Sequential tunneling and spin degeneracy of zero-dimensional states

The effects of the spin degeneracy of single, zero-dimensional, localized, donor impurity states are investigated. We report a nontrivial effect on the zero-magnetic-field current-voltage $\left[I\right(V\left)\mathrm{}\right]$ characteristics of a localized state resulting from its spin degeneracy. We detect a deviation from the expected Fermi function thermal broadening of the observed current step in the $I\left(V\right)\mathrm{}$ characteristics. We quantitatively model this deviation in a sequential tunneling picture in terms of a new phenomenological parameter, the occupancy of the localized state $\mathrm{}\left(p\right).$ The spin degeneracy of the state is lifted in a magnetic field (Zeeman splitting) causing the current step to split. The two fragments of the split current step are observed to have different magnitudes. An investigation of this effect also enables the measurement of p as reported earlier [Phys. Rev. Lett. 76, 1328 (1996)]. We compare the two methods of determining the occupancy (p) and find a good agreement between them. Both these methods also enable us to determine the electron tunneling rates across each of the two potential barriers of the device independently. We also identify certain features in the $I\left(V\right)\mathrm{}$ characteristics at higher bias that have different thermal and magnetic-field properties than most other regular features. We attribute these to double occupancy of the electrons in the localized states when the barrier for that is overcome at higher bias. The phenomenological theory developed in this paper explains these observations quite accurately.