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 Si0.75 Ge0.25
3	22.5	Si0.75 Ge0.25 layer
4	15.0	Si0.75 Ge0.25 doping layer		2 $\cdot$ 1018 (fully ionized)
5	10.0	Si0.75 Ge0.25 barrier
6	18.0	Si channel	strained w.r.t Si0.75 Ge0.25
7	69.5	Si0.75 Ge0.25 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 2.4.130 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 2.4.130 Calculated conduction band edge profile.

Figure 2.4.131 shows the lowest three wave functions (${\mathrm{\Psi }}^2$) 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 2.4.131 Calculated probability densities of the lowest electron states.

The electron density (in units of 1 $\cdot$ 10¹⁸ cm^-3) is plotted in Figure 2.4.132. 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 2.4.132 Calculated electron density profile.

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