# 2.4.13. 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 2.4.13.1 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 2.4.13.2 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.

The electron density (in units of 1 $$\cdot$$ 1018 cm-3) is plotted in Figure 2.4.13.3. 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.