DeviceHuckelCalculator¶
- class DeviceHuckelCalculator(electrode_calculators=None, basis_set=None, pair_potentials=None, numerical_accuracy_parameters=None, iteration_control_parameters=None, device_algorithm_parameters=None, weighting_scheme=None, poisson_solver=None, contour_parameters=None, electrode_voltages=None, electrode_temperatures=None, checkpoint_handler=None, spin_polarization=None, dynamical_matrix_parameters=None, hamiltonian_derivatives_parameters=None, parallel_parameters=None)¶
Class for representing calculations using the extended Huckel Model for DeviceConfigurations.
- Parameters:
electrode_calculators (tuple of
HuckelCalculator
) – A tuple ofHuckelCalculator
objects containing a calculator for each electrode.basis_set (list of
HuckelBasisParameters
) – An object describing the basis set used for the Extended-Huckel calculation. Default:HoffmannHuckelParameters.All
pair_potentials (
PairPotential
) – The repulsive pair potentials used for total energy and force calculations. Default: No pair potentialnumerical_accuracy_parameters (
NumericalAccuracyParameters
) –The
NumericalAccuracyParameters
used for the self-consistent Huckel calculation. Default:NumericalAccuracyParameters( density_mesh_cutoff=10.0*Hartree, k_point_sampling=MonkhorstPackGrid(1, 1, 100), radial_step_size=0.01*Angstrom, density_cutoff=1.0e-6, interaction_max_range=10*Angstrom, number_of_reciprocal_points=1024, reciprocal_energy_cutoff=1250.0*Hartree, occupation_method=FermiDirac(300.0*Kelvin))
iteration_control_parameters (
IterationControlParameters
) – TheIterationControlParameters
used for the self- consistent Huckel calculation. For non-self-consistent calculations set this parameter toNonSelfconsistent
. Default:NonSelfconsistent
.device_algorithm_parameters (
DeviceAlgorithmParameters
) –The
DeviceAlgorithmParameters
used for the device simulation. Default:DeviceAlgorithmParameters( initial_density_type=NeutralAtom( electrode_constraint_length=10.0*Angstrom), electrode_constraint=ElectrodeConstraint.Off, self_energy_calculator_real=RecursionSelfEnergy( storage_strategy=SaveInMemory(), tolerance=1.0e-13, maximum_iteration=400), self_energy_calculator_complex=RecursionSelfEnergy( storage_strategy=SaveInMemory(), tolerance=1.0e-13, maximum_iteration=400), non_equilibrium_method=GreensFunction(), equilibrium_method=GreensFunction(), store_grids=True, store_basis_on_grid=Automatic, scf_restart_step_length=0.1*Angstrom, enforce_different_electrodes=False)
Note that the electrode constraint for a SurfaceConfiguration will be set to
ElectrodeConstraint.DensityMatrix(electrode_constraint_length=10.0*Angstrom
.weighting_scheme (HoffmannWeighting | WolfsbergWeighting) – The weighting scheme used for calculating off-site matrix elements of the Huckel Hamiltonian. Default: WolfsbergWeighting
poisson_solver (
DirectSolver
|MultigridSolver
|FastFourier2DSolver
) – The Poisson solver used to determine the electrostatic potential. Default: Configuration dependent.FastFourier2DSolver
for aDeviceConfiguration
without any metallic or dielectricSpatialRegion
. For others:MultigridSolver
. The default boundary conditions are[PeriodicBoundaryCondition, PeriodicBoundaryCondition, DirichletBoundaryCondition]
.contour_parameters (
ContourParameters
) –The parameters used for the complex contour integration. Default:
ContourParameters( equilibrium_contour=SemiCircleContour( integral_lower_bound=1.5*Hartree, circle_eccentricity=0.3, logarithmic_bunching=0.3, circle_points=30, fermi_line_points=10, fermi_function_poles=8), non_equilibrium_contour=RealAxisContour( real_axis_point_density=0.001*Hartree, real_axis_infinitesimal=0.001*Hartree, real_axis_kbt_padding_factor=5.0), method=DoubleContour())
electrode_voltages (PhysicalQuantity of type electrical potential) – The voltages applied to the two electrodes. Default:
(0.0, 0.0) * Volt
electrode_temperatures (Sequence of PhysicalQuantity of type temperature) – The temperatures used in the Fermi-Dirac distribution of the electrodes. They represent the physical temperatures used for the integration of the transmission spectra. Default:
(300, 300) * Kelvin
checkpoint_handler (
CheckpointHandler
) – TheCheckpointHandler
used for specifying the save-file and the time interval. between saving the calculation during the scf-loop. Default: A defaultCheckpointHandler
object.spin_polarization (
Unpolarized
|Polarized
|Noncollinear
|SpinOrbit
) – Flag indicating if the calculation is spin-polarized or not. Default:Unpolarized
dynamical_matrix_parameters (not used) – Deprecated: from v2015, see the
DynamicalMatrix
analysis object.hamiltonian_derivatives_parameters (not used) – Deprecated: from v2015, see the
HamiltonianDerivatives
analysis object.parallel_parameters (
ParallelParameters
) – The parameters used to control parallelization options. Default:ParallelParameters(processes_per_saddle_search=1)
- basisSet()¶
- Returns:
The basis set.
- Return type:
list of
HuckelBasisParameters
- checkpointHandler()¶
- Returns:
The
CheckpointHandler
used for specifying the save-file and the time interval. between saving the calculation during the scf-loop.- Return type:
- contourParameters()¶
- Returns:
The contour integral parameters.
- deviceAlgorithmParameters()¶
- Returns:
The device algorithm parameters.
- Return type:
- dynamicalMatrixParameters()¶
This method is deprecated.
- electrodeCalculators()¶
- Returns:
The electrode calculator of each electrode.
- Return type:
list of
SemiEmpiricalCalculator
- electrodeTemperatures()¶
- Returns:
The electrode temperatures.
- Return type:
Sequence of PhysicalQuantity of type temperature.
- electrodeVoltages()¶
- Returns:
The electrode voltages as PhysicalQuantity of length 2.
- Return type:
PhysicalQuantity of type electrical potential
- hamiltonianDerivativesParameters()¶
This method is deprecated.
- hamiltonianParametrization()¶
- Returns:
The Hamiltonian parametrization associated with a semi-empirical calculator.
- Return type:
SemiEmpiricalHamiltonianParametrization
- isConverged()¶
- Returns:
True when the call to “update()” resulted in a converged SCF loop.
- Return type:
bool
- iterationControlParameters()¶
- Returns:
The
IterationControlParameters
used for a self-consistent calculation. For non-self-consistent calculations this parameter isNonSelfconsistent
.- Return type:
- metatext()¶
- Returns:
The metatext of the object or None if no metatext is present.
- Return type:
str | None
- numberOfSpins()¶
- Returns:
The number of spins.
- Return type:
int
- numericalAccuracyParameters()¶
- Returns:
The
NumericalAccuracyParameters
used for the self-consistent Huckel calculation.- Return type:
- pairPotentials()¶
- Returns:
The repulsive pair potentials used for total energy and force calculations.
- Return type:
- parallelParameters()¶
- Returns:
The parameters used to control parallelization options.
- Return type:
- poissonSolver()¶
- Returns:
The Poisson solver used to determine the electrostatic potential.
- Return type:
DirectSolver
|MultigridSolver
|FastFourierSolver
|FastFourier2DSolver
- setCheckpointHandler(checkpoint_handler)¶
Set the the checkpoint handler.
- Parameters:
checkpoint_handler (
CheckpointHandler
) – TheCheckpointHandler
used for specifying the save-file and the time interval. between saving the calculation during the scf-loop.
- setHamiltonianParametrization(hamiltonian_parametrization)¶
Set and check the Hamiltonian parametrization.
- Parameters:
hamiltonian_parametrization (
HamiltonianParametrization
) – An object describing the Hamiltonian parametrization for the semi-empirical calculation.
- setIterationControlParameters(iteration_control_parameters)¶
Set the iteration control parameters.
- Parameters:
iteration_control_parameters (
IterationControlParameters
) – TheIterationControlParameters
used for a self-consistent calculation. For non-self-consistent calculations this parameter isNonSelfconsistent
.
- setMetatext(metatext)¶
Set a given metatext string on the object.
- Parameters:
metatext (str | None) – The metatext string that should be set. A value of “None” can be given to remove the current metatext.
- setNumericalAccuracyParameters(numerical_accuracy_parameters)¶
Set the numerical accuracy parameters.
- Parameters:
numerical_accuracy_parameters (
NumericalAccuracyParameters
) – TheNumericalAccuracyParameters
used for the self-consistent Huckel calculation.
- setPairPotentials(pair_potentials)¶
Set the pair potentials.
- Parameters:
pair_potentials (
PairPotential
) – The repulsive pair potentials used for total energy and force calculations.
- setParallelParameters(parallel_parameters)¶
Set the parallel paramters.
- Parameters:
parallel_parameters (
ParallelParameters
) – The parameters used to control parallelization options.
- setPoissonSolver(poisson_solver)¶
Set the poisson solver.
- Parameters:
poisson_solver (
DirectSolver
|MultigridSolver
|FastFourierSolver
|FastFourier2DSolver
) – The Poisson solver used to determine the electrostatic potential.
- setSpinPolarization(spin_polarization)¶
Set the spin polarization.
- Parameters:
spin_polarization (
Unpolarized
|Polarized
|Noncollinear
|SpinOrbit
) – Flag indicating if the calculation is spin-polarized or not.
- spinPolarization()¶
- Returns:
Flag indicating if the calculation is spin-polarized or not.
- Return type:
Unpolarized
|Polarized
|Noncollinear
|SpinOrbit
- uniqueString()¶
Return a unique string representing the state of the object.
- upgrade(configuration)¶
Private method for updating the calculator from the configuration, if it is possible @private
- versionUsed()¶
- Returns:
The version of ATK used to update the calculator.
- Return type:
str
- weightingScheme()¶
- Returns:
The weighting scheme used for calculating off-site matrix elements of the Huckel Hamiltonian.
- Return type:
Attention
The DeviceHuckelCalculator is being deprecated. Use the DeviceSemiEmpiricalCalculator with the HuckelHamiltonianParametrization instead.
Usage Examples¶
Define a DeviceHuckelCalculator with user defined NumericalAccuracyParameters, MultigridSolver, and DoubleContourIntegralParameters
numerical_accuracy_parameters = NumericalAccuracyParameters(
density_mesh_cutoff=10.*Units.Hartree,
k_point_sampling=(3,2,100),
interaction_max_range=10.*Angstrom,
)
electrode_poisson_solver = MultigridSolver(
boundary_conditions=[PeriodicBoundaryCondition,
PeriodicBoundaryCondition,
PeriodicBoundaryCondition]
)
poisson_solver = MultigridSolver(
boundary_conditions=[PeriodicBoundaryCondition,
PeriodicBoundaryCondition,
DirichletBoundaryCondition]
)
electrode_calculator = HuckelCalculator(
numerical_accuracy_parameters=numerical_accuracy_parameters,
poisson_solver=electrode_poisson_solver
)
contour_parameters = DoubleContourIntegralParameters(
integral_lower_bound=5.0*Units.Hartree
)
device_calculator = DeviceHuckelCalculator(
electrode_calculators=[electrode_calculator,electrode_calculator],
contour_parameters=contour_parameters,
numerical_accuracy_parameters=numerical_accuracy_parameters,
poisson_solver=poisson_solver,
electrode_voltages=(0.2*Volt, -0.3*Volt)
)
Perform a voltage sweep, and calculate I-V characteristics
calculator = DeviceHuckelCalculator()
device_configuration = DeviceConfiguration(...)
# Define voltages for voltage ramp, [0.0,0.1, ..., 1.0]*Volt
voltages = numpy.linspace(0.0,1.0,11)*Volt
for v in voltages:
# Set the calculator on the configuration using the old calculation as starting input.
device_configuration.setCalculator(
calculator(electrode_voltages=(0*Volt,v)),
initial_state=device_configuration,
)
# Calculate the transmission
t = TransmissionSpectrum(device_configuration)
# Calculate the current.
current = t.current()
print t.bias(), t.current()
Perform a gate bias scan
calculator = DeviceHuckelCalculator()
device_configuration = DeviceConfiguration(...)
metal_region = BoxRegion(...)
# Define gate_voltages for scan, [0.0,0.1, ..., 1.0]*Volt
gate_voltage=numpy.linspace(0.0,1.0,11)*Volt
for v in gate_voltage:
device_configuration.setMetallicRegions(
[metallic_region(value = gate_voltage)]
)
# Set the calculator on the configuration using the old calculation as starting input.
device_configuration.setCalculator(
calculator(),
initial_state=device_configuration,
)
# Calculate the transmission
t = TransmissionSpectrum(device_configuration)
# Calculate the conductance
print t.bias(), t.conductance()
Notes¶
The parameters for the constructor of a DeviceHuckelCalculator object and the parameters of its electrode calculators must fulfill the following conditions: In case the user does not set an electrode parameter, QuantumATK will generate that parameter using the rules below.
The NumericalAccuracyParameters must be the same for the electrodes and the device. The central region of the device does not use k-points in the C-direction and this parameter is only used for the electrodes. The electrodes need a very dense k-point sampling in the C direction.
The
poisson_solver
must be set to either the FastFourier2DSolver (default, and normally recommended) or the MultigridSolver or DirectSolver in case electrostatic gates and/or dielectric regions are included. The same boundary conditions in the A and B directions must be used for the electrodes as for the device calculator. In the C directions the user setting is ignored and the program always usesPeriodicBoundaryCondition
for the electrodes andDirichletBoundaryCondition
for the device.The
electrode_voltages
give rise to a shift of the Fermi levels of the electrodes by \(-e V_\mathrm{bias}\) , where \(V_\mathrm{bias}\) is the applied bias. Thus, a higher \(V_\mathrm{bias}\) on the right electrode than the left gives rise to an electron flow from left to right, corresponding to an electrical current from right to left (the current will be negative in this case; see TransmissionSpectrum).
For the details of the extended-Hückel model, see the chapter on Semi Empirical.