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.xml. This XML file can be edited by the users to modify material parameters or to add further materials.

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, …

Elements and binary compounds

<!-- binary compound -->
   <Material>

      <Name>GaAs</Name>

      <ConductionBandOffset  Unit = "eV"     >   2.979     </ConductionBandOffset>
      <ValenceBandOffset     Unit = "eV"     >   1.346     </ValenceBandOffset>

      <BandGap               Unit = "eV"     >   1.519     </BandGap>
      <BandGapAlpha          Unit = "eV/K"   >   0.5405e-3 </BandGapAlpha>
      <BandGapBeta           Unit = "K"      > 204         </BandGapBeta>

      <ElectronMass          Unit = "m0"     >   0.067     </ElectronMass>

      <EpsStatic                             >  12.93      </EpsStatic>
      <EpsOptic                              >  10.10      </EpsOptic>

      <LOPhononEnergy        Unit = "eV"     >  35e-3      </LOPhononEnergy>
      <LOPhononWidth         Unit = "eV"     >   3e-3      </LOPhononWidth>

      <DeformationPotential  Unit = "eV"     >  -9.36      </DeformationPotential>
      <MaterialDensity       Unit = "kg/m^3" >   5.3616e3  </MaterialDensity>
      <VelocityOfSound       Unit = "m/s"    >   4.73e3    </VelocityOfSound>
      <AcousticPhononEnergy  Unit = "eV"     >   5e-3      </AcousticPhononEnergy>

      <Lattice_a             Unit="nm"       >  0.56611    </Lattice_a>
      <Elastic_c11           Unit="GPa"      > 12.5        </Elastic_c11>
      <Elastic_c12           Unit="GPa"      >  5.34       </Elastic_c12>
      <Elastic_c44           Unit="GPa"      >  5.42       </Elastic_c44>
      <Piezo_e14             Unit="C/m^2"    > -0.015      </Piezo_e14>

   </Material>

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

\(T\) [K]

\(8 \cdot 10^{-45}\)

\(4\)

\(1.3 \cdot 10^{-6}\)

\(30\)

\(0.000297\)

\(50\)

\(0.017524\)

\(100\)

\(0.151055\)

\(200\)

\(0.348148\)

\(300\)

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 \(e_{14}\)

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</Name>

      <Alloy>InAs(x)</Alloy>
      <Alloy>GaAs(1-x)</Alloy>
      <ValenceBandOffset     Unit = "eV"     > -0.38  </ValenceBandOffset>
      <BandGap               Unit = "eV"     >  0.477 </BandGap>
      <BandGapAlpha          Unit = "eV/K"   >  0     </BandGapAlpha>
      <BandGapBeta           Unit = "K"      >  0     </BandGapBeta>
      <ElectronMass          Unit = "m0"     >  0.0091</ElectronMass>
      <EpsStatic                             >  0     </EpsStatic>
      <EpsOptic                              >  0     </EpsOptic>
      <DeformationPotential  Unit = "eV"     >  2.61  </DeformationPotential>
      <MaterialDensity       Unit = "kg/m^3" >  0     </MaterialDensity>
      <VelocityOfSound       Unit = "m/s"    >  0     </VelocityOfSound>
      <LOPhononEnergy        Unit = "eV"     >  0     </LOPhononEnergy>
      <LOPhononWidth         Unit = "eV"     >  0     </LOPhononWidth>
      <AcousticPhononEnergy  Unit = "eV"     >  0     </AcousticPhononEnergy>

   </Material>

Note

Currently, the Varshni parameters \(\alpha\) (BandGapAlpha) and \(\beta\) (BandGapBeta) are interpolated. It is better and more meaningful to interpolate the band gap instead.

Quaternary compounds

Quaternary compounds like \(\text{In}_{x}\text{Ga}_{y}\text{Al}_{1-x-y}\text{As}\) are implemented as follows:

<!-- quaternary compounds -->
   <Material>

      <Name>In(x)Ga(y)Al(1-x-y)As</Name>

      <Alloy>InAs(x)</Alloy>
      <Alloy>GaAs(y)</Alloy>
      <Alloy>AlAs(1-x-y)</Alloy>

   </Material>
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.