The Schrödinger Equation Interface
The Schrödinger Equation (schr) interface (), found under the Semiconductor branch () when adding a physics interface, solves the Schrödinger equation for the wave function of a single particle in an external potential. By default, the Schrödinger equation is added to all the domain selections of the interface.
When this physics interface is added, these default nodes are added to the Model Builder: Effective Mass, Electron Potential Energy, Zero Flux, and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions or additional contributions to the potential energy. You can also right-click Schrödinger Equation to select physics features from the context menu.
Settings
The Label is the default physics interface name.
The Name is used primarily as a scope prefix for variables and coupling operators defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is schr.
Model Properties
Use Model properties to set the particle type and study-specific variables in the model.
Particle Type
Select an option from the Particle type list: Electrons (the default) or Holes.
Azimuthal Quantum Number
For axisymmetric models, enter an integer for the azimuthal quantum number m (unitless). The default is 0.
Eigenvalue Scale
Enter a constant value for the Eigenvalue scale λscale (J) for eigenvalue studies. The eigenenergy is defined as the product of the eigenvalue scale and the eigenvalue (dimensionless). The default is 1 eV, so that the eigenvalue will be the numerical value of the eigenenergy in unit of eV.
Energy
Enter a constant value or a global parameter for the Energy E (J) for stationary studies. This specifies the total energy of the stationary Schrödinger equation.
Discretization
Use this section to change the discretization of the Schrödinger equation.
Dependent Variables
The dependent variable (field variable) is for the particle Wave function psi. The name can be changed but the names of fields and dependent variables must be unique within a model.
The particle Wave function psi can be a scalar (single component, the default), or a vector (multiple component, by entering an integer larger than the default value of 1 in the input field Number of wave function components). Not all options or features are available for the multicomponent wave function.
In the case of multicomponent wave function, it is recommended to determine and fix the number of wave function components, before configuring the physics settings.