Quantum Dot FRET Cascade | mysimulator.uk

Cascade Geometry

Dot spacing r 4.0 nm

Förster radius R₀ 5.0 nm

Donor lifetime τ_D 2.0 ns

Excitation

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FRET efficiency / hop

Transfer rate k_FRET

0 ns⁻¹

Cascade efficiency (measured, QD1→QD4)

— (0 runs)

QD1 440 nm → QD2 510 nm → QD3 580 nm → QD4 650 nm

Excitons pumped: 0 Reached QD4: 0

How it works

Förster resonance energy transfer (FRET) is non-radiative dipole–dipole coupling between an excited "donor" and a nearby "acceptor" whose absorption spectrum overlaps the donor's emission. In a quantum-dot cascade, each dot's bandgap (and hence emission colour) is tuned by its size, so a chain of progressively larger dots relays an exciton from a high-energy donor down to a low-energy terminal acceptor, one hop at a time.

E(r)      = 1 / (1 + (r / R₀)⁶)
k_FRET(r) = (1 / τ_D) · (R₀ / r)⁶
R₀ = Förster radius: the r at which E = 50%

The steep inverse-sixth-power distance dependence is what makes FRET useful as a "spectroscopic ruler" — efficiency collapses from near 100% to near 0% over a few nanometres. It also sets a hard competition at every hop: transfer (rate k_FRET) races against the donor's own radiative/non-radiative decay (rate 1/τ_D). This simulator runs that race stochastically for each pumped exciton.

Dot spacing r — the edge-to-edge distance between adjacent quantum dots; increasing it suppresses transfer as 1/r⁶.
Förster radius R₀ — set by the spectral-overlap integral J and dipole orientation factor κ²; larger R₀ means efficient transfer over a longer range.
Donor lifetime τ_D — the intrinsic excited-state lifetime; a longer-lived donor gives FRET more time to win the race before radiative decay.
Excite donor — injects one exciton at QD1 and lets it random-walk down the cascade (or decay early) using the real per-hop probabilities above.

Real-world relevance: exactly this cascade geometry is used in QD-based light-harvesting antennas, FRET biosensors, and multi-step energy-transfer LEDs, where a directional relay concentrates excitation onto a single low-bandgap emitter.

QD1 donor QD2 QD3 QD4 acceptor

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