Normal metal - insulator - normal metal (N-I-N) junctions

occupied states vacant states

I_1-2 µ T₁₂(E) N₁(E -eV) f(E-eV) N₂(E) [1-f(E)] dE

I_2-1 µ T₂₁(E) N₁(E-eV) [1-f(E-eV)] N₂(E) f(E-eV) dE

Assuming T₁₂(E) = T₂₁(E)

I = A T₁₂(0) † N₁(E-eV) N₂(E) [f(E-eV) -f(E)] dE

For small voltages eV << U₂

T₁₂(E) - independent of E

N₁(E-eV) @ N₁(E) = N₁(0) and N₂(E) = N₂(0)

With this approximations

I µ T₁₂(0) N₁(0) N₂(0) † [f(E-eV) -f(E)] dE
For small voltages

† [f(E-eV) -f(E)] dE = eV

I = A T₁₂(0) N₁(0) N₂(0) eV