[ Home ] [ News ] [ Contact ] [ Search ] [ nextnano.com ] binary-zb-default

 Download Software
 Copyright notice
 Publications

 GUI: nextnanomat
 Tool: nextnano
 Tool: nextnano++
 Tool: nextnano.QCL
 * password protected

 

 
Up
 

binary-zb-default

More information can be found under the keyword binary-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_array   required !
average valence band edge energy Ev,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 = 3
total 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     (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 = 2 8 12
including spin degeneracy

 

conduction-band-nonparabolicities = 0d0   0d0   0d0  ! [1/eV] Gamma, L , 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 = 1.5d0 2.0d0 2.3d0  ! [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 (Gamma, L, X).

conduction-band-energies = 0d0 0d0 0d0
conduction 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 = 3
total 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 hole
Ordering of numbers corresponds to band no. 1, 2, 3 (heavy, light, split-off hole).

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

 

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

 

valence-band-energies = 0d0
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.

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 = 0d0
to 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 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...

 

piezo-electric-constants = -0.350d0                  ! [C/m^2] e14                (1st   order coefficients)
                           0d0     0d0      0d0      ! [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.

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

 

static-dielectric-constants = 9.28d0 9.28d0 9.28d0
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 = 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-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     = -16.22d0 -3.86d0 -17.58d0  ! L    M      N     [hbar2/(2m0)]
                        0.341d0             
     ! Deltaso (spin-orbit split-off energy) [eV]

8x8kp-parameters     =  1.420d0 -3.86d0  0.056d0  ! L'   M'=M   N'    [hbar2/(2m0)]
                        0.0d0   28.8d0  -2.876d0 
! B  [hbar2/(2m0)]    EP  [eV]    S []

   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 = 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      0d0

components of k-vector along crystal xyz [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     0d0

components 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     1d0

Normalization will be done internally by the program

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