Quantum Dot Charging Energy Explorer

Every quantum dot has a charging energy — the electrostatic cost of squeezing one more electron onto a nanoscale island, E_C = e²/2C_Σ. This simulator renders a 3D quantum dot whose radius and dielectric environment set its capacitance, and lets you sweep a gate voltage while watching electrons dock onto the dot one at a time in a Coulomb staircase. A live energy-ladder chart plots E(N) = E_C(N − n_g)² for the electron numbers nearest the ground state, and a temperature control shows how raising k_BT toward E_C thermally smears the sharp steps into a smooth ramp — the same competition between charging energy and thermal energy that determines whether Coulomb blockade is observable in a real single-electron device.