GATE 2026 EC Q.64: solution and answer

GATE 2026 · ECQ.64 · 2 marks · NAT

Consider that the concentration of electrons in a semiconductor bar varies linearly from $2 \times 1 0^{17} cm^{- 3}$ at $x = 1 μ m$ to $1 \times 1 0^{16} cm^{- 3}$ at $x = 4 μ m$ along the $x$ -direction. Assume that the concentration of electrons is not varying along other directions (that is along $y$ - and $z$ -directions).

[Given: the mobility of electron is $1400 cm^{2} V^{- 1} s^{- 1}$ , thermal voltage is $25 mV$ and electronic charge is $1.6 \times 1 0^{- 19}$ Coulomb.]

The density of electron diffusion current (in $A/mm^{2}$ ) is ___.

(rounded off to two decimal places)

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Answer and solution

ANSWER

The electron diffusion current density is J_n,diff ≈ 35.47 A/mm² (magnitude).

Official answer: -36.50 to -34.50, or 34.50 to 36.50Source: Official answer key, GATE 2026 EC (IIT Guwahati)

Concentration gradient: $\frac{d n}{d x} = \frac{( 1 \times 1 0 ^{16} - 2 \times 1 0 ^{17} ) cm ^{- 3}}{( 4 - 1 ) μ m} = \frac{- 1.9 \times 1 0 ^{17} cm ^{- 3}}{3 \times 1 0 ^{- 4} cm} = - 6.3333 \times 1 0^{20} cm^{- 4}$
Diffusion coefficient via Einstein relation: $D_{n} = μ_{n} V_{T} = 1400 \times 0.025 = 35 cm^{2} / s$
Electron diffusion current density: $J_{n, diff} = q D_{n} \frac{d n}{d x}$
Magnitude: $∣ J_{n, diff} ∣ = (1.6 \times 1 0^{- 19}) (35) (6.3333 \times 1 0^{20}) = 3546.67 A/cm^{2}$
Convert $cm^{2} \to mm^{2}$ (since $1 cm^{2} = 100 mm^{2}$ ): $J_{n, diff} = \frac{3546.67}{100} = 35.47 A/mm^{2}$

KEY IDEA

Diffusion current density is $J_{n, diff} = q D_{n} \frac{d n}{d x}$ , with $D_{n}$ obtained from the mobility via the Einstein relation $D_{n} = μ_{n} V_{T}$ ; only the magnitude and unit conversion (cm² to mm²) need care here.

WATCH OUT FOR

Forgetting that $1 cm^{2} = 100 mm^{2}$ , so converting A/cm² to A/mm² requires DIVIDING by 100 (not multiplying), and mixing up the sign convention or the direction of the gradient (which point's concentration is subtracted from which).

From the GATE 2026 EC paper. Every question of this paper · Download the full paper · All 9 Carrier transport questions, with notes

GATE 2026 EC Q.64: solution and answer

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