$region-cluster

Regions can be clustered to bigger objects by the keyword $region-cluster. Any region must be assigned to a cluster which is labeled by its cluster-number.

Also the so-called default region must be assigned to a cluster. The default region is the rest of the simulation domain which is not filled out by defined regions. It might happen that the default region is an empty region. Nevertheless, it must be assigned to a cluster.

In any case it holds:

default region number = maximum region number defined + 1

The regions which have to be clustered to one cluster are specified by their numbers like this region-number = 2 3 5.

$region-cluster                                    required
 cluster-number                   integer          required
 region-numbers                   integer_array    required
 apply-constant-el-Fermi-level    double           optional
 apply-constant-hl-Fermi-level    double           optional
$end_region-cluster                                required

cluster-number

type

integer >= 1

presence

required

An integer number to refer to clustered geometry element.

region-numbers
type

integer array containing integers >= 1

Region numbers belonging to this cluster cluster-number.

apply-constant-el-Fermi-level
type

double

unit

[eV]

example

0.2

Applies a constant electron Fermi level \(E_{\text{F,n}}\) to this 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

unit

[eV]

example

-0.1

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

Example

We have defined 5 regions under keyword $regions, region 2 and 4 are clustered to form cluster-number 2 (i.e. region 2 and 4 now will consist of the same material as a material kind is assigned to a cluster and not to a region). region-number 6 is an undefined default region (Assumption: We have defined only 5 regions.) and must be the default rest. Now there are two possibilities:

Possibility 1:

!-------------------------------------------------!
$region-cluster                                   !
 cluster-number = 1      region-numbers = 1       ! e.g. GaAs
 cluster-number = 2      region-numbers = 2  4    ! e.g. AlAs
 cluster-number = 3      region-numbers = 3       ! e.g. GaAs
 cluster-number = 4      region-numbers = 5  6    ! e.g. InP, 6 = default region
$end_region-cluster                               !
!-------------------------------------------------!

Here, the default region has the same material properties as cluster-number 4. The default region can consist of some undefined region (the remaining part of the simulation area which is not filled yet) or it can be empty if the whole simulation area is already filled with other objects.

Possibility 2:

!-------------------------------------------------!
$region-cluster                                   !
 cluster-number = 1      region-numbers = 1       ! e.g. GaAs
 cluster-number = 2      region-numbers = 2  4    ! e.g. AlAs
 cluster-number = 3      region-numbers = 3       ! e.g. GaAs
 cluster-number = 4      region-numbers = 5       ! e.g. InP
 cluster-number = 5      region-numbers = 6       ! e.g. InP, 6 = default region
$end_region-cluster                               !
!-------------------------------------------------!

Here, the default region has its own material properties which have to be defined later under keyword $material. Again, the default region can consist of some undefined region (the remaining part of the simulation area which is not filled yet) or it can be empty if the whole simulation area is already filled with other objects.

Useful application for a default region

If one has a complicated geometry such as a quantum dot which is surrounded by a GaAs cap layer, one can define the complicated geometry as usual and for the (complicated) surrounding material one just uses the default option.

Note

Be careful in 3D when you specify for strain calculation strain-minimization (see $strain-minimization-model) to define your substrate as a separate cluster.