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ternary-zb-default

Ternary zinc blende parameters

Parameters for zinc blende type ternary alloys. This parameter set refers to the binary constituents and their material parameters and specifies the bowing parameters for interpolation between the binaries.

Please check the Database section for more details: $ternary-zb-default

Bowing parameters b are defined for

Q[AxB1-xC] = x * Q[AC] + (1-x) * Q[BC] - b * x * (1-x).

b is defined as  b = 4Q(A0.5B0.5C) - 2[ Q[AC] + Q[BC] ].

The advantage of the bowing model is that it requires knowledge of the relevant quantity only at a composition x=0.5 together with the values for the binaries.

 

!---------------------------------------------------------------!
$ternary-zb-default                                    optional !
 ternary-type                          character       required ! Al(x)Ga(1-x)As-zb-default, must be a declared binary material
 ternary-name                          character       optional !

 apply-to-material-numbers             integer_array   required !
 binary(x)                             character       optional ! AlAs-zb-default, must be a defined binary material
 binary(1-x)                           character       optional ! GaAs-zb-default, must be a defined binary material
                                                                !
 bow-conduction-band-masses            double_array    optional !
 bow-conduction-band-nonparabolicities double_array    optional !
 bow-band-gaps                         double_array    optional !
 bow-conduction-band-energies          double_array    optional !
                                                                !
 bow-valence-band-masses               double_array    optional !
 bow-valence-band-nonparabolicities    double_array    optional !
 bow-valence-band-energies             double          optional ! average valence band edge energy
                                                                !
 bow-lattice-constants                 double_array    optional !
 bow-elastic-constants                 double_array    optional !
 bow-piezo-electric-constants          double_array    optional !
                                                                !
 bow-static-dielectric-constants       double_array    optional !
 bow-optical-dielectric-constants      double          optional !
                                                                !
 band-shift                            double          optional ! to adjust band alignments (should be zero in database)
 bow-band-shift                        double          optional ! to adjust band alignments, using band shifts specified for binaries
                                                                !
 bow-abs-deformation-pot-vb            double          optional !
 bow-abs-deformation-pots-cbs          double_array    optional ! bow absolute deformation potentials of conduction band minima
 bow-uniax-vb-deformation-pots         double_array    optional ! b,d related
 bow-uniax-cb-deformation-pots         double_array    optional !
                                                                !
 bow-Luttinger-parameters              double_array    optional !
 bow-6x6kp-parameters                  double_array    optional !

 bow-8x8kp-parameters                  double_array    optional !
                                                                !
 bow-LO-phonon-energy                  double          optional !
                                                                !

$end_ternary-zb-default                                optional !
!---------------------------------------------------------------!

ternary-type = character
            
= Al(x)Ga(1-x)As-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
The binary constituents can still be either known or unknown binary materials.

ternary-type                          = In(x)Ga(1-x)As-4K-zb-default
 
e.g. Al(x)Ga(1-x)As-zb-default, must be a defined ternary material
String is usually a known material, e.g. In(x)Al(1-x)As-zb-default. If a material-type with material-model = ternary-zb-default is specified within the $material keyword which is unknown, you have to provide a complete set of input data for this material type.  In this case the material-type must be equal to string. However, the binary constituents can still be either known or unknown binary materials.

ternary-name = string
String is a name of your choice. Currently this string is not used in the code.

apply-to-material-numbers = num1 num2 ...
Intended to change only some parameters for some materials which are otherwise identical.

binary(x)                             = InAs-4K-zb-default
must be a binary material of type binary-zb-default
 
e.g. AlAs-zb-default, must be a defined binary material
String can be either a known binary or an arbitrary name. In case this binary is not a known material, you will be prompted for all material parameters. In its current implementation, there are only a few checks with respect to the number of data expected for each parameter. Most likely, the program will simply crash if something is specified which differs from the data structure of a known material.

binary(1-x)                           = GaAs-4K-zb-default
must be a binary material of type binary-zb-default
 
e.g. GaAs-zb-default, must be a defined binary material
The name of the second binary for the alloy. Limitations and problems as for the other binary.

 

bow-conduction-band-masses            = 0d0     0d0     0d0
                                        0d0     0d0     0d0
                                        0d0     0d0     0d0

Bowing parameters b are defined for Q[A(x)B(1-x)C] = x*Q[AC]+(1-x)*Q[BC]-b*x*(1-x)
Bowing parameters for the effective masses in the conduction band minima. The ordering corresponds to the ordering of the masses in the binary constituents.
For each set of degenerate minima a triplet of bowing parameters for the three masses associated to the minimum.

 

bow-conduction-band-nonparabolicities = 0.0d0 0.0d0 0.0d0
Bowing parameters for the nonparabolicity parameters in the conduction band minima. One nonparabolicity parameter for each set of degenerate minima.

 

bow-band-gaps = 0d0 0d0 0d0  ! [eV]  Note that this flag is optional. It is only used if the flag use-band-gaps = yes is used.
Bowing parameter of the energy band gaps of the three valleys (Gamma, L, X).

bow-conduction-band-energies          = 0.52d0  0d0     0d0
Bowing parameters for conduction band energies. One bowing parameter for each set of degenerate minima.

bow-valence-band-nonparabolicities    = 0d0      0d0      0d0   
see comments for bow-conduction-band-nonparabolicities

bow-valence-band-masses               = 0.0025d0 0.0025d0 0.0025d0
                                        0d0      0d0      0d0   
                                        0d0      0d0      0d0   

 

bow-valence-band-energies             = 0.0
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.

 

 

bow-band-shift                        = 0d0
to adjust band alignments, using band shifts specified for binaries
Bowing parameter to interpolate rigid band shift of binaries.

band-shift                            = 0d0
to adjust band alignments (should be zero in database)
Can be used to rigidly shift the band energies.

 

bow-abs-deformation-pot-vb            = 0d0     ! a_v [eV]
Bowing parameter for absolute deformation potential of valence band.

bow-abs-deformation-pots-cbs          = 0d0     0d0     0d0
absolute deformation potentials of conduction band minima a_cd , a_ci's
Bowing parameters for absolute deformation potential of conduction bands.

 

 

bow-uniax-vb-deformation-pots         = 0d0     0d0     ! b,d [eV]
                                        ! b,d
related
Bowing parameters for uniaxial deformation potentials of valence bands.

bow-uniax-cb-deformation-pots         = 0d0     0d0     0d0  ! Xi_u(at minimum)
Bowing parameters for uniaxial deformation potentials of conduction bands.

 

 

bow-lattice-constants                 = 0d0     0d0     0d0  ! [nm]
Bowing parameters for lattice constants.

bow-elastic-constants                 = 0d0     0d0     0d0
Bowing parameters for elastic constants c11,c12,c44.

Bowing parameters for elastic constants c11,c12,c44.

bow-piezo-electric-constants = double1 double2 double3 double4
Bowing parameters for piezoelectric constants.
For option piezo-second-order = 4th-order-Tse-Pal different parameters can be specified, see $numeric-control.

bow-piezo-electric-constants          = 0d0     0d0     0d0     0d0
Bowing parameters for piezoelectric constants.

 

 

bow-static-dielectric-constants       = 0d0      0d0      0d0
Bowing parameters for static dielectric constants.

bow-optical-dielectric-constants      = 0d0
Bowing for high frequency dielectric constant.

 

 

bow-Luttinger-parameters = gamma1  gamma2  gamma3 ! []
                           kappa   q             ! []
bow-Luttinger-parameters              = 0d0     0d0     0d0 ! gamma1  gamma2  gamma3 []
                                        0d0     0d0         ! kappa   q      []
Note: The Luttinger parameters are only used if the following $numeric-control flag is set: Luttinger-parameters = yes

bow-6x6kp-parameters     = L       M       N     ! [hbar2/(2m0)]
                           DeltaSO                   
 ! [eV]
bow-6x6kp-parameters                  = 0d0     0d0     0d0 ! L    M      N     [hbar2/(2m0)]
                                        0d0   
             ! Deltaso (spin-orbit split-off energy) [eV]
Bowing parameters for 6-band k.p model.

bow-8x8kp-parameters     = L'      M'=M    N'    ! [hbar2/(2m0)]
                           B       EP       S       ! [hbar2/(2m0)]   [eV]   []

bow-8x8kp-parameters                  = -14d0  3.0d0  -12d0 ! L'   M'=M   N'    [hbar2/(2m0)]
                                         0d0   1.8d0   0d0  ! B  [hbar2/(2m0)]    EP  [eV]    S []
Bowing parameters for 8-band k.p model.

   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).
F = (S - 1)/2
Consequently, as one can show, the bowing parameter for S has the value 2 * F.

More information on k.p parameters...

 

bow-LO-phonon-energy = 0d0            ! [eV]   low-temperature optical phonon energy