Simulation of single-electron charging effects in planar nanoscale devices

Electronic structure and properties of single and coupled planar quantum dots are investigated. Three-dimensional Schroedinger equations coupled to Poisson equations are solved under the density functional formalism, for a small number of electrons in the dots. In particular, the effects of electron-electron interaction on the shell structure of single quantum dots are studied by considering two types of dots---the grid-gate dot with a two-dimensional symmetry and the quad-gate dot with a rectangular symmetry. It is observed that electron-electron interaction does not appreciably alter the shell structure of the grid-gate dot, whereas it does alter the shell structure in the quad-gate dot in an unpredictable manner. For the grid-gate dot the addition energy spectrum concurs well with the experimental results of Tarucha et al. [1], given that our model does not explicitly account for electron spin.;By expanding the model to incorporate electron spin under the Local Spin Density Approximation, the charging properties of the double quantum dot are investigated in terms of electron spin and interdot interaction. It is shown that both electrostatic and quantum mechanical coupling between the dots affect the charging properties. For weak interdot coupling, simultaneous or double charging of the two constituent dots occurs, as seen in recent experiments by Waugh and co-workers [2]. It is argued that the double charging model may be used to explain the phenomenon of pair tunneling in vertical dots observed by Ashoori et al. [3]. It is also shown that a spin polarized state can be realized for weak interdot coupling, with four electrons in each dot, a situation explained in terms of Hund's rules. Lastly, it is shown that a ferromagnetic-like state can be obtained for three electrons in the double-dot by varying the interdot coupling strength. As the interdot barrier is lowered, the pz states in the two dots couple to form a bonding state that is delocalized over both. For small energy spacing between the 1 s and the bonding states, the ground state for three electrons has an electron in the 1s state of each dot and the delocalized pz bonding state, with the spins of all the electrons aligned parallel.