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M.sc physics general lab

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Experiments in physics

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October 29, 2023
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Users Manual




RESISTIVITY OF SEMICONDUCTORS BY FOUR PROBE METHOD
AT DIFFERENT TEMPERATURES




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,
, INTRODUCTION

The properties of the bulk material used for the fabrication of transistors
and other semiconductor devices are essential in determining the characteristics of the
completed devices. Resistivity and lifetime (of minority carriers) measurements are
generally made on germanium crystals to determine their suitability. The resistivity, in
particular, must be measured accurately since its value is critical in many devices. The
value of some transistor parameters, like the equivalent base resistance, are at least
linearly related to the resistivity.

ELECTRONIC CONDUCTION IN SOLIDS

The electrical properties of semiconductors involve the motion of charged
particles within them. Therefore, we must have an understanding of the forces which
control the motion of these particles. It is of course, the physical structure of the solid
which exerts their control. This topic is very large, and hence only the high lights will be
covered. The reader is referred to many excellent sources which are listed at the end, for
more details on specific aspects.

Atoms, of which a solid is composed, consist of positively charged nuclei
with electron orbiting around them. The positive charge is compensated by negatively
charged electrons, so that a complete atom is electrically neutral. Electrons are arranged
in shells, and the closer they are to the nucleus the more strongly they are bound. If we
take the particular case of silicon, a well known semiconductor, we find that it has 14
electrons which are accommodated in the shells as (1S)2, (2S)2 , (2P)6, (3S)2 , (3P)2.
Since the third shell is not even half filled, the 4 electrons are available for chemical
binding giving silicon a valency of four. (Germanium also has a chemical valency of 4, but
from the fourth shell). Fig. 1 shows an energy diagram of an individual atom.

Let us now concentrate our attention on solids, if we bring many atoms
close to one another, interatomic forces become quite strong as electronic orbits begin to
overlap. The outer shell electrons play an important role, because their orbits are the
most disturbed. These electrons are no longer associated with a particular atom, the
outer shell electron may make an orbit around one atom and continue about another. In
this fashion, the outer shell or valency electrons are continually traded among atoms and
wander all over the solid. The continuous interchange of valence electrons between
atoms holds the solid together. This is the predominant type of bonding in silicon and
germanium, and is called the valence bonding.
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