Question

At 0K, an intrinsic semiconductor behaves like a:

• A. Conductor
• B. Insulator
• C. Superconductor
• D. Metal

Hint:

As temperature increases ($T > 0\text{ K}$), thermal energy excites electrons across the band gap.
This causes the electrical conductivity of a semiconductor to increase with temperature (negative temperature coefficient of resistance), which is the opposite of how metals behave.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the electrical conduction behavior of a pure (intrinsic) semiconductor at absolute zero temperature ($0\text{ K}$).

Step 2: Key Formula or Approach:
The electrical conductivity of a semiconductor is given by:
\[ \sigma = n_i e (\mu_e + \mu_h) \]
where $n_i$ is the concentration of intrinsic charge carriers, which depends on temperature:
\[ n_i \propto \exp\left(-\frac{E_g}{2k_BT}\right) \]

Step 3: Detailed Explanation:

• An intrinsic semiconductor has a valence band that is completely filled with electrons and a conduction band that is completely empty, separated by a relatively small band gap ($E_g \approx 1\text{ eV}$).

• At absolute zero temperature ($T = 0\text{ K}$), the thermal energy of the system is zero ($k_BT = 0$).

• Because there is no thermal energy, no covalent bonds can break, and no electrons can gain the energy required to cross the band gap into the conduction band ($n_i = 0$).

• With no free electrons in the conduction band and no holes in the valence band, there are no charge carriers available to conduct electricity.

• Consequently, the electrical conductivity is exactly zero, and the semiconductor behaves as a perfect electrical insulator.

Step 4: Final Answer:
At $0\text{ K}$, an intrinsic semiconductor behaves like an insulator.