Phonon Bottleneck: Hot-Carrier Cooling — 2D Ensemble View

Quantum confinement turns a semiconductor's continuous conduction band into a discrete ladder of energy levels, and single-LO-phonon emission only conserves energy when that level spacing matches the crystal's fixed phonon energy — a mismatched ladder stalls relaxation for far longer than in bulk material, the phonon bottleneck. Where the 3D version follows one photoexcited electron down the ladder, this 2D counterpart runs a real ensemble of 240 independently-simulated carriers through the same continuous-time Markov process and plots the population statistics directly: a live waterfall of the whole swarm, the Lorentzian phonon-resonance curve every carrier's hazard rate is drawn from, and a real-time check of the simulated mean level against its closed-form Poisson-process prediction. Tune the dot material, level spacing, phonon linewidth and Auger coupling to see the swarm's cooling rate and its theoretical curve move together.