Question

Match List-I with List-II.

List-I	List-II
A. Drift current B. Einstein's equation C. Diffusion current D. Continuity equation	I. Law of conservation of charge II. Electric field III. Thermal voltage IV. Concentration gradient

• A. A-IV, B-II, C-I, D-III
• B. A-IV, B-III, C-II, D-I
• C. A-II, B-I, C-IV, D-III
• D. A-II, B-III, C-IV, D-I

Hint:

Important semiconductor relations: \[ \text{Drift Current} \rightarrow \text{Electric Field} \] \[ \text{Diffusion Current} \rightarrow \text{Concentration Gradient} \] \[ \text{Einstein Relation} \rightarrow \text{Thermal Voltage} \] \[ \text{Continuity Equation} \rightarrow \text{Conservation of Charge} \]

Answer 1

The Correct Option is D

Concept: In semiconductor physics:
• Drift current arises due to electric field.
• Diffusion current arises due to concentration gradient.
• Einstein’s relation connects diffusion coefficient and mobility through thermal voltage.
• Continuity equation is based on conservation of charge. Understanding these relationships is extremely important in semiconductor device analysis.

Step 1: Match Drift Current. Drift current occurs because charge carriers move under the influence of an electric field. Mathematically: \[ J_{drift}=q(n\mu_n+p\mu_p)E \] where:
• \(E\) is electric field
• \(\mu_n,\mu_p\) are mobilities Thus: \[ \text{Drift current} \rightarrow \text{Electric field} \] Hence: \[ A \rightarrow II \]

Step 2: Match Einstein's Equation. Einstein relation is: \[ \frac{D}{\mu}=\frac{kT}{q} \] where: \[ \frac{kT}{q}=V_T \] and \(V_T\) is thermal voltage. Therefore: \[ \text{Einstein's equation} \rightarrow \text{Thermal voltage} \] Hence: \[ B \rightarrow III \]

Step 3: Match Diffusion Current. Diffusion current arises because carriers move from high concentration region to low concentration region. Thus: \[ \text{Diffusion current} \rightarrow \text{Concentration gradient} \] Hence: \[ C \rightarrow IV \]

Step 4: Match Continuity Equation. Continuity equation expresses: \[ \text{Conservation of charge} \] The continuity equation is: \[ \frac{\partial \rho}{\partial t}+\nabla\cdot J=0 \] Thus: \[ \text{Continuity equation} \rightarrow \text{Law of conservation of charge} \] Hence: \[ D \rightarrow I \]

Step 5: Write the complete matching sequence. Therefore: \[ A-II,\ B-III,\ C-IV,\ D-I \] Hence, the correct option is: \[ \boxed{(D)\ A-II,\ B-III,\ C-IV,\ D-I} \]