The Schrödinger–Poisson Coupling (
) node takes user inputs to generate the variables and equations necessary for the bidirectional coupling between the
Electrostatics interface and the
Schrödinger Equation interface, to model charged particles in quantum-confined systems.
The Label is the default multiphysics coupling feature name.
The Name is used primarily as a scope prefix for variables defined by the coupling node. The software refer to variables in expressions using the pattern
<name>.<variable_name>. In order to distinguish between variables belonging to different coupling nodes or 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 multiphysics coupling feature in the model) is
schrp1.
The default setting is All domains, which couples all domains in the selected
Schrödinger Equation interface that overlap with the domain selection of the selected
Electrostatics interface.
Enter the temperature T (SI unit: K) of the system to be modeled. The default value is 293.15 K.
Enter the Fermi energy level Ef (SI unit: J), density-of-state effective mass
md (SI unit: kg), and the degeneracy factor
gi (dimensionless). The default values are 0 eV, 0.067·
me_const, and 1, respectively.
Directly enter the formula for the statistically weighted effective density of states Ni (1/m
2 in 1D, 1/m in 2D and 1D axial symmetry, dimensionless in 3D and 2D axial symmetry). The default expression is 0.
Enter the charge number zq (dimensionless) for the particle, for example,
-1 for electrons and
1 for positrons. The default value is
−1.
If the Minimization of global variable option is used in the Schrödinger–Poisson study step settings, enter the formula for the
Global error variable (dimensionless). The default expression is
(schrp1.max(abs(V-schrp1.V_old)))/1[V], which computes the max difference between the electric potential profiles from the two most recent iterations, scaled by 1 V.
An additional tuning parameter α (dimensionless) can be entered to either accelerate the convergence at low temperatures using positive values, or provide extra damping using negative values. The default value is 0.