ISRO EC 2025 Q.64: solution and answer

ISRO 2025 · ECQ.64 · 1 mark · MCQ

Which of the following conditions will maximize the diffusion current in a semiconductor?

(A)
Uniform doping profile
(B)
High electric field
(C)
Steep concentration gradient
(D)
Zero temperature gradient

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Answer and solution

ANSWER

The diffusion current is maximum for a steep concentration gradient, option (c).

Official answer: CSource: ISRO's final answer key of 15 May 2026

Diffusion current is carried by charge moving from a region of high carrier concentration to one of low concentration. It does not need an applied field.
For electrons the diffusion current density is $J_{n} = q D_{n} \frac{d n}{d x}$ , and for holes it is $J_{p} = - q D_{p} \frac{d p}{d x}$ , where $D = μ V_{T}$ is the diffusion coefficient.
The magnitude of the diffusion current is therefore proportional to the concentration gradient $\frac{d n}{d x}$ (or $\frac{d p}{d x}$ ). The steeper the gradient, the larger the current.
(a) A uniform doping profile gives $d n / d x = 0$ , so the diffusion current is zero. Wrong.
(b) A high electric field drives drift current, $J = q μ n E$ , not diffusion current. Wrong.
(c) A steep concentration gradient makes $d n / d x$ large, so the diffusion current is largest. Correct.
(d) A zero temperature gradient has no direct role. Diffusion current is set by $D$ and the concentration gradient, not by a temperature gradient. Wrong.

KEY IDEA

Diffusion current density is $J = \pm q D \frac{d ( carrier concentration )}{d x}$ , so it grows with the concentration gradient and vanishes when the profile is uniform.

WATCH OUT FOR

Confusing diffusion with drift: a high electric field increases drift current, not diffusion current. A uniform doping profile gives no concentration gradient, hence no diffusion current.

From the ISRO EC 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 2 ISRO Carrier transport questions, with notes