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.; We have imaged the last electron in a quantum dot in a strong perpendicular magnetic field. Images show a ring of high conductance between zero and one electrons that shrinks in size and changes shape as the magnetic field is increased. We demonstrate that change in the ring diameter is mainly due to the diamagnetic shift in the one-electron ground state energy level in the dot: we estimate the diamagnetic shift, independent of the images, assuming a non-interacting electron picture, and show that the shrinking of the Coulomb blockade ring is consistent with the estimated diamagnetic energy shift. The shrinking of the ring can therefore be used as a measure of the diamagnetic shift of electrons in a quantum dot.