In standard simulators for semiconductor devices the electrical behavior of the
devices is calculated using the drift-diffusion model. The development of more
complex and smaller devices demands for more exact simulation methods, such as
the Monte Carlo method examined within this work.
An important application of the Monte Carlo method is the study of the electrical
behavior of Silicon and Germanium. Mechanical strain can raise significantly
the carrier mobility in a semiconductor.
This effect has been utilized over the last few years to enhance performance of
CMOS technology.
This work starts with an introduction of the stress- and strain tensors. Then the symmetry properties of the band structure of the relaxed and the strained diamond lattice are presented. The irreducible domains of the Brillouin zone for band structure calculation are derived for important strain configurations. The band structure is calculated using the pseudo potential method and discretized on a mesh.
The main part of this work is about the simulation of carrier transport using the full-band Monte Carlo method. Important numerical algorithms and scattering models are presented. The scope is on new algorithms, which reduce simulation times. In this regard the generation of locally refined meshes for the Brillouin zone and the efficient implementation of rejection algorithms are explored.
Results from band structure and carrier transport calculations are
discussed in the context of recent theoretical findings. In strained Silicon
the degeneration of the X-valleys is lifted. As a consequence the valleys lower
in energy are higher populated. Band structure calculations show, that in
addition to the shift of the conduction band valleys relative to each other,
the effective electron masses can be changed. This is caused by shear strain,
which leads to an deformation of the valley minima. An analysis of the valence
bands of a strained crystal shows that the degeneration of the heavy hole and
light hole bands at the 
-point is lifted. Shear strain increases the
hole mobility along certain directions, an effect caused by a
deformation of the valence bands.
Mass manufactured CMOS transistors feature a uniaxially tensile strained
channel in [110] direction. Simulations at 1.5GPa for this strain
configuration show a mobility gain by a factor of 1.68 to 2410cm
/Vs for
electrons in bulk Silicon. For compressively strained Germanium hole mobility is
raised by a factor of 2.55 up to 4790cm
/Vs at 1.5GPa stress in [110]
direction.
The final part of this work deals with the simulation of blocked impurity band
photo detectors.
These devices operate in the long wave length infrared range at temperatures
below 
K. A photon is detected by lifting a carrier from a heavy doped
impurity band by optical excitation to the conduction band. The simulator is
extended by an inelastic scattering model for acoustic phonons, which is
appropriate for simulations at low device temperature. A model for individual
simulation of every carrier from an avalanche caused by impact ionization is
also implemented.
The distribution in energy and arrival time of the carrier avalanche is
calculated.