Single-shot measurement and tunnel-rate spectroscopy of a Si/SiGe few-electron quantum dot

We investigate the tunnel rates and energies of excited states of small numbers of electrons in a quantum dot fabricated in a Si/SiGe heterostructure. Tunnel rates for loading and unloading electrons are found to be strongly energy dependent, and they vary significantly between different excited states. We show that this phenomenon enables charge sensing measurements of the average electron occupation that are analogous to Coulomb diamonds. Excited-state energies can be read directly from the plot, and we develop a rate model that enables a quantitative understanding of the relative sizes of different electron tunnel rates.