In a Hall effect experiment on an intrinsic semiconductor, which of the following
statements are correct?
Options:
(A) Hall voltage is always zero
(B) Hall voltage is negative if the effective mass of holes is larger than those of
electrons
(C) Hall coefficient can be used to estimate the carrier concentration in the
semiconductor
(D) Hall voltage depends on the mobility of the carriers
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.52)**
**1. Semiconductor Physics (Hall Effect in Intrinsic Semiconductors)**:
- In an intrinsic semiconductor, electron concentration equals hole concentration:
$n = p = n_i$
- Hall coefficient for two-carrier conduction:
$R_H = \frac{p\mu_h^2 - n\mu_e^2}{e(p\mu_h + n\mu_e)^2} = \frac{1}{e n_i} \frac{\mu_h^2 - \mu_e^2}{(\mu_h + \mu_e)^2} = \frac{\mu_h - \mu_e}{e n_i (\mu_h + \mu_e)}$
**2. Detailed Step-by-Step Evaluation**:
- Hall voltage $V_H = \frac{R_H I B}{w}$.
- Since electron mobility $\mu_e$ is typically significantly larger than hole mobility $\mu_h$ (due to lower effective mass in conduction band), $R_H < 0$ and depends strongly on mobility.
- Thus, $V_H$ is explicitly dependent on the carrier mobilities $\mu_e, \mu_h$. **Statement (D) is TRUE**.
**3. Official Verification**:
The verified official IIT Master Answer is **Option (D)**.
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