Chapter 3 Semiconductor Properties

In this section you will learn about basic physics of conduction, conduction behavior of pure semiconductors and behavior of doped semiconductors. At the end of this section, you will be able to calculate dimension and concentration parameters of a semiconductor resistor.

3.1 Conduction

Conduction occurs in a solid if mobile charge carriers are available. In metals such as copper the atoms are arranged in a systematic manner called crystals. The valence electrons are loosely bound to the nucleus creating what is called an "electron sea". These free floating electrons are more precisely called "delocalized" electrons are responsible for conduction, because they are able to move thus enabling carrying of charge.

When an electric field of E volts/m is applied, electrons accelerate and move opposite to the direction of applied field crating current flow. Electron is a negative charge carrier. It carries a charge of 1.6 10-19 Coulombs, abbreviated by the symbol C. Note that charge is integral of current over time; hence C is dimensionally Amp-seconds, or simply denoted as A-s.

We also have a positive charge carrier called electron hole, abbreviated by the symbol h. It is described as the absence of an electron and therefore has a positive charge. Its charge carrying capacity is exactly equal to that of an electron except for its sign.

e: - 1.6 x 10-19 C

h: + 1.6 x 10-19 C

 

Conductivity of a material depends on the number of charge carriers present and their mobility under an applied electric field. That is

Conductivity = {mobility } { number density of carriers} {charge carried by each}

 

The above can be expressed as

= µ n q

 

whereis conductivity, n is number density and q is the magnitude of charge carried by each electron or hole. The parameter, µ, is the charge mobility and is the velocity of a unit charge carrier when subjected to unit applied field, E. That is

 

The units of conductivity is therefore given by

 

In this relationship, we have replaced V/A with ohm. Inverse ohm is called Siemen and it is common to refer to the units of ohm-1 m-1 as simply Siemens per meter.

Recall that resistance of a conductive element is inversely proportional to area of conductive path and directly proportional to conductor length. This can be expressed mathematically as

where the proportionality constant is indicated as. The term,is resistivity and has the dimensions of ohm-m. Inverse of resistivity is conductivity, . That is

Let us now examine howof semiconductors can be systematically altered and how one would determine the concentration of dopants needed to obtain a desired level of conductivity.