Transport and Capacitance Spectroscopy of Quantum Dots

A review of recent theoretical studies on a single-electron tunneling in quantum dots is presented. This effect underlies the transport spectroscopy performed on the vertical gated quantum dots and the capacitance spectroscopy on the self-assembled quantum dots. The conditions of the single-electron tunneling are formulated in terms of electrochemical potentials of the electrons in the leads and in the quantum dot. The electrochemical potentials for the electrons confined in the quantum dots can be calculated by solving the many-electron Schrödinger equation. The results obtained by the Hartree-Fock method are presented. For the vertical gated quantum dot, the realistic confinement potential is obtained from the Poisson equation. The application of the self-consistent procedure to the solution of the Poisson-Schrödinger problem is discussed. The calculated positions of the current peaks at zero bias and boundaries of the Coulomb diamonds for non-zero bias are in good agreement with experiment. The influence of an external magnetic field on the single-electron tunneling is also discussed. The spin-orbital configurations of the electrons confined in the quantum dots change with the magnetic field, which leads to features observed in the current-voltage and capacitance-voltage characteristics.