Ballistic Mean Free Path Research Articles

Subcycle observation of lightwave-driven Dirac currents in a topological surface band.

Harnessing the carrier wave of light as an alternating-current bias may enable electronics at optical clock rates1. Lightwave-driven currents have been assumed to be essential for high-harmonic generation in solids2-6, charge transport in nanostructures7,8, attosecond-streaking experiments9-16 and atomic-resolution ultrafast microscopy17,18. However, in conventional semiconductors and dielectrics, the finite effective mass and ultrafast scattering of electrons limit their ballistic excursion and velocity. The Dirac-like, quasi-relativistic band structure of topological insulators19-29 may allow these constraints to be lifted and may thus open a new era of lightwave electronics. To understand the associated, complex motion of electrons, comprehensive experimental access to carrier-wave-driven currents is crucial. Here we report angle-resolved photoemission spectroscopy with subcycle time resolution that enables us to observe directly how the carrier wave of a terahertz light pulse accelerates Dirac fermions in the band structure of the topological surface state of Bi2Te3. While terahertz streaking of photoemitted electrons traces the electromagnetic field at the surface, the acceleration of Dirac states leads to a strong redistribution of electrons in momentum space. The inertia-free surface currents are protected by spin-momentum locking and reach peak densities as large as two amps per centimetre, with ballistic mean free paths of several hundreds of nanometres, opening up a realistic parameter space for all-coherent lightwave-driven electronic devices. Furthermore, our subcycle-resolution analysis of the band structure may greatly improve our understanding of electron dynamics and strong-field interaction in solids.

Ultrafast Hot Carrier Dynamics in GaN and Its Impact on the Efficiency Droop.

GaN is a key material for lighting technology. Yet, the carrier transport and ultrafast dynamics that are central in GaN light-emitting devices are not completely understood. We present first-principles calculations of carrier dynamics in GaN, focusing on electron-phonon (e-ph) scattering and the cooling and nanoscale dynamics of hot carriers. We find that e-ph scattering is significantly faster for holes compared to electrons and that for hot carriers with an initial 0.5-1 eV excess energy, holes take a significantly shorter time (∼0.1 ps) to relax to the band edge compared to electrons, which take ∼1 ps. The asymmetry in the hot carrier dynamics is shown to originate from the valence band degeneracy, the heavier effective mass of holes compared to electrons, and the details of the coupling to different phonon modes in the valence and conduction bands. We show that the slow cooling of hot electrons and their long ballistic mean free paths (over 3 nm at room temperature) are a possible cause of efficiency droop in GaN light-emitting diodes. Taken together, our work sheds light on the ultrafast dynamics of hot carriers in GaN and the nanoscale origin of efficiency droop.

Practical concept of an all-optical hot carrier solar cell

The all-optical hot carrier solar cell (aoHCSC) is an intriguing device concept which circumvents HC thermalization by feeding HCs into local radiative recombination centers. These have transition energies above the HC absorber (HCA) bandgap and are located within the HCA to match the HC ballistic mean free path, suppressing HC cooling as major loss mechanism. HC energy extraction proceeds by photon emission. We propose a technologically feasible concept of the aoHC energy converter (aoHCEC) which feeds into a conventional solar cell with its bandgap matching the emitted photons. Using real materials, the concept builds upon waveguides within a HCA which consist of highly polar direct bandgap material to promote radiative carrier recombination.

Static hot carrier populations as a function of optical excitation energy detected through energy selective contacts by optically assisted IV

ABSTRACTWe investigated the behavior of carrier populations generated at the interface of an n‐Si wafer to an Si quantum dot (QD) array embedded in SiO2 with a photon flux ranging from 1.24 to 2.48 eV (1000 to 500 nm). The optically assisted IV method was used with the Si wafer as hot carrier (HC) absorber and the Si QD array as energy selective contact (ESC). Charge carriers obtain excess energy from photons with energies significantly exceeding the band gap, resulting in an HC population. This reduces the bias field required to provide kinetic energy by field emission. The ESC can collect HCs at lower bias voltages. Tunneling resonances show the energy selective behavior under illumination at 80 K and room temperature (295 K). The data at 80 K can arguably be interpreted as an HC population in Si within the range of the ballistic mean free path from the QD array. We discovered a correlation between the energetic shift of the average hot hole temperature near the valence band edge and the energy of the photons impinging on the mesa structures. The optically assisted IV technique delivers a proof of principle for operation of an Si QD array as an ESC at room temperature, and furthermore for an HC solar cell with one ESC at 80 K. Copyright © 2013 John Wiley & Sons, Ltd.

Temperature-dependent ballistic transport in a channel with length below the scattering-limited mean free path

The temperature-dependent ballistic transport, using nonequilibrium Arora distribution function (NEADF), is shown to result in mobility degradation with reduction in channel length, in direct contrast to expectation of a collision-free transport. The ballistic mean free path (mfp) is much higher than the scattering-limited long-channel mfp, yet the mobility is amazingly lower. High-field effects, converting stochastic velocity vectors to streamlined ones, are found to be negligible when the applied voltage is less than the critical voltage appropriate for a ballistic mfp, especially at cryogenic temperatures. Excellent agreement with the experimental data on a metal-oxide-semiconductor field-effect transistor is obtained. The applications of NEADF are shown to cover a wide spectrum, covering regimes from the scattering-limited to ballistic, from nondegenerate to degenerate, from nanowire to bulk, from low- to high-temperature, and from a low electric field to an extremely high electric field.

Concentration dependence of drift and magnetoresistance ballistic mobility in a scaled-down metal-oxide semiconductor field-effect transistor

The degradation of ballistic mobility in a metal-oxide semiconductor field-effect transistor is attributed to the nonstationary ballistic injection from the contacts as the length of a channel shrinks to the length smaller than the scattering-limited mean free path. Apparent contradiction between the rise of magnetoresistance mobility and fall of drift mobility with increasing channel concentration is attributed to scattering-dependent magnetoresistance factor. The ballistic mean free path of injected carriers is found to be substantially higher than the long-channel drift mean free path. Excellent agreement with the experimental data on length-limited ballistic mobility is obtained.

The channel mobility degradation in a nanoscale metal–oxide–semiconductor field effect transistor due to injection from the ballistic contacts

The ballistic mobility degradation is shown to originate from nonstationary (transient) transport in response to the ohmic electric field. The source and drain reservoirs launch electrons into the channel with injection velocity transiting the channel with finite ballisticity defined as the probability of a collision-free flight. The distinction is made between the ballistic mean free path and that present in a long channel. The results are in excellent agreement with those obtained from Monte Carlo procedures and experiments.

Contact Resistance to a One-Dimensional Quasi-Ballistic Nanotube/Wire

A distributed contact model is presented for a 1-D quasi-ballistic conductor deriving a contact resistance versus contact length as a hyperbolic cotangent relationship in terms of the quantum of resistance, the coupling conductance g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> of the contact, and the ballistic mean free path (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> ). The model gave excellent fits to recent contact resistance-versus-contact length data for carbon nanotubes giving g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> = 2 μS/nm and λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> = 380 nm.

Ballistic electron mean free path of titanylphthalocyanine films grown on GaAs

AbstractIn this article, Au/titanylphthalocyanine/n‐GaAs diodes incorporating ultrathin films of the archetypal organic semiconductor titanylphthalocyanine were investigated by ballistic electron emission microscopy/spectroscopy (BEEM/S). BEEM/S measurements were used to determine the transmission of ballistic electrons through titanylphthalocyanine as a function of energy and temperature. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Hot-electron bend resistance in a ballistic GaAs/AlGaAs cross junction

Nonlinear bend resistance is studied in a six-terminal mesoscopic ballistic junction in the hot-electron regime. Non-equilibrium electrons are generated by a voltage drop across a quantum point contact (QPC) embedded in the current lead of an orthogonal cross junction. The barrier height of the QPC constriction is tuned by a large-area top gate electrode which covers junction and leads. The junction enables to study the ballistic bend voltage in local and remote configuration. In local configuration the ballistic voltage is detected between the voltage probes opposed to the orthogonal current leads. Independent from the current polarity a negative bend resistance verifies the ballistic motion of electrons. For small gate voltages, i.e. a high QPC barrier, the absolute value of the bend resistance is enhanced if the electrons are injected through the constriction. We attribute this nonlinearity to the current-polarity-dependent excess energy gained in the negatively biased current lead. If the transfer voltage is detected between two remote orthogonal voltage probes ballistic effects are observed only for small excess energies. The remote configuration implies that the electron ballistic mean-free path decreases at high excess energies.

The superconductor proximity effect in Au–YBa2Cu3O7−δ bilayer films: the role of order parameter anisotropy

Scanning tunneling spectroscopy of Au–YBa2Cu3O7−δ bilayers reveals proximity effect features that reflect the anisotropic dx2−y2-wave order parameter in YBa2Cu3O7−δ (YBCO). No proximity effect takes place at the (001)YBCO–Au interface, manifesting the quasi two-dimensional nature of the order parameter. Proximity gaps are induced in the gold primarily via (100)YBCO facets, and their size decays exponentially on a scale of ∼30nm, in good agreement with estimations for the dirty limit. In the nodal (110)YBCO–Au interface, the proximity effect manifests itself by the penetration of Andreev bound states into the gold. The corresponding zero bias conductance peaks are nearly constant in magnitude for Au layers thinner than 7nm, and then decay abruptly with Au thickness, vanishing above 10nm, on the scale of the (ballistic) mean free path.

Anomalous Proximity Effect in Gold Coated (110)YBa2Cu3O7−δFilms: Penetration of the Andreev Bound States

Scanning tunneling spectroscopy of (110)YBa(2)Cu(3)O(7-delta)/Au bilayers reveal a proximity effect markedly different from the conventional one. While proximity-induced mini-gaps rarely appear in the Au layer, the Andreev bound states clearly penetrate into the metal. Zero bias conductance peaks are measured on Au layers thinner than 7 nm with a magnitude similar to those detected on the bare superconductor films. The peaks then decay abruptly with Au thickness and disappear above 10 nm. This length is shorter than the normal coherence length and corresponds to the (ballistic) mean free path.

Room-temperature ballistic electron emission luminescence spectroscopy with a scanning tunneling microscope

We present a luminescence spectroscopy for semiconductor heterostructures based on local hot electron injection from a scanning tunneling microscope tip. In addition to a tip voltage bias exceeding the metal-semiconductor Schottky barrier height, this process requires a collector bias voltage to satisfy energy conservation. These results indicate that this method could be used to study local electron transport and simultaneous electroluminescence in buried luminescent layers at depths greater than the ballistic electron mean free path in the collector.

Radiative emission rate modulation in semiconductor heterostructures coupled to a mirror: A probe of ballistic electron mean free path

Absolute electroluminescence intensities of InP/InGaAs heterostructures are monitored as a function of the position of the active layer from a mirror deposited on the semiconductor surface. The strong observed modulation is explained in terms of confinement of the electromagnetic field in the semi-infinite cavity delimited by the reflecting interface. This effect is shown to be a powerful probe of electron spatial distributions in the direction perpendicular to the layer plane, which allows minority ballistic electron mean free path, and hence femtosecond scattering times, to be precisely measured.

Direct measurement of ballistic electron distribution and relaxation length in InP-based heterojunction bipolar transistors using electroluminescence spectroscopy

The electroluminescence signal emitted from operating InP-based heterojunction bipolar transistors (HBT) is analyzed, giving clear evidence of ballistic electron transport through the base. The luminescence signal is studied as a function of base thickness, providing direct access to the ballistic electron mean free path. This continuous wave technique proves to be very efficient to measure ballistic electron scattering rates: 30 fs at 77 K and 19 fs at 300 K for a base Be doped to 1019 cm−3.Quasiballistic transport range is found to be comparable to base width accessible by state of the art device technology, demonstrating its importance for ultrafast HBT operation.

Transport and optics in quantum wires fabricated by MBE overgrowth on the (110) cleaved edge

The MBE double-growth technique that we call cleaved-edge overgrowth has, over the past several years, proved itself to be especially suitable for making quantum wires of the very highest quality. We will review our recent progress in measuring the transport and quantum optics characteristics of these wires, and the MBE growth issues that arise with cleaved-edge overgrowth fabrication. Our transport experiments have resulted in 250 Å wide quantum wires with ballistic mean free paths exceeding 10 μm. We verify the prediction that in the ballistic regime the electron conductivity in a quantum wire is independent of the wire length and shows quantized steps proportional to e 2 h . The deviation of our observed step heights from exactly e 2 h is taken as evidence for correlated electron behaviour. The electrons are tightly confined on three sides by atomically smooth GaAs/AlGaAs heterojunctions and in the fourth direction by an electric field. This results in a quantum wire of nominal square cross-section 250 × 250 A ̊ . Magneto-transport measurements reveal quantum wire sub-band separations in excess of 20 meV as well as the symmetries of the wave functions of the one-dimensional modes. For optics studies our quantum wires are made using cleaved-edge overgrowth to form a line junction as two quantum wells are made to intersect with the cross-section forming a letter ‘T’. This line intersection separately forms a quantum wire bound-state for holes, for electrons, and even for excitons. We have characterized our optical wires by PL, by PLE, and by scanning near-field optics. An important application of this work is our demonstration of the first quantum laser using this T-geometry.

Observation of ballistic transport in the upper subband of a two-dimensional electron system.

We report a specially designed transverse magnetic focusing experiment on a two-dimensional electron system confined to a square quantum well with two electric subbands occupied. The reflecting barrier of a usual magnetic focusing device is replaced by a surface-gate-induced, tunable potential barrier that allows us to selectively reflect and magnetically focus the upper subband electrons while the lower subband electrons pass over the barrier and are not focused. We observe the focusing of the upper subband electrons. The weakness of the focusing signal for the upper subband ballistic electrons suggests that they have a surprisingly short ballistic mean free path compared to the lower subband electrons.

Electroluminescence measurement of ballistic electron distribution in AlGaAs/GaAs heterojunction bipolar transistor structures with base width modulation

Electroluminescence from the base region of Npn-AlGaAs/GaAs heterojunction bipolar transistors (HBTs) are analyzed to investigate the behavior of electrically injected ballistic electrons in hetero-structure. The low temperature luminescence reveals ballistic electron spectra, subsequent optical-phonon emissions and quasi-equilibrium hot electron spectra, which are the first observations in HBT structures. Modulation of the neutral base width by varying the base-collector voltage enables the evaluation of the spatial electron distribution. The ballistic mean free path is determined to be 130 ± 20 nm at 18 K for an acceptor concentration of 2.5 × 10 17 cm -3.

Ballistic and elastic mean free paths determined by magnetic electron focusing effect in GaAs/AlGaAs

The ballistic mean free paths determined by magnetic electron focusing effect have been investigated in multi-terminal GaAs/AlGaAs devices with different electron mobility. The ballistic mean free path (1 b) is shorter than the elastic mean free path (1 e) determined by the resistivity and mobility. However, the reduction ratio of 1 b to 1 e is nearly the same in the different mobility samples. The increasing rates of 1 e and 1 b with respect to electron concentration are also similar. It is interesting that the proportion of 1 b to 1 e hardly depends on electron concentrations and electron mobility.

Ballistic electron optics

We demonstrate a method to directly measure the ballistic mean free path λ b of electrons in ultrahigh mobility GaAs/AlGaAs heterostructures. λ 0 and the elastic mean free path from mobility measurements λ micro are measured and compared over the temperature range 0.3–10 K. We also demonstrate that ballistic electrons in these systems can be electrostatically refracted in structures ≳ 10 microm in size, however, problems arise when the refractive structures are reduced to length scales on the order of a few micrometers.