4.13 Sspd_chapter_2.2.6. drift velocity in semiconductor/metal and

2.2.7. drift velocity in semiconductor/metal and its conductivity.

In conductors it is the drift of the electrons which gives rise an electric current. It is the drift of the electrons which gives rise to Ohm’s Law (V/I = R). The flow of electrons in an electric circuit is shown in Figure 2.2.32.

Notice here there is only electron flow from the negative terminal to the positive terminal of the battery and right from the middle of 18 ^th century we have been mistakenly calling it a current flowing from positive to the negative terminal as if it is a flow of some positive charges. In an electric circuit there is the flow of electrons only.

The electric conductor obeys Ohm’s Law:

(2.2.7.1)

A = cross-sectional area of the conductor, l = length of the conductor.

In contrast semiconductor allows the current to be carried by electrons as well as by holes. Hence electric current is partly carried by electrons and partly carried by holes as shown in Figure 2.2.33.

As shown in Figure 2.2.33. since the Si Rod is intrinsic in nature, 50% of current is carried by electrons and 50% is carried by holes within the Si-Rod. In external circuit, 100% of the current is carried by electrons sourced from the negative terminal of the battery and drained out by the positive terminal of the battery. At the negative terminal all the holes flowing in the Si-Rod recombine with a part of the electrons brought by the external circuit. In this particular example 50 holes/sec recombine with 50 electrons/sec. At the positive terminal equal number of electrons and holes are generated and maintain the continuity of the current across the positive interface.In this example 50 EHP/sec are generated and maintain the continuity of current.

If the Si-Rod is extrinsic then major portion of the current is carried by the majority carriers and minor portion of the current is carried by the minority carriers.

In Chapter 1, Part 12, the quantum mechanical interpretation of Resistance of a conductor is given.

As seen in Figure 2.2.34. the drift velocity (v _d ) is a perturbation in the random thermal motion of the conducting electrons under an applied electric field E _y . The otherwise centrally placed momentum sphere gets displaced in Y-direction by v _d under the application of an Y-directed electric field.

The thermal velocity of electron or hole in Si-Rod is given by the following equation:

In Chapter 12, Part 12, we saw that electron or hole gets accelerated in spurts. At short intervals of time it loses all energy to the crystal and its motion is reset. That is it restarts from zero velocity. This will happen as long as drift velocity<<thermal velocity.Under this condition:

Drift Velocity is directly proportional to the applied Electric Field and v _d │ _Y = μE _Y . The constant of proportionality is called mobility μ.

We will show that under this direct proportionality condition Ohm’s Law is satisfied.