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5. Semiconductor Modeling

In pedestrian solid state physics terms semiconductors (e.g. silicon, germanium,
gallium arsenide …) are materials whose electrical conductivity properties lie
between those of a conductor (i.e. a metal) and those of an insulator (e.g.
glass). This is precisely what allows to control the electrical properties of the
material by systematic and appropriate modification from the outside. This
modification is usually done by implanting impurity atoms into the semicon-
ductor, which – once inserted into the semiconductor crystal lattice – become
ionised by either donating a conduction band electron (creating an additional
free negative charge) or absorbing a valence band electron (creating an ad-
ditional free positive charge, a so called hole). The implantation process is
called doping of the semiconductor. Typically, a semiconductor has a conduc-
3
tion band density of 10 11 free electrons per cm ,bydopingthisnumbercan
20
be raised to 10 !!! The doping process, typically carried out through diffu-
sion processes in high tech clean rooms of the chip production companies
and laboratories, controls the electrical properties of semiconductor devices.
More precisely, the position densities of the dopants, for electron donors and
for electron acceptors, determine the electrical functioning of the produced
device.
For the subsequent mathematical discussion we denote by C = C(x)the
signed dopant position density, i.e. the difference of the donor and acceptor den-
sities. Here x denotes the position variable as element of the (three-dimensional)
domain D representing the semiconductor device.
The main use of industrially produced semiconductor devices is in VLSI (=
Very Large Scale Integration) structures, where millions of devices are fabricated
on a single semiconductor chip with a specific usage, i.e. a processor or a RAM
modul of a modern computer or a CCD or CMOS imaging sensor in a digital
camera. The Images 5.1 to 5.6 show a motherboard with two processor slots,
1
an ATA controller chip, a Celeron Processor , a RAM modul array and chips on
a graphics card.
The most important semiconductor device, making up at least 95% of the
overall semiconductor device production, is the transistor, more specifically the
MOS (Metal-Oxide-Semiconductor) transistor, which acts as a switch, allowing
current to flow between its source and drain contacts when the voltage between
thegateand thebasecontact is turned on.Itrepresentsa‘bit’ having thestate 1
when current flows and 0 when no current flows. It is the main ‘logical’ device
in VLSI chipsets.

1
http://www.intel.com/products/processor/celeron/index.htm