New documentation for FAQ https://www.nextnano.com/manual/faq/index.html

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In the literature, there are two different notations used:

• Dresselhaus–Kip–Kittel (DKK): $L$, $M$, $N^+$, $N^-$ (zinc blende); $L_1$, $L_2$, $M_1$, $M_2$, $M_3$, $N_1^+$, $N_1^-$, $N_2^+$, $N_2^-$ (wurtzite)
• Luttinger parameters: $\gamma_1$, $\gamma_2$, $\gamma_3$, $\kappa$ (zinc blende); Rashba–Sheka–Pikus (RSP) parameters $A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $A_6$, $A_7$ (wurtzite)

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

• 6-band $\bf{k} \cdot \bf{p}$ and
• 8-band $\bf{k} \cdot \bf{p}$.

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{}.

• See section Choice of $\bf{k} \cdot \bf{p}$ parameters in $numeric-control.
• See section $\bf{k} \cdot \bf{p}$ parameters in Which material parameters are used?.
• See section Luttinger-parameters in $binary-zb-default.

You can cite any of the following papers:

• nextnano: General Purpose 3-D Simulations
  S. Birner, T. Zibold, T. Andlauer, T. Kubis, M. Sabathil, A. Trellakis, P. Vogl
  IEEE Trans. Electron Dev. 54, 2137 (2007)
• The 3D nanometer device project nextnano: Concepts, methods, results
  A. Trellakis, T. Zibold, T. Andlauer, S. Birner, R. K. Smith, R. Morschl, P. Vogl
  J. Comput. Electron. 5, 285 (2006)

For simulations including electrolytes, you should cite:

• Theoretical model for the detection of charged proteins with a silicon-on-insulator sensor
  S. Birner, C. Uhl, M. Bayer, P. Vogl
  J. Phys.: Conf. Ser. 107, 012002 (2008)

For simulations that use the Contact Block Reduction method (CBR) (ballistic transport), you should cite any of the following papers:

• Efficient method for the calculation of ballistic quantum transport
  D. Mamaluy, M. Sabathil, P. Vogl
  J. Appl. Phys. 93, 4628 (2003)
• Ballistic quantum transport using the contact block reduction (CBR) method - An introduction
  S. Birner, C. Schindler, P. Greck, M. Sabathil, P. Vogl
  J. Comput. Electron. 8, 267 (2009)

nextnano.MSB software: For simulations that use the multi-scattering Büttiker (MSB) probe model (NEGF), you should cite:

• Efficient method for the calculation of dissipative quantum transport in quantum cascade lasers
  P. Greck, S. Birner, B. Huber, P. Vogl
  Optics Express 23, 6587

nextnano.QCLsoftware: For simulations that use the NEGF method, you should cite:

• Contrasting influence of charged impurities on transport and gain in terahertz quantum cascade lasers
  T. Grange
  Phys. Rev. B 92, 241306(R) (2015)

For simulations that use the NEGF algorithm included in the nextnano³ software, you should cite any of these publications:

• Modeling techniques for quantum cascade lasers
  C. Jirauschek, T. Kubis
  Appl. Phys. Rev. 1, 011307 (2014)
• Theory of non-equilibrium quantum transport and energy dissipation in terahertz quantum cascade lasers
  T. Kubis, C. Yeh, P. Vogl, A. Benz, G. Fasching, C. Deutsch
  Phys. Rev. B 79, 195323 (2009)

There might be further papers in the literature that are more suited to be cited in certain cases.