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

There are about 23 identical 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: ac, L = av + agap, 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 Ep: \(P^2 = \hbar^2/(2m_0) \cdot E_p\)

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 ac,a = a2

value:

double

unit:

eV

defpot_absolute_l

absolute deformation potential of the Gamma conduction band perpendicular along hexagonal c axis ac,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 Ev (=Ev,av) for all three bands and adding the spin-orbit-splitting and crystal-field splitting energies afterwards. The “average” valence band energy Ev (=Ev,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 Deltacr = 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 Deltaso.

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 = Sparallel for 8-band \(\mathbf{k} \cdot \mathbf{p}\)

value:

double

S2

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

value:

double

E_P1

Kane’s momentum matrix elements Ep1 = Ep, parallel

value:

double

E_P2

Kane’s momentum matrix elements Ep2 = Ep,perpendicular

value:

double

Note

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

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