Question

If the temperature of a piece of a metal is increased, does the probability of occupancy 0.1 eV above the Fermi level increase, decrease, or remain the same?

Short answer

The increase in temperature increases the probability of the occupancy above the Fermi level.

Step-by-step solution

The given data

1. Temperature is increased.
2. Fermi energy of the material,$∆\mathrm{E}=0.1eV$

Understanding the concept of occupancy probability

Using the basic concept of the probability of occupied states, we can get the required occupancy probability change of the material. Thus, this helps in determining energy change as per the given condition.

Formula:

The probability of the condition that a particle will have energy E according to Fermi-Dirac statistics,$P\left(E\right)=\frac{1}{e^{\left(E_1-E_F\right)/kT}+1}$ (i)

Calculation of the energy change

Using the occupancy probability equation (i), we can get that for increased temperature, the exponential term decreases. This in turn increases the probability value.

Hence, for the given energy above the Fermi level and for the temperature increase, the occupancy probability increases.