Numerical Investigation of Photo-Generated Carrier Recombination Dynamics on the Device Characteristics for the Perovskite/Carbon Nitride Absorber-Layer Solar Cell

The nitrogenated holey two-dimensional carbon nitride (C2N) has been efficaciously utilized in the fabrication of transistors, sensors, and batteries in recent years, but lacks application in the photovoltaic industry. The C2N possesses favorable optoelectronic properties. To investigate its potential feasibility for solar cells (as either an absorber layer/interface layer), we foremost detailed the numerical modeling of the double-absorber-layer–methyl ammonium lead iodide (CH3NH3PbI3) –carbon nitride (C2N) layer solar cell and subsequently provided in-depth insight into the active-layer-associated recombination losses limiting the efficiency (η) of the solar cell. Under the recombination kinetics phenomena, we explored the influence of radiative recombination, Auger recombination, Shockley Read Hall recombination, the energy distribution of defects, Band Tail recombination (Hoping Model), Gaussian distribution, and metastable defect states, including single-donor (0/+), single-acceptor (−/0), double-donor (0/+/2+), double-acceptor (2/−/0−), and the interface-layer defects on the output characteristics of the solar cell. Setting the defect (or trap) density to 1015cm−3 with a uniform energy distribution of defects for all layers, we achieved an η of 24.16%. A considerable enhancement in power-conversion efficiency ( η~27%) was perceived as we reduced the trap density to 1014cm−3 for the absorber layers. Furthermore, it was observed that, for the absorber layer with double-donor defect states, the active layer should be carefully synthesized to reduce crystal-order defects to keep the total defect density as low as 1017cm−3 to achieve efficient device characteristics.


Introduction
At present, photovoltaic modules based on wafer-based crystalline silicon solar cells account for >90% of the global photovoltaic market [1][2][3][4][5]. Laudable enhancements in power conversion efficiency (η) have been experienced for this technology over the last few years, leading to thin film, tandem, and various lab-based architectures [6][7][8][9][10][11][12][13]. Additionally, the manufacturing process of crystalline-based solar modules requires expensive materials and high production costs. Given that, double-absorber-layer (DAL) solar cells, rivaling the tandem solar cells, can be considered a promising candidate, among emerging photovoltaic technology, achieving a high device performance while cutting costs [14].
Despite perceptible advancements in tandem solar cells (perovskite/silicon tandem solar cells that have been reported recently, with an impressive η ∼ 29.15% [15]), the ease of fabricating DAL solar cells is one of the major advantages reducing complexity in tuning two-terminal tandem solar cells or managing the four-terminal tandem device circuitry. Besides this, DAL solar cells can be characterized by low production costs, compared to tandem solar cells, making them a potential candidate for the future of the photovoltaic industry [16].
The composition of DAL solar cells requires the absorber layers (or active layers) to have an almost similar lattice structure [16]. The active layers can be chalcogenides, perovskites, polymers, or other organic/inorganic layers. In such an architecture, the absorber layer with varied energy band gaps, which form the junctions sequentially, harness photo-generated power from their respective portions of the solar spectrum. This makes the multi-junction devices efficient and comparable to single-junction ones. However, the success of such DAL devices lies in the current matching of the active-layer junctions and efficient recombination of photo-generated carriers from the adjacent junctions.
Here, we proposed a novel structured DAL, employing metal halide perovskite and Carbon Nitride (C 2 N) as the absorber layers. Carbon Nitride (C 2 N) is a 2D material with a structural composition similar to graphene, with a wider energy band gap ∼ 1.8 eV, and a higher optical absorption in the visible spectrum. C 2 N has been used for photocatalysis, and in the fabrication of field effect transistors FETs, biosensors, batteries, and hydrogen storing [20][21][22][23]. C 2 N material has favorable properties for use as a primary absorber for photovoltaic applications. It has been numerically explored for photovoltaic cell modeling but has not yet been reported in the literature. We, therefore, focused on a defect-based study for the absorber layers, to comprehensively investigate the proposed active layered structure solar cell favorability for future thin-film photovoltaic applications.

Numerical Modeling and Material Parameters
The proposed solar cell is composed of FTO/TiO 2 /C 2 N/CH 3 NH 3 PbI 3 /SpiroOmeTAD/ Au-back metal contact (see Figure 1) and was numerically modeled and investigated in SCAPS-1D, which is based on three coupled semiconductor differential equations: Poisson's equation, and the continuity equations for electrons and holes (1) [7]. The material parameters for the simulation are enlisted in Appendix A Table A1. The SCAPS numerically evaluates the steady-state solution of these equations with appropriate boundary conditions [24][25][26][27].
where ∇ 2 V is the electrostatic potential, q is the electronic charge, p(x) and n(x) are the position-dependent hole and electron concentration, N D + (x) and N A − (x) is the positiondependent ionized dopant and acceptor concentration, N tr ± is the shallow/bulk trap (or defect) carrier concentration. The electron-hole pair generation, G(x) in the absorber layer is a result of incident photon flux (N phot ) of wavelength (λ), at each position (x) within Nanomaterials 2022, 12, 4012 3 of 14 the layer, and follows the mathematical relation (2) [28]. λ min , λ max are the minimum and maximum wavelengths of the incoming solar spectrum.
Nanomaterials 2022, 12, x FOR PEER REVIEW 4 of 14 In the above equation, T f ront (λ) is the transmission at the front contact (wavelengthdependent), R back (λ) is the reflection at the back contact (wavelength-dependent), R int is the internal reflection at the front contact, and d is the layer thickness.
Further, we employed one of the four SCAPS inbuilt optical absorption (α) models following the expression (4) [28]. In this model energy band gap, E g follows the square root law and α = 0 if the incident photon energy is < E g .
The device with only the perovskite absorber layer demonstrated an η of 23.83%, an opencircuit voltage (V oc ) of 1.22 V, a short circuit current density (J sc ) of 23.3418 mA/cm 2 , and a fill factor (FF) of 83.18%. The devices with optimized thicknesses with perovskite/C 2 N demonstrated an increased η of 24.17%, an open-circuit voltage (V oc ) of 1.22 V, a short circuit current density (J sc ) of 23.6392 mA/cm 2 , and a fill factor (FF) of 83.27%. The current density-voltage curve of the DAL solar, under standard illumination conditions, is depicted in Figure 2a. Figure 2b illustrates the energy level diagram of the solar cell. Furthermore, the external quantum efficiency of the solar cell with C 2 N (see Figure 2c) remained at > 90% for the nearultraviolet region, (360 nm ≤ incident light ≥ 360 nm or photon energy, E p~3 .44 eV) to the major part of the visible-light spectrum (incident light wavelengths ≤ 360 nm or E p~3 .44 eV), clearly showing a better quantum efficiency response than a single-absorber layer. It should be noted that, in further sections, defects are simultaneously introduced/changed in perovskite/carbon nitride absorber layers for investigation into the impact of the recombination phenomenon on device performance.

Influence of Recombination on Device Performance
Ideally, photovoltaic material has a higher absorption coefficient to effectively harvest incident solar energy photons and convert them into free charge carriers. However, recombination losses in solar cells are inevitable due to material defects [29]. Recombination losses affect the collection current, as well as the forward-bias injection current. This directly influences the short-circuit current density and open-circuit voltage of the solar cell, thereby limiting the fill factor and efficiency of the solar cell [30]. Recombination mechanisms considered in this investigation for the CH 3 NH 3 PbI 3 /C 2 N absorber layer include radiative recombination (R Rad ), Auger (R Aug ) and Shockley Read Hall recombination (R SRH ), following expression (5). More insight into the recombination phenomenon is provided in Figure 3.
where K is the radiative recombination coefficient, C A n C A p is the Auger electron (hole) recombination coefficient, n (p) is the electron (hole) carrier concentration, τ n (τ p ) is the electron (hole) carrier lifetime, E i is the intrinsic energy level, E t is the trap energy level, and T is the temperature at room temperature. The K factor for CH 3 NH 3 PbI 3 , as calculated by the first principles, is reported in the range of (0.5-1.5) × 10 −9 cm 3 /s . The range of C A n C A p The factor for CH 3 NH 3 PbI 3 perovskite material, as evaluated from time-and excitation-energy-dependent photoluminescence spectroscopy, has been reported to lie between 1.8 and 3.7. The point defect study on C 2 N confirmed that such materials exhibit both a direct and indirect energy bandgap nature. We therefore set similar

Influence of Energy Distribution of Defects on the Device Performance
In organic-inorganic absorber layers, the energy distribution of defect modeling is imperative to accurately model the device. The total defect density of state (DOS) in the absorber layer is assumed to comprise shallow level defects, modeled by exponentially decaying conduction or valence band tail states, and deep-level defects modeled by Gaussian distribution in the mid-gaps (see Figure 7a) [31,32]. The Gaussian conduction/valence band tail state, and energy distribution in the SCAPS environment follow the mathematical relation (6-8) [28] where is the tap energy level, is the characteristic energy, is the width of Gaussian energy distribution, is the width of tail-like distribution, ( ) is the defect density in cm /eV, and is the peak density of the energy distribution. Band tailing hampers the mobility of photo-generated carriers to a great extent by trapping and de-trapping. The ( ) is related to the degree of disorder in crystals [33]. Experimentally reported values for perovskite material are in the range of 15 − 63 (meV) [34].
However, we kept the as 0.564 eV, while = 0.1 eV for the absorber layers. The in all the above-mentioned energy distributions is 10 (1/eV/cm ), with total defect density states of 10 cm . To investigate the impact of radiative recombination, we varied the K factor in the range of 10 −8 − 10 −14 cm 3 /s (see Figure 4b). An increased value of K has an adverse effect on the output characteristics of the solar cell. It was observed that the device demonstrated a maximum η~24.17%, V oc ∼ 1.22 V, and J sc ∼ 23.64 mA/cm 2 at K = 10 −14 cm 3 /s, as illustrated in Figure 4. The highest FF∼ 87.31% was obtained at K = 10 −10 cm 3 /s. The device's η fell to~16% as we increased the K to 10 −8 cm 3 /s. To investigate the influence of R Aug on device performance, we varied the C n,aug C p,aug at 10 −25 − 10 −31 cm 6 /s (see Figure 5). The device demonstrated a maximum η at C n,aug = 10 −31 cm 6 /s and a minimum C n,aug = 10 −25 cm 6 /s. To analyze R SRH , we employed the trap density model as it has been elaborated in previous studies. The trap density for the double-absorber layer, N tr,DAL was within the range 10 14 − 10 17 cm −3 (see Figure 6). As discussed earlier, the device was simulated with a defect density of 10 15 cm −3 . On decreasing the defect density to 10 14 cm −3 , the device demonstrated a maximum η~26.18%, V oc ∼ 1.34 V, and J sc ∼ 26.79 mA/cm 2 , and the device η reduced to~17%, including other device parameters, as we increased the defect density to 10 17 cm −3 .

Influence of Energy Distribution of Defects on the Device Performance
In organic-inorganic absorber layers, the energy distribution of defect modeling is imperative to accurately model the device. The total defect density of state (DOS) in the absorber layer is assumed to comprise shallow level defects, modeled by exponentially decaying conduction or valence band tail states, and deep-level defects modeled by Gaussian distribution in the mid-gaps (see Figure 7a) [31,32]. The Gaussian conduction/valence band tail state, and energy distribution in the SCAPS environment follow the mathematical relation (6-8) [28] where E t is the tap energy level, E c is the characteristic energy, w G is the width of Gaussian energy distribution, w t is the width of tail-like distribution, N t (E) is the defect density in cm −3 /eV, and N peak is the peak density of the energy distribution. Band tailing hampers the mobility of photo-generated carriers to a great extent by trapping and de-trapping. The w G (or w t ) is related to the degree of disorder in crystals [33]. Experimentally reported values for perovskite material are in the range of 15 − 63 (meV) [34].

Influence of Metastable Defects on the Device Performance
In this section, we investigated the impact of metastable defect transition on the absorber layers. In CH NH PbI , halide ion segregation requires the migration of halide ions, which is a defect-driven process resulting in halide vacancy defects [35]. For the absorber layer, we induced double-vacancy defects, including a single donor ( ( / ) ), double acceptor ( ( / ) ), double donor ( ( / / / ), and double acceptor ( ( / / / ) , at varying total trap densities. The single (double)-donor defect states per unit of volume are concentrated closer to the conduction band edge, while single (double) acceptors are concentrated closer to the valence band [36,37]. The impact of metastable defects on device output characteristics at varied trap densities (10 − 10 cm ) is summarized in Tables 2-5. It was observed that single-donor defects affected the device output characteristics the least. However, the ( / / / ) defect considerably affected solar cell performance in all conditions. The current density voltage characteristics for metastable state defects are depicted in Figure 8a, while Figure 8b provides more insight into the results. Table 2. Defect state effect on output characteristics of solar cell at trap density of 10 cm . However, we kept the w G as 0.564 eV, while w t = 0.1 eV for the absorber layers. The N peak in all the above-mentioned energy distributions is 10 15 1/eV/cm 3 , with total defect density states of 10 15 cm −3 . The device was simulated with the above modeling, and current density vs. voltage characteristics are shown in Figure 7b. the device η was decreased to 22.12% from 24.17%, V oc to ∼1.14 V, J sc to ∼23.634 mA/cm 2 , and FF∼ 81 as can be observed in the figure. The current density curve under both conditions is summarized in Table 1.

Influence of Metastable Defects on the Device Performance
In this section, we investigated the impact of metastable defect transition on the absorber layers. In CH 3 NH 3 PbI 3 , halide ion segregation requires the migration of halide ions, which is a defect-driven process resulting in halide vacancy defects [35]. For the absorber layer, we induced double-vacancy defects, including a single donor (SD (0/+) ), double acceptor (SD (−/0) ), double donor (DD (0/+/2/+) ), and double acceptor (DA (2/−/0/−) ), at varying total trap densities. The single (double)-donor defect states per unit of volume are concentrated closer to the conduction band edge, while single (double) acceptors are concentrated closer to the valence band [36,37]. The impact of metastable defects on device output characteristics at varied trap densities (10 14 − 10 17 cm −3 ) is summarized in Tables 2-5. It was observed that single-donor defects affected the device output characteristics the least. However, the DD (0/+/2/+) defect considerably affected solar cell performance in all conditions. The current density voltage characteristics for metastable state defects are depicted in Figure 8a, while Figure 8b provides more insight into the results.

Influence of Interface Defects on the Device Performance
Interfacial recombination plays a significant role in determining the performance of the solar cell. Interface defects emerge due to recombination centers at the interface of the absorber material/hole-transport layer (or electron-transport layer) [38]. These recombination centers can be present inside the absorber layer or hole-transport layer (or electron-transport layer), at the interface. Other reasons for interface defects can be an unfavorable HTL/absorber layer (or absorber layer/ETL), band alignment, and backtransfer-induced recombination [39], as illustrated in Figure 9.

Influence of Interface Defects on the Device Performance
Interfacial recombination plays a significant role in determining the performance of the solar cell. Interface defects emerge due to recombination centers at the interface of the absorber material/hole-transport layer (or electron-transport layer) [38]. These recombination centers can be present inside the absorber layer or hole-transport layer (or electron-transport layer), at the interface. Other reasons for interface defects can be an unfavorable HTL/absorber layer (or absorber layer/ETL), band alignment, and backtransfer-induced recombination [39], as illustrated in Figure 9.
The current density-voltage curve shown in Figure 10a illustrates the effect of varying interface defect densities at the hole transport layer/absorber layer interface, N tr,H/A . The N tr,H/A was varied in the range of 10 14 − 10 17 (cm −3 ). Interface defects considerably affected the device power conversion efficiency of the solar cell, in comparison to J sc , V oc , FF, as can be observed from Figure 10b. At N tr,H/A = 10 14 cm −3 , the device η was 23.19% and was decreased to 18.24% at N tr,H/A = 10 14 cm −3 , indicating high recombination at the interface ( Figure 11). Similarly, interface defect density at the absorber layer/electron transport layer interface, N tr,A/E . was also varied in the range of 10 14 − 10 17 (cm −3 ). Unlike N tr,H/A , N tr,A/E did not significantly affect the device performance. The device η, V oc , FF, and J sc retained their initial optimized values at N tr,A/E of 10 14 − 10 16 cm −3 . However, η fell slightly to 23.83%, from 24.17%, on a further increase in interface defects. 23.19% and was decreased to 18.24% at , / = 10 cm , indicating high recombination at the interface ( Figure 11). Similarly, interface defect density at the absorber layer/electron transport layer interface, , / . was also varied in the range of 10 − 10 (cm ). Unlike , / ,, , / did not significantly affect the device performance. The device , , FF, and retained their initial optimized values at , / of 10 − 10 cm . However, fell slightly to 23.83%, from 24.17%, on a further increase in interface defects.   , / tion at the interface ( Figure 11). Similarly, interface defect density at the absorber layer/electron transport layer interface, , / . was also varied in the range of 10 − 10 (cm ). Unlike , / ,, , / did not significantly affect the device performance. The device , , FF, and retained their initial optimized values at , / of 10 − 10 cm . However, fell slightly to 23.83%, from 24.17%, on a further increase in interface defects.

Conclusions
The combination of two absorber layers, carbon nitride and a perovskite absorber layer, aided in the utilization of a broader range of solar spectrum for solar energy conversion. The device demonstrated high efficiency (24.17%), open-circuit voltage (1.2 V), and fill factor (83.2%), with a uniform DOS energy bandgap. However, the focus was on the computational investigation of dominant recombination mechanisms associated with the absorber layer, to accurately investigate the device performance. The device re-

Conclusions
The combination of two absorber layers, carbon nitride and a perovskite absorber layer, aided in the utilization of a broader range of solar spectrum for solar energy con-version. The device demonstrated high efficiency (24.17%), open-circuit voltage (1.2 V), and fill factor (83.2%), with a uniform DOS energy bandgap. However, the focus was on the computational investigation of dominant recombination mechanisms associated with the absorber layer, to accurately investigate the device performance. The device η remained > 16% under higher radiative, auger coefficient, and trap-assisted recombination. Thereafter, we modeled the Gaussian distribution energy profile for shallow-level defects and Urbach tail states for shallow-level defects. This resulted in device efficiency falling to 22.14%. Further, various double-vacancy-based metastable defect states were induced in the absorber layer. It was observed that double-donor metastable defects highly affected the performance of the solar cell. Finally, we also investigated the influence of interface defects. It was revealed that. for the proposed device architecture, increased defects in the HTL/absorber layer dominantly affected the device performance, instead of absorber-layer/ETL interface defects.   Table A1. Input layer parameters for numerical modeling of double-absorber-layer solar cell. The material parameters were adopted from the literature [16,40], as well as being self-ascribed. Electron mobility, µ e (cm 2