Numerical
analysis and simulation of semiconductor devices

M. R. is one
of the authors of HFIELDS, a general-purpose simulation tool for
silicon
devices using the box-integration method and the Scharfetter-Gummel
discretization
scheme, which has been adopted in several research groups in industrial
or academic
environments since its first appearance in 1985 [69,126]. The code,
supplemented
with flexible mesh generator [77] and user interface [82], has been
improved in
the subsequent years by implementing the small-signal analysis [74],
the
transient analysis [72,79], the sensitivity analysis and device
optimization
[21,28,73,135], the mixed circuit-device simulation [75], the
three-dimensional
version [25,78,81,84,85,88], and the description of the thermal
behavior of the
lattice [10]. Further developments of the activity on HFIELDS were the
incorporation
of the amorphous and polycrystalline silicon (outlined in another point
below), and the
extension of the simulation capability to the case of solid-state
sensors (see also below). In 1986, while visiting the IBM Thomas
J. Watson
Research Center
at Yorktown
Heights, M. R.
first proposed an efficient
discretization scheme for the so-called hydrodynamic model of
semiconductor
devices [19,20,145]. The hydrodynamic model improves over the customary
drift-diffusion one because it is based on higher moments of the
Boltzmann
Transport Equation. Due to this, it is able to determine, apart from
the
electric potential and the concentration of the mobile charge carriers
(electrons
and holes), also the carrier temperature. In this way, the model lends
itself to
describing a number of non-local phenomena, like velocity overshoot and
impact ionization,
that are typical of modern submicron devices. The discretization scheme
made it
possible to easily incorporate the hydrodynamic model into existing
device-analysis
codes like HFIELDS [22,35,130,131]. Particular issues of the numerical
analysis of semiconductor devices have also been dealt with in
connection with the
main stream of research, specifically: accurate methods for calculating
the
charge concentration [15], problems of grid optimization
[16,23,26,67,68,80,129,132],
solution of the semiconductor equation by an integral-equation approach
[17],
extension of discretization schemes to incorporate impact-ionization
[34],
methods improving the computational efficiency of the box-integration
method
solution of the semiconductor equations [70,46,136,139] and of the
spherical-harmonics solution of the Boltzmann Transport equation
[41,48,141].