Bands groups in database{ …_zb{} } and database{ …_wz{} }¶

There are about 18 identicall groups available directly under all zincblende- and wurtzite-related groups. In this section we describe four of them, specifically all groups related to band paramters:

conduction_bands{}

valence_bands{}

kp_6_bands{}

kp_8_bands{}

Bands for zincblende in database{}¶

database{ …{ conduction_bands{} } } for zincblende¶

Gamma{}
material parameters for the conduction band valley at the Gamma point of the Brillouin zone:

mass
electron effective mass (isotropic, parabolic)

value:

double

unit:

m₀

This mass is used for the single-band Schrödinger equation and for the calculation of the densities.

bandgap
band gap energy at 0 K

value:

double

unit:

eV

bandgap_alpha
Varshni parameter \(\alpha\) for temperature dependent band gap

value:

double

unit:

eV/K

bandgap_beta
Varshni parameter \(\beta\) for temperature dependent band gap

value:

double

unit:

K

defpot_absolute
absolute deformation potential of the Gamma conduction band: \(a_{c, \Gamma} = a_v + a_{\Gamma}\)

value:

double

unit:

eV

g
g-factor (for Zeeman splitting in magnetic fields)

value:

double

L{}
Material parameters for the conduction band valley at the L point of the Brillouin zone

mass_l
longitudinal electron effective mass (parabolic)

value:

double

unit:

m₀

mass_t
transversal electron effective mass (parabolic)

value:

double

unit:

m₀

These masses are used for the single-band Schrödinger equation and for the calculation of the densities.

bandgap
band gap energy at 0 K

value:

double

unit:

eV

bandgab_alpha
Varshni parameter \(\alpha\) for temperature dependent band gap

value:

double

unit:

eV/K

bandgab_beta
Varshni parameter \(\beta\) for temperature dependent band gap

value:

double

unit:

K

defpot_absolute
absolute deformation potential of the L conduction band: a_{c, L} = a_v + a_{gap, L}

value:

double

unit:

eV

defpot_uniaxial
uniaxial deformation potential of the L conduction band

value:

double

unit:

eV

g_l
longitudinal g factor (for Zeeman splitting in magnetic fields)

value:

double

g_t
transversal g factor (for Zeeman splitting in magnetic fields)

value:

double

X{}
material parameters for the conduction band valley at the X point of the Brillouin zone. The options are the same as for L{}

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. The options are the same as L{}, however Delta{} has an extra paramter position:

position

value:

double

Note

At present, the value for position does not enter into any of the equations.

database{ …{ valence_bands{} } } for zincblende¶

material parameters for the valence band valley at the Gamma point of the Brillouin zone

bandoffset
average valence band energy \(E_{v,av} = (E_{hh} + E_{lh} + E_{so}) / 3\)

value:

double

unit:

eV

HH{}

mass
heavy hole effective mass (isotropic, parabolic!)

value:

double

unit:

m₀

g
g factor (for Zeeman splitting in magnetic fields)

value:

double

LH{}

mass
light hole effective mass (isotropic, parabolic!)

value:

double

unit:

m₀

g
g factor (for Zeeman splitting in magnetic fields)

value:

double

SO{}

mass
split-off hole effective mass (isotropic, parabolic!)

value:

double

unit:

m₀

g
g factor (for Zeeman splitting in magnetic fields)

value:

double

defpot_absolute
absolute deformation potential of the valence bands (average of the three valence bands: \(a_v\))

value:

double

unit:

eV

defpot_uniaxial_b
uniaxial shear deformation potential b of the valence bands

value:

double

unit:

eV

defpot_uniaxial_d
uniaxial shear deformation potential d of the valence bands

value:

double

unit:

eV

delta_SO
spin-orbit split-off energy \(\Delta_{so}\)

value:

double

unit:

eV

database{ …{ kp_6_bands{} } } for zincblende¶

gamma1
Luttinger parameter \(\gamma\)₁

value:

double

gamma2
Luttinger parameter \(\gamma\)₂

value:

double

gamma3
Luttinger parameter \(\gamma\)₃

value:

double

Note

The user can either specify the Luttinger parameters (\(\gamma\)₁, \(\gamma\)₂, \(\gamma\)₃) or the Dresselhaus parameters (L, M, N) parameters

L
Dresselhaus parameter L

value:

double

unit:

\(\hbar^2/(2m_0)\)

M
Dresselhaus parameter M

value:

double

unit:

\(\hbar^2/(2m_0)\)

N
Dresselhaus parameter N

value:

double

unit:

\(\hbar^2/(2m_0)\)

Warning

There are different definitions of the L and M parameters available in the literature. Definition used in nextnano++:

\[\mathrm{L = (-\gamma_1 - 4 \gamma_2 - 1) \cdot \left[\frac{\hbar^2}{2m_0}\right]}\]

\[\mathrm{M = (2 \gamma_2 - \gamma_1 - 1 ) \cdot \left[\frac{\hbar^2}{2m_0}\right]}\]

database{ …{ kp_8_bands{} } } for zincblende¶

S
electron effective mass parameter S for 8-band k.p. 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).

value:

double

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).

E_p
Kane’s momentum matrix element. The momentum matrix element parameter P is related to E_p: \(P^2 = \hbar^2/(2m_0) \cdot E_p\)

value:

double

unit:

eV

B
bulk inversion symmetry parameter (B=0 for diamond-type materials)

value:

double

unit:

\(\hbar^2/(2m_0)\)

gamma1
Luttinger parameter \(\gamma\)₁’

value:

double

gamma2
Luttinger parameter \(\gamma\)₂’

value:

double

gamma3
Luttinger parameter \(\gamma\)₃’

value:

double

Note

The user can either specify the modified Luttinger parameters (\(\gamma\)₁’, \(\gamma\)₂’, \(\gamma\)₃’) or the L’, M’ = M, N’ parameters.

L
Dresselhaus parameter L’

value:

double

unit:

\(\hbar^2/(2m_0)\)

M
Dresselhaus parameter M’

value:

double

unit:

\(\hbar^2/(2m_0)\)

N
Dresselhaus parameter N’

value:

double

unit:

\(\hbar^2/(2m_0)\)

Bands for Wurtzite in database{}¶

database{ …{ conduction_bands{} } } for wurtzite¶

Gamma{}
material parameters for the conduction band valley at the Gamma point of the Brillouin zone:

mass_t
electron effective mass perpendicular to hexagonal c axis (parabolic)

value:

double

unit:

m₀

mass_l
electron effective mass along hexagonal c axis (parabolic)

value:

double

unit:

m₀

This mass is used for the single-band Schrödinger equation and for the calculation of the densities.

bandgap
band gap energy at 0 K

value:

double

unit:

eV

bandgap_alpha
Varshni parameter \(\alpha\) for temperature dependent band gap

value:

double

unit:

eV/K

bandgap_beta
Varshni parameter \(\beta\) for temperature dependent band gap

value:

double

unit:

K

defpot_absolute_t
absolute deformation potential of the Gamma conduction band perpendicular to hexagonal c axis a_c,a = a₂

value:

double

unit:

eV

defpot_absolute_l
absolute deformation potential of the Gamma conduction band perpendicular along hexagonal c axis a_c,c = a₁

value:

double

unit:

eV

Note

Note that I. Vurgaftman et al., JAP 94, 3675 (2003) lists a₁ and a₂ parameters. They refer to the interband deformation potentials, i.e. to the deformation of the band gaps. Thus, we have to add the deformation potentials of the valence bands to get the deformation potentials for the conduction band edge.

\[\mathrm{a_{c,a} = a_{2} = a_{2, Vurgaftman} + D2}\]

\[\mathrm{a_{c,c} = a_{1} = a_{1, Vurgaftman} + D1}\]

g_t (optional)
g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

g_l (optical)
g factor along hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

database{ …{ valence_bands{} } } for wurtzite¶

material parameters for the valence band valley at the Gamma point of the Brillouin zone

bandoffset

value:

double

unit:

eV

average energy of the three valence band edges (S.L. Chuang, C.S. Chang, “\(\mathbf{k} \cdot \mathbf{p}\) method for strained wurtzite semiconductors”, Phys. Rev. B 54 (4), 2491 (1996)):

\[\mathrm{E_{v,av} = (E_{hh} + E_{lh} + E_{ch}) / 3 - 2/3 \cdot \mathrm{Delta_{cr}}}\]

The valence band energies for heavy hole (HH), light hole (LH) and crystal-field split-hole (CH) are calculated by defining an “average” valence band energy E_v (=E_v,av) for all three bands and adding the spin-orbit-splitting and crystal-field splitting energies afterwards. The “average” valence band energy E_v (=E_v,av) is defined on an absolute energy scale and must take into accout the valence band offsets which are “averaged” over the three holes.

Note

This energy determines the valence band offset (VBO) between two materials:

\[\mathrm{VBO_{v,av} = bandoffset_{material1} - bandoffset_{material2}}\]

HH{}

mass_t
heavy hole effective mass perpendicular to hexagonal c axis (parabolic !)

value:

double

unit:

m₀

mass_l
heavy hole effective mass along hexagonal c axis (parabolic !)

value:

double

unit:

m₀

g_t (optional)
g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

g_l (optional)
g factor along hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

LH{}

mass_t
light hole effective mass perpendicular to hexagonal c axis (parabolic !)

value:

double

unit:

m₀

mass_l
light hole effective mass along hexagonal c axis (parabolic !)

value:

double

unit:

m₀

g_t (optional)
g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

g_l (optional)
g factor along hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

SO{}

mass_t
crystal-field split-off hole effective mass perpendicular to hexagonal c axis (parabolic !)

value:

double

unit:

m₀

This mass is used for the single-band Schrödinger equation and for the calculation of the densities.

mass_l
crystal-field split-off hole effective mass along hexagonal c axis (parabolic !)

value:

double

unit:

m₀

This mass is used for the single-band Schrödinger equation and for the calculation of the densities.

g_t (optional)
g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

g_l (optional)
g factor along hexagonal c axis (for Zeeman splitting in magnetic fields)

value:

double

defpotentials
deformation potential of the valence bands: [D1, D2, D3, D4, D5, D6]

value:

vector of 6 real numbers

units:

eV

example:

[-3.7, 4.5, 8.2, -4.1, -4.0, -5.5] (for GaN)

delta
crystal-field splitting energy Delta_cr = Delta₁, spin-orbit splitting energy parameter Delta₂, spin-orbit splitting energy parameter Delta₃: [Delta₁, Delta₂, Delta₃]

value:

vector of 3 real numbers

units:

eV

example:

[0.010, 0.00567, 0.00567] (for GaN)

Very often one assumes Delta₂ = Delta₃ = 1/3 Delta_so.

database{ …{ kp_6_bands{} } } for wurtzite¶

A1
6-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A1 (Rashba-Sheka-Pikus parameter)

value:

double

A2
6-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A2 (Rashba-Sheka-Pikus parameter)

value:

double

A3
6-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A3 (Rashba-Sheka-Pikus parameter)

value:

double

A4
6-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A4 (Rashba-Sheka-Pikus parameter)

value:

double

A5
6-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A5 (Rashba-Sheka-Pikus parameter)

value:

double

A6
6-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A6 (Rashba-Sheka-Pikus parameter)

value:

double

database{ …{ kp_8_bands{} } } for wurtzite¶

S1
electron effective mass parameter S₁ = S_parallel for 8-band \(\mathbf{k} \cdot \mathbf{p}\)

value:

double

S2
electron effective mass parameter S₂ = S_{perpendicular} for 8-band \(\mathbf{k} \cdot \mathbf{p}\)

value:

double

E_P1
Kane’s momentum matrix elements E_p1 = E_{p, parallel}

value:

double

E_P2
Kane’s momentum matrix elements E_p2 = E_{p,perpendicular}

value:

double

Note

The momentum matrix element parameter P is related to E_p : P² = \(\frac{\hbar^2}{2m_0}\) E_p

B1
bulk inversion symmetry parameter B1

value:

double

B2
bulk inversion symmetry parameters B2

value:

double

B3
bulk inversion symmetry parameters B3

value:

double

A1
8-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A1’ (Rashba-Sheka-Pikus parameter)

value:

double

A2
8-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A2’ (Rashba-Sheka-Pikus parameter)

value:

double

A3
8-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A3’ (Rashba-Sheka-Pikus parameter)

value:

double

A4
8-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A4’ (Rashba-Sheka-Pikus parameter)

value:

double

A5
8-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A5’ (Rashba-Sheka-Pikus parameter)

value:

double

A6
8-band \(\mathbf{k} \cdot \mathbf{p}\) hole effective mass parameter A6’ (Rashba-Sheka-Pikus parameter)

value:

double