Concept:The Einstein relation links carrier diffusion (driven by concentration gradients) with carrier drift mobility (driven by electric fields) through thermal energy \( k T \).
Formula:$$\frac{D_n}{\mu_n} = \frac{D_p}{\mu_p} = \frac{k T}{q} = V_T \approx 25.9\text{ mV} \quad (\text{at } 300\text{ K})$$
Solution:- The ratio of the diffusion coefficient \( D \) to carrier mobility \( \mu \) equals the thermal voltage \( V_T = \frac{k T}{q} \).
- This fundamental relationship applies to both electrons (\( D_n / \mu_n \)) and holes (\( D_p / \mu_p \)).
Why other options are incorrect:- Option A: The relation is a ratio \( D / \mu \), not a product \( D \times \mu \).
- Option C: \( q / (k T) \) is the reciprocal of the thermal voltage.
- Option D: Adding \( D \) and \( \mu \) is dimensionally invalid.
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