Analysis of the silicon solar cells efficiency. Type of doping and level optimization

The theoretical analysis of photovoltaic conversion efficiency of highly effective silicon solar cells (SC) has been performed for n-type and p-type bases. Considered here is the case when the Shockley–Read–Hall recombination in the silicon bulk is determined by the deep level of Fe. It has shown th...

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Дата:	2016
Автори:	Sachenko, A.V., Kostylyov, V.P., Gerasymenko, M.V., Korkishko, R.M., Kulish, M.R., Slipchenko, M.I., Sokolovskyi, I.O., Chernenko, V.V.
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Опубліковано:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2016
Назва видання:	Semiconductor Physics Quantum Electronics & Optoelectronics
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Цитувати:	Analysis of the silicon solar cells efficiency. Type of doping and level optimization / A.V. Sachenko, V.P. Kostylyov, M.V. Gerasymenko, R.M. Korkishko, M.R. Kulish, M.I. Slipchenko, I.O. Sokolovskyi, V.V. Chernenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 1. — С. 67-74. — Бібліогр.: 14 назв. — англ.

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spelling	irk-123456789-1215272017-06-15T03:05:20Z Analysis of the silicon solar cells efficiency. Type of doping and level optimization Sachenko, A.V. Kostylyov, V.P. Gerasymenko, M.V. Korkishko, R.M. Kulish, M.R. Slipchenko, M.I. Sokolovskyi, I.O. Chernenko, V.V. The theoretical analysis of photovoltaic conversion efficiency of highly effective silicon solar cells (SC) has been performed for n-type and p-type bases. Considered here is the case when the Shockley–Read–Hall recombination in the silicon bulk is determined by the deep level of Fe. It has shown that, due to asymmetry of recombination parameters inherent to this level, the photovoltaic conversion efficiency is increased in SC with the n-type base and decreased in SC with the p-type base with the increase in doping. Two approximations for the band-to-band Auger recombination lifetime dependence on the base doping level are considered when performing the analysis. The experimental results are presented for the key characteristics of SC based on a-Si:H–n-Si heterojunctions with intrinsic thin layer (HIT). A comparison between the experimental and calculated values of the HIT cell characteristics has been made. The surface recombination velocity and series resistance are determined from it with a complete coincidence of the experimental and calculated SC parameters’ values. Apart from the key characteristics of SC, surface recombination rate and series resistance were determined from the results of this comparison, in full agreement with the experimental findings. 2016 Article Analysis of the silicon solar cells efficiency. Type of doping and level optimization / A.V. Sachenko, V.P. Kostylyov, M.V. Gerasymenko, R.M. Korkishko, M.R. Kulish, M.I. Slipchenko, I.O. Sokolovskyi, V.V. Chernenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 1. — С. 67-74. — Бібліогр.: 14 назв. — англ. 1560-8034 DOI: 10.15407/spqeo19.01.067 PACS 73.40.-c, 79.20.Fv, 88.40.H-, 88.40.jj http://dspace.nbuv.gov.ua/handle/123456789/121527 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The theoretical analysis of photovoltaic conversion efficiency of highly effective silicon solar cells (SC) has been performed for n-type and p-type bases. Considered here is the case when the Shockley–Read–Hall recombination in the silicon bulk is determined by the deep level of Fe. It has shown that, due to asymmetry of recombination parameters inherent to this level, the photovoltaic conversion efficiency is increased in SC with the n-type base and decreased in SC with the p-type base with the increase in doping. Two approximations for the band-to-band Auger recombination lifetime dependence on the base doping level are considered when performing the analysis. The experimental results are presented for the key characteristics of SC based on a-Si:H–n-Si heterojunctions with intrinsic thin layer (HIT). A comparison between the experimental and calculated values of the HIT cell characteristics has been made. The surface recombination velocity and series resistance are determined from it with a complete coincidence of the experimental and calculated SC parameters’ values. Apart from the key characteristics of SC, surface recombination rate and series resistance were determined from the results of this comparison, in full agreement with the experimental findings.
format	Article
author	Sachenko, A.V. Kostylyov, V.P. Gerasymenko, M.V. Korkishko, R.M. Kulish, M.R. Slipchenko, M.I. Sokolovskyi, I.O. Chernenko, V.V.
spellingShingle	Sachenko, A.V. Kostylyov, V.P. Gerasymenko, M.V. Korkishko, R.M. Kulish, M.R. Slipchenko, M.I. Sokolovskyi, I.O. Chernenko, V.V. Analysis of the silicon solar cells efficiency. Type of doping and level optimization Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Sachenko, A.V. Kostylyov, V.P. Gerasymenko, M.V. Korkishko, R.M. Kulish, M.R. Slipchenko, M.I. Sokolovskyi, I.O. Chernenko, V.V.
author_sort	Sachenko, A.V.
title	Analysis of the silicon solar cells efficiency. Type of doping and level optimization
title_short	Analysis of the silicon solar cells efficiency. Type of doping and level optimization
title_full	Analysis of the silicon solar cells efficiency. Type of doping and level optimization
title_fullStr	Analysis of the silicon solar cells efficiency. Type of doping and level optimization
title_full_unstemmed	Analysis of the silicon solar cells efficiency. Type of doping and level optimization
title_sort	analysis of the silicon solar cells efficiency. type of doping and level optimization
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2016
url	http://dspace.nbuv.gov.ua/handle/123456789/121527
citation_txt	Analysis of the silicon solar cells efficiency. Type of doping and level optimization / A.V. Sachenko, V.P. Kostylyov, M.V. Gerasymenko, R.M. Korkishko, M.R. Kulish, M.I. Slipchenko, I.O. Sokolovskyi, V.V. Chernenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 1. — С. 67-74. — Бібліогр.: 14 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
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fulltext	Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 67 PACS 73.40.-c, 79.20.Fv, 88.40.H-, 88.40.jj Analysis of the silicon solar cells efficiency. Type of doping and level optimization A.V. Sachenko1, V.P. Kostylyov1, M.V. Gerasymenko2, R.M. Korkishko1, M.R. Kulish1, M.I. Slipchenko2, I.O. Sokolovskyi1, V.V. Chernenko1 1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine 41, prospect Nauky, 03028 Kyiv, Ukraine 2Kharkiv National University of Radio Electronics 14, Lenin ave., 61166 Kharkiv, Ukraine Corresponding author e-mail addresses: sach@isp.kiev.ua (A.V. Sachenko), vkost@isp.kiev.ua (V.P. Kostylyov), n.v.gerasimenko@mail.ru (M.V. Gerasymenko), romkin.ua@gmail.com (R.M. Korkishko), n_kulish@yahoo.com (M.R. Kulish), nslip@kture.kharkov.ua (M.I. Slipchenko), i.o.sokolovskyi@gmail.com (I.O. Sokolovskyi), vvch@isp.kiev.ua (V.V. Chernenko) Abstract. The theoretical analysis of photovoltaic conversion efficiency of highly effective silicon solar cells (SC) has been performed for n-type and p-type bases. Considered here is the case when the Shockley–Read–Hall recombination in the silicon bulk is determined by the deep level of Fe. It has shown that, due to asymmetry of recombination parameters inherent to this level, the photovoltaic conversion efficiency is increased in SC with the n-type base and decreased in SC with the p-type base with the increase in doping. Two approximations for the band-to-band Auger recombination lifetime dependence on the base doping level are considered when performing the analysis. The experimental results are presented for the key characteristics of SC based on a-Si:H–n-Si heterojunctions with intrinsic thin layer (HIT). A comparison between the experimental and calculated values of the HIT cell characteristics has been made. The surface recombination velocity and series resistance are determined from it with a complete coincidence of the experimental and calculated SC parameters’ values. Apart from the key characteristics of SC, surface recombination rate and series resistance were determined from the results of this comparison, in full agreement with the experimental findings. Keywords: silicon solar cell, heterojunction, doping level, Shockley–Read–Hall recombination, Auger recombination. Manuscript received 12.11.15; revised version received 26.01.16; accepted for publication 16.03.16; published online 08.04.16. 1. Introduction When analyzing the dependence of the silicon solar cells (SC) on the base doping level, the assumption is commonly used that the deep levels close in Et energy to the middle of the band gap with close electron- and hole- capture cross-sections are responsible for the Shockley– Read–Hall (SRH) recombination. Specifically, the Au level meets these criteria (Hangleiter, 1987). At the same time, the SRH recombination can be determined by the energy levels which do not agree with the middle of the band gap and electrons σn and holes σp cross-sections differ essentially. The level of Fe is one of such levels [2, 3]. According to [2], it is characterized by the values Ec – Et = 0.774 eV (Ec is the conduction band edge), σn = 5·10–14 cm2, σp = 7·10–17 cm2. In this case, the SRH lifetime value τSRH can significantly depend both on the SC base doping and on the excess electron-hole pairs’ Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 68 concentration Δn in the base. These dependences can significantly affect the minority-carriers effective bulk lifetime τeff determined by the relation of different recombination mechanisms, including the SRH recombination, radiative recombination and band-to- band Auger recombination. The analysis of the photovoltaic conversion efficiency η is carried out in this research for highly effective silicon SC and HIT1 (heterojunction with intrinsic thin layer) SC, depending on the base type and doping level for the case when the SRH recombination lifetime is determined by the Fe level. Calculation results are compared to the experimental values of the photovoltaic conversion efficiency η, open-circuit voltage VOC, fill-factor FF and some other parameters of SC based on a-Si:H–n-Si SC. A simple approach is used in the analysis, which makes it possible to model characteristics of SC produced on the crystalline base [4]. Its special feature is the fact that one of the main characteristics of SC is the short-circuit current density JSC is found experimentally and the remaining SC parameters are calculated. This essentially simplifies the analysis of the experimental results, which can serve as a basis for optimization of such characteristics of the HIT cells as the doping level of the base Nd (Na) under the given SRH lifetime τSRH value, surface recombination velocity S0 and Sd on the SC frontal and rear surfaces and series resistance RS. 2. Analysis of τSRH dependence on the base doping level for the cases of the base area of p- and n-type Using the approach developed in [4], let us write the expressions for τSRH value, when the recombination time determines the level of Fe for the SC base of p- and n- type, respectively [5]: ( ) ( ) ( )nN npNnn a anpp SRH Δ+ Δ++τ+Δ+τ ≡τ 1010 , (1) ( ) ( ) ( )nN npnnN d ndpn SRH Δ+ Δ+τ+Δ++τ ≅τ 1010 , (2) where p SRHτ and n SRHτ are the SRH lifetimes for the p- and n-type bases, ( ) s1019.1 19 0 −−⋅=τ tp N , ( ) s105.8 17 0 −−⋅=τ tn N , n1 and p1 are concentrations of electrons and holes for the cases when the position of the recombination level coincides with the Fermi level, and ( )327.8exp)(1 −= Tnn i , ( )327.8exp)(1 Tnp i= , ni (T) is the intrinsic carriers concentration in silicon, T = 25 °С. Numerical parameters for τp0, τn0, n1 and p1 for calculation are taken from [2]. We note that, in the expressions (1) and (2), it is implicitly assumed that the excess densities of electrons and holes are equal. This condition holds, if these 1 HIT (heterojunction with intrinsic thin layer) is a trademark of Panasonic Group densities notably exceed the concentration of recom- bination levels. In the case considered here, this is indeed the case, as will be discussed below. Hereinafter, the case of Si with high effective bulk lifetime values will be considered, when the minority charge carriers diffusion length is significantly higher than the SC base thickness d throughout the doping level range, i.e. the effective diffusion length Leff = ( ) dD pn effpn >>τ 2/1)( )( . Here )( pnD and )( pn effτ are the diffusion coefficient and effective lifetime for electrons (holes). In this case, the excess minority charge carriers concentration Δn is constant along the base. Fig. 1 demonstrates dependences of p SRHτ and n SRHτ on the base doping level for two Δn values: 5·1014 and 5·1015 cm–3. Note that the first value for the base doping levels less or equal to 1015 cm–3 is typical for the silicon SC operating at AM1.5 under the maximum power take-off conditions, and the second value is typical for the case of the silicon SC operating in the open circuit mode. When calculating the τSRH value, the Nt value was supposed to be equal to 6·1011 cm–3. Thus, the inequality Δn >> Nt holds well for SC considered here. Fig. 1 shows that the p SRHτ value decreases strongly (more than two orders of magnitude) with the base doping level increase, and strongly depends on the Δn value. At the same time, the n SRHτ value practically does not depend either on the base doping or on the Δn value. With the concentration of the iron recombination centres equal to 6·1011 cm–3 chosen for calculations, it is equal to n SRHτ = 1.4 ms and concides with the measured value of the bulk lifetime in the n-type material with the doping level 1.6·1015 cm–3. Such a lifetime is typical for high quality silicon. This result is close to that obtained in the work [6], which shows that the SRH lifetime as a function of the doping level is practically constant at 315 cm10 −≥dN . 3. Fundamental relations determining the silicon SC efficiency Using the approach developed in [4], let us write the relations determining the photovoltaic conversion efficiency of the highly effective silicon SC and HIT SC η. Let us note in the beginning that, in addition to the dLeff >> inequality, the ( )adOC NNn ≥Δ condition is usually implemented, where OCnΔ is the excess electron-hole pairs concentration in the base for the open circuit case. So, the expressions for the open circuit voltage VOC in the p- and n-type base cases can be written [7], respectively, as ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Δ ++⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Δ ≅ d OCOC OC N n q kT p n q kTV 1lnln 0 , (3) Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 69 ( )( )( ) n npnnpnn R Δ ⋅+Δ⋅+⋅+⋅Δ+Δ+ = −−−− 158.02765.0 0 2565.0 0 24 00 Auger 105.9103106108.1 . (8) ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Δ ++⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Δ ≅ a OCOC OC N n q kT n n q kTV 1lnln 0 , (4) where k is the Boltzmann constant, T – SC temperature, q – elementary charge, ( ) di NTnp 2 0 = – equilibrium concentration of holes in the n-type base, and ai NTnn )(2 0 = – equilibrium concentration of electrons in the p-type base. For ( )adOC NNn ≥Δ , the open-circuit voltage VOC is higher than VOC for the standard case, when ( )adOC NNn <Δ . The generation-recombination balance equation in the case of the open-circuit mode, when implementing inequality Leff >> d, can be written as OC b SCSC nSdAqI Δ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + τ = . (5) Here ISC is the short-circuit current, ASC – surface area of SC, ( )[ ] 1 Auger 1 SRH )()( −− +Δ++Δτ=τ RnNNAn OCadOCb is the bulk lifetime, A ≈ 6.3·10–15 cm3/s [8] is the radiative recombination coefficient in silicon, S = S0 + Sd. The rate (inverse time) of the band-to-band Auger recombination (RAuger) in the n-type silicon is determined using the expression ( ) ( ) OCOCdpOCdn nnNCnNCR ΔΔ++Δ+= 2 Auger , (6) where ( ) scm105.2108.2 6 5.0 22 31 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ+ ⋅ +⋅= − − OCd n nN C , Cp =10–31 cm6/s [9, 10]. The second term in the expression for Cn takes into account the many-electron effects, namely the effect of spatial correlation for distribution of two electrons and one hole involved in the act of Auger recombination, conditioned by the Coulomb interaction [9]. In the p-type silicon ( ) ( ) OCOCanOCap nnNCnNCR ΔΔ++Δ+≡ 2 Auger and scm105.2108.2 6 5.0 22 31 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ ⋅ +⋅= − − OC n n C . (7) Note that the expressions (6) and (7) for Cn are approximate. A choice of this expression was discussed in more details in [10]. It was demonstrated that various dependences were obtained in different experiments. The analysis of numerous experimental data, obtained in the case of silicon, makes it possible to derive the empirical expression fully describing the dependence of RAuger on the equilibrium concentrations of electrons n0 and holes p0 in the SC base, as well as on the con- centration of excess electron-hole pairs Δn at Т = 300 K [11]: 1013 1014 1015 1016 1017 10-6 10-5 10-4 10-3 τ S R H , s Nd (Na) , cm-3 1 2 3 4 Fig. 1. SRH lifetime versus the base doping level: curves 1 and 2 are for the p-type base and curves 3 and 4 are for the n-type base. Curves 1 and 3 calculated with Δn = 5 1015 cm–3 and curves 2 and 4 calculated with Δn = 5 1014 cm–3. The latter term in the rightmost parentheses (8) takes into account radiative recombination. In the work [11] based on the analysis of quite a number of experimental data for silicon, a more precise [than (5) and (6)] empirical formula was proposed to completely describe RAuger as a function of equilibrium electron and hole densities, n0 and p0, in the SC base region, as well as on the density of excess electron-hole pairs Δn at Т = 300 K. Using the experimental data [11] and based on the expressions (5) and (6), we have obtained the empirical expression for SC with an n-type base: ( ) ( )(([ ( ) ) )].103.6101.3 105.1 155.0 0 22 0 30 0 −− − ⋅+Δ+⋅+ +Δ+⋅Δ+= nn nnnnRAuger (9) It should be noted that discrepancy between Eqs (8) and (9) for based doping level 1015 cm–3≤ n0 ≤ 4·1016 cm– 3 is less than 6% (see Fig. 2). Shown in Fig. 2 the effective lifetime τb as a function of the doping level Nd obtained either from (8) and (9) [in combination with (5)], taking into account all the recombination mechanisms mentioned above. We note that within the relevant range of the doping levels, they by not more than 6%. Equations (3) and (4) are the quadratic equations in regard to the ΔnOC value, and their solution can be written as ( ) .1exp 4 )( 2 )( 2 2 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ −⎟ ⎠ ⎞ ⎜ ⎝ ⎛++ +−=Δ kT qV n NN NN n OC i ad ad OC (10) Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 70 1015 1016 1017 0.0 2.0x10-4 4.0x10-4 6.0x10-4 8.0x10-4 1.0x10-3 τ b , s Nd , cm-3 1 2 3 4 Fig. 2. Dependence of the effective lifetime in the bulk base on the n-type base doping level of SC obtained using (8) (curves 1 and 3) and (9) (curves 2 and 4). The parameters used are: τSR = 1.4 ms, ISC = 142.7 mА, S = 12 cm/s (curves 1 and 2) and 1 cm/s (curves 3 and 4). To calculate the photovoltaic conversion efficiency, a theoretical expression for SC current-voltage characteristic is needed. With this aim in view, we proceed as follows. Let us replace VOC in (10) by the applied forward bias V value. Besides, it is also necessary to take into account the voltage drop on the series resistance Rs. This operation makes it possible to determine Δn(V): ( ) ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ++ +−=Δ 1exp 4 )( 2 )()( 2 2 kT IRVqnNN NNVn s i ad ad (11) where I is the current. In what follows, let us generalize equation (5), correct for the open circuit case, for the V < VOC case, i.e. for nonzero current. Then, this equation can be written as: )()( VIIVI recSC −= , (12) where )()( VnSdqAVI b SCrec Δ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + τ = , (13) and the τb value can be found using (5) (with the replacement of ΔnOC by Δn(V). The Vm value is found from the maximum power take-off condition 0/))(( =dVVVJd , and its substitution in (13) makes it possible to determine the value of Im. As a result, we obtain the photoconversion power: mmVIP = . (14) For the fill-factor, the standard expression can be used: OCSC mm VI VIFF = . (15) The photoconversion efficiency is also given by the known formula: SSC mm PA VI =η , (16) where PS is the incident solar radiation power density. 4. Comparative analysis of the obtained relations for the SC base of n- and p-types When building theoretical dependences for charac- teristics of silicon SC with the base of the n-type, the expressions for RAuger defined both by the relation (9) and the expression (8) were used. The following figures were built using (9) and (8) for SC with the n-type base and (5), (7) in the case of SC with p-type base. Fig. 3 demonstrates the theoretical dependence for the open-circuit voltage on the base doping level for the p- and n-type bases. The same parameters values determining the SRH lifetime were used for plotting the curves in Figs. 3 and 1. The values of the surface recombination rate S and short-circuit current density JSC varied when calculating the curves 1–4. As Fig. 3 suggests, the VOC values coincide both for n- and p-type bases when the doping levels are low ( 315 cm10 −≤ ) (compare 1, 2 and 3, 4 curves calculated with the same S and JSC values). It should be noted that VOC values do not depend on the doping level, if ( )ad NNn >>Δ 0 inequality is satisfied. With 315 cm10 −≥dN , the VOC values in SC with the n-type base increase, subsequently they reach a maximum and begin to decrease. In this case, the VOC value decline is caused by the prevalence of the Auger band-to-band recombination. The VOC (Na) dependences in SC with p-type base behave quite differently. With 314 cm10 −≥aN the VOC values initially decrease slowly, and with 315 cm105 −⋅>aN the rate of VOC decline increases significantly. In this case, the VOC (Na) decline is associated with the SRH lifetime decrease. Strictly speaking, in the framework of the used approximations the calculated dependences VOC (Na) will be sufficiently accurate, with the inaccuracy not exceeding 2%, only with the fulfilment of the L > 2d condition, which is implemented with 315 cm109 −⋅<aN . At higher doping levels, not all of electron-hole pairs generated in the SC base will reach the p-n junction, which will primarily result in the short-circuit current ISC reduction due to the reduction of the current collection coefficient. In our calculations, we use the experimental value of the short-circuit current and, furthermore, we consider it as independent of the doping level. Therefore, the inequality dL 2≥ is also necessary so that the quantum yield ISC does not decrease with increasing the doping level. Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 71 1014 1015 1016 1017 0.65 0.70 0.75 V O C , V Nd , cm-3 1 2 3 4 Fig. 3. Dependences of the open-circuit voltage on the n-type base doping level (curves 1 and 3) and p-type base doping level (curves 2 and 4). Parameters used for calculation: d = 300 μm, τSR = 1.4 ms, Т = 298 K. Curves 1 and 3 calculated with S = 12 cm/s, JSC = 36 mA/cm2 and curves 2 and 4 calculated with S = 1 cm/s, JSC =39.5 mA/cm2. 1014 1015 1016 1017 0.40 0.45 0.50 0.55 0.60 0.65 V m , V Nd , cm-3 1 2 3 4 Fig. 4. Dependence of voltage on the base doping level in the mode of the maximum power take off: curves 1 and 3 correspond to the n-type base, curves 2 and 4 correspond to the p-type base. RS = 0.21 Ohm. Fig. 4 demonstrates the theoretical dependences of voltage Vm on the p- and n-type base doping level in the mode of the maximum power take off. The same parameters values were used for construction of Fig. 4 as for Fig. 3. As it was evidenced by the comparison between Figs. 3 and 4, behavior of VOC and Vm depending on the base doping level is very similar in both cases with the only difference that for the dependences ( )( )adm NNV the Vm value region of independence on Nd (Na) and the point of the Vm (Na) minimum are shifted to the region of lower doping levels’ values. Thus, the region of independence of Vm on Nd (Na) is realized when ( ) 314 cm10 −≤ad NN , and the point of the Vm minimum is realized when 315 cm10 −≈aN . It should be noted that, in the case of p-type base, the L > 2d condition, necessary for the Vm correct calculation, is fulfilled if 315 cm10 −≤aN . Fig. 5 demonstrates the theoretical dependences of the photovoltaic conversion efficiency η on the doping level of the p- and n-type bases. The same parameter values were used for construction of Fig. 5 as for Figs. 3 and 4. As Fig. 5 suggests, the dependences of photo- voltaic conversion efficiency η on the base doping level repeated the dependence Vm on Nd (Na) (see Fig. 4) with a certain scaling. The essential difference of these dependences for SC with the base of the n- and p-types is that in SC with the n-type base the η values grow with the growth of the base doping level and in solar cells with p-type base the η values decrease. As already mentioned above, the decrease in η(Na) with the increase in Na in SC with the p-type base is associated with a decrease in the SRH lifetime. Fig. 5 shows that, for the typical doping levels of SC bases (1…4)·1015 cm–3, the efficiency of SC with the n-type base significantly exceeds the efficiency of SC with the p-type base. The increase in the η value in SC with the p-type base can be achieved by reducing the concentration of the recombination centres of iron. Fig. 6 shows the calculated dependence of the photovoltaic efficiency η on the base doping level for the n- and p-type bases for the case where only the base thickness varies. The calculation was performed for the case when the base thickness d was equal to 100, 200 and 300 μm. As can be seen from Fig. 6, the lower the thickness of the base, the greater the efficiency η. This increase is associated with the increase in the open- circuit voltage VOC, more precisely, in the voltage in the mode of the maximum power take off Vm due to the bulk recombination reduction. The doping levels’ values, with which the dependences η(Na) are broken in the case of SC with the p-type base, correspond to the ( ) dNL aeff 2≈ conditions. As Fig. 6 suggests, the lower the base thickness d, the higher doping levels required for the ( ) dNL aeff 2≥ condition fulfilment. 1014 1015 1016 1017 10 15 20 25 η , % Nd , cm-3 1 2 3 4 Fig. 5. Dependence of the photovoltaic conversion efficiency on the doping level base: curves 1 and 3 correspond to the n-type base, and curves 2 and 4 correspond to the p-type base. The same parameter values were used for construction of Fig. 5 as for Fig. 3. RS = 0.21 Ohm. Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 72 1014 1015 1016 1017 15 20 25 6 5 η , % Nd , cm-3 1 2 3 4 Fig. 6. Photovoltaic conversion efficiency dependence on the base doping level Nd (Na) with different base thicknesses: curves 1, 3, 5 are plotted for the n-type base, and curves 2, 4, 6 are plotted for the p-type base. The following parameters were used in construction of the plot: JSC = 39.5 mA/cm2, S = 1 cm/s, RS = 0.21 Ohm. The base thickness d was equal to 300 μm (1, 2), 200 μm (3, 4), 100 μm (5, 6). The rest parameters were the same as those used in Fig. 3 curves plotting. 5. Comparison of the experimental and calculated a-Si:H–n-Si HIT cells parameters’ values Experimental samples HIT SC were made at Institute for Solar Energy Research Hamelin (ISFH, Germany) with participation of one of this paper authors (M.V. Ge- rasimenko). The best sample with the efficiency 19.4%, that is very close to the calculated values, was made on (100)-oriented and on textured Si wafer substrates. After a-Si:H deposition, we perform quasi-steady state photoconductance decay measurements [12] and obtain the lifetime data equal to 1.4 ms. Short-circuit current ISC was measured under illumination with a flash light while the current-voltage curves are measured under LED-array illumination (λ = 950 nm) with an intensity that produces the same ISC. In what follows, let us compare the calculated and experimental characteristics of HIT solar cells with those obtained in the experiment in SC with the base of n-type: JSC = 36.03 mA/cm2, VOC = 0.703 V, FF = 0.77, η = 19.4%, SSC = 3.96 cm2 for the case when the SC base region parameters were equal to the following values: Nd ≈ 1.6·1015 cm–3, d ≈ 300 μm, τSR ≈ 1.4 ms. HIT solar cell manufacturing technology included operations of cleaning of crystalline silicon wafer sur- face, surfaces texturing (pyramidal surface relief pat- terning), acid underetching of the surface layer, putting of optimum thickness layer of intrinsic amorphous hydrogenated silicon (i) a-Si:H on both wafer surfaces. Then, n-cSi / (n+) a-Si:H isotype heterojunction was formed on the back side surface and n-cSi / (p+) a-Si:H anisotype heterojunction was formed on the front side surface. The transparent conductive layers of indium and tin oxides mixture were deposited on both surfaces, and then the low-temperature annealing was realized to reduce the series resistance. The contacts deposition was the finishing operation: a solid contact was deposited on the back side and the net-like contact was deposited on the front side. The HIT solar cell area was about 4 cm2. This technology was described in detail in the publication [13]. To fabricate SC, we used n-type silicon obtained using zone melting technique. Its resistivity at Т = 300 K was 3 Ohm cm. The doping level, as determined from the capacitance-voltage profiling at inverse bias, is Nd = 1.6·1015 cm–3 with 15% inaccuracy. Let us compare next the calculated and experimental characteristics of HIT solar cells with those obtained in the experiment in SC with the base of n-type: ISC = 142.7 mA, VOC = 0.703 V, FF = 0.77, η = 19.4%, SSC = 3.96 cm2 for the case when the SC base region parameters were equal to the following values: Nd ≈ 1.6·1015 cm–3, d ≈ 300 μm, τSR ≈ 1.4 ms. The short- circuit current density was JSC = 36.03 mA/cm2. Fig. 7 shows the current-voltage curve of SC studied here. The theoretical current-voltage curve was obtained using the expressions (12) and (13). Its good agreement with the experimental values confirms the correctness of our model. To calculate RAuger, the relation (8) was used when composing Table 1, and the relation (9) was used when composing Table 2, respectively. The first line of Tables 1 and 2 shows the calculated characteristics of the HIT solar cells and base region parameters obtained as a result of calculation by using formulas given above. As can be seen from a comparison of the calculated and experimental parameters given in the first lines of Tables 1 and 2, they are identical, if S = 12 cm/s, and RS = 0.21 Ohm. Note that the calculated value of the fill- factor FF for current-voltage characteristic in this case is 0.77, and it coincides well with the experimental value. 0 200 400 600 800 0 50 100 150 I, m A V, mV Fig. 7. The experimental (symbols) and theoretical (line) current-voltage curves of an illuminated HIT element. Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 73 For the moderate levels of the base doping (~1.6·1015 cm–3) the HIT solar cell parameters, given in the second line of Tables 1 and 2, practically coincide. The calculated SC parameters were obtained using the following values: S = 1 cm/s, JSC = 39.5 mA/cm2 [4, 14]. Also, the parameters in the third and the fourth rows of the Tables 1 and 2, obtained using (8) and (9), are somewhat different. However, as seen from these tables, the photoconversion efficiency increases with doping level, whereas the parameters obtained using (8) and (9) differ by not more than 1%. Thus, as seen from our analysis, the base doping level should be optimized in order to achieve the highest efficiency at the fixed values of the remaining parameters. 6. Conclusions The theoretical analysis of high-efficient silicon SC efficiency is carried out depending on the type and level of doping of the base for the case when Fe level induces the SRH recombination. It has been shown that the photovoltaic conversion efficiency in the case of n-type base increases with increasing the base doping level, reaches its maximum and begins to decrease. This decrease is determined by the band-to-band Auger recombination predominance. In the case of SC with the p-type base, the photovoltaic conversion efficiency decreases with the base doping level increase. The obtained result is asso- ciated with a strong asymmetry of Fe level parameters, due to it the strong decrease in the τSRH value occurs in the p-type samples in the field of the doping levels’ values range characteristic for the Si solar cells. The calculated and experimental values of characteristics of HIT SC based on a-Si:H–n-Si are compared. The effective surface recombination velocity and serial resistance values are defined from the comparison; complete coincidence is achieved between theory and practice. It is shown that the base doping level is one of the most important parameters of the HIT solar cells. This parameter is subject to optimization and the use of its optimal values for SC of the order of (2–4)·1016 cm–3 with the n-type base makes it possible to increase significantly the η value. References 1. A. Hangleiter, Nonradiative recombination via deep impurity levels in silicon: Experiment // Phys. Rev. B, 35(17), p. 9149-9160 (1987). DOI: 10.1103/PhysRevB.35.9149. 2. L.G. Geerings and D. Macdonald, Base doping and recombination activity of impurities in crystalline silicon solar cells // Progr. Photovolt: Res. Appl. 12(4), p. 309-316 (2004). DOI: 10.1002/pip.546. 3. B.L. Sopori, L. Jastrzebski, T. Tan, A comparison of gettering in single- and multicrystalline silicon for solar cells // 25th IEEE Photovoltaic Specialists Conference, 1996, p. 625-628. DOI: 10.1109/ PVSC.1996.564206. 4. A.V. Sachenko, A.I. Shkrebtyi, R.M. Korkishko, V.P. Kostylyov, N.R. Kulish, I.O. Sokolovskyi, Features of photoconversion in highly efficient silicon solar cells // Semiconductors, 49(2), p. 264- 269 (2015). DOI: 10.1134/S1063782615020189. Table 1. The HIT SC parameters obtained using (8). Sample Nd, сm–3 d, μm τSRH, ms exp SCJ , mA/сm2 VOC, mV η, % FF, % S, сm/s RS, Ohm n-type 1.6·1015 300 1.4 36.03 704 19.4 76.6 12 0.21 n-type 1.6·1015 300 1.4 39.5 719 21.8 76.6 1 0.21 n-type 4·1016 300 1.4 36.03 710 21.0 82.1 12 0.21 n-type 2·1016 300 1.4 39.5 719 23.2 81.8 1 0.21 Table 2. The HIT SC parameters obtained using (9). Sample Nd, сm–3 d, μm τSRH, ms exp SCJ , mA/сm2 VOC, mV η, % FF, % S, сm/s RS, Ohm n-type 1.6·1015 300 1.4 36.03 704 19.4 76.5 12 0.21 n-type 1.6·1015 300 1.4 39.5 719 21.7 76.5 1 0.21 n-type 4·1016 300 1.4 36.03 709 20.7 81.0 12 0.21 n-type 2·1016 300 1.4 39.5 719 22.9 80.8 1 0.21 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 67-74. doi: 10.15407/spqeo19.01.067 © 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 74 5. J.S. Blakemore, Semiconductor Statistics. Pergamon Press, Oxford, 1962. 6. A. Richter, S.W. Glunz, F. Werner, J. Schmidt, A. Cuevas, Improved quantitative description of Auger recombination in crystalline silicon // Phys. Rev. B, 86, 165202 (2012). DOI: 10.1103/ PhysRevB.86.165202. 7. A.P. Gorban, A.V. Sachenko, V.P. Kostylyov et al., Effect of excitons on photoconversion efficiency in the p+-n-n+- and n+-p-p+-structures based on single- crystalline silicon // Semiconductor Physics, Quantum Electronics and Optoelectronics, 3(3), p. 322-329 (2000). 8. A.V. Sachenko, A.P. Gorban, V.P. Kostylyov, I.O. Sokolovskyi, The radiative recombination coefficient and the internal quantum yield of electroluminescence in silicon // Semiconductors, 40(8), p. 884-889 (2006). DOI: 10.1134/ S1063782606080045. 9. A. Hangleiter, and R. Häcker, Enhancement of band-to-band Auger recombination by electron- hole correlations // Phys. Rev. Lett. 65(2), p. 215- 218 (1990). DOI: 10.1103/PhysRevLett.65.215. 10. A.V. Sachenko, A.P. Gorban, V.P. Kostylyov, I.O. Sokolovskyi, Quadratic recombination in silicon and its influence on the bulk lifetime // Semiconductors, 41(3), p. 281-284 (2007). DOI: 10.1134/S1063782607030074. 11. M.J. Kerr and A. Cuevas, General parameterization of Auger recombination in crystalline silicon // J. Appl. Phys. 91(4), p. 2473-2480 (2002). DOI: 10.1063/1.1432476. 12. R.A. Sinton, A. Cuevas, and M. Stuckings, Quasi- steady-state photoconductance, a new method for solar cell material and device characterization // 25th IEEE Photovoltaic Specialists Conf., 1996, p. 457-460. DOI: 10.1109/PVSC.1996.564042. 13. R. Gogolin, R. Ferre, M. Turcu, N.-P. Harder, Silicon heterojunction solar cells: Influence of H2-dilution on cell performance // Solar Energy Materials & Solar Cells, 106, p. 47-50 (2012). DOI: 10.1016/j.solmat.2012.06.001. 14. A. Janо, S. Tohoda, K. Matsuyama et al., 24.7 record efficiency hit solar cell on thin silicon wafer // 28th European Photovoltaic Solar Energy Conference and Exhibition, 2013, p. 1846-1848. DOI: 10.4229/28thEUPVSEC2013-2AO.2.5.

Analysis of the silicon solar cells efficiency. Type of doping and level optimization

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