nextnano^{3}  Tutorial
next generation 3D nano device simulator
1D Tutorial
Si/SiGe MODQW (Modulation Doped Quantum Well)
Authors:
Stefan Birner
==> 1DSiGe_Si_Schaeffler_SemicondSciTechnol1997_nn3.in
 input file for the nextnano^{3} software
==> 1DSiGe_Si_Schaeffler_SemicondSciTechnol1997_nnp.in  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
HighMobility 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. Si_{0.75}Ge_{0.25} 


3 
22.5 
Si_{0.75}Ge_{0.25} layer 



4 
15.0 
Si_{0.75}Ge_{0.25} doping layer 

2 x 10^{18} cm^{3} (fully ionized) 

5 
10.0 
Si_{0.75}Ge_{0.25} barrier (spacer) 



6 
18.0 
Si channel 
strained w.r.t. Si_{0.75}Ge_{0.25} 


7 
69.5 
Si_{0.75}Ge_{0.25} buffer layer 









Step 2: Material parameters
The material parameters were taken from:
F. Schäffler
HighMobility 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_{0.75}Ge_{0.25}
substrate (buffer layer).
Step 3: Method
Selfconsistent solution of the SchrödingerPoisson equation within singleband
effectivemass approximation (using ellipsoidal effective mass tensors) for both
Delta conduction band edges.
Step 4: Results
 The following figure shows the selfconsistently calculated conduction
band profile and the lowest wave functions of an ntype 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 (Delta_{6})
and leads to a splitting into a twofold (Delta_{2}) and a fourfold
(Delta_{4}) 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 10^{18} 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_{0.75}Ge_{0.25}
channel: 0.75 x 10^{12} cm ^{2}
 in the strained Si channel: 0.66 x 10^{12} cm ^{2}
