The Schrödinger–Poisson Equation Multiphysics Interface
The Schrödinger–Poisson Equation multiphysics interface creates a bidirectional coupling between an Electrostatics interface and a Schrödinger Equation 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 space 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.
On the Constituent Physics Interfaces
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.
Coupling Features
If a multiphysics interface is added from the Model Wizard or using the Add Physics window, then the appropriate coupling feature is automatically added to the model builder tree structure. Alternatively, the physics interfaces can be added one at a time, followed by the coupling features.
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.
Coupling features are available from the context menu (right-click the Multiphysics Couplings node) or from the Physics toolbar, Multiphysics menu.
Physics Interfaces and Coupling Features
Use the online help in COMSOL Multiphysics to locate and search all the documentation. All these links also work directly in COMSOL Multiphysics when using the Help system.
Coupling Features
The Schrödinger–Poisson Coupling node is described in the section Schrödinger–Poisson Coupling below.
Physics Interface Features
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).
In general, to add a node, go to the Physics toolbar, no matter what operating system you are using. Subnodes are available by clicking the parent node and selecting it from the Attributes menu.
The available physics features for The Schrödinger Equation Interface are listed in the section Domain and Boundary Nodes for the Schrödinger Equation Interface.
For theory and physics interface feature descriptions relating to the Electrostatics interface, see the COMSOL Multiphysics Reference Manual.