GATE 2022 PH – Question 52
In a Hall effect experiment on an intrinsic semiconductor, which of the following statements are correct?
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Correct answer: (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
Explanation
For an intrinsic semiconductor, the electron and hole concentrations are equal, $n=p$. The Hall coefficient with both carriers is
$$R_H=\frac{p\mu_h^2-n\mu_e^2}{e\,(p\mu_h+n\mu_e)^2}\;\xrightarrow{\ n=p\ }\;\frac{\mu_h-\mu_e}{e\,n\,(\mu_h+\mu_e)} .$$
- **A. The Hall voltage is always zero.** False. It is zero only if $\mu_h=\mu_e$.
- **B. The Hall voltage is negative if the effective mass of holes is larger than that of electrons.** Larger hole mass means a lower hole mobility, $\mu_h<\mu_e$, so $R_H<0$ and the Hall voltage has the electron-type (negative) sign. ✓
- **C. The Hall coefficient can be used to estimate the carrier concentration.** True (with known mobilities). ✓
- **D. The Hall voltage depends on the mobility of the carriers.** True, through $\mu_h$ and $\mu_e$ above. ✓
Answer **B, C and D**.