### What:

Monet simulates
the flight of several thousand electrons
through the silicon lattice and follows them individually as they drift
in the electric field, then scatter with phonons, impurities or
boundaries, and so on. This is a semi-classical approach
because
the scattering rates are computed quantum-mechanically (from Fermi's
Golden Rule using wave function overlap integrals) yet during the free
flight between scattering events the particles simply follow Newton's
Laws (F=ma). The method is called Monte Carlo (MC) because of the
stochastic nature in which the scattering events are simulated: a
random number is drawn and compared with a scattering probability, then
the scattering event is chosen based on this comparison.

### Download:

source code (in C) with three examples and user manual. [

4Mb zip file]

### How:

One key ingredient in all such MC codes is the electron band model.
Monet
uses analytic, non-parabolic bands. This is both easier to implement
and faster -- and it is a reasonable approximation for simulating
electron
transport in devices with operating voltages below the band gap (1.1 V
in silicon), such as future nanoelectronic devices. Full-band
simulators are mainly needed to resolve impact ionization and high band
structure transport details. Consequently Monet ignores sub-band gap
impact ionization. Here's a short summary of Monet's main features:

- analytic bands (non-parabolicity 0.5 eV
^{-1})
- scattering with six intervalley phonons
- separate scattering with intravalley LA and TA phonons
- phonon dispersion
used both
for
acoustic and optical phonon scattering
- new empirical set of phonon scattering
potentials, in better agreement with recent ab initio calculations and
strained silicon mobility data

One of the features that distinguish Monet
from other analytic-band MC codes is that all phonon generation and
absorption events are tallied. Hence, very detailed heat
generation statistics can be gathered. The simulation can be run
in a constant E-field to obtain velocity-field curves, electron
mobilities or the basic phonon distributions at the given E-field -- or
in 1- or 2-D with periodic boundary conditions on an E-field grid
extracted from another device simulator like Medici. Monet does
not solve the Poisson equation (this is also known as Monte Carlo in
the "frozen field" approximation). The total amount of charge
inside the device is given by the previous device simulator and only
two device
contacts can be included. This implies that electrons exiting the
device through one contact are immediately injected at the other
contact with thermally distributed energies and randomly oriented
velocity components.

Another feature of Monet is its treatment of acoustic
intravalley scattering. Scattering with LA and TA phonons is
treated separately and the full phonon dispersion is used when
calculating the acoustic intravalley scattering rates. The LA/TA
scattering deformation potentials are derived from the most recent
values of the shear and dilatation potentials available in the
literature. Other analytic-band MC codes group LA and TA
scattering together and assume a single phonon velocity, i.e. no phonon
dispersion.

The following figures illustrate the silicon band diagrams:

The figure on the left (courtesy IBM) shows the full
conduction band
diagram. The middle figure (courtesy C. Jungemann) shows
constant energy contours near the bottom of the conduction band (notice
the
ellipsoidal shape around the minima at 0.85). The third
figure shows the ellipsoidal energy pockets "inhabited" by conduction
band
electrons in an analytic-band MC code like Monet, and the possible
phonon scattering transitions.

updated Jul 2007