binary-zb-default

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binary-zb-default

More information can be found under the keywordbinary-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 E_v,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 = 3total 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 (m_longitudinal,m_transverse,m_transverse) 0.916d0 0.190d0 0.190d0 ! [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 12including spin degeneracy

conduction-band-nonparabolicities = 0d0 0d0 0d0 ! [1/eV]Gamma, L , XNonparabolicity 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
h_bar²k²/ (2 m*) = E_parabolic = E_nonparabolic (1 + aE_nonparabolic) where a is given by a = (1 - m*/m₀)²/ E_g.E_parabolic is the energy of the carriers in the usual parabolic band.E_nonparabolic 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 = 1.5d0 2.0d0 2.3d0 ! [eV] Note that this flag is optional. It is only used if the flaguse-band-gaps = yesis used.
Energy band gaps of the three valleys (Gamma, L, X).

conduction-band-energies = 0d0 0d0 0d0conduction 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 = 3total number of valence bands

valence-band-masses = 0.580d0 0.580d0 0.580d0 ! [m0]heavy hole 0.500d0 0.500d0 0.500d0 ! [m0]light hole 0.300d0 0.300d0 0.300d0 ! [m0]split-off holeOrdering of numbers corresponds to band no. 1, 2, 3 (heavy, light, split-off hole).

valence-band-degeneracies = 2 2 2including spin degeneracy

valence-band-nonparabolicities = 0d0 0d0 0d0 ! [1/eV]heavy, light, and split-off holesee comments for conduction-band-nonparabolicities

valence-band-energies = 0.0The valence band energies for heavy, light and split-off holes are calculated by defining an average valence band energy E_v,av for all three bands and adding the spin-orbit-splitting energy afterwards. The spin-orbit-splitting energy Delta_so is defined together with the k.p parameters.
The average valence band energy E_v,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 = 0.5405d-3 0.605d-3 0.460d0 ! alpha [eV/K](Gamma, L, X) Vurgaftman 204d0 204d0 204d0 ! beta [K] (Gamma, L, X) VurgaftmanTemperature dependent band gaps (here: GaAs values). More information...

band-shift = 0d0to adjust band alignments (should be zero in database): adds to all band energies

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 K3 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 = -0.350d0 ! [C/m^2] e₁₄ (1^st order coefficients) 0d0 0d0 0d0 ! [C/m^2] B₁₁₄ B₁₂₄ B₁₅₆(2^nd 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.

elastic-constants = 1d0 1d0 1.350d0 ! c₁₁ c₁₂ c₄₄ [GPa]

static-dielectric-constants = 9.28d0 9.28d0 9.28d0Static 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 = 10.10d0 !high frequency dielectric constant epsilon(infinity)

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 6-band k.p. i.e. not for 8-band k.p.
Note: The Luttinger parameters are only used if the following$numeric-controlflag 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 bandIf 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 [h_bar²/(2m₀)] 0.341d0 ! Delta_so (spin-orbit split-off energy) [eV]

8x8kp-parameters = 1.420d0 -3.86d0 0.056d0 ! L' M'=M N' [h_bar²/(2m₀)] 0.0d0 28.8d0 -2.876d0 ! B [h_bar²/(2m₀)] E_P [eV] S []

Important: There are different definitions of theLand M parameters available in the literature. (The gammas are called Luttinger parameters.) nextnano definition: L = ( - gamma₁ - 4gamma₂ - 1 ) * [h_bar²/(2m₀)] M = ( 2gamma₂ - gamma₁ - 1 ) * [h_bar²/(2m₀)] alternative definition: L = ( - gamma₁ - 4gamma₂ ) * [h_bar²/(2m₀)] M = ( 2gamma₂ - gamma₁ ) * [h_bar²/(2m₀)]Note: TheSparameter is also defined in the literature asFwhere 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...

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 0d0components of k-vector along crystalxyz [k0]in units of[2pi/a]where a is the lattice constant.

principal-axes-cb-masses = 1d0 0d0 0d0 ! 0d0 1d0 0d0 ! 0d0 0d0 1d0 ! ! 1d0 -1d0 0d0 ! L1 1d0 1d0 -2d0 ! 1d0 1d0 1d0 ! 1d0 -1d0 0d0 ! L2 -1d0 -1d0 -2d0 ! 1d0 1d0 -1d0 ! 1d0 1d0 0d0 ! L3 -1d0 1d0 -2d0 ! -1d0 1d0 1d0 ! 1d0 1d0 0d0 ! L4 1d0 -1d0 -2d0 ! -1d0 1d0 -1d0 ! ! 1d0 0d0 0d0 ! X1 0d0 1d0 0d0 ! 0d0 0d0 1d0 ! 0d0 -1d0 0d0 ! X2 0d0 0d0 -1d0 ! 1d0 0d0 0d0 ! 1d0 0d0 0d0 ! X3 0d0 0d0 -1d0 ! 0d0 1d0 0d0 ! -1d0 0d0 0d0 ! X4 0d0 1d0 0d0 ! 0d0 0d0 -1d0 ! 0d0 1d0 0d0 ! X5 0d0 0d0 -1d0 ! -1d0 0d0 0d0 ! -1d0 0d0 0d0 ! X6 0d0 0d0 -1d0 ! 0d0 -1d0 0d0 !Normalization will be done internally by the program

number-of-minima-of-vband = 1 1 1

valence-band-minima = 0d0 0d0 0d0 0d0 0d0 0d0 0d0 0d0 0d0components of k-vector along crystalxyz [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 1d0Normalization will be done internally by the program

More information can be found under the keywordbinary-zb-default (binary zinc blende parameters) under the section Keywords.