The Schrödinger-Poisson Equation multiphysics interface creates a bidirectional coupling between an
Electrostatics physics interface and a
Schrödinger Equation physics interface, to model charge carriers in quantum-confined systems. The electric potential from the Electrostatics contributes to the potential energy term in the Schrödinger Equation. A statistically weighted sum of the probability densities from the eigenstates of the Schrödinger Equation contributes to the space charge density in the Electrostatics. All spatial dimensions (1D, 1D axial symmetry, 2D, 2D axial symmetry, and 3D) are supported. A dedicated
Schrödinger-Poisson study type is available for automated generation of self-consistent iterations in the solver sequence.
When a predefined Schrödinger-Poisson Equation multiphysics interface is added from the
Semiconductor branch (
) of the
Model Wizard or
Add Physics windows,
Schrödinger Equation and
Electrostatics interfaces are added to the Model Builder.
In addition, a Multiphysics Couplings node is added, which automatically includes the multiphysics coupling feature
Schrödinger-Poisson Coupling.
The Schrödinger Equation interface solves the Schrödinger equation for general quantum mechanical problems, as well as for the electron and hole wave functions in quantum-confined semiconductors under the assumption of the envelope function approximation.
The Electrostatics interface is used to compute the electric field, the electric displacement field and potential distributions in dielectrics under conditions where the electric charge distribution is explicitly prescribed. The formulation is stationary but for use together with other physics, also eigenfrequency, frequency-domain, small-signal analysis and time-domain modeling are supported in all space dimensions. The physics interface solves Gauss' Law for the electric field using the scalar electric potential as the dependent variable.
For example, if single Electrostatics and
Schrödinger Equation interfaces are added, then COMSOL Multiphysics adds an empty
Multiphysics Couplings node. You can then choose the coupling feature:
Schrödinger-Poisson Coupling.
Physics nodes are available from the Physics ribbon toolbar (Windows users),
Physics context menu (Mac or Linux users), or right-click to access the context menu (all users).