The influences of the front work function and intrinsic bilayer (i₁, i₂) on p-i-n based amorphous silicon solar cell’s performances: A numerical study

Abstract

In this study, the front work function WF_ITO and absorber layer bandgap’s influences on two solar cells structure performances, namely ITO/(p)a-Si:H/(i)a-Si:H/(n)a-Si:H/metal (single intrinsic, S_int) structure and ITO/(p)a-Si:H/(i₁)a-Si:H/(i₂)a-Si:H/(n)a-Si:H/metal (double intrinsic, D_int) structure, fabricated using RF-PECVD method were simulated, using AFORS-HET (Automated FOR Simulation of Heterostructures) software. Based on these simulations, the work functions (WF_ITO) value ought to range from 4.9 to 5.7 eV, in order to determine the optimum WF_ITO for high solar cell efficiency, confirmed with the J-V dark characteristic, the band diagram in thermodynamics equilibrium, build-in electric field distribution, trapped holes density, as well as the quantum efficiency. The simulation results showed the D_int structure’s external parameters (e.g., V_OC,J_SC, FF, E_ff) are higher, compared to the S_int structure. Furthermore, the absorber (i₁ and i₂) layers bandgap is optimized in an effort to improve the D_int solar cell’s performance. According to the results, the D_int structure had a 10.76 % maximum efficiency (V_OC = 969.8 mV, J_SC = 16.03 mA/cm², and FF = 70 %), using WF_ITO, i₁ layer bandgap, and i₂ layer bandgap of 5.7 eV, 1.82 eV, and 1.86 eV, respectively.

Keywords:

• WF_ITO
• RF-PECVD
• AFORS-HET
• a-Si:H
• bandgap
• absorber layers

PUBLIC INTEREST STATEMENT

Hydrogenated amorphous silicon-based solar cells (a-Si:H) have several advantages to be developed as inexpensive, non-toxic, and environmentally friendly solar cells. In this study, optimization efforts were carried out to increase the conversion efficiency through simulation of the (p-i-n)a-Si:H structure solar cells fabricated using RF-PECVD realized by our research group. Modification of the work function at the ITO/(p)a-Si:H interface and the addition of intrinsic layers with different band gap values resulted in a new structure (p-i₁-i₂-n)a-Si:H which has been shown to increase the conversion efficiency, both based on experimental and simulation results. Furthermore, the simulation results are compared with the simulation results of other similar thin-film solar cells. The results showed that the structural modification using the work function value at the appropriate ITO/(p)a-Si:H interface and the addition of an intrinsic layer on the (p-i-n)a-Si:H structure resulted in higher V_OC values and good conversion efficiency. The proposed structure of the (p-i₁-i₂-n) solar cells provides a reference for further development in solar cells technology.

1. Introduction

Hydrogenated amorphous silicon (a-Si:H) is a semiconducting material explored in the last three decades, due to its potential application in thin-film solar cell development. Green et al, 2021, reported a-Si:H single-junction based solar cells have a low efficiency of about 10.2% (Green et al., 2021), due to several limitations, including parasitic optical absorption in doped layers, defects at p/i and i/n interfaces, lower optical absorption in the absorber layer, and limited light trapping within the cells (Shin et al., 2017). Therefore, one of the main issues to increase the a-Si: H solar cell’s efficiency is to improve the quality a-Si:H layers. The intrinsic layers (i-a-Si:H) must have good electrical transport, in order to sustain photogeneration for holes and electrons to exit the device before recombination. In addition, this layer must have a suitable ability to absorb light and consequently, generate more electron-hole (e-h) pairs (Son et al., 2018). According to a previous study, adding an active layer with a different bandgap in the p-i-n layer with an optimum thickness in order to maintain material quality improved the solar cell’s efficiency from 5.61 % (p-i-n type) to 8.86 % (p-i₁-i₂-n type; Prayogi et al., 2021). The TCO’s work function also strongly influences the cell’s performance (Belfar, 2015). Thus, quality TCO/(p)a-Si:H contact, as well as Ohmic contact, is achievable through increased TCO work function, in order to minimized the band offset, and consequently, reduce the device’s electron injection barrier height (Y. S. Park et al., 2013).

The energy band offset between semiconductor and TCO ought to be minimized, in order to improve ohmic contact. Therefore, inserted transparent conductive oxides (for instance, Indium Tin Oxide, ITO) with high conductivity (σ > 10³ S/cm), good transparency in the visible range (T > 90 %), and higher work function values are required for the higher possibility to carrier injection into TCO/(p)a-Si:H interface. For thin film solar cells, a work function of TCO associated with carrier injection into TCO/(p)-window interface which influences plays a dominant role in the device parameters such as V_OC and FF (Oh et al., 2012; Rached & Mostefaoui, 2008). The deposition of ITO films on Corning 1737 substrate, using RF-Magnetron Sputtering method improved ITO work function from 4.67 to 5.66 eV, by the O₂ plasma treatment and an almost stable resistivity (J. Park et al., 2013). Meanwhile, the electrical and optical characteristics of the ITO films are improved by doping the films with high permittivity materials (Zr, ZrO₂), and this results in high mobility and work functions due to the excellent surface (Hussain et al., 2014; Khokhar et al., 2020; Zhang, 2010). Furthermore, optical losses in TCO were reduced without compromising with R_s and recombination loss, using ITO/SiO_x stacks, to produce the short circuit current density (J_SC) > 41.3 mA/cm², with a 100 Ω sheet resistance, while ITO/SiN_x/SiO_x produced a 42 mA/cm² J_SC, with a 300 Ω sheet resistance (Herasimenka et al., 2016). Cruz et al., also reported the effect of various TCO (ITO, ZnO:Al, IO:H) as rear-junction of the silicon heterojunction solar cells, through experiments and simulation (Cruz et al., 2019).

In this study, the effect of changes in work function (WF_ITO) of the ITO/p-layer interface, on the single intrinsic layer, S_int (p-i-n type) and double intrinsic layer, D_int (p-i₁-i₂-n type) solar cell performances were simulated using AFORS-HET software. The band diagrams, J-V characteristics, electrical field distribution, trapped holes density, and quantum efficiency were also simulated, to further understand the solar cells’ high performances. In addition, the optimum absorber layer bandgaps’ influence in improving the D_int structure’s optical and electrical output was investigated.

2. Simulation methods

2.1. Physical model

This study used well-practiced AFORS-HET to accurately evaluate the effect of numerous parameters on the solar cell’s performances. This software solves the 1-D Poisson´s equation and the continuity equation for electrons as well as holes, using Shockley–Read–Hall (SRH) recombination statistics. Also, e-h pair generation in the absorber layer is estimated with the Beer–Lambert absorption equation, using the optical model in AFORS-HET. The detailed equation used in AFORS-HET is expressed in (Stangl, 2010).

(1) $\frac{{\epsilon }_o{\epsilon }_r\left(x\right)}{q}\frac{\mathrm{\partial }{\varphi }^2\left(x,t\right)}{\mathrm{\partial }{x}^2}=p\left(x,t\right)-n\left(x,t\right)+N_D\left(x\right)-N_A\left(x\right)+\sum _{trap}{\rho }_{trap}\left(x,t\right)$(1)

(2) $\frac{\mathrm{\partial }{J}_n\left(x,t\right)}{\mathrm{\partial }x}-\frac{1}{q}\left(\frac{\mathrm{\partial }{J}_n\left(x,t\right)}{\mathrm{\partial }x}\right)=G_n\left(x,t\right)+R_n\left(x,t\right)-\frac{\mathrm{\partial }n\left(x,t\right)}{\mathrm{\partial }t}$(2)

(3) $+\frac{1}{q}\left(\frac{\mathrm{\partial }{J}_p\left(x,t\right)}{\mathrm{\partial }x}\right)=G_p\left(x,t\right)-R_p\left(x,t\right)-\frac{\mathrm{\partial }p\left(x,t\right)}{\mathrm{\partial }t}$(3)

where ${\epsilon }_o{\epsilon }_r$ is the absolute dielectric constant, $\varphi \left(x,t\right)$ is the electric potential, $q$ is the electron charge, $n\left(x,t\right)$ and $p\left(x,t\right)$ are electrons and holes densities, $N_D\left(x\right)$ and $N_A\left(x\right)$ are the doping densities (donor and acceptor) at the fixed position $x$, ${\rho }_{trap}$ is the defect density of charge defect specifying the number of traps at any energy position E within band gap (the defect type can be empty or occupied with a single or double electron),$G\left(x,t\right)$ denotes the generation rate for carriers, $R\left(x,t\right)$ is the recombination rate, respectively.

Furthermore, localized state density describing layers a-Si:H is expressed as exponential band tail defect states (Urbach tails) and Gaussian mid-gap states (dangling bond) is expressed in (Stangl, 2010).

(4) $N_{trap}\left(E\right)=N_{trap}^{C,tail}exp\left[-\left(\frac{E_C-E}{E_{trap}^{C,tail}}\right)\right]$(4)

(5) $N_{trap}\left(E\right)=N_{trap}^{V,tail}exp\left[-\left(\frac{E_C-E}{E_{trap}^{V,tail}}\right)\right]$(5)

(6) $N_{trap}\left(E\right)=\frac{N_{trap}^{db}}{{\sigma }_{trap}^{db}\sqrt{2}}exp\left(-\frac{1}{2}{\left(\frac{\left(E-E_{trap}^{db}\right)}{{\sigma }_{trap}^{db}}\right)}^2\right)$(6)

where $N_{trap}^{C,tail}$ and $N_{trap}^{V,tail}$ are the tail state density per energy range at the conduction and valence bands, $E_{trap}^{C,tail}$ and $E_{trap}^{V,tail}$ are characteristic decay energy (Urbach energy) of the conduction and valence bands, E_V and E_C are the valence and conduction band energies, $N_{trap}^{db}$ is total dangling bond state density, $E_{trap}^{db}$ is specific energy of Gaussian dangling bond peak, and ${\sigma }_{trap}^{db}$ is standard deviation of the Gaussian dangling bond distribution.

2.2. Devices structures and input parameters

In this study, the S_int and D_int hydrogenated amorphous silicon solar cell structures were fabricated by our research group, fabricated using RF-PECVD (MVSystem Inc., USA), as shown in Figure 1. Meanwhile, Figure 2(a-e) shows the simulation details, ITO/(p)a-Si:H(15 nm)/(i)a-Si:H(600 nm)/(n)a-Si:H(25 nm)/metal (S_int), and ITO/(p)a-Si:H(15 nm)/(i₁)a-Si:H(300 nm)/(i₂)a-Si:H(300 nm)/(n)a-Si:H(25 nm)/metal (D_int). Meanwhile, the solar cell’s second structure was fabricated with the (i)a-Si:H split into two parts, (i₁)a-Si:H (300 nm and Eg = 1.70 eV) as well as (i₂)a-Si:H (300 nm and Eg = 1.85 eV). The structure detailed fabrication was carried out as described by (Prayogi et al., 2021). Figure 2(c-e) shows the (p)a-Si:H (i)a-Si:H, and (n)a-Si:H layers’ gap states distribution, described as exponential band tail defect states and Gaussian mid-gap states (dangling bond states).

Figure 1. Prototypes of p-i-n and p-i₁-i₂-n based amorphous silicon solar cell’s fabricated using RF-PECVD reactor realized in our research group.

Figure 2. Schematic of (a) single intrinsic (S_int) structure, (b) double intrinsic (D_int) structure, (c-e) the DOS for different types of the a-Si:H produced by AFORS-HET simulator. D-like and A-like declares donor like and acceptor like Gaussian mid-gap states, VB-tail and CB-tail declares valence band and conduction band, respectively.

The effects of WF_ITO at ITO/(p)a-Si:H interface on the S_int and D_int solar cell devices’ performances were observed numerically using AFORS-HET, however, this was not studied by Prayogi, et al. In addition, the absorber (i₁,i₂) layers’ bandgap was optimized for improved D_int solar cell performance. The radiation AM1.5 G spectrum with 100 mW/cm² power density was used as illuminating source, while the operational temperature was 300 K. Meanwhile, for parameters input simulation, the surface recombination velocity (S_it) of the front as well as back contact was assumed to be both 1.0 × 10⁷ cm/s. The barrier height at front contact ${\phi }_{b0}$ (ITO/(p)a-Si:H layer) was taken to the calculation by changing the WF_ITO, while the barrier height at back contact ${\phi }_{bL}$ ((n)a-Si:H layer/metal) was kept constant 0.2 eV. Also, the front contact was assumed to reflect (RF) 10 % of the incident light, while the back counterpart was assumed to be 0 or no back reflector (RB). The p-window and n layers’ mobility bandgap were set to be 2.0 eV and 2.2 eV, respectively, while the absorber layers (i₁ and i₂) counterpart ranged from 1.7 to 1.86 eV. Table 1 shows the typical parameters used in the simulations in more detail, as described in previous studies (Belfar, 2015; Hernández-Como & Morales-Acevedo, 2010; Prayogi et al., 2021).

Table 1. Parameters input for simulation of the solar cells using AFORS-HET

Parameters	(p)a-Si:H	(i1)a-Si:H	(i2)a-Si:H	(n)a-Si:H
Layer (nm)	15	100–500	100–500	25
Dielectric constant	11.9	11.9	11.9	11.9
Electron affinity (eV)	3.8	3.80	3.80	3.80
Bandgap (eV)	2.0	1.70–1.86	1.70–1.86	2.2
Effective cond. band density (cm^−3)	2.5 x 10^20	2.5 x 10^20	2.5 x 10^20	2.5 x 10^20
Effective val. band density (cm^−3)	2.5 x 10^20	2.5 x 10^20	2.5 x 10^20	2.5 x 10^20
Acceptor concentration, Na (cm^−3)	3.0 x 10^18	0	0	0
Donor concentration, Nd (cm^−3)	0	0	0	1.0 x 10^19
Electron (hole) mobility (cm^2V^−1s^−1)	10 (1)	20 (2)	20 (2)	10 (1)
Thermal velocity of electron (hole) (cms^−1)	1.0 x 10^7	1.0 x 10^7	1.0 x 10^7	1.0 x 10^7
Defect density at conduction (valence) band edge (cm^−3eV^−1)	6.67 x 10^20(6.67 x 10^20)	2.33 x 10^21(2.33 x 10^21)	2.0 x 10^21(2.0 x 10^21)	2.0 x 10^21(2.0 x 10^21)
Urbach energy for conduction (valence) band tail (eV)	0.03(0.06)	0.03(0.06)	0.03(0.06)	0.03(0.06)
Capture cross-section σe (σh) for conduction band tail (cm^2)	1.0 x 10^−17(1.0 x 10^−15)	1.0 x 10^−17(1.0 x 10^−15)	1.0 x 10^−17(1.0 x 10^−15)	1.0 x 10^−17(1.0 x 10^−15)
Capture cross-section σe (σh) for valence band tail (cm^2)	1.0 x 10^−15 (1.0 x 10^−17)	1.0 x 10^−15 (1.0 x 10^−17)	1.0 x 10^−15 (1.0 x 10^−17)	1.0 x 10^−15 (1.0 x 10^−17)
Gaussian density of states (cm^−3)	8.0 x 10^17	8.0 x 10^15	8.0 x 10^15	8.0 x 10^17
Gaussian peak energy for donor(acceptor) (eV)	1.22(0.70)	1.22(0.70)	1.22(0.70)	1.22(0.70)
Standard deviation of Gaussian for donor (acceptor) (eV)	0.23(0.23)	0.23(0.23)	0.23(0.23)	0.23(0.23)
Capture cross-section σe (σh) for donor-like Gaussian states (cm^2)	1.0 x 10^−14 (1.0 x 10^−15)	1.0 x 10^−14 (1.0 x 10^−15)	1.0 x 10^−14 (1.0 x 10^−15)	1.0 x 10^−14 (1.0 x 10^−15)
Capture cross-section σe (σh) for acceptor-like Gaussian states (cm^2)	1.0 x 10^−15 (1.0 x 10^−14)	1.0 x 10^−15 (1.0 x 10^−14)	1.0 x 10^−15 (1.0 x 10^−14)	1.0 x 10^−15 x 10^−14)

3. Simulation results and discussion

3.1. Influences of WF_ITO on the performances of the solar cells

In this simulation, the ITO work function’s values were varied between 4.9 to 5.7 eV, according to experimental results deposited by RF sputtering, depending on deposition conditions (Kim et al., 2009; Klein et al., 2010; Y. S. Park et al., 2013). Figure 3 illustrates the S_int and D_int solar cells simulated electrical parameters as a function of WF_ITO using AFORS-HET, in order to determine the optimum WF_ITO for high solar cell efficiency. According to Figure 3(a), the V_OC values increased with increase in WF_ITO from 4.9 to 5.3 eV for both structures, due to shift of the front contact barrier ${\varphi }_{b0}$ (reduction in the band bending), with a direct influence on increasing built-in potential, $V_{bi}$, as shown in expression (Belfar, 2015; Jensen et al., 2002).

Figure 3. Simulated electrical parameters of the S_int and D_int solar cell structures as a function of WF_ITO (a) open circuit voltage (V_OC), (b) current density (J_SC), (c) fill factor (FF), and (d) the conversion efficiency (E_ff).

(7) $V_{bi}=W{F}_{ITO}-{{\chi }_e}_{/x=0}-{\varphi }_{bL}$(7)

(8) $V_{OC}=\left\{V_{bi}-nKTln\frac{\left(q{N}_V{S}_{it}\right)}{J_{SC}}\right\}$(8)

where ${{\chi }_e}_{/x=0}$ is the electron affinity of p-window layer, ${\varphi }_{bL}$ is the barrier height at back contact, $n$ is diode ideality factor, $KT$ is the thermal energy, $N_V$ is the effective density of states in the valence band, $S_{it}$ is the interface recombination velocity. From eq. (7)(7) $V_{bi}=W{F}_{ITO}-{{\chi }_e}_{/x=0}-{\varphi }_{bL}$(7) -(8(8) $V_{OC}=\left\{V_{bi}-nKTln\frac{\left(q{N}_V{S}_{it}\right)}{J_{SC}}\right\}$(8) ), it is clear that the V_bi has a larger value when WF_ITO is higher and the V_OC increases with the built-in potential. However, when WF_ITO = 5.7 eV, the built-in potential V_bi = 1.7 eV which is enough to effectively separate the carriers and provides the strong electrical field, resulting in a high value of V_OC.

Figure 3(b) shows the current density values J_SC for both structures were observed to increase with change in WF_ITO, consequently, improving photogenerated hole passage from the p-window to ITO layer. According to Figure 3(c), as the WF_ITO increases, the two structures’ FF values also increased, due to migration of holes from the p-window layer to the ITO interface, with reduction in the surface band bending the hole injection barrier (Oh et al., 2012). Meanwhile, Figure 3(d) shows the S_int and D_int structure’s maximum efficiency is about 6.73 % (V_OC = 839.4 mV, J_SC = 14.78 mA/cm², and FF = 54.25 %) and 9.21% (V_OC = 858.1 mV, J_SC = 16.07 mA/cm², and FF = 66.80 %), respectively, at WF_ITO = 5.7 eV. Low FF values from the simulation result is following with the experimental results reported by (Park et al., 2012). This is presumably for both structures, due to the imperfect joint formation mechanism creating defect conditions at the ITO/p-window layer interface.

As previously mentioned, the D_int solar cell structure has a better performance, compared to the S_int solar cell structure, and is therefore to be the focus of the discussion. The correlation between the behavior of solar cells in the dark and the WF_ITO value will be analyzed to test the quality of the solar cells with electrical parameters in the dark (dark parameters), namely the reverse saturation current, J₀. Figure 4 shows the J-V characteristics under dark for typical WF_ITO of 4.9 eV, 5.3 eV, and 5.7 eV, applied to D_int structure. In reverse bias, the J₀ is not typically dependent on the WF_ITO and the J₀ values at V_app = −1000 mV were about 5.39 × 10⁻⁸ mA/cm² (WF_ITO = 4.9 eV), 5.29 × 10⁻⁸ mA/cm² (WF_ITO = 5.3 eV), and 5.26 × 10⁻⁸ mA/cm² (WF_ITO = 5.7 eV), respectively. Conversely, the dark current’s value in forward bias is influenced by WF_ITO. Figure 4 also shows the dark current is entirely controlled by recombination of e-h pairs through mid-gap states within the absorber layer (V_R region), at low forward bias (< 250 mV). Meanwhile, for voltage inside the exponential region (V_E), the dark current is limited by the combination of diffusion and recombination. However, for the region between V_R < V < V_E (250 < V < 400 mV), the dark current trundles, terraces more slowly with voltage, and is fully controlled by electron diffusion around virtual cathode. This region is the space charge limited current (SCLC) in region V > V_SC, as a function concentration of trapped electrons and holes (Sturiale et al., 2009). For forward bias V > 400 mV, the forward dark current increases significantly and is controlled by hole injection at the ITO/p-window layer interface (Belfar, 2015).

Figure 4. Simulated the J-V characteristic of the D_int solar cell structure under dark for typical WF_ITO = 4.9 eV, 5.3 eV, and 5.7 eV.

A study by Prayogi et al., (2021) reported the fabrication of D_int solar cell with RF-PECVD, using SiH₄ (10 % concentration in H₂ gas), B₂H₆ (10 % concentration in H₂ gas) for dopant source of the p-type layer, and PH₃ (10 % concentration in H₂ gas) for dopant source of the n-type layer gases mixture. The presence of hydrogen in a-Si:H film plays a role in filling localized states to degrade defect states. However, the excess hydrogen traced after filling localized states in the absorber layer tends to become an impurity. Consequently, the J_SC is reduced by the defects generated by hydrogen impurity (J. Park et al., 2013).

Figure 5 shows the D_int’s band diagram simulation generated using AFOSR-HET simulator for typical WF_ITO. An increase in WF_ITO requires an increase in the front contact barrier ${\varphi }_{b0}$ and a significant decrease in the downward band bending ${\varphi }_{hb0}$ emerges at the ITO/p-window layer leading to improvement of V_OC, as shown in Equations. (7)(7) $V_{bi}=W{F}_{ITO}-{{\chi }_e}_{/x=0}-{\varphi }_{bL}$(7) -(8(8) $V_{OC}=\left\{V_{bi}-nKTln\frac{\left(q{N}_V{S}_{it}\right)}{J_{SC}}\right\}$(8) ). Simultaneously, the FF values were increased due to the migration of holes to the front contact ITO/p-window layer interface, as the hole injection barrier, ${\varphi }_{hb0}$ was reduced (Oh et al., 2012). Table 2 shows the AFORS-HET simulation results from the D_int solar cell performances with different WF_ITO. The high WF_ITO of 5.7 eV produced a 9.21 % maximum efficiency in the D_int solar cell, due to the enhanced V_OC and FF, as shown in expression (Bechane et al., 2021; Singh et al., 2012; Sultana et al., 2017).

Figure 5. Simulated band diagram of the p-i₁-i₂-n solar cell generated by AFORS-HET for typical WF_ITO = 4.9 eV, 5.3 eV, and 5.7 eV.

(9) $V_{OC}=\frac{nkT}{q}ln\left(\frac{J_{ph}}{J_0}+1\right)$(9)

(10) $FF=\frac{v_{OC}-ln\left(v_{OC}+0.72\right)}{v_{OC}+1}$(10)

(11) $E_{ff}=FF\frac{V_{OC}{J}_{SC}}{P_{in}}$(11)

Table 2. AFORS-HET simulation results for the D_int solar cell performances with different the WF_ITO

WFITO	VOC	JSC	FF	Eff
(eV)	(mV)	(mA/cm^2)	(%)	(%)
4.9	529.1	13.69	39.7	2.88
5.3	854.5	14.70	56.6	7.11
5.7	858.1	16.07	66.8	9.21

where $J_{ph},J_0,q,V,n,kT$, $v_{OC}=\frac{q{V}_{OC}}{nkT}$ are the photogenerated current, the reverse saturation current, the elementary charge, the terminal voltage, the ideality factor, and thermal energy, the normalized $V_{OC}$ and $P_{in}$ is power density of light entering the cell, respectively. According to the Equations. (9)(9) $V_{OC}=\frac{nkT}{q}ln\left(\frac{J_{ph}}{J_0}+1\right)$(9) -(11(11) $E_{ff}=FF\frac{V_{OC}{J}_{SC}}{P_{in}}$(11) ), the open circuit voltage V_OC terrace with the photogenerated current ($J_{ph}$). It is clear from Table 2, that maximum value of the V_OC and FF are 858.1 mV and 66.8 % for WF_ITO = 5.7 eV. At the same time, the efficiency enhancement is due to increases in the V_OC and FF values.

However, the WF_ITO’s influence on optical properties and photogenerated current were examined for light spectrum at 300–800 nm. The AFORS-HET simulated results of the p-i₁-i₂-n solar cell’s quantum efficiency indicate a WF_ITO of 5.7 eV is able to improve in blue light response between 300 and 633 nm, with a maximum quantum efficiency of 94.3 % at 522 nm (Figure 6). The photogenerated current ($J_{ph}$) value can be written as (Belfar, 2015).

Figure 6. Simulated quantum efficiency of D_int solar cell for typically WF_ITO = 4.9 eV, 5.3 eV, and 5.7 eV which examined for the range of the light spectrum of 300–800 nm.

(12) $J_{ph}=q{\int }^{\mathrm{\Phi }}\left(\lambda \right)\left(1-R\left(\lambda \right)\right)QE\left(\lambda \right)d\lambda$(12)

where $\mathrm{\Phi }\left(\lambda \right)$ is the photon flux incident on the solar cell at wavelength $\lambda$, $R\left(\lambda \right)$ is the reflection coefficient from the top surface; $QE\left(\lambda \right)$ is the quantum efficiency. From eq. (12(12) $J_{ph}=q{\int }^{\mathrm{\Phi }}\left(\lambda \right)\left(1-R\left(\lambda \right)\right)QE\left(\lambda \right)d\lambda$(12) ), it is obvious that with high value of WF_ITO, $QE\left(\lambda \right)$ and $J_{ph}$ ($J_{ph}\approx J_{SC}$) of D_int solar cell are significantly improved, as shown in Table 2.

Furthermore, the changes in ${\varphi }_{hb0}$ with WF_ITO are due to alteration of the electric field at ITO/p-window layer interface, caused by different carrier concentrations, leading to a significant reduction in J₀, and consequently, improving the V_OC. Based on Figure 7, an increase in WF_ITO from 4.9 eV to 5.3 eV, results in a change in the electric field from +5.23 x 10⁵ to +2.51 x 10⁵ Vcm⁻¹ at ITO/p-window layer interface, and this impedes the photogenerated hole from reaching the front contact. Meanwhile, at a WF_ITO of 5.7 eV, the electric field’s value shifted to negative (−3.89 x 10⁵ Vcm⁻¹), thus, providing effective forces for holes transport to reach the front contact.

Figure 7. Simulated electric field distribution of the D_int solar cell for typical WF_ITO = 4.9 eV, 5.3 eV, and 5.7 eV. (inset) the electric field profiles at the (p)a-Si:H-window layer/(i₁)a-Si:H interface.

As mentioned above, reduction of the ${\varphi }_{hb0}$ associated with the barrier of the ITO/p- layer Schottky contact is lessened even to be negligible with high value ITO work function (WF_ITO). Consequently, the quantity of photogenerated holes more collect at front contact as trapped holes density (Kumar & Ranjan, 2020). Figure 8 shows that the trapped holes concentration at ITO/p-window layer increased to 1.14 × 10¹⁹ cm⁻³ for the highest WF_ITO of 5.7 eV, as compared to 7.14 × 10¹⁷ cm⁻³ and 2.38 × 10¹⁷ cm⁻³ for lower WF_ITO of 5.3 eV and 4.9 eV, respectively. However, for silicon thin film solar cells a change in the work function of ITO films (WF_TCO) is associated with a change of the front barrier height (${\varphi }_{b0}$) affects to the efficiency of carrier injection into TCO/(p)a-Si:H interface.

Figure 8. Simulated the trapped holes density the D_int solar cell for typical WF_ITO = 4.9 eV, 5.3 eV, and 5.7 eV.

3.2. Optimization results of the a-Si:H absorber layers

According to Benigno and Darminto, p-i-n a-Si:H based solar cell fabrication using RF-PECVD technique, by varying the hydrogen dilution ($R=\left[H_2\right]/\left[Si{H}_4\right]$) = 0, 16, 36 for intrinsic (absorber) layers with 600 nm optimum thickness, inserted between p-type and n-type layers, has been conducted, and a 5.78% maximum efficiency was achieved (Benigno & Darminto, 2017). Prayogi et al., reported an effort to enhance the p-i-n solar cell’s performance through modification by adding the intrinsic layer (i₂) with different hydrogen dilution to the original S_int structure produced a D_int solar cell structure with good optical properties, as well as an 8.61% maximum efficiency (Prayogi et al., 2021). The i₁-i₂ layers serial structure leads to a more excitonic (e-h pairs) state because the i₁ (= 1.70 eV) and i₂ (= 1.85 eV) layer bandgaps are different.

Figure 9(a-b) shows the optimized results of the i₁ and i₂ layer bandgap variations, in order to improve the p-i₁-i₂-n solar cell’s performance. During the absorber layers’ optimization, the (p)a-Si:H and (n)a-Si:H layers bandgap values were taken to be 2.0 and 2.2 eV, respectively. Meanwhile, the (p)a-Si:H, (i₁)a-S:H, (i₂)a-Si:H, and (n)a-Si:H films’ thicknesses were 15 nm, 300 nm, 300 nm, and 25 nm, respectively. In this case, the WF_ITO value as neutral contact at ITO/p-window layer was also taken to be 5.7 eV. Based on Figure 9(a) shows the V_OC values gradually increased from 858.1 to 1007 mV in the bandgap range of 1.70 to 1.86 eV, and this confirmed the p-i₁-i₂-n solar cell’s band diagram structures (Figure 10(a-c)). Furthermore, the bandgap offsets ($\mathrm{\Delta }{E}_V$) emerges in each junction at valence band, due to the bandgap difference between the p-i₁, i₁-i₂, and i₂-n layers, and this offset (discontinuity) is able to increase the recombination rate and trapped hole density at those interfaces, consequently, leading to low V_OC (Figure 10(a)). According to Figure 10(b,c), a change in the i₁ bandgap change to 1.78 eV and 1.84 eV, led to a decline in the $\mathrm{\Delta }{E}_V$ within the p-i₁ and i₁-i₂ valence band, associated with high V_OC. However, with a change in the i₂ layer band gap 1.70 to 1.78 eV, the i₁ layer bandgap remained 1.82 eV, and the V_OC values remained constant at 1004.4 mV, but slowly increased with changes in the i₂ layer bandgap (Figure 9(b)).

Figure 9. The external parameter results of (a) i₁-layer bandgap, (b) i₂-layer bandgap variations of the D_int solar cell.

Figure 10. Simulated band diagram of the D_int structure with different of the i₁ and i₂ bandgaps which valence band offsets were appeared at p/i₁, i₁/i₂, and i₂/n interfaces. (a) Eg-i₁ = 1.70 eV, Eg-i₂ = 1.86 eV, (b) Eg-i₁ = 1.78 eV, Eg-i₂ = 1.86 eV, (c) Eg-i₁ = 1.84 eV, Eg-i₂ = 1.86 eV.

Based on Figure 9(a), the J_SC values were discovered to be constant in the bandgap range of 1.70 to 1.74 eV, but were observed to drastically dwindle from 16.08 to 15.98 mA/cm², with a change in the i₁ bandgap from 1.74 to 1.86 eV, due to less generation of excitonic in absorber layers with increase in the i₁ bandgaps. Meanwhile, the i₂ bandgap (Eg-i₁ = 1.82 eV) change from 1.7 to 1.86 eV did not cause any significant change (Figure 9(b)). V_OC increased with the i₁ layer bandgap, from 1.70 to 1.80 eV, as well with the variations of FF, from 66.80 % to 69.12 %. FF also slightly declines for the i₁ layer bandgap > 1.80 eV. Conversely, the reduction in FF from 70.27 % to 67.10 % was associated with changes in the i₂-layer bandgap from 1.70 to 1.82 eV. However, beyond 1.82 eV, FF was observed to gradually increase, with a rise in the i₂ layer bandgap. Figure 9(a-b) shows the p-i₁-i₂-n simulated conversion efficiency increases with changes of the i₁ and i₂ layer bandgaps. The optimized bandgap used based on simulation were 1.82 eV (i₁-layer) and 1.86 eV (i₂-layer), while the maximum conversion efficiency obtained was 10.76 %.

Figure 11 shows the quantum efficiency analyzed and calculated with change in the i₁, i₂ layer bandgaps, using optimized WF_ITO of 5.7 eV, in order to obtain the D_int solar cell’s outstanding performance. The photocurrent density, $J_{ph}$ ($J_{ph}=J_{SC}$) denotes the quantum efficiency as stated in (Yang et al., 2016).

Figure 11. Simulated quantum efficiency of the D_int solar cell structure with i₁-i₂ layer bandgaps for optimized the front contact barrier of 5.7 eV.

(13) $J_{ph}=\underset{300nm}{\overset{800nm}{\int }}\frac{q\lambda }{hc}{\varphi }_{AM1.5}EQE\left(\lambda \right)d\lambda$(13)

Where, $q$, $\lambda$, $h$, $c$, ${\varphi }_{AM1.5}$, and $EQE$ are the unit charges, wavelength of light absorbed by D_int solar cell, Planck’s constant, speed of light in vacuum, the solar spectral irradiance under 1.5 G air mass, and the external quantum efficiency, respectively. As previously mentioned, with change in the i₁ layer bandgaps (1.70 eV, 1.78 eV, 1.84 eV), and a constant i₂ layer bandgap of 1.86 eV, there is a possibility of improving the quantum efficiency in the spectrum wavelength range from 300–550 nm, due to the additional electric field and reduced dangling bond density, consequently, more excitonic generated are separated at p/i interface, leading to higher J_SC, (Figure 9(a); Hao et al., 2019).

Figure 12 shows the simulated optimized D_int solar cell’s J-V characteristic. The V_OC,J_SC, FF, and E_ff are possibly enhanced with the higher work function of 4.9–5.7 eV and (i₁)a-Si:H and (i₂)a-Si:H layer bandgaps from 1.70 to 1.86 eV. Table 3 shows the comparison results with other simulation results for the p-i₁-i₂-n solar cell structure.

Figure 12. Simulated J-V characteristic under light for the D_int solar cell bandgaps for optimized the front contact barrier of 5.7 eV.

Table 3. Comparison of several simulation results of the p-i₁-i₂-n solar cell structures

Sources	Structures	VOC	JSC	FF	Eff	Simulator
		(mV)	(mA/cm^2)	(%)	(%)
This work	(p)a-Si:H/(i1)a-Si:H/(i2)a-Si:H/(n)a-Si:H	969.8	16.03	70.0	10.76	AFORS-HET
(Belfar, 2015)	(p)nc-Si:H/(p)nc-Si:H/(i)a-Si:H/(n)a-Si:H	936.0	13.96	71.4	9.35	AMPS-1D
(Ahmad et al., 2017)	(p)a-SiO:H/(i1)a-SiO:H/(i2)a-Si:H/(n)a-Si:H	905.0	12.98	72.0	8.41	TCAD
(Abega et al., 2021)	(p)a-SiOx:H/(i1)a-SiOx:H/(i2)a-Si:H/(i)a-Si:H	905.0	16.55	76.0	10.58	SCAPS
(Hamdani et al., 2022)	(p)a-SiOx:H/(i1)a-Si:H/(i2)a-Si:H/(n)µc-Si:H	925.5	12.64	72.8	8.52	AFORS-HET

4. Conclusion

In Summary, the ITO/(p)a-Si:H/(i)a-Si:H/(n)a-Si:H/metal (S_int) and ITO/(p)a-Si:H/(i₁)a-Si:H/(i₂)a-Si:H/(n)a-Si:H/metal (D_int)’s performances were successfully investigated, using AFORS-HET software. The front work function WF_ITO on performances of the S_int and D_int solar cells was first simulated. Through simulation, the WF_ITO value was varied from 4.9 to 5.7 eV, in order to determine the optimum WF_ITO for high solar cell efficiency, confirmed with the J-V dark characteristic, the band diagram in thermodynamics equilibrium, build-in electric field distribution, trapped holes density, and the quantum efficiency. At WF_ITO = 5.7 eV, the S_int and D_int solar cells had a maximum efficiency of about 6.73 % (V_OC = 839.4 mV, J_SC = 14.78 mA/cm², and FF = 54.25 %) and 9.21 % (V_OC = 858.1 mV, J_SC = 16.07 mA/cm², and FF = 66.80 %), respectively. Furthermore, in an effort to enhance the D_int solar cell’s electrical and optical properties, the i₁-i₂ layer bandgaps’ serial structures were optimized to created more excitonic states in the absorber layers, and consequently, improve the cell’s performance. The D_int solar cell was discovered to have a maximum efficiency of 10.76 % (V_OC = 969.8 mV, J_SC = 16.03 mA/cm², and FF = 70 %), with WF_ITO, i₁ layer bandgap, and i₂ layer bandgap of 5.7 eV, 1.82 eV, and 1.86 eV, respectively. Subsequently, the simulation results were compared with other relevant thin film solar cell simulation results. It can be seen that the structure with adding an intrinsic layer to the p-i-n structure solar cell produces a higher V_OC and good conversion efficiency.

Acknowledgements

One of the authors (DH) would like to thankfully acknowledges to the Ministry of Finance Republic of Indonesia for which provided the financial grant needed to carry out this research through BUDI-LPDP scholarship (Grant number: PRJ-5441/LPDP.3/2016). The authors are also grateful to Helmholtz-Zentrum Berlin for the AFORS-HET Software.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Lembaga Pengelola Dana Pendidikan (LPDP) Ministry of Finance Republik Indonesia [PRJ-5441/LPDP.3/2016].

Notes on contributors

Dadan Hamdani

Dadan Hamdani received Ph.D. degrees from Department of Physics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Currently he is Associate Professor in the Department of Physics, FMIPA, Mulawarman University, Samarinda, Indonesia. His current research is focused on modelling of amorphous thin film solar cells and photovoltaic-thermal (PV/T) system.

Darminto Darminto

Darminto Darminto received Ph.D. degrees from the Department of Physics, Bandung Institute of Technology, Bandung, Indonesia. Currently he is with the Department of Physics Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia, as Full Professor. His present research interests include superconductivity, Magneto-electronics, and Nano-and 2D materials.