binary-zb-default
Zinc blende material parameters
For materials which are not known to the database and for the use of nondefault values for some of the parameters of a known material.
For totally unknown materials, all parameters must be specified in the input
file. This will be required in very rare cases, however.
In most cases it is possible, to use an unknown material
name which can be associated to a known material type and to change only a few
parameters by this keyword and its specifiers.
More information can be found under the keyword
$binary-zb-default
under the section Database.
!--------------------------------------------------------------!
$binary-zb-default
optional !
binary-type
character
required !
binary-name
character
optional !
apply-to-material-numbers
integer_array required !
!
conduction-bands
integer
optional !
total number of conduction bands
conduction-band-masses
double_array
optional ! [m0]
ml,mt1,mt2 for each band. Ordering of numbers corresponds to band no. 1,
2, ... (Gamma, L, X)
conduction-band-degeneracies
integer_array optional ! including spin degeneracy
conduction-band-nonparabolicities double_array
optional !
As used in a hyperbolic dispersion k^2 ~ E(1+aE). a =
nonparabolicity (1/eV)
band-gaps
double_array
optional !
conduction-band-energies
double_array
optional !
conduction band edge energies relative to average valence band energy Ev,av
! (number corrsponds to the ordering of the entries below)
valence-bands
integer
optional !
total number of valence bands
valence-band-masses
double_array
optional ! [m0]
ml,mt1,mt2 for each band. Ordering of numbers corresponds to band no. 1,
2, ... (hh, lh, so)
valence-band-degeneracies
integer_array optional ! including spin degeneracy
valence-band-nonparabolicities
double_array
optional !
As used in a hyperbolic dispersion k^2 ~ E(1+aE). a =
nonparabolicity (1/eV)
valence-band-energies
double
optional !
average valence band edge energy Ev,av
varshni-parameters
double_array
optional !
alpha [eV/K]
(Gamma,L,X), beta [K]
(Gamma,L,X)
band-shift
double
optional !
!
absolute-deformation-potential-vb double
optional !
absolute-deformation-potentials-cbs double_array
optional !
absolute deformation potential of conduction band: a_cd, a_ci [eV]
uniax-vb-deformation-potentials
double_array
optional ! b,d [eV]
uniax-cb-deformation-potentials
double_array
optional !
!
lattice-constants
double_array
optional ! [nm]
lattice-constants-temp-coeff
double_array
optional ! [nm/K]
!
elastic-constants
double_array
optional !
piezo-electric-constants
double_array
optional !
!
static-dielectric-constants
double_array
optional !
optical-dielectric-constants
double
optional !
!
Luttinger-parameters
double_array
optional !
6x6kp-parameters
double_array
optional !
8x8kp-parameters
double_array
optional !
!
LO-phonon-energy
double
optional ! [eV]
!
number-of-minima-of-cband
integer_array optional !
required for 'conduction-band-minima'
conduction-band-minima
double_array
optional !
and 'principal-axes-cb-masses'
principal-axes-cb-masses
double_array
optional !
!
number-of-minima-of-vband
integer_array optional !
required for 'valence-band-minima'
valence-band-minima
double_array
optional !
and 'principal-axes-vb-masses'
principal-axes-vb-masses
double_array
optional !
!
!
$end_binary-zb-default
optional !
!--------------------------------------------------------------!
Syntax
binary-type = character
=
GaAs-zb-default
If the string is a known material-type, the default parameters for this
material type will be read from the database first. By specifying some of the
parameters by the present keyword and specifiers, the defaults will be
overwritten.
If the string is not known to the database, you will be prompted for
all of the material parameters. In this case you have to specify the relevant
specifiers in
$material (material-model,
material-type). If here a known material-type is specified,
however, then not all material parameters are needed as the defaults are taken
unless otherwise specified. See here for an example:
$material
binary-name = character
To specify a name for the present new defined material.
apply-to-material-numbers = integer1
integer2 integer3
...
Apply new or partially changed material data to material numbers specified.
- Note: If you want to overwrite the parameters of a ternary, you
also have to include the associated material numbers of the ternary
here, i.e. in
$binary-zb-default.
Consider this example:
$material
material-number = 1
material-name = GaN
...
material-number = 2
material-name = In(x)Ga(1-x)N
! = 2
...
! Note that the material parameters of the ternary InGaN are
interpolated from its binary constituents InN and GaN.
material-number = 3
material-name = InN
...
$binary-zb-default
binary-type = GaN-zb-default
! apply-to-material-numbers = 1 !
1
which is GaN but not the GaN values of which the ternary
In(x)Ga(1-x)N (material #2) is calculated.
! Therefore, for material #2, the default GaN values of the database
are used and not the ones specified in the input file.
apply-to-material-numbers = 1 2
! 1
which is GaN and the GaN values of which the
ternary In(x)Ga(1-x)N (material #2)
is calculated.
...
$binary-zb-default
binary-type = InN-zb-default
! apply-to-material-numbers = 3 !
3
which is InN but not the InN values of which the ternary
In(x)Ga(1-x)N (material #2) is calculated.
!
apply-to-material-numbers = 2 3
! 3
which is InN and the InN values of which the
ternary In(x)Ga(1-x)N (material #2)
is calculated.
...
$binary-zb-default
ternary-type = In(x)Ga(1-x)N-zb-default
apply-to-material-numbers = 2
! 2 which
is InGaN.
...
conduction-bands = int
total number of conduction band minima (Gamma, L, X)
conduction-band-masses = m m m
! Gamma
ml mt mt
! L
ml mt mt
! X
mij are the masses in the principal axes system of the
minima. These masses are associated to the eigenvectors of the minima in the
order they are given in the parameter set.
For the L and X valleys, one longitudinal and two transverse masses are
required.
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 = deg1 deg2 deg3
As many degeneracy factors as mass triplets above.
number-of-minima-of-cband = deg1 deg2 deg3
Number of minima (without spin degeneracy) in each set of degenerate minima.
conduction-band-minima = v11 v12 v13
v21 v22 v23
v31 v32 v33
...
k vectors to individual conduction band minima in units of
[2pi/a] where a is the lattice constant.
As many vectors (coordinate triplets in crystal coordinate system) as individual
minima.
Let's assume we have 3 conduction band minima 1,2,3 as specified above.
These minima are deg1,deg2,deg3-fold degenerate. In this case,
input for deg1/2+deg2/2+deg3/2 vectors has to be provided. The
factor 1/2 is due to spin degeneracy which is already included in the degeneracy
factors.
Note: Currently it is assumed in parts of the program, that the ordering
of the conduction minima is like 1=Gamma 2=L 3=X
Note:
number-of-minima-of-cband is required (!) for this specifier.
principal-axes-cb-masses = a11 a12 a13
b11 b12 b13
c11 c12 c13
....
....
....
a21 a22 a23
b21 b22 b23
c21 c22 c23
....
....
....
a31 a32 a33
b31 b32 b33
c31 c32 c33
....
....
....
Completely analog as conduction-band-minima, but this time 3 vectors
for each individual minimum. The orderering of the principal axes is associated
to the ordering of the conduction-band-masses.
Note:
number-of-minima-of-cband is required (!) for this specifier.
conduction-band-nonparabolicities = a_Gamma a_L
a_X
Nonparabolicity factors for the Gamma, L and X conduction bands as used in a hyperbolic dispersion k2 ~ E (1 +
aE) = E + aE2.
a = nonparabolicity [1/eV] (usually
denoted with alpha)
The energy of the
Gamma valley is assumed to be nonparabolic, spherical, and of the form
hbar2 k2 / (2 m*) = Eparabolic = Enonparabolic (1 + aEnonparabolic)
where a is given by a = (1 - m*/m0)2 / Eg.
Note that this nonparabolicity correction only influences the classically
calculated electron densities.
Quantum mechanically calculated densities are unaffected.
band-gaps = e1 e2 e3 ! [eV]
Note that this flag is optional. It is only used if the flag use-band-gaps
= yes is used.
Energy band gaps of the three valleys.
conduction-band-energies = e1 e2 e3
Absolute conduction band edge energies. One number for each set of degenerate
minima.
varshni-parameters = 0.5405d-3 0.605d-3 0.460d0
! alpha [eV/K](Gamma, L, X) Vurgaftman
204d0 204d0
204d0 ! beta [K]
band-shift = double
Can be used to rigidly shift all band energies by this amount.
absolute-deformation-potential-vb = double
absolute-deformation-potentials-cbs = a_c_Gamma
a_c_L
a_c_X ! [eV] (Gamma, L, X)
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 =
b d
! [eV]
uniax-cb-deformation-potentials =
d1 d2 d3 ...
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...
elastic-constants =
c11 c12 c44
Elastic constants c11,c12,c44 in [GPa] with their usual meaning.
piezo-electric-constants = e14 ! [C/m^2]
e14
(1st order coefficients)
B114 B124 B156 ! [C/m^2] B114 B124
B156
(2nd order coefficients)
- [111] direction (zincblende)
- [0001] direction (wurtzite)
goes from the cation to the anion.
For option
piezo-second-order
= 4th-order-Tse-Pal
different parameters can be specified, see
$numeric-control.
static-dielectric-constants = eps1 eps2
eps3
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-constants = eps
high frequency dielectric constant
epsilon(infinity)
Luttinger-parameters = gamma1
gamma2 gamma3 ! [] Luttinger
parameters for the valence band
kappa q ! []
In the database, the Luttinger parameters are defined for 6-band
k.p. i.e. not for 8-band k.p.
Note: The Luttinger parameters are only used if the following
$numeric-control flag is set:
Luttinger-parameters =
6x6kp (or)
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 = L M N ! [hbar2/(2m0)]
DeltaSO ! [eV]
8x8kp-parameters = L' M'=M N'
! [hbar2/(2m0)]
B EP
S ! [hbar2/(2m0)]
[eV] []
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).
F = (S - 1)/2
N = N+ + N-
For 6-band k.p, one can obtain an isotropic dispersion if
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 = ELO,ph
! [eV] low-temperature optical phonon energy
valence-bands
= integer
valence-band-masses
= double_array
valence-band-degeneracies
= integer_array
valence-band-nonparabolicities =
double_array ! see comments for conduction-band-nonparabolicities
valence-band-energies
= double
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 account the valence band offsets which are
averaged over the three holes.
number-of-minima-of-vband
= integer_array
valence-band-minima
= double_array !
Note:
number-of-minima-of-vband is required (!) for this specifier.
principal-axes-vb-masses
= double_array ! number-of-minima-of-vband is required (!) for this specifier.
Valence band parameters in complete analogy to conduction band parameters.
More detailed information can be found
here.
More information can be found under the keyword
$binary-zb-default
under the section Database.
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