The 3D twin of this simulator approximates each quantum dot as an infinite cubic box. Here every dot is solved as a genuine finite square well (depth V₀ = 0.8 eV, InAs-in-GaAs conduction-band offset, effective mass m* = 0.023 mₑ): the transcendental equations
even: √(z₀²−z²) = z·tan(z)
odd: √(z₀²−z²) = −z·cot(z)
z = kL/2, z₀ = (L/2)·√(2m*V₀)/ħ
are solved numerically (bisection) for the ground and first-excited confined levels. As V₀ → ∞ these roots converge exactly to the infinite-box result the 3D scene uses (verified: z → π/2 and π, giving the same ΔE) — but at a realistic finite barrier, a dot below a size threshold literally supports only one bound state and has no intersubband transition at all. Shrink Mean dot diameter far enough and watch "Dots with 2 levels" fall toward zero — a genuine physical cutoff the infinite-box model cannot show.
Real dot arrays are never one exact size — Size dispersion σ draws a Gaussian ensemble of dot diameters, each solved independently. Their individual Lorentzian absorption lines sum into one inhomogeneously-broadened ensemble spectrum, plotted live above the band diagram. A narrow σ gives a sharp resonance; a wide σ flattens and smears it — this is why real QDIP absorption bands are broad while a single dot's line is not.
An excited electron escapes the dot by tunneling through the tilted barrier under bias. This model computes the actual WKB transmission through a triangular barrier (field F = V/d, d = 12 nm):
T_WKB = exp[ −4√(2m*)·Eₐ^1.5 / (3ħqF) ]
where Eₐ = V₀ − E₁ is read directly off the same finite-well solution — not an arbitrary logistic curve. Dark current instead escapes thermally, and the barrier it climbs is lowered by the field via the Poole-Frenkel effect (image-charge lowering of a Coulomb-like barrier edge):
ΔΦ_PF = √(q³F / (πε)), ε = 12.9·ε₀ (GaAs)
I_dark ∝ T²·exp[ −(Eₐ−ΔΦ_PF) / (k_B T) ]
Photocurrent and dark current are therefore driven by two physically distinct escape mechanisms — field tunneling versus thermally-assisted barrier lowering — rather than sharing one ad-hoc bias dependence.