Electronic band structure¶
Attention
This page is under construction.
Definition of band offsets¶
The definition is identical to nextnano++, see Figure 2.3.1. The database contains the values \(E_\mathrm{c}^\Gamma, E_\mathrm{v,av}, \Delta_\mathrm{so}\) and the band gap parameters \(E_\mathrm{g}^\Gamma(T=0), \alpha, \beta\). The choice UseConductionBandOffset results in different temperature dependence of the heterostructure band offsets via the Varshni formula described in temperature_dependent_bandgap.
Note
The band offsets get an additional shift if strain is present.
Single-band model¶
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2-band model¶
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3-band model¶
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8-band model¶
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Output of effective mass in the multiband case¶
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Rescaling of \(\mathbf{k} \cdot \mathbf{p}\) parameters (for multiband)¶
When diagonalizing the \(\mathbf{k} \cdot \mathbf{p}\) Hamiltonian for a given wave vector, if the coefficient \(S(L+1)\) of \(k^4\) in the secular equation is positive, two different \(k\) may correspond to the same eigenenergy. One is the expected correct solution, but the other is an oscillatory solution with a large \(k\), and a smooth wave function may not be obtained. To prevent this, the Material{ RescaleS } option rescales \(S\) to 0 (per default) while maintaining the effective mass of the conduction band.
The effect of rescaling on \(S\) and \(E_P\) is the following:
while the effective mass at bandedge is conserved.
while for 3 bands it corresponds to:
Smoothing of the \(\mathbf{k} \cdot \mathbf{p}\) parameters (for multiband)¶
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Last update: 30/10/2024