nnm:faq
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nnm:faq [2022/01/18 15:25] carola.burkl [Can I take advantage of parallelization of the nextnano software on multi-core CPUs?] |
nnm:faq [2022/01/18 16:01] carola.burkl [I don't understand the $\bf{k} \cdot \bf{p}$ parameters] |
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| - | ==== I don't understand the $\bf{k} \cdot \bf{p}$ parameters ==== | ||
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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. | ||
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| - | 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. | ||
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| - | 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 $E_{{\rm P}1}$, $E_{{\rm P}2}$. | ||
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| - | 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 $E_{{\rm P}1}$, $E_{{\rm P}2}$. | ||
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| - | Finally there is the inversion asymmetry parameter $B$ for zinc blende. For wurtzite there are $B_1$, $B_2$, $B_3$. | ||
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| - | For more details on these equations, please refer to Section //3.1 The multi-band $\bf{k} \cdot \bf{p}$ Schrödinger equation// in the [[http://www.nextnano.com/downloads/publications/PhD_thesis_Stefan_Birner_TUM_2011_WSIBook.pdf|PhD thesis of S. Birner]]. | ||
| - | |||
| - | === Spurious solutions === | ||
| - | 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 $E_{{\rm P}1}$, $E_{{\rm P}2}$. | ||
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| - | For more details, please refer to Section //3.2 Spurious solutions// in the [[http://www.nextnano.com/downloads/publications/PhD_thesis_Stefan_Birner_TUM_2011_WSIBook.pdf|PhD thesis of S. Birner]]. | ||
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| - | === Specific implementation nextnano++ === | ||
| - | See section ''kp_8band{}'' in [[http://www.nextnano.com/nextnanoplus/software_documentation/input_file/quantum.htm|quantum{}]]. | ||
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| - | === Specific implementation nextnano³ === | ||
| - | * See section //Choice of $\bf{k} \cdot \bf{p}$ parameters// in [[http://www.nextnano.com/nextnano3/input_parser/keywords/numeric-control.htm|$numeric-control]]. | ||
| - | * See section //$\bf{k} \cdot \bf{p}$ parameters// in [[http://www.nextnano.com/nextnano3/input_parser/database/docu/How-to-add-material-parameters.htm|Which material parameters are used?]]. | ||
| - | * See section //Luttinger-parameters// in [[http://www.nextnano.com/nextnano3/input_parser/keywords/binary-zb-default.htm|$binary-zb-default]]. | ||
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| - | ---- | ||
| ==== How shall I cite the nextnano software in publications? ==== | ==== How shall I cite the nextnano software in publications? ==== | ||
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