J. Cent. South Univ. (2016) 23: 598-603

DOI: 10.1007/s11771-016-3106-0

An analytical model to explore open-circuit voltage of a-Si:H/c-Si heterojunction solar cells

ZHONG Chun-liang(钟春良)^{1, 2}, GENG Kui-wei(耿魁伟)², LUO Lan-e(罗兰娥)¹, YANG Di-wu(杨迪武)¹

1. Department of Electronics Science and Information Engineering,

Hunan University of Technology, Zhuzhou 412007, China;

2. school of Electronics and Information Engineering, South China University of Technology,Guangzhou 510640, China

 Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: The effect of the parameters on the open-circuit voltage, V_oc of a-Si:H/c-Si heterojunction solar cells was explored by an analytical model. The analytical results show that V_OC increases linearly with the logarithm of illumination intensity under usual illumination. There are two critical values of the interface state density (D_it) for the open-circuit voltage (V_OC), D_it^crit,1 and D_it^crit,2 (a few 10¹⁰ cm^-2·eV^-1). V_OC decreases remarkably when D_it is higher than D_it^crit,1. To achieve high V_OC, the interface states should reduce down to a few 10¹⁰ cm^-2·eV^-1. Due to the difference between the effective density of states in the conduction and valence band edges of c-Si, the open-circuit voltage of a-Si:H/c-Si heterojunction cells fabricated on n-type c-Si wafers is about 22 mV higher than that fabricated on p-type c-Si wafers at the same case. V_OC decreases with decreasing the a-Si:H doping concentration at low doping level since the electric field over the c-Si depletion region is reduced at low doping level. Therefore, the a-Si:H layer should be doped higher than a critical value of 5×10¹⁸ cm^-3 to achieve high V_OC.

Key words: solar cells; a-Si:H/c-Si heterojunctions; open-circuit voltage

1 Introduction

Amorphous hydrogenated silicon and crystalline silicon (a-Si:H/c-Si) heterojunctions are of great interest for photovoltaic applications due to the high conversion efficiencies achieved so far up to 23% and the possibility of complete fabrication at low temperature process [1]. The open-circuit voltage V_OC is a key parameter for the properties of solar cells. V_OC is affected by many parameters of solar cells, such as interface states and the doping level of the a-Si:H layer. In particular, the suppression of carrier recombination at the a-Si:H/c-Si heterojunction interface is crucial to improve the open-circuit voltage. Surface passivations [2-5], such as using hydrofluoric acid-based solutions, had been proposed to reduce interface recombination in the past two decades. In the recent decade, the use of a thin intrinsic a-Si:H buffer layer between the emitter and the wafer was proposed to decrease interface states [6-8]. The passivation of c-Si surfaces by an intrinsic a-Si:H ((i) a-Si:H) layer leads to very low effective surface recombination velocities [9]. Sanyo used the passivation property of (i) a-Si:H in their so-called HIT structure solar cell consisting of (p⁺) a-Si:H/(i) a-Si:H/(n) c-Si/(i) a-Si:H/(n⁺) a-Si:H. high open-circuit voltage of more than 720 mV was achieved with conversion efficiencies higher than 23.0%. It is usually assumed that interface states should reduce down to very low levels in order to achieve high V_OC as well as high conversion efficiency.

Effect of other parameters on the open-circuit voltage, such as the doping concentration of a-Si:H layer and the illumination intensity, was widely investigated by experiments and simulations [10-12]. V_OC decreases with decreasing the doping level of the a-Si:H layer in Ref. [11]. However, the quantitative relation between the open circuit voltage and parameters is not clear, and needs to further study. Furthermore, the effect of some other parameters on the open-circuit voltage of a-Si:H/c-Si heterojunction solar cells is obscure. V_OC is different from the polarity of the c-Si wafer type [13-15]. HIT solar cells fabricated on n-type c-Si wafers achieve V_OC higher than 720 mV [1], while the one on p-type c-Si wafers is about 680 mV. And a-Si:H/c-Si heterojunction solar cells without the (i) a-Si:H layer fabricated on n-type c-Si wafers achieved V_OC of about 640 mV whereas on p-type c-Si wafers was about 629 mV [16]. However, higher V_OC of a-Si:H/c-Si heterojunction solar cells fabricated on p-type c-Si wafers with higher efficiency was found [17-18]. It seems to be contradictory. Therefore, it is indispensible to further investigate the observed effect, especially combining with an analytical model of the open-circuit voltage for a-Si:H/c-Si heterojunction solar cells. Recently, an analytical model of the open-circuit voltage for silicon heterojunction solar cells is derived by integrating the equation of the electron current density at the depletion region and solving the excess density at c-Si under illumination and open-circuit [19]. In this work, the analytical model of the open circuit voltage was applied to various cases, such as the interface state intensity, the polarity of the c-Si wafer type and the a-Si:H doping concentration to quantitatively explore effect of the parameters on the open- circuit voltage.

2 Experimental and simulation details

To explore effect of the parameters on the open- circuit voltage of a-Si:H/c-Si heterojunction solar cells, a set of simulations were performed, and (n⁺) a-Si:H/(p) c-Si heterojunction solar cells were fabricated. Heterojunction solar cells were fabricated by PECVD deposition of n-type a-Si:H layer onto p-type crystalline Si substrate (FZ, 1-5 Ω·cm, (111), 300 μm) with back surface field at a substrate temperature of 200 °C. The thickness of the (n⁺) a-Si:H emitter was about 10 nm. Before the thin film deposition, the c-Si wafers were prepared by removing the native oxide using a wet chemical etching procedure (HF diluted at 5% in water). Contact to the a-Si:H emitter was made by a 80 nm thick ITO deposited by magnetron sputtering. Evaporated aluminium was used for the grid and rear contacts. I-V characteristics were measured under various illumination intensities at 300 K.

A set of simulations were performed using the AFORS-HET v.2.2 program [20]. We changed D_it in the range of 1×10⁹ -4×10¹² cm^-2·eV^-1 and N_{D2 in the range of 1×10}¹⁸-2×10¹⁹ cm^-3. The density of gap states (DOS) was adopted for a-Si:H. It consisted of two exponential band tails with characteristic energies of 0.036 eV and 0.05 eV for the conduction and valence band, respectively, and with a pre-exponential factor of 1×10²¹ cm^-3·eV^-1, and two Gaussian deep defect distributions of donor and acceptor natures being located at 0.6 eV and 0.7 eV above the maximum valence band, respectively, with a maximum value of 2.4×10¹⁹ cm^-3·eV^-1 and a standard deviation of 0.15 eV [21]. The DOS at the Fermi level was equal to 10¹⁹ cm^-3·eV^-1. The interface is described by introducing a very thin defective c-Si interface layer between a-Si:H and c-Si. The defect distribution in this interface layer is taken as constant through the band gap, assuming donor/acceptor-like defects in the lower/upper part of the band gap. These material parameters of the c-Si and a-Si:H layers are given in Table 1 for the numerical simulations. All the results presented in this work from numerical simulation were obtained at 300 K under AM1.5 illumination.

Table 1 Main parameters of a-Si:H/c-Si heterojunction layers used in simulations

3 Results and discussion

3.1 Analytical model of open-circuit voltage

By integrating the equation of the electron current density at the depletion region and combining with the band diagram of (n⁺) a-Si:H/(p) c-Si heterojunctions at equilibrium and under illumination and open-circuit shown in Fig. 1, an analytical model of the open circuit voltage for (n⁺) a-Si:H/(p) c-Si heterojunction solar cells is given by [19]

                  (1)

where β=kT/q, E_g1 is the band gap of c-Si; N_c1 is the effective density of states in the conduction band edge of c-Si; n_p0 and n_n0 are the free electron densities at neutral  regions of the c-Si at the thermal equilibrium; △n(x_p) is the excess of the carriers at the boundary of the c-Si depletion region (x=x_p); and δ_p1 is the activation energy of p-type c-Si wafers, which can be deduced from the doping impurity concentration of the substrate, N_A1. Deduced from Eq. (1), V_OC is related with △n(x_p). By solving the hole continuity equation under illumination and open circuit, the excess electron density at x=x_p under a low-injection condition is given by [22]

                       (2)

where △n=gτ_eff (g is the average photogeneration of the electron-hole pairs in c-Si; τ_eff is the effective lifetime of the excess carries); the interface recombination velocity for holes is S_p=C_pD_it; the diffusion length of holes is L_p=(D_pτ_eff)^1/2; C_p is the capture rate coefficient; and D_p is the hole diffusion constant. Substituting Eq. (2) into Eq.(1) and neglecting n_p0 (), the open-circuit voltage of (n) a-Si:H/(p) c-Si heterojunction solar cells is given by

       (3)

Similarly, the open-circuit voltage of (p) a-Si:H/(n) c-Si heterojunction solar cells is given by

                (4)

where δ_n1 is the activation energy of n-type c-Si wafers; S_n is the interface recombination velocity for electrons; L_n is the diffusion length of electrons; and N_V1 is the effective density of states in the valence band edge of c-Si.

Fig. 1 Energy band diagram of (n) a-Si:H/(p) c-Si heterojunctions at equilibrium (black lines) and under illumination and open circuit (blue lines) (where V_D1 and V_D2 are the diffusion potentials on c-Si and a-Si:H layers, respectively; and V_OC1 and V_OC2 are photogenerated potentials on the c-Si and a-Si:H layers, respectively)

Deduced from the analytical model of the open- circuit voltage (Eq. (3) and Eq. (4)), V_OC mostly depends on the activation energy of the c-Si substrate, δ_p1 or δ_n1 (or the doping concentration of the c-Si substrate), the interface state density, D_it, the average photogeneration of the electron-hole pairs g, the effective lifetime of the excess carries, τ_eff, and the diffusion length L_p or L_n. τ_eff and L_p (or L_n) are linked to the recombination velocities at the heterojunction interface, at the rear surface and in the bulk. g is related with the illumination intensity. Therefore, the open-circuit voltage mostly depends on the interface state density, the illumination intensity, the recombination velocities at the rear surface and in the bulk, and the activation energy of the c-Si substrate. And it is apparently independent on the a-Si:H doping concentration.

3.2 Application of analytical model of open circuit voltage

Figure 2 shows the dependence of the illumination intensity on the open-circuit voltage of a-Si:H/c-Si heterojunction solar cells fabricated, where the irradiance of 100 mW/cm² corresponds to one-sun irradiance. As τ_eff can be approximately assumed constant under usual illumination [7], Eq. (3) reduces to

                               (5)

where  is the open-circuit voltage at one-sun irradiance (X=1). The theoretical dependence of V_OC on the illumination intensity, which is deduced from Eq. (5), is also shown in Fig. 2. it is in accordance with the experimental curve. Deduced from Eq. (5), V_OC increases linearly with the logarithm of X under usual illumination.

Fig. 2 Experimental V_OC and theoretical V_OC of a-Si:H/c-Si heterojunction solar cells under various illumination intensity

The dependence of the simulated open-circuit voltage, V_OC^sim, on D_it is shown in Fig. 3. Simultaneously, the curve of the theoretical open-circuit voltage V_OC^Cal versus D_it is also plotted in Fig. 3, where V_OC^Cal are calculated from Eq. (1) and △n(x_p) is shown in Fig.4. Seen from Fig. 3, the curve of V_OC^cal is in accordance with the V_OC^sim. And the dependence of the open-circuit voltage is divided into three zones, and there are two critical values of D_it for V_OC, D_it^crit,1 and D_it^crit,2. For very low values of D_it (D_it≤D_it^{crit, 2}), V_OC does not almost depend on D_it. By increasing D_it from D_it^crit,2 to D_it^crit,1, V_OC decreases, and further increasing D_it at D_it> D_it^crit,1 leads to a dramatic decrease of V_OC.

Deduced from Eq. (3), the effect of interface states on the open-circuit voltage of a-Si:H/c-Si heterojunction solar cells is related with the parameter △n (gτ_eff). The simulated values of △n under illumination and open circuit for different values of D_it are shown in Fig. 4. It is known that τ_eff is determined by the interface recombination velocity and the recombination velocities in the c-Si bulk and at the rear contact of solar cells. As the recombination velocities in the c-Si bulk and at the rear contact may be dominant comparable with S_p at D_it≤D_it^crit,1, τ_eff is almost not affected by D_it. It results in △n keeping unchanged. However, as S_p may be comparable or dominant above D_it^crit,1, τ_eff decreases with increasing D_it. It results in △n decreasing.

Fig. 3 Simulated and theoretical dependences of V_OC of (n⁺) a-Si:H/(p) c-Si heterojunction solar cells on D_it

Fig. 4 free excess electron density at x=x_p, △n(x_p), and excess electron density out of c-Si depletion and diffusion regions, △n, under illumination and at open circuit for various D_it

There is another critical value of D_it for D_p/L_p, D_it^crit,2. When D_it ≤D_it^crit,2, since △n is independent on D_it, and simultaneously S_p is small enough to neglect comparing with D_p/L_p, V_OC is almost independent of D_it. When D_it^crit,2< D_it ≤D_it^crit,1, S_p is comparable with D_p/L_p, and increases with increasing D_it, while △n keeps unchanged, and it results in V_OC decreasing. Further increasing D_it when D_it> D_it^crit,1, S_p increases with D_it, and furthermore △n decreases with D_it. It results in a dramatic decrease of V_OC.

D_it^crit,1 is dependent on the recombination velocities in the c-Si bulk and at the rear contact of solar cells. The second critical value of D_it is D_it^{crit, 2}. Equation (3) reduces to

                   (6)

with

 and

where β=26 mV at 300 K, and D_p is 13 cm²/s. D_it^crit,2 is dependent on D_p/L_p. Since D_it^crit,2it^crit,1, L_p and then D_it^crit,2 are dependent on the recombination velocity in the c-Si bulk. The dependence of Φ versus α is shown in Table 2. Seen from Table 2, the ratio of S_p to D_p/L_p, α, should decrease down to 0.1 in order to achieve high value of V_OC. Deduced from the simulated Internal quantum efficiency measurement, L_p=1.21×10^{-2 cm. The critical value of S}_p is about 100 cm/s. And D_it^crit,2 is usually a few 10¹⁰ cm^-2·eV^-1. Therefore, the interface states should reduce down to a few 10¹⁰ cm^-2·eV^-1 to achieve high V_OC as well as high performance of a-Si:H/c-Si heterojunction solar cells. To reduce interface states lower than D_it^crit,2, the passivation of a thin intrinsic a-Si:H layer introduced between the emitter and the wafer was proposed by Sayno. It leads to very low effective interface recombination velocity of 3 cm/s. The interface states (or the interface recombination velocity) are lower than the critical value D_it^crit,2. The solar cell achieved high efficiency with the open-circuit voltage higher than 720 mV. Therefore, the i-a-Si:H buffer layer mainly plays the role of interface passivation in decreasing interface states. To achieve high performance of a-Si:H/c-Si heterojunction solar cells, it is usually assumed that interface states should reduce down to very low levels as possible. Deduced from the analytical model of the open-circuit voltage, when the interface states are lower than D_it^crit,2, it is of no great significance to further decrease the interface states to improve the open-circuit voltage.

Table 2 Dependence of Φ on α

Figure 5 shows the simulated I-V characteristics of a-Si:H/c-Si heterojunction solar cells fabricated on both p- and n-type c-Si wafers with the same activation energy of c-Si (δ_p1=δ_n1) and the same value of the interface recombination velocity. Seen from Fig. 7, the open-circuit voltage of a-Si:H/c-Si heterojunction solar cells fabricated on n-type c-Si wafers is about 22 mV higher than that fabricated on p-type c-Si wafers. The discrepancy is in accordance with the value deduced from the analytical model of the open-circuit voltage  Eq. (3) and Eq. (4). The discrepancy origins from the difference of N_c1 and N_V1 (N_c1=2.80×10¹⁹ cm^-3 and N_V1=1.04×10¹⁹ cm^-3). Therefore, n-type c-Si wafers have superiority to achieve higher values of V_OC as well as higher performance of a-Si:H/c-Si heterojunction solar cells.

Fig. 5 J-V characteristics of (n) a-Si:H/(p) c-Si and (p) a-Si:H/(n) heterojunction solar cells

The simulated dependence of V_OC on the a-Si:H doping concentration N_D2 is shown in Fig. 6. Seen from Fig. 6, V_OC decreases with decreasing the doping level of the a-Si:H layer at low doping levels (N_D2 < 5×10¹⁸ cm^-3)  as it was reported in Ref. [11]. It seems to contradict with Eq. (3). In fact, at low doping levels, the depletion region has shift towards the a-Si:H layer. The diffusion voltage is mainly distributed over the a-Si:H layer. The electric field over the c-Si depletion region is strongly reduced. It allows more holes to diffuse from the c-Si neutral region towards the heterojunction interface. Higher hole concentration in the c-Si depletion region in combination with the high accumulation of electrons near theinterface causes a strong increase of the interface recombination. Deduced from Eq. (3), it results in the decrease of V_OC at low doping levels.

Fig. 6 Simulated dependence of V_OC on a-Si:H impurity concentration N_D2.

However, at a high doping levels (N_D2>5×10¹⁸ cm^-3), V_OC is independent on N_D2. It is in accordance with Eq. (3). For a-Si:H/(p) c-Si heterojunction solar cells with high doping levels, the total diffusion potential is mainly accommodated in the c-Si. Only a small fraction of the total diffusion potential is accommodated inside the (n⁺) a-Si:H layer so that it can be neglected. It results in low interface recombination, and then high value of V_OC. Therefore, to achieve high V_OC as well as high performance of a-Si:H/c-Si heterojunction solar cells, the a-Si:H layer should be doped higher than 5×10¹⁸ cm^-3.

4 Conclusions

Effect of the parameters on the open-circuit voltage was explored by an analytical model. The analytical results show that V_OC increases linearly with the logarithm of illumination intensity under usual illumination. And n-type c-Si wafers have superiority to achieve higher values of V_OC as well as higher performance of a-Si:H/c-Si heterojunction solar cells. To achieve high V_OC as well as high performance of a-Si:H/c-Si heterojunction solar cells, the interface states should reduce down to 10¹⁰ cm^-2·eV^-1, and the a-Si:H layer should be doped higher than a critical value of 5×10¹⁸ cm^-3.

References

[1] Tsunomura Y, Yoshimine Y, Taguchi M, BABA T, KINOSHITA T, KANNO H, SAKATA H, MARUYAMA E, TANAKA M. Twenty-two percent efficiency HIT solar cell [J]. Sol Energy Mater Sol Cells, 2009, 93: 670-673.

[2] Wang T H, Wang Q, Page M R, Bauer R E, Ciszek T F. Hydrogen passivation and junction formation on APIVT-deposited thin-layer silicon by hot-wire CVD [J]. Thin Solid Films, 2003, 430: 261-264.

[3] Ikhmayies S J, Ahmad-Bitar R N. Using HF rather than NH₄F as doping source for spray-deposited SnO₂:F thin films [J]. Journal of Central South University, 2012, 19(3): 791-796.

[4] Tanaka Y, MatsukiN, Fujiwara H. Characterization ofa-Si:Hthin layers incorporated into textureda-Si:H/c-Si solar cellstructures by spectroscopic ellipsometry usingatilt-angle optical configuration [J]. Thin Solid Films,2014, 569: 64-69.

[5] Pehlivan , Menda D, YIlmazO, A O, zdemir O, Duygulu , KUTLU K, TOMAK M. Structural and interfacial properties of large area n-a-Si:H/i-a-Si:H/p-c-Siheterojunctionsolar cells [J]. Materials Science in Semiconductor Processing,2014, 22: 69-75

[6] Kim S K, Lee J C, Park S J, Kim Y J, Yoon K H. Effect of hydrogen dilution on intrinsic a-Si:H layer between emitter and Si wafer in silicon heterojunction solar cell [J]. Sol Energy Mater Sol Cells, 2008, 92: 298-301.

[7] D, Voz C, Martin I, Orpella A, Puigdollers J, Alcubilla R, Villar F, Bertomeu J, Andreu J, Damon-Lacoste J, Roca i Cabarrocas P. Progress in a-Si:H/c-Si heterojunction emitters obtained by Hot-Wire CVD at 200 °C [J]. Thin Solid Films, 2008, 516: 761-764.

[8] Veschetti Y, Muller J C, Damon-Lacoste J, Roca i, Cabarrocas P, Gudovskikh A S, Kleider J P, Ribeyron P J, Rolland E. Optimisation of amorphous and polymorphous thin silicon layers for the formation of the front-side of heterojunction solar cells on p-type crystalline silicon substrates [J]. Thin Solid Films, 2006, 511/512: 543-547.

[9] Dauwe S, Schmidt J, Hezel R. Very low surface recombination velocities on p- and n-type silicon wafers passivated with hydrogenated amorphous silicon films [C]// Conference Record of the Twenty-Ninth IEEE Louisiana. New Orleans: Photovoltaic Specialists Conference, 2002: 1246-1249.

[10] Froitzheim A, Brendel K, Elstner L, Fuhs W, Kliefoth K, Schmidt M. Interface recombination in heterojunctions of amorphous and crystalline silicon [J]. J Non-cryst Solids, 2002, 299/302: 663-667.

[11] van Cleef M W, Rubinelli F A, Rath J K. Photocarrier collection in a-SiC:H/c-Si heterojunction solar cells [J]. J Non-cryst Solids, 1998, 227/230: 1291-1294.

[12] Page M R, Iwaniczko E, Xu Y Q, Roybal L, Hasoon F, Wang Q, Crandall R S. Amorphous/crystalline silicon heterojunction solar cells with varying i-layer thickness [J]. Thin Solid Films, 2011, 519: 4527-4530.

[13] Nath M, Chatterjee P, Damon-Lacoste J, Roca i, Cabarrocas P. Criteria forimproved open-circuit voltage in a-SiH/c-Si(P) front heterojubnction solar cells [J]. J Appl Phys, 2008, 103: 034506.

[14] Wang Q, Page M R, Iwaniczko E, Xu Y Q, Roybal L, Bauer R, To B, Yuan H C, Duda A, Yan Y F. Crystal silicon heterojunction solar cells by hot wire CVD [C]// Proceedings of the 33rd PVSEC-IEEE. San Diego, USA: IEEE, 2008: 1-5.

[15] Damian P P, Bivour M, Hermle M, Stefan W G. Amorphous silicon carbide heterojunction solar cells on p-type substrates [J]. Thin Solid Films, 2011, 519: 2550-2554.

[16] Schmidt M, Korte L, Laades A, Stangl R, Schubert C, Angermann H, Conrad E, Maydell K V. Physical aspects of a-Si:H/c-Si hetero-junction solar cells [J]. Thin Solid Films, 2007, 515: 7475-7480.

[17] Tucci M, della Noce M, Bobeico E, Roca F, de Cesare G, Palma F. Comparison of amorphously crystalline heterojunction solar cells based on n- and p-type crystalline silicon [J]. Thin Solid Films, 2004, 451/452: 355-360.

[18] Voz C, D, Fonrodona M, Martin I, Puigdollers J, Alcubilla R, Escarre J, Bertomeu J, Andreu J. Bifacial heterojunction silicon solar cells by hot-wire CVD with open-circuit voltages exceeding 600 mv [J]. Thin Solid Films, 2006, 511/512: 415-419.

[19] Zhong C L, Luo L E, Tan H S, Geng K W. Band gap optimization of the window layer in silicon heterojunction solar cells [J]. Solar Energy, 2014, 8: 570-575

[20] Stangl R, Froitzheim A, Kriegel M, Brammer T, Kirste S, Elstner L, Stiebig H, Schmidt M, Fuhs W. AFORS-HET, a numerical PC-program for simulation of heterojunction solar cells, Version 1.1 (open-source on demand), to be distributed for public use [C]// Proc 19th European Photovoltaic. France: Solar Energy Conference, 2004: 1497-1500.

[21] Schmidt M, Schoepke A, Korte L, MLICH O, FUHS W. Density distribution of gap states in extremely thin a-Si:H layers on crystalline silicon wafers [J]. J Non-cryst Solids, 2004, 211: 338-340.

[22] Zhong C L, Yao R H, Geng K W. Characterization of interface states in a-Si-H/c-Si heterojunctions by an expression of the theoretical diffusion capacitance [J]. J Phys D: Appl Phys, 2010, 43: 495102.

(Edited by YANG Hua)

Foundation item: Project(11374094) supported by the National Natural Science Foundation of China; Project(2013HZX23) supported by Natural Science Foundation of Hunan University of Technology, China; Project(2015JJ3060) supported by Natural Science Foundation of Hunan Province of China

Received date: 2014-12-29; Accepted date: 2015-05-25

Corresponding author: ZHONG Chun-liang, PhD, lecturer; Tel +86-15974381036; E-mail: zhongcljust2007@163.com