Database for zincblende and diamond-type materials
(cubic crystal structure)
=> ../Syntax/database_nnp.in
Group IV, III-V, II-VI, I-VII materials
binary_zb {
name = GaAs
# material name, e.g. Si,
GaAs, InP, ...
valence = III_V
# IV_IV for group IV materials (like Si, Ge,
SiC, ...)
# III_V for III-V materials
(like GaAs, AlP, ...)
# II_VI for II-VI materials (like ZnO, HgTe,
...)
# I_VII for I-VII materials (like CuCl, ...)
lattice_consts{
a =
5.65325 # [Angstrom] lattice constant at 300
K
#
a_expansion = 3.88e-5
# [Angstrom/K] The lattice constants are temperature dependent => a(T).
# The lattice constant a in the
database should be given for 300 K.
# For all other temperatures, the lattice
constant is calculated by the following formula
# where T is the temperatue in units of [K]:
# a(T) = a(300 K) + a_expansion * (T - 300 K)
# The lattice constants are needed for the
calculation of the strain.
}
dielectric_consts{
static_a = 12.93
# [-] static or low frequency (epsilon(omega=0)) dielectric
constant
optical_a = 10.10 #
[-]
#
# 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.
}
elastic_consts{
c11 = 122.1
# [GPa] elastic constants
c12 = 56.6
# -> 12.21
* 1011 dyn/cm2
= 122.1 GPa
c44 = 60.0
#
}
piezoelectric_consts{
e14 = -0.160 # [C/m2] piezoelectric constants
#
#
B114 = -0.439
# [C/m2] 2nd order piezoelectric constant (optional)
B124 = -3.765
# [C/m2] 2nd order piezoelectric constant (optional)
B156 = -0.492
# [C/m2] 2nd order piezoelectric constant (optional)
}
conduction_bands{
Gamma{
# material parameters for the conduction band valley at the Gamma point
of the Brillouin zone
mass
= 0.067 # [m0]
#
bandgap =
1.519 # [eV]
bandgap_alpha = 0.5405e-3
# [eV/K] alpha for temperature dependent
band gap
bandgap_beta = 204
# [K] beta for
temperature dependent band gap
defpot_absolute = -9.36
# [eV] ac,Gamma = av + agap,Gamma
g
= -0.30
# [] g factor (for Zeeman splitting in
magnetic fields)
}
L{
#
mass_l =
1.9 # [m0]
mass_t =
0.0754 # [m0]
#
bandgap =
1.815 # [eV]
bandgap_alpha = 0.605e-3
# [eV/K] alpha for temperature dependent
band gap
bandgap_beta = 204
# [K] beta for
temperature dependent band gap
defpot_absolute = -4.91
# [eV] ac,L
= av + agap,L
defpot_uniaxial = 6.5
# [eV] uniaxial deformation potential of the L conduction band
g_l
= 0
# []
g_t
= 0
# []
}
X{
#
mass_l =
1.3 # [m0]
mass_t =
0.23 # [m0]
#
bandgap =
1.981 # [eV]
bandgap_alpha = 0.460e-3
# [eV/K] alpha for temperature dependent
band gap
bandgap_beta = 204
# [K] beta for
temperature dependent band gap
defpot_absolute = -0.16
# [eV] ac,X
= av + agap,X
defpot_uniaxial = 14.26
# [eV] uniaxial deformation potential of the X conduction band
g_l
= 0
# []
g_t
= 0
# []
}
}
valence_bands{
# material parameters for the valence band valley at the Gamma point of
the Brillouin zone
bandoffset = 1.346
#
Ev,av = (Ehh + Elh + Eso) / 3
#
Note: This energy determines the valence band offset (VBO) between two
materials
#
(with respect to the
average of the three valence band edges!)
#
VBOv,av =
bandoffset(material1) - bandoffset(material2)
HH{ mass = 0.5
# [m0]
heavy hole effective mass (isotropic, parabolic !)
g = 0
} # []
LH{ mass = 0.068 # [m0]
g = 0
}
# []
SO{ mass = 0.172 # [m0]
g = 0
}
# []
#
defpot_absolute = -1.21
# [eV] av
defpot_uniaxial_b = -2.0
# [eV] uniaxial shear deformation potential b of the valence
bands
defpot_uniaxial_d = -4.8
# [eV] uniaxial shear deformation potential d of the valence
bands
delta_SO =
0.341 # [eV] Deltaso
}
kp_6_bands{
# Note: The user can either specify the Luttinger
parameters (gamma1, gamma2, gamma3)
#
gamma1 = 6.98
# [] gamma1
gamma2 = 2.06
# [] Luttinger parameter gamma2
gamma3 = 2.93
# [] Luttinger parameter gamma3
or
L = -16.22
# [hbar2/(2m0)] L
M = -3.86
# [hbar2/(2m0)] Dresselhaus
parameter M
N = -17.58
# [hbar2/(2m0)] Dresselhaus
parameter N
}
Important: There are different definitions of the
L and M parameters available in the literature.
L = ( - gamma1
- 4gamma2 - 1 ) * [hbar2/(2m0)]
M = ( 2gamma2 - gamma1 - 1 ) * [hbar2/(2m0)]
alternative definition: L = ( -
gamma1 - 4gamma2 ) * [hbar2/(2m0)]
M = ( 2gamma2 - gamma1
) * [hbar2/(2m0)]
kp_8_bands{
# Note: The user can either specify the modified Luttinger
parameters (gamma1', gamma2', gamma3')
# or the L', M' = M, N' parameters.
S = -2.876
# [-] S for 8-band
k.p
E_P = 28.8
# [eV]
# P is related
to Ep: P2
= hbar2/(2m0) Ep
# The units of P are
[eV Angstrom].
B = 0
# [hbar2/(2m0)] bulk inversion
symmetry parameter (B=0 for
diamond-type materials)
gamma1 = ...
# [] gamma1'
gamma2 = ...
# [] Luttinger parameter gamma2'
gamma3 = ...
# [] Luttinger parameter gamma3'
or
L = 1.420
# [hbar2/(2m0)] L'
M = -3.86
# [hbar2/(2m0)] Dresselhaus
parameter M (same value as 6-band k.p
parameter)
N = 0.056
# [hbar2/(2m0)] N'
}
Note: The S
parameter (S = 1 + 2F) is also defined in the literature as F
where F = (S - 1)/2, e.g. I. Vurgaftman et al., JAP 89,
5815 (2001).
mobility_constant{...}
#
mobility_masetti{...}
#
mobility_arora{...}
#
mobility_minimos{...}
#
mobility_simba{...}
#
recombination{
SRH
{...}
#
Auger {...}
#
radiative{...}
#
}
}
The deformation potentials are only used if strain is
present. They enter the k.p equations. If the single-band approximation
is used, the deformation potentials are used to shift and split the conduction
and valence band edges.
The g factors (g, g_l, g_t)
are optional. If the g factors are specified in the input file, the database
value for the g factors are overwritten with the value in the input file. If no
g factors are present in the input file or in the database, a g factor of 2 is
assumed by default.
Note: In Si, Ge and GaP we have a
Delta valley instead of the X conduction band valley:
Delta{
# material parameters for the conduction band valley at the X point of
the Brillouin zone
mass_l =
0.916 # [m0]
mass_t =
0.190 # [m0]
#
bandgap =
1.17 # [eV]
bandgap_alpha = 0.4730e-3
# [eV/K] alpha for temperature dependent
band gap
bandgap_beta = 636
# [K] beta for
temperature dependent band gap
defpot_absolute = 3.40
# [eV] ac,Delta
= av + agap,Delta
defpot_uniaxial = 9.16
# [eV] uniaxial deformation potential of the X conduction band
position =
0.85 #
0.85 Delta
instead of 1.0 for X
valley
#
g_l
= 0
# []
g_t
= 0
# []
}
}
Three options are possible for the interpolation of binary material
parameters in ternary alloys (AxB1-xC
or CAxB1-x):
- TABC = x BAC + (1
-x) BBC
(linear interpolation)
For the lattice constants, this is called "Vegard's law".
- TABC = x BAC + (1
-x) BBC
- x (1-x) CABC (quadratic
interpolation) where CABC is the bowing parameter
For CABC
= 0 (which is the default), linear interpolation is used.
(In eq. (E.3) in the PhD thesis of T. Zibold the last term includes a '+'
sign instead of the '-' sign, i.e. + x (1-x) CABC
instead of - x (1-x) CABC.)
- TABC = x BAC + (1
-x) BBC
- x (1-x) CABC(x) (cubic interpolation)
Note that here the bowing parameter CABC is a function
of the alloy composition x.
Examples:
######### indium gallium arsenide (InGaAs) ############################
ternary_zb {
name =
"In(x)Ga(1-x)As"
valence = III_V
binary_x = InAs
binary_1_x = GaAs
conduction_bands{
Gamma{ mass = 0.0091
} # Bowing parameter CABC for the electron
effective mass at the Gamma point in units of [m0].
}
...
kp_8_bands{
S = 3.54
# S = 1 + 2F = 2 * 1.77
# S
parameter (S = 1 + 2F) is also defined in the literature as F
where F = (S - 1)/2, e.g. I. Vurgaftman et al., JAP 89,
5815 (2001).
#
S
has the value 2 * F.
# In(x)Ga(1-x)As
Vurgaftman lists the bowing parameter F = 1.77.
...
}
} : {
#
name =
"Ga(1-x)In(x)As"
#
valence = III_V
binary_x = InAs
binary_1_x = GaAs
} : {
name =
"Ga(x)In(1-x)As"
#
valence = III_V
binary_x = GaAs
binary_1_x = InAs
} : {
name =
"In(1-x)Ga(x)As"
#
valence = III_V
binary_x = GaAs
binary_1_x = InAs
}
Special case: Bowing parameter depends on alloy concentration x
Note: To describe the band gap bowing at the Gamma point in AlxGa1-xAs,
a linear or even a quadratic interpolation is not sufficient.
Here, the bowing parameter is not constant, it depends on the alloy composition
x.
Thus, this bowing parameter is given by: CABC(x)
= -0.127 + 1.310 * x
(Table XII., I. Vurgaftman et al., J. Appl. Phys. 89, 5815 (2001))
In order to describe such a material, we introduced a new type of material:
ternary2_zb
For
ternary2_zb, bowing is not symmetric in x and 1-x.
The nextnano++ implementation is the following: Use
ternary2_zb{} (and
bowing_zb{}) instead of
ternary_zb{}.
######### aluminum gallium arsenide (AlGaAs) ##########################
ternary2_zb{
name =
"Al(x)Ga(1-x)As"
# AlxGa1-xAs
valence = III_V
binary_x = AlAs
binary_1_x = GaAs
bowing_x = AlGaAs_Bowing_Ga
# x=1
bowing_1_x = AlGaAs_Bowing_Al
# Bowing parameter CABC(x) for x=0
}
bowing_zb{
name =
"AlGaAs_Bowing_Ga" #
AlxGa1-xAs (x=1)
valence = III_V
conduction_bands{
Gamma{ bandgap =
-0.127 + 1.310 * 1 } # x=1)
= -0.127 + 1.310 * x = 1.183
L { bandgap =
0
} # Bowing parameter CABC
X { bandgap =
0.055
} #
}
valence_bands{
delta_SO = 0
#
}
}
bowing_zb{
name =
"AlGaAs_Bowing_Al" # x=0)
valence = III_V
conduction_bands{
Gamma{ bandgap =
-0.127 + 1.310 * 0 } # x=0)
= -0.127 + 1.310 * x = -0.127
L { bandgap =
0
} # Bowing parameter CABC
X { bandgap =
0.055
} #
}
valence_bands{
delta_SO = 0
#
}
}
bowing_zb,
linear interpolation for
ternary2_zb is assumed.
The same (i.e.
ternary2_zb) is also used for the band gap at the Gamma point of AlxGa1-xSb
and to the diluted nitrid material GaAs1-xNx.
Example
In our database AlxGa1-xAs
is considered a
ternary2_zb because its bowing parameter CABC(x)
for the bandgap at the Gamma point depends on the alloy composition x
by the formula:CABC(x)
= -0.127 + 1.310 * x
(Table XII., I. Vurgaftman et al., J. Appl. Phys. 89, 5815 (2001))
CABC(x)where CABC(0)and CABC(1)For this reason, for describing the
bandgap bowing parameter for this material we require to specify
in the
AlGaAs_Bowing_Ga
block the value of
AlGaAs_Bowing_GaCABC(1)
+ β
-0.127 + 1.310 = 1.183 #
Bowing parameter CABC(x) for x=1and for
AlGaAs_Bowing_Al
AlGaAs_Bowing_AlCABC(0)
=
-0.127 # Bowing parameter CABC(x) for x=1
Then, the final result for the bandgap is:AlxGa1-xAs
=
Bandgap(AlAs)(GaAs)CABC(x)
=(GaAs)
AlGaAs_Bowing_Ga
AlGaAs_Bowing_Al
=
Alternative: An easier and much more intuitive solution would be to overwrite
the respective bowing material parameter in the input file by defining a formula
which uses the alloy concentration as a variable.
This is meanwhile possible. (To do: Add a tutorial on this topic.)
Material parameters in quaternary materials: Interpolation of binary material
parameters including the bowing parameters that are used for the ternary
constituents
A brief introduction to quaternaries is shown in this Powerpoint presentation
(Quaternaries.pptx,
Quaternaries.pdf).
Three different quaternaries can be constructed where a) and c) are basically
identical from an algorithmic point of view:
a) AxByC1-x-yD,
e.g. AlxGayIn1-x-yAs
(III-III-III-V quaternaries)
b) ABxCyD1-x-y,
e.g. AlAsxSbyP1-x-y
(III-V-V-V quaternaries)
c) AxB1-xCyD1-y,
e.g. GaxIn1-xAsyP1-y
(III-III-V-V quaternaries)
Three options are possible for the interpolation of binary material
parameters in quaternary alloys (AxB1-xC
or CAxB1-x):
- c) QABCD = x y BAC + (1-x)
y BBC + (1-x)
(1-y) BBD + x (1-y) BAD +
(linear interpolation)
+ x (1-x) y CABC +
(1-x) y (1-y) CBCD + x (1-x)
(1-y) CABD + x y (1-y) CACD
The second line introduces a quadratic
interpolation where CABC, CABD, CBCD
are the bowing parameters of the ternary constituents.
For CABC
= CABD = CACD = 0 (which is the default), linear interpolation is used.
Constituent limiting binaries and ternaries are defined by
the following constraints:
binary1: x = 1, y = 1
binary2: x = 0, y = 1
binary3: x = 0, y = 0
binary4: x = 1, y = 0
ternary12: y = 1
ternary23: x = 0
ternary34: y = 0
ternary14: x = 1
Example:
######### indium aluminum arsenide antimonide (InAlAsSb) ##############
quaternary4_zb {
name =
"In(x)Al(1-x)As(y)Sb(1-y)"
valence =
III_V
binary1 =
InAs
#
binary2 = AlAs
#
binary3 = AlSb
#
binary4 = InSb
#
ternary12 = "In(x)Al(1-x)As"
# Note: In(x)Al(1-x)As
and
In(1-x)Al(x)As are equivalent
ternary23 =
"AlAs(x)Sb(1-x)" #
ternary34 =
"Al(x)In(1-x)Sb" #
ternary14 =
"InAs(x)Sb(1-x)"
}
Quinternaries
########################### QUINTERNARY ZINCBLENDE #######################
# alloys of
the type A(x)B(y)C(z)D(1-x-y)
quinternary_zb : _alloy_zb{ TYPE=group OPT=1
binary_a{
TYPE=string } # A
binary_b{
TYPE=string } # B
binary_c{
TYPE=string } # C
binary_d{
TYPE=string } # D
ternary_ab{ TYPE=string } # A(x)B(1-x)
ternary_ac{ TYPE=string } # A(x)C(1-x)
ternary_ad{ TYPE=string } # A(x)D(1-x)
ternary_bc{ TYPE=string } # B(x)C(1-x)
ternary_bd{ TYPE=string } # B(x)D(1-x)
ternary_cd{ TYPE=string } # C(x)D(1-x)
quaternary_abc{ TYPE=string } # A(x)B(y)C(1-x-y)
quaternary_abd{ TYPE=string } # A(x)B(y)D(1-x-y)
quaternary_acd{ TYPE=string } # A(x)C(y)D(1-x-y)
quaternary_bcd{ TYPE=string } # B(x)C(y)D(1-x-y)
# from
base group, optional quinternary bowing parameters
}
# alloys of
the type A(x)B(y)C(1-x-y)D(z)E(1-z)
quinternary6_zb : _alloy_zb{ TYPE=group OPT=1
binary_a_d{ TYPE=string } # AD
binary_b_d{ TYPE=string } # BD
binary_c_d{ TYPE=string } # CD
binary_a_e{ TYPE=string } # AE
binary_b_e{ TYPE=string } # BE
binary_c_e{ TYPE=string } # CE
ternary_ab_d{ TYPE=string } # A(x)B(1-x)D
ternary_ac_d{ TYPE=string } # A(x)C(1-x)D
ternary_bc_d{ TYPE=string } # B(x)C(1-x)D
ternary_ab_e{ TYPE=string } # A(x)B(1-x)E
ternary_ac_e{ TYPE=string } # A(x)C(1-x)E
ternary_bc_e{ TYPE=string } # B(x)C(1-x)E
ternary_a_de{ TYPE=string } # AD(x)E(1-x)
ternary_b_de{ TYPE=string } # BD(x)E(1-x)
ternary_c_de{ TYPE=string } # CD(x)E(1-x)
quaternary_abc_d{ TYPE=string } # A(x)B(y)C(1-x-y)D
quaternary_abc_e{ TYPE=string } # A(x)B(y)C(1-x-y)E
quaternary_ab_de{ TYPE=string } # A(x)B(1-x)D(y)E(1-y)
quaternary_ac_de{ TYPE=string } # A(x)C(1-x)D(y)E(1-y)
quaternary_bc_de{ TYPE=string } # B(x)C(1-x)D(y)E(1-y)
# from
base group, optional quinternary bowing parameters
}
#
two-parameter alloys A(x)B(1-x)C(y)D(1-y)E(z)F(1-z)
quaternary8_zb : _alloy_zb{ TYPE=group OPT=1
binary_a_c_e{ TYPE=string } # ACE
binary_b_c_e{ TYPE=string } # BCE
binary_a_d_e{ TYPE=string } # ADE
binary_b_d_e{ TYPE=string } # BDE
binary_a_c_f{ TYPE=string } # ACF
binary_b_c_f{ TYPE=string } # BCF
binary_a_d_f{ TYPE=string } # ADF
binary_b_d_f{ TYPE=string } # BDF
ternary_ab_c_e{ TYPE=string } # A(x)B(1-x)CE
ternary_ab_d_e{ TYPE=string } # A(x)B(1-x)DE
ternary_ab_c_f{ TYPE=string } # A(x)B(1-x)CF
ternary_ab_d_f{ TYPE=string } # A(x)B(1-x)DF
ternary_a_cd_e{ TYPE=string } # AC(x)D(1-x)E
ternary_b_cd_e{ TYPE=string } # BC(x)D(1-x)E
ternary_a_cd_f{ TYPE=string } # AC(x)D(1-x)F
ternary_b_cd_f{ TYPE=string } # BC(x)D(1-x)F
ternary_a_c_ef{ TYPE=string } # ACE(x)F(1-x)
ternary_b_c_ef{ TYPE=string } # BCE(x)F(1-x)
ternary_a_d_ef{ TYPE=string } # ADE(x)F(1-x)
ternary_b_d_ef{ TYPE=string } # BDE(x)F(1-x)
quarternary_ab_cd_e{ TYPE=string } # A(x)B(1-x)C(y)D(1-y)E
quarternary_ab_cd_f{ TYPE=string } # A(x)B(1-x)C(y)D(1-y)F
quarternary_ab_c_ef{ TYPE=string } # A(x)B(1-x)CE(y)F(1-y)
quarternary_ab_d_ef{ TYPE=string } # A(x)B(1-x)DE(y)F(1-y)
quarternary_a_cd_ef{ TYPE=string } # AC(x)D(1-x)E(y)F(1-y)
quarternary_b_cd_ef{ TYPE=string } # BC(x)D(1-x)E(y)F(1-y)
# from
base group, optional quinternary bowing parameters
}
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