$binary-wz-default

Wurtzite material parameters

More information can be found under the keyword $binary-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] mxx, myy, mzz 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 Ev (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 minima a_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 = 3

total number of conduction bands

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

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

conduction-band-nonparabolicities = 0.6  0.2  0.3

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 (CHECK: is this also true for wurtzite?), 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]

Note that this specifier is optional. It is only used if the flag use-band-gaps = yes is used. Energy band gaps of the three valleys (Gamma, ?, ?).

conduction-band-energies = 3.500  10.0  10.0

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 = 0.370 0.370 2.090 ! [m0] heavy hole (HH) masses m_|_, m_|_, m|| (with respect to c-axis)
                      0.390 0.390 0.740 ! [m0] light   hole (LH) masses  m_|_, m_|_, m|| (with respect to c-axis)
                      0.940 0.940 0.180 ! [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, crystal-field split-off hole).

valence-band-degeneracies = 2 2 2

including spin degeneracy

valence-band-nonparabolicities = 0.0 0.0 0.0

see comments for conduction-band-nonparabolicities

valence-band-energies = 0.0

The “average” valence band edge energy is according to Ev 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 Ev for all three bands and adding the
spin-orbit-splitting and crystal-field splitting energies
afterwards. The crystal-field splitting energy Deltacr and
the spin-orbit-splitting energies Delta2 = Delta3 =
1/3 Deltaso are defined together with the 6-band k.p
parameters.
The “average” valence band energy Ev 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: Ev,av =
(EHH + ELH + ECH ) / 3 = Ev + 2/3
Deltacr

varshni-parameters = 0.909e-3  0.0  0.0  ! alpha [eV/K](Gamma, indirect, indirect) Vurgaftman
                     830.0     0.0  0.0  ! beta  [K]   (Gamma, indirect, indirect) Vurgaftman

Temperature dependent band gap

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] (not used in wurtzite)

Absolute deformation potential of valence bands.

absolute-deformation-potentials-cbs = -10.0          -10.0           -5.0           ! [eV]
                                    = ac,a (a axis)   ac,a (a axis)   ac,c (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.

ac,a = a2 = a2 + D2

ac,c = a1 = a1 + D1

uniax-vb-deformation-potentials = -3.7  4.5  8.2 ! D1, D2, D3 [eV]
                                  -4.1 -4.0 -5.5 ! D4, D5, D6 [eV]

Uniaxial deformation potentials of valence bands.

uniax-cb-deformation-potentials  = 0.0     0.0     0.0  ! not used in wurtzite

Uniaxial deformation potentials of conduction bands. Xi_u (at minimum)

lattice-constants = 0.3189  0.3189d0  0.5185d0  ! [nm]  a  a  c  (300 K)

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 => Add Link “How-to-add-material-parameters.htm”

elastic-constants = 374.0 106.0 70.0         ! C11,C12,C13
                    379.0 101.0              ! C33,C44

Elastic constants C11,C12,C13,C33,C44 in [GPa]. C66 is not needed as it can be calculated. C66 = 0.5 * (C11 - C12).

piezo-electric-constants  = 0.73 -0.49 -0.30                 ! [C/m^2] e33  e31   e15                                (1st order coefficients)
                            0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  ! [C/m^2] B311  B312  B313  B333  B115  B125 B135  B344 (2nd order coefficients)

Conventionally, the sign of the piezoelectric tensor components is fixed by assuming that the positive direction along the [111] direction (zincblende) and [0001] direction (wurtzite) points from the cation to the anion.

pyro-polarization = 0.0  0.0 -0.029  ! [C/m^2] 0.0  0.0  P_sp

static-dielectric-constants = 9.28 9.28 10.01  ! eps_a  eps_a  eps_c

Static dielectric constants. The numbers correspond to the crystal directions: In wurtzite: eps1 = eps2 eps_c is parallel to the c direction in wurtzite. eps_a are perpendicular to the c direction in wurtzite. low frequency dielectric constant epsilon(0)

optical-dielectric-constants = 5.35 5.35 5.35

high frequency dielectric constant epsilon(infinity); perpendicular and parallel to c axis

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

8x8kp-parameters = -7.21  -0.44     6.68     ! 8-band k.p Rashba-Sheka-Pikus parameters
                   -3.46  -3.40    -4.90     ! 8-band k.p Rashba-Sheka-Pikus parameters
                    0.0    0.0      0.0      ! B1   B2  B3  [hbar2/(2m0)]
                    14.5  14.5               ! EP1  EP2      [eV]
                    1.0    1.0               ! S1   S2      []

Note: The S parameters are also defined in the literature as F where S = 1 + 2F, e.g. I. Vurgaftman et al., JAP 89, 5815 (2001).

LO-phonon-energy = 0.09212 0.09212 0.09113 ! [eV]

low-temperature optical phonon energy (perpendicular, perpendicular, parallel to c axis)

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

conduction-band-minima = 0.0     0.0     0.0        ! Gamma

                        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

components of k-vector in crystal coordinate system [k0]

principal-axes-cb-masses = 1.0     0.0     0.0
                           0.0     1d0     0.0
                           0.0     0d0     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

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