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nextnano³ software


  1D Si/SiGe MODQW




nextnano3 - Tutorial

next generation 3D nano device simulator

1D Tutorial

Si/SiGe MODQW (Modulation Doped Quantum Well)

Authors: Stefan Birner

==> - input file for the nextnano3 software
==> -
input file for the nextnano++ software

These input files are included in the latest version.

Si/SiGe MODQW (Modulation Doped Quantum Well)

This tutorial aims to reproduce Fig. 11 of
    F. Schäffler
    High-Mobility Si and Ge structures
Semiconductor Science and Technology 12, 1515 (1997)


Step 1: Layer sequence

  width [nm] material strain doping  
1   Schottky barrier 0.8 eV      
2 15.0 Si cap strained w.r.t. Si0.75Ge0.25    
3 22.5 Si0.75Ge0.25 layer      
4 15.0 Si0.75Ge0.25 doping layer   2 x 1018 cm-3 (fully ionized)  
5 10.0 Si0.75Ge0.25 barrier (spacer)      
6 18.0 Si channel strained w.r.t. Si0.75Ge0.25    
7 69.5 Si0.75Ge0.25 buffer layer      


Step 2: Material parameters

The material parameters were taken from:
    F. Schäffler
    High-Mobility Si and Ge structures
Semiconductor Science and Technology 12, 1515 (1997)

The temperature was set to 0.1 Kelvin.

The Si layers are strained pseudomorphically with respect to a Si0.75Ge0.25 substrate (buffer layer).


Step 3: 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.


Step 4: Results

  • The following figure shows the self-consistently calculated conduction band profile and the lowest wave functions of an n-type Si/Si0.75Ge0.25 modulation doped quantum well (MODQW) grown on a relaxed Si0.75Ge0.25 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.

  • The following figure shows the lowest three wave functions (psi²) of the structure. Two eigenstates that have very similar energies and are occupied (i.e. they are below the Fermi level) whereas the third eigenstate is not occupied at 0.1 K.

  • The electron density (in units of 1 x 1018 cm-3) is plotted in this figure. The lowest states in each channel are occupied, i.e. are below the Fermi level.

    The integrated electron densities are:
    - in the parasiticSi0.75Ge0.25 channel: 0.75 x 1012 cm-2
    - in the strained Si channel:        0.66 x 1012 cm-2