5.4. Material database¶
The material parameters for zinc blende and wurtzite materials that are used by the nextnano.MSB software are stored in a file called materials.negf.
The user can add further materials if needed.
If you run nextnano.MSB via the nextnanomat GUI, you can choose to read in a customized material database as follows:
nextnanomat ==> Tools ==> Options ==> Material database
In the database there are entries for binary compounds like GaAs, AlAs, InP, …, as well as for ternary compounds like AlGaAs, InGaAs, …
5.4.1. Elements and binary compounds¶
Note that the material database contains parameters that are not used by the nextnano.MSB code. This is because we unify the database with the nextnano.NEGF software.
# binary compound Material{ Name = GaAs CrystalStructure = Zincblende ConductionBandOffset = 2.979 # Unit = eV ValenceBandOffset = 1.346 # Unit = eV BandGap = 1.519 # Unit = eV BandGapAlpha = 0.5405e-3 # Unit = eV/K BandGapBeta = 204 # Unit = K ElectronMass = 0.067 # Unit = m0 EpsStatic = 12.93 EpsOptic = 10.89 DeformationPotential = -9.36 # Unit = eV ValenceDefPotHydro = 1.16 # Unit = eV ValenceDefPotUniaxial_b = -2.0 # Unit = eV ValenceDefPotShear_d = -4.8 # Unit = eV MaterialDensity = 5.316e3 # Unit = kg/m^3 VelocityOfSound = 4.73e3 # Unit = m/s LOPhononEnergy = 35e-3 # Unit = eV LOPhononWidth = 3e-3 # Unit = eV TOPhononEnergy = 33.86e-3 # Unit = eV AcousticPhononEnergy = 5e-3 # Unit = eV S = -2.88 Ep = 28.8 # Unit = eV kp_8_bands{ B = 7.979 L = 2.73984 M = -3.86 N = 1.37984 kappa = -1.74 } DeltaSO = 0.341 # Unit = eV Lattice_a = 0.565325 # Unit = nm Lattice_a_expansion = 3.88e-5 Elastic_c11 = 122.1 # Unit = GPa Elastic_c12 = 56.6 # Unit = GPa Elastic_c44 = 60.0 # Unit = GPa Piezo_e14 = -0.160 # Unit = C/m^2 }
ConductionBandOffset¶
- type:
double
- unit:
[eV]
Energy value that defines the position of the conduction band edges on an absolute energy scale. The zero point of energy is arbitrary. It can be used to define a conduction band offset between two different materials.
ValenceBandOffset¶
- type:
double
- unit:
[eV]
Energy value that defines the position of the average valence band edge energy \(E_{\text{v,av}}\) on an absolute energy scale. The zero point of energy is arbitrary. It can be used to define a valence band offset between two different materials.
average valence band edge energy: \(E_{\text{v,av}} = ( E_{\text{hh}} + E_{\text{lh}} + E_{\text{so}} ) / 3\)
BandGap¶
- type:
double
- unit:
[eV]
Band gap at the \(\Gamma\) point given for temperature of \(T = 0 \text{ K}\).
The code automatically calculates the temperature dependent band gap using the Varshni formula.
If the band gap is specified here for another temperature, the Varshni parameters BandGapAlpha and BandGapBeta should be set to zero.
BandGapAlpha¶
- type:
double
- unit:
[eV/K]
Varshni parameter \(\alpha\) to allow for temperature dependent band gap.
BandGapBeta¶
- type:
double
- unit:
[K]
Varshni parameter \(\beta\) to allow for temperature dependent band gap.
Note
BandGap, BandGapAlpha, BandGapBeta are not used inside the calculation.
They are just needed to output the valence band edge (which is not used either).
ElectronMass¶
- type:
double
- unit:
[m0]
Isotropic effective electron mass of the \(\Gamma\) conduction band.
EpsStatic¶
- type:
double
- unit:
[]
Static dielectric constant, low frequency dielectric constant \(\varepsilon _0\)
EpsOptic¶
- type:
double
- unit:
[]
Optical dielectric constant, high frequency dielectric constant :math:varepsilon_ infty
LOPhononEnergy¶
- type:
double
- unit:
[eV]
Longitudinal optical (LO) phonon energy \(E_\text{OP}\).
This parameter must not be set to zero as there will be a divison by zero in this case, see p. 44 of PhD thesis of Peter Greck:
\(N_\text{OP} = \frac{1}{\exp(E_\text{OP}/(k_\text{B}T)) - 1} ... = 1 / (1 - 1) = \text{NaN}\) (not a number)
\(N_\text{OP}\) is the phonon distribution and a prefactor of the equation (eq. (7.5)) where the LO phonon scattering strength is calculated, i.e. if \(N_\text{OP} \ll 1\), then the LO phonon scattering is rather small.
\(E_\text{OP} = 35 \text{ meV}\) in GaAs
\(N_\text{OP}\) for GaAs |
\(T\) |
\(8 \cdot 10^{-45}\) |
\(4\) |
\(1.3 \cdot 10^{-6}\) |
\(30\) |
\(0.000297\) |
\(50\) |
\(0.017524\) |
\(100\) |
\(0.151055\) |
\(200\) |
\(0.348148\) |
\(300\) |
LOPhononWidth¶
- type:
double
- unit:
[eV]
This is a numerical value that avoids reducing the coupling strength to a \(\delta\) function:
\(E + E_\text{OP} \rightarrow E + E_\text{OP} \pm \Delta E/2\), where \(\Delta E =\) LOPhononWidth.
Note
The following 4 variables are only relevant for acoustic phonon scattering.
DeformationPotential¶
- type:
double
- unit:
[eV]
Scalar deformation potential
It is used for acoustic phonon scattering.
MaterialDensity¶
- type:
double
- unit:
[kg/m^3]
Material density or mass density
VelocityOfSound¶
- type:
double
- unit:
[m/s]
Sound velocity
AcousticPhononEnergy¶
- type:
double
- unit:
[eV]
Acoustic phonon energy
Note
The following 5 variables are only relevant for strain calculations.
Lattice_a¶
- type:
double
- unit:
[nm]
Lattice constant \(a\)
Elastic_c11¶
- type:
double
- unit:
[GPa]
Elastic constant \(c_{11}\)
Elastic_c12¶
- type:
double
- unit:
[GPa]
Elastic constant \(c_{12}\)
Elastic_c44¶
- type:
double
- unit:
[GPa]
Elastic constant \(c_{44}\)
Piezo_e14¶
- type:
double
- unit:
[C/m^2]
Piezoelectric constant \(e_{14}\)
5.4.2. Ternary compounds¶
For ternary compounds like \(\text{Al}_{x}\text{Ga}_{1-x}\text{As}\), we have to specify bowing parameters. The material parameters in many ternary alloys (\(\text{A}_{x}\text{B}_{1-x}\text{C}\) or \(\text{CA}_{x}\text{B}_{1-x}\)) can be approximated in the form of the usual quadratic function
\(T_{\text{ABC}} = x B_{\text{AC}} + (1-x) B_{\text{BC}} - x (1-x) C_{\text{ABC}}\)
where \(C_{\text{ABC}}\) is the bowing parameter.
# ternary compound Material{ Name = "In(x)Ga(1-x)As" Binary1 = "InAs(x)" Binary2 = "GaAs(1-x)" CrystalStructure = Zincblende ConductionBandOffset = 0 # Unit = eV ValenceBandOffset = -0.38 # Unit = eV BandGap = 0.477 # Unit = eV BandGapAlpha = 0 # Unit = eV/K BandGapBeta = 0 # Unit = K DeltaSO = 0.15 # Unit = eV ElectronMass = 0.0091 # Unit = m0 EpsStatic = 0 EpsOptic = 0 S = 3.54 # Unit = eV Ep = -1.48 # Unit = eV kp_8_bands{ B = 0.0 L = 0.0 M = -1.140907266 N = 0.0 } DeformationPotential = 2.61 # Unit = eV ValenceDefPotHydro = 0 # Unit = eV ValenceDefPotUniaxial_b = 0 # Unit = eV ValenceDefPotShear_d = 0 # Unit = eV MaterialDensity = 0 # Unit = kg/m^3 VelocityOfSound = 0 # Unit = m/s LOPhononEnergy = 0 # Unit = eV LOPhononWidth = 0 # Unit = eV AcousticPhononEnergy = 0 # Unit = eV Lattice_a = 0 # Unit = nm Elastic_c11 = 0 # Unit = GPa Elastic_c12 = 0 # Unit = GPa Elastic_c44 = 0 # Unit = GPa Piezo_e14 = 0 # Unit = C/m^2 }
Note
Currently, the Varshni parameters \(\alpha\) (BandGapAlpha) and \(\beta\) (BandGapBeta) are interpolated.
It is better and more meaningful to interpolate the band gap instead.
5.4.3. Quaternary compounds¶
Quaternary compounds like \(\text{Al}_{x}\text{In}_{y}\text{Ga}_{1-x-y}\text{N}\) are implemented as:
# quaternary compounds Material{ Name = "Al(x)In(y)Ga(1-x-y)N" CrystalStructure = Wurtzite Alloy = "AlN(x);InN(y);GaN(1-x-y)" Binary1 = "AlN(x)" Binary2 = "InN(y)" Binary3 = "GaN(1-x-y)" Ternary_xy = "Al(x)In(1-x)N" Ternary_x = "Al(x)Ga(1-x)N" Ternary_y = "In(x)Ga(1-x)N" ConductionBandOffset = 0 # Unit = eV ValenceBandOffset = 0 # Unit = eV }
- Final remark
It is recommended to use position dependent material parameters, i.e. for parameters like LO phonon energy, deformation potential, sound velocity, material density and acoustic phonon energy. Obviously, the Büttiker probes \(B(x)\) depend on position. But in fact, the parameters for the wells are the most important ones. The parameters in the barriers only have a minor influence. One can include them in the calculation but the Büttiker probes in the barriers should not have any significant influence on the final result.