Question

Which of the following statements best describes the effect of increasing the temperature on the conductivity of an intrinsic semiconductor?

• A. Conductivity decreases
• B. Conductivity remains constant
• C. Conductivity increases
• D. Conductivity first increases then decreases

Hint:

Semiconductor Conductivity vs Temperature. Intrinsic Semiconductor: Conductivity increases strongly (exponentially) with temperature due to increased carrier generation (\(n_i\)). Extrinsic Semiconductor: More complex behavior, but generally conductivity increases initially, then may decrease at very high temperatures. Metals: Conductivity decreases with temperature due to increased scattering.

Answer 1

The Correct Option is C

In an intrinsic (pure) semiconductor, electrical conductivity (\(\sigma\)) depends on the concentration of thermally generated charge carriers (electrons \(n\) and holes \(p\)) and their mobilities (\(\mu_e, \mu_h\)): \( \sigma = (n\mu_e + p\mu_h)e \).
In an intrinsic semiconductor, \(n=p=n_i\), where \(n_i\) is the intrinsic carrier concentration.
The intrinsic carrier concentration \(n_i\) is highly dependent on temperature, increasing exponentially as temperature rises according to: \( n_i \propto T^{3/2} e^{-E_g / (2kT)} \), where \(E_g\) is the band gap energy.
While carrier mobility (\(\mu\)) generally decreases slightly with increasing temperature due to increased lattice scattering, the exponential increase in carrier concentration (\(n_i\)) dominates.
Therefore, the overall electrical conductivity of an intrinsic semiconductor increases significantly (usually exponentially) as temperature increases.