Question

In a semiconductor, the ratio of the effective mass of hole to electron is 2:11 and the ratio of average relaxation time for hole to electron is 1:2. The ratio of the mobility of the hole to electron is

• A. 4:9
• B. 4:11
• C. 9:4
• D. 11:4

Hint:

The mobility ratio depends on both the effective mass and relaxation time of the carriers.

Answer 1

The Correct Option is D

Step 1: Mobility \( \mu \) is given by the relation: \[ \mu = \frac{q \tau}{m^} \] where \( q \) is the charge, \( \tau \) is the relaxation time, and \( m^ \) is the effective mass.

Step 2: The mobility ratio between hole and electron is: \[ \frac{\mu_h}{\mu_e} = \frac{\tau_h \cdot m_e}{\tau_e \cdot m_h} \] where \( \tau_h \) and \( \tau_e \) are the relaxation times for hole and electron, and \( m_h \) and \( m_e \) are the effective masses of hole and electron.

Step 3: Substituting the given values: \[ \frac{\mu_h}{\mu_e} = \frac{1 \times 11}{2 \times 2} = \frac{11}{4} \] Thus, the correct answer is (D).