Periodic and Aperiodic Bunching in the Addition Spectra of Quantum Dots

We study electron addition spectra of quantum dots in a broad range of electron occupancies starting from the first electron. Spectra for dots containing $<200\mathrm{}$ electrons reveal a surprising feature. Electron additions are not evenly spaced in gate voltage. Rather, they group into bunches. With an increasing number of electrons the bunching evolves from occurring randomly to periodically at about every 5th electron. The periodicity of the bunching and features in electron tunneling rates suggest that the bunching is associated with electron additions into spatially distinct regions within the dots.