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ternary-wz-default

Ternary wurtzite parameters

Parameters for wurtzite 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.

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-wz-default                                      optional !
 ternary-type                            character       required ! Al(x)Ga(1-x)N-wz-default, must be a declared binary material
 ternary-name                            character       optional !
 apply-to-material-numbers               integer_array   required !
 binary(x)                               character       optional ! AlN-wz-default, must be a defined binary material
 binary(1-x)                             character       optional ! GaN-wz-default, must be a defined binary material
                                                                  !
 bow-conduction-band-masses              double_array    optional ! Bowing parameters b are defined for Q[A(x)B(1-x)C] = x*Q[AC]+(1-x)*Q[BC]-b*x*(1-x)
 bow-conduction-band-nonparabolicities   double_array    optional ! [m0]
 bow-band-gaps                           double_array    optional !
 bow-conduction-band-energies            double_array    optional !
                                                                  !
 bow-valence-band-masses                 double_array    optional ! [m0]
 bow-valence-band-nonparabolicities      double_array    optional !
 bow-valence-band-energies               double          optional ! "average" valence band edge energy Ev (see comments below)
                                                                  !
 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 ! not used in wurtzite
 bow-abs-deformation-pots-cbs            double_array    optional !

 bow-uniax-vb-deformation-pots           double_array    optional !

 bow-uniax-cb-deformation-pots           double_array    optional ! not used in wurtzite
                                                                  !
 bow-lattice-constants                   double_array    optional !
 bow-elastic-constants                   double_array    optional !
 bow-piezo-electric-constants            double_array    optional !
 bow-pyro-polarization                   double_array    optional !
                                                                  !

 bow-static-dielectric-constants         double_array    optional !
 bow-optical-dielectric-constants        double_array    optional !
                                                                  !
 bow-6x6kp-parameters                    double_array    optional !
 bow-8x8kp-parameters                    double_array    optional !
                                                                  !
 bow-LO-phonon-energy                    double_array    required !
                                                                  !

$end_ternary-wz-default                                  optional !
!-----------------------------------------------------------------!

 

Syntax

ternary-type = Al(x)Ga(1-x)N-wz-default
            
= Al(x)In(1-x)N-wz-default

             = In(x)Ga(1-x)N-wz-default
e.g. Al(x)Ga(1-x)N-wz-default, must be a defined ternary material

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-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)    = AlN-wz-default
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.

must be a binary material of type binary-wz-default
e.g. AlN-wz-default, must be a defined binary material

 

binary(1-x)  = GaN-wz-default
The name of the second binary for the alloy. Limitations and problems as for the other binary.

must be a binary material of type binary-wz-default
e.g. GaN-wz-default, must be a defined binary material

 

bow-conduction-band-masses = 0d0   0d0   0d0 ! [m0] masses at the Gamma point m_|_, m_|_, m|| (with respect to c-axis)
                             0d0   0d0   0d0
! [m0]
masses at the indirect ??? point
                             0d0   0d0   0d0
! [m0]
masses at the indirect ??? point
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.

Bowing parameters b are defined for Q[A(x)B(1-x)C] = x*Q[AC]+(1-x)*Q[BC]-b*x*(1-x)

 

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

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, ?, ?).

bow-conduction-band-energies = 0d0 0d0     0d0

Bowing parameters for conduction band energies. One bowing parameter for each set of degenerate minima.

 

bow-valence-band-masses    = 0d0   0d0   0d0 ! [m0] heavy hole (HH) masses m_|_, m_|_, m|| (with respect to c-axis)
                             0d0   0d0   0d0
! [m0] light   hole (LH)  masses m_|_, m_|_, m|| (with respect to c-axis)
                             0d0   0d0   0d0 ! [m0]
crystal-field split-hole (CH) masses m_|_, m_|_, m|| (with respect to c-axis)

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

 

bow-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

 

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

bow-abs-deformation-pots-cbs = a2  a2  a1
bow-abs-deformation-pots-cbs  = 0d0     0d0     0d0      !  (a2  a2  a1)
Bowing parameters for absolute deformation potentials of Gamma conduction band minima a_c (a axis), a_c (a axis), a_c (c axis)

bow-uniax-vb-deformation-pots = 0d0     0d0     0d0   
                                0d0     0d0     0d0   
 

Bowing parameters for uniaxial deformation potentials of valence bands.
b,d related [eV]

bow-uniax-cb-deformation-pots = 0d0     0d0     0d0    ! not used in wurtzite
 

bow-lattice-constants = 0d0     0d0     0d0    ! [nm]

Bowing parameters for lattice constants.

bow-elastic-constants = 0d0     0d0     0d0    0d0     0d0

Bowing parameters for elastic constants C11,C12,C13,C33,C44.

 

bow-piezo-electric-constants = 0d0 0d0 0d0   0d0 0d0 0d0 0d0 0d0 0d0 0d0 0d0  ! [C/m^2]
Bowing parameters for piezoelectric constants e33  e31  e15  B311  B312  B313  B333  B115  B125 B135  B344
For option piezo-second-order = 2nd-order-Tse-Pal and 4th-order-Tse-Pal different parameters can be specified, see $numeric-control.

bow-pyro-polarization = 0  0  bow-Psp  ! [C/m2]
bow-pyro-polarization        = 0d0     0d0     0d0  ! [C/m^2] 0d0  0d0  Psp
Bowing parameters for components of spontaneous pyroelectric polarization.

3 numbers

 

bow-static-dielectric-constants  = 0d0     0d0     0d0

Bowing parameters for static dielectric constants.

bow-optical-dielectric-constants = double_perpendicular  double_perpendicular  double_parallel
bow-optical-dielectric-constants = 0d0     0d0     0d0

Bowing for high frequency dielectric constant.

 

bow-6x6kp-parameters  = 0d0     0d0     0d0    ! 6-band k.p Rashba-Sheka-Pikus parameters
                        0d0     0d0     0d0   
!
6-band k.p Rashba-Sheka-Pikus parameters
                        0d0     0d0     0d0   
! Delta1   Delta2   Delta3       [eV]

bow-8x8kp-parameters  = 0d0     0d0     0d0    !
8-band k.p Rashba-Sheka-Pikus parameters
                        0d0     0d0     0d0   
!
8-band k.p Rashba-Sheka-Pikus parameters
                        0d0     0d0     0d0   
! B1   B2  B3  [hbar2/(2m0)]
                        0d0     0d0           
! EP1  EP2      [eV]
                        0d0     0d0            ! S1   S2      []

bow-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]

Bowing parameters for 6-band k.p model.

bow-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)]
old version:           P1     P2            ! [eVAngstrom]
                       E_P1   E_P2          ! [eV]
                       S1     S2
            ! []

Bowing parameters for 8-band k.p model.

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)]
old version: P1,P2:
momentum matrix element parameters derived from Kane's momentum matrix elements Ep1, Ep2 in units of [eVAngstrom]
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
Consequently, as one can show, the bowing parameter for S has the value 2 * F.

Note: For testing purposes, one might want to input the "zinc blende" k.p material parameters into the wurtzite section.
Then the results of the "wurtzite" k.p Hamiltonian should be the same as for the "zinc blende" k.p Hamiltionian.
However, as it is only possible to input the Rashba-Sheka-Pikus parameters A1,...,A6, this works only if it holds for the zincblende N = L - M (isotropic symmetry), i.e. L and M are given, N is determined from them.
The relevant relations are:
 ! Here, L,M are given, everything else is determined once A1 and A2 is determined.
 ! This corresponds to zincblende parameters L,M but with isotropic symmetry because is holds: N1 = L1 - M1.
 !     A1 =   ...        = L + 1
 !     A2 =   ...        = M + 1
 ! ==> A3 =   A2 - A1    = - N
 ! ==> A4 = - A3 / 2     = N / 2
 ! ==> A5 =   A4         = N / 2
 ! ==> A6 = SQRT(2) * A5 = N / SQRT(2)

Example:
 6x6kp-parameters = -6.74d0 -2.18d0 -4.56d0                              ! GaN(zb)  L,M,N=L-M [hbar^2/2m] (zincblende)
                     0.017d0                                             ! GaN(zb)  Delta_so [eV]         (zincblende)
 6x6kp-parameters = -5.74d0 -1.18d0  4.56d0                              ! GaN(zb)  A1 = L2 + 1 = L + 1        , A2 = M3 + 1 = M + 1 , A3 = M2 - L2 = M - L            (wurtzite)
                    -2.28d0 -2.28d0 -3.2244069222106567112678502911981d0 ! GaN(zb)  A4 = (L1+M1-2M3)/2 = -A3/2 , A5 = N1 / 2 = N / 2 , A6 = N2 / SQRT(2) = N / SQRT(2) (wurtzite)
                     0d0     0.00566666666666666666666666666667d0        ! GaN(zb)  Delta_1(cr),Delta_2    ! Delta_so = 0.017 [eV], Delta_2=Delta_3=0.017/3=Delta_so/3 (wurtzite)
                             0.00566666666666666666666666666667d0        ! GaN(zb)              Delta_3                                                                (wurtzite)
!
Note: The relation N1 = L1 - M1 is due to sixfold rotational symmetry. It means isotropic dispersion in the plane perpendicular to the c axis.
! A5 = (L1 - M1) / 2 = (L - M) / 2  = A4       = -2.28
! A5 =  N1 / 2 = N / 2             /= A4 (!!!) = -3.33
(In zinc blende, we do not have sixfold rotational symmetry!!! Thus we have to use N1 and not L1 - M1 when calculation A5.)
For equations, see p. 42 in PhD thesis of S. Birner.

 

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