Single-Electron Tunneling Events in a Quantum Dot

Bias Controls

Gate charge n_g (e) 0.20

Source–drain bias V (meV) 0.80

Temperature T (K) 4.0

Tunneling rate Γ₀ (Hz) 2.0

Live Readouts

Dot charge n

0 e

Tunnel current I

0.0 pA

Total rate Γ

0.0 Hz

Electrons moved

Regime

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How it works

A quantum dot weakly coupled to source and drain leads through tunnel junctions, and capacitively coupled to a gate, forms a single-electron transistor (SET). Adding one electron costs a charging energy set by the dot's tiny total capacitance C:

E(n) = E_C (n − n_g)²,     E_C = e² / 2C
n_g = C_g V_g / e   (gate-induced charge, in units of e)

Each of the four possible tunneling events (source→dot, dot→source, drain→dot, dot→drain) has an energy cost ΔE built from E(n), the bias V and the lead it crosses. The orthodox theory of single-electron tunneling gives its rate from Fermi's golden rule for a metallic tunnel junction:

Γ(ΔE) = Γ₀ · (ΔE / E_C) / (1 − exp(−ΔE / k_B T))

ΔE>0 means the process costs energy — it is exponentially suppressed once k_BT ≪ E_C, which is Coulomb blockade: no electron can hop on or off the dot, so current is pinned near zero. Away from a charge-degeneracy point (n_g half-integer) the dot sits in a well-defined blockade valley; at n_g = 0.5, 1.5, … the n and n+1 charge states are degenerate and current flows freely — the periodic Coulomb oscillation peaks that make an SET the most sensitive electrometer known.

n_g slider — moves the gate-induced charge; sweeping it traces out a Coulomb oscillation, the same measurement used to read out a nearby charge qubit.
Bias V — the source–drain voltage; larger |V| widens the conducting region.
Temperature — raises k_BT, smearing the blockade until thermal fluctuations overwhelm E_C.
Γ₀ — an overall attempt-rate scale (proportional to 1/R of the tunnel junctions); it only rescales the animation speed, not the physics.

At every animation frame the simulator draws a real stochastic event from these four Poisson rates (a Gillespie-style Monte Carlo of the master equation) — the flying spheres you see are individual electrons, not a smoothed average.

Electron on dot Fermi sea (leads) Tunneling electron

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🔘 Single-Electron Tunneling Events in a Quantum Dot