Question

Pure silicon at 300K has equal electron and hole concentration of \( 1.5 \times 10^{16} \) m\(^{-3}\). If the hole concentration increases to \( 3 \times 10^{22} \) m\(^{-3}\), then the electron concentration in the silicon is:

• A. \( 0.75 \times 10^9 \) m\(^{-3}\)
• B. \( 750 \) m\(^{-3}\)
• C. \( 75 \) m\(^{-3}\)
• D. \( 7.5 \times 10^9 \) m\(^{-3}\)

Hint:

In semiconductors, carrier concentration follows \( n_e = \frac{n_i^2}{n_h} \).

Answer 1

The Correct Option is D

Step 1: Apply Carrier Concentration Formula For intrinsic semiconductors: \[ n_i^2 = n_e n_h \] Step 2: Compute Electron Concentration \[ n_e = \frac{n_i^2}{n_h} \] \[ n_e = \frac{(1.5 \times 10^{16})^2}{3 \times 10^{22}} \] \[ n_e = \frac{2.25 \times 10^{32}}{3 \times 10^{22}} \] \[ n_e = 7.5 \times 10^9 { m}^{-3} \] Thus, the correct answer is \( 7.5 \times 10^9 \) m\(^{-3}\).