binary-zb-default
More information can be found under the keyword
binary-zb-default (binary zinc blende parameters) under the section
Keywords.
!------------------------------------------------------------!
$binary-zb-default
required !
binary-type character
required !
conduction-bands
integer
required !
conduction-band-masses
double_array
required !
conduction-band-degeneracies
integer_array required !
conduction-band-nonparabolicities
double_array
required !
conduction-band-energies
double_array
required !
valence-bands
integer
required !
valence-band-masses
double_array required !
valence-band-degeneracies
integer_array required !
valence-band-nonparabolicities
double_array
required !
valence-band-energies
double_array required ! average valence band edge energy
Ev,av
!
varshni-parameters
double_array required !
alpha [eV/K] beta [K]
(Gamma,L,X)
band-shift
double
required !
absolute-deformation-potential-vb
double
required !
absolute-deformation-potentials-cbs
double_array
required !
uniax-vb-deformation-potentials
double_array
required !
uniax-cb-deformation-potentials
double_array required !
!
lattice-constants
double_array
required ! [nm]
lattice-constants-temp-coeff
double_array required !
[nm/K]
!
elastic-constants
double_array
required !
piezo-electric-constants
double_array required !
!
static-dielectric-constants
double_array required !
optical-dielectric-constant
double
required !
!
Luttinger-parameters
double_array required !
6x6kp-parameters
double_array required !
8x8kp-parameters
double_array required !
!
LO-phonon-energy
double
required ! [eV]
!
number-of-minima-of-cband
integer_array required !
conduction-band-minima
double_array required !
principal-axes-cb-masses
double_array required !
!
number-of-minima-of-vband
integer_array
required !
valence-band-minima
double_array
required !
principal-axes-vb-masses
double_array required !
!
$end_binary-zb-default
required !
!------------------------------------------------------------!
Syntax
binary-type = Si-zb-default
conduction-bands = 3
total number of conduction band minima (Gamma, L, X)
conduction-band-masses = 0.156d0 0.156d0 0.156d0
! [m0] Gamma (m,m,m)
1.420d0 0.130d0 0.130d0 ! [m0] L (mlongitudinal,mtransverse,mtransverse)
0.916d0 0.190d0 0.190d0 ! [m0] X (mlongitudinal,mtransverse,mtransverse)
3 numbers per band,
ordering of numbers corresponds to band
no. 1, 2, 3 (Gamma, L, X)
conduction-band-degeneracies = 2 8 12
including spin degeneracy
conduction-band-nonparabolicities = 0d0 0d0 0d0
As used in a hyperbolic dispersion k2 ~ E(1+aE). a =
nonparabolicity [1/eV]
The nonparabolicity can be calculated from the Kane model. The energy of the
Gamma valley is assumed to be nonparabolic, spherical, and of the form h_bar2k2/2m*=E(1+aE)
where a is given by a=(1-m*/m0)2/Eg.
conduction-band-energies = 0d0 0d0 0d0
conduction band edge energies relative to a reference level (could be
vacuum) (numbering according
to cb numbering)
conduction band edge energies relative to valence band number 1 (number
corrsponds to the ordering of the entries below)
valence-bands = 3
total number of valence bands
valence-band-masses = 0.580d0 0.580d0 0.580d0
! [m0]
heavy hole
0.500d0 0.500d0 0.500d0 ! [m0]
0.300d0 0.300d0 0.300d0 ! [m0]
valence-band-degeneracies = 2 2 2
including spin degeneracy
valence-band-nonparabolicities = 0d0
0d0 0d0
As used in a hyperbolic dispersion k^2 ~ E(1+aE). a =
nonparabolicity [1/eV]
valence-band-energies = 0d0
The valence band energies for heavy, light and split-off holes are calculated by
defining an average valence band energy Ev,av for all three bands and adding the
spin-orbit-splitting energy afterwards. The spin-orbit-splitting energy Deltaso is
defined together with the k.p parameters.
The average valence band energy Ev,av is defined on an absolute
energy scale and must take into accout the valence band offsets which are
averaged over the three holes.
varshni-parameters = 0.5405d-3 0.605d-3 0.460d0
!r! alpha [eV/K](Gamma, L, X) Vurgaftman
204d0 204d0
204d0 !r! beta [K]
band-shift = 0d0
absolute-deformation-potential-vb = 0d0
a_v [eV]
absolute-deformation-potentials-cbs =
-10.44d0 -2.07d0 3.35d0 ! [eV] (Gamma, L, X) (Si values)
The absolute deformation potentials for the conduction band edges are
calculated from the band gap deformation potentials (a_gap) in the following
way:
a_gap = a_c - a_v -> a_c =
a_gap + a_v
uniax-vb-deformation-potentials = 0d0
0d0
b,d [eV]
uniax-cb-deformation-potentials = 0d0
0d0 0d0
Xi_u (at minimum)
lattice-constants =
0.543d0 0.543d0 0.543d0 ! [nm] 300 K
3 positive numbers
lattice-constants-temp-coeff = 3.88d-6
3.88d-6 3.88d-6 ! [nm/K]
More
information on temperature dependent lattice constants...
piezo-electric-constants = 0d0
0d0 -0.350d0 ! - -
e14 [C/m^2]
elastic-constants = 1d0
1d0 1.350d0 !
c11 c12 c44 [GPa]
static-dielectric-constants = 9.28d0 9.28d0
9.28d0
Static dielectric constants. The numbers
correspond to the crystal directions (similar to lattice-constants):
- in zinc blende: eps1 = eps2
= eps3
- in wurtzite: eps1 =
eps2 eps3
eps3 is parallel to the c direction in wurtzite.
eps1 and eps2 are perpendicular to the c direction in wurtzite.
low frequency dielectric constant
epsilon(0)
optical-dielectric-constant = 10.10d0
Luttinger-parameters = 6.98d0
2.06d0 2.93d0
! gamma1 gamma2 gamma3 []
Luttinger parameters for the valence band
1.72d0 0.04d0 !
kappa q []
In the database, the Luttinger parameters are defined for 6x6 k.p. i.e. not for 8x8 k.p.
Note: The Luttinger parameters are only used if the following
$numeric-control flag is
set:
Luttinger-parameters =
6x6kp yes
=
6x6kp-kappa
=
6x6kp-kappa-only
=
8x8kp
! []
=
8x8kp-kappa
! []
=
8x8kp-kappa-only ! []
kappa is not known it
can be approximated: kappa = - N/6 + M/3 - 1/3. (This corresponds
to H2 = 0, i.e. N- = M and N+
= N - M.)
If gamma2 =
gamma3 , then the dispersion is isotropic (spherical
approximation).
If gamma2 =
gamma3 = 0, then the dispersion is isotropic (spherical
approximation) and parabolic.
6x6kp-parameters =
-16.22d0 -3.86d0 -17.58d0
! L M N
[hbar2/(2m0)]
0.341d0
! Deltaso (spin-orbit split-off energy) [eV]
8x8kp-parameters =
1.420d0 -3.86d0 0.056d0
! L' M'=M N'
[hbar2/(2m0)]
0.0d0 28.8d0 -2.876d0
! B [hbar2/(2m0)]
EP [eV] S []
Important: There are different definitions of the
L and M parameters available in the literature. (The
gammas are called Luttinger parameters.)
L = ( - gamma1
- 4gamma2 - 1 ) * [hbar2/(2m0)]
M = ( 2gamma2 - gamma1 - 1 ) * [hbar2/(2m0)]
alternative definition: L = ( -
gamma1 - 4gamma2 ) * [hbar2/(2m0)]
M = ( 2gamma2 - gamma1
) * [hbar2/(2m0)]
Note: The S
parameter is also defined in the literature as F
where S = 1 + 2F, e.g. I. Vurgaftman et al., JAP 89,
5815 (2001).
N = N+ + N-
N2 - (L - M)2 = 0, i.e. N = L - M
(spherical approximation).
L = M, and N = 0, the dispersion is both
isotropic and parabolic.
LO-phonon-energy = 0.063d0 ! [eV]
low-temperature optical phonon energy
number-of-minima-of-cband = 1 4 6
conduction-band-minima = 0d0 0d0
0d0
0.860d0 0.860d0 0.860d0
0.860d0 0.860d0 -0.860d0
-0.860d0 0.860d0 0.860d0
-0.860d0 0.860d0 -0.860d0
0d0 0d0
1d0
1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 -1d0
-1d0 0d0 0d0
0d0 -1d0 0d0
components of k-vector along crystal
xyz [k0] in units of
[2pi/a] where a is the lattice constant.
principal-axes-cb-masses = 1d0 0d0
0d0 !r!
0d0 1d0
0d0
!r!
0d0 0d0
1d0
!r!
!c
1d0 -1d0
0d0 !r! L1
1d0 1d0
-2d0 !r!
1d0 1d0
1d0
!r!
1d0 -1d0
0d0 !r! L2
-1d0 -1d0
-2d0 !r!
1d0 1d0
-1d0 !r!
1d0 1d0 0d0
!r! L3
-1d0 1d0
-2d0 !r!
-1d0 1d0
1d0
!r!
1d0 1d0 0d0
!r! L4
1d0 -1d0 -2d0 !r!
-1d0 1d0
-1d0 !r!
!c
1d0 0d0
0d0
!r! X1
0d0 1d0 0d0
!r!
0d0 0d0
1d0
!r!
0d0 -1d0
0d0 !r! X2
0d0 0d0
-1d0
!r!
1d0 0d0
0d0
!r!
1d0 0d0
0d0
!r! X3
0d0 0d0 -1d0 !r!
0d0
1d0 0d0
!r!
-1d0 0d0
0d0
!r! X4
0d0
1d0 0d0
!r!
0d0 0d0
-1d0 !r!
0d0 1d0
0d0
!r! X5
0d0 0d0
-1d0 !r!
-1d0 0d0
0d0
!r!
-1d0 0d0
0d0
!r! X6
0d0 0d0
-1d0 !r!
0d0 -1d0
0d0 !r!
number-of-minima-of-vband = 1 1 1
valence-band-minima = 0d0
0d0 0d0
0d0 0d0 0d0
0d0 0d0 0d0
components of k-vector along crystal
xyz [k0]
!
principal-axes-vb-masses = 1d0 0d0
0d0
0d0 1d0 0d0
0d0 0d0 1d0
1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 1d0
1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 1d0
Normalization will be done internally by the
program
More information can be found under the keyword
binary-zb-default
(binary zinc blende parameters) under the section
Keywords.
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