Question

1. Please write down the resistivity as a function of temperature for a metal. Please separate it into four regions, such as resistivity is proportional to T, proportion to $T^5$ proportional to$T^2$ and proportional to$T^0$ . Please also explain why is that?
2. What will be happened if the doped impurities in the non-magnetic metal is magnetic ions?
3. What is the resistivity as a function of temperature for an intrinsic semiconductor?
4. How about the resistivity charge as function of temperature in a insulator?
   
   (Please be as short as possible and clearly written , the electronic format is the best)

Answer 1

The resistivity of materials depend on the temperature.

ρ_t = ρ₀ [1 + α (T – T₀) is the equation that shows the relation between the temperature and the resistivity of a material.

In the equation ρ₀ is the resistivity at a standard temperature, ρ_t is the resistivity at t⁰C, T₀ is the reference temperature and α is the temperature co – efficient of resistivity.

So, resistivity is almost directly proportional to temperature T. It is so, because as we increase the temperature of metals, the ion movement and amplitude increases and so the collissions increase. This increases the resistivity.

The resistivity of intrinsic semiconductor decreases with increase in temperature. Semiconductors are in between metals and non conductors. As moving electrons are responsible for conductivity, so in semiconductors these electrons are trapped and can not move freely. When we increase the temperature the mobility and amplitude of these electrons increases and thus increasing the conductivity or in other words, reducing the resistivity.

In case of conductor, the valance band and conduction band overlap with each other. So, there are excess electrons in the conduction band of a conductor. When you increase the temperature, more electrons will go to the conduction band from valance band by absorbing the energy. So, the conduction band becomes crowded and there will be more collision between the electrons which increases the resistance. So, with increase in temperature, the resistance of conductor increases.

But in case of insulator, there is a large energy gap between the two bands. So, if the temperature rise is high, the electrons will go to the upper band. But since it is not crowded due to less number of electrons, so the conductance will increase due to availability of free electrons in the conduction band. So, the resistance decreases with increase in temperature in insulator.