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In the literature, there are two different notations used:
They are equivalent and can be converted into each other.
Some authors only use 3 parameters $L$, $M$, $N$ (or $\gamma_1$, $\gamma_2$, $\gamma_3$) which is fine for bulk semiconductors without magnetic field but not for heterostructures because the latter require 4 parameters, i.e. $N^+$, $N^-$ (instead of $N$ only) or $\kappa$. If these parameters are not known, they can be approximated.
There are different $\bf{k} \cdot \bf{p}$ parameters for
The 8-band $\bf{k} \cdot \bf{p}$ parameters can be calculated from the 6-band parameters taking into account the temperature dependent band gap $E_{\rm gap}$ and the Kane parameter $E_{\rm P}$ (zinc blende). For wurtzite the parameters are $E_{\rm gap}$ and the Kane parameters $E_{{\rm P}1}$, $E_{{\rm P}2}$.
The 8-band Hamiltonian also needs the conduction band mass parameter $S$ (zinc blende) or $S_1$, $S_2$ (wurtzite). They can be calculated from the conduction band effective mass $m_{\rm c}$, the band gap $E_{\rm gap}$, the spin-orbit split-off energy $\Delta_{\rm so}$ and the Kane parameter $E_{\rm P}$ (zinc blende). For wurtzite the parameters are $m_{{\rm c},\parallel}$, $m_{{\rm c},\perp}$, $E_{\rm gap}$, $\Delta_{\rm so}$, the crystal-field split-off energy $\Delta_{\rm cr}$ and the Kane parameters $E_{{\rm P}1}$, $E_{{\rm P}2}$.
Finally there is the inversion asymmetry parameter $B$ for zinc blende. For wurtzite there are $B_1$, $B_2$, $B_3$.
For more details on these equations, please refer to Section 3.1 The multi-band $\bf{k} \cdot \bf{p}$ Schrödinger equation in the PhD thesis of S. Birner.
Some people rescale the 8-band $\bf{k} \cdot \bf{p}$ in order to avoid spurious solutions. The 8-band $\bf{k} \cdot \bf{p}$ parameters can be calculated from the 6-band parameters taking into account the band gap $E_{\rm gap}$, the spin-orbit split-off energy $\Delta_{\rm so}$ and the Kane parameter $E_{\rm P}$ (zinc blende). For wurtzite the parameters are $E_{\rm gap}$, the spin-orbit split-off energy $\Delta_{\rm so}$, the crystal-field split-off energy $\Delta_{\rm cr}$ and the Kane parameters $E_{{\rm P}1}$, $E_{{\rm P}2}$.
For more details, please refer to Section 3.2 Spurious solutions in the PhD thesis of S. Birner.
See section kp_8band{}
in quantum{}.
You can cite any of the following papers:
For simulations including electrolytes, you should cite:
For simulations that use the Contact Block Reduction method (CBR) (ballistic transport), you should cite any of the following papers:
nextnano.MSB software: For simulations that use the multi-scattering Büttiker (MSB) probe model (NEGF), you should cite:
nextnano.QCLsoftware: For simulations that use the NEGF method, you should cite:
For simulations that use the NEGF algorithm included in the nextnano³ software, you should cite any of these publications:
There might be further papers in the literature that are more suited to be cited in certain cases.