binary-wz-default

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binary-wz-default

Wurtzite material parameters

More information can be found under the keywordbinary-wz-default(binary wurtzite parameters) under the section Keywords.

!-------------------------------------------------------------------! $binary-wz-default                                        required ! binary-type                                character      required ! conduction-bands                           integer        required !total number of conduction bands conduction-band-masses                    double_array required ! [m0]for each band. Ordering of numbers corresponds to band no. 1, 2, ... conduction-band-degeneracies               integer_array required !including spin degeneracy conduction-band-nonparabolicities          double_array required !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 required !conduction band edge energies relative to a reference level (could be vacuum) (numbering according cb numbering                                                                    ! valence-bands                             integer        required !total number of valence bands valence-band-masses                       double_array required ! [m0] m_xx, m_yy, m_zz for each band (heavy, light and crystal-field split-off hole). Ordering of numbers corresponds to band no. 1, 2, ... valence-band-degeneracies                  integer_array required !including spin degeneracy valence-band-nonparabolicities             double_array required !As used in a hyperbolic dispersion k^2 ~ E(1+aE).a = nonparabolicity (1/eV) valence-band-energies                      double      required ! "average" valence band edge energy E_v (see comments below)                                                                    ! varshni-parameters                         double_array   required ! alpha [eV/K] (Gamma,indirect,indirect), beta [K] (Gamma,L,indirect,indirect) band-shift                                 double         required !to adjust band alignments (should be zero in database): adds to all band energies                                                                    !
absolute-deformation-potential-vb          double         required !not used in wurtzite absolute-deformation-potentials-cbs        double_array required !absolute deformation potentials of conduction band minimaa_c, a_ci's                                                                     !
uniax-vb-deformation-potentials            double_array required ! b,d related[eV] uniax-cb-deformation-potentials           double_array required !not used in wurtzite                                                                    ! lattice-constants                          double_array required ! [nm]3 positive numbers lattice-constants-temp-coeff               double_array   required ! [nm/K]                                                                     ! elastic-constants                          double_array required ! piezo-electric-constants                  double_array required ! pyro-polarization                          double_array required !3 numbers                                                                    ! static-dielectric-constants                double_array required ! optical-dielectric-constants               double_array   required !                                                                     ! 6x6kp-parameters                           double_array required ! 8x8kp-parameters                          double_array required !                                                                   ! LO-phonon-energy                          double_array 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-wz-default                                    required ! !-------------------------------------------------------------------!

Syntax

binary-type = GaN-wz-default

conduction-bands = 3total number of conduction bands

conduction-band-masses = 0.202d0 0.202d0 0.206d0 ! [m0]masses at the Gamma point m_{_|_}, m_{_|_}, m_|| (with respect to c-axis) 0.330d0 0.330d0 1.430d0 ! [m0]masses at the indirect ??? point 0.280d0 0.280d0 2.170d0 ! [m0]masses at the indirect ??? point

conduction-band-degeneracies = 2 8 6including spin degeneracy

conduction-band-nonparabolicities = 0.6d0 0.2d0 0.3d0Nonparabolicity 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 (CHECK: is this also true for wurtzite?), 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, ?, ?).

conduction-band-energies = 3.500d0 10.00d0 10.00d0conduction 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 = 0.370d0 0.370d0 2.090d0 ! [m0]heavy hole (HH) masses m_{_|_}, m_{_|_}, m_|| (with respect to c-axis) 0.390d0 0.390d0 0.740d0 ! [m0] light hole (LH) masses m_{_|_}, m_{_|_}, m_|| (with respect to c-axis) 0.940d0 0.940d0 0.180d0 ! [m0]crystal-field split-hole (CH) masses m_{_|_}, m_{_|_}, m_|| (with respect to c-axis)
Ordering of numbers corresponds to band no. 1, 2, 3 (heavy, light, crysta-field split-off hole).

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

valence-band-nonparabolicities = 0.0d0 0.0d0 0.0d0see comments for conduction-band-nonparabolicities

valence-band-energies = 0.0The "average" valence band edge energy is according to E_v in:
   S.L. Chuang, C.S. Chang
   k.p method for strained wurtzite semiconductors
   Phys. Rev. B 54 (4), 2491 (1996)The valence band energies for heavy hole (HH), light hole (LH) and crystal-field split-hole (CH) are calculated by defining an "average" valence band energy E_v for all three bands and adding the spin-orbit-splitting and crystal-field splitting energies afterwards. The crystal-field splitting energy Delta_cr and the spin-orbit-splitting energies Delta₂= Delta₃= 1/3 Delta_so are defined together with the 6-band k.p parameters.
The "average" valence band energy E_v is defined on an absolute energy scale and must take into account the valence band offsets which are "averaged" over the three holes.
Note: The real average of the three holes is: E_v,av = (E_HH + E_LH + E_CH ) / 3 = E_v+ 2/3 Delta_cr

varshni-parameters = 0.909d-3 0d0 0d0 ! alpha [eV/K](Gamma, indirect, indirect) Vurgaftman 830d0 0d0 0d0 ! beta [K] (Gamma, indirect, indirect) VurgaftmanTemperature dependent band gaps (here: GaN values). More information...

band-shift = 0d0 to adjust band alignments (should be zero in database): adds to all band energies

absolute-deformation-potential-vb = 0.0d0 ! a_v [eV] -not used in wurtziteAbsolute deformation potential of valence bands.

absolute-deformation-potentials-cbs = a_c,a (a axis) a_c,a (a axis) a_c,c(c axis)! [eV] = -10.0d0 -10.0d0 -5.0d0 ! [eV]absolute deformation potentials of Gamma conduction band minimaa_c,a=a₂(a axis), a_c,a=a₂(a axis), a_c,c=a₁ (c axis)

Note that I. Vurgaftman et al., JAP 94, 3675 (2003) lists a₁ and a₂ parameters.
They refer to the interband deformation potentials, i.e. to the deformation of the band gaps.
Thus we have to add the deformation potentials of the valence bands to get the deformation potentials for the conduction band edge.
a_c,a = a₂ =a₂ + D2
a_c,c = a₁ =a₁ + D1

uniax-vb-deformation-potentials = -3.7d0 4.5d0 8.2d0 ! D1, D2, D3 [eV] -4.1d0 -4.0d0 -5.5d0 ! D4, D5, D6 [eV]Uniaxial deformation potentials of valence bands.

uniax-cb-deformation-potentials = 0d0 0d0 0d0 !not used in wurtziteUniaxial deformation potentials of conduction bands.Xi_u(at minimum)

lattice-constants = 0.3189d0 0.3189d0 0.5185d0 ! [nm] 300 K = a a c3 positive numbers
For the ideal c/a ration it holds: c/a = SQRT(8/3) = 1.63299...

lattice-constants-temp-coeff = 3.88d-6 3.88d-6 3.88d-6 ! [nm/K]More information on temperature dependent lattice constants...

elastic-constants = 374.0d0 106.0d0 70.0d0 ! C11,C12,C13 379.0d0 101.0d0 ! C33,C44Elastic constants C11,C12,C13,C33,C44 in [GPa] with their usual meaning.
(C66 is not needed as it can be calculated.C66 = 0.5 * (C11 - C12).)

piezo-electric-constants = 0.73d0 -0.49d0 -0.30d0 ! [C/m^2] e₃₃ e₃₁ e₁₅ (1^st order coefficients)
0d0 0d0 0d0 0d0 0d0 0d0 0d0 0d0 ! [C/m^2] B₃₁₁ B₃₁₂ B₃₁₃ B₃₃₃ B₁₁₅ B₁₂₅ B₁₃₅ B₃₄₄(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.

pyro-polarization = 0d0 0d0 -0.029d0 ! [C/m^2] 0d0 0d0 P_sp

static-dielectric-constants = 9.28d0 9.28d0 10.01d0                               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.
             eps1and eps2 are perpendicular to the c direction in wurtzite.
low frequency dielectric constant
epsilon(0)

optical-dielectric-constants = 5.35d0 5.35d0 5.35d0 ! high frequency dielectric constant epsilon(infinity); perpendicular and parallel to c axis

6x6kp-parameters = -7.21d0 -0.44d0 6.68d0 !6-band k.p Rashba-Sheka-Pikus parameters -3.46d0 -3.40d0 -4.90d0 !6-band k.p Rashba-Sheka-Pikus parameters 0.010d0 0.00567d0 0.00567d0 ! Delta1 Delta2 Delta3 [eV]

8x8kp-parameters = -7.21d0 -0.44d0 6.68d0 !8-band k.p Rashba-Sheka-Pikus parameters -3.46d0 -3.40d0 -4.90d0 ! 8-band k.p Rashba-Sheka-Pikus parameters 0d0 0d0 0d0 ! B1 B2 B3 [h_bar²/(2m₀)] 14.5d0 14.5d0 ! E_P1 E_P2 [eV] 1d0 1d0 ! S1 S2 []Note: TheSparameters are also defined in the literature asFwhere S = 1 + 2F, e.g. I. Vurgaftman et al., JAP 89, 5815 (2001).

LO-phonon-energy = 0.09212d0 0.09212d0 0.09113d0 ! [eV]low-temperature optical phonon energy (perpendicular, perpendicular, parallel to c axis)

number-of-minima-of-cband = 1 4 3

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 components of k-vector along crystal xyz [k0]

principal-axes-cb-masses = 1d0 0d0 0d0 0d0 1d0 0d0 0d0 0d0 1d0 !c 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 !c 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 0d0Normalization 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 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 1d0Normalization will be done internally by the program

More information can be found under the keywordbinary-wz-default (binary wurtzite parameters) under the section Keywords.