13. Material list

On this page, we list all the materials available in QTCAD, along with their parameter values.

This page tabulates default values for each material attribute.

More detail on the choice of attribute values (with references to the scientific literature) may be found in the code of the following module:

qtcad/src/qtcad/device/materials.py

This module is intentionally left open source for users to be able to directly access material properties and comments that substantiate values used in QTCAD.

Description of material attributes

We give a brief description of each material attribute tabulated here.

• Electron effective mass – The density-of-states effective mass, \(m_c\), used to calculate bulk electron densities in classical regions, assuming quadratic bands, in the non-linear Poisson solver.

• Exchange-correlation effective mass – The effective mass, \(m_\mathrm{xc}\), used when including an exchange-correlation correction to the confinement potential in the Schrödinger-Poisson solver.

• Hole effective mass – The effective mass, \(m_v\), for each valence band used to calculate bulk hole densities in classical regions, assuming quadratic bands, in the non-linear Poisson solver.

• Inverse effective mass tensor – The inverse effective mass tensor, \(M_e^{-1}\), used by the effective-mass Schrödinger solver for electrons. In the tables, below, we only display the diagonal entries of the inverse effective mass tensor. Indeeed, for all the materials considered here, the effective mass tensor is diagonal in the conventional unit cell.

• Total conduction band degeneracy – The total degeneracy, \(g_c\), of conduction bands (including spin) used to compute the density of states when calculating bulk electron densities in classical regions, assuming quadratic bands, in the non-linear Poisson solver.

• Total valence band degeneracy – The degeneracy, \(g_v\), of each valence band used to compute the density of states when calculating bulk hole densities in classical regions, assuming quadratic bands, in the non-linear Poisson solver.

• Total degeneracy of electrons – The total degeneracy, \(g_{q,e}\), of the quantized energy levels (including spin) used to calculate electron density quantum-mechanically in the Schrödinger-Poisson solver.

• Permittivity – The static dielectric permittivity, \(\varepsilon\). In the tables below, this quantity is expressed in units of \(\varepsilon_0\), the vacuum permittivity. The permittivity is used in linear and non-linear Poisson solvers.

• Bandgap – The bandgap, \(E_g\), of the material. The bandgap is used when setting up certain boundary conditions for the Poisson solvers, when calculating electric potential in regions occupied by classical carrier gases in the non-linear Poisson solver, and when aligning bands for Schrödinger calculations.

• Electron affinity – The electron affinity, \(\chi\), of the material. The electron affinity is used when setting up certain boundary conditions for the Poisson solvers, when calculating electric potential in regions occupied by classical carrier gases in the non-linear Poisson solver, and when aligning bands for Schrödinger calculations.

• Insulator – Whether the material is modeled as an ideal insulator or not. In an ideal insulator, the following two quantities are forced to zero in any QTCAD simulation: (i) the classical charge density in bulk carrier gases when solving non-linear Poisson, and (ii) the wave function of electrons when solving Schrödinger.

• Luttinger parameters for holes – The first three Luttinger parameters (\(\gamma_1\), \(\gamma_2\), and \(\gamma_3\)) used in the four-band Luttinger-Kohn-Foreman model [For93] considered by default by the \(\mathbf k \cdot \mathbf p\) solver.

• Spin-orbit splitting – The splitting, \(\Delta\), between the twofold degenerate spin-orbit band and the fourfold degenerate heavy-hole and light-hole bands at the \(\Gamma\) point of semiconductors with a zincblende or diamond lattice. This is the fourth Luttinger parameter used in four-band \(\mathbf k\cdot \mathbf p\) models.

• Hole Zeeman parameters – The parameters (\(\kappa\) and \(q\)) that determine the Zeeman coupling for holes. These parameters play a role analogous to \(g^\ast\) for holes.

• Effective electron g-factor – The dimensionless quantity, \(g^\ast\), that determines the Zeeman splitting of electron spins in a material as a function of magnetic field.

• Macroscopic potential difference – The energy difference, \(\Delta V\), between the macroscopic potential of the material and its value in a reference material. When aligning bands from atomistic calculations, this macroscopic potential difference is involved in the definition of the material’s reference potential \(\varphi_F\), which itself determines band offsets. Note that this parameter are currently only implemented for GaAs and \(\mathrm{Al}_{0.33}\mathrm{Ga}_{0.66}\mathrm{As}\).

• Valence band macroscopic potential – The energy difference, \(\delta E_V\), between the valence band edge and the macroscopic potential in the material. This parameter is currently only implemented for GaAs and \(\mathrm{Al}_{0.33}\mathrm{Ga}_{0.66}\mathrm{As}\).

Note about alloys

The properties of an alloy depend on its material composition, which is typically parameterized by a unitless quantity \(x\). Numerical values for these alloy attributes are typically obtained though an empirical interpolation rule between the attributes of the components of the alloy. Typical interpolation functions are coded in the materials module of QTCAD. These interpolation functions are kept open source. An alloy material may then be produced using an alloy-generating function, which is a function of \(x\) only that outputs a Material object for a given alloy.

Examples of alloy-generating function are provided for SiGe and for AlGaAs in the materials module. For these functions, we follow a naming convention in which a prefix gen_ is used, followed by the name of the alloy material (e.g., gen_SiGe). These alloy-generating functions are sampled at a single default value of \(x\) for each alloy when producing the materials table below. For example, for \(\mathrm{Si}_{1-x}\mathrm{Ge}_{x}\), the default value is \(x=0.3\), while for \(\mathrm{Al}_x\mathrm{Ga}_{1-x}\mathrm{As}\), the default value is \(x=0.33\).

Materials and their attribute tables

AlAs:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.361\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.296\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.786, 0.786, 0.163, 0.163]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([4.55, 4.55, 1.03]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(12\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(10.1\)
Bandgap	\(E_g\)	eV	Eg	\(2.24\)
Electron affinity	\(\chi\)	eV	chi	\(3.5\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([3.76, 0.82, 1.42]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.3\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(1.52\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

Al2O3:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.28\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.28\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.786, 0.786, 0.163, 0.163]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([3.57, 3.57, 3.57]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(9.0\)
Bandgap	\(E_g\)	eV	Eg	\(6.2\)
Electron affinity	\(\chi\)	eV	chi	\(1.95\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([3.76, 0.82, 1.42]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.3\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

Al2O3_ideal:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.28\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.296\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.786, 0.786, 0.163, 0.163]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(9.0\)
Bandgap	\(E_g\)	eV	Eg	\(6.2\)
Electron affinity	\(\chi\)	eV	chi	\(1.95\)
Insulator	–	–	insulator	True
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

GaAs:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.067\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.067\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.61, 0.61, 0.0821, 0.0821]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([14.9, 14.9, 14.9]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(12.9\)
Bandgap	\(E_g\)	eV	Eg	\(1.52\)
Electron affinity	\(\chi\)	eV	chi	\(4.07\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([6.98, 2.06, 2.93]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.341\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([1.2, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(-0.44\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(14.6\)

Ge:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.219\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.219\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.346, 0.346, 0.0423, 0.0423]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([12.3, 12.3, 0.621]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(8\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(16.5\)
Bandgap	\(E_g\)	eV	Eg	\(0.666\)
Electron affinity	\(\chi\)	eV	chi	\(4.0\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([13.4, 4.24, 5.69]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.296\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([3.41, 0.06]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(-3.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

HfO2:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.11\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.11\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.5\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(25.0\)
Bandgap	\(E_g\)	eV	Eg	\(5.7\)
Electron affinity	\(\chi\)	eV	chi	\(2.5\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

HfO2_ideal:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.11\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.11\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.5\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(25.0\)
Bandgap	\(E_g\)	eV	Eg	\(5.7\)
Electron affinity	\(\chi\)	eV	chi	\(2.5\)
Insulator	–	–	insulator	True
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

InAs:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.026\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.026\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.481, 0.481, 0.0264, 0.0264]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([38.5, 38.5, 38.5]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(15.2\)
Bandgap	\(E_g\)	eV	Eg	\(0.417\)
Electron affinity	\(\chi\)	eV	chi	\(4.9\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([20.0, 8.5, 9.2]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.38\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

InP:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.0795\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.0795\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.835, 0.835, 0.112, 0.112]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([12.6, 12.6, 12.6]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(12.5\)
Bandgap	\(E_g\)	eV	Eg	\(1.42\)
Electron affinity	\(\chi\)	eV	chi	\(4.38\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([5.08, 1.6, 2.1]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.11\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

InSb:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.0135\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.0135\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.405, 0.405, 0.0149, 0.0149]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([74.1, 74.1, 74.1]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(16.8\)
Bandgap	\(E_g\)	eV	Eg	\(0.235\)
Electron affinity	\(\chi\)	eV	chi	\(4.59\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([34.8, 15.5, 16.5]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.8\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([15.6, 0.39]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(-51.6\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

PbS:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.092\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.092\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.09\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([10.9, 10.9, 10.9]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(18.0\)
Bandgap	\(E_g\)	eV	Eg	\(0.41\)
Electron affinity	\(\chi\)	eV	chi	\(3.8\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

Si:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.321\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.258\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.549\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(12\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(11.8\)
Bandgap	\(E_g\)	eV	Eg	\(1.12\)
Electron affinity	\(\chi\)	eV	chi	\(4.05\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	2
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

SiC_4H:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.371\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.365\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.914\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([2.38, 2.38, 3.45]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(6\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(6.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(9.72\)
Bandgap	\(E_g\)	eV	Eg	\(3.29\)
Electron affinity	\(\chi\)	eV	chi	\(3.2\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

SiO2:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.005\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.005\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.58\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(3.9\)
Bandgap	\(E_g\)	eV	Eg	\(9.0\)
Electron affinity	\(\chi\)	eV	chi	\(0.75\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

SiO2_ideal:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.005\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.005\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.58\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(3.9\)
Bandgap	\(E_g\)	eV	Eg	\(9.0\)
Electron affinity	\(\chi\)	eV	chi	\(0.75\)
Insulator	–	–	insulator	True
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

ZrO2:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.91\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.91\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.5\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(25.0\)
Bandgap	\(E_g\)	eV	Eg	\(5.5\)
Electron affinity	\(\chi\)	eV	chi	\(2.7\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

ZrO2_ideal:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.91\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.91\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(0.5\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([5.26, 5.26, 1.09]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(25.0\)
Bandgap	\(E_g\)	eV	Eg	\(5.5\)
Electron affinity	\(\chi\)	eV	chi	\(2.7\)
Insulator	–	–	insulator	True
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

vacuum:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(1.0\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(1.0\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\(1.0\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([1.0, 1.0, 1.0]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\(2\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(1.0\)
Bandgap	\(E_g\)	eV	Eg	\(1020000.0\)
Electron affinity	\(\chi\)	eV	chi	\(0.0\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([4.28, 0.339, 1.45]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.0441\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(2.0\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

SiGe:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.291\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.247\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.442, 0.442, 0.0862, 0.0862]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([7.39, 7.39, 0.951]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(12\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(4.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(13.2\)
Bandgap	\(E_g\)	eV	Eg	\(0.977\)
Electron affinity	\(\chi\)	eV	chi	\(4.03\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([7.01, 1.51, 2.72]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.12\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([0.729, 0.025]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(0.5\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.0\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(0.0\)

AlGaAs:

Parameter	Symbol	Unit	QTCAD name	Value
Electron effective mass	\(m_c\)	\(m_e\)	mc	\(0.164\)
Exchange-correlation effective mass	\(m_\mathrm{xc}\)	\(m_e\)	mc_xc	\(0.143\)
Hole effective mass	\(m_v\)	\(m_e\)	mv	\([0.668, 0.668, 0.109, 0.109]\)
Inverse effective mass tensor	\(M_e^{-1}\)	\(m_e^{-1}\)	Me_inv	\([11.5, 11.5, 10.3]\)
Total conduction band degeneracy	\(g_c\)	–	gc	\(2\)
Total valence band degeneracy	\(g_v\)	–	gv	\([1.0, 1.0, 1.0, 1.0]\)
Total degeneracy of electrons	\(g_{q,e}\)	–	gqc	\(2.0\)
Permittivity	\(\varepsilon\)	\(\varepsilon_0\)	eps	\(12.0\)
Bandgap	\(E_g\)	eV	Eg	\(1.97\)
Electron affinity	\(\chi\)	eV	chi	\(3.88\)
Insulator	–	–	insulator	False
Luttinger parameters for holes	\(\gamma_i\)	–	hole_kp_params[0:3]	\([5.92, 1.65, 2.43]\)
Spin-orbit splitting	\(\Delta\)	eV	hole_kp_params[3]	\(0.327\)
Hole Zeeman parameters	\(\kappa\), \(q\)	–	hole_Zeeman_params	\([-0.42, 0.01]\)
Effective electron g-factor	\(g^*\)	–	g_star	\(0.207\)
Macroscopic potential difference	\(\Delta V\)	eV	macro_diff	\(0.189\)
Valence band macroscopic potential	\(\delta E_V\)	eV	vlnce_band_macro	\(14.3\)