Question

The temperature coefficient of resistance of a semiconductor:
A. Is always positive
B. Is always negative
C. Is zero
D. May be positive or negative or zero.

Answer 1

Hint: The temperature coefficient for the material is proportional to the difference in resistance of material at temperature (t) and absolute zero temperature (0K) and inversely proportional to the product of temperate and resistance at absolute zero. The temperature coefficient is positive for metal and alloys. It is negative for insulators and semiconductors.

Formula used:
$\alpha = \dfrac{{{R_t} - {R_o}}}{{{R_o}t}}$

Complete step-by-step answer:
The temperature coefficient of resistance is equal to the change in resistance of the wire of resistance one ohm at ${0^0}C$ when the temperature changes by${1^0}C$.
That is denoted by$\alpha $.
$\alpha = \dfrac{{{R_t} - {R_o}}}{{{R_o}t}}$
Where,
$\alpha $=temperature coefficient
Let's consider a case,
If ${R_o}$=1 and t= ${1^0}C$ then, $\alpha = {R_t} - {R_o}$
In general, for two different temperature and resistance, we can write the equation as,
$\alpha = \dfrac{{{R_2} - {R_1}}}{{{R_1}t - {R_2}t}}$
From this equation, we can say that as the temperature of a semiconductor increases, resistance decreases.
Then the value ${R_2} - {R_1}$ becomes a negative value. Therefore the entire value becomes negative in the case of the semiconductor.
Thus, the temperature coefficient of resistance ($\alpha $ ) of a semiconductor is always negative.

Hence, the correct option is (B).

Additional information:
Resistivity,$\rho = \dfrac{m}{{n{e^2}\tau }}$
Where m is the mass the conductor
n is the free electron per unit volume.
e is the charge of an electron.
$\tau $ is relaxation time.
From this equation, we can say, resistivity or resistance is inversely proportional to n and relaxation time$\tau $. As temperature increases, the density of the electrons increases, the average speed of the electron also increases, then collision between electron increases means there is a very fast collision. Because of this fast collision, the relaxation time of the collision of the charge carrier decreases. But the effect of the increase in ‘n’ is much higher than the effect of a decrease in$\tau $. As a result, the resistance of a semiconductor decreases with an increase in temperature and vice versa.

Note:
Resistance is the opposition offered by the substance to the flow of electric current.
The resistance of a conductor depends on the nature of the material and temperature.