$ternary-zb-default

Ternary zinc blende parameters

Parameters for zinc blende type ternary alloys. This set of parameters refers to the binary constituents and their material parameters. Here, the bowing parameters for interpolation between these binaries are specified.

A bowing parameter \(b\) is defined as follows for the material parameter \(Q\). Note that there is a minus sign in front of the term \(bx(1-x)\).

\(Q[\text{A}_x\text{B}_{1-x}\text{C}] = x \cdot Q[\text{AC}] + (1-x) \cdot Q[\text{BC}] - b \cdot x \cdot (1-x)\)

\(b\) is defined as \(b = 4 Q (\text{A}_{0.5}\text{B}_{0.5}\text{C}) - 2 ( Q[\text{AC}] + Q[\text{BC}] )\).

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.

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

For the meaning of the material parameters and its units, please check the keywords section for $binary-zb-default for more details. The units for binary material parameters and for the bowing parameters are the same.

$ternary-zb-default                                           required
 ternary-type                                character        required
 binary(x)                                   character        required
 binary(1-x)                                 character        required
 bow-conduction-band-masses                  double_array     optional
 bow-conduction-band-nonparabolicities       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_array     optional
 bow-band-gaps                               double_array     optional
 bow-static-dielectric-constants             double_array     optional
 bow-optical-dielectric-constants            double           optional
 bow-lattice-constants                       double_array     optional
 bow-elastic-constants                       double_array     optional
 bow-piezo-electric-constants                double_array     optional
 bow-abs-deformation-pot-vb                  double           optional
 bow-abs-deformation-pots-cbs                double_array     optional
 bow-uniax-vb-deformation-pots               double_array     optional
 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
 bow-band-shift                              double           optional
 band-shift                                  double           optional
$end_ternary-zb-default                                       required

Example 1

If no bowing parameters are specified, linear interpolation is done.

!--------------------------------------------------------------!
$ternary-zb-default
 ternary-type                 = Al(x)In(1-x)Sb-zb-default
 binary(x)                    = AlSb-zb-default
 binary(1-x)                  = InSb-zb-default
$end_ternary-zb-default
!--------------------------------------------------------------!

Example 2

If a bowing parameter is nonzero, bowing is used. Bowing can be quite complicated, especially if

  • valence band offset (average valence band edge energy)

  • spin-orbit splitting energy

  • band gap

are bowed simultaneously.

Note that you can use band-shift to shift the resulting band edges by the desired amount.

It is hard to find bowing parameters for a default material database that works for every alloy parameter.

!------------------------------------------------------------------------!
$ternary-zb-default
 ternary-type                 = In(x)Ga(1-x)As-zb-default
 binary(x)                    = InAs-zb-default
 binary(1-x)                  = GaAs-zb-default

 bow-conduction-band-masses   = 0.0091   0.0091   0.0091                 ! => 0.04300 [m0] (for In0.53Ga0.47As)
                                0.0      0.0      0.0                    ! no bowing for L
                                0.0      0.0      0.0                    ! no bowing for X

 bow-band-gaps                = 0.477    0.33     1.4                    ! [Vurgaftman1]
 bow-conduction-band-energies = 0.477    0.33     1.4                    ! [Vurgaftman1] for gaps. This is good (better than zero bowing).

 bow-valence-band-masses      = -0.145   -0.145   -0.145                 ! hh along [001]
                                 0.0202   0.0202   0.0202                ! lh along [001]
                                 0.0      0.0      0.0                   ! so

 bow-valence-band-energies    = -0.38                                    ! [Vurgaftman1] (valence band offset bowing) (Does this value refer to the valence band edge or to the average valence band edge?)
!bow-valence-band-energies    = -0.0511107                               ! to get a band gap of 0.816 eV (for In0.53Ga0.47As)

 bow-abs-deformation-pots-cbs = 2.61     2.61     2.61                   ! [Vurgaftman1] (Gamma) absolute deformation potentials of conduction band minima (Gamma, L, X)

 bow-Luttinger-parameters     = 11.52388599   5.191489362   5.67282216   ! [Vurgaftman1] to get original values of Alavi et al. for In0.53Ga0.47As, recommended by Vurgaftman
!bow-Luttinger-parameters     = 0.0      0.0      0.0                    ! gamma3 - gamma2 =  0.481 [Vurgaftman1]
                                0.0      0.0                             !
 bow-6x6kp-parameters         = -32.28984344 -1.140907266 -34.03693296   ! L = -28.73, M = -3.65, N = -29.04 (for In0.53Ga0.47As)
                                 0.15                                    ! Delta_so [Vurgaftman1]
 bow-8x8kp-parameters         = 0.0          -1.140907266  0.0           !
                                0.0  -1.48         3.54                  ! bowing(E_P) = -1.48 eV ([Vurgaftman1] => E_P = 25.3 eV), bowing(S) = 2 * bowing(F) = 2 * 1.77 ([Vurgaftman1])
!                               0.0  12.1678040    3.54                  ! bowing(E_P) = 12.1678040 eV (Sirtori => E_P = 21.9 eV = 21.5 * 0.53 + 28.8 * 0.47 - 0.53 * 0.47 * 12.16780409)

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

Example 3

You can define special ternaries for certain conditions, e.g. low temperature or high In content.

!--------------------------------------------------------------!
$ternary-zb-default
 ternary-type                 = Al(x)In(1-x)Sb-4K-zb-default
!ternary-type                 = Al(x)In(1-x)Sb-zb-default
 binary(x)                    = AlSb-zb-default
 binary(1-x)                  = InSb-zb-default

 ! Define here special bowing parameters for 4 K.
 ...

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

ternary-type e.g. Al(x)Ga(1-x)As-zb-default, must be a defined ternary material. This string is usually a known material. 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.

binary(x) and binary(1-x) must be a binary material of type binary-zb-default, e.g. AlSb-zb-default, must be a defined binary material. This 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.

band-shift
type:

double

presence:

optional

value:

0.0

If nonzero, the resulting ternary material is shifted by this amount (independent of the alloy-conent). So the default value should be 0.0.

bow-valence-band-energies
type:

double

presence:

optional

value:

0.0

This bowing applies to the average valence band edge energy and not to the valence band maximum.