This is the 2D companion to the 3D resonant-tunneling-diode scene: instead of a rendered double-barrier nanostructure, this solves the identical 1-D effective-mass Schrödinger equation with the same transfer-matrix method, computed independently, and reads the result off three analytic plots.
Each constant-potential region Vi carries a wavevector
k_i = sqrt(2 m* (E − V_i)) / ħ (real → propagating, imaginary → evanescent)
Matching ψ and ψ′ at every interface chains 2×2 complex matrices into one transfer matrix; the transmission probability is T(E) = (k_out/k_in)·|A_in/A_out|² for a unit-amplitude wave incident from the emitter with nothing incoming from the collector.
Because the well only supports discrete quasi-bound levels, T(E) is sharply peaked at the resonant energy Eres — an electron at that exact energy tunnels through with T ≈ 1 even though each barrier alone would nearly block it. Applying a bias voltage tilts the potential, dragging Eres down through the fixed emitter Fermi energy EF; current I(V) ∝ ∫₀^E_F T(E,V) dE rises to a peak then falls as bias keeps increasing — negative differential resistance (NDR), the property that makes real RTDs useful as GHz–THz oscillators.
- Top panel — potential profile V(x) and the sampled |ψ(x)|² at the current bias, on the same emitter→collector x-axis.
- Bottom-left — the transmission spectrum T(E) at the current bias; the marker sits at EF.
- Bottom-right — the I–V curve; the marker tracks where you are on the peak → NDR → valley curve.
V0, b sharpen the resonance (taller/wider barriers → narrower T(E) peak). w lowers Eres (particle-in-a-box scaling ∝ 1/w²) and packs in more levels. Vbias tilts the structure and sweeps Eres across EF.