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]
0d0 0d0 0d0 ! [m0]
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]
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 "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
!
0d0 0d0 0d0
! Delta1 Delta2 Delta3
[eV]
bow-8x8kp-parameters = 0d0 0d0
0d0 !
0d0 0d0 0d0
!
0d0 0d0 0d0
! B1 B2 B3 [hbar2/(2m0)]
0d0 0d0
! EP1 EP2 [eV]
0d0 0d0
! S1 S2 []
bow-6x6kp-parameters = A1 A2 A3
!
A4 A5 A6
!
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' !
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: [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 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
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