Domain coordinates
Orientation of crystal relative to simulation coordinate
system
The overall simulation domain, that is the real space region in which the
device is defined, is restricted to a cuboid, a rectangle, or a line - dependent
on the dimension for the simulation. The extension of this domain must be
specified by its minimum and maximum value along the corresponding
coordinate axes. The complete simulation domain will be "filled" with
material information later.
Additionally, the orientation of the global three-dimensional coordinate
system must be oriented with respect to the crystal and some information about a
substrate for pseudomorphic growth must be given.
Keyword - Specifier syntax
!----------------------------------------------------!
$domain-coordinates required ! The global simulation domain is
restricted to be a cuboid, a plane or a line.
domain-type
integer_array optional ! 1 1 1
for xyz-domain,
! 1 0 1 xz-domain,
! 1 1 0
for
xy-domain, ...,
! 1 0 0
for x-domain
! redundant: $simulation-dimension, orientation = ...
is now used.
x-coordinates
double_array
optional ! xmin,xmax of simulation domain
y-coordinates double_array
optional ! ymin,ymax of simulation domain
z-coordinates
double_array
optional ! zmin,zmax of simulation domain
!
hkl-x-direction-zb
integer_array optional ! Miller
indices of x-coordinate
axis, e.g. [1 0 0]; required for two axes
hkl-y-direction-zb
integer_array optional ! y-coordinate
axis, e.g. [0 1 0]
hkl-z-direction-zb
integer_array optional ! Miller
indices of z-coordinate
axis, e.g. [0 0 1]
!
hkil-x-direction
integer_array optional !
four-digit Miller-Bravais indices of x-coordinate
axis direction [ 1 0 -1 0]
hkil-y-direction
integer_array optional ! four-digit Miller-Bravais indices of y-coordinate
axis direction [-1 2 -1 0]
hkil-z-direction
integer_array optional !
four-digit Miller-Bravais indices of z-coordinate
axis direction [ 0 0 0 1]
growth-coordinate-axis integer_array optional !
pseudomorphic-on character optional ! a default material or
user defined name (Actually it currently is required.)
alloy-concentration double optional ! in case, that default material is a ternary
lattice-constants
double_array optional !
lattice-constants-temp-coeff double_array optional !
crystal-type character optional ! required for
nondefault substrate material: e.g.
zincblende, wurtzite
$end_domain-coordinates
required !
!----------------------------------------------------!
Description
domain-type = l m n
l={0,1} ,
m={0,1} , n={0,1} ,
l+m+n=dimension (see
$simulation-dimension)
It must be identical to orientation (see
$simulation-dimension) and
has the same meaning. Used for internal consistency cross checks.
Domain extension - Minimum and maximum coordinates:
x-coordinates = xmin xmax
y-coordinates = ymin ymax
z-coordinates = zmin zmax
Only entries for the coordinate axes specified by orientation.
min, max
are double precision reals.
x-coordinates = 0.0d0 350.0d0
Orientation of the crystal with respect to the general three-dimensional
simulation coordinate system is fixed by specification of the Miller direction
indices of two simulation coordinate axes.
hkl-x-direction-zb = 0 1 0
hkl-y-direction-zb = 0 0 1
In this example, the x-axis of the simulation coordinate system is directed
along [0 1 0] of the zincblende crystal (crystal coordinate
system).
The y-axis of the simulation coordinate system is directed along [0 0 1]
of the
zincblende crystal. The direction of the third axis
is calculated internally.
The default directions can be specified in the database ($zb-restrictions). This default
coincides with the crystal fixed cartesian
coordinate system.
Default is:
hkl-x-direction-zb = 1 0 0
hkl-y-direction-zb = 0 1
0
(hkl-z-direction-zb = 0 0 1)
Example:
hkl-z-direction-zb = 3 1
1
hkl-y-direction-zb = 0 1 -1
(hkl-x-direction-zb calculated internally.) Here, the z-axis of the
simulation system is directed along [3 1 1] and the y-axis along
[0 1 -1].
The same as above for wurtzite:
hkil-x-direction = 1 0 -1 0
hkil-y-direction = -1 2 -1 0
hkil-z-direction = 0 0
0 1 ! (calculated internally)
Usually for wurtzite, the four-digit Miller-Bravais indices (h k i l)
are used where i = - h - k, i.e. i is not
independent.
In this example, the x-axis of the simulation coordinate system is directed
along [1 0 0] of the crystal.
The y-axis of the simulation coordinate system is directed along [0 1 0] of the
crystal. The direction of the third axis is calculated
internally (oriented along [0 0 1] of the crystal).
The default directions can be specified in the database ($wz-restrictions). This default
coincides with the crystal fixed cartesian
coordinate system.
Homogeneous strain
growth-coordinate-axis = 1 0 0 !
along 'hkl-x-direction-zb = ...'
= 0 1 0 ! along 'hkl-y-direction-zb =
...'
= 0 0 1 ! along 'hkl-z-direction-zb =
...'
= l m n ! l={0,1} ,
m={0,1} , n={0,1} ,
l+m+n=1
This selects one of the simulation coordinate axes (i.e. either the
x-axis, y-axis or z-axis) as the growth direction.
For example
growth-coordinate-axis = 0 0 1
hkl-z-direction-zb = 0 0 1
but can be chosen to be oriented along any other crystal direction, e.g.
along [311]:
hkl-z-direction-zb = 3
1 1
The growth direction is important for the calculation of pseudomorphic
strain as it enters the equation to calculate the strain tensor:
$simulation-flow-control
...
strain-calculation = homogeneous-strain
Specification on which material all layers are grown pseudomorphically. This can
be either a material known from the database or a user defined name. In the
latter case, an entry for the lattice constants and the crystal type of this
user defined material must be supplied. In case of pseudomorphic growth on a
known ternary, its alloy concentration must be specified.
pseudomorphic-on = GaAs
GaAs would be a known binary material, so no further input is required here.
Alloy concentration of ternary substrate (e.g. pseudomorphic-on
= Al(x)Ga(1-x)As)
alloy-concentration = 0.3d0 !
Al0.3Ga0.7As
alloy-concentration = x
! x={0.0d0,1.0d0}
If pseudomorphic growth is assumed to take place on an unknown material (e.g.
pseudomorphic-on = banana) the lattice constants of this material
and its crystal structure must be specified. For the structure of the crystal,
only wurtzite and zincblende are possible choices at the moment. In wurtzite,
the lattice constant orderering is a, a,
c.
lattice-constants = 0.4d0 0.4d0 0.4d0
lattice-constants-temp-coeff = 3.88d-6
3.88d-6 3.88d-6 ! [nm/K]
More information on temperature dependent lattice constants...
crystal-type =
zincblende ! also used for diamond-type materials
=
wurtzite
More
information on how the rotation is carried out in the program ...
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