Dear Abdullah,

At first i would like to pay your attention that there is good analytical solutions for the the carrier transport in silicon solar cells that have been approved many time and showed fairly good agreement with the measured properties.

In case of numerical solution of the semiconductor equations to get the I-V relationship of the device under illumination, one used the so called regional approximation where one divides the device into quasinutral regions separated by space charge regions after which one solves the transport equations in these regions.

Dividing the device into space charge regions around the junction and neutral regions is justified in bipolar devices including the solar cells. In the way one do not need to consider the Poisson equation. It is needed only to consider the solution of the continuity and current equations in the neutral regions with the specific boundary conditions. The current in the semiconductor is caused by diffusion and drift and so you need to have a model for the mobility and the diffusion constants. Both are related bu the Einstein equation. The mobility depends on doping and temperature.

As for the continuity equations, thee is the continuity equation of holes and for electrons. The parameters here is the the recombination rate which depends on the recombination mechanism and also there is the generation rate caused by the incident photons. the photo generation rate depends on the intensity of the radiation and wavelength.

The solution can be simplified by assuming some valid assumptions such as:

 - the current is dominated by the flow of minority carriers

-the solution is a super position of dark current and the short circuit current and the illuminated current.

These assumptions are also made for the analytical solutions.

The exact solution dictates the solution of the semiconductor equations in the whole device area between the metallic area. Here one has to fully describe the construction of the device including the physical and technological parameters of every device layer. There is some commertial device simulators performing such solution.

For more information about the parameters please refer to the link:https://www.researchgate.net/publication/236003006_Electronic_Devices

wish you success

Book Electronic Devices

Dear Abdullah,

At first i would like to pay your attention that there is good analytical solutions for the the carrier transport in silicon solar cells that have been approved many time and showed fairly good agreement with the measured properties.

In case of numerical solution of the semiconductor equations to get the I-V relationship of the device under illumination, one used the so called regional approximation where one divides the device into quasinutral regions separated by space charge regions after which one solves the transport equations in these regions.

Dividing the device into space charge regions around the junction and neutral regions is justified in bipolar devices including the solar cells. In the way one do not need to consider the Poisson equation. It is needed only to consider the solution of the continuity and current equations in the neutral regions with the specific boundary conditions. The current in the semiconductor is caused by diffusion and drift and so you need to have a model for the mobility and the diffusion constants. Both are related bu the Einstein equation. The mobility depends on doping and temperature.

As for the continuity equations, thee is the continuity equation of holes and for electrons. The parameters here is the the recombination rate which depends on the recombination mechanism and also there is the generation rate caused by the incident photons. the photo generation rate depends on the intensity of the radiation and wavelength.

The solution can be simplified by assuming some valid assumptions such as:

 - the current is dominated by the flow of minority carriers

-the solution is a super position of dark current and the short circuit current and the illuminated current.

These assumptions are also made for the analytical solutions.

The exact solution dictates the solution of the semiconductor equations in the whole device area between the metallic area. Here one has to fully describe the construction of the device including the physical and technological parameters of every device layer. There is some commertial device simulators performing such solution.

For more information about the parameters please refer to the link:https://www.researchgate.net/publication/236003006_Electronic_Devices

wish you success

Book Electronic Devices

You can read my paper Wei E.I. Sha, Wallace C.H. Choy, Yumao Wu, and Weng Cho Chew, “Optical and Electrical Study of Organic Solar Cells with a 2D Grating Anode,” OSA, Optics Express, vol. 20, no. 3, pp. 2572-2580, Jan. 2012.

you should solve poison, drift-diffusion, and current continuity equation simultaneously. There are many parameters such as mobility, recombination coefficient, band gap and electron affinity, injection barrier and surface recombination velocity at electrodes, doping density (Na and Nd),  etc. 

Dear Abdullah Bin Shams,

I am going to try as short as possible. You need to learn how you can drive "Shockley diode equation" I mean which physical assumption has been considered during the derivation of this equation. And you have to learn all physical/mathematical steps. After that you will get a chance to understand what’s going on in semiconductor device physics world. After all these steps, I am sure that you are going to see that; there is 2 basic simulation parameters one of them is diode factor (n) , the other one is reverse saturation current (Io). However there are some other factors which lead you to realistic device simulation. They are parasitic resistances (series and shunt resistance). Please keep in mind that generally, due to semiconductor nature, all these parameters strongly exhibit temperature dependent behavior.  And also diode factor versus applied DC forward voltage sometimes does not exhibit flat function, actually it exhibits forward voltage dependent due to unideal effects (real WORLD)..

Regards..Good luck....

How "real" is the diode (non-)ideality factor, by the way? Let me be a bit provocative: I think it only arises phenomenologically in a macroscopic description of the diode currents. However, if physics is treated on the microscopic level, its value is given by the respective mechanism (cf. the 2001 University of New South Wales PhD thesis of Keith Reid McIntosh, "Lumps, humps and bumps: Three detrimental effects in the current-voltage curve of silicon solar cells"). This also means that -- without deeper interpretation -- values of the diode (non-)ideality factor that differ from well-known ones (related to microscopic processes) are unphysical. So, dear colleagues, what do you think about these provocative thoughts?

Jan-Martin, if a solar cell that satisfies the detailed balance theory well, such as silicon, GaAs, perovksite, etc, the ideality factor determined at Voc point suggests the dominate recombination mechanism of the solar cell including radiative, SRH (mono-molecular), Auger recombination. 

I agree with Jan-Martin that the ideality factor is an output of the microscopic modelling of the dark i-v relationship of the solar cell. It is a dependent parameter rather than an independent parameter. If the device is correctly modeled, the correct ideality factor will automatically results. 

The value of ideality factor itself depends on the region of the recombination. The experience shows that n=1 for recombination current in the neutral regions of the diode, or n=2 for recombination current in the space charge region and/or various value for the recombination current at the the interface of the heterojunctions.

Best wishes