Question

The resistance of germanium ……. with rise in temperature.
A. increases
B. decreases
C. remains the same
D. first increases then decreases

Answer 1

Due to difference in the valence energy level and the conduction energy level, the conduction in different kinds of materials differs. Hence, the materials are characterized as conductors, insulators and semiconductors. Due to the increase in temperature, the rate of movement of charge carriers increases in all the materials.

Complete step by step answer:
To understand the solution, we must first understand the different kinds of materials based on the difference in the energy level. The following are the 3 categories:

1. Conductors: Here the bandgap, which is the gap between the valence and the conduction bands, isn’t present at all. These 2 bands overlap, hence causing a free flow of electrons from the electron rich valence band to conduction band even at room temperature. This ease in the conduction ability leads us to calling these kinds of materials as conductors. Its examples are essentially all kinds of metals, which are excellent conductors.

2. Insulators: Here, the energy band gap between the valence and conduction bands is very large. This makes it impossible for electrons to flow from valence band to conduction band, which is necessary for conduction. Hence, these kinds of materials having very large energy band gaps are known as insulators. The examples for insulators include plastics, rubber, ceramics etc.

3. Semiconductors: Semiconductors have an intermediate energy band gap between insulators and conductors. The semiconductors can act as conductors upon application of external electric fields. If the applied external electric field is greater than the band gap of the material then, conduction will occur in the semiconductor.

Now, let’s understand the temperature dependency of the semiconductors. The semiconductors have a positive temperature coefficient, which means that the rise in temperature of the material directly leads to a corresponding increase in the conduction of the material, that is the resistance of the material decreases correspondingly with rise in temperature. Due to the increase in temperature of the material, the valence band electrons gain energy making them excited. These excited electrons need a lesser amount of external electric field to jump to the conduction band. Hence effectively the energy band gap difference between the valence and the conduction band is reduced due to increment in the temperature of a semiconductor, leading to reduced resistance of the material.
Hence, the correct answer is option B.

Note:
The temperature dependence in the conductors and insulators are:

All kinds of metals or conductors have negative temperature coefficient. That means, with the raise in temperature the resistance of the material will increase leading to reduced conduction or corresponding increase in resistance. This phenomenon occurs due to increased atomic lattice vibrations with rise in temperature causing the free flowing electrons to have more collisions thereby increasing the resistance in metals.
Since the insulators have a very high energy band gap, the rise in temperature even though the band gap decreases, it never causes any kind of conduction in the material. Hence, we may consider that temperature doesn’t lead to any change in resistance of the insulators.