Mark Allen Topinka

Coherent branched flow in a two-dimensional electron gas.

Semiconductor nanostructures based on two-dimensional electron gases (2DEGs) could form the basis of future devices for sensing, information processing and quantum computation. Although electron transport in 2DEG nanostructures has been well studied, and many remarkable phenomena have already been discovered (for example, weak localization, quantum chaos, universal conductance fluctuations), fundamental aspects of the electron flow through these structures have so far not been clarified. However, it has recently become possible to image current directly through 2DEG devices using scanning probe microscope techniques. Here, we use such a technique to observe electron flow through a narrow constriction in a 2DEG—a quantum point contact. The images show that the electron flow from the point contact forms narrow, branching strands instead of smoothly spreading fans. Our theoretical study of this flow indicates that this branching of current flux is due to focusing of the electron paths by ripples in the background potential. The strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coherence in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design of future nanostructure devices.Semiconductor nanostructures based on two dimensional electron gases (2DEGs) have the potential to provide new approaches to sensing, information processing, and quantum computation. Much is known about electron transport in 2DEG nanostructures and many remarkable phenomena have been discovered (e.g. weak localization, quantum chaos, universal conductance fluctuations)1,2 - yet a fundamental aspect of these devices, namely how electrons move through them, has never been clarified. Important details about the actual pattern of electron flow are not specified by statistical measures such as the mean free path. Scanned probe microscope (SPM) measurements allow spatial investigations of nanostructures, and it has recently become possible to directly image electron flow through 2DEG devices using newly developed SPM techniques3-13. Here we present SPM images of electron flow from a quantum point contact (QPC) which show unexpected dynamical channeling - the electron flow forms persistent, narrow, branching channels rather than smoothly spreading fans. Theoretical study of this flow, including electron scattering by impurities and donor atoms, shows that the channels are not due to deep valleys in the potential, but rather are caused by the indirect cumulative effect of small angle scattering. Surprisingly, the channels are decorated by interference fringes well beyond where the simplest thermal averaging arguments suggest they should be found. These findings may have important implications for 2DEG physics and for the design of future nanostructure devices.

Imaging Electron Flow

New scanning probe techniques provide fascinating glimpses into the detailed behavior of semiconductor devices in the quantum regime.

Imaging electron density in a two-dimensional electron gas

Spatial profiles of the electron density in a two-dimensional electron gas were obtained from the spacing of interference fringes in coherent electron flow. Images of electron flow from a quantum point contact formed in a GaAs/AlGaAs heterostructure were recorded with a liquid He cooled scanned probe microscope. The images are decorated with interference fringes spaced by half the Fermi wavelength; the fringe spacing measures the electron density below the scanned probe microscope tip. As the density is decreased with a back gate, the fringe spacing increases in agreement with a planar capacitor model.

Charge-imaging field-effect transistor

Charge-imaging field-effect transistors (FETs) were fabricated from a GaAs/AlGaAs heterostructure containing a near-surface two-dimensional electron gas. These FETs have quantum point contact geometries to minimize the size of the channel and to improve the spatial resolution. The charge noise at T=4.2 K has a 1/f behavior and reaches values ≪1e/Hz1/2 at 30 kHz. The spatial resolution of the FET was measured at liquid He temperatures using a scanned probe microscope with a charged tip. The charge sensitivity of the FET is confined to a disk with full width at half maximum 340 nm. These FETs are suitable for integration onto a GaAs/AlGaAs scanned probe microscopy cantilever.

Imaging coherent electron wave flow in a two-dimensional electron gas

Abstract We measure the energy distribution of electrons passing through a two-dimensional electron gas using a scanning probe microscope (SPM). We present direct spatial images of coherent electron wave flow from a quantum point contact formed in a GaAs/AlGaAs two-dimensional electron gas using a liquid He cooled SPM. A negative voltage is placed on the tip, which creates a small region of depleted electrons that backscatters electron waves. Oscillating the voltage on the tip and locking into this frequency gives the spatial derivative of electron flow perpendicular to the direction of current flow. We show images of electron flow using this method. By measuring the amount of electrons backscattered as a function of the voltage applied to the tip, the energy distribution of electrons is measured.

Imaging coherent electron flow in a two-dimensional electron gas

Images of coherent electron ow through a two-dimensional electron gas in a GaAs/AlGaAs heterostructure from a quantum point contact (QPC) were obtained at liquid He temperatures by using a scanning probe microscope with a charged tip that backscatters electrons. Near the QPC, at distances less than 500 nm, the images show angular lobes of electron ow in patterns determined by the quantum modes of the QPC. At greater distances, narrow branches of electron ow are observed, formed by the cumulative e;ects of small-angle scattering. In addition, the images show fringes spaced by half the Fermi wavelength, evidence that the electron ow is coherent. These observations agree well with theoretical simulations of electron ow. ? 2003 Published by Elsevier Science B.V.