Kelvin Probe Spectroscopy of a Two-Dimensional Electron Gas Below 300 mK

A scanning force microscope with a base temperature below 300 mK is used for measuring the local electron density of a two-dimensional electron gas embedded in an Ga[Al]As heterostructure. At different separations between AFM tip and sample, a dc-voltage is applied between the tip and the electron gas while simultaneously recording the frequency shift of the oscillating tip. Using a plate capacitor model the local electron density can be extracted from the data. The result coincides within 10% with the data obtained from transport measurements.