The Schrödinger-Poisson Coupling () node takes user inputs to generate the variables and equations necessary for the bidirectional coupling between the Electrostatics physics interface and the Schrödinger Equation physics 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 physics interface that overlap with the domain selection of the selected Electrostatics interface.

This section defines the physics involved in the coupling. By default, the software selects an appropriate physics interface for you from the Schrödinger Equation and Electrostatics lists. These selections determine the two physics interfaces that are coupled by this feature.

Enter the temperature T (SI unit: K) of the system to be modeled. The default value is 293.15[K].

From the Particle density computation drop-down menu, select Fermi-Dirac statistics, parabolic band (the default) or User defined.

This option computes the statistically weighted effective density of states for each eigenstate, assuming Fermi-Dirac statistics and parabolic band approximation. See the Equation section of the user interface for the formula used, which varies according to the space dimension.

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/m2 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.

From the Charge density computation list, select Modified Gummel iteration (the default), Damped iteration, or User defined.

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.

This option updates the space charge density contribution from the sum of the statistically weighted probability density profile for each eigenstate, by making a prediction based on the high temperature limit (Maxwell-Boltzmann statistics). See the Equation section of the user interface for the formula used.

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.

This option updates the space charge density contribution from the sum of the statistically weighted probability density profile for each eigenstate, by adding a fractional contribution to the space charge density from the previous iteration (with the same fraction removed from the previous charge density). See the Equation section of the user interface for the formula used.

The fraction is specified by the damping factor α (dimensionless). The default value is 0.1.

Directly enter the formula for the space charge density ρv (SI unit: C/m3). The default expression is 0.