A QUALITATIVE THEORETICAL STUDY OF INORGANIC HTM-FREE RbGeI 3 BASED PEROVSKITE SOLAR CELLS USING SCAPS-1D AS A PATHWAY TOWARDS 3.601% EFFICIENCY †

The presence of toxic lead in perovskite solar cells has hindered its commercial viability. In this present work, a mesoscopic inorganic lead-free perovskite solar cells based on RbGeI 3 was proposed and implemented using SCAPs simulation tool. The effect of electron transport material (ETM) and Absorber thickness were analyzed. When the device was first simulated, its power conversion efficiency (PCE), fill factor (FF), current density ( J sc ), and open circuit voltage ( V oc ) all reached values of 3.584% for PCE, 48.477% for FF, 25.385 mA/cm 2 for J sc , and 0.291 V for V oc . When the ETM and absorber are at their ideal thicknesses of 0.08 m  and 0.40 m  , the development of efficiency becomes stable. Using the aforementioned parameters, the optimized PSC device produced the following values: PCE = 3.601%, J sc = 25.386 mA/cm 2 , V oc = 0.291 V, and FF = 48.637%. The PCE improvement over the basic device without optimization is around 1.01 times. The findings indicate that perovskite solar cell lacking HTM has a substantial capacity to absorb photon energy and produce electrons. It has also shown how to create environmentally clean and economically viable technology.


INTRODUCTION
Organic-inorganic halide perovskites have attracted a lot of scientific interest due to their many benefits, such as their high coefficient of absorption, good solution processability, simplicity in synthesis, variable bandgap, and long diffusion length, to name just a few [1][2][3].With a power conversion efficiency of 3.8%, Kojima et al. published the first study on their use in solar cells in 2009 [4].
In the past decade, a transformation in efficiency has risen to a value exceeding 25% [5][6][7].However, the presence of toxic lead in perovskite absorber is considered as one of the major drawbacks towards its commercial viability.To carter for such problem, researchers have invested much efforts on other cations that are divalent among which are Sn 2+ and Ge 2+ , whose oxidation state is +2 and some of their properties close to that of lead [8].
Sn 2+ and Ge 2+ both have ionic radius smaller than Pb 2+ with Sn 2+ to be (1.35Å), Ge 2+ to be (0.73 Å) and Pb 2+ to be (1.49Å), so when Sn 2+ and Ge 2+ act as divalent cations to replace Pb 2+ , it will not destroy the perovskite crystal structure [5,9].The ionic radius of Ge 2+ is smaller than that of Sn 2+ and Pb 2+ , indicating that Ge-based perovskites have higher conductivity than Pb-based and Sn-based perovskites.Saikia et al. studied the effect of thickness, defect concentration, and dopant concentration on CsGeI 3 -based PSCs [10].Krishnamoorthy et al. fabricated CsGeI 3 -based PSCs for the first time and achieved a PCE of 0.11%, which can be seen as a result of Ge 2+ oxidation during fabrication [11].Jayan and Sabastian [12] determined the optoelectronic, thermodynamic, structural, thermoelectric, and mechanical properties of RbGeI 3 perovskites as a function of various exchange correlations.Pindolia et al. investigated the effect of different hole transport materials (HTM) and electron transport materials (ETM) with RbGeI 3 as the light absorbing layer [5].
The instability in perovskite solar cells which is seen to result from organic compounds has been a major problem in the photovoltaic horizon [13,14].The commonly used HTM, Spiro-OMeTAD, involves a complex synthetic route with yields below 40% [5,15,16].Organic charge transport materials become unstable under ambient conditions and light exposure [5,[17][18][19][20].Devices without HTM are practical solutions to the problem of the expensive and unstable Spiro-OMeTAD that has limited the commercialization of PSCs technologies due to structural complexity, high cost, and poor stability.Etgar et al. created the first HTM-free PSC by using a Pb-based perovskite absorber as both a light harvester and a hole transport material at the same time [21].To the best of our research knowledge, the utilization of RbGeI3 as a perovskite absorber in a hole transport free structure has not been reported.In this research paper, an inorganic RbGeI 3 based PSC was investigated without HTM.The structure was proposed and implemented using SCAPS-1D software.By utilizing TiO 2 as ETM, fluorine doped tin oxide (FTO) as front contact and silver (Ag) as back contact, two layers' properties such as thickness of ETM and thickness of perovskite layer were optimized to obtain a PCE of 3.601%, FF of 48.637%, J sc of 25.386 mA/cm 2 and V oc of 0.291 V.The manuscript is categorized into four sections which include, the introduction, theoretical method & simulations, results and discussions and the conclusion part.

THEORETICAL METHODS AND DEVICE STRUCTURE
In this study, SCAPS-1D software version 3.3.10was used to carry out the simulation.This software is based on basic semiconductor equations: the Poisson equation and the continuity equation of both charge carriers (holes and electrons) under steady-state condition [1].
The proposed device follows the configuration of FTO/TiO2/RbGeI3/Ag, which is depicted in Figure 1.Starting from illumination point, FTO is used as a front contact, ETL as TiO 2 , the absorber layer as  1 and 2 summarized the information for each layer and the interface settings.

RESULTS AND DISCUSSIONS
3.1.Initial simulation In accordance to the parameters presented in Tables 1 and 2, the initial device characteristics are shown in Figure 2. Figure 2a shows the current density-voltage (J-V) curve, Figure 2b shows the quantum efficiency (QE) curve with respect to wavelength, Figure 2c shows the quantum efficiency curve with respect to photon energy and Figure 2d shows the calculated energy band diagram profile.In this initial simulation, we ignored the reflection of each layer, as well as the interface and the additional series resistance brought on by front contact or back contact.
The incidence to photon conversion efficiency curve with respect to wavelength is shown in Figure 2b for the initial device.Based on the given curve in Figure 2c, the band gap energy of RbGeI 3 is 1.31 eV, which is narrower than the leadbased counter part of 1.55 eV, and this results to a red shift in the absorption wavelength of the lead-free perovskite absorber to 900 nm.The curve sweeps across the visible range of the electromagnetic spectrum, and the absorption from 380 to 780 nm is the strongest, seen above 78%, which is in good agreement with the QE spectrum in similar literature [5].
Based on the values listed in Tables 1 and 2, the band gap profile was calculated and is shown in Figure 2d.The highest energy level of the valence band is represented by E v (eV), and the lowest energy level of the conduction band is represented by E c (eV).The offset energy of the valance band is 2.186 eV while the interface conduction band offset is 0.319 eV.The offset value existing between valance band of RbGeI 3 and ETL prevents the positive charges from flowing to the TiO 2 side from the absorber layer whereas the offset value at their conduction band blocks the electron from diffusing to the absorber from the TiO 2 .Thus, the recombination processes at the interface are minimal thereby resulting to good photovoltaic performance.

Effect of changing ETM thickness
To understand the influence of ETM thickness on PCE of the proposed PSC, we utilized the parameters in Tables 1 & 2 for the simulation while varying the thickness from 10 to 100 nm.The results are presented in Table 3 and Figure 3.The quantum efficiency versus wavelength curve is depicted in Figure 3b.The simulated results of our study show that PCE increased with increasing TiO 2 thickness from 10 to 80 nm before it starts decreasing.This decrease is attributed to lower transmittance at excessive values of ETM thickness that prohibit solar radiation from reaching the perovskite skeleton and partial TiO 2 layer absorption of incident light [1].From Table 3 and Figure 3a, it can be seen that the 80 nm thickness gave V oc = 0.291 V, J sc = 25.385mA/cm 2 , FF = 48.637%,and PCE = 3.598%.The QE is a crucial property of solar cell, which shows the ratio of the electron-hole pairs collected to the number of striking photons [2].QE is seen as a function of wavelength in nm or photon energy in eV.The curve was measured within the wavelength range of 300-900 nm.The simulated QE increased from 5% at 300 nm to a maximum of 78% at 600 nm but gradually decreases to 60% at a wavelength value of 900 nm.The absorption is within the visible and near infrared region.The correlation between the PCE and FF with respect to thickness is shown in Figure 3c and the relationship between J sc and V oc with thickness is shown in Figure 3d.

Effect of changing absorber layer thickness
One of the important parameters that should not be overlooked in choice for good device performance is the perovskite layer thickness.This thickness is affected by the diffusion lengths and life-time of the photo-generated electrons and holes [22,23], as such should be properly chosen.For its influence in solar cells to be fully explored, the layer thickness was controlled in the range of 100-1000 nm while maintaining other parameters fixed as shown in Tables 1 & 2.
Figure 4a shows the J-V curves of the simulated device with varied RbGeI3 layer thicknesses.As can be seen from the curve, when the absorber layer is increased, the J sc increases significantly upto thickness of 500 nm, after which the J sc value tends to have a downward trend as the absorbing layer thickness keeps increasing, which shows that absorber layer exceeding 500 nm encourages charge recombination.This rise in J sc is due to a significant photon absorption in this range (as seen by the QE-wavelength curve).Along with the increase in absorber layer thickness from 100 to 400 nm, we also observed a rise in PCE.The thicker perovskite layer absorbs enough photons to produce charge carriers when the absorption layer thickness of the perovskite layer rises above 400 nm.
The PCE curve, however, tends to become flatter as absorption layer thickness increases due to increased recombination and diffusion length.The carriers may recombine before reaching the metal electrode if the thickness of the absorption layer is greater than the diffusion length of the carrier [22].
The research above determined the ideal value for the thickness of the absorber layer used for additional simulation and taken into account to be 400 nm (see Table 4).Due to a rise in series resistance, the value of FF as a function of absorber layer thickness decreases [22].
The impact of the RbGeI3 layer's thickness on the QE (%) with respect to wavelength is depicted in Figure 4b.Since the absorption grows more potent and quantum efficiency also rises with thickness, carrier extraction rises along with thickness.Figure 4c displays the relationship between the PCE and FF with regard to thickness, whereas Figure 4d displays the relationship between the J sc and V oc with respect to thickness.5 shows the curve of the optimized (black color) and initial (red color) device.The optimized ETM thickness is 80 nm while the optimized RbGeI 3 layer thickness is 400 nm.
The optimized device gave a PCE of 3.601%, J sc of 25.386 mA/cm 2 , V oc of 0.291 V, and FF of 48.637%.This shows an improvement of ~ 1.01 times in PCE over the initial device without optimization.The results obtained demonstrate that, ETM and absorber thickness have crucial role in improving the performance of RbGeI 3 HTM free perovskite solar cell.This can provide proper guidance to researchers involved in experimental development of perovskite solar cells for realizing high performance.

Influence of temperature on the performance of the optimized PSC device
To explore the properties of the optimized device, we simulated the device at different temperature which include 240, 250, 260, 270, 280, 290, 300, 310 and 320 K. Figure 6a depicts the J-V behavior, while Figures 6b-f show the power density with the changing temperature, variation of the PCE Figure 5.The initial and optimized J-V curves with the temperature, correlation of the FF with respect to the temperature, variation of J sc with the temperature and correlation of the V oc with respect to the temperature.The performance of the device is significantly impacted by temperature changes, as can be readily shown in Table 5.With an increase in temperature, the V oc , J sc , and PCE continuously decrease.The increase in saturation current, which also causes an increase in recombination rate, is responsible for these observed properties [24].Low PCE and J sc are a result of recombination, which has an impact on the carrier concentration, electron and hole mobilities, and the ability of the electron to reach the depletion area [1,2].The increase in flaws with rising temperature is thought to be the cause of the observed drop in V oc .

CONCLUSION
We utilized SCAPS software which is based on the three basic equations of semiconductor to simulate the proposed HTM-free RbGeI 3 PSC structure.On initial device simulation, its power conversion efficiency, fill factor, current density and open circuit voltage attained values of 3.584%, 48.477%, 25.385 mA/cm 2 and 0.291 V.For the solar cell device to be optimized, the ETM and RbGeI 3 thicknesses were varied individually from 10 to 100 nm and from 100 to 1000 nm while keeping other parameters fixed.The optimized thickness of ETM was 80 nm and the optimized thickness of RbGeI 3 was 400 nm.The optimized PSC device using the aforementioned parameters gave a PCE of 3.601%, J sc of 25.386 mA/cm 2 , V oc of 0.291 V, and FF of 48.637% respectively.The performance of the optimized device is greatly affected by the temperature.Increase in temperature leads to decrease in PCE, J sc and V oc .

10 
RbGeI 3 and silver (Ag) as the back contact.The front electrode's work function is 4.40 eV, whereas the counter electrode's work function is 4.63 eV.The simulation was run with an A.M. 1.5 spectrum light intensity (1000 W/m 2 ), a simulation temperature of 300 K, a simulation frequency of 16 1 Hz, and a scanning voltage range of 0 to 1.40 V. Tables

Figure 2 .
Figure 2. (a) J-V curve under illumination for initial device, (b) QE versus wavelength for initial device, (c) QE versus photon energy for the initial device and (d) energy profile diagram of the initial device

Figure 3 .
Figure 3. (a) J-V curve under illumination with different ETM thickness, (b) QE versus wavelength, (c) variation of ETM thickness with PCE and FF, and (c) variation of ETM thickness with Jsc and Voc

Figure 4 .
Figure 4. (a) J-V curve under illumination with different absorber thickness, and (b) QE versus wavelength, (c) variation of ETM thickness with PCE and FF, and (d) variation of ETM thickness with Jsc and Voc

Figure 6 .
Figure 6.(a) J-V curve with varied temperature under illumination, (b) P-V curve with varied temperature under illumination (c) PCE with respect to temperature, (d) FF with respect to temperature, (e) Jsc with respect to temperature and (f) Voc with respect to temperature

Table 2 .
Defect parameter values of the interfaces of the device

Table 3 .
J-V characteristic parameters with the variation of thickness of ETM

Table 4 .
J-V characteristic parameters with the variation of thickness of Absorber

Table 5 .
J-V characteristic parameters with temperature variation