Mapping the wave functions in quantum dots

We use magneto-tunnelling spectroscopy to investigate the form of the wave functions of the confined electron states in InAs self-assembled quantum dots. We are able to observe the wave functions corresponding to the ground and the two lowest excited states for dots grown on (1 0 0)- and (3 1 1)B-oriented GaAs substrates. For both orientations, the wave functions are found to have a biaxial symmetry in the growth plane, with axes parallel to main crystallographic directions. In addition, we have performed magneto-tunnelling spectroscopy measurements on tunnel diodes that incorporate gate electrodes. By observing how the energies of particular states vary with gate bias, we are able to identify the states associated with an individual dot. This allows us to measure quantitatively both the energy levels and wave functions of the dot states.