AFM AND RELATED MICROSCOPY

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I. SCANNING GATE MICROSCOPY OF A QUANTUM RING

We have carried out low-temperature Scanning Gate Microscopy (SGM) measurements on semiconductor quantum rings (QRs) in a magnetic field using the cryogenic AFM developped in our lab and briefly described below (part II). The electrically-polarized AFM tip is scanned over the surface, both inside and outside the quantum structure, with the ultimate goal of mapping in real space its electron transport propreties and possibly building an image of the wavefunction of the coherent electron system.

Our QRs have been patterned from a high-mobility 2DEG (GaInAs heterostructure) buried close to the sample surface (25 nm) to ensure an efficient coupling with the AFM tip. They have typical outer (inner)  diameters of 650 (200) nm. GaInAs has been chosen because it has favorable coherence length scales for electron transport at low temperature (Hackens et al., PRL 94, 146802 (2005)). Our measurements are performed at 4.2 K and in a magnetic field up to 6 T. Aharonov-Bohm (AB) oscillations are seen in the QR magnetoconductance as a clear signature for the contribution of coherent effects.

The SGM images reveal striking oscillations of the conductance both inside and outside the ring as the tip scans over the surface: see images on our welcome page. Inside the ring, these oscillations follow the QR radial symmetry with a characteristic length of 100 nm much larger than the Fermi wavelength (25 nm). Outside the ring, the SGM images also exhibit oscillations, but they are concentric with the ring. A detailed analysis of the conductance maps as a function of relevant experimental parameters (e.g. tip voltage) allows us to discriminate clearly between coherent contributions, related to electron interferences inside the ring, and ballistic contributions, due to billiard ball-like trajectories of the electrons within the QR. In particular, we have shown that the concentric fringes outside the ring are from a coherent origin and form a real-space image of the AB effect.
 

II. Electric Force Microscopy (EFM)

The main goal of this project is the local electric coupling of an AFM tip (see figure) with electric charges  in semiconductor nanostructures in order to  detect and study their spatial distribution, down to a single electron, and to possibly manipulate them with the tip. In nanostructures that are burried at a few nm depth below the free surface and that are subjected to a very low bias during the electric measurements, it is mandatory to work at low temperature (4.2K) in a non-contact mode with a very good force sensitivity (< 1 pN ; 1 pN= 10^-12 newton, that is the magnitude of the Coulomb interaction between two elementary charges located at 15 nm apart).

In this context, we have developped (collaboration with  J. Chevrier et F. Marchi, LEPES, CNRS Grenoble) a low-temperature AFM along the lines of the instrument developped by  K. Karrai at the University of Munich (see M. Vogel et al., Appl. Phys. Lett. 78, 2592 (2001)). In this AFM, the cantilever deflection is measured by means of a Perot-Fabry microcavity that can be electrically or piezoelectrically tuned. This allows to work at low temperature, thereby reducing the thermal noise on the cantilever, and to adjust the force sensitivity by tuning the cavity length. As a result, the force sensitivity has been measured at 2 fN.(Hz)^-1/2 at 33 K by analysing the thermal noise, see figure below.