$quantum-cluster

For quantum mechanical calculations, you have to define quantum regions ($quantum-regions) and quantum clusters on which certain quantum models ($quantum-model-electrons, $quantum-model-holes) are applied. As for the regions and current-regions, quantum-regions can be clustered. At least cluster number 1 has to be specified if the quantum mechanical properties should be calculated at all.

The syntax of the region-cluster, quantum-cluster, and current-cluster is very similar. For more information on these specifiers see $region-cluster and $current-cluster.

$quantum-cluster                                  optional
 cluster-number                   integer         required
 region-numbers                   integer_array   required
 deactivate-cluster               character       optional
 apply-constant-el-Fermi-level    double          optional
 apply-constant-hl-Fermi-level    double          optional
$end_quantum-cluster                              optional

Explanation of specifiers

cluster-number
type

integer >= 1

presence

required

An integer number to refer to clustered geometry element.

region-numbers
type

integer array containing integers >= 1

presence

required

Region numbers belonging to the cluster cluster-number.

deactivate-cluster
type

character

presence

optional

value

yes or no

default

no

Flag to switch off quantum cluster. Switching off quantum calculation means classical simulation. This is a very convenient way to turn the quantum calculation off and on. For a first test, it is recommended to a classical calculation as it is much faster. Then you can check whether the geometry and the doping regions are defined correctly, and if the strain has the expected influence on the conduction and valence band edges. Once you are convinced that you have set up the structure correctly, you can do a quantum mechanical simulation.

apply-constant-el-Fermi-level
type

double

presence

optional

unit

[eV]

example

0.2

Applies a constant electron Fermi level \(E_{\text{F,n}}\) to this quantum cluster. The energetic distance of the conduction band edges with respect to this Fermi level determines the electron density.

apply-constant-hl-Fermi-level
type

double

presence

optional

unit

[eV]

example

-0.1

Applies a constant hole Fermi level \(E_{\text{F,p}}\) to this quantum cluster. The energetic distance of the valence band edges with respect to this Fermi level determines the hole density.

Examples

Here, only one quantum cluster is defined.

!----------------------------------------------
$quantum-cluster
 cluster-number = 1     region-numbers = 1
 deactivate-cluster = no
!deactivate-cluster = yes
$end_quantum-cluster
!----------------------------------------------

Here, two quantum regions are combined to form a common quantum cluster.

!----------------------------------------------
$quantum-cluster
 cluster-number = 1     region-numbers = 1 2
$end_quantum-cluster
!----------------------------------------------

Here, three separate quantum clusters are defined that are treated independently, i.e. three different Schrödinger equations are solved. Typically, it is best to have only one quantum cluster. However, in some cases, using separate clusters can lead to faster calculations. But this should be used with care, as often the wavefunctions with higher energies are distributed over the whole device.

!----------------------------------------------
$quantum-cluster
 cluster-number = 1     region-numbers = 1
 cluster-number = 2     region-numbers = 2
 cluster-number = 3     region-numbers = 3
$end_quantum-cluster
!----------------------------------------------