Publications

Fractional quantum statistics are a signature prediction of fractional quantum Hall states, which have long been elusive in experiments. Here, we present the observation of anyonic interference and exchange phases in a novel co-propagating 'optical-like' Mach-Zehnder Interferometer. This architecture is free of charging and backscattering effects that often plague the widely used Fabry-Perot interferometer, thus exhibiting pristine Aharonov-Bohm (AB) interference without fractional phase slips. We studied the three lowest Jain filling factors, {\nu}=1/3, 2/5, and 3/7, which host quasiparticles with fractional charges e*=e/3, e/5, and e/7, respectively. The observed AB interference patterns, plotted as a function of magnetic field B and modulation-gate voltage, VMG (known as pajamas), exhibited the expected flux periodicities: 3{\Phi}0, 5{\Phi}0, and 7{\Phi}0, with {\Phi}0 being the flux quantum. A small biased top gate (TG) deposited in the center of the interferometer induces local quasiparticles that are spatially isolated from the interfering modes. At non-zero TG voltage VTG, quantized phase slips appear in the AB pajamas approximately with every flux quantum that pierces the effective area below the TG. Moreover, when tuning VTG, at a constant magnetic field, abrupt phase jumps corresponding to adding one localized quasiparticle at a time under the top gate appear in the B-VTG pajamas.

Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an 'entanglement pointer' and a 'statistics-induced entanglement entropy'. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics; (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following 'collisions'), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.

Interferometry is a vital tool for studying fundamental features in the quantum Hall effect. For instance, Aharonov-Bohm interference in a quantum Hall interferometer can probe the wave-particle duality of electrons and quasiparticles. Here, we report an unusual Aharonov-Bohm interference of the outermost edge mode in a quantum Hall Fabry-Pérot interferometer, whose Coulomb interactions were suppressed with a grounded drain in the interior bulk of the interferometer. In a descending bulk filling factor from νb=3 to νb≈(5/3), the magnetic field periodicity, which corresponded to a single "flux quantum,"agreed accurately with the enclosed area of the interferometer. However, in the filling range, νb≈(5/3) to νb=1, the field periodicity increased markedly, a priori suggesting a drastic shrinkage of the Aharonov-Bohm area. Moreover, the modulation gate voltage periodicity decreased abruptly at this range. We attribute these unexpected observations to edge reconstruction, leading to area changing with the field and a modified modulation gate-edge capacitance. These reproducible results support future interference experiments with a quantum Hall Fabry-Pérot interferometer.

Correlations of partitioned particles carry essential information about their quantumness1. Partitioning full beams of charged particles leads to current fluctuations, with their autocorrelation (namely, shot noise) revealing the particles charge2,3. This is not the case when a highly diluted beam is partitioned. Bosons or fermions will exhibit particle antibunching (owing to their sparsity and discreteness)4,5,6. However, when diluted anyons, such as quasiparticles in fractional quantum Hall states, are partitioned in a narrow constriction, their autocorrelation reveals an essential aspect of their quantum exchange statistics: their braiding phase7. Here we describe detailed measurements of weakly partitioned, highly diluted, one-dimension-like edge modes of the one-third filling fractional quantum Hall state. The measured autocorrelation agrees with our theory of braiding anyons in the time domain (instead of braiding in space); with a braiding phase of 2θ=2π/3, without any fitting parameters. Our work offers a relatively straightforward and simple method to observe the braiding statistics of exotic anyonic states, such as non-abelian states8, without resorting to complex interference experiments9.

The topological order of a quantum Hall state is mirrored by the gapless edge modes owing to bulk-edge correspondence. The state at the filling of ν = 5/2, predicted to host non-abelian anyons, supports a variety of edge modes (integer, fractional, neutral). To ensure thermal equilibration between the edge modes and thus accurately determine the states nature, it is advantageous to isolate the fractional channel (1/2 and neutral modes). In this study, we gapped out the integer modes by interfacing the ν = 5/2 state with integer states ν = 2 and ν = 3 and measured the thermal conductance of the isolated-interface channel. Our measured half-quantized thermal conductance confirms the non-abelian nature of the ν = 5/2 state and its particle-hole Pfaffian topological order. Such an isolated channel may be more amenable to braiding experiments.

According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines the topological order in the gapped bulk. As the bulk is less accessible, the last two decades saw the emergence of several experimental techniques that invoke the study of the compressible edge. We review the properties of the edge, and describe several experimental techniques that include shot noise and thermal noise measurements, interferometry, and energy (thermal) transport at the edge. We pay special attention to the filling factor 5/2 in the first excited Landau level (in two-dimensional electron gas in GaAs), where experimental evidence of a non-Abelian topological order was found. A brief discussion is devoted to recent interferometry experiments that uncovered unexpected physics in the integer quantum Hall effect. The article also addresses the theory of edge states, for systems with Abelian and non-Abelian topological orders.

Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum. Only under certain experimental parameters, a closing of the superconducting bulk-gap that is followed by its reopening, appears simultaneously with a ZBCP at the edge. Such events suggest the occurrence of a topologically non-trivial phase. Yet, we also find that ZBCPs are observed under different tuning parameters without simultaneous reopening of a bulk-gap. This demonstrates the importance of simultaneous probing of bulk and edge in the identification of Majorana edge-states.

Topological states of matter are characterized by topological invariants, which are physical quantities whose values are quantized and do not depend on the details of the system (such as its shape, size and impurities). Of these quantities, the easiest to probe is the electrical Hall conductance, and fractional values (in units of e ²/h, where e is the electronic charge and h is the Planck constant) of this quantity attest to topologically ordered states, which carry quasiparticles with fractional charge and anyonic statistics. Another topological invariant is the thermal Hall conductance, which is harder to measure. For the quantized thermal Hall conductance, a fractional value in units of κ ₀ (κ ₀ = π ²k _B²/(3h), where k _B is the Boltzmann constant) proves that the state of matter is non-Abelian. Such non-Abelian states lead to ground-state degeneracy and perform topological unitary transformations when braided, which can be useful for topological quantum computation. Here we report measurements of the thermal Hall conductance of several quantum Hall states in the first excited Landau level and find that the thermal Hall conductance of the 5/2 state is compatible with a half-integer value of 2.5κ ₀, demonstrating its non-Abelian nature.

The thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized noninteger value κxy=5/2 (in units of temperature times π2kB2/3h), which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict κxy=3/2 or 7/2. We resolve this contradiction by invoking the disorder-induced formation of mesoscopic puddles with locally κxy=3/2 or 7/2. Interactions between these puddles generate a coherent macroscopic state that exhibits a plateau with quantized κxy=5/2. The non-Abelian quasiparticles characterizing this phase are distinct from those of the microscopic puddles and, by the same mechanism, could even emerge from a system comprised of microscopic Abelian puddles.

The nature of edge reconstruction in the quantum Hall effect (QHE) and the issue of where the current flows have been debated for years. Moreover, the recent observation of proliferation of 'upstream' neutral modes in the fractional QHE has raised doubts about the present models of edge channels. Here, we present a new picture of the edge reconstruction in two of the hole-conjugate states. For example, while the present model for 1/2 = (2/3) consists of a single downstream chiral charge channel with conductance (2/3)(e 2 /h) and an upstream neutral mode, we show that the current is carried by two separate downstream chiral edge channels, each with conductance (1/3)(e 2 /h). We uncover a novel mechanism of fragmentation of upstream neutral modes into downstream propagating charge modes that induces current fluctuations with zero net current. Our unexpected results underline the need for better understanding of edge reconstruction and energy transport in all fractional QHE states.

This Rapid Communication was motivated by the quest for observing interference of fractionally charged quasiparticles. Here, we study the behavior of an electronic Mach-Zehnder interferometer at the integer quantum Hall effect regime at filling factors greater than 1. Both the visibility and the velocity were measured and found to be highly correlated as a function of the filling factor. As the filling factor approached unity, the visibility quenched, not to recover for filling factors smaller than unity. Alternatively, the velocity saturated around a minimal value at the unity filling factor. We highlight the significant role interactions between the interfering edge and the bulk play as well as that of the defining potential at the edge. Shot-noise measurements suggest that phase averaging (due to phase randomization), rather than single-particle decoherence, is likely to be the cause of the dephasing in the fractional regime.

The fractional quantum Hall effect is a canonical example of topological phases. While electric currents flow downstream in edge modes, neutral edge modes, observed only in hole-conjugate states and in v 1/2=5/2, flow upstream. It is believed that the latter transport results from multiple counter-propagating channels-mixed by disorder that is accompanied by Coulomb interaction. Here we report on sensitive shot noise measurements that reveal unexpected presence of neutral modes in non-hole-conjugate fractional states; however, not in the integer states. Furthermore, the incompressible bulk is also found to allow energy transport. While density reconstructions along the edge may account for the energy carrying edge modes, the origin of the bulk energy modes is unidentified. The proliferation of neutral modes changes drastically the accepted transport picture of the fractional quantum Hall effects. Their apparent ubiquitous presence may explain the lack of interference of fractional quasiparticles-preventing observation of fractional statistics.

We report an observation, via sensitive shot noise measurements, of charge fractionalization of chiral edge electrons in the integer quantum Hall effect regime. Such fractionalization results solely from interchannel Coulomb interaction, leading electrons to decompose to excitations carrying fractional charges. The experiment was performed by guiding a partitioned current carrying edge channel in proximity to another unbiased edge channel, leading to shot noise in the unbiased edge channel without net current, which exhibited an unconventional dependence on the partitioning. The determination of the fractional excitations, as well as the relative velocities of the two original (prior to the interaction) channels, relied on a recent theory pertaining to this measurement. Our result exemplifies the correlated nature of multiple chiral edge channels in the integer quantum Hall effect regime.

Controlled dephasing of electrons, via "which path" detection, involves, in general, coupling a coherent system to a current driven noise source. However, here we present a case in which a nearly isolated electron puddle within a quantum dot, at thermal equilibrium and in millikelvin range temperature, fully dephases the interference in a nearby electronic interferometer. Moreover, the complete dephasing is accompanied by an abrupt π phase slip, which is robust and nearly independent of system parameters. Attributing the robustness of the phenomenon to the Friedel sum rule-which relates a system's occupation to its scattering phases-proves the universality of this powerful rule. The experiment allows us to peek into a nearly isolated quantum dot, which cannot be accessed via conductance measurements.

The evolution of the fractional quantum Hall state at filling 5/2 is studied in density tunable two-dimensional electron systems formed in wide wells in which it is possible to induce a transition from single- to two-subband occupancy. In 80 and 60 nm wells, the quantum Hall state at 5/2 filling of the lowest subband is observed even when the second subband is occupied. In a 50 nm well, the 5/2 state vanishes upon second subband population. We attribute this distinct behavior to the width dependence of the capacitive energy for intersubband charge transfer and of the overlap of the subband probability densities.

Charged excitations in the fractional quantum Hall effect are known to carry fractional charges, as theoretically predicted and experimentally verified. Here we report on the dependence of the tunneling quasiparticle charge, as determined via highly sensitive shot noise measurements, on the measurement conditions, in the odd denominators states v=1/3 and v=7/3, and in the even denominator state v=5/2. In particular, for very weak backscattering probability and sufficiently small excitation energies (temperature and applied voltage), tunneling charges across a constriction were found to be significantly higher than the theoretically predicted fundamental quasiparticle charges.

Charge excitations in a two dimensional electron gas, under a quantizing magnetic field and in the fractional quantum Hall effect regime, flow in one dimensional-like strips along the edges of the sample. These excitations (quasiparticles) may be independent or condense into an interacting chiral Luttinger liquid. Adding a backscattering potential, which reflects a forward propagating quasiparticle to a backward propagating one, partitions the stream of quasiparticles and induces quantum shot noise. The noise is proportional to quasiparticles charge and may be affected by their mutual interactions. The dependence of the determined charge on the temperature, excitation energy, and partitioning will be describes for a few fractional states, revealing in some cases a universal behavior.

The growth of wurtzite GaAs and InAs nanowires with diameters of a few tens of nanometers with negligible intermixing of zinc blende stacking is reported. The suppression of the number of stacking faults was obtained by a procedure within the vapor-liquid-solid growth, which exploits the theoretical result that nanowires of small diameter (∼10 nm) adopt purely wurtzite structure and are observed to thicken (via lateral growth) once the axial growth exceeds a certain length.

We report on noise measurements in a quantum dot in the presence of Kondo correlations. Close to the unitary limit, with the conductance reaching 1.8 e2 h, we observed an average backscattered charge of e* ∼5e 3, while weakly biasing the quantum dot. This result held to bias voltages up to half the Kondo temperature. Away from the unitary limit, the charge was measured to be e as expected. These results confirm and extend theoretical predictions that suggested that two-electron backscattering processes dominate over single-electron backscattering processes near the unitary limit, with an average backscattered charge e* ∼5e 3.

The fractional quantum Hall effect, where plateaus in the Hall resistance at values of h/νe² coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. (Here h is Planck's constant, ν the filling factor and e the electron charge.) Current flows along the sample edges and is carried by charged excitations (quasiparticles) whose charge is a fraction of the electron charge. Although earlier research concentrated on odd denominator fractional values of ν, the observation of the even denominator ν = 5/2 state sparked much interest. This state is conjectured to be characterized by quasiparticles of charge e/4, whose statistics are 'non-abelian'-in other words, interchanging two quasiparticles may modify the state of the system into a different one, rather than just adding a phase as is the case for fermions or bosons. As such, these quasiparticles may be useful for the construction of a topological quantum computer. Here we report data on shot noise generated by partitioning edge currents in the ν = 5/2 state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other possible values, such as e/2 and e. Although this finding does not prove the non-abelian nature of the ν = 5/2 state, it is the first step towards a full understanding of these new fractional charges.

A consistent approach in forming the 0.7 structure by using a quantum dot rather than a quantum point contact is demonstrated. With this scheme, it was possible to tune on and off the 0.7 structure. The 0.7 structure continuously evolved into a normal integer conductance plateau by varying the tuning condition. Unlike the conventional 0.7 plateau, the new 0.7 structure was observed even at low electron temperatures down to 100 mK, with unprecedented flatness. From our results, it is concluded that electron interference should be taken into consideration to explain the 0.7 structure.

Resonant tunneling through two identical potential barriers renders them transparent, as particle trajectories interfere coherently. Here we realize resonant tunneling in a quantum dot (QD), and show that detection of electron trajectories renders the dot nearly insulating. Measurements were made in the integer quantum Hall regime, with the tunneling electrons in an inner edge channel coupled to detector electrons in a neighboring outer channel, which was partitioned. Quantitative analysis indicates that just a few detector electrons completely dephase the QD.

Fractionally charged quasiparticles in edge states, are expected to condense to a chiral Luttinger liquid (CLL). We studied their condensation by measuring the conductance and shot noise due to an artificial backscatterer embedded in their path. At sufficiently low-temperatures backscattering events were found to be strongly correlated, producing a highly nonlinear current-voltage characteristic and a nonclassical shot noiseboth are expected in a CLL. When, however, the impinging beam of quasiparticles was made dilute, either artificially via an additional weak backscatterer or by increasing the temperature, the resultant outgoing noise was classical, indicating the scattering of independent quasiparticles. Here, we study in some detail this surprising crossover from correlated particle behavior to an independent behavior, as a function of beam dilution and temperature.

The direct measurement of charge and its distribution was reported in a Kondo correlated quantum dot (QD). It was revealed by a noninvasive potential-sensitive detector that, although the conductance of the QD was significantly enhanced as it entered in the Kondo regime, the average charge remained unaffected. The separation between spin and charge degrees of freedom was also demonstrated. An abrupt redistribution of charge in the QD, taking place with an onset of Kondo correlation was found under certain conditions. A correlation between the spin and charge degrees of freedom was suggested.

Transmission phase of a quantum dot (QD) with Kondo correlation near the unitary limit was studied. It was observed that the transition phase was linear when the Fermi energy was scanned through a spin degenerate energy level of the QD. The phase in the Coulomb Blockade regime was however strongly affected by a preexistence of Kondo correlation.

We measured the phase evolution of electrons as they traverse a quantum dot (QD) formed in a two-dimensional electron gas that serves as a localized spin. The traversal phase, determined by embedding the QD in a double path electron interferometer and measuring the quantum interference of the electron wave functions manifested by conductance oscillation as a function of a weak magnetic field, evolved by π radians, a range twice as large as theoretically predicted. As the correlation weakened, a gradual transition to the familiar phase evolution of a QD was observed. The specific phase evolution observed is highly sensitive to the onset of Kondo correlation, possibly serving as an alternative fingerprint of the Kondo effect.

In this chapter we review recent developments in both theoretical and experimental aspects of quantum shot noise. We discuss the properties of shot noise in systems of various sizes from mesoscopic, ballistic, systems to classical diffusive conductors. In particular we consider the effect of the elctron's Fermi statistics on shot noise. In addision, we discuss shot noise as a tool for charge measurements. The Fractional Quantum Hall system which gives rise to an appearance of new elementary excitations which carry a smaller charge, hence resulting in a suppressed shot noise.

The transport properties of electronic devices are usually characterized on the basis of conductance measurements. Such measurements are adequate for devices in which transport occurs incoherently, but for very small devices- such as quantum dots-the wave nature of the electrons plays an important role. Because the phase of an electron's wavefunction changes as it passes through such a device, phase measurements are required to characterize the transport properties fully. Here we report the results of a double-slit interference experiment which permits the measurement of the phase-shift of an electron traversing a quantum dot. This is accomplished by inserting the quantum dot into one arm of an interferometer, thereby introducing a measurable phase shift between the arms. We find that the phase evolution within a resonance of the quantum dot can be accounted for qualitatively by a model that ignores the interactions between the electrons within the dot. Although these electrons must interact strongly, such interactions apparently have no observable effect on the phase. On the other hand, we also find that the phase behaviour is identical for all resonances, and that there is a sharp jump of the phase between successive resonance peaks. Adequate explanation of these features may require a model that includes interactions between electrons.

Since Millikan's famous oil-drop experiments, it has been well known that electrical charge is quantized in units of the charge of an electron, e. For this reason, the theoretical prediction by Laughlin of the existence of fractionally charged 'quasiparticles'-proposed as an explanation for the fractional quantum Hall (FQH) effect-is very counterintuitive. The FQH effect is a phenomenon observed in the conduction properties of a two-dimensional electron gas subjected to a strong perpendicular magnetic field. This effect results from the strong interaction between electrons, brought about by the magnetic field, giving rise to the aforementioned fractionally charged quasiparticles which carry the current. Here we report the direct observation of these counterintuitive entities by using measurements of quantum shot noise. Quantum shot noise results from the discreteness of the current- carrying charges and so is proportional to both the charge of the quasiparticles and the average current. Our measurements of quantum shot noise show unambiguously that current in a two-dimensional electron gas in the FQH regime is carried by fractional charges-e/3 in the present case-in agreement with Laughlin's prediction.

We address the results presented recently by Yacoby et al. [Phys. Rev. Lett. 74, 4047 (1995)] on the coherency and phase evolution in a resonant tunneling quantum dot embedded in an Aharonov-Bohm (AB) ring. The observed phase rigidity of the AB conductance oscillations is theoretically explained by invoking simple symmetry arguments applicable to two terminal measurements, and is corroborated experimentally in generic experiments. We show that under certain conditions h/2e oscillations dominate completely the conductance of a single AB ring.

Via a novel interference experiment, which measures magnitude and phase of the transmission coefficient through a quantum dot in the Coulomb regime, we prove directly, for the first time, that transport through the dot has a coherent component. We find the same phase of the transmission coefficient at successive Coulomb peaks, each representing a different number of electrons in the dot; however, as we scan through a single Coulomb peak we find an abrupt phase change of . The observed behavior of the phase cannot be understood in the single particle framework.

Dephasing of ballistic electrons is measured as a function of both temperature and Fermi energy in a high-mobility two-dimensional electron gas. We find a qualitative agreement between the measured phase-breaking length and the theoretical prediction for the electron-electron scattering length using the value of E(F) measured with large-area Hall bars. A good quantitative agreement is obtained when a local value of E(F), measured via on-chip magnetic focusing, is used. The good agreement between the measured phase-breaking length and the theoretical electron-electron scattering length strongly suggests that these two quantities are the same in the ballistic regime.

We present a controlled interference experiment of ballistic electrons in a two-dimensional electron gas. While the phase along one interfering path is kept constant, the phase along the second interfering path is varied using a biased metallic gate, thereby enabling a direct measurement of the phase accumulated underneath this gate. Surprisingly, in addition to the expected oscillatory signal measured as a function of the gate bias, we observe a longer period signal with approximately half the expected frequency.

The long hot-electron mean free path observed by Sivan, Heiblum, and Umbach in high-mobility 2D electron-gas heterostructures is explained by electron transport in the second subband. Our estimates show that the mean free path in the second subband is longer by 2 orders of magnitude than that in the first subband. New magnetic-focusing measurements reveal hot-electron velocities lower than the Fermi velocity, as expected for a higher-subband transport. The electrostatic potential near a biased constriction used as the hot-electron injector is shown to induce nonadiabatic intersubband transfer.

Tunneling and thermionic emission through n+GaAsiAlxGa1−xAsnGaAs heterojunction barriers are studied as a function of temperature from 77 to 200 K and as a function of externally applied uniaxial stress up to 10 kbar. A procedure to extract parameters for theoretical calculations is also proposed. The parameters extracted from the IV characteristics of these heterostructures grown on (100) GaAs substrates with different aluminum mole fractions from 0.3 to 0.8 and thicknesses from 300 to 400 Å agree well with those of previous reports. The dependence of the IV characteristics on uniaxial stress in the 〈100〉 direction perpendicular to the heterojunction plane has also been measured. The experimental results show good agreement with theoretical calculations assuming there is a linear stressdependent decrease of the energyband edges of the longitudinal X valleys (Xl) in AlGaAs with respect to the Γ valley in GaAs. The slope of the decrease is found to be 14±2 meV/kbar. This results in an Xvalley shear deformation potential of 9.6±1.8 eV, which is believed to be the most accurate measured value to date.

A narrow channel patterned in a novel GaAs heterostructure with tunable electron density is used to study the conductance of the electron gas in the very low-density regime where only a single one-dimensional subband is occupied. Periodic oscillations of the conductance versus density and nonlinearities in the conductance suggest the formation of a one-dimensional charge-density wave or Wigner crystal.

Hot-electron transport in a 2D electron gas is investigated as a function of the electrons excess energy. The inelastic mean free path at energies below the longitudinal-optical-phonon energy is found to be an order of magnitude longer than theoretical predictions. For higher injection energies, LO-phonon emission is found to be the main scattering mechanism. This, together with the ballistic motion for energies below the phonon energy, leads to previously unobserved periodic oscillations in the maximum energy of hot electrons as a function of their injection energy.

We report an observation of a single optical phonon emission by monoenergetic hot electrons traversing thin n+-type GaAs and thin undoped AlGaAs layers in times much shorter than the classical phonon period. This was done by injecting ballistic electrons into the thin layers with energy around the threshold for optical phonon emission and monitoring their exit energy. We estimate a scattering time of ≃200 fsec for electrons with energy of about 85 meV in n+-type GaAs, and ≃550 fsec for 40-meV electrons in undoped AlGaAs.

Reproducible realization of high quality inverted interfaces (GaAs on AlGaAs) grown by molecular beam epitaxy is reported. Effective use of thinlayer GaAs/AlAs superlattices in place of an AlGaAs barrier was made to reduce the number of impurities and the roughness at these interfaces. The lowtemperature (≂4 K) mobility for electrons at these interfaces is as high as 2×106 cm2/Vs for an electron density of ≂5×1011 cm−2a factor of four improvement over the highest mobility reported for inverted interfaces.

Inverted heterointerfaces (GaAs on AlGaAs), which are basic constituents of all quantum wells and superlattices, have been significantly improved using electron diffraction and a refined molecular beam epitaxy growth procedure. Utilizing them in a novel structure allowed the variation of the electron density over a wide range, with peak mobilities of 4×105 cm2/Vs. The continuously variable electron density allowed comparison to a theoretical analysis of the lowtemperature scattering mechanisms, and their relation to the growth process, establishing the importance of interface charges and roughness. Highmobility samples were used to observe the quantum Hall effect with varying carrier concentrations in a single structure.

We present new data concerning the problem of two-subband transport in a two-dimensional electron gas. We find that the ratio of the mobilities of electrons in the two subbands depends on the details of the confinement potential, while the ratio of the relaxation times determined from the Shubnikov-de Haas effect does not. In all samples studied the relaxation time determined from the amplitude of quantum oscillations in the magnetoresistance is longer for electrons in the upper subband. In addition, we see evidence for the repulsion of quantum levels and the inhibition of spin-flip transitions between quantum levels.

Thin layers of Mo and Nb, 100400 Å thick, were deposited onto clean (100) and (1̄1̄1̄)GaAs substrates under ultrahigh vacuum conditions in a molecularbeam epitaxy system, at slow rates and at relatively low temperatures. The microstructure of the films and the orientation relationship with the substrates were determined by in situ reflection highenergy electron diffraction, by transmission electron microscopy, and by grazingincidence xray diffraction. In spite of the large lattice mismatch to GaAs (11% for Mo and 17% for Nb) and the low deposition temperatures(

The dependence of the Schottky barrier height of Mon:AlGaAs junctions, fabricated in situ by molecular beam epitaxy, on the Al mole fraction (x) was determined by internal photoemission measurements and by activation energy plots of the current versus voltage dependence on temperature. Both techniques yielded similar values. The difference in barrier height of MoAlGaAs as a function of x, compared to that of MoGaAs, was found to be equal to the conduction band discontinuity in AlGaAsGaAs heterojunctions for Al concentrations in the range 0≤x≤0.4. For x>0.4, values of the barrier heights were somewhat lower than values of the band discontinuity; however, both dependencies on x were quite similar. The temperature dependence of the currentvoltage characteristics showed that thermionic emission was the dominant transport mechanism at forward bias for temperatures higher than 250 K. At lower temperatures, current transport was governed by thermionic field emission.

Thin layers of Nb, 100400 Å thick, were grown by electron beam evaporation on (100)GaAs substrates in a molecular beam epitaxy system. The crystallographic relationship between deposit and substrate was monitored in situ by reflection highenergy electron diffraction, and after deposition by transmission electron microscopy and grazingincidence xray diffraction. In spite of the large lattice mismatch (17%) and the low deposition temperature (40400°C), a quite well oriented deposit with the orientation (100)Nb∥(100)GaAs and [001]Nb∥[011]GaAs was obtained for a substrate temperature of ∼170°C. Changing the substrate temperature from the optimum value of ∼170°C in either direction resulted in a gradual deterioration of the epitaxy.

In high electron density transistors of the field-effect type where the channel between the source and drain electrodes is made up of epitaxial thin layers that are alternately doped and essentially undoped, an increased number of carriers can be provided in the essentially undoped layers by constructing an energy condition that tends to retain the electrons in the vicinity of the layer interface. The energy condition is provided by the use of undoped and graded doping.

Tunneling hotelectron transfer amplifier (THETA) devices, based on GaAsAlGaAs heterojunctions, were fabricated and tested. Hotelectron transfer (α) through a 1100Å base in excess of 70% was found at 4.2 K. This resulted in a corresponding current gain (β) in a common emitter configuration of about 2.3. In the temperature range of 4.280 K and under constant biasing conditions, α was nearly temperature independent. Electron energy distributions for motion normal to the layers and electron total energy loss while traversing the device were estimated. Typical widths of the energy distributions were less than 200 meV, and both widths and energy peak positions were only slightly dependent on temperature and initial injection energy.

A summary of the results of a few experiments on a variety of structures based on GaAsAlGaAs heterojunctions, in which the AlGaAs was Si doped are reported. RHEED and SIMS results are presented for heavily and moderately doped AlGaAs, showing that Si segregated toward the growing front. Photoluminescence spectra of heavily doped AlGaAs has a dominant low energy peak and is absent of the exciton peak. Normal and inverted selectively doped structures were grown at a variety of conditions. Their properties demonstrate that Si segregates toward the growing front, and suggests that this effect could be the main cause of the low mobility in inverted structures.

Persistent photoconductivity (PPC) is studied in modulation doped AlGaAsGaAs heterostructures in the conductivity parallel to the heterojunctions. The results indicate that the macroscopic fields of the heterojunction and traps primarily in the GaAs rather than AlGaAs are responsible for the phenomenon. PPC is also reported in n+ GaAsundoped AlGaAsn+ GaAs heterostructures for current perpendicular to the heterojunctions.

Heavy Si doping of GaAs and AlGaAs grown by molecular beam epitaxy has been studied. By using a slow growth rate of 1000 Å/h, the electron concentration obtained for GaAs was 1.1×1019 cm−3, which is higher than the previously reported limit of 5×1018 cm−3. The accumulation of excess Si near the surfaces of GaAs and AlGaAs has been identified by secondary ion mass spectroscopy. A Siinduced 3×2 surface structure has been observed, and the influence of arsenic to gallium flux ratio on the surface morphology is discussed. Photoluminescence spectra of the doped layers are presented.

The effect of substrate temperature and As/Ga flux ratio on the incorporation of Si as a dopant in GaAs grown by molecular beam epitaxy has been studied by means of lowtemperature photoluminescence (PL) measurements. It is shown that the acceptor character of Si is enhanced as the substrate temperature increases from 590 to 720°C. The PL results suggest that the amount of Si selfcompensation decreases when the atomic flux ratio increases from 2 to 6.

We describe a new technique for controlled oxide growth using a directed lowenergy ion beam. The technique is evaluated by fabricating NioxideNi and CroxideNi tunneling junctions, using oxygen ion beams with energies ranging from 30 to 180 eV. High ion current densities are achieved at these low energies by replacing the conventional dual grid extraction system of the ion source with a single fine mesh grid. Junction resistance decreases with increasing ion energy, and oxidation time dependence shows a characteristic saturation, both consistent with a process of simultaneous oxidation and sputter etching, as in the rf oxidation process. In contrast with rf oxidized junctions, however, ion beam oxidized junctions contain less contamination by backsputtering, and the quantitative nature of ion beam techniques allows greater control over the growth process.