Question

The electrical resistivity of a semiconductor:
(a)Increase with temperature
(b)Decrease with temperature
(c)Increases at low temperature and then decreases
(d)Does not change with temperature

Answer 1

Hint: Conductivity and resistivity are always inversely proportional to one another. Remember the concept of conductivity with temperature and answer it.

Complete answer:
Semi -conductor is a substance/ material which has the conductivity( the ability of the substance to conduct electricity) intermediate between the insulator and the conductor (metals).E.g. germanium , silicon etched semi- conductors have the conductivity in the range ${{10}^{-6\text{ }}}to\text{ }{{10}^{4}}{{\Omega }^{-1}}{{m}^{-1}}$. The conductivity of the semiconductors is due to the presence of impurities and defects(holes).
By electrical resistivity, we simply mean to resist or to oppose the flow of the current that the material is carrying and it doesn’t allow electricity to further pass through. So, it does not depend upon the length and area of the cross section of a material. But the resistance of a material depends upon the length and area of the cross section of the material. The resistivity is expressed as:
ρ = R $\dfrac{A}{L} $
where R is the resistance in ohms, A is the area of cross section in square meters and L is the length in meters. The unit of resistivity is ohm meter. If A=1 and L=1, then:
$ρ = R$
so, can also be defined as the resistance offered by the conductor having unit (1 m) length and unit (1${{m}^ {2}} $) area of cross section. So, it does not depend upon the length and area of the cross section of a material.
Electrical resistivity of a semi- conductor varies very much with the temperature. The electrical resistivity and the conductivity are inversely proportional to one another i.e. if conductivity is increased then its resistivity will be decreased automatically and vice- versa.
At high temperature the conductivity of semi- conductors is increased and therefore, its resistivity is decreased. It is so because at the high temperature , the electrons get excited and the forbidden energy gap becomes very less between the filled valence band and the empty conduction band becomes very less and the electrons from their covalent bonds are able to move within the structure and thus, the electrons move from their valence band ( outermost filled energy band) to the conduction band( empty band lying next to the valence band in which the electrons can move after being got excited at high temperature). Since, the conductivity of electrons increases and hence their resistivity decreases.
On the other hand, at low temperature the conductivity of semiconductors decreases and resistivity increases. It is because the forbidden energy gap between the valence bond and the conduction band increases and the electrons cannot move and thus, their electrical resistivity increases first but after some time the electrons get excited slowly and slowly and move to the conduction band and hence, their resistivity decreases.
So, from above it is explained that the resistivity of a semi- conductor decreases at high temperature and at low temperature, it first increases and then decreases.

Hence, option (c)is correct.

Note:
Don’t get confused in the term’s resistance and electrical resistivity. Both have different meanings, resistance is that which opposes the flow of current whereas the resistivity defines the resistance of the substance to have definite area and length. Their formulas are as: Resistance(R)= ρ $\dfrac{L}{A} $ and Resistivity(ρ) = R $\dfrac{A}{L} $