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  Zincblende parameters

 

 

 
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binary-zb-default

Zinc blende material parameters

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

!--------------------------------------------------------------!
$binary-zb-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] ml,mt1,mt2 for each band. Ordering of numbers corresponds to band no. 1, 2, ... (Gamma, L, X)
 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 average valence band energy Ev,av
                                                               !  (number corrsponds to the ordering of the entries below)
 valence-bands                       integer         optional  ! total number of valence bands
 valence-band-masses                 double_array    optional  ! [m0] ml,mt1,mt2 for each band. Ordering of numbers corresponds to band no. 1, 2, ... (hh, lh, so)
 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,av
 varshni-parameters                  double_array    optional  ! alpha [eV/K] (Gamma,L,X), beta [K] (Gamma,L,X)
 band-shift                          double          optional  !
to adjust band alignments (should be zero in database)
                                                               !
 absolute-deformation-potential-vb   double          optional  !
 absolute-deformation-potentials-cbs double_array    optional  ! absolute deformation potential of conduction band: a_cd, a_ci [eV]
 uniax-vb-deformation-potentials     double_array    optional  ! b,d [eV]
 uniax-cb-deformation-potentials     double_array    optional  !
                                                               !
 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  !
                                                               !
 static-dielectric-constants         double_array    optional  !
 optical-dielectric-constants        double          optional  !
                                                               !
 Luttinger-parameters                double_array    optional  !
 6x6kp-parameters                    double_array    optional  !
 8x8kp-parameters                    double_array    optional  !
                                                               !
 LO-phonon-energy                    double          optional  ! [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-zb-default                               optional  !
!--------------------------------------------------------------!

 

Syntax

binary-type = character
           
= GaAs-zb-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 = character
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-zb-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-zb-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-zb-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-zb-default
       ternary-type = In(x)Ga(1-x)N-zb-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
total number of conduction band minima (Gamma, L, X)

conduction-band-masses = m    m    m     ! Gamma
                         ml   mt   mt     ! L
                         ml   mt   mt     ! X
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.
For the L and X valleys, one longitudinal and two transverse masses are required.

 

conduction-band-masses = 0.156d0 0.156d0 0.156d0 ! [m0] Gamma (m,m,m)
                         1.420d0 0.130d0 0.130d0
! [m0] L     (mlongitudinal,mtransverse,mtransverse)
                         0.916d0 0.190d0 0.190d0
! [m0] X     (mlongitudinal,mtransverse,mtransverse)
3 numbers per band, ordering of numbers corresponds to band no. 1, 2, 3 (Gamma, L, X)

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 in units of [2pi/a] where a is the lattice constant.
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 orderering of the principal axes 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_L a_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 = 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 = 0.5405d-3 0.605d-3 0.460d0 ! alpha [eV/K](Gamma, L, X) Vurgaftman
                     204d0     204d0    204d0   ! beta  [K]  
(Gamma, L, X) Vurgaftman
Temperature dependent band gaps (here: GaAs values). More information...

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

absolute-deformation-potential-vb   = double
 

absolute-deformation-potentials-cbs = a_c_Gamma  a_c_L   a_c_X ! [eV] (Gamma, L, X)
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     = b  d        ! [eV]
 

uniax-cb-deformation-potentials     = d1  d2  d3 ...

 

lattice-constants            = 0.543d0  0.543d0  0.543d0   ! [nm]   300 K
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  c44
Elastic constants c11,c12,c44 in [GPa] with their usual meaning.

piezo-electric-constants  = e14            ! [C/m^2] e14            (1st   order coefficients)
                            B114 B124 B156 ! [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.
For option piezo-second-order = 4th-order-Tse-Pal different parameters can be specified, see $numeric-control.

 

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 = eps
high frequency dielectric constant epsilon(infinity)

 

Luttinger-parameters = gamma1  gamma2  gamma3 ! [] Luttinger parameters for the valence band
                       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-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     = L       M       N     ! [hbar2/(2m0)]
                       DeltaSO                   
 ! [eV]

8x8kp-parameters     = L'      M'=M    N'    ! [hbar2/(2m0)]
old version:           B       P       S     ! [hbar2/(2m0)]   [eVAngstrom]   []
                       B       EP      
 S       ! [hbar2/(2m0)]   [eV]           []

   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).
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 = ELO,ph            ! [eV]   low-temperature optical phonon energy

 

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

valence-band-energies               = double_array
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.

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 detailed information can be found here.

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