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Electrostatics

Parameters for the electrostatics calculations.

orbital_basis#

orbital_basis: Literal['point-charge'] = 'point-charge'

The orbital basis to use to transform between the real-space and orbital-space representations of the potential and charge density.

Currently, only the "point-charge" basis is supported. Each orbital is represented as a point charge located at the corresponding atomic position.

solving_scheme#

solving_scheme: Literal['root-finding', 'direct'] = 'root-finding'

The scheme to solve the non-linear Poisson equation.

  • "root-finding": Solves the Poisson equation using an iterative predictor-corrector scheme where the charge density response is computed from the potential using a density model and the Poisson equation is solved iteratively until convergence.
  • "direct": Solves the Poisson equation directly using a linear solver. Due to the non-linearity of the Schrödinger-Poisson problem, this scheme is not recommended and should only be used with very cautious mixing and a good initial guess.

max_iterations#

max_iterations: PositiveInt = 20

The maximum number of inner iterations for the root-finding scheme.

Only used if solving_scheme is set to "root-finding".

convergence_tol#

convergence_tol: PositiveFloat = 0.001

The convergence tolerance for the root-finding scheme.

This is defined as the infinity norm of the potential update in the root-finding scheme.

Only used if solving_scheme is set to "root-finding".

density_model#

density_model: Literal['single-band', 'omen'] = 'single-band'

The density model to use for the root-finding scheme.

  • "single-band": Uses a simple single-band density model where the charge density is computed from the potential using a single-band approximation.
  • "omen": Uses the density model from the OMEN code. This is almost identical to the single-band model with density_model_dim = 2. However, it uses slightly different physical constants, i.e., not the CODATA values used everywhere else in quatrex.

Only used if solving_scheme is set to "root-finding".

density_model_dim#

density_model_dim: Literal[1, 2, 3] = 2

The dimensionality of the system to use for the single-band density model.

The density model does not have to match the actual dimensionality of the system. For example, a 2D density model might actually work best for systems of all dimensionalities.

Only used if solving_scheme is set to "root-finding" and density_model is set to "single-band".

initial_guess#

initial_guess: Literal['zero', 'constraints', 'file'] = 'zero'

The strategy to generate the initial guess for the potential.

  • "zero": Uses a zero potential as the initial guess.
  • "constraints": Solves a linear Poisson equation with the potential constraints to generate the initial guess. This is expected to work best at regimes close to equilibrium where the potential does not vary too much.
  • "file": Loads the initial guess from a file. The file should be located in the input_dir and named potential.npy.

default_epsilon_r#

default_epsilon_r: PositiveFloat = 1.0

The default relative permittivity to use for the Poisson solver.

This is used as a fallback for regions that do not have a specified relative permittivity.

electron_affinity#

electron_affinity: float | None = None

The electron affinity of the semiconductor channel.

This is used to align the voltage levels of any gates to the semiconductor channel levels in SCSP runs. If not set, the voltages of the gates are taken as absolute values without any alignment, i.e. they are directly used as the Dirichlet boundary conditions for the Poisson equation.