Numerical Simulation for Optimization of Ultra-thin n-type AZO and TiO2 Based Textured p-type c-Si Heterojunction Solar Cells

A maximum efficiency of 17 % for ultra-thin n-type AZO layer and 17.5 % for ultra-thin n-type TiO2 layer based silicon heterojunction solar cell is reported by optimizing its properties which is much higher than practically obtained efficiency signifying a lot of improvements can be performed to improve efficiency of TiO2/Si and AZO/Si heterojunction solar cell. AZO layer and TiO2 layer is used as n-type emitter layer and crystalline silicon wafer is used as p-type (p-cSi) layer for modelling AZO/Si and TiO2/Si heterojunctions solar cell respectively using AFORS HET automat simulation software. Various parameters like thickness of AZO, TiO2 layer, p-cSi layer, doping concentration of donors (Nd) and effective conduction band density (Nc) are optimized. Finally, texturing at different angle is studied and maximum efficiency is reported at 70 μm thick p-type crystalline Silicon (p-cSi) wafer, that can be very helpful for manufacturing low cost HJ solar cells at industrial scale because of thin wafer and removal of additional processing setup required for deposition of amorphous silicon i-layer. Utilization of TiO2 and Aluminium doped Zinc Oxide as n-type layer and p-cSi as p-type layer can help in producing low cost and efficient heterojunction (HJ) than compared to HJ with intrinsic thin layer HIT solar cells.


Introduction
Demand of energy consumption is tremendously increasing day by day in today's world and to meet the same, contribution from renewable energy sources has to be increased. Conventional non-renewable energy sources are limited and have many environmental concerns. Renewable energy sources are the solution to overcome the problems related to non-renewable energy sources like pollution, limited stock, environmental problems, etc. [1]. In recent times, solar energy is one of most widely commercially used renewable energy source. Photovoltaic solar cell technology is currently dominated by silicon wafer based solar cells by almost 90 % [2]. In recent past, silicon heterojunction solar cells developed by sanyo company based on heterojunction with intrinsic thin layer (HIT) concept is widely used to manufacture solar cells at industrial scale due to their good efficiency, cost effectiveness and economic viability [3,4]. Further, numerous research on thin film based silicon heterojunction solar cell is ongoing using metal oxides as n-type layer with crystalline silicon (p-cSi) wafer as p-type as well as metal oxides as p-type layer with n-type cSi (n-cSi) wafer due to their easy availability and environment friendly [5][6][7][8][9]. Aluminium doped zinc oxide (AZO) and zinc oxide can be used as window layers, antireflection coating (ARC) layer & as TCO layer in solar cells [10,11]. They also find applications in other devices like transducers, ultrasonic oscillators and gas sensors. ZnO can be used as a substitute for indium tin oxide (ITO) as it is cheaper than ITO and also enhances the efficiency of solar cells [12]. ZnO can be doped with elements like Al, B, F, Ga, In etc. to make it n-type ZnO. Titanium dioxide (TiO 2 ) can also be used as ntype layer which has significant electrical conductivity and high visible transparency [13]. TiO 2 can be doped to make further n-type or p-type material, where it can be doped with Cr 3+ , Fe 3+ , Ni + 2 and Co + 2 to make p-type and elements like Sn, N, Al, F etc. to make n-type TiO 2 . TiO 2 can be fabricated using physical and chemical deposition techniques. Some vaccum based techniques like sputtering, pulsed laser deposition (PLD), chemical vapour deposition (CVD) and some solution based techniques like sol-gel, dip/spin coating, and spray pyrolysis can be used for deposition of TiO 2 films. Vaccum based technology is used for fabrication of solid state device, although this technology is more expensive than solution based technology. Sputtering method is suitable for uniform coating on substrate with large area. It has been established as standard technique for deposition of transparent semiconducting oxide films. Pulsed laser deposition (PLD) technique is used for deposition of robust and nanostructured thin films. This technique is very efficient technique which is capable to assist laser desorption and ionization of low molecular weight. Chemical vapour deposition (CVD) offer various advantages over other techniques like purity of thin film, low cost than compared with other vaccum based technology, thin film with different morphology and good adhesion with substrate [13]. Although, sol-gel technique is not suitable to produce TiO 2 thin film for solar cell application, they offer other advantages like compositional control, homogeneity and low crystallization temperature [13]. Spray pyrolysis offers advantages like low cost, scalable and uniform deposition on large area substrate. TiO 2 thin film in its pure form, without doping has low conductivity that makes them unsuitable for solar cell application where doped TiO 2 layer can be used to make them suitable for photovoltaic [14,15]. However, practical efficiency is very low for such solar cells due to various defects and improper optimization of parameters. Their various parameters can be optimized using various numerical simulation softwares like PC1D, AFORS-HET [16], silvaco ATLAS [17,18], TCAD [19,20], AMPS [21], SCAPS 1D [22][23][24] etc. AFORS-HET is an automat simulation software based on Shockley-read-hall recombination statistics which solves one-dimension semiconductor Eqs. [7,25,26]. This software is used for modelling homojunction and heterojunction devices [25,27,28]. This program solves 1-D semiconductor equation which is based on physical differential equation like transport & continuity equation and poisson's equation [29]. Lambert beer law is used which is based on optical model for estimation of optical parameter [7]. In this work, AFORS-HET automat simulation software is used to simulate AZO/Si and TiO 2 /Si heterojunction solar cell and its various parameters like thickness of silicon wafer, thickness of AZO layer, thickness of TiO 2 layer, doping concentration of donors (N d ), effective conduction band density (N c ), and texturing at different angle is optimized [30]. Texturing of silicon wafer at different angle is performed to study the change in behaviour and performance of solar cell with respect to plane heterojunction solar cell [31,32]. Texturing plays important role for improvement in performance of thin film based silicon heterojunction solar cells due to increment in light trapping of incoming light and multiple internal reflection, which helps to increase charge carrier transport and hence, enhances the overall efficiency of solar cell [33,34]. Various literatures are reported for plane and textured (pyramidal and inverted pyramidal) solar cells [35,36]. Efficiency is also dependent at various texturing angle and hence, desired texturing angle can be applied to produce maximum power conversion efficiency from solar cell [37]. Using AZO as n-type material, an efficiency of 6.8 % is reported for Al:ZnO/CdS/CuInSe 2 polycrystalline solar cell in [10]. 6.8 % efficiency is reported for Al:ZnO/Si heterojunction solar cell in [38]. However, maximum theoretical efficiency of 29.43 % can be achieved for silicon heterojunction in [39][40][41] respectively. A maximum efficiency of 17 % for ultra-thin n-type AZO layer and 17.5 % for ultra-thin TiO 2 as n-type layer is achieved by optimizing its properties which is much higher than practically obtained efficiency signifying a lot of improvements can be performed to improve efficiency of TiO 2 /Si and AZO/Si heterojunction solar cell.

Simulation Details & Device Structures
AFORS-HET automat simulation software is used in this work for modelling the AZO/Si and TiO 2 /Si heterojunction solar cell where ultra-thin AZO layer & TiO 2 layer acts as ntype layer and crystalline p-type silicon (p-cSi) wafer acts as p-type absorber layer. Device structure used for modelling in this work is described in Fig. 1. All default values present in AFORS-HET software are considered for the modelling TiO 2 & AZO layer based silicon heterojunction (SHJ) solar cells except the parameters used to be optimized. Illuminance of radiation AM 1.5 is used with power density of 100 mW/cm 2 for simulation in present study. Standard values of Al:ZnO, TiO 2 and p-cSi are taken from references [7,15,25]. Flatband schottky front interface and flatband schottky back interface is chosen as default in present study. No interface effect is studied in this article, hence 'No Interface' is considered as default. Front contact boundary and back contact boundary are chosen as constant (zero) i.e. no absorption loss is considered. Carrier lifetime in silicon is considered as 5 µs; Diffusion length of carriers in silicon wafer is considered to be 80 μm [42]. Resistivity and order of series resistance and shunt resistance of layer has been taken as default values i.e. minimum for series resistance (R s : 0 ohm) and max for shunt resistance (R shunt : 10 30 ohm). However, due to limitations in simulation software, there is no provision to feed the values of carrier lifetime and diffusion length of carriers in silicon wafers and hence, values are reported from literature for the general description of properties related to silicon based solar cells [42]. In this work, following studies are carried out: (i) thickness optimization of p-cSi layer, (ii) thickness optimization of ultra-thin AZO and TiO 2 layer, (iii) optimization of doping concentration of donors (N d ), (iv) optimization of effective conduction band density (N c ) and (v) optimization of texturing at various angles.
Texturing plays important role in enhancing the efficiency of solar cells [33]. Texturing of silicon wafer surface can be performed through chemical etching. Due to textured morphology of layers in solar cells there is re-absorption of reflected rays which helps in minimizing the lost reflected light [12]. Texturing increases excess charge carriers due to light trapping and multiple internal reflection which helps in enhancing overall performance & conversion efficiency of solar cell. Moreover, efficiency also depends on angle at which texturing is performed to produce an efficient solar cell [43]. There are several reports on pyramidal and inverted pyramidal texturing for silicon solar cells [12,33]. In this article, texturing is performed at various texturing angle and performance of modelled AZO/Si heterojunction solar cell is optimized.

Thickness Optimization of P-cSi Silicon Wafer
In this section, thickness of p-type crystalline silicon wafer is optimized. Manufacturing of solar cells using thin p-cSi wafer can be cost effective up to certain extent at industrial scale. Though nowadays n-cSi ingots are also reasonable in cost compared to p-cSi and wafer of around 200 μm thickness are in use at industrial scale. However, through our simulation we have obtained that its thickness can further be reduced to upto 70 μm without affecting its performance. Thickness of silicon wafer is varied from 20 to 500 μm. Thickness of AZO layer and TiO 2 layer is considered as 10 nm; Effective CB density of p-Si, AZO layer and TiO 2 layer as 2.8 × 10 18 cm − 3 , 2.2 × 10 18 cm − 3 and 2.2 × 10 18 cm − 3 respectively and doping density of AZO layer and TiO 2 layer as 1 × 10 18 cm − 3 and 1 × 10 16 cm − 3 respectively; while all other parameters were in accordance with the values reported in Table 1. Efficiency rapidly increases with thickness initially, begins to saturate after 70 μm and remains constant upto 500 μm. This can be well explained as initially as thickness increases, more number of charge carriers are generated and contribute to flow of charge across p-n junction. However, after certain thickness, charge carriers generated does not travel across junction due to thickening of wafer and less diffusion length of charge carriers in silicon wafer which is around 100 μm. When thickness of silicon wafer gets thicker than its diffusion length, charger carriers generated does not travel upto p-n junction and gets recombined and hence charge carriers generated having diffusion length more than 100 μm does not participate in charge collection. Thus, efficiency begins to saturate after 70 μm. Also, film gets flexible when its thickness reduces beyond 50 μm. Experimentally, an ultrathin flexible film of thickness 45 μm has been fabricated by [44] using Cu-assisted chemical etching of bulk c-Si producing conversion efficiency of over 17 %. Also, mechanical stress, multi flexure, fracture and static test has been conducted by [45] for flexible thin films based crystalline silicon solar cells where thickness of flexible thin film varying from 20 to 50 μm. Thus, an ultrathin stable film can be utilized for silicon based HJ solar cells. Hence, the thickness of p-type silicon wafer at 70 μm is optimized in this work. Similar pattern is also observed for short circuit current (J sc ) curve. This behaviour is well illustrated in V oc vs. thickness curve Fig. 2(a), J sc vs. thickness curve Fig. 2(b) and fill factor (FF) vs. thickness curve Fig. 2(c). V oc , J sc and FF values remains nearly constant from 70 to 500 μm; V oc and J sc rapidly decreases on further reducing the thickness of p-cSi layer which accounts for the decrease in efficiency. Fill factor firstly increases slightly and then decreases but this increase is less significant than rapid decrease in V oc and J sc which results in decrease in efficiency. Hence, the

Thickness Optimization of Ultra-thin N-type AZO and TiO 2 Layer
Thickness of AZO and TiO 2 layer is varied from 0.5 nm to 10 nm. Thickness of silicon wafer optimized above is taken as 70 μm; Effective CB density of AZO layer and TiO 2 layer as 2.2 × 10 18 cm − 3 and 2.2 × 10 18 cm − 3 respectively and doping density of AZO layer and TiO 2 layer as 1 × 10 18 cm − 3 and 1 × 10 16 cm − 3 respectively; while all other parameters were in accordance with the values reported in Table 1. Thickness of AZO and TiO 2 layer is varied and open circuit voltage (V oc ), short circuit current (J sc ), fill factor (FF) and efficiency is recorded with respect to thickness of AZO & TiO 2 layer, Fig. 3(a) to (d) represents curve for each respectively. There is no effect of thickness variation of TiO 2 layer on V oc and it remains constant at 546.1 mV. Same pattern is observed for AZO layer as well, However, there is slight enhancement in V oc at 3-4 nm, giving maximum V oc of 549.2 mV below 3 nm. Short circuit current linearly decreases with increase in its thickness giving maximum J sc at 0.5 nm. However, due to practical limitations, deposition of layers using modern techniques is limited upto 3 nm for stable film and hence J sc at 3 nm giving short circuit current of 29.12 mA for ultra-thin AZO layer and 29.02 mA for ultra-thin TiO 2 layer based solar cell is considered as optimized short circuit current [7]. This behaviour is expected, since thinning of emitter layer will contribute to flow more number of charge carriers generated in absorber layer and easy transport across layer due to decrease in resistance, thus recombination rate also decreases; hence resulting in enhancement of short circuit current with decrease in thickness of emitter layer. Fill factor also decreases linearly with increasing thickness. This can be attributed due  to decrease of series resistance as we decrease its thickness. Hence, overall efficiency increases linearly with decreasing thickness and gives maximum efficiency of 12.84 % for ultra-thin n-type AZO layer and 12.59 % for ultra-thin n-type TiO 2 layer based HJ solar cell.

Doping Concentration of Donors (N d )
Doping of donor concentration plays an important role in enhancing the charge carriers which resulted in improved efficiency. Figure 4(a)

Effective Conduction Band Density
During carrier charge transport, effective conduction band density and effective valence band density are the major density of states that plays important role during charge transport. Conduction band density is varied to study the effect of density of states in solar cells as simulation of device without using DOS would give ideal results considering no defects in states. But in reality, there are defects in layers and hence DOS parameters are introduced in the simulated solar cell in order to achieve practical comparable characteristics. In the present study, density of states is in disordered induced tail states for AZO and TiO 2 based silicon HJ solar cells. Similar type of variation is reported by Slimane et al. where they varied tail density of states from 5 × 10 14 to 5 × 10 20 cm − 3 while keeping Gaussian density of states fixed. They also varied gaussian density of states from 1 × 10 16 to 5 × 10 18 cm − 3 while keeping tail density of states fixed [47]. In another kind of material, hydrogenated amorphous silicon is classified as strongly disorder semiconductor at 7.4 × 10 18 cm − 3 localized states [48]. Figure 5.1 to 5.4 represents the variation of V oc , J sc , FF and efficiency curve with respect to effective conduction band density respectively. Effective conduction band density is varied from 1 × 10 15 cm − 3 to 1 × 10 19 cm − 3 as shown in Fig. 5(a) to (d). Thickness of silicon wafer is taken as 70 μm; thickness of AZO & TiO 2 layer at 3 nm; and doping density of AZO layer and TiO 2 layer as 1 × 10 15 cm − 3 and 1 × 10 14 cm − 3 respectively; while all other parameters were in accordance with the values reported in Table 1. Similar variation in tail density of states from 10 13 cm − 3 to 10 21 cm − 3 has been reported in [47]. Open circuit voltage remains constant on varying conduction band density for both, AZO & TiO 2 layer. Short circuit current linearly decreases slightly on increasing N c giving maximum J sc of 30.4 mA at 10 15 cm − 3 for TiO 2 layer and 30.08 mA at 10 19 cm − 3 for AZO layer based solar cell. Fill factor is significantly influenced with N c and thus contributes more to efficiency. Hence, efficiency follows the pattern like fill factor. Efficiency increases initially exhibiting best efficiency at around 10 16 cm − 3 and remains nearly constant thereafter which can be attributed to increase in shunt resistance and decrease in series resistance initially thus affecting fill factor of device accordingly. After certain level, there is no significant change in shunt resistance and series resistance with change in effective conduction band density resulting in nearly constant fill factor, thus efficiency also gets saturated. However, initial increase in efficiency is more significant in case of TiO 2 based solar cell than compare to AZO based silicon solar cell and further study needs to be carried out for more fundamental reason behind this. Maximum efficiency of 13.24 % for AZO layer and 13.21 % for TiO 2 layer at 5 × 10 15 cm − 3 and 1 × 10 17 cm − 3 respectively is obtained for AZO/Si and TiO 2 /Si based HJ solar cells respectively.

Texturing Angle
Efficiency of solar cell can be significantly enhanced through texturing [35]. Many reports are there on pyramidal and inverted pyramid textured silicon wafer solar cell. Texturing angle is varied from 0°to 89°as shown in Fig. 6

Conclusions
Numerical simulation is performed using AFORS-HET software program to achieve a maximum efficiency of 17% and 17.5 % for ultra-thin n-type AZO and TiO 2 layer based silicon HJ solar cell by optimizing its various parameters. In this work, thickness of p-cSi wafer is optimized at 70 μm to obtain an efficiency of 12.84 % for ultra-thin AZO layer and 12.16 % for ultra-thin TiO 2 layer based p-cSi HJ solar cells respectively. It is followed by optimizing thickness of ultra-thin TiO 2 and AZO layer at 3 nm to obtain an efficiency of 12.84 % for AZO layer and 12.59 % for TiO 2 layer based HJ solar cell respectively. Doping concentration of donors (N d ) is optimized at 1 × 10 15 cm − 3 for ultra-thin AZO layer and 1 × 10 14 cm − 3 for ultra-thin TiO 2 layer to obtain efficiency of 13.13% and 13.21 % for AZO/Si and TiO 2 /Si HJ solar cells respectively. Effective conduction band density is optimized at 5 × 10 15 cm − 3 for AZO layer and at 1 × 10 17 cm − 3 for TiO 2 layer based solar cell and obtained an efficiency of 13.24% and 13.21 % respectively. Finally, the role of surface texturing at various angle is studied and reported the maximum efficiency of 17% and 17.5 % for AZO and TiO 2 layer based silicon HJ solar cells respectively. Linear increase in efficiency with respect to texturing angle is observed, where efficiency of 14.21 % for AZO layer and 14.45 % for TiO 2 layer based silicon HJ solar cells for pyramidal surface texturing is obtained. Thickness optimization of p-cSi at 70 μm and removal of intrinsic amorphous silicon layer can be very cost effective for manufacturing AZO/Si heterojunction solar cells at industrial scale for commercial production; as deposition of i-layer a-Si and other similar based HJ solar cells with intrinsic layer involves additional processing setup. Processing of such layers also has some serious environmental & safety issues. Optimization of texturing angle plays a significant role in enhancing the efficiency above 17 % for the above modelled HJ solar cell. Hence, efficiency reported using AZO and TiO 2 layer based silicon heterojunction solar cell in this article can be cost effective and efficient solar cell. Such results are encouraging and exciting for practical applications. However, practically it is challenging to texture the silicon wafer at such angle with high accuracy. Lasers can be used to texture silicon surface at such specific angles though such process may cost more. Further investigation on above modelled cell can be performed by introducing intrinsic thin layer, p + layer, n + layer and BSF layer to simulate HIT, HITBSF and HIT-BIFACIAL solar cells to further improve the efficiency of solar cell.
Data Availability This paper does not use any raw or processed data. It includes all the data necessary to perform the calculations and supports the findings of this study.

Declarations
Conflict of Interest Authors declare no conflict of interest that are directly or indirectly related to the work submitted for publication.
Research Involving Human Participants or Animals Not applicable. Fig. 6 The performance of modelled solar cell with variation in texturing angle where (a) -(d) represents the V oc , J sc , FF and η respectively with respect to texturing angle