The Si Solar Cell with Ray Optics app combines the Ray Optics Module and the Semiconductor Module to illustrate the operation of a silicon solar cell for a specific date and location. The Ray Optics Module computes the average illumination for a date and location that are chosen by the app's user. Then, the Semiconductor Module computes the normalized output characteristics of the solar cell with design parameters specified by the user.

The normalized output characteristics are multiplied by the computed average illumination to obtain the output characteristics of the cell at the specified date and location, assuming a simple linear relationship between the output and illumination. The user can then calculate the solar cell's efficiency and the amount of electricity generation over the course of the day.

The underlying model consists of a 1D silicon PN junction with carrier generation and Shockley-Reed-Hall recombination. The grounded anode is modeled as a thin ohmic contact deposited on an emitter (n-doped region). Similarly, the cathode is modeled as an ideal ohmic contact deposited on the base side (p-doped region) and connected to an external circuit.

**Application Library path for the Si Solar Cell with Ray Optics app:***Semiconductor_Module/Applications/solar_cell_designer*

*NOTE: In order to run this app, you need both the Semiconductor Module and Ray Optics Module.*

In COMSOL Multiphysics ^{®} 5.2 and prior versions, a constant extrapolation scheme is used at metal contacts for the Ideal Schottky boundary condition. This requires a much finer mesh at the boundary to produce results with acceptable accuracy. In version 5.2a, a high-order extrapolation scheme is used to achieve much better accuracy without the need for an extremely dense mesh at the boundary. For example, the Ideal Schottky boundary condition is applied on the left boundary of a rectangular domain with a uniform material and current density. The following plots from COMSOL Multiphysics ^{®} version 5.2a compare two meshes and the corresponding results, which are very accurate and practically indistinguishable from each other.

In previous versions of COMSOL Multiphysics ^{®} , a constant extrapolation scheme is used at heterojunctions for the Thermionic Emission boundary condition, similar to the Ideal Schottky boundary condition. This requires a much finer mesh at the boundary to produce results with acceptable accuracy. In version 5.2 a, a high-order extrapolation scheme is used to achieve much better accuracy without the need for an extremely dense mesh at the boundary.

COMSOL Multiphysics ^{®} now supports Fermi Dirac statistics for heterojunctions with Continuous Quasi-Fermi Level boundary conditions. In version 5.2 and prior, the Continuous Quasi-Fermi Level boundary condition is valid for only Maxwell-Boltzmann statistics. In version 5.2a, Fermi Dirac statistics are also supported for the boundary condition, and consequently, heterojunctions adjacent to degenerate domains are modeled more accurately, as shown in the following plot.

COMSOL Multiphysics ^{®} version 5.2a offers an improved electrostatics formulation for neighboring charge conservation domains to obtain more accurate results. This will be useful for models with different types of insulating (dielectric) materials that are adjacent to each other. The effect of different dielectric constants of the adjacent domains is accounted for accurately, as shown in the plot.

The study settings for the bipolar transistor tutorial models have been optimized to speed up the computation times. The 3D model now takes hours to solve, rather than days, and the 2D model solves in minutes instead of over an hour.