The GATE Grind

GATE 2024 EC – Question 22

Electronic Devices · Energy Bands and Carrier Concentration · 1 mark · Multiple choice

For non-degenerately doped n-type silicon, which one of the following plots represents the temperature ($T$) dependence of free electron concentration ($n$)?

Diagram for GATE 2024 EC question 22
  1. Plot (A)
  2. Plot (B)
  3. Plot (C)
  4. Plot (D)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Plot (A)

Explanation

Plotted as $\log n$ against $1/T$ there are three regions. At low temperature (large $1/T$) donors are only partly ionised (freeze-out), so $n$ falls as $1/T$ increases. In the middle range all donors are ionised and $n\approx N_D$ is flat. At high temperature (small $1/T$) intrinsic carriers dominate and $n$ rises steeply. Only plot (A) has all three regions in the right order.