Quantum model holes

Please also refer to the database section of $quantum-model-holes.

!------------------------------------------------------------------!
$quantum-model-holes                                     optional  !
 model-number                            integer         required  !
 model-name                              character       required  !
 cluster-numbers                         integer_array   required  !
 valence-band-numbers                    integer_array   required  !
 separation-model                        character       required  !
 number-of-eigenvalues-per-band          integer_array   required  !
 occupy-exactly-min-eigenvalues-per-band double_array    optional  ! Note: double_array and not integer_array to allow for partial occupation.
 occupy-exactly-max-eigenvalues-per-band double_array    optional  ! Note: double_array and not integer_array to allow for partial occupation.
 maximum-energy-for-eigenstates          double_array    required  !
 quantization-along-axes                 integer_array   required  !
 boundary-condition-100                  character       optional  !
 boundary-condition-010                  character       optional  !
 boundary-condition-001                  character       optional  !
 method-of-brillouin-zone-integration    character       optional  ! 1D/2D (k.p only)
 k-range-determination-method            character       optional  ! 1D/2D (k.p only)
 k-range                                 double          optional  ! 1D/2D (k.p only)
 num-kp-parallel                         integer         optional  ! 1D/2D (k.p only)
 num-ks-100                              integer         optional  ! superlattice only
 num-ks-010                              integer         optional  ! superlattice only
 num-ks-001                              integer         optional  ! superlattice only
 max-eigenvalue                          integer_array   optional  ! not used (for separation-model = eigenvalue)
 max-energy                              double_array    optional  ! not used (for separation-model = energy)
$end_quantum-model-holes                                 optional  !
!------------------------------------------------------------------!

If electrons are 8x8kp, holes cannot be 6x6kp (or 6x6kp). Can they be effective-mass in this case?

Syntax

model-number = 1

model-name   = 8x8kp           ! coupling between heavy, light and split-off holes and conduction band
             = 6x6kp           ! coupling between heavy, light and split-off holes
             = 4x4kp           ! coupling between heavy and light holes only
             = effective-mass
             = tight-binding (not implemented yet)
8x8kp or 6x6kp or 4x4kp or effective-mass or tight-binding

cluster-numbers = 1
cluster numbers to which this model applies

valence-band-numbers = 1 2 3
To select bands (minima) handled in Schrödinger equation: 1 = heavy hole, 2 = light hole, 3 = split-off hole
  Options possible:
  effective-mass:  1
              2
              3
              1 2
              2 3
              1 3
              1 2 3
  4x4 k.p:              1 2
  6x6 k.p:              1 2 3
  8x8 k.p:              1 2 3

separation-model = eigenvalue   !  -> specify number-of-eigenvalues-per-band
                 = energy       !  -> specify maximum-energy-for-eigenstates
                 = edge-model   !  -> Only localized states are considered for the quantum mechanical density.
To determine separation between classical and quantum mechanical density ('eigenvalue','energy','edge-model').
More information ...

number-of-eigenvalues-per-band = 3     ! If only one band is specified, then calculate 3 eigenvalues for this band.
                               = 6 3   ! If two bands are specified, then calculate 6 eigenvalues for the first band
                                       ! and 3 eigenvalues for the second band.
                               = 3 3 3 ! If heavy, light and split-off hole bands are specified, then calculate 3 eigenvalues for each.
Here one has to specify how many eigenstates have to be calculated in each valence band maximum. This is also relevant for the quantum mechanical density unless maximum-energy-for-eigenstates is specified in combination with separation-model = energy. However, in this case also number-of-eigenvalues-per-band has to be present in order to determine the maximum number of eigenstates to be calculated (although not all contribute to the density).

maximum-energy-for-eigenstates = 0.5d0             ! [eV]  If one valence band is specified.
                               = 0.5d0 0.5d0       ! [eV]  If two valence bands are specified.
                               = 0.5d0 0.5d0 0.5d0 ! [eV]  If three valence bands are specified.
Lower limit for energy of bound states.
Calculate eigenvalues up to this energy (relative to bulk band edge).
Use continuum model above this energy (relative to bulk band edge).
Relevant for specifier separation-model = energy.
For separation-model = eigenvalue this specifier is ignored.

quantization-along-axes        = 1 1 1  ! 3D
                               = 1 1 0  ! 2D
                               = 1 0 1  ! 2D
                               = 0 1 1  ! 2D
                               = 0 0 1  ! 1D
                               = 0 1 0  ! 1D
                               = 1 0 0  ! 1D
Zeros and ones: to select quantization direction (1D) / plane (2D) / volume (3D).
At present the entries must be identical to specifier orientation in keyword $simulation-dimension.
In 3D input like '0 1 1'  is not possible so far.
Currently no features are attributed to this specifier. A possible extension for the future would be to use a 2D simulation where only a 1D quantization is used or a 3D simulation with a 1D quantization direction or a 2D quantized plane.

boundary-condition-100  =  Neumann          ! neumann   or NEUMANN
                        =  Dirichlet        ! dirichlet or DIRICHLET
                        =  Mixed            ! mixed     or MIXED
                        =  Periodic         ! periodic  or PERIODIC  (for superlattice)
boundary-condition-010  =  [ as above ]
boundary-condition-001  =  [ as above ]

"Boundary conditions for [100]" means boundary conditions for Schrödinger equation in x-direction of simulation system and similar for [010 and [001].
Default is Neumann.

Remarks:
It is possible to specify something like this:
   boundary-condition-100  =  periodic
   boundary-condition-010  =  periodic
   boundary-condition-001  =  Dirichlet
This makes sense if one has a quantum well extending over the whole (x,y) plane and which is perpendicular to the z direction.

Restrictions:
If one specifies periodic boundary conditions, the quantum cluster must extend over the whole device in that direction.

 occupy-exactly-min-eigenvalues-per-band = ...
 occupy-exactly-max-eigenvalues-per-band = ...
See $quantum-model-electrons.

k.p only

method-of-brillouin-zone-integration = special-axis
                                     = simple-integration
                                     = gen-dos
  'special-axis'        Only for [0001] quantization direction in wurzite or
                        for isotropic energy dispersion E(k_||) which is in general not the case.
  'simple-integration'  Discretization of 2D Brillouin zone (only applicable to a 1D simulation).
  'gen-dos'             Evaluation of the density by integration over the density of states (DOS).
                        Not implemented yet for 2D simulations.
Only necessary for 1D and 2D k.p simulations.
More information ...

 

k-range-determination-method = bulk-dispersion-analysis  ! 1D/2D
                             = k-max-input               ! 1D/2D

k-range                      = 1.0d0                     ! 1D/2D (Units: [1/Angstrom])
Required if k-range-determination-method = k-max-input.
This also works for 2D (k_z) but does not make sense for 3D.
More information ...

 

num-kp-parallel = 100
                = 0    ! For k_x=k_y=0 only; if no k_|| should be considered (works only if one doesn't output densities).
Total number of k_|| points for Brillouin zone discretization.
Only necessary for 1D (k_x,k_y) and 2D (k_z) k.p simulations and optical absorption.
This also works for 2D (k_z) but does not make sense for 3D.
1D: It always refers to the total number of k_|| points in the whole 2D Brillouin zone.
2D: It always refers to the total number of k_z points in the whole 1D Brillouin zone.
More information ...

Superlattice only

num-ks-100 =
Number of k points in superlattice direction x.

num-ks-010 =
Number of k points in superlattice direction y.

num-ks-001 =
Number of k points in superlattice direction z.

Not used:

max-eigenvalue   = 8      ! If one valence band is specified.
                 = 5 5    ! If two valence bands are specified.
                 = 5 5 5  ! If three valence bands are specified.
This is for separation-model = eigenvalue.
Calculate quantum density up to this eigenvalue then use classical model.
(Has to be present if separation-model = eigenvalue, otherwise it is ignored.)

max-energy       = 2d0          ! [eV]  If one valence band is specified.
                           = 2d0 2d0      ! [eV]  If two valence bands are specified.
                 = 2d0 2d0 2d0  ! [eV]  If three valence bands are specified.
This is for separation-model = energy.
Calculate quantum density up to this energy (relative to bulk band edge).
(Has to be present if separation-model = energy, otherwise it is ignored.)

Please also refer to the database section of $quantum-model-holes.