Question

The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the
A. Crystal structure
B. Variation of the number of charge carriers with temperature
C. Type of bonding
D. Variation of scattering mechanism with temperature.

Answer 1

Hint: Define resistivity of a substance. Find out on which parameters the resistivity depends on. Define dependence of resistance on the temperature for both the metals and semiconductors. Find out the difference in the reasons.

Complete step by step answer:
Resistivity of a material can be defined as the property of a material which resists the flow of current in the material. It can also be defined as the resistance offered by a material of unit length and unit area of cross-section.
The resistivity of a material depends on the temperature of the material.
In case of metal, with the increase in temperature, the vibration of the metal ions in the lattice structure increases. As the atoms start to vibrate with more amplitude, the collision between the free electrons and the other electrons increases. These collisions drain out the energy of the free electrons making them unable to move. Since the free Electrons are not able to move freely, the conductivity of the metal decreases or we can say the resistivity of the material increases.
In the case of a semiconductor, the forbidden gap between the conduction band and the valence band is very small. When we give energy to the electrons the electrons can easily move from the valence band to the conduction band. When the temperature increases, the forbidden gap becomes very less and electrons can easily move from the valence band to the conduction band. So, with the increase in temperature the density of the charge carriers also increases and the resistivity of the semiconductor decreases.
So, we can say that the difference between the variation of resistivity of the metal and semiconductor is due to the variation of the number of charge carriers with temperature.

The correct option is (B).

Note: The dependence of resistivity of a material on temperature can be mathematically expressed as, ${{\rho }_{t}}={{\rho }_{0}}\left[ 1+\alpha \left( T-{{T}_{0}} \right) \right]$ , where $\alpha $ is the coefficient of resistivity. The value of the coefficient of resistivity is positive for metals and negative for semiconductors and insulators.