GATE 2026 EC Q.25: solution and answer

Official answer: ASource: Official answer key, GATE 2026 EC (IIT Guwahati)

1. Under thermal equilibrium (V = 0), electron and hole populations across the p-n junction are both described by a single, common Fermi level $E_F$: $E_{fn}=E_{fp}$.

2. Under forward bias, minority-carrier injection at the junction pushes both carrier populations far from their equilibrium values, so a single Fermi level can no longer describe both. Two separate quasi-Fermi levels are introduced: $E_{fn}$ for electrons and $E_{fp}$ for holes.

3. Deep in the quasi-neutral bulk regions on each side (away from the depletion region), majority carriers remain close to local equilibrium, so $E_{fn}$ and $E_{fp}$ are each essentially flat (constant with position) through most of each neutral region.

4. The applied forward bias $V$ does work $qV$ per carrier as it is transported across the junction; this work manifests exactly as the separation between the two flat quasi-Fermi levels in the neutral regions: $E_{fn}-E_{fp}=qV$.

5. Substituting the given bias $V=2\text{V}$: $E_{fn}-E_{fp}=q(2\text{V})=2\text{eV}$.

6. Since the question asks for an ENERGY difference, the answer must be expressed in eV, not V — this immediately rules out (C) 2 V and (D) 1 V on dimensional grounds, independent of their numeric value.

7. Therefore the magnitude of the quasi-Fermi level splitting is exactly $2\text{eV}$, matching option (A); option (B) 1 eV would require an applied bias of 1 V, which is not the value given in the problem.