We present the first direct evidence of hot electrons traversing ballistically a thin GaAs layer. The energy distribution of the hot electrons associated with the momentum in the direction of the current was measured with the use of a tunneling-hot-electron-transfer amplifier as an electron spectrometer. The width of the ballistic peak was found to be about 60 meV for hot electrons with excess energy of some 300 meV above the thermal electrons. Those values are close to the expected initial injection values. PACS numbers: 72.20.i As the dimensions of semiconductor devices get smaller, the probability that electrons can traverse them without scattering at all, i.e. , ballistically, increases. Under these conditions the transport of electrons in the solid resembles that in vacuum, but with the effective mass and group velocity of the electrons in the semiconductor.A purely ballistic transport model was first calculated by Shur and Eastman. ' In a diode structure composed of n+-n -n+ layers, with the ballistic transport occurring in the n layer, a dc current-voltage characteristic at high injection levels was shown to obey the Child-Langmuir law I -V of a vacuum-tube diode if ideal boundary conditions were assumed. However, more realistic boundary conditions (due to carrier spillover from the n+ layers into the n layer) led to a different I Vcharacteristi-c, 2 which made the ballistic effect difficult to prove. Note also that most test structures suffered from inherent difficulties. Typical examples were large series resistances due to the Ohmic contacts and transport regions which could not be made short enough for the observation of the effect. 3 Three-terminal structures have been used as electron spectrometers and have demonstrated that hot electrons traverse thin semiconductor layers,~7 but no evidence for ballistic transport has been reported. We have measured the energy distribution of hot electrons at low temperatures, after they have traversed a thin n+-GaAs layer and were collected by a heterojunction collector. As we will show, about 50% of the injected hot electrons reached the collector without any measurable loss of energy, which proves for the first time the existence of ballistic transport in semiconductors.The energy diagram of the device used for this experiment is shown schematically in Fig.

We present a systematic investigation of the influence of cross geometry on the Hall effect in narrow ballistic wires. Various differently shaped cross regions have been fabricated, which demonstrate that near zero magnetic field the Hall resistance can be quenched, enhanced over its classical value, or even negative. A "last plateau" is seen in all devices, proving that its cause is not intimately linked to the quenching. A simple physical picture is presented showing how these effects come about from the scattering of electrons in such geometries. PACS numbers: 72.20.My, 73.50.Jt, 73.60.Br The quenching of the Hall effect is an intriguing result observed in narrow high-mobility devices by Roukes et al x and others. 2,3 As the magnetic field B is reduced, the Hall resistance RH (measured at voltage probes on either side of a narrow channel) forms a plateaulike feature (the "last plateau") and then drops sharply below its classical value so as to be close to zero ("quenched") in some finite region around B-0. This phenomenon has received considerable theoretical attention but it still lacks a definitive explanation. It has not been clear whether or not the last plateau and the quench are related, or indeed whether the effects are explicable solely in terms of single-particle transport theory. In this Letter, we describe measurements on several different cross geometries which yield alternatively quenched, enhanced, or negative RH-The last plateau, however, appears in all samples.It has been proposed that RH would be quenched if the channel width were less than the size of the edge states formed by the Lorentz force, 4 but the quantitative agreement with experiment was limited. 2 Very recently such narrow channels have been modeled quantum mechanically by a direct numerical solution of the Schrodinger equation together with the multiprobe resistance formula 5 to calculate RH from the scattering coefficients. 6 "" 9 A perfect cross with an infinite squarewell potential ("hard walls") quenches only for very specific values of the Fermi energy Ef, 1 contrary to experimental results, 2 which quench for a wide range of Ef. A similar model with a parabolic potential obtains ranges of E F where realistic-looking quenches occur. For more than two subbands, however, the quench has almost disappeared, whereas early devices 1,2 probably had between three and nine subbands populated when quenching was observed.New theoretical work 9 obtains generic quenching over wide ranges of E F and width by modifying the geometry and by energy averaging. The important change incorporated into the new model is collimation of the electrons as they enter the cross region. This is accomplished by adiabatic widening of the wire near the junction. Because the widening of the wire is gradual, the electrons at the Fermi surface do not populate the extra subbands available in the wider region, and because the subbands are depressed in the wider region, the ratio of the longitudinal momentum to the transverse momentum increases: The electrons ar...

We observe the magnetic-field-induced bifurcation of quantum levels into surface states and bulklike Landau states. The disruption of the electric field quantization by a magnetic field is most dramatic for electrons bound in two dimensions perpendicular to the magnetic field. The interplay between competing spatial and magnetic quantization mechanisms results in a pronounced and complex level splitting. The observed splitting of zero-dimensional energy levels depends critically on the size of the quantum dots, and can be explained with a calculated single-particle energy spectrum.PACS numbers: 73.20.Dx, 73.40.Kp, 73.50.Jt For more than half a century confined electron systems in a magnetic field have been investigated theoretically in terms of their influence on the Landau diamagnetism of free electrons. 1 " 3 Investigations of surface states in confined electron systems have been revived more recently in order to explain the quantized Hall effect. 4,5 Their skipping orbit nature is also demonstrated by transport measurements with ballistic point contacts. 6,7 The influence of edge states on the properties of the electron system is expected to increase with decreasing system size and even more dramatically with decreasing dimensionality. In an electron system that is free to move in only one dimension perpendicular to the magnetic field each electric subband transforms into a hybrid band when the magnetic length /# = (ft/e/?) 1/2 becomes comparable to the width of the electron system. With increasing magnetic field the energy separation between adjacent hybrid bands approaches the cyclotron energy and the density of states at the bottom of each hybrid band increases, so that the bands become Landau-level-like at high magnetic fields. There is a continuous transition and a one-to-one correspondence between the electric subband structure at zero-magnetic field and Landau-level-like hybrid bands at high-magnetic field. 8 " 10 In contrast a far more complex behavior is predicted for zero-dimensional (OD) systems. 1 " 3 At zero magnetic field the discrete energy levels are each occupied by two electrons except for degeneracies that depend on the symmetry of the confinement. With increasing magnetic field this degeneracy is lifted and hybrid levels originating from the same zero-field energy level join different Landau levels at high magnetic field. In general, there is no one-to-one correspondence between energy levels at zero magnetic field and Landau levels at high magnetic fields.The splitting of OD energy levels at low magnetic field is similar to the normal Zeeman splitting of electronic states in atoms. However, in atomic physics the magnetic field is usually a weak perturbation of the Coulomb confinement. To observe Landau-level-like behavior of atomic electrons either the magnetic field must be several orders of magnitude larger than those experimentally realizable today 11 or the atoms must be highly excited. 12 Because of the low effective mass and the high dielectric constant the hydrogenic states of s...

We report a direct observation, via electron energy spectroscopy, of lateral tunneling and lateral ballistic electron transport in a two-dimensional electron gas (2D EG). This was accomplished through the use of a novel transistor structure employing two potential barriers, induced by 50-nm-wide metal gates deposited on a GaAs/AlGaAs selectively doped heterostructure. Hot electrons with very narrow energy distributions ( -5 meV wide) have been observed to ballistically traverse 2D EG regions ==170 nm wide with a mean free path of about 480 nm. PACS numbers: 73.40.Gk, 73.20.Dx Ballistic transport of hot electrons was established recently in n "'"-type GaAs by the use of energy spectroscopy in a hot-electron structure. l These experiments utilized an injector at one end of a transport region and a spectrometer at the other end, with the electrons moving normal to the plane of the layers (vertical transport). This technique proved to be very powerful since it permitted the energy distribution and the mean free path of the ballistic electrons to be determined. The very recent demonstration of quantized resistance in a confined quasi-two-dimensional electron gas (2D EG) 2,3 strongly suggests ballistic transport of electrons near equilibrium parallel to the interface between the layers (lateral transport). We report here the first utilization of an energy spectroscopy technique to establish directly lateral tunneling through an induced potential barrier and the existence of lateral ballistic transport in a 2D EG. This was done by inducing two closely spaced potential barriers in the 2D EG via two narrow Schottky metal gates deposited on the surface of the structure. One barrier was employed as a tunnel injector and the second as a spectrometer. We have measured narrow hot-electron distributions ballistically traversing lateral 2D EG regions 170 nm wide, and have estimated their mean free path.Several structures were made on a selectively doped GaAs/AlGaAs heterostructure grown by molecularbeam epitaxy. On top of an undoped GaAs buffer layer, an undoped AlGaAs layer (50 nm thick, AlAs mole fraction x=34%) was grown, followed by a thin heavily doped GaAs cap layer (15 nm thick). A sheet of Si atoms, with an areal density of -2x 10 12 cm ~2, was deposited under overpressure of As when growth of the AlGaAs was interrupted (planar doping), 30 nm away from the GaAs buffer layer; these supply the electrons in the 2D EG [ Fig. 1(a)]. The 2D EG had a carrier density of 3x10 ll cm -2 and a mobility of 3xl0 5 cm 2 /Vsec at 4.2 K. Two parallel AuPd gates, each 52 nm wide and 0.5 jam long, were patterned 93 nm apart using electron-beam nanolithography, on a 5-^m-wide isolated 2D EG line [ Fig. 1(b)]. Ohmic contacts were made to the three regions defined by both gates. Biasing the gates negatively with respect to the central region between them (called the base) depleted the 2D EG underneath the gates and prevented the free motion of the equilibrium electrons among the three regions [emitter (E), base (B), and collector (C)]. The...

This Letter reports the results of a systematic study of the current-induced noise at the superconducting transition in thin, high-resistivity films of aluminum and tin. Analysis of the noise suggests that the onset of resistance is due to discrete phase slips of magnitude less than 2K. The results are discussed in terms of the vortex unbinding models of the superconducting transition in two dimensions.