Which material parameters are used?
Input material parameters
Example: Si
There are basically two ways to introduce a new material to the simulator. If
you need the material permanently, you can specify the parameters in the
database, whereas if you only need it for a certain calculation you can add it
to the input file. Both structures are exactly the same so that it makes no
difference for the explanation.
The example demonstrates the introduction of the zinc blende material silicon
to the database. The parameters for the material are specified in the keyword
$binary-zb-default.
In this section the parameters are explained step by step and the important
details are pointed out.
The keyword looks like the following:
!---------------------------------------------------------------------!
$binary-zb-default
binary-type
= Si-zb-default
conduction-bands
= 3
conduction-band-masses
= 0.156d0 0.156d0 0.156d0
0.130d0 0.130d0 1.420d0
0.190d0 0.190d0 0.916d0
conduction-band-degeneracies =
2 8 12
conduction-band-nonparabolicities =
0d0 0d0
0d0
conduction-band-energies
= -3.53d0 -5.28d0 -5.78d0
valence-bands
= 3
valence-band-masses
= 0.537d0 0.537d0 0.537d0
0.153d0 0.153d0 0.153d0
0.234d0 0.234d0 0.234d0
valence-band-degeneracies
= 2 2 2
valence-band-nonparabolicities =
0d0
0d0 0d0
valence-band-energies
= -6.93d0
static-dielectric-constants
= 12.93d0 12.93d0 12.93d0
optical-dielectric-constants
= 10.10d0
varshni-parametes
= 0d0 0d0
0d0
0d0 0d0 0d0
band-shift
= 0d0
absolute-deformation-potential-vb =
2.05d0
absolute-deformation-potentials-cbs = -10.4d0 -2.07d0 3.35d0
uniax-vb-deformation-potentials =
-2.33d0
-4.75d0
uniax-cb-deformation-potentials =
0d0 16.14d0
9.16d0
lattice-constants
= 0.543d0 0.543d0 0.543d0
lattice-constants-temp-coeff
= 3.88d-6 3.88d-6
3.8d-6 ! [nm/K] (GaAs value)
piezo-electric-constants
= 0d0 0d0
0d0 0d0
elastic-constants
= 16.57d0 6.393d0 7.962d0
6x6kp-parameters
= -6.69d0 -4.62d0 -8.56d0
0.044d0
8x8kp-parameters
= -6.69d0 -4.62d0 -8.56d0
0d0 0d0 1d0
number-of-minima-of-cband
= 1 4
6
conduction-band-minima
= 0d0 0d0
0d0
0.860d0 0.860d0 0.860d0
0.860d0 0.860d0 -0.86d0
-0.86d0 0.860d0 0.860d0
-0.86d0 0.860d0 -0.86d0
0d0 0d0 1d0
1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 -1d0
-1d0 0d0 0d0
0d0 -1d0 0d0
principal-axes-cb-masses
= 1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 1d0
1d0 -1d0 0d0
1d0 1d0 -2d0
1d0 1d0 1d0
1d0 -1d0 0d0
-1d0 -1d0 -2d0
1d0 1d0 -1d0
1d0 1d0 0d0
-1.00d0 1d0 -2d0
-1.00d0 1d0 1d0
1d0 1d0 0d0
1d0 -1.00d0 -2d0
-1.00d0 1d0 -1d0
1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 1d0
0d0 -1.00d0 0d0
0d0 0d0 -1d0
1d0 0d0 0d0
1d0 0d0 0d0
0d0 0d0 1d0
0d0 -1.00d0 0d0
-1.00d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 -1d0
0d0 1d0 0d0
0d0 0d0 -1d0
-1.00d0 0d0 0d0
-1.00d0 0d0 0d0
0d0 -1.00d0 0d0
number-of-minima-of-vband
= 1 1 1
valence-band-minima
= 0d0 0d0
0d0
0d0 0d0 0d0
0d0 0d0 0d0
principal-axes-vb-masses
= 1d0 0d0
0d0
0d0 1d0 0d0
0d0 0d0 1d0
1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 1d0
1d0 0d0 0d0
0d0 1d0 0d0
0d0 0d0 1d0
$end_binary-zb-default
!---------------------------------------------------------------------!
!---------------------------------------------------------------------!
$default-materials
material-name
= Si
material-model
= binary-zb-default
material-type
= Si-zb-default
1. First of all a name for the material has to be provided. This is done
by:
binary-type |
Si-zb-default |
|
Name of material |
2. Specify electronic structure of material:
In this section the band structure of the material is defined including number
of bands, number of minima, band edges and effective masses.
Conduction bands:
Number of conduction bands:
conduction-bands |
3 |
|
Number of conduction bands |
Number of nondegenerate conduction bands (minima).You are free to specify
more or less conduction bands than 3 but for the case of silicon three is
enough.
Conduction band masses:
|
1. principal axis |
2. principal axis |
3. principal axis |
|
conduction-band-masses |
0.156d0 |
0.156d0 |
0.156d0 |
1. band (Gamma) |
| Unit: [m0] (free
electron mass) |
1.420d0 |
0.130d0 |
0.130d0 |
2. band (L) |
|
0.916d0 |
0.190d0 |
0.190d0 |
3. band (X) |
The effective masses are defined in the principal axes
system of the minima (principal-axes-cb-masses). These masses are
associated to the eigenvectors of the minima in the order they are given in
the parameter set. The eigenvectors are specified by their coordinates in the
cartesian coordinate system of the crystal.
ml, mt1, mt2
Degeneracy of conduction bands:
conduction-band-degeneracies |
2 |
8 |
12 |
|
Gamma band |
L band |
X (or DELTA) band |
The degeneracy includes the number of degenerate minima per band as well as
the twofold spin-degeneracy.
Nonparabolicity parameters:
conduction-band-nonparabolicities |
0d0 |
0d0 |
0d0 |
| Unit: [1/eV] |
Gamma band |
L band |
X (or DELTA) band |
As used in a hyperbolic dispersion k^2 ~ E(1+aE). a = nonparabolicity [1/eV]
Conduction band energies:
conduction-band-energies |
-3.53d0 |
-5.28d0 |
-5.78d0 |
| Unit: [eV] |
Gamma band |
L band |
X (or DELTA) band |
The conduction band energies are the absolute energies for the band edges
within the model-solid-model.
We take the values from the paper of
Wei and Zunger for
the valence-band-energies. From this averaged value, we add the
energy gaps for Gamma, L and X respectively + 1/3 Deltaso
(split-off) as the averaged valence band energy is 1/3 Deltaso below the
valence band edge.
The conduction band energies should be given for 0 Kelvin.
Varshni parameters should be used to get the
conduction band energies for e.g. 300 K.
See FAQ for details.
Valence bands:
Number of valence bands:
valence-bands |
3 |
|
Number of valence bands |
Number of nondegenerate valence bands (minima). Within the
model-solid-model the number of valence band in zinc blende materials should
always be equal to three!
Valence band masses:
|
1st principal axis |
2nd principal axis |
3rd principal axis |
|
valence-band-masses |
0.537d0 |
0.537d0 |
0.537d0 |
1. band (heavy hole) |
| Unit: [m0] (free
electron mass) |
0.153d0 |
0.153d0 |
0.153d0 |
2. band (light hole) |
|
0.234d0 |
0.234d0 |
0.234d0 |
3. band (split-off) |
The effective masses are
defined in the principal axes system of the minima (principal-axes-vb-masses).
By default only spherical masses for the valence bands have been implemented
into the database (i.e. the masses for all principal axes are equal.)
If one
wants to include valence band warping the k.p calculation should be
used. Alternatively, the user can enter arbitrary effective-mass tensors into
the database.
Degeneracy of valence bands:
valence-band-degeneracies |
2 |
2 |
2 |
|
heavy hole |
light hole |
split-off hole |
The degeneracy include the number of degenerate minima per band as well as
the twofold spin-degeneracy.
Nonparabolicity parameters:
valence-band-nonparabolicities |
0d0 |
0d0 |
0d0 |
| Unit: [1/eV] |
heavy hole |
light hole |
split-off hole |
As used in a hyperbolic dispersion k^2 ~ E(1+aE). a = nonparabolicity [1/eV]
Valence band energies:
valence-band-energies |
-6.93d0 |
| Unit: [eV] |
average valence band energy |
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.
3. Deformation potentials:
Valence band absolute deformation potential:
absolute-deformation-potential-vb |
2.05d0 |
| Unit: [eV] |
absolute deformation potential for
average valence band energy |
Within the model-solid theory there is only one absolute deformation
potential for the average valence band edge, all other band edges result from
relative changes.
Note: In wurtzite this specifier is not used.
Conduction band absolute deformation potentials:
absolute-deformation-potentials-cbs |
-10.4d0 |
-2.07d0 |
3.35d0 |
| Unit: [eV] |
Gamma band |
L band |
X (or DELTA) band |
The absolute deformation potentials for the conduction band edges are
calculated from the band gap deformation potentials (agap) in the following
way:
agap = ac - av -> ac
= agap + av
Valence band uniaxial deformation potentials:
uniax-vb-deformation-potentials |
-2.33d0 |
-4.75d0 |
|
| Unit: [eV] |
b |
d |
|
For the valence band in zinc blende materials there are only two shear
deformation potentials b and d.
Conduction band uniaxial deformation potentials:
uniax-cb-deformation-potentials |
0d0 |
16.14d0 |
9.16d0 |
| Unit: [eV] |
Gamma band |
L band |
X (or DELTA) band |
Each conduction band has its uniaxial deformation potential which causes
degenerate minima to split. For the nondegenerate Gamma valley there is no uniaxial deformation potential.
4. Specify other material parameters:
Static dielectric constants:
static-dielectric-constants |
12.93d0 |
12.93d0 |
12.93d0 |
| Unit: [eps_0] |
[1 0 0] |
[0 1 0] |
[0 0 1] |
static-dielectric-constants = 9.28d0 9.28d0
10.01d0
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/eps2 is perpendicular to the c direction in wurtzite
low frequency dielectric constant
epsilon(0)
The static dielectric constant enters the Poisson
equation.
It is also needed to calculate the optical absorption and enters the equation
for the exciton correction.
Optical dielectric constant:
optical-dielectric-constants |
10.10d0 |
| Unit: [eps_0] |
|
Lattice constants:
lattice-constants |
0.543d0 |
0.543d0 |
0.543d0 |
Unit: [l0] (l0 is the internal
length unit specified in
$input-scaling-factors;
default is
nm) |
[1 0 0] |
[0 1 0] |
[0 0 1] |
In a cubic crystal system (like diamond and zinc blende), the lattice constants in all three crystal
axes are equal.
lattice-constants-temp-coeff |
3.88d-6 |
3.88d-6 |
3.88d-6 |
Unit: [l0/K] (l0 is the internal
length unit specified in
$input-scaling-factors;
default is
nm/K) |
[1 0 0] |
[0 1 0] |
[0 0 1] |
The lattice constant is temperature dependent. The lattice constant in the
database should be given for 300 K. For all other temperatures, the lattice
constant is calculated by the following formula:
alc = alc(300 K) + b * (T - 300)
b = lattice-constants-temp-coeff
= 3.88d-6 3.88d-6
3.8d-6 ! [nm/K] (GaAs value)
T = temperature
The temperature dependent lattice constants can be switched off. See
$numeric_control for more details.
Example: group III nitrides
AlN, GaN and InN have different thermal expansion coefficients which results in
different strain values at different temperatures. This leads to a temperature
dependent gradient of the polarization at interfaces and thus to different
fields inside the barrier.
Example: pseudomorphic AlGaN (6 %) on GaN: electric field at room temperature
330 kV/cm
at 5 K
110 kV/cm
For wurtzite nitrides one can also fit it to a polynomium of degree 4 (between
100 und 1000 K):
Y = A + B1*x + B2*x2 + B3*x3 + B4*x4
GaN: Parameter value error
------------------------------------------------------------
A -2.02944E-6 1.7902E-7
B1 4.19934E-8 1.96339E-9
B2 -9.53432E-11 6.88747E-12
B3 9.58787E-14 9.36883E-15
B4 -3.52551E-17 4.29959E-18
------------------------------------------------------------
AlN: Parameter value error
------------------------------------------------------------
A -2.31192E-6 6.68671E-8
B1 2.67408E-8 7.3336E-10
B2 -3.72491E-11 2.57259E-12
B3 2.84248E-14 3.49942E-15
B4 -9.11638E-18 1.60597E-18
------------------------------------------------------------
InN: At present difficult to specify as the material is currently revised
profoundly.
Linear interpolation is not recommended for wurtzite nitrides, e.g. AlN has a
negative expansion coefficient below 100 K.
The lattice constants are needed for the calculation of
the strain.
Elastic constants:
elastic-constants |
165.7d0 |
63.93d0 |
79.62d0 |
Unit: [prs0] (prs0 is the
internal length unit specified in
$input-scaling-factors; default
is GPa: 10^9 pa) |
C11 |
C12 |
C44 |
1 * 1011 dyn/cm2 = 10 GPa -> 11.8
* 1011 dyn/cm2
= 118 GPa
The elastic constants are needed for the calculation
of the strain in heterostructures.
Piezoelectric constants:
piezo-electric-constants |
|
|
|
|
Unit: [C/m2]
(zinc blende) |
e14 |
|
|
(1st order coefficient) |
| |
B114 |
B124 |
B156 |
(2nd order coefficients) |
Unit: [C/m2]
(wurtzite) |
e33 |
e31 |
e15 |
(1st order coefficients) |
| |
... |
|
|
(2nd order coefficients) |
For zinc blende materials there is one relevant 1st order piezoelectric constant:
e14. For silicon and germanium there is no
piezoelectric effect at all, thus the constants are zero in this case. In
wurtzite there are three 1st order piezo constants: e33, e31,
e15
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.
k.p parameters:
The k.p parameters are necessary even if no quantum mechanical
calculation is performed because the valence band energies are calculated
by diagonalizing the bulk k.p Hamiltonian. They also contain the spin-orbit
coupling paramter Deltaso.
6-band k.p parameters:
6x6kp-parameters |
-6.69d0 |
-4.62d0 |
-8.56d0 |
Unit: [kp_k^2_zb] (see
$input-scaling-factors) |
L |
M |
N |
| |
0.044d0 |
|
|
| Unit: [eV] |
Deltaso |
|
|
The 6-band k.p parameters are given in the Dresselhaus notation L, M and N in
default units of [hbar² / 2m0] The conversion from Luttinger to Dresselhaus
notation
works as follows:
Ldatabase = L 2m0/hbar2
= - gamma1 - 4 gamma2 - 1
Mdatabase = M 2m0/hbar2 =
2 gamma2 - gamma1 - 1
Ndatabase = N 2m0/hbar2 = - 6
gamma3
If the units of the L, M and N parameters are not given in the above
defined defaults units of [hbar² / 2m0], the equations for the Luttinger parameters would read:
gamma1 = - 1/3 (L+2M) 2m0/hbar2
- 1
gamma2 = - 1/6 (L-M) 2m0/hbar2
gamma3 = - 1/6 N 2m0/hbar2
Additionally to the k.p parameters the spin-orbit coupling parameter
Deltaso (split-off energy) is specified in this set.
Important: There are different definitions of the
L and M parameters available in the literature. (The
gammas are called Luttinger parameters.)
L = ( - gamma1
- 4gamma2 - 1 ) * [hbar2/(2m0)] = A
- 1
M = ( 2gamma2 - gamma1 - 1 ) * [hbar2/(2m0)]
= B - 1
N
= N =
C
alternative definition: L = ( -
gamma1 - 4gamma2 ) * [hbar2/(2m0)]
= A
M = ( 2gamma2 - gamma1
) * [hbar2/(2m0)] = B
N
= N
= C
L = F + 2G
M = H1 + H2
N = F - G + H1 - H2 = N+ + N-
N+ = N - N- ~= N - M (Here, H2
= 0 has been assumed.)
N- = M H2
= 0 has been assumed.)
Operator odering: ki (N - M) kj + kj
M ki = ki N+ kj + kj
N- ki
Bulk:
ki (N - M) kj + kj M ki = (N - M
+ M) kikj = N ki kj
8-band k.p parameters:
8x8kp-parameters |
-6.69d0 |
-4.62d0 |
-8.56d0 |
Unit: [kp_k^2_zb] (see
$input-scaling-factors) |
L' |
M'=M |
N' |
| |
0d0 |
0d0 |
1d0 |
| |
B [hbar²/2m0] |
EP [eV] |
S [-] |
The 8-band k.p parameters consist of the corrected valence band
parameters L', M'=M and N' as well as the assymetry paramter B. The coupling
between conduction and valence bands is described by the matrix element EP and
the effective mass of the electron is S.
L' = L + Ep / Egap
M' = M
N' = N + Ep / Egap
S = 1/me - Ep (Egap + 2/3
Delta_so) / [ Egap
( Egap + Delta_so) ]
For exact definition and conversion of parameters:
k.p-definiton
We have prepared an
Excel sheet that calculates the parameters for the two different options:
rescaled model: S=1 (K=0) ==>
Ep=? ==>
L', N', EP
original model (convergence problems for S < 0): Ep given
==>
S = ? ==>
L', N', EP
Note: This Excel sheet probably still uses incorrect euqations for L'
and N'. (This has to be corrected.)
Number of conduction band minima
number-of-minima-of-cband |
1 |
4 |
6 |
| |
Gamma band |
L band |
X (or DELTA) band |
The number of minima per band is taken without spin-degeneracy
Position of conduction band minima:
conduction-band-minima:
| Gamma band |
0d0 |
0d0 |
0d0 |
|
|
|
|
| L band |
0.860d0 |
0.860d0 |
0.860d0 |
|
0.860d0 |
0.860d0 |
-0.860d0 |
|
-0.860d0 |
0.860d0 |
0.860d0 |
|
-0.860d0 |
0.860d0 |
-0.860d0 |
|
|
|
|
| X band |
0d0 |
0d0 |
1d0 |
|
1d0 |
0d0 |
0d0 |
|
0d0 |
1d0 |
0d0 |
|
0d0 |
0d0 |
-1d0 |
|
-1d0 |
0d0 |
0d0 |
|
0d0 |
-1d0 |
0d0 |
The position of the minima in k-space is defined by
this specifier. The coordinates are in units of [2pi/a] within the crystal
coordinate system where a is the lattice constant.
Note: Currently it is assumed in parts of the program, that the ordering
of the conduction band minima is like
1=Gamma
2=L
3=X
Principal axes for conduction band masses:
principal-axes-cb-masses |
1d0 |
0d0 |
0d0 |
| Gamma band, 1st minimum |
0d0 |
1d0 |
0d0 |
| |
0d0 |
0d0 |
1d0 |
The principal axis for the effective mass tensor are
provided in this keyword. The units are not important because only the direction
is.
In this example only one minimum is given!
Same for valence bands
Please check the effective masses site for
more details!!
(In a bulk semiconductor, both direct and indirect energy gaps in
semiconductor materials are temperature-dependent quantities, with the
functional form often fitted to the empirical Varshni form
Eg(T) = Eg (T=0) -
a T2 / ( T + b)
where alpha and beta are adjustable (Varshni) parameters.
Although other, more physically justified and possibly quantitative accurate,
functional forms have been proposed, they have yet to gain widespread
acceptance. Consistent sets of Varshni parameters for all III-V materials were
compiled in the paper by
Vurgaftman et al.
The Varshni parameters can be switched off. See
$numeric_control for more details.
Note: In an alloy composed of two binary materials, the Varshi
parameters are not interpolated linearly. For material no. 1, the
conduction band energy is calculated taking into account the Varshni parameters
for material no. 1, then the conduction band energy for material no. 2 is
calculated taking into account the Varshni parameters for material no. 2.
Finally the conduction band energy for the ternary is calculated by
interpolating between the conduction band energies of material no 1. and no. 2
including the bowing parameter for the conduction band energy (if it is
different from zero).
How to deal with the review paper of Vurgaftman et al.
Band parameters for III–V compound
semiconductors and their alloys
I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, J.
Appl. Phys. 89 (11), 5815 (2001)
| Vurgaftman |
units |
meaning |
nextnano3 |
units |
example (GaAs) |
| alc |
Angstrom |
lattice constant |
lattice-constants |
nm |
0.565325d0 |
| |
|
|
|
|
|
| EgGamma |
eV |
band gap at Gamma point |
conduction-band-energies |
|
|
| alpha(Gamma) |
eV/K |
Varshni band gap parameters |
+1/3 Deltaso + averaged valence band |
|
0.5404d-3 |
| beta(Gamma) |
K |
Varshni band gap parameters |
edge |
|
204d0 |
| EgL |
eV |
band gap at L point |
conduction-band-energies |
|
|
| alpha(L) |
eV/K |
Varshni band gap parameters |
+1/3 Deltaso + averaged valence band |
|
0.605d-3 |
| beta(L) |
K |
Varshni band gap parameters |
edge |
|
204d0 |
| EgX |
eV |
band gap at X point |
conduction-band-energies |
|
|
| alpha(X) |
eV/K |
Varshni band gap parameters |
+1/3 Deltaso + averaged valence band |
|
0.460d-3 |
| beta(X) |
K |
Varshni band gap parameters |
edge |
|
204d0 |
| Deltaso |
eV |
split-off energy gap |
6x6kp-parameters (Deltaso, 2nd
line) |
eV |
0.341d0 |
| |
|
|
|
|
|
| m*e(Gamma) |
|
electron effective mass at Gamma point |
|
|
|
| m*l(L) |
|
longitudinal electron effective mass at L point |
|
|
|
| m*t(L) |
|
transverse electron effective mass at L point |
|
|
|
| m*DOS(L) |
|
density of states (DOS) electron effective mass at L point |
|
|
|
| m*l(X) |
|
longitudinal electron effective mass at X point |
|
|
|
| m*t(X) |
|
transverse electron effective mass at X point |
|
|
|
| m*DOS(X) |
|
density of states (DOS) electron effective mass at X point |
|
|
|
| m*SO |
|
split-off hole mass |
|
|
|
| |
|
|
|
|
|
| gamma1 |
|
Luttinger parameters (GaAs 6.98) |
6x6kp-parameters |
|
-16.22d0 -3.86d0 -17.58d0 |
| gamma2 |
|
Luttinger parameters (GaAs 2.06) |
see equation
to get L, M, N |
|
to be put in 1 line (L, M, N) |
| gamma3 |
|
Luttinger parameters (GaAs 2.93 |
(see also
Excel sheet!) |
|
0.341d0 |
| kappa |
|
see P. Lawaetz, PRB 4, 3460 (1971) |
|
|
|
| q |
|
see P. Lawaetz, PRB 4, 3460 (1971) |
|
|
|
| |
|
|
8x8kp-parameters |
|
1.4199d0 -3.86d0 0.0599d0 |
| |
|
|
(maybe rescalce Ep to get S=1) |
|
to be put in 1 line (L', M', N') |
| |
|
|
|
|
0.0d0 10.475d0 -2.876d0 |
| |
|
|
|
|
(B EP S) |
| Ep |
eV |
interband matrix element |
goes into L', M, N' of 8x8kp |
|
|
| F |
|
(interband matrix element) (1 + 2S = F) |
Kane parameter (we use S instead) |
|
|
| |
|
|
|
|
|
| VBO |
eV |
valence band offset |
|
|
|
| ac |
eV |
conduction band deformation potential |
take Zunger's values (Diploma Thesis M. Sabathil) |
|
|
| av |
eV |
valence band deformation potential |
take Zunger's values (Diploma Thesis M. Sabathil) |
|
|
| b |
eV |
shear deformation potentials |
uniax-vb-deformation-potentials |
eV |
-1.6d0 -4.6d0 (b d) |
| d |
eV |
shear deformation potentials |
uniax-vb-deformation-potentials |
eV |
b and d to be put in 1 line |
| |
|
|
|
|
|
| c11 |
GPa |
elastic constants (error
in Vurgaftman |
elastic-constants |
GPa |
122.1 |
| c12 |
GPa |
elastic constants of
factor 10! |
elastic-constants |
GPa |
56.6 |
| c44 |
GPa |
elastic constants except
nitrides) |
elastic-constants |
GPa |
60.0 |
Others
piezo-electric constants = 0.16d0 ! [C/m2]
e14 (see e.g. Landolt-Börnstein)
static-dielectric-constants = 9.28d0 9.28d0
10.01d0
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/eps2 is perpendicular to the c direction in wurtzite
low frequency dielectric constant
epsilon(0) (see e.g. Landolt-Börnstein)
optical-dielectric-constants = 10.94d0
epsilon(infinity) (see e.g. Landolt-Börnstein)
Useful internet sites showing material properties
Errata in Vurgaftman's paper
The c11, c22, c33 elastic constants are in Gdyn/cm2 rather than in GPa
for the nonnitride materials and should be divided by a factor of 10.
Fortunately, only their ratios enter most bandstructure calculations.
The F parameter for zinc-blende InN should be -2.77.
In Table XI, the Gamma-valley and X-valley gaps for zinc-blende AlN are
interchanged (although they are correct in the text), and the correct value for
the F parameter in AlN is -0.76 (rather than 0.76 in the text).
Luttinger parameter gamma3 for GaP should be 1.25 (rather than 2.93, the
value for GaAs), and the X-valley and L-valley bowing parameters for GaPSb
should be 1.7 eV instead of 2.7 eV.
In Table XXVII, the correct values for the indirect-gap bowing parameters for
GaPSb are: C(EgX)=1.7 eV and C(EgL)=1.7
eV.
The bowing factor for zinc blende GaAsN reads 20.4-100x rather than 120.4-100x
(Table XXX).
Errata/addenda will be published by the
authors once they accumulated enough of these misprints and/or new info about
some material systems (See note in reference 10 of second Vurgaftman paper (Vurgaftman2)).
How to add new specifiers for the zinc blende and wurtzite material
parameters into the database
database_nn3_keywords.val
add new specifier to zinc blende, wurtzite, bowing for zinc blende, bowing for
wurtzite
database_nn3.in
enter material parameters for new specifier to all zinc blende, wurtzite,
bowing for zinc blende, bowing for wurtzite material parameters
keywords.val
add new specifier to zinc blende, wurtzite, bowing for zinc blende,
bowing for wurtzite
MODULE mod_type_binary_zb_dflt
MODULE mod_type_ternary_zb_dflt
MODULE mod_type_binary_wz_dflt
MODULE mod_type_ternary_wz_dflt
add variable for new specifier
- Generate a new module similar to, for instance,
MODULE mod_op_dielc (optical-dielectric-constants)
MODULE module_out_in
(To output material parameters, another specifier has to be added into
keywords.val:
$output-material)
MODULE mod_default_zb_binary_models
MODULE mod_default_wz_binary_models
MODULE mod_default_zb_ternary_models
MODULE mod_default_wz_ternary_models
MODULE mod_read_zb_binary_models
MODULE mod_read_wz_binary_models
MODULE mod_read_zb_ternary_models
MODULE mod_read_wz_ternary_models
MODULE mod_read_zb_quaternary_models
| 