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: 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{}
, howeverDelta{}
has an extra paramterposition
:
- 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, “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 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 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 = Sparallel for 8-band k.p
- value
double
- S2
electron effective mass parameter S2 = Sperpendicular for 8-band k.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 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