$binary-zb-default
Zinc blende material parameters
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 !
band-gaps double_array optional !
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 required ! average valence band edge energy Ev,av
!
varshni-parameters double_array required ! alpha [eV/K] (Gamma,L,X), 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-constants 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 = 0.156 0.156 0.156 ! [m0] Gamma (m,m,m)
1.420 0.130 0.130 ! [m0] L (m_longitudinal, m_transverse, m_transverse)
0.916 0.190 0.190 ! [m0] X (m_longitudinal, m_transverse, m_transverse)
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 = 0.0 0.0 0.0 ! [1/eV] Gamma, L , 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.
Eparabolic is the energy of the carriers in the usual parabolic band.
Enonparabolic is the energy of the carriers in the nonparabolic band.
The nonparabolic band factor a can be calculated from the Kane model. Note that this nonparabolicity correction only influences the classically calculated electron densities. Quantum mechanically calculated densities are unaffected.
band-gaps = 1.5 2.0 2.3 ! [eV]
Energy band gaps of the three valleys (Gamma, L, X).
Note that this specifier is optional.
It is only used if the flag use-band-gaps = yes is used.
conduction-band-energies = 0.0 0.0 0.0
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 = 0.580 0.580 0.580 ! [m0] heavy hole
0.500 0.500 0.500 ! [m0] light hole
0.300 0.300 0.300 ! [m0] split-off hole
Ordering of numbers corresponds to band no. 1, 2, 3 (heavy, light, split-off hole).
valence-band-degeneracies = 2 2 2
including spin degeneracy
valence-band-nonparabolicities = 0.0 0.0 0.0 ! [1/eV] heavy, light, and split-off hole
see comments for conduction-band-nonparabolicities
valence-band-energies = 0.0
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.
varshni-parameters = 0.5405e-3 0.605e-3 0.460 ! alpha [eV/K] (Gamma, L, X) Vurgaftman
204.0 204.0 204.0 ! beta [K] (Gamma, L, X) Vurgaftman
Temperature dependent band gaps (here: GaAs values). More information… ==> How-to-add-material-parameters.htm#Varshni%20parameters (Add link)
band-shift = 0.0
to adjust band alignments (should be zero in database): adds to all band energies
absolute-deformation-potential-vb = 0.0 ! a_v [eV]
absolute-deformation-potentials-cbs = -10.44 -2.07 3.35 ! [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 = 0.0 0.0 ! b, d [eV]
uniax-cb-deformation-potentials = 0.0 0.0 0.0 ! [eV]
Xi_u (at minimum)
lattice-constants = 0.543 0.543 0.543 ! [nm] 300 K
lattice-constants-temp-coeff = 3.88e-6 3.88e-6 3.88e-6 ! [nm/K]
More information on temperature dependent lattice constants… ==> How-to-add-material-parameters#Lattice%20constants (Add link)
elastic-constants = 1.0 1.0 1.350 ! c11 c12 c44 [GPa]
piezo-electric-constants = -0.350 ! [C/m^2] e14 (1st order coefficients)
0.0 0.0 0.0 ! [C/m^2] B114 B124 B156 (2nd order coefficients)
Conventionally, the sign of the piezoelectric tensor components is fixed by assuming that the positive direction along the
[111] direction (zincblende)
[0001] direction (wurtzite)
goes from the cation to the anion.
static-dielectric-constants = 9.28 9.28 9.28
Static dielectric constants. The numbers correspond to the crystal directions (similar to lattice-constants):
in zinc blende:
eps1 = eps2 = eps3in 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 = 10.10
high frequency dielectric constant epsilon(infinity)
Luttinger-parameters = 6.98 2.06 2.93 ! [] gamma1, gamma2, gamma3
1.72 0.04 ! [] kappa, q
Luttinger parameters for the valence band.
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 ! [] modified Luttinger parameters for the valence band
= 8x8kp-kappa ! [] modified Luttinger parameters for the valence band
= 8x8kp-kappa-only ! [] modified Luttinger parameter kappa' for the valence band
If 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 = -16.22 -3.86 -17.58 ! L M N
0.341 ! Delta_so (spin-orbit split-off energy) [eV]
L, M,N in units of [hbar2/(2m0)]
8x8kp-parameters = 1.420 -3.86 0.056 ! L' M'=M N'
0.0d0 28.8 -2.876 ! B E_P [eV] S []
L’, M’, N’, B in units of [hbar2/(2m0)]
Important: There are different definitions of the L and M parameters available in the literature. (The gammas are called Luttinger parameters.)
nextnano definition:
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).
If L = M, and N = 0, the dispersion is both isotropic and parabolic.
More information on k.p parameters… ==> How-to-add-material-parameters.htm
LO-phonon-energy = 0.063 ! [eV]
low-temperature optical phonon energy
number-of-minima-of-cband = 1 4 6
conduction-band-minima = 0.0 0.0 0.0
0.860 0.860 0.860
0.860 0.860 -0.860
-0.860 0.860 0.860
-0.860 0.860 -0.860
0.0 0.0 1.0
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 -1.0
-1.0 0.0 0.0
0.0 -1.0 0.0
components of k-vector in crystal coordinate system [k0] in units of [2pi/a] where a is the lattice constant.
principal-axes-cb-masses = 1.0 0.0 0.0 !
0.0 1.0 0.0 !
0.0 0.0 1.0 !
!
1.0 -1.0 0.0 ! L1
1.0 1.0 -2.0 !
1.0 1.0 1.0 !
1.0 -1.0 0.0 ! L2
-1.0 -1.0 -2.0 !
1.0 1.0 -1.0 !
1.0 1.0 0.0 ! L3
-1.0 1.0 -2.0 !
-1.0 1.0 1.0 !
1.0 1.0 0.0 ! L4
1.0 -1.0 -2.0 !
-1.0 1.0 -1.0 !
!
1.0 0.0 0.0 ! X1
0.0 1.0 0.0 !
0.0 0.0 1.0 !
0.0 -1.0 0.0 ! X2
0.0 0.0 -1.0 !
1.0 0.0 0.0 !
1.0 0.0 0.0 ! X3
0.0 0.0 -1.0 !
0.0 1.0 0.0 !
-1.0 0.0 0.0 ! X4
0.0 1.0 0.0 !
0.0 0.0 -1.0 !
0.0 1.0 0.0 ! X5
0.0 0.0 -1.0 !
-1.0 0.0 0.0 !
-1.0 0.0 0.0 ! X6
0.0 0.0 -1.0 !
0.0 -1.0 0.0 !
Normalization will be done internally by the program
number-of-minima-of-vband = 1 1 1
valence-band-minima = 0.0 0.0 0.0
0.0 0.0 0.0
0.0 0.0 0.0
components of k-vector in crystal coordinate system [k0]
principal-axes-vb-masses = 1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
Normalization will be done internally by the program