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1D Tutorial

Si/SiGe MODQW (Modulation Doped Quantum Well)

Note: This tutorial's copyright is owned by Stefan Birner, www.nextnano.de.

Authors: Stefan Birner

If you want to obtain the input files that are used within this tutorial, please contact stefan.birner@nextnano.de.
-> 1DSiGe_Si_Schaeffler_SemicondSciTechnol1997.in

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

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 Si_0.75Ge_0.25 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/Si_0.75Ge_0.25 modulation doped quantum well (MODQW) grown on a relaxed Si_0.75Ge_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.
  
  
   
• The following figure shows the lowest three wave functions (psi²) of the structure. Two eigenstates that have very similar energies 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 parasiticSi_0.75Ge_0.25 channel: 0.75 x 1012 cm-2
  - in the strained Si channel:        0.66 x 1012 cm-2
  
  
   

   

• Please help us to improve our tutorial! Send comments to support [at] nextnano.de.