Use the Schrödinger-Poisson (
) study and study step to automatically generate the iterations in the solver sequence for the self-consistent solution of the fully coupled Schrödinger-Poisson equation. Also see the
Semiconductor Module User’s Guide for the Schrödinger-Poisson Equation multiphysics interface.
To take advantage of the default settings detailed below, use the Model Wizard or the
Add Study button in the ribbon or toolbar of the COMSOL Desktop. A study step added by right-clicking a Study node does not include any default settings suggested by the physics.
The default option for the Eigenfrequency (Eigenvalue) search method drop-down menu is
Manual, because for a completely new problem, it is often necessary to use this option to find the range of the eigenenergies and a rough estimate of the number of eigenstates. Make sure that the
Unit menu is left as blank (default).
Once the range and number are found, switch to the Region search option with appropriate settings for the range and number of eigenvalues, in order to ensure that all significant eigenstates are found by the solver.
Make sure the Unit list is left as blank (default).
The default option for the Termination method drop-down menu is
Minimization of global variable, which updates a table displaying the history of a global error variable after each iteration during the solution process. This provides a good indication of the solution process to monitor whether the iteration is converging.
The default expression for the Global variable input field uses the built-in global error variable
schrp1.global_err, which computes the max difference between the electric potential fields from the two most recent iterations, in the unit of V, as discussed in the section
Charge Density Computation for the
Schrödinger-Poisson Coupling multiphysics node in the
Semiconductor Module User’s Guide. Note that the prefix for the variable, in this case
schrp1, should match the
Name input field of the Schrödinger-Poisson Coupling multiphysics node. Setting the
Absolute tolerance to
1e-6 thus means the iteration ends after the max difference is less than
1 uV.
Use the Auxiliary sweep option to solve for a set of parameters. For example, in the Self-Consistent Schrödinger-Poisson Results for a GaAs Nanowire tutorial model (
schrodinger_poisson_nanowire), it is used to solve for a set of azimuthal quantum numbers. See
Auxiliary Sweep for details.