Computer Modeling of Heterojunction with Intrinsic Thin Layer “HIT” Solar Cells: Sensitivity Issues and Insights Gained

Despite significant progress in research, the energy provided by photovoltaic cells is still a small fraction of the world energy needs. This fraction could be considerably increased by lowering solar cell costs. To achieve this aim, we need to economize on the material and thermal budgets, as well as increase cell efficiency. The silicon “Heterojunction with Iintrinsic Thin layer (HIT)” solar cell is one of the promising options for a cost effective, high efficiency photovoltaic system. This is because in “HIT” cells the P/N junction and the back surface field (BSF) layer formation steps take place at a relatively low temperature (~200°C) using hydrogenated amorphous silicon (a-Si:H) deposition technology, whereas in normal crystalline silicon (c-Si) cells the wafer has to be raised to ~800°C for junction and BSF layer formation by diffusion. This means not only a lower thermal budget, but also cost reduction from thinner wafers, since the danger of the latter becoming brittle is strongly reduced at lower (~200°C) temperatures. Thin intrinsic layers on either face of the c-Si substrate, effectively passivate c-Si surface defects, which would otherwise degrade cell performance. Moreover it has been demonstrated that carriers can pass through the passivating layers without significant loss. In this chapter, we use detailed electrical-optical modeling to understand carrier transport in these structures and the sensitivity of the solar cell output to various material and device parameters. The global electrical optical model “Amorphous Semiconductor Device Modeling Program (ASDMP)”, originally conceived to simulate the characteristics of solar cells based on disordered thin films, and later extended to model also mono-crystalline silicon and “HIT” solar cells (Nath et al, 2008), has been used for all simulations in this chapter. The model takes account of specular interference effects, when polished c-Si wafers are used, as well as of light-trapping when HIT cells are depositd on textured c-Si.

Inspired by the outstanding performance of Sanyo HIT cells, many research groups throughout the world have been working with these cells and a-Si:H layers have been deposited by PECVD, hot-wire CVD (HWCVD) and very-high-frequency PECVD (VHF-PECVD). A summary of the best HIT solar cells reported till date is given in Table 1. We find that currently, no group has been able to duplicate what Sanyo has achieved in terms of cell efficiency. Very few groups have reached beyond 19% efficiency: Helmholtz Zentrum Berlin on N-type textured wafers (Schimdt et al, 2007) and the National Renewable Energy Laboratory (NREL) on P-type textured wafers (Wang et al, 2008(Wang et al, , 2010 have achieved this feat. Good results have also been obtained by the group of EPFL, IMT, Neuchâtel, Switzrland with high open-circuit voltsge (V oc ) on flat wafers. The P-type HIT cell of Damon Lacoste et al (2008) from LPICM-Ecole Polytechnique, France also deserves mention. Here the efficiency is limited by the lower short-circuit current density (J sc ) characteristic of flat wafers. The difficulty in attaining the Sanyo HIT cell efficiency illustrates that the a-Si:H/c-Si HJ is indeed a very challenging structure to understand. Therefore, over the last decade scientists are using detailed computer modeling to fully understand the structure. In the next section we will briefly review the computer modeling of HIT solar cells. Recently a few groups have started fabricating HIT cells with intrinsic hydrogenated amorphous silicon oxide (I-a-SiO:H) as the buffer layer between crystalline and doped amorphous silicon. Sritharathikhun et al (2008) have achieved 17.9% cell efficiency with P-c-SiO:H /N-c-Si cell structure and I-a-SiO:H as the buffer layer. A group from AIST (Fujiwara et al, 2009) has reported 17.5% cell efficiency with a similar cell structure.

Detailed one-dimensional computer modeling of HIT solar cells:-
Pioneering work in detailed electrical modeling of a-Si:H solar cells was done by Hack and Schur (1985). Other notable models in this respect are the model AMPS (McElheny et al, 1988, Arch et al, 1991 by S. J. Fonash's group at the Pennsylvania State University, USA, the model of Guha's group (Guha et al, 1989), the ASDMP program by P. Chatterjee (Chatterjee, 1992(Chatterjee, , 1994(Chatterjee, , 1996, the ASPIN program of Smole and Furlan (1992) and the ASA program by von der Linden et al (1992). Regarding detailed electrical-optical models, which include textured surfaces and light-trapping kinetics to some extent, the first global electrical-optical model developed in the world was when ASDMP was integrated (Chatterjee et al, 1996) to a semi-empirical optical model by Leblanc et al (1994). This program also takes account of specular interference effects for cells with flat surfaces. Later the developed AMPS program (D-AMPS -Plà et al, 2003) and the ASA package, developed at the Delft University of Technology (Zeman et al, 2000) also introduced light trapping effects.
Modeling of HIT cells was started by van Cleef et al (1998 a,b) using the AMPS computer code (McElheny et al, 1988), which however does not have a proper built-in optical model; and the derivative of the AMPS program (D-AMPS), where a fairly good optical model has been introduced (Plà et al, 2003). The numerical PC program AFORS-HET (Stangl et al, 2001, Froitzheim et al, 2002 has been developed especially for simulating HIT solar cells. The latter has recently also been extended to include light-trapping effects. The ASA program in its later version (Zeman et al, 2000) models both the electrical and optical properties of HIT cells. The PC-1D program (Basore, 1990, Basore et al, 1997, developed at the University of News South Wales, Australia for modeling textured mono-crystalline silicon solar cells, has also been fairly successful in modeling HIT cells. The program ASDMP by Chatterjee et al (1994Chatterjee et al ( ,1996, has also been extended to model N-a-Si:H/P-c-Si type front (with a heterojunction only on the emitter side) (Nath et al, 2008) HIT cells and subsequently used to model double hetreojunction solar cells both on N-and P-type substrates ( Datta et al, 2008.

Simulation model ASDMP
We will discuss this model in a little more detail, since it has been used in all simulations in this chapter. The "Amorphous Semiconductor Device Modeling Program (ASDMP) " (Chatterjee et al, 1996, Palit et al, 1998, originally conceived to model amorphous silicon based devices, has been extended to also model c-Si and "HIT" cells (Nath et al, 2008). This one-dimensional program solves the Poisson's equation and the two carrier continuity equations under steady state conditions for the given device structure, without any simplifying assumptions, and yields the dark and illuminated current density -voltage (J-V), the quantum efficiency (QE) and the photo-and electro-luminescence characteristics of HIT cells. Its electrical part is described in P. Chatterjee (1994Chatterjee ( , 1996. The gap state model used in these calculations for the amorphous layers, consists of the tail states and the two Gaussian distribution functions to simulate the deep dangling bond states, while in the c-Si part, the tail states absent. The lifetime of the minority carriers inside the N(P) -c-Si wafer may be estimated using the formula: where  p ( n ), p(n) and p 0 (n 0 ) are the minority carrier lifetime, its density under the given experimental conditions (in this case under 100 mW cm -2 of AM1.5 light), and at thermodynamic equilibrium respectively; while R is the recombination rate in the c-Si wafer. The lifetime, calculated in this manner, is in general, position-dependent; however over a large region inside the c-Si wafer, away from the edges, it is a constant and it is this value that is taken to be the minority carrier lifetime in the wafer. van Cleef et al (1998a,b) and Kanevce et al (2009) have also used the DOS model to simulate their HIT cells. The generation term in the continuity equations has been calculated using a semi-empirical model (F. Leblanc et al, 1994) that has been integrated into the ASDMP modeling program (Chatterjee et al, 1996, Palit et al, 1998. Both specular interference effects and diffused reflectance and transmittance due to interface roughness can be taken into account. The complex refractive indices for each layer of the structure, required as input to the modeling program, have been measured by spectroscopic ellipsometry. In all cases studied in this article, experimentally or by modeling, light enters through the transparent conducting oxide (TCO)/emitter window, which is taken as x = 0 on the position and referred to as the front contact. Voltage is also applied at x = 0. The BSF/ metal contact at the back of the c-Si wafer is taken as x = L on the position scale, where L is the total thickness of all the semiconductor layers of the device. This back contact is assumed to be at ground potential.

Simulation of experimental results of P-type HIT cells
We have studied both front and double "HIT" structure solar cells on P-type c-Si wafers. These have the structure: N-a-Si:H emitter/ P-c-Si/ aluminum diffused BSF (front HIT) and N-a-Si:H emitter/ P-c-Si/ P + -a-Si:H BSF (double HIT  double HIT cells having the following structures: (A) 8 nm N-a-Si:H/ 3 nm pm-Si:H intrinsic layer/ P-c-Si wafer/ 23 nm P + -a-Si:H/ 1.5 m Al, and (B) the above structure, but with a 4 nm P + -a-SiC:H layer sandwiched between the P-c-Si wafer and a 19 nm P + -a-Si:H layer. The pm-Si:H intrinsic layer on the front surface (FS) of the c-Si wafer is there to passivate the defects on this surface. However, no such passivating layer has been deposited on the rear surface (RS) of the c-Si wafer. The defect density on FS was deduced by modeling to be 10 11 cm -2 . Cell B, which has a 4 nm P-type a-SiC:H layer on the rear c-Si wafer surface, has a slightly higher V oc but a lower FF relative to case A, leading to a better efficiency. However, we could not replicate these results in our modeling calculations by the introduction of a P +a-SiC:H layer of the given properties alone (case B1 in Table 2). In fact, the defect density on the rear wafer surface had to be slightly reduced (case B2, Table 2) to match the experimental results. Table 2 indicates good agreement between experiments and modeling, except that our modeling results appear to overestimate the FF and hence the efficiency of front HIT cells. In reality this is because screen-printed contacts with low temperature silver paint was used for these cells; resulting in high series resistance and low FF experimentally, which cannot be accounted for by modeling. For double HIT structures, developed later, improved contact formation resulted in very low series resistance and high fill factors experimentally, which agree well with model calculations (  Table 2. Comparison between measured (E) and modeled (M) solar cell output parameters of front and double P-c-Si HIT cells with a flat ITO front contact. DL refers to the defective layer on the wafer surface.
In Fig. 3 (a), we compare the experimentally measured external and internal quantum efficiency (EQE and IQE respectively) curves of the solar cell B to modeling results, while in Fig. 3 (b) we compare the measured IQE curves of a front HIT and the above-mentioned double HIT solar cells, both deposited in the same reactor and under approximately the same conditions of RF power and pressure as solar cells A and B above. The IQE is obtained from the EQE using the formula: www.intechopen.com We have used the above simulations to extract the parameters that characterize different layers of the double HIT cells A and B on P-type wafers. These are given in Table 3, together with the extracted parameters of double HIT cells on N-type wafers. The experimental results used to extract the latter and comments thereon, will be discussed in section 5.1. The data in Table 3 includes some measured data: the thickness and doping density of each layer/ wafer, the band gaps of the layers and the electron and hole mobility in the c-Si wafer (Sze, 1981). We also found that a higher value of N ss (as indicated in Case B2 in Table 2 and  Table 3) was necessary at the RS to simulate the experimental results. No layer was intentionally deposited to passivate these defects in cells A and B. Since the 4-nm P + -a-SiC:H layer on the RS of the c-Si wafer (part of the highly doped thin film BSF layer) produces a small but reproducible improvement in the overall device performance, we have tried to understand the basic reasons for this improvement. To realize the role of the thin P-a-SiC:H layer on the RS in case B2 we have made the P + -a-SiC:H layer thicker than in case B2 and adjusted the thickness of following P + -a-Si:H layer to yield a total BSF thickness of 23 nm. We found an all-round deterioration of the solar cell output for the thicker P + -a-SiC:H layers, including a striking fall in the fill factor. We have thus concluded that the introduction of the thin carbide layer as such is not responsible for the observed improvement in cell efficiency of case B2 relative to case A (Table 2). Rather, it appears likely that this wider band gap material helps in passivating the defects on the RS of the c-Si wafer (for which a very thin layer is sufficient) and thereby improves cell performance. In the next section we will discuss how solar cell performance is affected by the defects on the FS and RS of the c-Si wafer.  Table 3. Input parameters, extracted by modeling, that characterize the above HIT cells. The defect density of 3.3x10 17 cm -3 on the front wafer surface corresponds to a defect density of 10 11 cm -2 (FS) and 3.5x10 18 cm -3 to 8x10 11 cm -2 on the rear surface (RS). The P + -a-SiC:H BSF layer in P-type HIT cells has a larger band gap (1.84 eV), and broader band taills: ED=0.7 eV, EA=0.5 eV

Influence of the defect density on the front surface of the c-Si wafer:
The effect on the solar cell output parameters of varying the defect density, N ss , on front surface of the P-type c-Si wafer (that which faces the incoming light) is shown in Table 4, using as the base case the double HIT cell B2, but with an assumed textured wafer to reproduce state-of-the-art currents obtainable in HIT cells. The defect density on the RS is held at 10 11 cm -2 for all cases. The results indicate a sharp fall in V oc , and FF.
To understand the sensitivity, we turn to Fig. 4. We note that the electric field is higher at the amorphous -crystalline interface, when N ss = 3x10 13 cm -2 than when N ss = 10 11 cm -2 ( Fig.  4a). This is because when the N-a-Si:H layer is joined to a P-c-Si wafer, with a high defect density on its surface, most of the electrons that flow from the N-side to the P-side during junction formation, to bring the thermodynamic equilibrium Fermi levels on either side to the same level, are trapped in these states. The space charge region on the P-c-Si wafer side is therefore localized near the surface and does not extend appreciably into the c-Si wafer. We therefore have a huge density of trapped electrons, a very high interface field (Fig. 4a), 38.14 463 0.545 9.65 Table 4. Calculated values of the solar cell output parameters J sc , V oc , FF and , for different values of the defect density (N ss ) on that (front) surface of the crystalline silicon wafer through which light enters, indicating high sensitivity to the V oc and FF. The defect density at the rear surface of the c-Si wafer is 10 11 cm -2 .  (Table 4). For the case of low N ss , the space charge region on the P-c-Si wafer is not localized and more field exists up to the neutral zone of the c-Si wafer ( Fig. 4a inset and band diagram in Fig. 5b, solid lines); resulting in higher V oc and FF (Table 4). Table 5 gives the calculated solar cell output parameters J sc , V oc , FF and efficiency for different values of the defect density (N ss ) on the rear surface of the c-Si wafer (away from the side where light enters). We have again varied N ss between 10 11 cm -2 and 3x10 13 cm -2 , but this time the largest effect is on the fill factor and the short-circuit current density, as seen from Table 5 and Fig. 5 (a). In order to understand why, we have traced the band diagrams for different N ss on the RS, with the N ss at the FS held at 10 11 cm -2 ( Fig. 5b). We find that the band bending over the depletion region has completely disappeared for the highest value of N ss (3x10 13 cm -2 ) at RS. From our modeling calculations we also note that up to a defect density of ~10 12 cm -2 at RS, the solar cell output parameters do not deteriorate appreciably.

Influence of the defect density on the rear surface of the c-Si wafer
For higher values of N ss the decrease in J sc and FF in particular, is extremely rapid, the sensitivity to V oc being relatively small. Experimentally also it has been found that whether or not an intrinsic passivating layer is deposited on the rear face of the P-type c-Si wafer, the www.intechopen.com solar cell output is little affected. From this we may conclude that the defect density on the back wafer surface in the experimental as-deposited condition is probably ≤ 10 12 cm -2 , as also obtained by modeling the experimental characteristics (Table 2).  Table 5. Calculated values of the solar cell output parameters for different values of the defect density (N ss ) on that (rear) surface of the crystalline silicon wafer that is away from the incoming light, indicating that the maximum sensitivity is to the short circuit current density and fill factor. The defect density at the front surface of the c-Si wafer is 10 11 cm -2 .
In order to understand the sensitivity of the solar cell output to N ss on the RS, we turn to Fig.  6. We note that when N ss on the rear c-Si wafer surface is highest (3x10 13 cm -2 ), there is a huge concentration of trapped holes at the crystalline-amorphous interface on the c-Si wafer side where the high surface defect density exists (dashed line, Fig. 6a). The hole pile-up at the crystalline-amorphous interface slows down the arrival of holes to the back contact (the collector of holes), and encourages the back diffusion of photo-generated electrons in the absorber c-Si wafer. The result is that the electron current is negative over most of the device ( Fig. 6b -electron current towards the back contact is negative according to our sign convention). Thus little electron current is collected at the front contact (the collector of electrons, Fig. 6b). In addition, the back-diffusing electrons recombine with the photogenerated holes over most of the absorber c-Si, resulting in poor hole current collection at the back contact. Thus J sc and FF fall sharply for very high values of N ss at RS. More details can be found in Datta et al (2008).

Simulation of N-type HIT solar cells 5.1 Simulation of experimental results
Simulation of a range of experimental results on HIT cells developed by the Sanyo group and available in the literature (Maruyama et al, 2006, Takahama et al, 1992, Sawada et al, 1994, Taguchi et al, 2008 has been undertaken to extract typical parameters that characterize state-of-the-art HIT cells on N-type c-Si substrates, as well as to gain an insight into carrier transport and the general functioning of these cells. Both "front" HIT cells having an amorphous/ crystalline heterojunction on the emitter side only -where the light enters (Takahama et al, 1992), and "double" HIT cells having heterojunctions on both ends of the c-Si wafer (Maruyama et al, 2006, Sawada et al, 1994, Taguchi et al, 2008 have been simulated. The cells have the structure: ITO/ P-a-Si:H/ I-a-Si:H/ textured N-c-Si/ N-c-Si BSF/ metal (front HIT) (Takahama et al, 1992) and ITO/ P-a-Si:H/ I-a-Si:H/ textured N-c-Si/ I-a-Si:H/ N ++ -a-Si:H/ metal (double HIT) (Maruyama et al, 2006, Sawada et al, 1994, Taguchi et al, 2008. In Taguchi et al (2008), after depositing the undoped and doped a-Si:H layers on both ends of the c-Si wafer, ITO films were sputtered on both sides, followed by screen-printed silver grid electrodes. Simulation of these cells (Maruyama et al, 2006, Takahama et al, 1992, Sawada et al, 1994 gives us an insight into the parameters that play a crucial role in improving HIT cell performance. On the other hand, the article by Taguchi et al (2008) gives the temperature dependence of the dark current density -voltage characteristics and the solar cell output parameters as a function of the thickness of the intrinsic amorphous layer sandwiched between the emitter P-a-Si:H and the main absorber N-c-Si. A study of the temperature dependence of the dark J-V characteristics is particularly important to understand the carrier transport mechanism in these devices. The parameters extracted by such modeling (Table 3) will be used in the following sections to calculate the sensitivity of the solar cell performance to various controlling factors. In Table 6 we compare our simulation and experimental results of various HIT cells on Ntype c-Si substrates (Takahama et al, 1992, Sawada et al, 1994, Maruyama et al, 2006. Modeling indicates that improvements in V oc could be brought about (a) by going from a  front HIT to a double HIT structure, (b) by decreasing the defects on the front surface of the c-Si wafer that faces the emitter layer and (c) by improving the lifetime of the minority carriers in crystalline silicon. Results indicate that it is by decreasing N ss on the front surface of the c-Si wafer, that the largest increase in V oc could be achieved, without any fall in FF. We next used ASDMP to simulate the experimental results of Taguchi et al (2008). Here we have concentrated on the effect of varying the thickness of the intrinsic amorphous silicon layer at the P-amorphous emitter/ N-c-Si heterojunction. The terminology "normal" has been used to represent the thickness of the front I-a-Si:H buffer layer in the cell that yields the highest efficiency (Table 7). Modeling reveals that the I-a-Si:H thickness for this case is 3 nm. The I-a-Si:H buffer layers (front) in the cells named "Half", "Double" and "Triple" by Taguchi et al (2008) have therefore been assigned thicknesses of 1.5 nm, 6 nm and 9 nm respectively in the simulations. Results of our simulation of the experimental light J-V characteristics (Taguchi et al, 2008) as a function of this I-a-Si:H layer thickness are given in Table 7 and the input parameters extracted by such modeling, and also of the dark J-V characteristics (Figs. 7a and 7b) and typical internal quantum efficiencies of Sanyo N-c-Si HIT cells (Fig. 7c, Maruyama et al, 2006 ), are given in Table 3 (the same table that contains the extracted parameters of P-type HIT cells). Since modeling does not consider the resistance of the contacts; these results had to be modified by taking into account the series resistance of the contacts. The addition of the series resistance did not modify V oc and J sc but allowed to perfectly match the experimental fill factor and therefore the efficiency of the Sanyo HIT solar cells (Taguchi et al, 2008). In Table 7 we show the solar cell output parameters as obtained directly by modeling, without resistive losses (which gives an upper limit for the FF and therefore the efficiency) and the values of the FF and efficiency after considering the constant series resistance (marked by astericks). This resistance, comprising resistive losses in the TCO, the silver grid and the contacts, was estimated by Taguchi et al (2008) to be ~2.8 m.
www.intechopen.com   The dangling bond defect density in the I-a-Si:H layer, as extracted from modeling, is 9x10 16 cm -3 and its Urbach enegy is 70 meV (Table 8). We have assumed the same values for these quantities, as well as of the capture cross-sections of the defect states inside the I-a-Si:H layer in all the cases of Table 7. Modeling indicates that in order to simulate the lower V oc 's of the Taguchi et al (2008) cells "Normal" and "Half", the defect density on the surface of the c-Si wafer itself in these cases, must be higher (Table 7). We may justify this fact by assuming that a very thin buffer layer may not be as effective in passivating the defects on the surface of the c-Si wafer as a thicker buffer layer. In Table 7, we also had to assume higher carrier motilities in the front amorphous layers for the cases Half and Normal to match both the higher FF and lower V oc for these cases. Increasing carrier mobilities over the front amorphous layers improves hole collection and therefore the FF. However, higher electron mobility allows more electrons to recto-diffuse towards the front contact (collector of photogenerated holes) and recombine with holes, thus reducing V oc . However the main reason for the lower V oc for thinner I-a-Si:H layers (Half and Normal) is our assumption of higher surface defect density on the c-Si wafer in these cases ( Table 7). The experimental dark J-V characteristics of the cell "Normal" is shown in Fig. 7 (a) and the model curves in Fig. 7 (b). The diode ideality factor, n, calculated in the voltage range 0.4 volts V< 0.8 volts, from the model dark characteristics is 1.25 and compares well with the experimental value of 1.2. This value of "n" indicates that it is the diffusion current that dominates transport in this voltage range for N-c-Si HIT cells, as is also the case for homojunction c-Si solar cells. On the other hand, in the voltage range 0.1 volts< V< 0.4 volts, "n" calculated from the modeling data (Fig. 7b) is ~1, which indicates that the conductivity continues to be dominated by diffusion. The value of the slope, calculated from the experimental curves of Taguchi et al (2008) in the voltage range 0.1 volts < V < 0.4 is smaller than that of the recombination current model and remained almost constant for each temperature. The corresponding value of "n" derived from the experimental curves is greater than 2 (Fig. 7a). Taguchi et al (2008) therefore assumed that this is tunneling-limited current. If the value of "n" extracted from the experimental curves, had been due to current dominated by recombination, ASDMP would also have been able to reproduce this value of 'n', since the recombination current model is included in ASDMP. In fact ASDMP has already been used to successfully model forward and dark reverse bias characteristics of a-Si:H based PIN solar cells, where recombination plays a dominant role (Tchakarov et al, 2003). The fact that the value of "n" calculated from the ASDMP-generated dark J-V curves is ~1, while that from experiments is different, indicates that the current over this region is dominated by a phenomenon not taken account of by ASDMP (e.g. tunneling). Over this voltage region therefore the current could be dominated by the tunneling of electrons. However, as pointed out by Taguchi et al (2008), "the current density in this region is sufficiently low compared to the levels of short-circuit current density and does not affect solar cell performance". It therefore appears that cell performance under AM1 or AM1.5 light is not affected by tunnelling of electrons, although this phenomenon probably exists for V< 0.4 volts. Fig. 8 shows the temperature dependence of the solar cell output parameters. We have made the comparison between experiments (Taguchi et al, 2008) and modeling, after taking account of the series resistance of the contacts that is independent of temperature. As the temperature decreases, carrier density decreases. It means less carrier recombination and therefore a higher V oc at lower temperatures (Fig. 8a). However lower carrier density at www.intechopen.com lower temperatures, also means that the cell is now more resistive, resulting in a fall in the FF for the cells "double" and "triple" (Fig. 8c), where performance is dominated by the undoped a-Si:H layer. Also, for the value of the band gap assumed for the I-a-Si:H layer (Table 8), the holes are able to overcome the positive field barrier at the a-Si/ c-Si interface by thermionic emission to get collected at the front contact. Thermionic emission decreases at lower temperatures, resulting in a loss of FF for cells "double" and "triple". For cells "Normal" and "Half", performance is dominated by the temperature-independent resistance of the contacts; therefore no fall in FF is seen. Finally Fig. 8 (b), indicates that the calculated J sc is constant with temperature, while the measured J sc increases slightly. This is because the model does not take account of the temperature dependence of the band gap and absorption coefficient of the materials.

Effect of I-a-Si:H buffer layers on the performance of N-type HIT solar cells
HIT solar cells give efficiencies comparable to those of c-Si cells because of the amazing passivating properties of the intrinsic a-Si:H layers. In fact it is this layer that gives this group of solar cells its name -"HIT". We have already discussed that it is very effective in passivating the defects on the surface the c-Si wafer. However, it must be kept as thin as possible, as it reduces the fill factor when thick (Table 7). We have next studied the effect on solar cell performance of varying the defect density in this layer itself. For this purpose, we have assumed its thickness to be 6 nm (as in case "Double") where the best passivation of N ss has been attained (Table 7). An increase in the defect density in the I-a-Si:H layer may affect the defect density (N ss ) on c-Si, but in this study we assume N ss to be constant. We have found ) that unless the defect density of this intrinsic layer is greater than 3x10 17 cm -3 , no significant loss of cell performance occurs. Similar conclusions have been reached in the case of HIT cells on P-type c-Si wafers.

Effect of the defect density on the front and rear faces of the N-type c-Si wafer
The sensitivity of the solar cell output of HIT cells on N-type wafers to the surface defect density (N ss ) at the amorphous/crystalline interface is given in Table 9. All aspects of the solar cell output appear to be highly sensitive to the N ss on the front surface (on the side of the emitter layer) of the N-type c-Si wafer; however the sensitivity to N ss on the rear face is weak and is limited to the condition when these defects are very high. We have also given in Table 8, the values of the corresponding recombination speeds at the a-Si:H /c-Si front and the c-Si/a-Si:H rear heterojunctions, as calculated by ASDMP, under AM1.5 illumination and short circuit condition. We find that for a well-passivated front interface (N ss ≤ ~3x10 11 cm -2 ) the recombination speed at this heterojunction is less than 10 cm/sec (Table 8), in good agreement with measured interface recombination speeds (Dauwe et al, 2002).  Table 8. Sensitivity of the solar cell output to the defect density (N ss ) in thin surface layers (DL) on the front and rear faces of the c-Si wafer in N type double HIT solar cells. The Player thickness is 6.5 nm. The recombination speeds of holes (S p -at the front DL) and electrons (S n -at the rear DL), calculated under AM 1.5 light and 0 volts, are also shown.
In Fig.9 (a) we plot the light J-V characteristics and in Fig. 9 (b) the band diagram for various values of N ss on the front face of the c-Si wafer. We find that for a very high defect density on the surface of the c-Si wafer, the depletion region in the N-c-Si wafer completely vanishes, while the emitter P-layer is depleted (Fig. 9b). With a high N ss on the c-Si wafer, the holes left behind by the electrons flowing into the P-layer during junction formation, are localized on its surface, leading to a high negative field on the wafer surface and little field penetration into its bulk (Fig. 10a). Hence the near absence of the depletion zone in N-c-Si and a strong fall in V oc for the highest N ss (10 13 cm -2 ) . In Fig. 10 (b) we plot the trapped hole population over the front part in N-c-Si double HIT cells under AM1.5 bias light at 0 volts. We note that when N ss on the front c-Si wafer surface is the highest (10 13 cm -2 ), there is a huge concentration of holes at the amorphous / crystalline (a-c) interface on the c-Si wafer side, where the high surface defect density exists (dashed line, Fig. 10b). The hole pile-up at the amorphous / crystalline interface slows down the arrival of holes to the front contact (the collector of holes), and attracts photo-generated electrons, i.e., encourages their back diffusion towards the front contact. The result is that the electrns back-diffuse towards the front contact and recombine with the photo-generated holes resulting in poor carrier collection . Thus J sc and FF fall sharply for high values of N ss on the front surface of c-Si (Table 8). In fact we may arrive at the same conclusion also from Fig. 9 (b), which shows that for N ss = 10 13 cm -2 , there is almost no band bending or electric field in the c-Si wafer (the main absorber layer) so that carriers cannot be collected, resulting in the general degradation of all aspects of solar cell performance. On the other hand Table 8 indicates that there is little sensitivity of the solar cell output to the defect states on the rear face of the wafer, except at the highest value of N ss . To explain this fact, we note that the recombination over the rear region is determined by the number of holes (minority carriers) that can back diffuse to reach the defective layer. Not many succeed in doing so, since the high negative field due to the large valence band discontinuity at the c-Si/ a-Si rear interface pushes the holes in the right direction, in other words, towards the front contact. Therefore the defects over this region cannot serve as efficient channels for recombination, and there is no large difference between the recombination through these states for different values of N ss (Table 8). Moreover the conduction band discontinuity at the c-Si/ a-Si interface is about half that of the valence band discontinuity.

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Since the mobility of electrons, relative to that of holes, is also much higher, clearly this reverse field due to the conduction band discontinuity poses little difficulty for electron collection even when the defect density at this point is high, except when N ss ≥ 10 13 cm -2 , from which point the solar cell performance deteriorates.

Comparative study of the performances of HIT solar cells on P-and N-type c-Si wafers
Using parameters extracted by our modeling (given in Tables 3), we have made a comparative study between the performances of HIT solar cells on 300 m thick textured Pand N-type c-Si wafers (for more details refer to Datta et al, 2010).

Sensitivity of amorphous/crystalline band discontinuity in the performances of HIT solar cells
Since the band gap, activation energy of the amorphous layers and the band discontinuities at the amorphous/crystalline interface are interlinked, we treat these sensitivity calculations together. For HIT cells on P-c-Si, the large valence band discontinuity (ΔE v ) on the emitter side prevents the back-diffusion of holes and has a beneficial effect. Keeping this constant, we varied the mobility gap and therefore the conduction band discontinuity (ΔE c ) on the emitter side. We find that a ΔE c upto 0.3 eV, does not impede electron collection, but instead brings up both J sc and V oc , due to an improved built in ptential (V bi ). However high ΔE v at the crystalline/amorphous (c-a) interface on the BSF side of P-c-Si double HIT cells (Table 9), impedes hole collection, resulting in a pile up of holes on the c-Si side of this band discontinuity (Fig. 11a) and a consequent sharp fall in the FF and S-shaped J-V characteristics for high ΔE v , especially when the activation energy of the P-a-Si:H layer is also high (Fig. 11b). It is for this reason that a transition from a front to a double HIT structure does not appreciably improve cell performance for P-c-Si HIT cells. The accumulated holes at the c-a interface, furthermore, repel the approaching holes and encourage photo-generated electron back diffusion, resulting in increased recombination, that reduces even J sc for the highest ΔE v (Table 9, Fig. 11b). Finally, for high hole pile-up, the amorphous BSF is screened from the rest of the device, so that the large variation of its band gap and activation energy (Table  9) fails to alter the V oc of the device. The best double HIT performance is attained when the mobility gap (ΔE  ) of the amorphous BSF P-layer is ≤ 1.80 eV and E ac = 0.3 eV (Table 9).   Table 10. Variation of solar cell output parameters with mobility gap (E  ), activation energy (E ac ), and ΔE v at the emitter P-a-Si:H/c-Si interface in double N-c-Si HIT solar cells. ΔE c is held constant at 0.22eV. Table 10 indicates that for valence band offsets up to 0.51 eV, and E ac (P) ≤ 0.3 eV, the FF is high, indicating that the majority of the holes photo-generated inside the c-Si wafer, can surmount the positive field barrier due to the a-Si/ c-Si valence band discontinuity by thermionic emission and get collected at the front ITO/ P-a-Si:H contact. However solar cell performance deteriorates both with increasing band gap and increasing E ac of the P-layer. The latter is only to be expected as it reduces the built-in potential. Fig. 12 (a) shows the effect on the energy band diagram of increasing the P-layer band gap (therefore of increasing ΔE v , since ΔE c is held constant) and the activation energy. Increasing ΔE v at the P-a-Si:H/N-c-Si interface results in hole accumulation and therefore a fall in FF for ΔE v  0.56 eV, for a P-layer activation energy of ~0.3 eV, due to the reverse field it generates; that is further accentuated when E ac is high (Table 10). van Cleef et al (1998 a,b) have also shown that for a P-layer doping density of 9x10 18 cm -3 (same as ours - Table 3, giving E ac = 0.3 eV) and for ΔE v = 0.43 eV, normal J-V characteristics are achieved at room temperature and AM1.5 illumination, and that "S-shaped" characteristics begin to develop at higher ΔE v and E ac . In our case, for ΔE v  0.60 eV, Fig. 12(c) indicates that free holes accumulate over the entire c-Si wafer, resulting in a sharp reduction of the electric field and flat bands over the depletion region, on the side of the N-type c-Si wafer (Fig. 12b). This fact results in a sharp fall in the FF and conversion efficiency (Table 10). In fact under this condition, the strong accumulation of holes on c-Si, can partially deplete even the highly defective P-layer, resulting in a shift of the depletion region from c-Si to the amorphous emitter layer (Fig. 12a). This also means that the carriers can no longer be fully extracted at 0 volts, resulting in a fall in J sc (Table 10). We have found that the current recovers to the normal value of ~36 mA cm -2 only at a reverse bias of 0.3volts . Modeling indicates that for improved performance of N-c-Si HIT cells, the valence band offset has to be reduced by a lower emitter band gap, unless the tunneling of holes exists. where E  (P) and E ac (P) represent respectively the mobility band gap and the activation energy of the P-layer, and 'sbb' is the surface band bending due to a Schottky barrier at the TCO/P interface. With a change of the work function of the TCO, it is this 'sbb' that varies.
In this section we study the dependence of the solar cell output to changes in this surface band bending. We hold the band gap and the activation energies of the P-layer constant at 1.75 eV and 0.3 eV respectively, so that the TCO work function has a direct effect on the front contact barrier height. The results are summarized in Fig. 15. For these sensitivity calculations we have chosen the thickness of the P-layer to be 15 nm . Fig. 13 indicates that both V oc and FF fall off for  b0 ≤ 1.05 eV.
We have also studied the effect of changing the rear P-a-Si:H BSF/TCO barrier height , bL  , in P-c-Si HIT cells. The variation in the current-density -voltage characteristics follow a similar pattern as Fig. 15. Fig. 13. The current density -voltage characteristics under AM1.5 light and 0 volts for different front contact barrier heights. The band gap, the activation energy and the thickness of the P-layer are held constant at 1.75 eV, 15 nm and 0.3 eV respectively, so that only surface band bending changes.

Relative influence of different parameters on the performance of HIT cells
In this section we make a comparative study of the influence on HIT cell performance, of the N ss on the surface of the c-Si wafer, the lifetime () of the minority carriers in c-Si, and the surface recombination speeds (SRS) of free carriers at the contacts. The sensitivity to the first two is shown in Table 11. For all the cases studied here, the P layer has an activation energy of 0.3 eV and a surface band bending 0.21 eV. We note that when the defect density on the surfaces of the c-Si wafer is low, there is some sensitivity of the solar cell output to . In fact the conversion efficiency increases by ~3.22% and ~2.47% in double P-c-Si and N-c-Si HIT cells respectively as varies from 0.1 ms to 2.5 ms. By contrast there is a huge sensitivity to N ss , as already noted in sections 4.2, 4.3 and 5.3; the performance of the HIT cell depending entirely on this quantity when it is high, with no sensitivity to  (Table 11). The lone exception is the N ss on the rear face of N-c-Si, to which solar cell output is relatively insensitive as already noted Finally, the minority carrier SRS at the contacts, that regulates the back diffusion of carriers, has only a small influence in these double HIT cells. The majority carrier SRS does not affect cell performance up to a value of 10 3 cm/s, except the SRS of holes at the contact that is the   Table 11. Sensitivity of double HIT solar cell output parameters to N ss on the front and rear surfaces of the c-Si wafer and minority carrier life-time ().
hole-collector. Hole collection (at the rear contact in P-c-Si HIT and at the front in N-c-Si HIT) is already somewhat impeded by the large valence band discontinuity at the amorphous/ crystalline interface and the lower mobility of holes relative to electrons; hence a low value of SRS of holes at the contacts is expected to have a disastrous influence on hole collection. The effect of lowering S p0 for N-c-Si HIT cells is shown in Fig. 14, and is seen to lead to S-shaped J-V characteristics with a sharp fall in the FF when reduced to ≤ 10 4 cm/sec. In fact when sputtering ITO onto c-Si substrates coated with a-Si:H (intrinsic and doped) films, we sometimes obtain a rather degraded P/ITO interface, where the surface recombination speed is probably reduced. Therefore, Fig. 14 indicates that ITO deposition conditions can also be critical for good solar cell performance.

Conclusions
We have studied the performance of HIT cells on P-and N-type c-Si wafers, using detailed computer modeling. In order to arrive at a realistic set of parameters that characterize these cells, we have modeled several experimental results. We find that the major breakthroughs in improving the performance of these cells having textured N-type c-Si as the absorber layer, come from the introduction of an amorphous BSF layer, by passivating the defects on the c-Si wafer surface and, to a lesser extent, by improving the lifetime of the minority carriers in the c-Si wafer (Table 6).
Modeling indicates that both types of HIT cell output is very sensitive to the defects on the surface of the c-Si wafer, and good passivation of these defects is the key to attaining high efficiency in these structures. An exception to this rule is the defects on the rear face of c-Si in N-type HIT cells, to which there is not much sensitivity. The amorphous/crystalline valence band discontinuity also has a strong impact. In particular, large ΔE v at the emitter Pa-Si:H/N-c-Si contact leads to S-shaped J-V characteristics, unless tunneling of holes takes place; while that at the P-c-Si/P-BSF contact reduces the FF in double P-c-Si HIT cells. It is for this reason that a transition from a front to double HIT structure on P-c-Si does not produce the spectacular improvement observed for N-type HIT cells (Table 6). Solar cell output is also influenced to some extent by the minority carrier lifetime in c-Si. In Table 12 we compare the performance of a P-type and an N-type HIT cell, with low N ss on the wafer surface, and realistic input parameters. We find that the N-type HIT cell shows better performance than a P-c-Si HIT cell with a higher V oc and conversion efficiency, because of a higher built-in potential in the former. However, the fill factor of N-c-Si HIT cells is lower than in P-type HIT cells due to the assumption of ΔE v > ΔE c , resulting in the holes facing more difficulty in getting collected at the front contact in the former case. This fact has also been pointed out by other workers (Stangl et al, 2001, Froitzheim et al, 2002. In P-type HIT cells, the electrons are collected at the front contact and have to overcome the relatively low ΔE c at the crystalline/amorphous interface so that its FF is higher than in N-c-Si HIT.