The GATE Grind

GATE 2014 EC (EC4) – Question 19

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

The figure plots $\ln\rho_i$ against 1/T for silicon intrinsic resistivity $\rho_i$ and temperature T. The plot is almost linear. What can its slope estimate?

Diagram for GATE 2014 EC (EC4) question 19
  1. Silicon bandgap energy E_g
  2. Sum of electron and hole mobilities μ_n + μ_p
  3. Reciprocal of the sum of electron and hole mobilities
  4. Intrinsic carrier concentration n_i

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Silicon bandgap energy E_g

Explanation

Intrinsic carrier concentration contains exp(−Eg/2kT), and resistivity is inversely proportional to intrinsic conductivity. To leading exponential order lnρi≈constant+Eg/(2kT). Thus a plot against1/T has slope approximately Eg/(2k), enabling estimation of **silicon bandgap energy,A**. Mobility and temperature-power factors give slower corrections.