Semiconductor Module Updates

For users of the Semiconductor Module, COMSOL Multiphysics® version 5.2a brings a new app to evaluate the design parameters of a silicon solar cell at a specified date and location. The Ideal Schottky, Thermionic Emission, and Continuous Quasi-Fermi Level boundary conditions have been enhanced to improve the accuracy of your semiconductor models, while saving computational time and memory. Review all of the Semiconductor Module updates in further detail below.

New App: Si Solar Cell with Ray Optics

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_with_ray_optics

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

The user interface of the Si Solar Cell with Ray Optics app, showing the computation results and position of the sun. The user interface of the Si Solar Cell with Ray Optics app, showing the computation results and position of the sun.
The user interface of the Si Solar Cell with Ray Optics app, showing the computation results and position of the sun.

Enhanced Performance for the Ideal Schottky Boundary Condition at Metal Contacts

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.

The mesh without much refinement at the left boundary, where the Ideal Schottky boundary condition is applied. The mesh without much refinement at the left boundary, where the Ideal Schottky boundary condition is applied.
The mesh without much refinement at the left boundary, where the Ideal Schottky boundary condition is applied.
The mesh with much denser elements at the left boundary, where the Ideal Schottky boundary condition is applied. The mesh with much denser elements at the left boundary, where the Ideal Schottky boundary condition is applied.
The mesh with much denser elements at the left boundary, where the Ideal Schottky boundary condition is applied.
The results show very good uniformity of the current density (note that the max and min values are the same for up to 5 digits), even with the unrefined mesh. The results show very good uniformity of the current density (note that the max and min values are the same for up to 5 digits), even with the unrefined mesh.
The results show very good uniformity of the current density (note that the max and min values are the same for up to 5 digits), even with the unrefined mesh.
The results from the unrefined mesh are practically indistinguishable from the results using the refined mesh. The results from the unrefined mesh are practically indistinguishable from the results using the refined mesh.
The results from the unrefined mesh are practically indistinguishable from the results using the refined mesh.

Improved Performance for the Thermionic Emission Boundary Condition at Heterojunctions

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 5.2a, a high-order extrapolation scheme is used to achieve much better accuracy without the need for an extremely dense mesh at the boundary.

Enhanced Capability for the Continuous Quasi-Fermi Level Boundary Condition at Heterojunctions

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.
Fermi Dirac statistics for the Continuous Quasi-Fermi Level boundary condition at heterojunctions. The computed levels are as expected at the zero level. Fermi Dirac statistics for the Continuous Quasi-Fermi Level boundary condition at heterojunctions. The computed levels are as expected at the zero level.
Fermi Dirac statistics for the Continuous Quasi-Fermi Level boundary condition at heterojunctions. The computed levels are as expected at the zero level.

More Accurate Formulation for Electrostatics of Neighboring Charge Conservation Domains

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.
In version 5.2a, the results of the Electrostatics Physics interface (left) match those of the Semiconductor Module (right).

In version 5.2a, the results of the Electrostatics Physics interface (left) match those of the Semiconductor Module (right).

In version 5.2a, the results of the Electrostatics Physics interface (left) match those of the Semiconductor Module (right).

Optimized Study Settings Speed Up Computation Times for the Bipolar Transistor Tutorial Models

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.