# Photovoltaic Solar Cells: A Review
## 3 Simulation of Solar Cells and Modules
### Simulation of Solar Cells by COMSOL/Multiphysics  
Many investigations on PV simulation [104; 105; 106] also were performed by COMSOL to assess the performance of solar cells. The process includes many procedures:  
1. Creating a user-defined, spatially dependent variable for the generation rate, using an integral expression involving the solar radiation '\(F(\lambda)\)', which is used to find the rate of photon generation '\(\phi(\lambda)\)'. \[\phi(\lambda)=\frac{\lambda}{hc}\;F(\lambda)\] (19) '\(F(\lambda)\)' is approximated by the standard AM 1.5 Spectra [107]. The integral expression of the generation rate also involves the absorption coefficient of the employed material '\(\propto\)(\(\lambda\))', which is equal to: \[\propto(\lambda)=\;\frac{4\pi k(\lambda)}{\lambda}\] (20) '\(K(\lambda)\)' is a specific property of the absorbing material that represents the imaginary part of the absorbing coefficient. The integral expression for the electron-hole generation rate is expressed as: \[G(z)=\;\int\propto(\lambda)\phi(\lambda)exp(-\propto(\lambda)z)d\lambda\] (21) where '\(z\)' represents the depth from the surface of the device [108].
2. Create the geometry.
3. Define the materials.
4. Determine the uniform bulk and surface as well as the doping junction depth.
5. Boundary selection for doping profiles and metal contacts.
6. The Shockley-Read-Hall model (SRH) is employed using the feature of trap-assisted recombination for the uniform bulk doping by the analytic doping feature and surface doping by the geometric doping feature.
7. Meshing the geometry to get the results. Various meshing approaches produce ideal results [109; 110]. Figure 11 shows the doping profile under the front surface of a simple 1D model of a silicon PV cell performed with the COMSOL-Semiconductor Module.  
The generation and S-R-H recombination rates can also be found throughout the depth of the cell (Figure 12).  
Moreover, I-V and P-V curves of the PV cell can also be characterized, referring to Figure 7.  
Figure 11: Doping profile beneath the surface.  
COMSOL helps to adjust the properties of PV materials. such as light trapping, layer thickness, band structure, doping level, and many parameters that influence the obtained characteristics of PV cells. A theoretical model for GaAs-based solar cells with a p-i-n structure was analyzed by [44]. The influence of varying basic parameters on the obtained power was investigated using COMSOL Multiphysics. The mobilities of charge carriers were varied in combination with the lifetime of carriers and surface recombination velocity 'SRV'. The results showed that higher PV efficiencies can be achieved by increasing the mobility and carriers' lifetime while decreasing the surface recombination velocities [111; 112; 113]. Moreover, [31] developed a simulation model of PV modules in COMSOL Multiphysics to investigate the I-V and P-V characteristics of p-n junction space solar modules based on porous Si. The difference between the PV electrical characteristics COMSOL results and the experimental data obtained does not exceed 5%. Thus, the models developed by COMSOL help to investigate the electrical characteristics and establish the main factors affecting solar cell performance.