QB_PH_SEC7_018: Band Theory of Solids & Semiconductors

In a p-type semiconductor where holes dominate electrical conduction ($p \gg n$), the sign of the Hall coefficient $R_H$ is

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Lorentz Force on Free Holes**: $\vec{F} = +e (\vec{v}_d \times \vec{B})$ 2. **Transverse Hall Equilibrium**: The electrostatic Hall field balances the magnetic deflecting force: $e E_y = e v_{dx} B_z \implies E_y = v_{dx} B_z$ 3. **Current Density Relation**: $J_x = p e v_{dx} \implies v_{dx} = \frac{J_x}{p e}$ 4. **Hall Coefficient Definition**: $R_H = \frac{E_y}{J_x B_z} = \frac{v_{dx} B_z}{(p e v_{dx}) B_z} = +\frac{1}{p e}$ 5. **Sign Consequence**: For $p$-type conduction, $R_H > 0$ (strictly positive). Option (A) is correct.