Study of Au/n-Ti2S/p-Si/Al Schottky-Type Thin Film Heterojunction Solar Cells: Computer Simulation Modeling

E-mail: ali_02us@yahoo.com Abstract: The Au/n-Ti2S/p-Si/Al heterojunction with intrinsic thin-layer solar cells were analyzed by AFORS-HET software program. Thickness of the emitter intrinsic layer and the interface state density of such cells were studied. In which, the intrinsic layer inserted between the Ti2S and crystalline p-type silicon substrate, reduce the interface state density. The thinner intrinsic layer is better than thicker one, when the interface state density is lower than 10 10 cm −2 .V −1 . As the thickness of the emitter increased, both short-current density (J) and the conversion efficiency were decreased. The dependence of J-V characteristics of the Au/n-Ti2S/p-Si/Al heterojunction solar cell on Front and back Surface Recombination Velocity (SRV) was studied. By optimizing the initial parameters set, the Au/n-Ti2S/p-Si/Al solar cell reaches a high efficiency (η) up to 21.849% (FF: 0.834, Voc: 0.666 V, Jsc: 39.39 mA/cm 2 ).


Introduction
A silicon solar cell is a typical photovoltaic cell fabricated from poly-silicon and monocrystalline silicon solar cells with conversion efficiency of 19.8 and 24.4%, respectively (Zhoa et al., 1998). The amorphous silicon solar cell of multilayered p-i-n unit cell structure with a high open voltage of 2.0 V has been developed by (Hamakawa et al., 1979). A conversion efficiency of 17.0% of the thinner solar cells fabricated by (Reuter et al., 2009) has been obtained. To improve the conversion efficiency, the front surface of a solar cell was generally textured (Muller et al., 2004). To facilitate efficient light trapping, an additional textured photonic crystal and backside reflector were fabricated on the back surface (Zeng et al., 2008).
The simulated device performance is strongly related to the doping of the n-Ti 2 S layers. Sufficient doping and layer thickness has to be chosen to introduce the band bending at the n-Ti 2 S/p-Si interface determining the built-in voltage and therefore the upper limit of V oc (Stangl et al., 2004;Leendertz et al., 2011;Schulze et al., 2011;Chen and Zhu, 2012). However, with high doping the junction recombination can increase V oc is lowered for doping concentration above a certain level (Chakraborty et al., 2013;Haque et al., 2013). A fundamental problem when contacting the ptype Si with the n-type n-Ti 2 S transparent conductive oxides TCO's is the formation of a Schottky barrier. To account for the Schottky barrier, a higher n-Ti 2 S doping and/or layer thickness are required, which can lead to a trade-off between V oc and FF and J sc and FF, respectively (Martın de Nicolas et al., 2011;Saron et al., 2013). A solar cell design characterized by a silicon heterojunctions SHJ (emitter) only at the rear and a diffused Front Surface Field (FSF) featuring negligible parasitic absorption at the front to overcome these limitations (Bivour et al., 2010;Wunsch et al., 2006). The design of such solar cell is referred as a hybrid SHJ solar cell. This device structure is featuring a well-known and robust front and allows an increased degree of freedom for the design of the SHJ since parasitic absorption in the n-Ti 2 S layers tack is not an issue. Therefore, junction optimization can be focused on carrier transport and/or carrier recombination. A contact layer for a wide range of higher TCO can be used, indispensable for its lateral conductivity at the front of SHJ solar cells, is not mandatory for the rear SHJ.
In this study, The characteristics of Au/n-Ti 2 S/p-Si/Al hetrojunction (HIT) solar cells based on silicon a solar cell structure designed with AFORS-HET simulation program have been studied. Also, the best TCO layer regarding the work function, in addition to the required low interface state density at the silicon surface has been determined.

Solar Cell Simulation Tools
The simulation programs are mostly reduced to one dimensional analysis as compared with highly expensive commercial programs, which can make two and three dimensional device simulations and requiring workstations for running. The simulation programs solve numerically the Poisson equations (charge neutrality), in addition the continuity equations for holes and electrons. The boundary conditions and some effects associated with the interfaces in a solar cell (such as, interface carrier recombination) is the fundamental difference in the way that they handle.
SimWindow is a freely available one dimensional drift/diffusion simulator for semiconductor devices. ADEPT-F from the group of Jeff Gray, Purdue University (Gray et al., 1991) has been widely used. The program ASPIN of the University of Ljubljana (Smole et al., 1994) has been used for CIGS cells and for a: Si cells. AFORS-HET has been developed by a group of the Hahn-Meitner Institute of Berlin (Froitzheim et al., 2003) for simulating hetero-junction solar cells. Programs such as SILVACO-ATLAS (Michael and Michalopoulos, 2002) and Cross Light-APSYS (Brown et al., 2010) are expensive programs used in the silicon microelectronic industry; they are also usable for solar cells, especially for developing microelectronic devices and also implement a multi-dimensional (two-or three-dimensional) simulation of Si wafer processing. In the case of polycrystalline thinfilm solar cells require of two-or even three-dimensional programs because of grain boundaries and non-planar interfaces. Grain boundary effects seem to be more prominent in CdTe cells than in CIGS cells. Though onedimensional problems effectively average the effect of grain boundary states over the bulk, they have been surprisingly successful.

Solar Cell Numerical Modeling
Before any simulation process for a solar cell, a good understanding of the cell structure and the physical parameters involved is required. This sometimes is not possible because there is not a full characterization of the real cell structure. As example. The real structure for CdS/CIGS solar cells is not well known because an interfacial layer between the CdS and the CIGS layer may appear with special properties depending upon the cell preparation method. It has been suggested that close to this interface a thin inversion (n-type) CIGS layer exist in contact with a more stoichiometries p-type CIGS layer. Some parameters which are well known for bulk materials are not adequately known for thin polycrystalline materials and therefore it is not easy to select the appropriate values for simulating the solar cells based on such materials. The existence and properties of such layer depends upon the deposition method and conditions for both the CIGS and the CdS layers. Moreover, the efficiency of solar cells has been obtained experimentally, but not the properties of each of the layers and vice versa.

Results and Discussion
The light J-V characteristics, at the spectrum of air mass 1.5 used in the AFORS-HET software modeling tool is shown in Fig. 1b. This corresponds to a power density of 100 m W/cm 2 . The values of cell parameters including short circuit current density (J sc = 36 mA/cm 2 ), open circuit voltage (V oc = 0.650 V), fill factor (FF = 82%) and efficiency of the cell is 18.5%. At the same time, the schematic diagram of the fabricated Au/n-Ti 2 S/psi/Al HIT thin film solar cell is shown in Fig. 1a.
The dark current-voltage curve of Au/n-Ti 2 S/p-Si/Al heterojunction in both forward and reverse bias is shown in Fig. 2. The formation of a depletion region between Ti 2 S layer and Si(111) single crystal is probably the reason for exponential dependence of the forward current in the lower voltage range. It is evident that the junction exhibits strong rectifying characteristics showing diodelike behavior. According to the relation: The rectification ratio, R r , (the ratio of the forward current to the reverse current at a certain applied voltage), of the Au/n-Ti 2 S/p-Si/Al heterojunction thin film solar cell can be obtained.

Optimization of the Intrinsic Layer Thickness
Photovoltaic characteristics of High Efficiency Computer Simulation HECS solar cell vary with the thickness of the intrinsic layer I is shown in Fig. 3. From the data it is evident that, the conversion efficiency of HECS is up to 19.27% with 1nm intrinsic layer is inserted, which is 0.4% higher compared with no intrinsic layer solar cell. But as I layer thickness increases, the conversion efficiency decreases. When the thickness of an intrinsic layer reaches 5 nm, the conversion efficiency of HECS solar cell with intrinsic layer is equivalent to solar cell with no intrinsic layer. Compromising the production processes and the conversion efficiency, the optimal intrinsic layer thickness should be set at 3 nm. In addition, from Fig. 3, we can see that, with the increase of intrinsic layer thickness, the open circuit voltage keeps almost unchanged, while the short circuit density decreases. This is because, as I layer thickness increases, the electric field strength of space charge region decreases and the short-spectrum absorption of amorphous silicon increases. The corresponding light-induced carriers cannot be effectively collected, resulting in the decrease of short circuit current density.  For the actual solar cell production processes, the impact of interface state density cannot be ignored. In this study, the interface defect states are assumed to insert between the layer and the p-type crystalline silicon substrate layer. The interface states are assumed as continuous donor-like states and acceptorlike states with an average distribution in the band gap, with the capture cross sections of electron and hole both are 10 −14 cm 2 . Theinterface state density of n-Ti 2 S/p-Si interface varies from 10 9 cm −2 .eV −1 to 10 13 cm −2 .eV −1 and its effects on the photovoltaic performances of the solar cell are shown in Fig. 4.
As the emitter thickness increases, the open circuit voltage changed little, while the short circuit current is dramatically reduced as shown in Fig. 5. This is because as the emitter thickness increases, the absorption of the photon in emitter has increased. Considering the large amounts of recombination centers and the feature of no electric field in emitter, the photo-induced carriers are impossible to reach the edge of space charge region and contribute to light current. On the contrary, they will be recombined in the region and disappeared, resulting in the reduced short-spectrum response and short-circuit current. Fill factor also decreases with the n region thickness increases. While, as the n layer thickness increases, series resistance will increases, which will reduce the fill factor (Ren et al., 2008). The conduction mechanisms' information can be obtained by plotting current-voltage curves at different temperatures. Semi logarithmic plots of the forward current-voltage for an Au/n-Ti 2 S/p-Si/Al heterojunction in the dark are given in Fig. 6. It is clear from the figure that, there are two different conduction mechanisms which characterize these curves for the two distinct regions. The exponential behavior, within the narrow, low forward voltage (V≤0.5 V), agrees with rectification characteristics which are generally described by different models (Oueriagli et al., 1992). These data in the range (V≤0.5 V) were fitted using the Schottky Equation 2 (Sze, 1981): where, k B is Boltzmann's constant, n is the diode quality factor and I s is the saturation current which can be obtained by extrapolating the ln I-V portion to the ln I axis at zero voltage and found to be 8.3×10 −7 A at room temperature and increases with increasing elevated temperatures to be of 3.3×10 −6 A at 363 K as shown in Fig. 6. The diode quality factor n is found to be independent of temperature in the investigated range. This behavior indicates thermionic emission mechanism in the cell under investigation. The recombination of electrons and holes in the depletion region and/or the increase of the diffusion current due to increasing the applied voltage leads to the change of the diode quality factor from unity (Rhoderick, 1978;Van and Potje-Kamloth, 2001;El-Nahass et al., 2005;Forrest et al., 1984). The temperature dependence of electrical resistivity for Ti 2 S thin films of different thicknesses is shown in Fig. 7. It is clear from the figure that the electrical resistivity depends on thickness in the investigated range. It is also clear that the relation gives two straight lines which mean that there are two conduction mechanisms: Where: ∆E = The activation energy ρ o = The pre-exponential factor of the resistivity.
It is found that the activation energy decreases from 0.453 to 0.392 eV with the increase in the film thickness from 100 to 600 mm, respectively, which may attribute to the quantum size effect.

Simulated J-V Characteristics as a Function of the Surface Recombination Velocity (Front and Back)
The variation in J-V characteristics with respect to S1 is shown in Fig. 8. For most semiconductors, the surface recombination velocity is of the order of 10 7 cm/s but, experimentally, it has become possible to reduce the value of S1 to 10 3 cm/s. As the front surface recombination velocity increases, the values of cell performance parameters such as J sc , V oc , fill factor and efficiency decreases. Table 1 shows the calculated values of the cell parameters with the variation of S1.  The current density also reduces as S2 increases (Fig.  9). It is revealed that, as S2 decreases the values of Jsc increases. This is because, as S2 increases, the carriers start recombining at the front surface which reduces the current and other associated cell parameters. For this structure, the oxidation and metallization followed by photolithography on the front surface. The metal contact helps to collect carriers and SiO 2 reduces the recombination on the front surface. Table 2 shows the calculated values of the cell parameters according to S2.

Conclusion
In this study, a computer simulation modeling for the Au/n-Ti 2 S/p-Si/Al Schottky-type thin film HIT solar cell with AFORS-HET program has been done.
It was found that with the increase of the (n) layer thickness, the short-spectrum response and the shortcircuit current density of solar cell will decrease. An intrinsic amorphous silicon layer is used to reduce the interface defect state density. If the interface state density is low, the better intrinsic thickness is no more than 5nm. The thickness of BSF has little effect on the conversion efficiency, while reasonable doping and band gap design can improve efficiency more than 2 percentage points. The photovoltaic parameters of HIT solar cells were Voc = 678.9 mV, J sc = 37.35 mA/cm 2 , FF = 83.97 and η = 21.88% for back surface recombination velocity of 10 3 cm/s. While, the photovoltaic parameters of HIT solar cells are V oc = 666 mV, Jsc = 39·39 mA/cm 2 , FF = 0·834 and η = 21.88% of the front surface recombination velocity of 10 3 cm/s.

Acknowledgement
The author wishes to thank Prof. O. Shalabiea from the Physics department/faculty of Science/NBU/KSA for his revision of the article.

Author's Contributions
The author developed a computer simulation for Au/n-Ti 2 S/p-Si/Al Schottky-type Thin Film Heterojunction Solar Cells to perform the solar cell efficiency.

Ethics
This article is original and contains unpublished material. The corresponding author confirms that no ethical issues involved.