Question

The contribution to the total current in a semiconductor, due to electrons and holes are \(0.75\) and \(0.25\) respectively. The drift velocity of electrons is \(\dfrac{3}{2}\) times that of holes at this temperature. Then the ratio between electron concentration and hole concentration is

• A. \(1:3\)
• B. \(3:2\)
• C. \(6:5\)
• D. \(4:1\)
• E. \(2:1\)

Hint:

In semiconductors: \[ I \propto nqv \] So compare current contributions by comparing concentration and drift velocity together.

Answer 1

The Correct Option is D

Current due to electrons: \[ I_e \propto n v_e \] Current due to holes: \[ I_h \propto p v_h \] Given: \[ I_e:I_h=0.75:0.25=3:1 \] Also, \[ v_e=\frac{3}{2}v_h \] So, \[ \frac{n v_e}{p v_h}=3 \] \[ \frac{n}{p}\cdot \frac{3}{2}=3 \] \[ \frac{n}{p}=2 \] So the direct calculation gives: \[ \boxed{2:1} \] which corresponds to option (E), not (D).