$zb-restrictions¶
Some restrictions apply for zinc blende materials.
$zb-restrictions required miller-size integer required miller-default-direction-of-x integer_array required miller-default-direction-of-y integer_array required direction-cosines double_array required miller-direction-of-cx integer_array required miller-direction-of-cy integer_array required miller-direction-of-cz integer_array required lattice-constants-for-cxyz double_array required gamma-is-cb-number integer required l-is-cb-number integer required x-is-cb-number integer required $end_zb-restrictions required
Explanations
- miller-size
- type:
integer
- presence:
required
- value:
3
There are three Miller indices altogether that define the (hkl) plane. Coincidently, in zincblende the [hkl] vector is perpendicular to the (hkl) plane.
- miller-default-direction-of-x
- type:
integer_array
- presence:
required
Three-digit Miller indices of the (hkl) plane perpendicular to x axis of simulation coordinate system.
- miller-default-direction-of-y
- type:
integer_array
- presence:
required
Three-digit Miller indices of the (hkl) plane perpendicular to y axis of simulation coordinate system.
miller-default-direction-of-x = 1 0 0 ! (100 plane) ==> [100] direction miller-default-direction-of-y = 0 1 0 ! (010 plane) ==> [010] direction
This corresponds to x axis and y axis, respectively, in simulation coordinate system, i.e. the x axis is perpendicular to the (1 0 0) plane, i.e. x axis is along the [100] direction in zinc blende,
and the y axis is perpendicular to the (0 1 0) plane, i.e. y axis is along the [010] direction in zinc blende.
These value can be overwritten in $domain-coordinates (hkl-x-direction, hkl-y-direction, hkl-z-direction).
Direction cosines
- direction-cosines
- type:
double_array
- presence:
required
- value:
0.0 0.0 0.0
Direction cosines between lattice vectors. g1*g2, g2*g3, g1*g3 gi … unit vectors in lattice directions.
Direction cosine refers to the cosine of the angle between any two vectors. Direction cosines are useful for forming direction cosine matrices that express one set of orthonormal basis vectors in terms of another set, or for expressing a known vector in a different basis. For zinc blende, we use:
( 1 0 0 ) g_ik = ( 0 1 0 ) ( 0 0 1 )
Three-digit Miller indices of the (hkl) plane:
- miller-direction-of-cx
- type:
integer_array
- value:
1 0 0
Corresponds to x axis in crystal coordinate system, i.e. the x axis is perpendicular to the (1 0 0) plane, i.e. x axis is along the [100] direction in zinc blende.
- miller-direction-of-cy
- type:
integer_array
- value:
0 1 0
Corresponds to y axis in crystal coordinate system, i.e. the y axis is perpendicular to the (0 0 1) plane, i.e. y axis is along the [010] direction in zinc blende.
- miller-direction-of-cz
- type:
integer_array
- value:
0 0 1
Corresponds to z axis in crystal coordinate system, i.e. the z axis is perpendicular to the (0 0 1) plane, i.e. z axis is along the [001] direction in zinc blende.
miller-direction-of-cx = 1 0 0 ! (100) plane ("[100] direction") miller-direction-of-cy = 0 1 0 ! (010) plane ("[010] direction") miller-direction-of-cz = 0 0 1 ! (000) plane ("[001] direction")
These are the default orientations.
- lattice-constants-for-cxyz
- type:
double_array
- value:
1.0 1.0 1.0
Lattice constants to interpret the Miller indices.
Define how how the bands are labeled.
- gamma-is-cb-number
- type:
integer
- value:
1
The conduction band minimum at the Gamma point has the number 1.
- l-is-cb-number
- type:
integer
- value:
2
The conduction band minimum at the L point has the number 2.
- x-is-cb-number
- type:
integer
- value:
3
The conduction band minimum at the X point (or Delta in Si or Ge) has the number 3.
Example
!--------------------------------------------------! $zb-restrictions miller-size = 3 miller-default-direction-of-x = 1 0 0 miller-default-direction-of-y = 0 1 0 direction-cosines = 0.0 0.0 0.0 ! g1*g2, g2*g3, g1*g3 gi ... unit vectors in lattice directions miller-direction-of-cx = 1 0 0 miller-direction-of-cy = 0 1 0 miller-direction-of-cz = 0 0 1 lattice-constants-for-cxyz = 1.0 1.0 1.0 gamma-is-cb-number = 1 l-is-cb-number = 2 x-is-cb-number = 3 $end_zb-restrictions !--------------------------------------------------!