COMSOL 6.4 - Si Solar Cell 1D

Si Solar Cell 1D

This tutorial uses a simple 1D model of a silicon solar cell to illustrate the basic steps to set up and perform a semiconductor simulation with the COMSOL Semiconductor Module.

Introduction

The solar cell model consists of a 1D silicon p–n junction with carrier generation and Shockley–Read–Hall recombination.

The p–n junction is formed by p-doping the front surface of an n-type Si wafer. The uniform bulk n-doping is assumed to be 1·1016 cm−3. The front surface p-doping is assumed to have a peak concentration of 1·1019 cm−3, and a Gaussian drop off with a junction depth of 0.25 μm.

The carrier generation mechanism from the photovoltaic effect is not modeled in detail. Instead, for simplicity, a user-defined spatially dependent variable is created for the generation rate, using an integral expression involving the solar irradiance and silicon absorption spectra. In addition, the Shockley–Read–Hall model is employed to capture the main recombination effect.

Under normal operating conditions, photo-generated carriers are swept to each side of the depletion region of the p–n junction. A small forward bias voltage is applied to extract the electric power, given by the product of the photocurrent and the applied voltage.

Model Definition

This model simulates the behavior of the solar cell under forward bias with a voltage between 0 and 0.61 V. The modeled domain has a thickness of 150 μm. The built-in Si material data is assumed.

An feature is used for the uniform bulk doping and a is used for the front surface doping (the surface is specified in the subnode).

The Shockley–Read–Hall recombination model is implemented in a feature, and the photo-generation is done in a feature. The electrical connections to the front and back surfaces are done with two features.

The integral expression for the photo-generation rate is

(1)

where z is the depth into the device from the surface, λ is the wavelength, α(λ) is the absorption coefficient defined by

(2)

where κ(λ) is the imaginary part of the refractive index (data given by Ref. 1), and ϕ(λ) is the photon generation rate defined by

(3)

where F(λ) is the spectral irradiance (here approximated by the AM 1.5 spectrum given by Ref. 2)

The mesh is adjusted from the default in order to resolve the steep gradients near the surface of the relatively thick device. The voltage sweep is done using a Stationary study with enabled, using the solution from a study step as the initial condition.

Results and Discussion

Figure 1 shows the donor and acceptor concentrations for the depths of first 10 μm beneath the front surface. It is always a good idea to check the doping profile for unintentional setup errors.

Figure 1: Donor and acceptor concentrations for the depths of first 10 μm beneath the front surface.

Figure 2 shows the Shockley–Read–Hall recombination rate and the user-defined photo-generation rate throughout the thickness of the cell.

Figure 2: Shockley–Read–Hall recombination rate and user-defined photo-generation rate throughout the thickness of the cell.

Figure 3 and Figure 4 show the I–V and P–V curves. These graphs allow us to read off essential operating parameters such as the open circuit voltage (~0.61 V), the short circuit current (~33 mA), and the max power (~16.7 mW).