From the parametric amplification in Electric Force Microscopy to the Scanning Gate Microscoppy of Quantum Rings

The continuous size reduction of electronic devices have brought new technical and scientific demands. Firstly, because new peculiar physical effects appear at small scales. Secondly, probing electronic properties at the local scale requires new adapted instrumentation. These two issues have become crucial to the development of the so-called nano-electronics. The objective of this thesis is two fold: enhancing the sensitivity of charge detection deposed over surfaces and the real-space imaging of the wave-function inside buried open nano-devices. To achieve these goals we have conceived a low temperature Atomic Force Microscope (AFM) adapted to study electrical properties over surfaces. In the first chapter of this thesis we describe the operation of the AFM and the technical options. In the second chapter, we describe a parametric method to increase the sensitivity of an AFM to deposed charges over a surface. The movement of the AFM probe is described analytically which is confirmed by numerical solutions and experiments. We conclude that with such a method the thermal noise limit can be beaten. In the same chapter, we make a remark concerning a widespread technique: the Kelvin Force Microscopy (KFM). We show that, in this case, and even if it is not intentional, parametric effect is always present which might substantially change the expected resolution calculated from classical approaches. In the third and last chapter, we address the electronic transport in mesoscopic systems fabricated from two-dimensional electron gases (2DEGs). Traditionally, this kind of samples are characterized with four-point conductance measurements at low temperature. This technique provides information which is averaged over the size of the whole device and, as such, losses the local information. Here, we complement this analysis using the AFM probe as a polarized moving gate that induces a local perturbation of the potential experienced by the 2DEG. As the tip is scanned over the surface, a conductance map is built. This technique is called Scanning Gate Microscopy (SGM). So far, only a limited number of SGM experiments were performed. Here, we use a model sample fabricated from InGaAs heterostructure: a quantum ring (QR). By coupling experiments and quantum mechanical simulations we conclude that SGM permits probing the coherent transport and imaging the electronic probability density inside the QR.