binary-wz-default
Wurtzite material parameters
For materials which are not known to the database and for the use of non
default values for some of the parameters of a known material.
For totally unknown materials, all parameters must be specified in the input
file. This will be required in very rare cases, however.
In most cases it is possible to use an unknown material name which can be
associated to a known material type and to change only a few parameters by this
keyword and its specifiers.
More information can be found under the keyword
binary-wz-default under the section Database.
!--------------------------------------------------------------!
$binary-wz-default
optional !
binary-type
character
required !
binary-name
character
optional !
apply-to-material-numbers
integer_array required !
!
conduction-bands
integer
optional ! total number of conduction bands
conduction-band-masses
double_array
optional ! [m0] for each band. Ordering of numbers corresponds to band
no. 1,
2, ...
conduction-band-degeneracies
integer_array optional !
including spin degeneracy
conduction-band-nonparabolicities double_array
optional ! As used in a hyperbolic
dispersion k^2 ~ E(1+aE). a = nonparabolicity (1/eV)
band-gaps
double_array
optional !
conduction-band-energies
double_array
optional !
conduction band edge energies relative to valence bands
!
valence-bands
integer
optional ! total number of
valence bands
valence-band-masses
double_array
optional ! [m0] mxx, myy,
mzz for each band (heavy, light and crystal-field split-off
hole). Ordering of numbers corresponds to band no. 1,
2, ...
valence-band-degeneracies
integer_array optional !
including spin degeneracy
valence-band-nonparabolicities
double_array
optional ! As used in a hyperbolic
dispersion k^2 ~ E(1+aE). a = nonparabolicity (1/eV)
valence-band-energies
double
optional ! "average" valence band edge energy Ev
(see comments below)
!
varshni-parameters
double_array
optional ! alpha [eV/K]
(Gamma,indirect,indirect), beta [K]
(Gamma,L,indirect,indirect)
band-shift
double
optional !
!
absolute-deformation-potential-vb double
optional ! not used in wurtzite
absolute-deformation-potentials-cbs double_array
optional
! absolute deformation potential of conduction band: ac,a(=a2) ac,a(=a2)
ac,c(=a1) [eV]
!
uniax-vb-deformation-potentials
double_array
optional ! b,d related [eV]
uniax-cb-deformation-potentials
double_array
optional ! not used in wurtzite
!
lattice-constants
double_array
optional ! [nm]
lattice-constants-temp-coeff
double_array
optional ! [nm/K]
!
elastic-constants
double_array
optional !
piezo-electric-constants
double_array
optional !
pyro-polarization
double_array
optional !
!
static-dielectric-constants
double_array
optional !
optical-dielectric-constants
double_array
optional
!
!
6x6kp-parameters
double_array
optional !
8x8kp-parameters
double_array
optional !
!
LO-phonon-energy
double_array
required ! [eV]
!
number-of-minima-of-cband
integer_array optional !
required for 'conduction-band-minima'
conduction-band-minima
double_array
optional !
and 'principal-axes-cb-masses'
principal-axes-cb-masses
double_array
optional !
!
number-of-minima-of-vband
integer_array optional !
required for 'valence-band-minima'
valence-band-minima
double_array
optional !
and 'principal-axes-vb-masses'
principal-axes-vb-masses
double_array
optional !
!
$end_binary-wz-default
optional !
!--------------------------------------------------------------!
Syntax
binary-type = character
=
GaN-wz-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
binary-name = string
To specify a name for the present new defined material.
apply-to-material-numbers = integer1
integer2 integer3
...
Apply new or partially changed material data to material numbers specified.
- Note: If you want to overwrite the parameters of a ternary, you
also have to include the associated material numbers of the ternary
here, i.e. in
$binary-wz-default.
Consider this example:
$material
material-number = 1
material-name = GaN
...
material-number = 2
material-name = In(x)Ga(1-x)N
! = 2
...
! Note that the material parameters of the ternary InGaN are
interpolated from its binary constituents InN and GaN.
material-number = 3
material-name = InN
...
$binary-wz-default
binary-type = GaN-zb-default
! apply-to-material-numbers = 1 !
1
which is GaN but not the GaN values of which the ternary
In(x)Ga(1-x)N (material #2) is calculated.
! Therefore, for material #2, the default GaN values of the database
are used and not the ones specified in the input file.
apply-to-material-numbers = 1 2
! 1
which is GaN and the GaN values of which the
ternary In(x)Ga(1-x)N (material #2)
is calculated.
...
$binary-wz-default
binary-type = InN-zb-default
! apply-to-material-numbers = 3 !
3
which is InN but not the InN values of which the ternary
In(x)Ga(1-x)N (material #2) is calculated.
!
apply-to-material-numbers = 2 3
! 3
which is InN and the InN values of which the
ternary In(x)Ga(1-x)N (material #2)
is calculated.
...
$binary-wz-default
ternary-type = In(x)Ga(1-x)N-wz-default
apply-to-material-numbers = 2
! 2 which
is InGaN.
...
conduction-bands = int
Number of nondegenerate conduction bands (minima). Most likely, only 3 is a
working number.
conduction-band-masses = m_perp m_perp
m_par !
[m0] masses at the Gamma point m_|_, m_|_, m||
(with respect to c-axis)
m4 m5 m6
! [m0]
m7 m8 m9 ! [m0]
mij are the masses in the principal axes system of the
minima. These masses are associated to the eigenvectors of the minima in the
order they are given in the parameter set.
conduction-band-degeneracies = deg1 deg2 deg3
As many degeneracy factors as mass triplets above.
number-of-minima-of-cband = deg1 deg2 deg3
number of minima (without spin degeneracy) in each set of degenerate minima.
conduction-band-minima = v11 v12 v13
v21 v22 v23
v31 v32 v33
....
k-vectors to individual conduction band minima.
As many vectors (coordinate triplets in crystal coordinate system) as individual
minima.
Let's assume we have 3 conduction band minima 1,2,3 as specified above.
These minima are deg1,deg2,deg3-fold degenerate. In this case,
input for deg1/2+deg2/2+deg3/2 vectors has to be provided. The
factor 1/2 is due to spin degeneracy which is already included in the degeneracy
factors.
Note: Currently it is assumed in parts of the program, that the ordering
of the conduction minima is like 1=Gamma
???? 2=L 3=X ????
Note:
number-of-minima-of-cband is required (!) for this specifier.
principal-axes-cb-masses = a11 a12 a13
b11 b12 b13
c11 c12 c13
....
....
....
a21 a22 a23
b21 b22 b23
c21 c22 c23
....
....
....
a31 a32 a33
b31 b32 b33
c31 c32 c33
....
....
....
Completely analog as conduction-band-minima, but this time 3 vectors
for each individual minimum. The ordering of the principal axis is associated to
the ordering of the conduction-band-masses.
Note:
number-of-minima-of-cband is required (!) for this specifier.
conduction-band-nonparabolicities = a_Gamma a_?
a_?
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 (CHECK: is this also true
for wurtzite?), and of the form
hbar2 k2 / (2 m*) = Eparabolic = Enonparabolic (1 + aEnonparabolic)
where a is given by a = (1 - m*/m0)2 / Eg.
Note that this nonparabolicity correction only influences the classically
calculated electron densities.
Quantum mechanically calculated densities are unaffected.
band-gaps = e1 e2 e3 ! [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.
conduction-band-energies = e1 e2 e3
Absolute conduction band edge energies. One number for each set of degenerate
minima.
varshni-parameters = 0.909d-3 0.0d0 0.0d0 !
alpha [eV/K](Gamma, indirect, indirect) Vurgaftman
830d0 0.0d0 0.0d0 ! beta
[K]
band-shift = double
Can be used to rigidly shift all band energies by this amount.
absolute-deformation-potential-vb = 0.0d0
! a_v [eV] - not used in wurtzite
Absolute deformation potential of valence bands.
absolute-deformation-potentials-cbs = ac,a (a axis) ac,a (a axis)
ac,c (c axis) ! [eV]
= -10.0d0 -10.0d0 -5.0d0 ! [eV]
absolute deformation potentials of Gamma conduction band minima
ac,a=a2 (a axis),
ac,a=a2 (a axis), ac,c=a1 (c
axis)
Note that I. Vurgaftman et al., JAP 94, 3675 (2003) lists
a1 and a2
parameters.
They refer to the interband deformation potentials, i.e. to the
deformation of the band gaps.
Thus we have to add the deformation potentials of the valence bands to get
the deformation potentials for the conduction band edge.
ac,a = a2
= a2 + D2
ac,c = a1
= a1 + D1
uniax-vb-deformation-potentials = -3.7d0
4.5d0 8.2d0 ! D1, D2, D3 [eV]
-4.1d0 -4.0d0 -5.5d0 ! D4, D5, D6 [eV]
Uniaxial deformation potentials of valence bands.
uniax-cb-deformation-potentials = 0d0
0d0 0d0 ! not used in wurtzite
Xi_u
lattice-constants =
0.3189d0 0.3189d0 0.5185d0
! [nm] 300 K
= a a
c
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...
elastic-constants = C11 C12 C13 C33 C44
Elastic constants C11,C12,C13,C33,C44 in [GPa] with their usual
meaning.
(C66 is not needed as it can be calculated. C66 = 0.5 * (C11
- C12).)
piezo-electric-constants = e33 e31 e15 ! [C/m^2]
e33 e31 e15
(1st order coefficients)
B311 B312 B313 B333 B115 B125 B135 B344 ! [C/m^2] B311
B312 B313 B333 B115
B125 B135 B344
(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.
For option
piezo-second-order
= 2nd-order-Tse-Pal
and
4th-order-Tse-Pal
different parameters can be specified, see
$numeric-control.
pyro-polarization = 0d0 0d0 Psp ! [C/m^2]
Components of spontaneous polarization in crystal fixed cartesian coordinate
system.
The spontaneous polarization Psp is due to the deviation of the
lattice constants a and c from their "ideal" value.
ideal: c/a=(8/3)1/2=1.633
real: c/a=1.626 (GaN)
c/a=1.601 (AlN)
c/a=1.613 (InN)
Thus the vector sum of the dipole moments does not vanish leading to a
spontaneous polarization along the c axis of the crystal (pointing from N to
Ga(Al,In) atom).
static-dielectric-constants = eps1 eps2
eps3
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 = epsu_perpendicular
epsu_perpendicular epsu_parallel
high frequency dielectric constant
epsilon(infinity); perpendicular and parallel to c axis
6x6kp-parameters = A1 A2 A3
! 6-band k.p Rashba-Sheka-Pikus
parameters
A4 A5 A6
!
Delta1 Delta2 Delta3 ! [eV]
8x8kp-parameters = A1' A2' A3'
! 8-band k.p Rashba-Sheka-Pikus
parameters
A4' A5' A6' !
B1 B2 B3
! [hbar2/(2m0)]
E_P1 E_P2 !
[eV]
S1 S2 !
[]
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)]
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
LO-phonon-energy = ELO,ph,perp ELO,ph,perp
ELO,ph,parallel ! [eV] low-temperature optical phonon energy
(perpendicular and parallel to c axis)
m_perp=1.6 , m_perp=1.6 , m_par=1.1 - http://www.ioffe.rssi.ru/SVA/NSM/Semicond/GaN/bandstr.html
valence-bands = integer
valence-band-masses = 0.370d0 0.370d0 2.090d0 !
[m0] heavy hole (HH) masses m_|_, m_|_, m||
(with respect to c-axis)
0.390d0 0.390d0 0.740d0 ! [m0]
light hole (LH) masses m_|_, m_|_, m||
(with respect to c-axis)
0.940d0 0.940d0 0.180d0 !
[m0]
valence-band-degeneracies = integer_array
valence-band-nonparabolicities =
double_array
! see comments for conduction-band-nonparabolicities
valence-band-energies =
double
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
number-of-minima-of-vband
= integer_array
valence-band-minima
= double_array !
Note:
number-of-minima-of-vband is required (!) for this specifier.
principal-axes-vb-masses
= double_array ! number-of-minima-of-vband is required (!) for this specifier.
Valence band parameters in complete analogy to conduction band parameters.
More information can be found under the keyword
binary-wz-default under the section Database.
| 