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binary-wz-default

Wurtzite material parameters

For materials which are not known to the database and for the use of non default 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-wz-default under the section Database.

!--------------------------------------------------------------!
$binary-wz-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] for each band. Ordering of numbers corresponds to band no. 1, 2, ...
 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 valence bands
                                                               !
 valence-bands                       integer         optional  ! total number of valence bands
 valence-band-masses                 double_array    optional  ! [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   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_array    optional  ! "average" valence band edge energy Ev (see comments below)
                                                               !
 varshni-parameters                  double_array    optional  ! alpha [eV/K] (Gamma,indirect,indirect), beta [K] (Gamma,L,indirect,indirect)
 band-shift                          double          optional  !
to adjust band alignments (should be zero in database)
                                                               !
 absolute-deformation-potential-vb   double          optional  ! not used in wurtzite
 absolute-deformation-potentials-cbs double_array    optional  ! absolute deformation potential of conduction band: ac,a(=a2) ac,a(=a2)  ac,c(=a1) [eV]
                                                               !
 uniax-vb-deformation-potentials     double_array    optional  ! b,d related [eV]
 uniax-cb-deformation-potentials     double_array    optional  ! not used in wurtzite
                                                               !
 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  !
 pyro-polarization                   double_array    optional  !
                                                               !
 static-dielectric-constants         double_array    optional  !
 optical-dielectric-constants        double_array    optional  !
                                                               !
 6x6kp-parameters                    double_array    optional  !
 8x8kp-parameters                    double_array    optional  !
                                                               !
 LO-phonon-energy                    double_array    required  ! [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-wz-default                               optional  !
!--------------------------------------------------------------!

 

Syntax

binary-type = character
           
= GaN-wz-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 = string
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-wz-default.
    Consider this example:

    Assume that you have used the following materials in your input file:

      $material
       material-number = 1
       material-name   = GaN
       ...

       material-number = 2
       material-name   = In(x)Ga(1-x)N   !
    material number of ternary = 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
       ...

    Then you have to overwrite the material parameters as follows.

      $binary-wz-default
       binary-type = GaN-zb-default
     ! apply-to-material-numbers = 1   !
    Obviously, this overwrites the material parameters of material #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 !
    This overwrites the material parameters of material #1 which is GaN and the GaN values of which the ternary In(x)Ga(1-x)N (material #2) is calculated.
       ...

      $binary-wz-default
       binary-type = InN-zb-default
     ! apply-to-material-numbers = 3   !
    Obviously, this overwrites the material parameters of material #3 which is InN but not the InN values of which the ternary In(x)Ga(1-x)N (material #2) is calculated.
                                       !
    Therefore, for material #2, the default InN values of the database are used and not the ones specified in the input file.
       apply-to-material-numbers = 2 3 !
    This overwrites the material parameters of material #3 which is InN and the InN values of which the ternary In(x)Ga(1-x)N (material #2) is calculated.
       ...

      $binary-wz-default
       ternary-type = In(x)Ga(1-x)N-wz-default
       apply-to-material-numbers = 2   !
    This overwrites the material parameters (here: bowing parameters) of the ternary material #2 which is InGaN.
       ...
     

 

conduction-bands = int
Number of nondegenerate conduction bands (minima). Most likely, only 3 is a working number.

conduction-band-masses = m_perp  m_perp  m_par ! [m0] masses at the Gamma point m_|_, m_|_, m|| (with respect to c-axis)
                         m4      m5      m6    ! [m0]
masses at the indirect ??? point
                         m7      m8      m9  
 ! [m0]
masses at the indirect ??? point
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.

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.
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 ordering of the principal axis 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_? a_?
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 = 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 = 0.909d-3 0.0d0 0.0d0  ! alpha [eV/K](Gamma, indirect, indirect) Vurgaftman
                     830d0    0.0d0 0.0d0  ! beta  [K]  
(Gamma, indirect, indirect) Vurgaftman
Temperature dependent band gaps (here: GaN values). More information...

band-shift = double
Can be used to rigidly shift all band energies by this amount.

 

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

 

absolute-deformation-potentials-cbs = ac,a (a axis)   ac,a (a axis)   ac,c (c axis) ! [eV]
                                    = -10.0d0      -10.0d0     -5.0d0     ! [eV]
absolute deformation potentials of Gamma conduction band minima ac,a=a2 (a axis), ac,a=a2 (a axis), ac,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.
ac,a = a2 = a2 + D2
ac,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 wurtzite
Uniaxial deformation potentials of conduction bands.
Xi_u
(at minimum)

 

lattice-constants            = 0.3189d0  0.3189d0  0.5185d0  ! [nm]   300 K
                             = a        a        c
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   C13  C33  C44
Elastic 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  = e33  e31  e15                           ! [C/m^2] e33  e31   e15                           (1st   order coefficients)
                            B311 B312 B313 B333 B115 B125 B135 B344 ! [C/m^2] B311  B312  B313  B333  B115  B125 B135  B344 (2nd order coefficients)
Example: For pseudomorphic AlxGa1-xN layers grown on GaN, the strain is tensile. The induced piezoelectric polarization is positive for compressive and negative for tensile strain leading to a gradient in the polarization at the interface. (This can lead to the formation of a 2-dimensional electron gas.)
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.
For option piezo-second-order = 2nd-order-Tse-Pal and 4th-order-Tse-Pal different parameters can be specified, see $numeric-control.

pyro-polarization  = 0d0  0d0  Psp  ! [C/m^2]
Components of spontaneous polarization in crystal fixed cartesian coordinate system.
The spontaneous polarization Psp is due to the deviation of the lattice constants a and c from their "ideal" value.
   ideal: c/a=(8/3)1/2=1.633
   real:  c/a=1.626 (GaN)
           c/a=1.601 (AlN)
           c/a=1.613 (InN)
Thus the vector sum of the dipole moments does not vanish leading to a spontaneous polarization along the c axis of the crystal (pointing from N to Ga(Al,In) atom).

 

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

 

6x6kp-parameters   = A1     A2     A3     ! 6-band k.p Rashba-Sheka-Pikus parameters
                     A4     A5     A6    
!
6-band k.p Rashba-Sheka-Pikus parameters
                     Delta1 Delta2 Delta3
! [eV]

8x8kp-parameters   = A1'    A2'    A3'    ! 8-band k.p Rashba-Sheka-Pikus parameters
                     A4'    A5'    A6'   
!
8-band k.p Rashba-Sheka-Pikus parameters
                     B1     B2     B3    
! [hbar2/(2m0)]
                     E_P1   E_P2
          ! [eV]
                     S1     S2
            ! []

A1,A2,A3,A4,A5,A6: 6-band (or 8-band) Rashba-Sheka-Pikus k.p parameters for wurtzite
Delta1
:
crystal field split-off energy [eV]
Delta2 = Delta3
= 1/3 Delta_so [eV]
Delta_so:
spin-orbit split-off energy [eV)]
B1,B2,B3:
8-band k.p inversion symmetry parameters in units of [hbar2/(2m0)]
E_P1,E_P2:
Kane's momentum matrix elements EP1, EP2 in units of [eV]
S1,S2:
8-band k.p parameters for the conduction band mass (dimensionless)
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

 

LO-phonon-energy = ELO,ph,perp  ELO,ph,perp  ELO,ph,parallel     ! [eV] low-temperature optical phonon energy (perpendicular and parallel to c axis)

m_perp=1.6 , m_perp=1.6 , m_par=1.1  - http://www.ioffe.rssi.ru/SVA/NSM/Semicond/GaN/bandstr.html

valence-bands                  = integer
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)
valence-band-degeneracies      = integer_array
valence-band-nonparabolicities = double_array  ! see comments for conduction-band-nonparabolicities

 

valence-band-energies          = double_array
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

 

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  !
Note: number-of-minima-of-vband is required (!) for this specifier.
Valence band parameters in complete analogy to conduction band parameters.

More information can be found under the keyword binary-wz-default under the section Database.

 

 
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