive to the surface than JSC. Fig. 5.12 shows JSC and VOC for one hydrogen passivated solar cell based on EMC and one based on SOLAREX material as a function of different annealing processes. In addition, JSC and VOC before and after the applied MIRHP process are shown. A very different behavior of JSC and VOC due to the annealing processes is seen on these two materials. For EMC, a decrease in VOC starts at 375°C and in JSC at 400°C. The small decrease in JSC between 400°C base material: EMC 22 base material: SOLAREX 23,0 595 590 375°C V 22,8 590 V ] 400°C ] 400°C oc oc -2 MIRHP -2 21 MIRHP 375°C [mV] 425°C [mV] 425°C 585 22,6 450°C 585 450°C 475°C MIRHP [mAcm 22,4 475°C MIRHP 580 [mAcm before 580 sc sc 20 J J MIRHP annealing (15 min for each temperature) 22,2 575 before annealing 575 MIRHP (15 min for each temperature) 22,0 19 570 Fig. 5.12: The short circuit current density JSC and the open circuit voltage VOC for solar cells based on EMC (left side) and SOLAREX (right side) Si material measured after various H-effusion (15 min annealing) processes. Before the first and after the last annealing step was carried out, the cells were fully H-passivated by the MIRHP process. 84 5 Diffusion and effusion of hydrogen in silicon and 450°C is most probably due to the H-diffusion out of the surface, whereas for T = 475°C the diffusion from the base starts in agreement with the IQE-curves shown in the previous section. For the SOLAREX cell in JSC a slight increase, which is within the measurement uncertainty, up to an annealing temperature of 450°C and a small decrease during the annealing at 475°C is observed. Above 400°C a decrease in VOC is seen. Both materials behave differently when comparing the decrease in VOC. After the annealing processes at 475°C for EMC, the value of VOC of the unpassivated cell is nearly reached and for SOLAREX VOC decreases only slightly when compared to the large increase due to the first MIRHP process. Similar effusion processes were carried out on one cell based on EFG material. Fig. 5.13 shows the influence of different annealing processes on JSC and VOC. To determine very accurately the temperature where the H-effusion starts, the effusion time was considerably increased to 3 h. It is seen in Fig. 5.13 that at 350°C JSC and VOC start to decrease and after 56 h annealing at 375°C the hydrogen is completely diffused out of the cell, resulting even in smaller values for JSC and VOC as before the MIRHP process. A second MIRHP process applied after the long time annealing resulted in the same high values for JSC, VOC and the fill factor, as measured directly after the first MIRHP process. This proves that the decrease in JSC and VOC during the annealing process is only due to the effusion of hydrogen and not due to a degeneration of the cell performance. The observation, that JSC and VOC are lower after the long time annealing than before the first MIRHP process, is most probably due to the presence of hydrogen in the EFG cell before any MIRHP process is applied. This additional hydrogen is diffused into the cell during the final annealing in Ar/H2 at 380°C at the end of the homogeneous and selective emitter cell process presented in chapter 2.4. The Ar/H2 annealing supports mainly molecular hydrogen, which is known to diffuse very slowly in most silicon materials and has to be dissociated into atomic hydrogen inside the silicon material to contribute to the passivating effect. For EFG, where compared to the other mc-Si materials of investigation the fastest diffusion of hydrogen is observed (see Table 5.6), also this effect might contribute to the H-passivation. Fig. 5.13: The short circuit 22 base material: 600 current density JSC and the open after EFG V MIRHP circuit voltage V of one solar oc OC ] 21 cell based on EFG material -2 580 [mV] measured after an annealing 20 300°C 200°C 250°C 325°C processes. Before the first 150°C [mAcm 350°C 560 sc annealing step was carried out the 12h 375°C, J 19 cells were fully passivate by the annealing 375°C MIRHP process. 540 18 (3h for each temperature) 375°C, 56h 375°C, 17 520 before MIRHP 16 500 In Fig. 5.14 the dark I-V characteristics are shown for the same cell as in Fig. 5.13. Annealing the H-passivated cell at 350°C for 3 h does slightly change the I-V curve. The dark current increases for medium voltages but decreases for small voltages. This behavior can be explained in the frame of the two-diode model presented in section 3.3.1. The first diode current dominates for medium voltages and represents recombination in the base and emitter, whereas the second diode current dominates for small voltages and is determined by recombination in the space charge region. Hydrogen diffusing out of the base region and probably also out of 5.6 Conclusions 85 the emitter region causes an increase of the recombination in the first diode current. The second diode current is reduced because the hydrogen has to diffuse through the space charge region, therefore further reducing the recombination in the space charge region. The second diode current decreases further during the additional 9 h annealing process at 375°C. Also shown in the figure is that after the long time annealing at 375°C over 56 h the total dark current increases above the value as before the MIRHP process. This can be explained again by the presence of hydrogen in the EFG cell before any MIRHP process is applied. During the annealing all hydrogen diffuses out of the cell, resulting in a worse cell performance than before the MIRHP was applied. Note that at the maximum power point the improvement of JD due to the MIRHP process is considerably larger than the contribution of the hydrogen implemented during cell processing. Fig. 5.14: The dark I-V -1 10 characteristics for the same cell as base material: shown in Fig. 5.13. Annealing of -2 EFG 10 the H-passivated cell below 350°C does not change the I-V curve. -3 10 Before the first annealing step was ] carried out, the cells were fully -2 10-4 passivate by the MIRHP process. before MIRHP [Acm -5 after MIRHP D J 10 annealing: 350°C, 3 h -6 annealing: 375°C, 3 h 10 annealing: 375°C, 12 h -7 annealing: 375°C, 56 h 10 0,0 0,2 0,4 0,6 voltage [V] 5.6 Conclusions Theoretical work on the diffusion of atomic hydrogen in silicon and the two most commonly used measurement techniques, thermal effusion and secondary ion mass spectroscopy, for determining hydrogen in silicon were presented in the first sections of this chapter. Because of the limitations discussed in section 5.3.4 it is concluded that an additional non-destructive electrically sensitive method for the determination of the passivation depth of hydrogen in multicrystalline silicon is needed. This new method is based on the two-layer IQE derived in section 5.4.2 with a summary on this theoretical work given in section 5.4.2.6. Using one of the derived approximated total IQEs for a cell with two base regions 1 and 2, which differ in their minority carrier diffusion length L1 and L2, a not completely H-passivated cell can be simulated. The H-passivation depth corresponds to the width of the first base region with high diffusion length L1, whereas the second base region is assumed to be completely non-passivated with low diffusion length L2. A considerable agreement between the derived analytical expressions of the IQE for the two-layer model with simulations using PC-1D is found. The method is experimentally verified in section 5.4.3 by using cells based on SOLAREX material. By applying the evaluation methods presented in section 5.2, it is found that for SOLAREX material the square root law between H-passivation depth and passivation time is satisfied within the uncertainty of the IQE measurement and evaluation method. For SOLAREX cells the following diffusion parameters were obtained: activation energy of 86 5 Diffusion and effusion of hydrogen in silicon 0.6 - 0.7 eV and diffusion coefficients of 810-10 cm2/s (410-9 cm2/s) for T = 275°C (350°C). A comparison of cells based on SOLAREX, EMC, BAYSIX and EFG material shows that the diffusion coefficient of these materials increases in this order. Compared to SOLAREX material an approximately ten times higher H-diffusion constant is observed in EFG material. These results suggest that high oxygen concentrations and high defect densities can reduce the H-diffusion in multicrystalline silicon. In section 5.5 the H-diffusion out of completely H-passivated cells due to annealing steps applied at various temperatures was investigated indirectly by spectral response and I-V measurements. It was found that the effusion of hydrogen is strongly material dependent. In EFG the effusion starts at 350°C, in EMC at 450 - 475°C and in SOLAREX material above 475°C. These observations suggests different diffusion channels and bonding states of hydrogen atoms in the investigated materials. For SOLAREX material it was also found that the atomic hydrogen diffuses into the bulk for T 275°C, but the diffusion out of the bulk starts above 475°C. From these differences it is supposed that atomic hydrogen diffuses mainly along shallow traps. The high effusion temperature is explained by the strong bonding of hydrogen at deep traps, which mainly contributes to the recombination activity. 6 The MIRHP process within an industrial cell production line 6.1 Introduction As mentioned in chapter 1, the cost of the Si wafer contributes to almost 1/2 of the total PV module cost. This number will further increase in a very large scale (500MWp/y) module fabrication as shown by the recent European APAS study [7]. With the use of multicrystalline silicon (mc-Si) instead of monocrystalline Si, the wafer cost factor can be reduced. The higher recombination activity of mc-Si due to higher defect densities and higher impurity concentrations [50,53] makes defect passivation techniques such as hydrogen passivation a key issue for high efficiencies on mc-Si solar cells. This fact is even more valid for the next generation Si material such as ribbon or crystalline thin film silicon. Currently, two very promising candidates for mc-Si hydrogen bulk passivation with industrial importance are under development: • the direct incorporation of atomic hydrogen during a microwave induced remote hydrogen plasma (MIRHP) process in combination with the deposition of a standard AR coating as capping layer against the out-diffusion of hydrogen during contact firing or • the covering of the cell front side by a hydrogen rich silicon nitride antireflection coating (SiN ARC) deposited by PECVD (plasma enhanced chemical vapor deposition) followed by driving the hydrogen during the contact firing step into the cell. To demonstrate the potential of the MIRHP passivation in combination with a standard TiO2 ARC, this passivation technique is applied within the industrial cell production lines at Eurosolare and Solarex. After a description in section 6.2 of the standard cell processes at these two companies the results obtained by the MIRHP process are presented in section 6.3. The alternative using a PECVD SiN ARC is discussed in section 6.4. Finally in section 6.5 it is found that for low quality mc-Si material a combination of both processes, MIRHP and PECVD SiN, result in a considerably improved cell performance. 6.2 Industrial solar cell production at Eurosolare and Solarex The processing techniques applied in the PV industry differ decisively from the laboratory techniques used for the processing of cells presented in the previous chapters. Instead of expensive photolithographic processes and metal evaporation, screen-printing is the predominant metallization technique for terrestrial crystalline silicon PV modules. For the following investigations standard industrial cells with a structure shown in Fig. 6.1 are used. This cell structure consists of a phosphorus doped front junction, a front side TiO2 ARC, optionally a highly p+ doped backside region as well as a screen-printed front contact. As we will see in the following section, different concepts for the back contact are applied in the industry. 88 6 The MIRHP process within an industrial cell production line Some companies do not use any antireflection coating especially when monocrystalline silicon with a surface orientation of <100> is used as base material, because chemical surface texturing of <100> oriented Si surfaces reduce the reflectance from 35% to 10% [157]. Due to the anisotropic nature of multicrystalline silicon chemical surface texturing is not effective on mc-Si and an ARC is needed. Currently TiO2 is the most commonly used antireflection coating. SiN PECVD as an alternative to the deposition of TiO2 is discussed in section 6.4. Screen-printed Ag finger Fig. 6.1: Schematic representation of the screen-printed solar cell structure as used in this work. TiO 2 n+ ARC p p+ Al back contact In Table 6.1 the process diagrams of the standard mc-Si cell production lines at Eurosolare (left row) and Solarex (right row) are shown. The cell processing at Eurosolare consists of the emitter diffusion, the deposition of a TiO2 ARC done by APCVD (atmospheric pressure chemical vapor deposition) followed by the printing of the front and back contacts and the concurrent firing (cofiring) of both contacts. The highly doped back side region is formed during the firing step when an aluminum containing paste is used for back contact formation. At 577°C, which is considerably lower than typical firing temperatures between 700 and 850°C, the Al forms an eutectic alloy with Si. During the cooling down, the silicon recrystallizes and is doped with Al. The advantages of the Al back side doping are threefold [3]: 1) during the firing process the molten Al-Si acts as a sink for impurities, resulting in an ideal gettering effect, 2) the highly doped Al-Si region creates a BSF (back surface field) which reflects minority carriers and reduces the back side recombination velocity and 3) the n-type emitter deposited also on the back side is compensated. standard process I standard process II (Eurosolare) (Solarex) NaOH defect etching NaOH defect etching emitter-diffusion front side: emitter-diffusion front side: TiO2 ARC front side: screen-printing of Ag firing of the front contact front/back side: screen-printing of Ag/Al front side: TiO2 ARC contact cofiring back side: Al-spray Table 6.1: Processing sequences of the industrial solar cell production lines at Eurosolare and Solarex. The cell size is 1010 cm2 for the Eurosolare process and 11.411.4 cm2 for the Solarex process. 6.3 MIRHP of screen-printed cells. 89 In contrast to the production line at Eurosolare, at Solarex the emitter is only diffused on the front side by a special spray technique and the TiO2 is deposited after the firing of the contacts [158]. Finally the back contact is deposited by a low temperature aluminum backspray technique. Due to different handling equipments, the cells used within the Eurosolare study had a size of 1010 cm2 and within the Solarex study a size of 11.411.4 cm2. 6.3 MIRHP of screen-printed cells. In chapter 3 and 4 it was shown that the MIRHP technique increases the electrical parameters such as the bulk minority carrier diffusion length Lb of several mc-Si base materials. Additionally also the homogeneity of Lb increases due to a MIRHP process as was seen in section 3.2.1 from SPV measurements. Therefore, MIRHP passivation can be a key technology to increase the electrical parameters of low quality regions for example at the borders of an ingot in order to reduce the width of the performance distribution. A large number of studies can be found in literature on MIRHP passivation of solar cells made with evaporated contacts [55, 121, 123, 130] but despite of its industrial importance only a few papers have been published so far on the application of the MIRHP process within a screen-printed solar cell process [159, 160]. 6.3.1 MIRHP after cell processing In order to find the optimum MIRHP passivation time, screen-printed solar cells of size 55 cm2 without antireflection coating based on BAYSIX and EMC silicon material were passivated by a MIRHP process. Due to the MIRHP process applied on these cells, the largest increases in the open circuit voltage VOC and the short circuit current density JSC are within the first 30 min, as can be seen in Fig. 6.2. The much lower increases during the additional 90 min (the slight decrease of JSC of one of the EMC cells lies within the accuracy of the I-V measurement) indicate for these materials an optimum MIRHP passivation time of approximately 1 h. Note that the optimum passivation times given in chapter 4 for these materials are higher because there the optimum was defined where a saturation in the illuminated I-V parameters occurs. For industrial application there is no need to increase the MIRHP time considerably above 1 h to also obtain the last 1/10 of the efficiency increase. 590 BAYSIX 22,0 BAYSIX ] 580 -2 21,5 [mV] OC [mAcm V 570 SC J 21,0 EMC EMC 560 20,5 0 306090120 0306090120 MIRHP-passivation time [min] MIRHP-passivation time [min] Fig. 6.2: Influence of the MIRHP passivation time on VOC (left side) and JSC (right side) of screen-printed solar cells based on BAYSIX and EMC Si material. For both materials considerable increases in VOC and JSC were obtained within the first 30 min. The MIRHP process was carried out after the cell metallization. 90 6 The MIRHP process within an industrial cell production line There is one problem involved with the MIRHP process applied after cell processing. On some cells there is a degeneration of the fill factor during the MIRHP process observed. It is yet not clear if this effect can be avoided by the use of other MIRHP process parameters, especially another microwave power and gas flow. The influence of the MIRHP process on the fill factor seems also to depend on the used contact firing process because, an increase of the fill factor was observed in cooperation with ASE8. Therefore, in the case where the MIRHP has to be applied after contact printing, it has to be checked separately for each company if the MIRHP process results in an improvement of the cell performance. 6.3.2 MIRHP in industrial cell processes To show the potential of the MIRHP process, this technique was applied within the production lines at Eurosolare and Solarex, which are described in Table 6.2. It will be shown in section 6.3.2.2 that during the low temperature MIRHP process atomic hydrogen does not diffuse through the APCVD TiO2, therefore the MIRHP process has to be applied before the deposition of the TiO2 ARC. For the implementation of the MIRHP process into the pilot line at Eurosolare it has to be considered that applying the MIRHP before the contact firing step, a diffusion barrier is needed to prevent the diffusion of hydrogen out of the cell. It will be shown in the following section that the TiO2 ARC used in the Eurosolare process is a sufficient barrier against the diffusion of hydrogen out of the cell during the high temperature contact firing step. At the Solarex process no H-diffusion barrier exists during the front contact firing and therefore the MIRHP process has to be applied after the front contact firing. For the MIRHP process the following parameters were used: a passivation temperature of 350°C, a passivation time of 2 h, a gas pressure of 0.1 mbar, a gas flow of 4 ml/min and a microwave power of 150 W. standard process I standard process II (Eurosolare) (Solarex) NaOH defect etching NaOH defect etching emitter-diffusion emitter-diffusion optional: MIRHP front side: TiO2 ARC front side: screen-printing of Ag annealing of TiO2 ARC firing of the front contact optional: MIRHP front/back side: screen-printing of Ag/Al front side: TiO2 ARC contact cofiring back side: Al-spray Table 6.2: Processing sequences of the industrial solar cell production lines at Eurosolare and Solarex inclusive the additional MIRHP processing step applied in this study. For the Eurosolare process it is found that an annealing step of the TiO2 prior to the contact printing and firing is necessary for an improvement due to the MIRHP process, which will be explained in the next section. The cell size is 1010 cm2 for the Eurosolare process and 11.411.4 cm2 for the Solarex process. 8 Recent investigations carried out on cells processed at ASE indicate that VOC increases by 8 - 10 mV and FF by up to 1% due to a 30 min MIRHP process. 6.3 MIRHP of screen-printed cells. 91 6.3.2.1 MIRHP within the production line at Eurosolare As shown in Table 6.2 the MIRHP process was applied before the deposition of the TiO2. It is found that an annealing step of the TiO2 prior to the contact printing and firing is necessary for an improvement due to the MIRHP process. During this annealing step the TiO2 layer becomes thinner and more dense which can be obviously seen in the change of the color from light-blue to dark blue. The more dense TiO2 layer acts as a barrier against the diffusion of hydrogen out of the cell during contact firing. Table 6.3 shows a clear improvement of the cell performance due to the MIRHP process for different mc-Si base materials. For each material only wafers with the same crystal structure are taken. For cells based on EUROSIL material, the relative cell efficiency increases between 5 and 9%, which is mainly due to the increase of the short -2 circuit current density between 0.4 and 1.4 mAcm . For EMC VOC increases by 7 mV, JSC by 1.4 mAcm-2 and the cell efficiency by 8% relative. In consistency with theory, the highest voltages are obtained on cells based on the EUROSIL material with the lowest base resistivity. The relatively low fill factors and low short circuit currents are probably due to difficulties during the phosphorus diffusion at Eurosolare, resulting in a non optimal screen-printing process. However the cell process was very homogeneous as can be seen by the small standard deviations, also given in the Table 6.3. From these results it can be concluded that the MIRHP process applied within an industrial screen-printed mc-Si cell process results in a considerably improved cell performance. Supplier Eurosolare (material taken from the border of the ingot) Sumitomo Sitix Base Si material EUROSIL P48 EUROSIL C50 EMC Base resistivity [Ωcm] 1-1.5 1-1.5 0.5 1 Eff. bulk-lifetime [µs] ca. 2.5 >2.5 2.5 1.5-2.5 MIRHPnoyesnoyesnoyesnoyes VOC [mV] 5771 5811 5852 5912 6011 6062 5711 5782 -2 JSC [mAcm ] 24.70.2 25.10.3 26.20.5 27.60.2 26.20.3 27.10.4 26.50.1 27.90.1 FF [%] 71.31.7 72.51.7 66.23.1 67.53.1 70.81.6 71.52.2 68.73.3 69.52.4 η [%] 10.10.2 10.60.2 10.10.6 11.00.6 11.20.3 11.70.4 10.40.5 11.20.5 ∆ηrel [%] +5 +9 +5 +8 Table 6.3: Using different mc-Si base materials with different effective bulk lifetimes (measured before cell processing) a clear improvement of the mean illuminated I-V parameters after a MIRHP process is obtained. Averaging is carried out over 10 cells for EUROSIL P48 material and over 4 cells for EUROSIL C50 and EMC. The EUROSIL materials are taken from the border of the ingot and the EMC material is the same as used for the photolitho cells in chapter 0. The effective bulk lifetimes were measured at Eurosolare. Internal quantum efficiencies (IQE) calculated from spectral response and reflection measurements demonstrate a clear improvement in the long wavelength region of the hydrogen passivated cell as compared to a non hydrogen passivated solar cell based on EMC material as -2 seen in Fig. 6.3. The increase in the measured JSC of 1.3 mAcm is in good agreement with the increase in the diffusion length from 111 µm to 183 µm determined by a fit of eq. (3.23) to the IQE. To reduce the influence of the varying crystal structure, these cells were fabricated using wafers which were next to each other in the ingot and the SR-measurement was done for both cells on the same crystal structure. From Fig. 6.3 it can also be seen that a slightly different measurement position does not change the SR-measurement result of the hydrogen passivated cell. 92 6 The MIRHP process within an industrial cell production line Fig. 6.3: Influence of the MIRHP 1,0 passivation on the IQE of solar cells based on EMC material. Due 0,8 to the MIRHP process, the minority carrier bulk diffusion µ length Lb increases from 111 m 0,6 to 183 µm. Measuring the H-passivated cell B also at a IQE cell HP J V FF η slightly different position does not 0,4 sc oc eff change the SR-measurement [mAcm-2] [mV] [%] [%] result. A no 26.9 578 70.6 11.0 0,2 B yes 28.2 585 70.7 11.7 B yes other measurement position 0,0 500 600 700 800 900 1000 1100 λ [nm] Table 6.4 shows the results of the illuminated I-V parameters of cells based on compensated EUROSIL C50 material. By comparing hydrogen passivated with non-hydrogen passivated cells only a small increase in the I-V parameters can be seen. Within this material high impurity concentrations rather than defects determine the bulk-lifetime, which was measured before cell processing to be only 0.5 µs. The high open circuit voltage can be explained by the low base resistivity of this material. Cells based on compensated C50 Si material Base resistivity [Ωcm] 0.5 Effective bulk-lifetime [µs] 0.5 MIRHP no yes VOC [mV] 590.82.2 592.40.9 -2 JSC [mAcm ] 24.70.4 24.90.2 FF [%] 71.52.4 72.41.5 η [%] 10.40.5 10.70.2 Table 6.4: Using compensated EUROSIL C50 material only a small improvement of the illuminated I-V parameters after a MIRHP process was obtained. Averaging was carried out over 10 cells. 6.3.2.2 MIRHP within the production line at Solarex In contrast to the production line at Eurosolare, at Solarex the TiO2 is deposited after the firing of the contacts [158]. As seen in Table 6.2, the MIRHP process was carried out after the front contact firing and before the deposition of the TiO2 ARC layer. The results of the average values of the illuminated I-V parameters for the MIRHP passivated cells compared to the non MIRHP passivated reference cells are shown in Table 6.5. Compared to the considerable increases of VOC, JSC and η due to the MIRHP applied within the industrial process at Eurosolare, the increases obtained within the Solarex production line are considerably smaller. Additionally on small laboratory cells also larger increases in the illuminated I-V parameters are observed on cells based on SOLAREX material as shown in section 4.3.2. One reason for the moderate improvement could be the for SOLAREX material relatively short MIRHP 6.3 MIRHP of screen-printed cells. 93 passivation time of 2 h at 350°C. Experiments carried out later and presented in chapter 4.3.3 show that the optimum passivation time for this material is 3 h at 375°C. Another reason for the lower increase in cell performance could be an influence of the MIRHP process on the front contact, which has to be investigated in further studies in more detail. Cells based on SOLAREX Si material MIRHP no yes VOC [mV] 5751 5781 -2 JSC [mAcm ] 27.10.1 27.30.2 FF [%] 73.20.6 74.10.6 η [%] 11.40.1 11.70.2 Table 6.5: Using SOLAREX material only a small improvement of the illuminated I-V parameters averaged over 10 cells after a MIRHP process was obtained. The possibility to apply the MIRHP process also after the deposition of the TiO2 is investigated in the following by carrying out the hydrogenation on some of the reference cells of the previous study. The influence of the MIRHP process on the dark current characteristics of two SOLAREX cells one with (cell B) and one without (cell A) TiO2 ARC are seen in Fig. 6.4. The dark current density and open circuit voltage VOC of cell A improve due to the MIRHP process, whereas only a small change is seen on the TiO2 coated cell B, which proves that the diffusion of hydrogen is impeded by the TiO2 layer. Fig. 6.4: Influence of the MIRHP 0,1 Cells made with process on the dark current characteristics of two mc-Si cells, SOLAREX material 0,01 one with (cell B) and one without (cell A) TiO2 ARC. The dark current density and the open 1E-3 ] circuit voltage of cell A improve -2 due to the MIRHP process, 1E-4 whereas nearly no change is seen [Acm D Cell TiO HP V [mV] on the TiO coated cell B, which J 2 OC 2 1E-5 shows that the diffusion of A no no 569 hydrogen is impeded by the TiO2 no yes 578 1E-6 layer. A MIRHP processing B yes no 567 temperature of 350°C and time of yes yes 568 90 min was taken. -0,2 0,0 0,2 0,4 0,6 0,8 voltage [V] 6.3.3 Industrial importance of the MIRHP processes In sections 6.3.2.1 it was shown that the MIRHP process clearly improves the performance of mc-Si solar cells within the production line at Eurosolare. In the following the attractive features of the MIRHP process are listed: • compatibility with standard industrial process sequences using a conventional TiO2 ARC, • almost complete bulk passivation for most mc-Si materials within passivation times of 30 -60 min, • MIRHP passivation conditions can be directly adjusted to the mc-Si material in use, 94 6 The MIRHP process within an industrial cell production line • simple 1 Torr vacuum technology with short loading and heating times, • possible full automatic wafer handling, • simple construction of the MIRHP system, • MIRHP inline systems possible. The first two points can be concluded from the work presented in the previous sections. The third point will become especially important for the hydrogen passivation of ribbon silicon. As was seen in chapter 4.3, the optimum MIRHP process conditions are strongly dependent on the used ribbon material. Because of the last four points, the investment as well as the running costs for a MIRHP system are low. The low investment and the running costs of the MIRHP process in combination with a TiO2 ARC are currently an important advantage compared to the PECVD SiN process described in the following section. Additionally with the MIRHP process, toxic or explosive gases such as silane used for the SiN deposition are avoided, because the MIRHP gas mixture with 10% H2 and 90% He is incombustible. 6.4 PECVD SiN As an alternative to the MIRHP process in combination with a firing through TiO2 ARC cell process presented in the previous sections, H-bulk passivation can also be obtained by using a silicon nitride ARC deposited by PECVD (plasma enhanced chemical vapor deposition). In the following the symbol SiN is used which should not be mixed with the stoichiometric composition of an ideal Si3N4 film. A variety of compositions SixNyHz is possible because of large amounts of atomic hydrogen of up to 25 at.% [135] in the silicon nitride films and the influence of the PECVD process parameters (mainly the ratio of the silane-to-ammonia gas flow) on the amount of silicon in the films [43, 161, 162]. The large amount of atomic hydrogen can be driven into the silicon bulk during a post anneal [163, 164] or during the contact firing within a screen-printed solar cell process [137, 165, 166] resulting in an almost ideal bulk passivation of conventionally cast mc-Si material such as EUROSIL, BAYSIX and EMC. Two alternative PECVD processes are available, the remote [167] and the direct [165] PECVD, where only the last one has proven until now the capability within an industrial screen printed mc-Si cell process. The major advantage of the PECVD process is the combination of the deposition of an AR coating and a bulk passivating agent. Including V-texturization into the SiN process sequence resulted in a 100 cm2 selective emitter multicrystalline silicon solar cell with 16.5% efficiency [168]. NaOH defect etching emitter-diffusion front side: SiN ARC with PECVD front/back side: srceen-printig of Ag/Al contact cofiring Table 6.6: Sequences of the firing through PECVD SiN ARC process first applied at IMEC [165]. The major obstacle in the dissemination of the PECVD SiN process in PV industry is the limited throughput of the commercially available batch-type PECVD reactors combined with the not yet satisfyingly solved automation of the loading and unloading of the systems resulting in not negligible investment and running costs. Currently different manufacturers of PECVD systems are busy to overcome those limitations. Another problem is that in addition to the 6.5 Combination of PECVD SiN and MIRHP 95 silicon wafers also the PECVD chamber is covered by SiN. The removal of SiN with etching gases such as CFCs is cost intensive, environmentally hazardous and results in relatively low up-times of 70%. In the following section it will be shown that for mc-Si material with large defect densities and reduced H-diffusion the cell bulk is not completely passivated during the firing of a PECVD SiN. 6.5 Combination of PECVD SiN and MIRHP In order to investigate the influence of the MIRHP passivation in combination with a PECVD SiN ARC, solar cells were processed according to the processing sequence shown in Table 6.6. For some of the cells an additional MIRHP process was applied before the deposition of the SiN ARC. The optimization of the PECVD SiN deposition considering the refractive index, the bulk as well as the surface passivation can be found in [43, 169]. Fig. 6.5 shows results of the internal quantum efficiency of SiN coated cells based on low and high quality mc-Si with and without a MIRHP process. Despite the good surface and bulk passivation properties of our PECVD SiN AR coating [137], a considerable increase in the IQE due to the MIRHP alone is seen on cells based on low quality material. Comparing the SiN ARC with and without MIRHP passivation, VOC increases by 12 mV and JSC by -2 1.9 mAcm . Compared to a reference cell which was not H-passivated but coated with a TiO2 ARC, the cell with a SiN ARC (no MIRHP) has a 18 mV larger VOC and a JSC increased by 1.4 mAcm-2. This shows again the importance of the MIRHP process for low quality material when an AR coating not containing hydrogen such as TiO2 is used. The dark current measurements shown in Fig. 6.6 and the first saturation current density extracted from a fit to the two diode model given in eq. (3.4) further confirm the superiority of the combined H-passivation from an PECVD SiN layer and from the MIRHP compared to a process without MIRHP passivation. For good quality EMC material an additional MIRHP process leads to nearly identical IQEs and only a small improvement of the illuminated I-V parameters as can be seen in Fig. 6.5. voltage [V] 0,35 0,40 0,45 0,50 0,55 1,0 MIRHP ARC VOC JSC ] no SiN 588 28,7 -2 -2 0,8 EMC- yes SiN 590 28,9 10 material 0,6 no SiN 485 13,1 low quality yes SiN 497 15,0 10-3 Si-material no TiO2 467 11,7 IQE 0,4 MIRHP ARC J [pAcm-2] 10-4 01 0,2 no TiO2 106 no SiN 73 dark current density [Acm density current dark yes SiN 62 0,0 400 600 800 1000 -0,2 0,0 0,2 0,4 0,6 λ [nm] voltage [V] Fig. 6.5: Influence of the MIRHP passivation on the Fig. 6.6: Measured dark current characteristics of the internal quantum efficiency (IQE) for cells of low low quality solar cells from Fig. 6.5. The saturation quality Si material and high quality EMC material. current of the first diode J01 is extracted from the The MIRHP process was carried out before the two-diode model according to eq. (3.4) with n1 = 1. deposition of a PECVD SIN ARC. The following PECVD conditions were used: a temperature of 300°C, a plasma power of 80 mWcm-2, a gas pressure of 300 mTorr and gas flow ratios of 1.6 for N2/NH3 and 8 for (N2+NH3)/SiH4. 96 6 The MIRHP process within an industrial cell production line 6.6 Conclusions The successful application of the MIRHP process in a screen-printed cell process is clearly proven in this chapter. Due to the MIRHP process applied within the firing through TiO2 process at Eurosolare the efficiency of cells (area 100cm2) increases of up to 9% relative for EUROSIL material taken from the border of the ingot and of up to 8% relative for conventional EMC material. For a further demonstration of the industrial importance of the MIRHP process, this process was also carried out within the cell production line at Solarex. In contrast to Eurosolare, the TiO2 AR coating at Solarex is deposited after the front contact printing and firing, which makes it necessary to apply the MIRHP process after the front contact firing and before the deposition of the TiO2 ARC. The smaller increase in efficiency of 3% relative of this process sequence indicates that the application of the MIRHP process can influence the printed front contact. The results obtained together with Eurosolare suggest that the MIRHP process together with a conventional TiO2 ARC is an alternative to the SiN PECVD process for bulk passivation. As suggested in section 4.3.3 by increasing the passivation temperature from 350°C to 400°C an almost complete bulk passivation is obtained after only 30 min MIRHP processing. In the case if the contact firing process is applied after the MIRHP process, this time can be further reduced. The complete bulk passivation is then obtained during the contact firing. From this we expect that with the MIRHP technique the industrial bench mark of 1000 wafers per hour can be reached at reasonable costs. Further work will be done to develop an industrial prototype MIRHP system. 7 Summary This thesis deals with the volume (bulk) recombination of multicrystalline silicon (mc-Si) solar cells. Bulk recombination of generated minority carriers is an important limiting factor for the efficiency of various mc-Si solar cells. The microwave induced remote hydrogen plasma (MIRHP) technique has been applied in this work to reduce the bulk recombination in various mc-Si materials. This work further concentrated on the characterization of bulk recombination with the means of spectral response measurements. Intensive theoretical work was focused on a two-layer model of the total internal quantum efficiency, with which hydrogen diffusion processes can be studied on the solar cell level. Besides the study of the hydrogen passivation, diffusion and effusion on small laboratory cells, the MIRHP process was also applied within industrial screen-printed cell processes. An overview on the production and some structural as well as electrical properties of the block and ribbon cast multicrystalline silicon materials used in this work was given in chapter 2. The cell processing sequences of small laboratory cells was described including the necessary modifications for the ribbon silicon materials under study. The bulk recombination of multicrystalline silicon wafers was characterized by means of the surface photovoltage technique. Solar cells were characterized by dark/illuminated I-V, light- beam-induced current and spectral response measurements. It was shown in chapter 3 that the well known experimentally observed connection between the inverse of the internal quantum efficiency (IQE) and the inverse of the absorption coefficient has not been theoretically consistently explained in literature. Because of the importance of an appropriate interpretation of the spectral response measurement for the characterization of bulk recombination, this gap in theory has been filled resulting in an approximated equation for the total IQE including the contributions of the emitter, space charge region and base of a cell. Besides the theoretical understanding, this approach also provides rules for selecting the fit range of the wavelength in which the bulk minority carrier diffusion length is obtained. The effectiveness of the MIRHP technique as a function of the passivation parameters for various mc-Si materials has been presented in chapter 4. It has been shown that the MIRHP passivation is very effective in improving various mc-Si cells resulting in relative increases of the cell efficiency of up to 15% when cast silicon and of up to 31% when ribbon silicon is used as base material. For oxygen rich RGS (ribbon growth on substrate) material a reduced H-diffusion is found, resulting in a high optimum passivation temperature of 450°C. For the first time efficiencies above 11% for RGS crystalline silicon solar cells (4 cm2) have been obtained with an increase in absolute cell efficiency of 1.9% due to the MIRHP process alone. The MIRHP process was also found to be very effective for improving high efficiency mc-Si PERL (passivated emitter, rear locally-diffused) cells with average increases in the short circuit current density of 1.2 mAcm-2 and in the open circuit voltage of 7 mV. After hydrogen 98 7 Summary passivation an efficiency of 14.7% was obtained on one 11 cm2 PERL cell without antireflection coating but slight surface texturing with average front surface reflectance of 27%. Besides the passivation effect of atomic hydrogen, the diffusion of hydrogen in multicrystalline silicon is studied. To overcome the limitations of thermal effusion and secondary ion mass spectroscopy measurement techniques, a new non-destructive electrically sensitive method for the determination of the passivation depth of hydrogen in mc-Si is described in chapter 5. This method is based on a fit of the internal quantum efficiency of hydrogen passivated cells with a two-layer model of the IQE. Experimentally this method is verified for cells based on oxygen rich mc-Si SOLAREX material. From the obtained H-depth data an activation energy for the H-diffusion of 0.6 - 0.7 eV and a diffusion coefficient of 810-10 cm2/s at 275°C was obtained for this material. Further it was found that within the measurement uncertainty the t -law is valid for the diffusion of atomic hydrogen in SOLAREX material. Diffusion coefficients obtained for other mc-Si materials also suggest that high oxygen concentrations and high defect densities can reduce the H-diffusion. From effusion experiments it was found that the temperature, where diffusion of atomic hydrogen out of the cell bulk starts is strongly dependent on the used mc-Si base material. Effusion temperatures between 350 and 475°C were determined. These observations suggest different diffusion channels and bonding states of hydrogen atoms in the investigated materials. From the large temperature differences for MIRHP passivation and H-effusion of over 200°C for SOLAREX material it is supposed that atomic hydrogen diffuses mainly along shallow traps. Finally in chapter 6 the successful application of the MIRHP passivation within a screen-printed cell process has clearly been proven. 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Bitnar, 'Oberflächenpassivierung von kristallinen Silizium Solarzellen', thesis, University of Konstanz, Konstanz, 1998, p. 147. 9 Appendixes 9.1 Single-layer IQE The IQE in dependence of the light absorption coefficient α of a homogeneously doped base region can be found in [106] and was derived first by M. Wolf and M. B. Prince [99] using a slightly different mathematical notation. By changing indices, the following procedure can also be applied to a homogeneously doped emitter region. In the following, the internal quantum efficiency of the base of a solar cell with a homogeneous bulk minority carrier diffusion length is calculated. For the calculation, the cell thickness is assumed to be large compared to the light penetration depth (H >> α-1). This results in an exponential generation profile: gx()=⋅⋅−α F()1 R ⋅ e−⋅α x with F the flux of photons onto the front cell surface and R the front surface reflectance. The differential equation of the excess minority carrier density ∆n in the base is given by [106]: 2∆∆ dnx()−=−nx () gx() 22 (9.1) dx Lxb () Db with the minority carrier diffusion length Lb and the minority carrier diffusion coefficient Db. The following calculations can be simplified by defining a reduced excess minority carrier density: D ∆∆nx′=()b nx () with dimension [cm2]. α ⋅⋅−FR()1 With this substitution, the differential equation changes to: 2∆∆′ ′ dnx()− nx ()=− −⋅α x 22 e (9.2) dx Lxb () The general solution of eq. (9.2) is: 2 x x L −⋅α ∆nA′= ⋅cosh +⋅B sinh + b ⋅ e x (9.3) 11 L L −⋅()α 2 bb1 Lb with the coefficients A1 and B1 labeled with index 1 for consistency with the double-layer model where labeling is done with index 1 for the first layer and 2 for the second layer. 106 9 Appendixes The boundary conditions are the same as for ∆n: at the edge scr - base ∆nw′()= 0, (9.4) ∆∆′ ′ ⋅ dn() x =− ⋅ nH ( ) = SLbb at the back surface sb with sb (9.5) dx xH= Lb Db with the back surface recombination velocity Sb. With the boundary conditions, the coefficients A1 and B1 can be calculated. The IQE of the base is obtained from the photo-current from the base jb, determined at the edge to the space charge region x = w: dnx∆ () qD⋅⋅ −=jx() w b dx ∆ ′ (9.6) αα= b = xw= =⋅dn() x IQEb () ⋅⋅−() ⋅⋅−() . qF11 R qF R dx xw= Inserting the boundary condition ∆nw′( )= 0 into equation (9.3) results in: −⋅α e w L2 A =⋅1 −⋅Bwtanh() 1 ()α 2 − 11 (9.7) cosh w1 1 1 with w1 = w/L1 and α1 = αLb. Inserting eq. (9.7) in (9.3), differentiating ∆n′ and using eq. (9.6), the IQE is obtained in dependence of the coefficient B1: αα()tanh()w + B IQE ()α = 111⋅+e−⋅α w 1 . (9.8) b α 2 − ()⋅ 1 1 cosh wL11 The coefficient B1 includes all information about the influence of the cell thickness and the back side recombination velocity on the IQE. B1 has to be calculated by inserting eq. (9.3) into the second boundary condition and canceling the coefficient A1 with the use of eq. (9.7). Finally eq. (3.10) of section 3.4.2.1 is obtained. Equation (9.8) will be helpful for the derivation of the two-layer IQE in chapter 5.4. With this equation, the four appearing coefficients A1/2 and B1/2 are reduced to only one coefficient B1, which again contains all information about the influence of the recombination parameters and cell thickness on the IQE. 9.2 Single-layer IQE at α = 1/Lb For physical consistency, the internal quantum efficiency of a solar cell has to be continuous within the whole wavelength region and therefore for all absorption lengths. Because eq. (3.10) is not defined at α = 1/Lb, it has to be proven that the left and right limit are equal, making it possible to expand this equation continuously at α = 1/Lb. For the single-layer IQE this has already been mentioned without going into detail by [150]. However, we need this procedure also to prove that the two-layer IQE presented in chapter 5.4 can also be expanded continuously at even two undefined places. Therefore we show in the following the prove in 9 Appendixes 107 detail for the single-layer IQE and apply the same procedure, but in a condensed mathematical formulation, for the two-layer IQE in appendix 9.5. For a compact calculation, the reduced ′ = base width wwLbbb and w = we + wscr is used. In the following, the absorption coefficient α is the sum of the inverse of Lb and a small positive or negative value ∆α depending if the right or left limit is calculated. Using eq. (3.10), the IQE can be written as: α =+1 ∆α ≈ IQEb () Lb −′w ′+ ′+()() +∆α − − ∆α b swbbcosh sinh w b11 Lswe bbb w +−∆α −+ ∆αw 1 Lb 1 + ∆αL L sw⋅ sinh′ + cosh w′ b e b bb b ()++∆α ()+⋅−∆α 11Lb 11Lb −′w −′w −′w ′−bb + ′− +∆α −′−()b swebb()cosh sinh weLb b ()11wsebb w 1 +−∆α −+ ∆αw Lb 1 + ∆αL sw⋅ sinh′ + cosh w′ b Lb bb b + ∆α e ∆α ⋅ 2 Lb Lb −′w −′−()b ()11wsebb w +⋅−−⋅∆α ∆α −+ ∆αw 11LLbb 1 + ∆αL sw⋅ sinh′ + cosh w′ b Lb bb b + ∆α e ∆α ⋅ 2 Lb Lb w + ∆α −+ ∆αw − ′ ()− 1 Lb L 11wsbb −′w b 1− b + ∆α e ⋅′+′e 2 Lb swbbsinh cosh w b − w − ′ ⋅−() ∆α→±0 1 L 11wsbb −′w →⋅bb ⋅−1 ⋅ . e ⋅′+′e 2 swbbsinh cosh w b With this calculation it is proven that the left and right limits of the single-layer IQE at α = 1/Lb are equal and the value at α = 1/Lb can be defined as this limit. 9.3 Single-layer IQE and weak surface texturization In the following, the IQE of a cell with weak surface texturization, as described in section 3.4.4.8 and also seen in Fig. 3.14, is deduced. It was stated in section 3.4.4.8 that the generation profile for this case is given by [111]: α −⋅x α ()ϕ ⋅ IQE of the base: The differential equation of the minority carrier density in the base for the flat cell is given in appendix 9.1. By the following substitution, the differential equation of the minority carrier density in the base for the textured cell becomes the same form as for the flat cell: αα==+−cos() ϑand x x w() cos() ϑ cos() ϕ cos() ϕ (9.10) These substitutions result in: 2∆∆ α dnx()−=−nx ()gx (, ) 22 dx Lb Db (9.11) with gx(,αα )=⋅⋅−⋅ F()1. R e−⋅α x From the spatial substitution given in eq. (9.10) follows that w and H has to transform according to: w==+− wcos()ϑϕ cos() and H H w() cos() ϑ cos() ϕ cos() ϕ. (9.12) With these transformations, the boundary conditions for the textured cell have the same form as for the flat cell: ∆nw()= 0 (9.13) and ∆∆ ⋅ dnx()=− ⋅nH ( ) =SLbb sb with sb . (9.14) dx xH= Lb Db Because of eq. (9.12) the width of the bulk wb =H - w does not change. Therefore the contribution of the base to the IQE of a weakly textured cell can be expressed by the base IQE of a flat cell (exact eq. (3.10)): textured αα==flat IQEb (,) w IQEb (, Lbbb ,, w w ,) s wb wb −⋅α s ⋅++⋅−⋅cosh sinh ()α Lsewb α ⋅ L b L L bb (9.15) b ⋅⋅⋅−eL−⋅α w α b b α ⋅−2 b w w ()Lb 1 ⋅+b b sb sinh cosh Lb Lb IQE of the emitter and space charge region: For the calculation of the IQE of the emitter and space charge region only a substitution of the absorption coefficient is necessary: αα= cos() ϕ (9.16) 9 Appendixes 109 to define the generation profile and therefore also the differential equation in the same form as for the flat cell. Inserting eq. (9.16) into eq. (3.32), the generation profile becomes: −⋅α gx(,αα )=⋅⋅− F()1. R ⋅ e x (9.17) Because x is not affected by this substitution, the boundary conditions are the same as for the flat cell resulting in the following identity: textured ()αα= flat IQEescr,, IQEescr(). (9.18) Total IQE To obtain the approximated total IQE, the same approximations on the base, emitter and scr as in section 3.4.4.1 are carried out, resulting for the base in: L ⋅αϑcos() −⋅αϕ() textured α ≈ b ⋅ w cos (9.19) IQEb () ⋅+αϑ() e Lb cos 1 and for the emitter and scr in: textured α ≈−−⋅w αϕcos() IQEescr+ ()1. e (9.20) Adding the IQEs of the three regions leads to the total IQE of the textured cell: −⋅αϕ() Le⋅+−αϑcos()1 w cos textured α = b (9.21) IQEtotal () ⋅+αϑ() . Lb cos 1 Applying approximation A3.7 ((wα)2 << 1) results in: αϑϕ⋅+[]Lwcos() cos() w cos()ϑ L ⋅αϑcos() textured α = b =+ ⋅ ⋅ b . (9.22) IQEtotal () ⋅+αϑ() 1 ()ϕ ⋅+αϑ() Lbbcos 1 L cos Lb cos 1 and 11 1 = + . textured α + ()()ϑϕαϑϕ() ()+ () (9.23) IQEtotal () 1 wLcos()bb cos() L cos w cos With the approximation A3.8 (w << Lb) eq. (9.23) simplifies to: 1 1 ≈+1 (9.24) textured α ⋅αϑ() IQEtotal () Lb cos which is analogous to equation (3.25) for a flat cell. Equation (9.22) will be used as a starting point for the discussion in section 3.4.4.8. With little modification, the equations derived for a weak surface textured cell can also be applied to the case of a flat cell with light incidencing under an oblique angle γ relative to the 110 9 Appendixes direction of the surface. In this case light passes with the same angle ϕ relative to the emitter and base and the substitution in eq. (9.10) - (9.24) of ϑ by ϕ leads the right result. 9.4 Double-layer IQE For the double-layer model the coefficient B1 defined in eq. (5.23) is determined in this section. In the following the hyperbolic sine, cosine and tangent functions are abbreviated by sh, ch and th, respectively. Inserting the second boundary condition eq. (5.25) into eq. (5.23) results in: 2 +⋅ L −⋅α α − s ch() H s sh () H A = 2 ⋅⋅e H 22 − 22 2⋅ B (9.25) 2 − α 2 ()+⋅ () ()+⋅ ()2 1 2 sh H22 s ch H 2sh H22 s ch H 2 with H2 = H/L2 and the other parameters defined in chapter 5.4.2.1. Substituting with eq. (9.7) the coefficient A1 by B1 and with eq. (9.25) the coefficient A2 by B2 results, by using the third boundary condition eq. (5.26), in: ch() H+⋅ s sh () H B() shd()−⋅ thw () chd () =⋅− B shd() 22 2⋅ ch() d 11 1 1 2 2 ()+⋅ () 2 sh H22 s ch H 2 (9.26) 2 −⋅α H ⋅−()α −⋅α d ⋅−()2 2 −⋅α w 2 () L es eLL2 1 eL⋅ ch d + 2 ⋅ 22 ⋅+ch() d + 1 ⋅ 1 − α 2 ()+⋅ () 1 ()()−⋅−αα2 2 − α 2 () 1 2 sh H22 s ch H 2 112 1 1 1 ch w1 with d1 = d/L1 and d2 = d/L2 and the other parameters defined in chapter 5.4.2.1. With the fourth boundary condition (5.27) and the same substitutions for the coefficients as before, follows: ()+⋅ () L ch H22 s sh H 2 B 2 ()ch() d−⋅ th () w sh () d =⋅− B ch() d ⋅ sh() d 1 L 11122 sh() H+⋅ s ch () H 2 1 22 2 (9.27) 2 −⋅α H α ⋅⋅−−⋅α d 2 2 −⋅α w 2 L es⋅−()α 21eLL()2 eLL⋅ sh() d + 2 ⋅ 22⋅+sh() d + 1 ⋅⋅2 1 . − α 2 ()+⋅ () 1 −⋅−αα2 2 − α 2 L () 1 2 sh H22 s ch H 2 ()()112 1 1 1 1 ch w1 Eliminating B2 in the two equations (9.26) and (9.27) after results in the final expression for B1: −⋅α α ⋅ L e w 11 ⋅−⋅+⋅⋅+⋅+⋅+[]th() H d[] L s L th () d[] s L L th() d 1 − α 2 ch() w 2212212121 B = 1 1 1 ()⋅⋅−⋅ () + −⋅⋅() + th d1212[] s L L th w 1[] L 221 s L th w 1 −⋅α ααα()LLthHd2 −⋅2 []() −[][]1 − s +− s −αd LL⋅⋅αα() − se H (9.28) 12 1 22 2222⋅+e 12 22 2 −−αα2 2 () − α 2 ()()− ()()112 1 ch d1 () 12 ch H22 d ch d 1 . ()()−⋅ ⋅−⋅⋅ () +⋅−⋅() th H22 d[] th d 1122[] L s L th w 1[] s 221 L L th w 1 9 Appendixes 111 9.5 Double-layer IQE at α = 1/L1 and α = 1/L2 The exact double-layer IQE given in eq. (5.34) is not defined at α = 1/L1 and α = 1/L2. However, it can be shown in the same way as in appendix 9.2 for the single-layer IQE that at these places the left and right limits are both finite and equal. Therefore eq. (5.34) can be expanded continuously at these two places. In the following the results of the calculations of the limits at these places are given, including also the different approximations used for the derivation of the base IQEs. In the following the hyperbolic sine, cosine and tangent functions are abbreviated by sh, ch and th, respectively. The case α = 1/L2: Calculating for equation (5.34) the left and right limit at α = 1/L2 results in: LL − = 12 ⋅⋅w2 lim IQEb 2 e α→± ()− 10L2 LL12 1 2 ()−⋅++− ()()() −−⋅−() L th H222 d s111 d 2 w 2 th H 22 d s 2−−()dw 2 −1 e 22+ 2 ⋅⋅() () L L1 2 ch d11 ch w 1 +−th() w L 1 L L 2 th() d⋅−⋅ s 2 th() w +−⋅ 2 sthw() + 12 L 1 L 21 . 1 1 L2 L2 th() H−+ d1 s th() d ++ s th() d −−() 22 2 12 1 2 []−−()() − Hw22 L1 L1 L 11Hw22 se 2 + +−1 2 ch2 () w L2 2 ⋅−ch( H d )()() ch d ch w 1 1 22 1 1 +−⋅⋅−⋅⋅()() L2 ()+⋅−L2 () th H22 d th d 11 s 2 th w12 s th w1 L1 L1 Because the left and right limit are equal, this expression is used to define the base IQE at α = 1/L2: LL − L ()α == =12 ⋅⋅−w2 1 IQEb 1 L2 lim IQEb 2 e C6 (9.29) α→± ()− L 10L2 LL12 1 2 with 2 ()−⋅++− ()() −−⋅−() L th H222 d s111 d 2 w 2() th H 22 d s 2−−() 2 −1 e dw22+ L2 2 ⋅⋅ch() d ch () w Cthw=−() + 1 11 61 ()⋅−⋅L2 ()+−⋅L2 ()+ th d12 s th w1 sthw21 L1 L1 L2 L2 th() H−+ d1 s th() d ++ s th() d −−() 22 2 12 1 2 −−()() − Hw22 L1 L1 L []11Hw22 se 2 + +−1 2 ch2 ()w L2 2 ⋅−ch( H d )()() ch d ch w 1 1 22 1 1. +−⋅⋅−⋅⋅()() L2 ()+⋅−L2 () th H22 d th d 11 s 2 th w12 s th w1 L1 L1 112 9 Appendixes Applying approximation A5.2a ( H2 - d2 >> 1 ) to C6 the results in: L2 ch() d + sh() d −−() 1 L 1 L2 e dw22 1 +− 2 1 ch() w L2 2 Cthw=−() 1 1 61H 1 ()⋅−⋅ () L2 ()+⋅⋅− ()L2 () () sh d11 ch w sh w11 ch d ch w11 sh w L1 L1 which can be further simplified by using the addition theorems for the hyperbolic sine and cosine functions: −−() L L2 e dw22 ch() d−+ w 2 sh() d −+ w 2 −1 11L 11 L2 2 = 1 1 C61H . ()−+L2 () − sh d11 w ch d11 w L1 Note that due to approximation A5.2a, the last term of C6 is canceled at the pole α = 1/L2. This is the main result of our calculations of the limit value of the IQE at α = 1/L2, which explains why C6H2, defined in eq. (5.37) of chapter 5.4, can also be used at the pole α = 1/L2. The limit value for the total IQE is calculated in analogy to the calculation of the total IQE out side the pole region, as shown in section 5.4.2.3. Using eq. (3.20) for the contribution of the emitter and space charge region and eq. (9.29) for the base IQE, the total IQE at α = 1/L2 is given by: −−−LL L IQE()αα==−+11 L ew222 IQE() ==−+ 11 L e ww12 ⋅⋅−e 1 C . total 22b ()2 − L 6 LL12 1 2 2 Applying the approximations A5.3 ( (αw) << 1 ) and A5.4 ( w1 << 1 ) in the same way as in section 5.4.2.3 finally results in: LL L IQE()α ==1 L 12 ⋅− 1 C total 2 ()2 − L 6 LL12 1 2 which proves that equation (5.43) and (5.44) can also be used at α = 1/L2. In this equation either the exact coefficient C6 or the approximated one C6H1 can be used. The case α = 1/L1: Calculating for equation (5.34) the left and right limit at α = 1/L1 results in: 9 Appendixes 113 1 − =⋅w1 ⋅ lim IQEb e α→± 2 10L1 2 ⋅−()sLL −−() 221 ⋅+e Hw11 −⋅−()2 () 1 ()1 LL12 chH22 d 1 +⋅ ch()() d ch w 11()⋅−⋅L2 ()+−⋅L2 ()+ th d12 s th w1 sthw21 L1 L1 2 L L L −−() −+ ()−− 2 +−2 −+2 ()() − dw11 dw11 2 th H22 d s2 1 s2 1 sthH222 d e − () L L L 1 LL12 1 1 1 +−⋅⋅−⋅⋅()() L2 ()+⋅−L2 () th H2212 d th d1 s th w12 s th w1 L1 L1 Because the left and right limit values are equal, this expression can be used to define the base IQE at α = 1/L1. With approximation A5.2a applied to the base IQE at α = 1/L1 and using the addition theorems for the hyperbolic sine and cosine functions, it follows: 1 − IQE()α ==⋅⋅1 L e w1 b 1 2 −− −−() ()Hw11 Hd221 4 ⋅−()sLLe e 2 L L −−() 221 +−+ 2 − − 2 dw11 dw11 2 1 e −+2 − () L L ()11()LL() s 1 LL12 1 1 + 12 2 1 . ()−+⋅L2 () − sh d11 w ch d11 w L1 Using this equation for the base IQE and eq. (3.20) for the contribution of the emitter and space charge region, the total IQE can be calculated by applying first approximation A5.3 and secondly approximation A5.4, which results for the total IQE at α = 1/L2 in the following expression: − ⋅ () − dw L dw− 2 LL21 L 2 −1 ⋅ + − 2 ⋅ e L1 + () 1 1 L11L 1 LL12 L1 IQE()α ==+1 L . total 1 2 2 dw− L dw− sh +⋅2 ch L1 L11L This is the second main result of the limit calculations of the pole places, which is used in equation (5.44) to define the total IQE at α = 1/L1. The same procedure can be applied to calculate the limit values of the IQE at α = 1/L1 and α = 1/L2 in the case of a high back side recombination velocity. For this case only approximation A5.2b ( s2 >> 1 ) instead of A5.2a ( H2 - d2 >> 1 ) has to be used for the calculations. With this we have shown now that the exact as well as approximated equations for the IQEs derived in section 5.4 can be expanded continuously at their non-defined places α = 1/L1 and α = 1/L2. 114 9 Appendixes 9.6 From the double-layer IQE back to the single-layer IQE It is shown that the approximated IQE of the double-layer model given in eq. (5.44) proceeds to the approximated IQE of the single-layer model given in eq. (3.25) for the three cases: a) L2 = L1, b) d ≈ H 9 and c) d-w ≈ 0 µm 10. In the following, the IQE of the double-layer model and of the single-layer model are distinguished by an additional lower index i = 2 and 1, respectively. In the case of α 1/L1, it follows that: a) L2 = L1 α ⋅ L chdwshdw()()−+ − α ==1 ⋅⋅−α 11 11 = IQEtotal (, L , L L ,, d w ) L 2121 ()α ⋅−2 1 shdwchdw()()−+ − L1 1 11 11 α ⋅ L α ⋅ L 1 ⋅⋅−=[]α L 1 1 = IQE(,α L ) ()α ⋅−2 1 α ⋅+L 1 11total L1 1 1 b) d ≈ H α ≈≈ IQE212total (, L , L , d H , w ) −⋅α () − L L2 e Hw 11+⋅2 th() H − w +− 2 ⋅ 11 2 ()()+⋅α − α L1 L1 1 211ch H w 1 ⋅−α α 2 −1 1 L 1 th() H−+ w 2 11 L1 2 −⋅α ()− −−()Hw L L 2e H w e 111 −>> 11++2 2 − −>> Hw111 2 + α Hw111 α L1 L ()1 ≈ 1 α − 1 2 ≈ IQE(,α L ) α 2 −1 1 L 11total 1 1 + 2 L 1 The use of the additional approximation H1 - w1 = (H - w)/L1 >> 1 is no restriction, because it was also used for the derivation of eq. (3.25). 9 Because of the application of approximation A5.2a H2 - d2 >> 1 for the derivation of eq. (5.44), it is mathematically incorrect to use d = H. For mathematical correctness d ≈ H in combination with A5.2a is chosen, which means that L2 has to be small. However, it is interesting that eq. (5.44) proceeds to eq. 3.25 even for d = H. To show this in a mathematically consistent way, the approximation H2 - d2 << 1 instead of A5.2a has to be used, followed by the same procedure as it was done to derive eq. (5.44). 10 The depth d has to be larger than w, otherwise problems arise with the third and fourth boundary conditions (eq. (5.26) and (5.27)) on page 69. 9 Appendixes 115 c) d ≈ w L2 2 + α 2 α L L2 IQE(,α L , L , d≈≈ w , w ) 1 ⋅−α 1 1 = 212total α 2 − 1 + α 1 1 L2 1 2 L αα()+− 2 + α L2 121 1 α ⋅ α L 1 L α 2 − 1 1 ⋅ 1 = 1 ⋅ 1 = IQE(,α L ) α 2 − 1 + α α 2 − 1 + α 12total 1 1 2 1 1 2 For α = 1/L1 follows that cases a) and b) result in IQE2total = 1/2 = IQE1total(α = 1/L1, L1), whereas case c) results in IQE2total = IQE1total(α = 1/L1, L2). The author has also shown that all in chapter 5.4.2 derived approximated and the exact double-layer IQEs proceed for the cases a) - c) to the corresponding single-layer IQEs. This is also valid if approximation A5.2b ( s2 >> 1 ) instead of A5.2a ( H2 - d2 >> 1 ) is used. 9.7 Double-layer IQE and weak surface texturization The IQE of a cell with weak surface texturization and two base regions with different diffusion lengths can be calculated in the same way as it was done in chapter 3.4 for the single-layer model. For the notation of the additional parameters see Fig. 3.6 of section 3.4.2. With the substitutions: αα= cos() ϑ xxw=+()cos()ϑϕϕ − cos() cos() ww= cos()ϑϕ cos() (9.30) ddw=+()cos()ϑϕϕ − cos() cos() HHw=+()cos()ϑϕϕ − cos() cos() the differential equation of the minority carrier density in the base and the boundary conditions become the same form as for the flat cell. From this follows that the base IQE of the weakly textured cell can be expressed by the IQE of the flat cell (exact eq. (5.34)): textured = flat α IQEb IQEb (, L12 , L ,,, d w H , s 2 ). (9.31) Because of the equality dwdw−=− and same equalities valid for H - w and H - d, the coefficients C4 and C5 in eq. (5.34) do not change. For the other coefficients C2 and C3, only α has to be changed according to eq. (9.30), resulting in the textured base IQE: α ⋅ L −⋅α IQEtextured()α ,,,,,,, w = 1 ⋅⋅−−−−eLCdwHdHwLLs w []αα(). b ()α ⋅−2 16 122 (9.32) L1 1 116 9 Appendixes with any one of the coefficients C6 derived in chapter 5.4.2. For the emitter and space charge region, the approximated eq. (9.20) can be used, resulting in the textured total IQE: α −⋅w textured =−cos()ϕ +texturedαα =−−⋅α w + textured (9.33) IQEtotal 11 e IQEb (,) w e IQEb (,) w . Carrying out approximations A5.3 and A5.4 as shown in chapter 5.4.2.3, the total IQE of a textured cell can be calculated from the total IQE of a flat cell by only changing the absorption coefficient: textured = flat α IQEtotal IQEtotal (). (9.34) Note that instead of transformation (9.30) also the following transformation can be used to calculate the textured base IQE from the flat base IQE: ww= cos()ϕ dd=+⋅−cos()ϑϕϑ w()11 cos() cos() HH=+⋅−cos()ϑϕϑ w()11 cos() cos() (9.35) xx=+⋅−cos()ϑϕϑ w()11 cos() cos() = ()ϑ LL12// 12 cos with α as well as s2 unchanged. Using this transformation, the differential equation of the minority carrier density and the boundary conditions of the flat and textured cell are the same and the same procedure as shown above can be applied. 10 List of abbreviations, symbols, figures and tables 10.1 List of abbreviations abbreviation description ARC antireflection coating APCVD atmospheric pressure chemical vapor deposition BSF back-surface-field Ci interstitial carbon Cz Czochralski silicon DARC double layer antireflection coating DLTS deep level transient spectroscopy EFG edge-defined film-fed growth EQE cell external quantum efficiency EMC electromagnetic casting ESR electron spin resonance FGA forming gas annealing FhG-ISE Frauenhofer Gesellschaft-Institut Solare Energiesysteme, Freiburg, Germany FZ Float zone silicon GB grain boundary HP hydrogen passivation IMEC Interuniversitair Micro-Electronica Centrum at Leuven, Belgium IQE cell internal quantum efficiency LBIC light- beam-induced current mc-Si multicrystalline silicon MIRHP microwave induced remote hydrogen plasma MW-PCD microwave-detected photoconductance decay Oi interstitial oxygen PC-1D quasi-one-dimensional finite-element program [131] PECVD plasma enhanced chemical vapor deposition PERL passivated emitter, rear locally-diffused RGS ribbon growth on substrate scr space charge region SIMS secondary ion mass spectroscopy SiN silicon nitride SiO2 silicon dioxide SOPLIN solidification by planar interface SR cell spectral response SPV surface photovoltage TE thermal effusion TiO2 titanium dioxide 118 10 List of abbreviations, symbols, figures and tables UNSW University of New South Wales UKN University of Konstanz 10.2 List of symbols Symbol units description A cm2 cell area α µm-1 silicon absorption coefficient α1/2 - reduced silicon absorption coefficient (α1/2 = αL1/2) -1 αH µm scaling factor in eq. (5.10) β - exponential factor in eq. (5.11) -1 BX s dissociation coefficient -3 [Ci]cm concentration of interstitial carbon ∆n cm-3 excess electron concentration in base of a np-solar cell -3 ∆n1/2 cm excess electron concentration in base region 1/2 of a np-solar cell ∆n’ cm2 reduced excess electron concentration (defined in appendix 9.1) ∆ ′ 2 n12/ cm reduced excess electron concentration introduced in section 5.4.2.1 d µm depth of passivated region dgrain mm average grain diameter di - reduced d (di = d/Li) of base region i = 1/2 D cm2s -1 diffusion coefficient of hydrogen in silicon 2 -1 D0 cm s diffusion constant of hydrogen in silicon 2 -1 De/b cm s diffusion coefficient of minority carriers in emitter/base of np-solar cell 2 -1 DH/D cm s diffusion coefficient of hydrogen/deuterium in silicon -3 [D]0 cm deuterium concentration at the front surface -3 [D]x cm deuterium concentration at distance x from the front surface ∆n/∆p cm-3 excess minority carrier concentration of electrons/holes EA eV activation energy for diffusion EX eV binding energy of the HX complex F(λ) cm-2s -1 flux of photons of wavelength λ onto cell surface FF % fill factor of the illuminated cell γ ° facet angle of texturization g(x) cm-3s -1 spatial carrier generation rate H µm cell thickness H2 µm reduced cell thickness (H2 = H/L2) [H]cm-3 hydrogen concentration -3 [H]0 cm hydrogen concentration at the front surface -3 [H]x cm hydrogen concentration at distance x from the front surface [HX]cm-3 concentration of the hydrogen-trap complex η % cell efficiency Ilight(λ) W light intensity in dependence of wavelength λ ISC(λ) A short-circuit current in dependence of wavelength λ IQE - cell’s internal quantum efficiency IQEe, scr, b - internal quantum efficiency of emitter, scr and bulk, respectively IQEtotal - total internal quantum efficiency inclusive emitter, scr and bulk ϕ ° angle with which light passes the emitter and the space charge region ϑ ° angle with which light passes the base 10 List of abbreviations, symbols, figures and tables 119 -2 J01/02 Acm first/second diode saturation current density -2 JD Acm cell dark current density -2 JL Acm light induced current density -2 JSC Acm short-circuit current density k J/K Boltzmann constant 3 -1 KX cm s reaction coefficient L µm minority carrier diffusion length Li µm bulk minority carrier diffusion length of base region i = 1/2 L21 - fraction of bulk minority carrier diffusion lengths (L21 = L2/L1) Lb µm minority carrier diffusion length in the base/bulk Le µm minority carrier diffusion length in the emitter Leff µm effective base minority carrier diffusion length λ nm wavelength of light -1 νX s the vibrational frequency for dissociation n/p cm-3 electron/hole concentration n1/2 - first/second diode ideality factor nSi - refractive index of silicon -2 ND cm dislocation density -3 [Oi]cm concentration of interstitial oxygen q C electron charge R % external front surface reflectance of a cell R(H,X) cm capture radius for a chemical reaction 2 Rs Ωcm series resistance 2 Rsh Ωcm shunt resistance Rsheet Ω/ sheet resistance S cms -1 recombination velocity at the surface of a semiconductor -1 Se/b cms front/back surface recombination velocity of np-solar cell se/b - reduced Se/b of np-cell (se/b = Se/bLe/b/De/b) s2 - reduced Sb of np-cell with two base regions (s2 = SbL2/Db) T °C temperature Topt °C optimum MIRHP passivation temperature topt min optimum MIRHP passivation time τeff µs effective minority carrier lifetime τ1/2 µs bulk minority carrier lifetime of base region i = 1/2 τb µs bulk minority carrier lifetime V mV measured voltage of cell VMPP mV voltage at the maximum power point VOC mV open circuit voltage under illumination Vth mV thermal voltage ( = kT/e = 25.7 mV for T = 25°C) wb µm width of the neutral base region ′ µ ′ = wb m reduced width of the neutral base region wwLbbb we µm junction depth / width of the emitter region wscr µm width of the space charge region w µm width of the emitter and space charge region (w = we + wscr) w1/2 - reduced width of the emitter and space charge region (w1/2 = w/L1/2) [X]cm-3 concentration of defects or impurities causing traps for H 120 10 List of abbreviations, symbols, figures and tables 10.3 List of figures Fig. 1.1: Total world photovoltaic module shipment...... 1 Fig. 1.2: The contribution of the Si wafer to the total costs of a PV module...... 3 Fig. 2.1: Processing sequence of homogeneous emitter solar cells...... 7 Fig. 2.2: Processing sequence of selective emitter solar cells...... 8 Fig. 3.1: Distribution of Lb, determined with the SPV method, on EMC material wafer before and after hydrogen passivation...... 11 Fig. 3.2: LBIC measurement results obtained on one cell based on EMC cells before and after a MIRHP process...... 15 Fig. 3.3: Influence of a bias light on the IQE of RGS and BAYSIX cells...... 16 Fig. 3.4: Influence of a bias light on the IQE of homogeneous emitter EFG cells...... 16 Fig. 3.5: Comparison of the IQE of homogeneous and selective emitter EFG cells...... 17 Fig. 3.6: Sketch of a solar cell for the single-layer IQE model...... 18 Fig. 3.7: Contributions of the base, emitter and space charge region to the total IQE...... 21 Fig. 3.8: Comparison of the exact total IQE with several approximated IQEs...... 25 Fig. 3.9: Relative deviations of the approximated total IQEs from the exact total IQE...... 25 Fig. 3.10: Approximated contributions of the emitter and space charge region to the IQE. ....26 Fig. 3.11: Influence of the space charge region width wscr on the approximated IQE...... 26 Fig. 3.12: Influence of the front surface recombination velocity Se on the approximated IQE.27 Fig. 3.13: Influence of the emitter width we on the approximated IQE...... 27 Fig. 3.14: Sketch of a solar cell with a weak surface texturization...... 31 Fig. 3.15: Influence of the refractive index of silicon nSi(λ) on the angle with which light passes the emitter...... 31 Fig. 3.16: Comparison of the total IQE for a flat and a textured cell...... 32 Fig. 4.1: Schematic diagram of the MIRHP device...... 34 Fig. 4.2: Optimization results of Al-gettering on cells based on EUROSIL material...... 35 Fig. 4.3: Influence of the MIRHP process conditions on VOC and JSC of EMC cells...... 36 Fig. 4.4: Influence of the MIRHP process conditions on VOC and JSC of SOLAREX cells. ...37 Fig. 4.5: Influence of the passivation temperature and time on VOC and JSC of BAYSIX and SOLAREX cells...... 39 Fig. 4.6: Influence of the passivation temperature on VOC and JSC of RGS and EFG cells.....40 Fig. 4.7: Influence of the passivation temperature on JSC, VOC, FF and η of defect rich RGS cells...... 41 Fig. 4.8: LBIC measurement results obtained on SOLAREX and EFG cells before and after hydrogen passivation...... 42 Fig. 4.9: IQE measurements and IQE PC-1D simulations of RGS cells...... 45 Fig. 4.10: Influence of the MIRHP passivation on the IQE of RGS cells...... 46 Fig. 4.11: Influence of the MIRHP passivation on the dark I-V characteristics of RGS cells.. 47 Fig. 4.12: Influence of different processes on the dark I-V characteristics of V-grooved RGS cells...... 50 Fig. 4.13: Influence of different processes on the IQE of V-grooved RGS cells...... 50 Fig. 4.14: Influence of different processes on the illuminated I-V parameters of V-grooved RGS cells...... 52 Fig. 4.15: Improvement of the IQE of mc-Si PERL cells due to a MIRHP passivation...... 54 Fig. 4.16: Improvement of VOC and JSC of mc-Si PERL cells due to a MIRHP passivation.....55 Fig. 4.17: Degeneration of the dark current density of homogeneous emitter cells due to MIRHP process...... 58 Fig. 5.1: Relative rate of deuterium effusion from EUROSIL material determined by thermal effusion...... 65 10 List of abbreviations, symbols, figures and tables 121 Fig. 5.2: Intragrain deuterium SIMS profiles from EMC material...... 66 Fig. 5.3: Sketch of a solar cell with two base regions...... 68 Fig. 5.4: Comparison of the exact two-layer total IQE with the approximated IQE...... 75 Fig. 5.5: Influence of the passivation depth d on the two-layer IQE...... 75 Fig. 5.6: Influence of the passivation depth d on the IQE of one SOLAREX cell...... 78 Fig. 5.7: A detailed view of Fig. 5.6 with the IQE as a function of the mean light penetration depth...... 78 Fig. 5.8: IQEs from Fig. 5.6 together with simulation results using PC-1D...... 79 Fig. 5.9: Extraction of diffusion parameters with the topt-method ...... 80 Fig. 5.10: Extraction of diffusion parameters with the Tconst-method...... 80 Fig. 5.11: H-Effusion experiment with EFG, EMC and SOLAREX cells based on the internal quantum efficiency...... 83 Fig. 5.12: Influence of H-Effusion on VOC and JSC of EMC and SOLAREX cells...... 83 Fig. 5.13: Influence of H-Effusion on VOC and JSC of one EFG cell...... 84 Fig. 5.14: Influence of H-Effusion on the dark I-V characteristics of one EFG cell...... 85 Fig. 6.1: Screen-printed solar cell structure as used in this work...... 88 Fig. 6.2: Influence of the MIRHP passivation time on VOC and JSC of screen-printed solar cells based on BAYSIX and EMC Si material...... 89 Fig. 6.3: Influence of the MIRHP passivation on the IQE of screen-printed EMC solar cells.92 Fig. 6.4: Influence of the MIRHP process on the dark current characteristics of one screen-printed cell with and one without TiO2 ARC...... 93 Fig. 6.5: Influence of the MIRHP passivation and a PECVD SIN ARC on the IQE for cells of low quality Si material and high quality EMC material...... 95 Fig. 6.6: Measured dark current characteristics of the low quality solar cells from Fig. 6.5. . 95 10.4 List of tables Table 2.1: The used block casted mc-Si materials, the material supplier and the maximum efficiency reached up to date...... 5 Table 2.2: Structural properties and the bulk minority carrier diffusion length of the mc-Si materials used in this work...... 6 Table 3.1: The structural and electrical parameters of the solar cells used for the simulations.21 Table 3.2: The theoretical accuracy of the approximated IQEs...... 28 Table 3.3: The influence of the experimental accuracy on the fit results of the approximated IQEs...... 28 Table 4.1: MIRHP processing conditions used for the optimization of cells based on EMC. 36 Table 4.2: The optimum MIRHP process temperature and time together with the relative increases in cell efficiency for the materials of investigation...... 43 Table 4.3: Illuminated I-V parameters of the best mc-Si solar cells without ARC...... 43 Table 4.4: Range of the illuminated I-V parameters of RGS cells...... 44 Table 4.5: Effect of the duration of a FGA on the I-V parameters of RGS cells...... 48 Table 4.6: Dark and illuminated I-V parameters of the record 11.1% RGS cell...... 49 Table 4.7: Influence of MIRHP and FGA on the illuminated I-V parameters of PERL cells. 54 Table 4.8: The illuminated I-V parameters of the best multicrystalline PERL cells...... 56 Table 5.1: The accuracy of determining the passivation depth d from the approximated two-layer IQE...... 76 Table 5.2: Equations for the approximated coefficient C6 used for the calculation of the approximated base IQE for the two-layer model...... 77 Table 5.3: Equations for the approximated total IQE of the two-layer model...... 77 122 10 List of abbreviations, symbols, figures and tables Table 5.4: Dependence of the passivation depth d obtained by the step model of the IQE on the MIRHP passivation temperature and time of SOLAREX cells...... 79 Table 5.5: Results of the diffusion parameters of SOLAREX material obtained by the methods proposed in chapter 5.2.3...... 81 Table 5.6: The influence of base mc-Si material on the diffusion constant D for T = 350°C is shown...... 81 Table 6.1: Processing sequences of the industrial solar cell production lines at Eurosolare and Solarex...... 88 Table 6.2: Processing sequences of the industrial solar cell production lines at Eurosolare and Solarex inclusive an additional MIRHP processing step...... 90 Table 6.3: Improvement of the illuminated I-V parameters after a MIRHP process within the Eurosolare process...... 91 Table 6.4: MIRHP passivation of cells based on compensated mc-Si material...... 92 Table 6.5: Influence of the MIRHP process on the Solarex process...... 93 Table 6.6: Sequences of the firing through PECVD SiN ARC process...... 94 11 List of Publications • M. Spiegel, P. Fath, K. Peter, B. Buck, G. Willeke and E. Bucher, 'Detailed study on microwave induced remote hydrogen plasma passivation of multicrystalline silicon', Proceedings of the 13th EC Photovoltaic Solar Energy Conference, Nice, France, 1995, p. 421-424. • M. Spiegel, G. Willeke, P. Fath and E. Bucher, 'Colored solar cells with single, multiple and continuous layer antireflection coatings', Proceedings of the 13th EC Photovoltaic Solar Energy Conference, Nice, France, 1995, p. 714-720. • M. Spiegel, G. Willeke and E. Bucher, 'Colored antireflection coatings for high efficiency PV modules', Proceedings of the 4th Conference on Solar Energy in Architecture and Urban Planning, Berlin, Germany, 1996, p. 625-630. • E. Bucher, G. Willeke, K. Friemelt, F.P. Baumgartner, C. Kloc, P. Fath, M. Spiegel, K. Fess, W. Käfer and K. Peter, 'New ideas to promote the application of alternative energies to improve the quality of city life', in Scientific and Technological Achievements Related to the Development of European Cities, edited by S. Radautsan and G. Parissakis, Kluwer Academic Publishers, 1997, p. 213. • M. Spiegel, S. Keller, P. Fath, G. Willeke and E. Bucher, 'Microwave induced remote hydrogen plasma (MIRHP) passivation of solar cells using different silicon base materials', Proceedings of the 14th EC Photovoltaic Solar Energy Conference, Barcelona, Spain, 1997, p. 743-746. • G. Hahn, M. Spiegel, S. Keller, P. Fath, G. Willeke, E. Bucher, C. Häßler, H.-U. Höfs and S. Thurm, 'Characterisation of RGS (ribbon growth on substrate) silicon material and solar cell', Proceedings of the 14th EC Photovoltaic Solar Energy Conference, Barcelona, Spain, 1997, p. 81-84. • P. Fath, C. Zechner, B. Terheiden, A. Boueke, C. Marckmann, C. Gerhards, R. Tölle, M. Spiegel, G. Willeke and E. Bucher, 'Processing, characterisation and simulation of advanced mechanically textured mono- and multicrystalline silicon solar cells', Proceedings of the 14th EC Photovoltaic Solar Energy Conference, Barcelona, Spain, 1997, p. 73-76. • R. Kühn, P. Fath, M. Spiegel, G. Willeke, E. Bucher, N. Mason and T. Bruton, 'Multicrystalline silicon buried contact solar cells using a new electroless plating metallization sequence and a high throughput mechanical groove formation', Proceedings of the 14th EC Photovoltaic Solar Energy Conference, Barcelona, Spain, 1997, p. 672-677. • B. Bitnar, R. Glatthaar, S. Keller, J. Kugler, M. Spiegel, P. Fath, G. Willeke, E. Bucher, F. Duerinckx, J. Szlufcik, J. Nijs, R. Mertens, H. Nussbaumer and F. Ferrazza, 'Investigation of the passivation properties of PECVD-silicon-nitride layers on silicon 124 11 List of Publications solar cells', Proceedings of the 14th EC Photovoltaic Solar Energy Conference, Barcelona, Spain, 1997, p. 1431-1434. • S. Keller, C. Zechner, M. Spiegel, A. Boueke, B. Terheiden, P. Fath, G. Willeke and E. Bucher, 'Quantum efficiency simulation and analysis of crystalline Si solar cells by two dimensional device modeling', Proceedings of the 14th EC Photovoltaic Solar Energy Conference, Barcelona, Spain, 1997, p. 81 • M. Spiegel, R. Tölle, C. Gerhards, C. Marckmann, H. Nussbaumer, P. Fath, G. Willeke and E. Bucher, 'Implementation of hydrogen-passivation into an industrial low-cost mc-silicon solar cell process', Proceedings of the 26th IEEE Photovoltaics Specialists Conference, Anaheim, California, 1997, p. 151-154. • G. Hahn, W. Jooss, M. Spiegel, S. Keller, P. Fath, G. Willeke and E. Bucher, 'Improvement of mc-Si solar cells by Al-gettering and hydrogen passivation', Proceedings of the 26th IEEE Photovoltaics Specialists Conference, Anaheim, California, 1997, p. 75-78. • C. Gerhards, C. Marckmann, R. Tölle, M. Spiegel, P. Fath, G. Willeke and E. Bucher, 'Mechanically V-textured low cost multicrystalline silicon solar cells with a novel printing metallization', Proceedings of the 26th IEEE Photovoltaics Specialists Conference, Anaheim, California, 1997, p. 43-46. • C. Zechner, W. Jooss, G. Hahn, M. Wibral, B. Bitnar, S. Keller, M. Spiegel, P. Fath, G. Willeke and E. Bucher, 'Systematic study towards high efficiency multicrystalline silicon solar cells with mechanical surface texturization', Proceedings of the 26th IEEE Photovoltaics Specialists Conference, Anaheim, California, 1997, p. 243-246. • M. Spiegel, G. Hahn, P. Fath, G. Willeke und E. Bucher, 'Wasserstoffpassivierung von multikristallinen Si-Solarzellen', Beitrag auf der Frühjahrestagung des Arbeitskreises Energie der Deutschen Physikalischen Gesellschaft, Regensburg, 1998 • G. Hahn, W. Jooss, C. Zechner, M. Spiegel, P. Fath, G. Willeke und E. Bucher, 'Defektuntersuchungen in RGS Foliensilizium und Solarzellenergebnisse', Beitrag auf der Frühjahrestagung des Arbeitskreises Energie der Deutschen Physikalischen Gesellschaft, Regensburg, 1998 • P. Fath, C. Zechner, B. Terheiden, A. Boueke, C. Marckmann, C. Gerhards, M. Spiegel, G. Willeke und E. Bucher, 'Herstellung, Charakterisierung und Simulation von neuartigen kristallinen Siliziumsolarzellen', Beitrag auf der Frühjahrestagung des Arbeitskreises Energie der Deutschen Physikalischen Gesellschaft, Regensburg, 1998 • M. Spiegel, H. Nussbaumer, M. Roy, F. Ferrazza, S. Narayan, P. Fath, G. Willeke and E. Bucher, 'Successful implementation of the microwave induced remote hydrogen plasma passivation in a standard multicrystalline silicon solar cell production line', Proceedings of the 2nd WCPEC, Vienna, Austria, 1998. • M. Spiegel, G. Hahn, W. Jooss, P. Fath, G. Willeke and E. Bucher, 'Investigation of hydrogen diffusion, effusion and passivation in solar cells using different multicrystalline silicon base materials', Proceedings of the 2nd WCPEC, Vienna, Austria, 1998. • G. Hahn, C. Zechner, M. Spiegel, W. Jooss, P. Fath, G. Willeke and E. Bucher, 'Mechanical texturization and hydrogen passivation of RGS (ribbon growth on substrate) silicon solar cells', Proceedings of the 2nd WCPEC, Vienna, Austria, 1998. • C. Gerhards, C. Marckmann, M. Spiegel, P. Fath, G. Willeke, E. Bucher, J. Creager and S. Narayanan, 'Progress in production line implementation of V-textured low cost multicrystalline silicon solar cells', Proceedings of the 2nd WCPEC, Vienna, Austria, 1998. 11 List of Publications 125 • R. Kühn, A. Boueke, M. Wibral, M. Spiegel, P. Fath, G. Willeke and E. Bucher, '11% semitransparent bifacially active POWER crystalline silicon solar cells', Proceedings of the 2nd WCPEC, Vienna, Austria, 1998. • B. Bitnar, R. Glatthaar, C. Marckmann, M. Spiegel, R. Tölle, P. Fath, G. Willeke and E. Bucher, 'Lifetime investigations on screenprinted silicon solar cells', Proceedings of the 2nd WCPEC, Vienna, Austria, 1998. • S. Keller, M. Spiegel, P. Fath, G. Willeke and E. Bucher, 'A critical evaluation of the effective diffusion length determination in crystalline silicon solar cells from an extended spectral analysis', IEEE Transactions on Electron Devices, 45 (7), 1998, p. 1569-1574. • G. Hahn, C. Zechner, B. Bitnar, M. Spiegel, W. Jooss, P. Fath, G. Willeke, E. Bucher and H.-U. Höfs, 'Solar cells on Ribbon Growth on Substrate silicon with 11% efficiency', Progress in Photovoltaics, 6 (3), 1998, p. 163-167. • M. Spiegel, C. Zechner, B. Bitnar, G. Hahn, W. Jooss, P. Fath, G. Willeke, E. Bucher, H.-U. Höfs and C. Häßler, 'Ribbon growth on substrate (RGS) silicon solar cells with microwave induced remote hydrogen plasma passivation and efficiencies exceeding 11%', Solar Energy Materials and Solar Cells, 55, 1998, p. 331-340. 12 Zusammenfassung Thema dieser Arbeit war die Reduzierung der Volumen- (Bulk-) Rekombination in multikristallinen Silizium Solarzellen. Um die Kosten der photovoltaischen Energiegewinnung zu senken, hat in den letzten Jahren in zunehmenden Maße band- und blockgegossenes multikristallines gegenüber monokristallinem Silizium an Bedeutung gewonnen. Verglichen zu monokristallinem Silizium reduzieren Kristalldefekte und die Segregation von Fremdatomen den Wirkungsgrad von Solarzellen basierend auf band- und blockgegossenes Silizium. Eine Vielzahl von Passivierungstechniken (direktes H-Plasma, H-Ionenstrahltechnik, Formiergastempern, etc) sind in der Literatur angegeben, welche die Eigenschaft des Wasserstoffatoms ausnutzen, die elektronische Aktivität von Defekten zu vermindern. Eine relativ neue Technik zur Wasserstoffpassivierung von multikristallinen Siliziumsolarzellen ist der MIRHP (Microwave Induced Remote Hydrogen Plasma) Prozeß, auf dem diese Arbeit aufbaut. Schwerpunkt dieser Arbeit war die Optimierung des MIRHP Prozesses in Abhängigkeit verschiedener multikristalliner Basismaterialen. Mittels SPV (Surface PhotoVoltage) Messungen an multikristallinen Siliziumwafern konnte gezeigt werden, daß die Minoritätsladungsträgerdiffusionslänge durch den MIRHP Prozeß zum einen steigt und zum anderen, daß deren Streuung abnimmt. An Hand von Dunkel-/Hellkennlinien, LBIC (Light- Beam-Induced Current) und Spectral Response Messungen wurde der MIRHP Prozeß auf Siliziumsolarzellen in Abhängigkeit des verwendeten multikristallinen Basismaterials bzgl. der MIRHP Prozeßparameter optimiert. Durch die MIRHP Technik konnten Wirkungsgrad- steigerungen auf blockgegossenem Silizium um bis zu 15% und auf bandgegossenem Silizium um bis zu 31% erzielt werden. Die optimalen Passivierungstemperaturen betrugen für die blockgegossenen Siliziummaterialien (EUROSIL, BAYSIX, EMC, SOLAREX) zwischen 350 und 375°C bei Passivierungszeiten zwischen 90 min und 3 h. Um diese Passivierungszeiten weiter zu reduzieren, wurde ein zweistufiger MIRHP Prozeß vorgeschlagen, bestehend aus einem MIRHP Prozeß bei hoher Temperatur zur Bulkpassivierung und einem zweiten kurzen Prozeß bei 350°C zur Passivierung der oberflächennahen Region. Für sauerstoffarmes EFG (Edge-defined Film-fed Growth) Material konnte eine vollständige Bulkpassivierung bei 350° schon nach 30 min erzielt werden. Für sauerstoffreiches RGS (Ribbon Growth on Substrate) Material wurde eine reduzierte Wasserstoffdiffusion beobachtet, welche eine hohe optimale Passivierungstemperatur von 450°C verlangt. Auf einer RGS Solarzelle (4 cm2) wurde ein Rekordwirkungsgrad von 11.1% erzielt, mit einem absoluten Anstieg im Wirkungsgrad um 1.9% aufgrund des MIRHP Prozesses. Mit einem durchschnittlichen Anstieg in der Kurzschlußstromdichte von 1.2 mAcm-2 und in der offenen Klemmspannung von 7 mV wurde ebenfalls gezeigt, daß der MIRHP Prozeß zu einer deutlichen Verbesserung von multikristallinen PERL (Passivated Emitter, Rear Locally-diffused) Hochleistungszellen führt. Nach der Wasserstoffpassivierung wurde auf einer 11 cm2 PERL Zelle ohne Antireflexionsbeschichtung aber mit schwacher Oberflächentexturierung mit durchschnittlich 27% Reflexion ein Wirkungsgrad von 14.7% erzielt. 12 Zusammenfassung 127 Im Zuge der Optimierung des MIRHP Prozesses wurde innerhalb dieser Arbeit die Theorie der internen Quantenausbeute einer Solarzelle weiterentwickelt. Es wurde gezeigt, daß der oft experimentell beobachtete lineare Zusammenhang zwischen inverser interner Quantenausbeute und inversem Absorptionskoeffizienten zu einem nicht zu vernachlässigenden Teil auf die Beiträge von Emitter und Raumladungszone zurückzuführen ist. Die in der Literatur angegebene Herleitung dieses linearen Zusammenhangs über den Beitrag des Bulks ist demnach unzureichend. In dieser Arbeit wurden geeignete Nährungen vorgeschlagen und analysiert, die den oben genannten linearen Zusammenhang unter Einbeziehung der Beiträge des Emitters, der Raumladungszone und des Bulks, begründen. Neben dem theoretischen Verständnis liefert dieses neue Vorgehen auch Auswahlregeln über den Wellenlängenbereich, innerhalb dessen die Minoritätsladungsträgerdiffusionslänge des Bulks gefittet werden soll. Neben der Passivierung von Rekombinationszentren mittels atomaren Wasserstoffs wurde auch die Diffusion von Wasserstoff in multikristallinem Silizium untersucht. Um die Begrenzungen von thermischen Effusionsexperimenten und SIMS (Secondary Ion Mass Spectroscopy) Messungen zu überbrücken wurde eine neue elektronisch sensitive Methode für die Bestimmung der Eindringtiefe von Wasserstoff in Silizium entwickelt. Sie basiert auf einem Fit der internen Quantenausbeute von H-passivierten Solarzellen mittels eines Zweischichtenmodells des Bulks einer Solarzelle. Experimentell wurde diese Methode auf sauerstoffreiches SOLAREX Material angewandt. Von den über dieses Modell erhaltenen Wasserstoffeindringtiefen in Abhängigkeit von der Passivierungstemperatur und der Passivierungszeit wurde für die Diffusion von atomaren Wasserstoff eine Aktivierungsenergie von 0.6 -0.7 eV und ein Diffusionskoeffizient von 810-10 cm2/s bei 275°C bestimmt. Zusätzlich wurde herausgefunden, daß das Wurzel-t-Diffusionsgesetz auch in SOLAREX Material die Diffusion von atomaren Wasserstoff beschreibt. Die für die anderen multikristallinen Siliziumaterialien innerhalb dieser Arbeit bestimmten Diffusionskoeffizienten lassen darauf schließen, daß hohe Sauerstoffkonzentrationen und hohe Defektdichten die Wasserstoffdiffusion reduzieren. Mit Wasserstoff-Effusionsexperimenten an Solarzellen wurde herausgefunden, daß die Temperatur, bei der atomarer Wasserstoff aus dem Bulk diffundiert, stark vom verwendeten multikristallinen Siliziummaterial abhängt. Die Effusionstemperaturen lagen zwischen 350 und 475°C. Diese Beobachtungen legen es nahe, daß in den untersuchten Materialien verschiedene Diffusionskanäle und Bindungszustände der Wasserstoffatome vorhanden sind. Neben den wissenschaftlichen Arbeiten an Laborzellen wurde der MIRHP Prozeß auch in einem industriellen Siebdrucksolarzellenprozeß, basierend auf einem TiO2-Durchfeuerprozeß, erfolgreich integriert. Durch den MIRHP Prozeß konnten in Zusammenarbeit mit Eurosolare auf 100 cm2 multikristallinen Siliziumsolarzellen relative Steigerungen im Wirkungsgrad zwischen 5 und 9% erzielt werden. Aufgrund dieser Ergebnisse ist der MIRHP Prozeß zusammen mit einer konventionellen TiO2 Antireflexionsbeschichtung eine Alternative zu einem SiN PECVD (Plasma Enhanced Chemical Vapor Deposition) Prozeß für die Bulkpassivierung von Industriesolarzellen. Mit dem in dieser Arbeit vorgeschlagenen zweistufigen MIRHP Prozeß kann die MIRHP Passivierungszeit auf 30 min reduziert werden, und ist somit für den industriellen Einsatz in der Photovoltaik interessant. 13 Danksagung Allen, die mich bei meiner Doktorarbeit unterstützt haben, möchte ich danken. Mein besonderer Dank gilt: • meinem Doktorvater Herrn Prof. Dr. E. Bucher für die Aufnahme an seinen Lehrstuhl, wodurch er mir ermöglichte, auf dem interessanten Gebiet der Photovoltaik zu arbeiten. • Herrn Prof. Dr. W. Rehwald für die Übernahme der Zweitkorrektur. • Herrn Priv. Doz. Dr. Gerd Willeke, der mir das aktuelle und interessante Thema der MIRHP Solarzellen Passivierung vorschlug und das Korrekturlesen übernahm.. • Dr. Peter Fath, der mit seinem umfangreichen Wissen über die Siliziumtechnologie wesentlich zum Gelingen meiner Doktorarbeit beigetragen hat. • Steffen Keller und Giso Hahn, für wertvolle Diskussionen bzgl. SR-Messungen und RGS Silizium, sowie für das Korrekturlesen von Teilen der Doktorarbeit. • Dr. Bernd Bitnar für seine PhotoCurrent/Voltage Decay Messungen, für die sehr interessanten physikalischen und nicht physikalischen Einfälle, sowie für die erholsamen Spielabende. • Dr. Kristian Peter für die Zeit und Geduld, wenn beim Cary nichts lief. • Frank Huster, der mir gerade in der Endphase meiner Doktorarbeit viele Aufgaben bzgl. der MIRHP Passivierungsanlage abgenommen hat und ein gutes Händchen bei technischen Problemen der PECVD Anlage zeigte. • Benita von Finckenstein und Arnd Boueke, welche die zeitaufwendige Aufgabe der PECVD Abscheidungen ebenfalls am Ende meiner Doktorandenzeit übernahmen. • Christoph Zechner, der mit seiner positiven Kritik an dem von mir empirisch hergeleiteten Zweistufenmodel der internen Quantenausbeute mich veranlaßte, dieses Model exakt zu berechnen. • Christoph Gerhards, Christoph Marckmann und Rainer Tölle, die mir beim Siebdruckprozeß geholfen haben. • Thomas Pernau, für die Konstanzer LBIC Messungen. • Andreas Tickart und Steffen Scheibenstock für viele wertvolle Computertips. • Manfred Keil, für seine Hilfe beim Zellenprozessieren und bei meßtechnischen Problemen. • Stefan Kühne, ohne den unser Netzwerk nicht funktioniert. • Gisa Kragler für Ellipsometrie-Messungen an den PECVD Silizumnitrid Filmen. • Barbara Terheiden, Wolfgang Jooss, Ralf Kühn und allen noch nicht genannten Silizianern, die auf ihre Weise zum Erfolg unserer Gruppe und meiner Doktorarbeit beigetragen haben. • Said Riazi, Jochen Köhler, Franz Richardt, Manfred Albrecht sowie den nicht mehr am Lehrstuhl arbeitenden Dr. Jan Hendrik Schön, Michael Wendel, Dr. Klaus Friemelt, Dr. Franz Baumgartner, Dr. Christian Kloc, Martin Steiner und allen anderen Nichtsilizianern, die mich bei kleinen und großen Problemen unterstützten. • unserer Sekretärin Frau Schellinger für ihre freundliche und hilfsbereite Art und für ihre Hilfe, wenn wieder einmal das Faxgerät ausgetauscht wurde. • Dr. Hartmut Nussbaumer, der während seiner Beschäftigung bei Eurosolare, für eine schnelle Durchführung der Siebdrucksolarzellenprozesse sorgte. • Ralf Lüdemann, für die Freiburger LBIC Messungen und interessante Diskussionen über den Remotewasserstoffprozeß. • Dr. Jianhua Zhao, für die sehr fruchtbare und unkomplizierte Zusammenarbeit, bei der MIRHP Passivierung der multikristallinen Silizium PERL Zellen. • Dr. Madhu Roy, für die sehr gute Zusammenarbeit mit der Firma Solarex. • Meinen Eltern, die mir durch ihr Vertrauen und ihre finanzielle Unterstützung mein Studium ermöglichten. • und meiner Frau Wiebke für alle außerphysikalische Unterstützung.