Scanning tunneling spectroscopy is used to investigate single InAs nanocrys
tals, 2 to 8 nm in diameter. The tunneling current-voltage characteristics
exhibit a pronounced size dependence of both single electron charging energ
y and quantum-confined electronic states. These are well described using th
e "Orthodox Model" for single electron tunneling through a quantum dot with
a discrete level structure. Quantum confined states having atomic-like S a
nd P symmetries are directly identified in the tunneling spectra as two and
six-fold single electron charging multiplets, respectively. The tunneling
spectra acquired on un-passivated nanocrystals show clear evidence of sub-g
ap surface states. Surprisingly, excellent agreement is found between the s
trongly allowed optical transitions and spacing of levels detected in the t
unneling experiment.