Si/ SiGe MODQW (Modulation Doped Quantum Well)¶
- Input files:
1DSiGe_Si_Schaeffler_SemicondSciTechnol1997_nnpp.in
- Scope:
This tutorial aims to reproduce Fig. 11 of [Schäffler1997].
Introduction¶
Layer sequence¶
width [nm] |
material |
strain |
doping [cm-3] |
|
1 |
Schottky barrier 0.8 eV |
|||
2 |
15.0 |
Si cap |
strained w.r.t \(Si_{0.75}Ge_{25}\) |
|
3 |
22.5 |
\(Si_{0.75}Ge_{25}\) layer |
||
4 |
15.0 |
\(Si_{0.75}Ge_{25}\) doping layer |
2 \(\cdot\) 1018 (fully ionized) |
|
5 |
10.0 |
\(Si_{0.75}Ge_{25}\) barrier |
||
6 |
18.0 |
Si channel |
strained w.r.t \(Si_{0.75}Ge_{25}\) |
|
7 |
69.5 |
\(Si_{0.75}Ge_{25}\) buffer |
Material parameters¶
The material parameters were taken from [Schäffler1997]. The temperature was set to 0.1 K. The \(Si\) layers are strained pseudomorphically with respect to a \(Si_{0.75}Ge_{0.25}\) substrate (buffer layer).
Method¶
Self-consistent solution of the Schrödinger-Poisson equation within single-band effective-mass approximation (using ellipsoidal effective mass tensors) for both Delta conduction band edges.
Results¶
Figure 2.4.2.6 shows the self-consistently calculated conduction band profile and the lowest wave functions of an n-type \(Si\)/ \(Si_{0.75}Ge_{0.25}\) modulation doped quantum well (MODQW) grown on a relaxed \(Si_{0.75}Ge_{0.25}\) buffer layer. The strain lifts the sixfold degeneracy of the lowest conduction band (Delta6) and leads to a splitting into a twofold (Delta2) and a fourfold (Delta4) degenerate conduction band edge.
Figure 2.4.2.6 Calculated conduction band edge profile.¶
Figure 2.4.2.7 shows the lowest three wave functions (\(\Psi^2\)) of the structure. Two eigenstates that have very similar energies and are occupied (i.e. they are below the quasi-Fermi level), whereas the third eigenstate is not occupied at 0.1 K.
Figure 2.4.2.7 Calculated probability densities of the lowest electron states.¶
The electron density (in units of 1 \(\cdot\) 1018 cm-3) is plotted in Figure 2.4.2.8. The lowest states in each channel are occupied, i.e. are below the Fermi level. The integrated electron densities are:
in the parasitic \(Si_{0.75}Ge_{0.25}\) channel: 0.75 \(\cdot\) 1012 cm-2.
in the strained \(Si\) channel: 0.66 \(\cdot\) 1012 cm-2.
Figure 2.4.2.8 Calculated electron density profile.¶