Imaging Electrons in Few-Electron Quantum Dots

Electrons in a one-electron quantum dot were imaged in the Coulomb blockade regime at liquid He temperatures using a cooled scanning probe microscope (SPM). The SPM images are obtained by scanning a charged tip above the surface of the quantum dot and recording the conductance through the quantum dot in the Coulomb blockade regime as a function of tip position. The lowest energy level in the dot is shifted by the charged SPM tip. This creates a ring of high conductance in the SPM image corresponding to a Coulomb Blockade peak. Fits to the lineshape of the ring determine the tip-induced shift of the electron energy state in the dot. A technique for extracting the amplitude of the electronic wavefunction inside a quantum dot using a scanning probe microscope was proposed. A map of the shift in the energy level inside the quantum dot as a function of tip position is calculated from the SPM images. This energy shift, in first order perturbation theory, is given by a convolution of the wavefunction inside the quantum dot and the SPM tip potential. The wavefunction can therefore be calculated using a deconvolution method. The requirements for utilizing this technique include having a sharp tip perturbation relative to the size of the dot, low noise in the conductance measurements and knowing the shape of the tip perturbation accurately.