Semiconductor Module Updates

For users of the Semiconductor Module, COMSOL Multiphysics® version 5.4 brings a new Schrödinger-Poisson Equation multiphysics interface, a new Trap-Assisted Surface Recombination feature, and a new quantum tunneling feature under the WKB approximation. Read about these semiconductor features and more below.

Schrödinger-Poisson Equation Multiphysics Interface

The new Schrödinger-Poisson Equation multiphysics interface creates a bidirectional coupling between the Electrostatics and Schrödinger Equation physics interfaces in order to model charge carriers in quantum-confined systems. The electric potential from the Electrostatics interface contributes to the potential energy in the Schrödinger equation. A statistically weighted sum of the probability densities from the eigenstates of the Schrödinger Equation interface contributes to the space-charge density in the Electrostatics interface. All space dimensions (1D, 1D axial symmetry, 2D, 2D axial symmetry, and 3D) are supported.

A dedicated Schrödinger-Poisson study type is also included to automate the generation of self-consistent iterations in the solver sequence. Finally, a new benchmark model named Self-Consistent Schrödinger-Poisson Results for a GaAs Nanowire is included in the Application Library to demonstrate how to use this new feature. The animation shows the solver converging to the self-consistent solution for a Schrödinger-Poisson system.

Trap-Assisted Surface Recombination

A new boundary condition called Trap-Assisted Surface Recombination is available, and replaces the check box Surface traps in the features Insulation, Thin Insulator Gate, and Insulator Interface. Unlike the old check box, which only allows one option of explicit traps, the new boundary condition has two options for explicit traps and SRH recombination, the same as its domain counterpart (Trap-Assisted Recombination domain condition). Additionally, the new boundary condition is extended to include Schottky contacts. A new benchmark model, Interface Trapping Effects of a MOSCAP, is included in the Application Library to demonstrate how to use this new feature.

An example of using the Trap-Assisted Surface Recombination boundary condition in a MOSCAP model. The computed terminal capacitance and the equivalent parallel conductance as functions of the gate voltage reproduce the qualitative behavior of experimental data found in the literature. The computed terminal capacitance and the equivalent parallel conductance as functions of the gate voltage reproduce the qualitative behavior of experimental data found in the literature.

WKB Tunneling Model

A new tunneling feature based on the WKB approximation is now available to account for the additional current densities for the carrier transport across a heterojunction or a Schottky barrier via quantum tunneling. To enable this feature, a new Extra Current Contribution section has been added to the Continuity/Heterojunction and MetalContact (when the Type is set to Ideal Schottky) features, where you can select "WKB tunneling model". A new benchmark model, Heterojunction Tunneling, is included in the Application Library to demonstrate how to use this new feature.


This animation shows an electron penetrating a classically forbidden potential barrier via quantum tunneling.

Key Enhancements

  • A linear shape function option is now available for discretizing the finite element quasi-Fermi level formulation
  • User-defined extra current contributions to heterojunctions (thermionic emission) and Schottky contacts in the new Extra Current Contribution section
  • For thermionic emission in heterojunctions, a single value of A* (Richardson's coefficient) is computed so that the total current density consistently cancels to zero at equilibrium
  • It is easier to enter a user defined tunneling current density across insulators, as the variable for the perpendicular electric field in the insulator (semi.E_ins) is now always available
  • The Fletcher mobility model and the SRH, Auger, and Direct recombination models incorporate nonnegative carrier concentration values in the formulation in order to improve stability
  • When duplicating or pasting metal contacts, insulated gates, or electrostatic terminals, the duplicated entity now has a new unique terminal name
  • The terminal current variable for the small signal analysis now includes the contribution from the displacement current
    • It is now easier to compute lumped parameters, such as the differential capacitance of a biased Schottky contact
  • The small-signal analysis can now be performed on systems with continuous trapping levels
  • For the Semiconductor Equilibrium study step, the formulation is improved for current-driven metal contacts

New Tutorial Models

COMSOL Multiphysics® version 5.4 brings several new Semiconductor Module tutorial models.

Tutorial Model Improvements

  • Updated the Si Solar Cell 1D model to use AM 1.5 solar irradiance and silicon absorption spectra for the photogeneration rate
  • Updated the Heterojunction 1D model
    • Four different ways to achieve better convergence
      • Study 1: Manual scaling
      • Study 2: Inherit solution from Study 1 (same as before)
      • Study 3: Semiconductor Equilibrium study step as initial condition
      • Study 4: Ramp both doping and thermionic current from 1e-8 (doping ramp was off before)
    • Removed outdated solver tweaks (initial damping, iteration number)
    • Updated comments, model description, and model documentation; renamed labels
  • GaN Double Heterostructure LED model
    • Replaced ramping and tweaking of initial values and solver settings by the Semiconductor Equilibrium study step
    • Removed solver tweaks for current bias study
    • Updated model description, setup comments, and model documentation
  • For the EEPROM model, Study 1 changed to the default solver and manual scaling for better convergence