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

Note

This section is under construction

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, “k.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 k.p hole effective mass parameter A1 (Rashba-Sheka-Pikus parameter)

value

double

A2

6-band k.p hole effective mass parameter A2 (Rashba-Sheka-Pikus parameter)

value

double

A3

6-band k.p hole effective mass parameter A3 (Rashba-Sheka-Pikus parameter)

value

double

A4

6-band k.p hole effective mass parameter A4 (Rashba-Sheka-Pikus parameter)

value

double

A5

6-band k.p hole effective mass parameter A5 (Rashba-Sheka-Pikus parameter)

value

double

A6

6-band k.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 k.p

value

double

S2

electron effective mass parameter S₂ = S_{perpendicular} for 8-band k.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 k.p hole effective mass parameter A1’ (Rashba-Sheka-Pikus parameter)

value

double

A2

8-band k.p hole effective mass parameter A2’ (Rashba-Sheka-Pikus parameter)

value

double

A3

8-band k.p hole effective mass parameter A3’ (Rashba-Sheka-Pikus parameter)

value

double

A4

8-band k.p hole effective mass parameter A4’ (Rashba-Sheka-Pikus parameter)

value

double

A5

8-band k.p hole effective mass parameter A5’ (Rashba-Sheka-Pikus parameter)

value

double

A6

8-band k.p hole effective mass parameter A6’ (Rashba-Sheka-Pikus parameter)

value

double