Energy Band Gap Using Four Probe Method Viva Questions

A semiconductor is a material with electrical conductivity between that of a conductor (like metals) and an insulator (like glass). The forbidden energy gap between the valence band and conduction band is very small i.e. less than 3 eV.

An enormously large number of energy levels closely spaced in a very small energy range constitute an energy band.

The highest energy band filled with valence electrons is called valence band.

The lowest unfilled allowed energy band next to valence band is called conduction band.

The gap between the top of valence band and bottom of the conduction band in which no allowed energy levels for electrons can exist is called energy band gap or energy gap.

As shown in the figure, the lowest conduction band energy is E_c and the highest valence band energy is E_v and the energy band gap between them is E_g=E_c-E_v.

The highest energy level in the conduction band filled up with electrons at absolute zero is called
Fermi level and the energy corresponding to Fermi level is called Fermi Energy.

The vacancy or absence of an electron in the bond of a covalently bonded crystal is called a hole.

A pure (free from impurity) semiconductor which has a valency 4 is called an intrinsic semiconductor. Pure germanium, silicon or carbon in their natural state are intrinsic semiconductors. Here, number of holes=number of electrons

There are two types of extrinsic semiconductors:
p-type semiconductors and n-type semiconductors

Introducing a trivalent impurity atom (like boron, aluminum, or gallium) into a germanium or silicon crystal creates a p-type semiconductor. In this material, holes are the majority charge carriers. Conversely, adding a pentavalent impurity atom (such as phosphorus, arsenic, or antimony) results in an n-type semiconductor, where electrons are the majority charge carriers. Importantly, both p-type and n-type semiconductors remain electrically neutral.

When a thin layer of n-type semiconductor sandwiched between two p-type semiconductors, then it is known as p-n-p transistor.

When a thin layer of p-type semiconductor sandwiched between two n-type semiconductors, then it is known as n-p-n transistor.

The emitter-base junction is always forward biased and collector-base terminal is always reverse biased.

The arrangement consists of four equally spaced collinear probes. The outer probes are used to pass current through the specimen. The inner pair probes measure voltage by a digital voltmeter.

The formula for measuring resistivity is
where: – V is the voltage, – I is the current, – s is the separation between the probes.
But this formula is applicable for a thick sample, that is when the width of the sample is much greater than the separation between the probes (). Therefore, for a thin sample the modified formula is:

   

The forbidden energy band gap of a semiconductor is related to the resistivity as:

   

where is the required band-gap, is the Boltzmann constant (), and is the absolute temperature. This is an equation of a straight line. Drawing the graph between and gives the slope, which will be equal to . Then,

   

The correction factor is a constant. If we don’t use it, it behaves like a constant that is multiplied with all the values of resistivity. This does not change the slope, and the band gap, , depends only on the slope ().