Thermal analysis in 3-D Simulation of Thin-Film ZnO/MoS 2 /Si solar cells

: ZnO and MoS₂ thin -film solar cells hold immense research potential due to their unique and exceptional photoswitching characteristics and piezotronics behavior. This work unveils the 3D simulation of an n-ZnO/MoS₂/p -Si heterostructure solar cell, where photovoltaic and temperature distributions are modeled using Multiphysics. By coupling optical, semiconductor, and thermal modules, the simulation reveals crucial insights into total generating rate, current density-voltage curve, heat generation, recombination, and electric field profile. Notably, optimizing layer thicknesses and analyzing the heat profile led to enhanced total heat generation and the simulated device achieved a significant boost in both short-circuit current density (36.3 mA/cm²), open-circuit voltage (1.1206 V) and a conversion efficiency of 36.286%. This study not only demonstrates the first instance of multi-state photoswitching in these devices but also paves the way for further optimizing their remarkable efficiency through meticulous thermal management.


1.INTRODUCTION
Thin-film photovoltaic (PV) solar cells are gaining significant traction as a promising alternative to siliconbased devices.While research efforts are diverse, CZTSSe-based cells stand out for their impressive efficiency gains, rising from 8% to 12% in recent years (NREL).However, a major challenge facing thinfilm solar cells is their relatively low conversion efficiency.
One key limitation is the lower open-circuit voltage (Voc) observed in CZTSSe devices (0.513 V) compared to other thin-film technologies like CdTe and CIGS (0.9-1 V).Elevated temperatures further exacerbate this issue, causing a drop in both efficiency and Voc.Understanding this thermal behavior is crucial for optimizing thin-film solar cell performance.3D COMSOL Multiphysics simulations coupled with optical, semiconductor, and heat transfer modules can provide valuable insights into heat distribution within the device.
*Corresponding Author: ram28020@gmail.comThermal analysis in 3-D Simulation of Thin-Film ZnO/MoS 2 /Si solar cells Parasuraman R 1 Rathnakannan K 2  Previous studies exploring thermal management in perovskite devices demonstrate the effectiveness of such simulations in analyzing temperature profiles and their impact on key parameters like short-circuit current density (Jsc), Voc, fill factor (FF), and efficiency (e.g., 28.5 mA/cm², 1.05 V, 0.77, and 21.9%, respectively) [1].However, these studies highlight the detrimental effects of increased heat generation on recombination rate and operating stability [1,2].
In this context, the unique switching characteristics of MoS2 emerge as a promising avenue for improving solar cell performance.Its multiple resistive states, controllable by electric fields, enable fast switching between dark and light modes.This mechanism, facilitated by polarization charges at the interfaces, holds great potential for photovoltaic applications [16].Additionally, ZnO materials exhibit superior charge carrier separation and nonradiative recombination suppression, making them ideal candidates for the top layer of solar cells [18].Furthermore, incorporating antireflective coatings with light trapping capabilities adds another layer of optimization for light management in the top layer [18].
It is important to note that conventional simulation tools like PC1D, SCAPS, and AMPS lack the capacity for intricate 3D mapping [18,19,24,26].In contrast, 3D COMSOL Multiphysics provides a robust platform for modeling, with excellent agreement between simulated and measured results when incorporating key factors like material properties, doping distribution, layer thicknesses, and defect degradation [20].
Our present work leverages the power of 3D COMSOL Multiphysics to delve deep into the intricate workings of a ZnO/MoS2/p-Si solar cell.We provide a comprehensive analysis of carrier transport, thermal distribution, optical generation rate, electric field profile, and the groundbreaking role of MoS2 interfaces in enhancing ZnO/Si performance.Additionally, the thin MoS2 absorber layer employed in our design paves the way for maximizing solar cell efficiency.Ultimately, this research contributes to the ongoing pursuit of high-performance thin-film solar cells through the innovative implementation of multilevel switching in the MoS2 layer.

2.MULTIPHYSICS, MODEL, AND MESH CONFIGURATION
The 3D model wizard builds a heterostructure solar cell consisting of Aluminum, n-type ZnO, MoS₂ (absorber layer), Si (hole transport layer), a front contact of Ag, and an air region as the top layer.Figure 1 illustrates the thickness of each layer.The physics component encompasses all three electromagnetic waves in the frequency domain module (lightwave), the semiconductor module, and the heat transfer module.
Semiconductor, optical wave, and thermal properties are sourced from the literature.Refractive index and thermal conductivity properties for the ZnO, MoS₂ and Si layer semiconductor materials are specifically taken from references [2] and [3].Using optical constants, electromagnetic waves in the frequency domain, illumination intensity, and refractive index (GT), the total generation rate is calculated.The generating rate within the semiconductor module originates from the electromagnetic wave module and accounts for trapassisted recombination.In the heat transfer module, the total heat generated by the semiconductor module is used as input.Coupled physics are then employed to solve the current-continuity equation, thereby investigating the solar cell's performance.

Figure.2. Meshed structure device
The meshing configuration follows the approach presented in [8] and illustrated in Figure 2. It employs a combination of user-controlled mesh for the overall geometry and a customized mesh for the semiconductor physics region.The maximum element size is set to 37.5 nm, while the minimum element size is set to 10 nm.To account for potential curvature, a maximum element growth rate of 1.13 is applied.The semiconductor regions have a higher mesh resolution of 0.85.For the MoS₂ and ZnO layers, the mesh element type is fixed with the smallest possible element size.These two layers are the thinnest and therefore require the finest meshing within the device.The defined mesh is then used to analyze the device's performance.

3.SIMULATION RESULTS AND DETAILS
The optical, electrical, and heat transfer coupled physical modeling described in this section.

Optical modeling
While Multiphysics doesn't explicitly simulate this optical model, the Helmholtz equation with its defined materials and refractive indices can be utilized.Using an optical RF module in the frequency domain and an AM1.5G spectrum, the optical response of the heterostructure is simulated at each wavelength [9].The geometry (including layer thickness), refractive indices of various components, and optical model parameters are all crucial inputs.The refractive index for each layer is extracted from reference [10].Based on the frequency domain study results of the optical model, the photoelectric effect due to periodic grading, generation rate, and absorption of the photoactive layer can all be calculated.Incident photons are converted to electromagnetic waves and used as input and output port boundary conditions.Equations ( 1)-( 4) define the incident wave of the air medium in terms of plane waves across the x, y, and z axes.With incident photons to electromagnetic waves, the input, and output port boundary conditions.In the planes wave (x, y, and z), the incident wave of the air medium express as ( 1)-( 4):   = ewfd. 0 (1)   =   * sinƟ (2)   = 0 (3) The boundary condition of the medium of the Si layer and the planes wave defined as ( 5)-( 8) The optical field boundary for the MoS2 with plane waves from the Equ.( 9)-( 12)   = (n_MoS 2 − j * k_Mo 2 ) * ewfd. 0 (9) The boundary condition for the ZnO layer denoted from (3)-( 16) The magnitude electric power intensity and the derivative electric power intensity defined from ( 17)-( 18) The photo-generation over the solar spectrum [7] calculated from the equation The optical carrier generation integrating over the wavelength (λ), the total generating rate estimated from (20).
Between 200 nm and 1500 nm, the electromagnetic wave model was swept across the entire spectrum.This analysis revealed the optimal thickness for each layer, where the 50 nm ZnO nanostructured film demonstrated a superior light trapping mechanism.Using the frequency domain study, we calculated the absorption at the top ZnO surface.By combining this absorption with the photogeneration collection, we determined the External Quantum Efficiency (EQE).The total generation rate serves as the input for the electrical model, which ultimately defines the short-circuit current density (Jsc) as described by Eq.21 in reference [11].
The expression "k(λ)" signifies the extinction coefficient for each wavelength.Guided by this formula, we designed the 3D electromagnetic wave models and modeled the optical performance of the proposed structure.Multiphysics' optical and electrical models further enabled us to calculate the absorption, total photogeneration rate, electric field, and short-circuit current density.For reference, the proposed device design and layer thicknesses are illustrated in Figure 1.

Fig.3.Carrier Generating profile for the optimized thickness of ZnO and MoS2 of solar cell
Replacing zinc oxide (ZnO) with a planar surface in the active layer resulted in a notable increase in both total generation rate and short-circuit current density.Absorption climbed from 82.5% to 89.85% for wavelengths between 200 nm and 600 nm.Furthermore, optimizing the thicknesses of the nano-ZnO and MoS₂ films to 50 nm and 70 nm, respectively, significantly enhanced the photogeneration rate to a peak of 1024 m⁻³s⁻¹ within the 1000 nm to 1600 nm range, as illustrated in Figure 3.This improvement can be attributed to the strong and uniform electric field distribution observed at longer wavelengths, as shown in We focus on the electric field profiles at specific wavelengths.Owing to the presence of the nanostructured thin-film active layer, the electric field is significantly enhanced for a range of selected wavelengths between 800 nm and 1400 nm. Figure 5 reveals that the absorption peaks within the 200 nm to 600 nm range, and the absorption coefficient steadily declines as the wavelength approaches 780 nm.Consequently, lowering the wavelength beyond this point leads to an unacceptably low short-circuit current density.To address this issue, we focused on improving the current density at selected wavelengths between 800 nm and 1200 nm by optimizing the interfaces between the MoS₂ and Si layers.However, within the 1200 nm to 1600 nm range, the short-circuit current density still exhibits a decreasing trend, as shown in Figure 6.

3.2.Electrical Modelling
PV Simulations require both semiconductor and optical modules.Calculating the spatial distribution of electrostatic potential (ϕ), electron concentration (n), and hole concentration (p) is an integral part of solar PV simulations.This is achieved through the semiconductor module physics.Additionally, the semiconductor module solves for the electron and current densities (Jn and Jp), respectively.According to Poisson's equations, continuity equations, and transport equations, these densities have drift and diffusion components, as described in [13] and [22].
The boundary condition depends on the type of metal contacts and the carrier concentrations and recombination velocity of electrons and holes (Sn and Sp) at the metal/semiconductor interface in below Equations ( 23) to ( 28), collectively known as the "semiconductor equations," play a crucial role in solving the numerical methods employed in solar cell simulations.The finite element method is the most common approach for calculating electron and hole flow, often aided by the Scharfetter-Gummel model, which is readily available in most semiconductor modeling software.Moving on to the boundary conditions, the electrostatic potential is defined as The semiconductor module offers built-in recombination and generation rate options for both electrons and holes.The photogeneration rate is calculated based on an optical modeling function.Table 1 presents the doping profile and electrical parameters for the ZnO/MoS₂/Si solar cell model.While the 1nm-thick MoS₂ layer in this structure is estimated to absorb only 5-10% of incident light, its potential can be improved.
Materials like GaAs, with their higher-order absorption characteristics, could be further explored.References

3.3.Thermal modeling
Several factors contribute to heat and energy losses in solar cells, including Shockley-Read-Hall (SRH) nonradiative recombination, absorption, Joule heating, and thermalization.These heat sources induce temperature rise, potentially impacting device stability.Thermal analysis, incorporating these heat sources through the heat transfer module, helps optimize the device design for improved stability.Coupled physics simulations determine the temperature profile and heat distribution within the device.Table 1 summarizes the thermal conductivity, heat capacity, and heat transfer coefficient for each layer.The semiconductor module, acting as the heat source, interacts with the heat transfer module.Heat generation within the solar cell is configured as boundary conditions for both convection and conduction.Nonradiative recombination heat and Joule heat contribute significantly to solar cell degradation under operating temperatures [36].
However, our optimized heat generation management has significantly reduced such degradation.
Where k is the thermal conductivity of the material as a function of temperatureWm -1 K -1 ,   is the density, QT is the total heat generation rate, Cp is the specific heat values denote in Table .1 .The heat transfer module incorporates various heat generation sources: bulk recombination, surface recombination, Peltier heat at the metal contact interface, nonradiative recombination, Joule heat, and thermalization.A doping concentration of 10¹⁷ cm⁻³ moderates the conduction band barrier height, facilitating electron flow and leading to improved conversion efficiency [39].
Direct contact between ZnO and the Si layer increases back surface recombination due to a problematic barrier height at the interface.This recombination process generates heat through the loss of energy from the recombining electrons.To address this issue, we implemented a band alignment structure at the MoS₂ interface between ZnO and Si, aiming to reduce recombination.Notably, while nonradiative recombination heat reaches its peak within the junction itself, modulating photons in MoS₂ (as shown in Figure 12) significantly reduces the overall heat generation across the junction, down to a range of 3×10⁵ W m⁻³ to 6×10⁵ W m⁻³.Furthermore, optimizing the work function of the front contact further improves barrier height modulation and reduces Shockley-Read-Hall (SRH) recombination within the thin MoS₂ region.
The nonradiative recombination heating rate is defined by   = (  + 3) + Figure 17 illustrates the calculated heat transfer within the solid layers of the solar cell under stationary conditions.Due to the thinness of each layer, the model reveals no significant temperature difference across the cell in this scenario.However, Figure 16 demonstrates the temperature gradient that arises when heat dissipation at the contact side occurs.This dissipation can degrade device performance and reduce overall operational efficiency.Conversely, reducing the nonradiative recombination heat distribution throughout the cell, as achieved in our optimized design, can significantly enhance device reliability.This highlights the crucial role of thermal analysis in developing efficient solar cells.Furthermore, as shown in Figure 15, neglecting heat transfer analysis altogether results in a zero temperature gradient across the entire device.By incorporating a heat transfer module in our simulation, we were able to investigate the impact of heat dissipation, including the formation of the temperature gradient observed in Figure 16.thickness.An increase from 0.501 V to 1.1206 V in the open-circuit voltage exemplifies the significant performance improvement achievable through this approach.Furthermore, analyzing the temperature distribution and total heat source magnitude within the device using the heat profile study facilitates further optimization of conversion efficiency.This deeper understanding of thermal behavior allows us to identify and address key heat dissipation pathways, ultimately leading to enhanced solar cell performance.

CONCLUSIONS
The 3D Multiphysics simulation of an n-ZnO/MoS₂/p-Si heterostructure solar cell model reported in this paper established a comprehensive thermal analysis through coupling optical, semiconductor, and thermal modules with a fine-meshed structure.Notably, incorporating a MoS₂ layer between ZnO and Si did not affect photogeneration but the multi-level switching in this middle layer allowed for optimized thickness selection and suitable doping profiles that significantly reduced non-radiative heating.This, along with Highlighting the interplay between the maximum electric field in MoS₂ which facilitating photoswitching, ZnO's light trapping capability, and thermal analysis, our work paves the way for designing highly efficient and thermally stable thin-film solar cells.This 3D simulation structure serves as a valuable technical roadmap for future implementation of such devices.

Figure 4 .Figure. 4 .
Figure 4. Figure 4 displays the electric field profile for a selected wavelength range of 200 nm to 1600 nm with a 200 nm interval.

[ 27 ]Fig. 7 .Fig 2 )Fig. 9 .Figure 9
photoswitching layer improves the short-circuit density from 21.72 mA/cm² to 36.30mA/cm² by reducing non-radiative recombination and Joule heating at the ZnO/MoS₂ interface.The heat distribution profile across the device has been assessed in the next section in this article.Finally, the charge modulation within the device is facilitated by the photo-switching characteristics of the materials.

2 )Fig. 10 .
Fig.10.Total heat source profile for the semiconductor domain Thermal analysis can mitigate excessive carrier generation and defect density in solar cells.By incorporating temperature, voltage, and light illumination as parameters, a current density function can be calculated [21].The current density as a function of voltage and light intensity represents in Sections A and B.The temperature profile derived from the differential equation of conduction with internal heat generation −∇ 2  +   =

Fig. 13 .Fig. 14 .Fig. 16 .Fig. 17 .
Fig.13.Joule Heat profile for the semiconductor region reduced recombination heating by several orders of magnitude at the MoS₂ interfaces, led to a remarkable improvement in open-circuit voltage (Voc) from 0.501 V to 1.1206 V.The simulation further revealed important insights into SRH nonradiative recombination and Joule heating mechanisms within the device.