$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
!--------------------------------------------------!