Ballistic Electron Research Articles

Entanglement of magnetic impurities through electron scattering in an electric field

We show that the entanglement between two distant magnetic impurities, generated via electron scattering, can be easily modulated by controlling the magnitude of an applied external electric field. We assume that the two magnetic impurities are fixed and located on an one-dimensional quantum wire. A ballistic electron moving through the wire is scattered off by both impurities, so the electron spin can be seen as a mediator between the spins of the impurities. Heisenberg operators are used to describe the interactions between electron and impurities spins. We use a wave guide formalism to model the ballistic electron wave-function. Entanglement control is shown to be possible for three different protocols of entanglement detection. The effect of detection protocols on the entanglement extraction is discussed.

(Invited) Electronic and Acoustic Applications of Anodized Nano-Crystalline Silicon

Electrochemically anodized nano-crystalline Si (nc-Si) behaves as a functional material with a confined structure. In the electron transport through a chain of nc-Si dots, phonon scattering losses are minimized due to discrete energy levels in the conduction band, and then ballistic electrons are generated at the early stage of injection [1]. This induces efficient ballistic hot electron emission from an nc-Si diode. It is possible to use this emitter not only in vacuum, but also in atmospheric-pressure gases and solutions [2]. Extremely lowered thermal conductivity and heat capacity of the nc-Si layer [3], on the other hand, significantly enhances thermo-acoustic effect. In contrast to the conventional piezoelectric transducer, the thermally induced acoustic emission exhibits no resonant peaks in the frequency response. Here we discuss topics in the studies on these subjects. The nc-Si emitter is a kind of MIS diode consisting of a thin film surface electrode, an nc-Si layer (~1 μm thick), a crystalline silicon wafer substrate, and a back contact. The nc-Si layer includes chains of nc-Si dots (~3 nm in mean diameter) interconnected with tunnel oxides. When a positive voltage is applied to the surface electrode, electrons are accelerated in the nc-Si layer toward the outer surface, and then some of them are emitted through the surface electrode as ballistic hot electrons with a small angle dispersion (±10°with respect to the normal). At applied voltages of 12-20 V, the mean energy of output electrons reaches 3-7 eV [2]. One possible application of the nc-Si emitter is the use as an exposure source of multibeam parallel lithography. The emitter array is fabricated on a Si substrate by planar processes. Each emitter with an active area of 10 μm☐ is connected to an active matrix driving circuit through a TSV technique. The evaluation was performed with the 1:1 exposure test system, in which an EB-resist coated target wafer was placed at about 4 mm distance from the emitter surface. The wafer was grounded, and emitter surface was set at -5 kV for accelerating the electron. It has been demonstrated that the selected emitter patterns is delineated well corresponding to the activated emitters [4]. The integrated nc-Si emitter array is compatible with the active-matrix drive for multi-beam massive parallel lithography. Another application is thin film deposition using the reducing activity of ballistic hot electrons. When the emitter is driven in metal-salt solutions such as CuSO4, CuCl2, NiCl2, SiCl4, and GeCl4, injected electrons directly reduce Cu2+, Si4+ and Ge4+ ions, and then thin Cu films [5] and amorphous Si and Ge films [6,7] are grown on the emitting area with neither contaminations nor byproducts. Based on this observation, a printing scheme has been employed, in which a target substrate is separately located in close proximity to the emitter. A gap between the nc-Si emitter and the target substrate is controlled by a piezoelectric actuator depending the ambient (N2 gas) pressure. Emitted electrons hit metal-salt solutions on the substrate leading to the reducing reaction. The first printing experiment was sought for deposition of thin metal film, where an extremely small amount of CuSO4 or CuCl2 solution was coated on a single-crystalline Si wafer and used as a target substrate. It has been observed that thin Cu films are deposited on the irradiated area. The broad-band flat emissivity of the nc-Si thermo-acoustic device is useful for developing low-distortion digital speaker [8] and reproducing complicated ultrasonic communication calls between mice [9].

(Invited) The Landauer Approach to Electron and Phonon Transport

Semiclassical electron and phonon transport is typically simulated by solving the electron or phonon Boltzmann transport equation. More recently, quantum transport of electrons and phonons has been simulated by the non-equilibrium Green’s function (NEGF) approach. The Landauer approach is a simple, physical approach to analyze electron and phonon transport. It is widely used to treat ballistic electron transport at the nanoscale. Less well known is that under the right conditions, it works all the way from the ballistic to diffusive limits in nanoscale to macroscale structures. The Landauer approach can also be used for phonon transport – and also from the ballistic to diffusive limits and from the nano- to macro-scales. Because the Landauer approach can be derived from the Boltzmann equation or from the NEGF equations, it provides a direct connection to more rigorous and fine-grained treatments. We believe that it should be more widely-used for three reasons: 1) it provides a smooth bridge from the ballistic to diffusive limits and from small to large structures, 2) it provides a common “language” for electron and phonon transport, and 3) it provides a clear connection to more fundamental semiclassical and quantum approaches to transport. Our goals in this talk are: 1) to review the Landauer approach to electron and phonon transport, 2) to illustrate how it compares to more rigorous treatments with some new benchmarking calculations, and 3) to illustrate how this approach helps identify good thermoelectric materials. The electrical conductance can be written as the quantum of electrical conductance, times the number of thermally active channels for electrical conduction, times the transmission. The quantum of conductance is a set of fundamental constants. The number of thermally active channels depends only on electronic structure and can be rigorously computed from first principles. The transmission is one for a ballistic conductor and small for a diffusive conductor. For large structures, this approach reduces to the traditional (Boltzmann equation) expressions of near-equilibrium electron transport. For small structures, it describes quantized, ballistic conduction. It is common to use the Landauer approach for nanostructures and the Boltzmann equation for large structures, but there is no need for two separate approaches – the Landauer approach covers both regimes of transport. The Landauer approach also applies to phonon transport using the same physical concepts described above. For example, the thermal conductance can be written as the quantum of thermal conductance, times the number of thermally active channels for phonon conduction, times the phonon transmission. This talk will present a brief overview of this technique applied to electron and phonon transport, and will discuss some new examples that benchmark the Landauer approach and illustrate the benefits and limitations of the method. It is sometimes felt that electrons and phonons are different because electrons are fermions and phonons are bosons. It turns out that this makes little difference. It does affect the thermal window functions that determine the number of thermally active channels, but the window functions turn out to be quite similar in shape. There are two significant differences – in practice, but not in principle. The first is that the energy bandwidth of the electron dispersion is typically much, much larger than the width of the thermal window function for electrons, so that simplified dispersions often work very well (e.g. parabolic energy bands). For phonons, the width of the thermal window function is comparable to the width of the phonon dispersion, so simplified phonon dispersions usually lead to large errors. The second major difference has to do with the electron and phonon mean-free-paths. Both mean-free-paths are energy-dependent, but since electrons typically occupy only a small range of energies near the bottom or top of a band, the use of a constant mean-free-path is often sufficient. In contrast, there is a very strong energy dependence of the phonon mean-free-path, and phonons with a very wide range of mean-free-paths contribute to the thermal conductivity. In spite of these technical differences, the formal equations and computational approaches are essentially identical for electrons and phonons. For most electronic devices, both electron and phonon transport play a role, and for thermoelectric devices, the intimate coupling of the two flows is critical. For problems like thermoelectrics, the use of a common approach to analyze electron and phonon transport is beneficial and can provide new insights. In this talk, we will illustrate what makes a good thermoelectric material from a Landauer perspective considering both traditional bulk and novel 2D materials as examples. Figure 1

Quantum interference phenomena in the Casimir effect

We propose a definitive test of whether plates involved in Casimir experiments should be modeled with ballistic or diffusive electrons--a prominent controversy highlighted by a number of conflicting experiments. The unambiguous test we propose is a measurement of the Casimir force between a disordered quasi-2D metallic plate and a three-dimensional metallic system at low temperatures, in which disorder-induced weak localization effects modify the well-known Drude result in an experimentally tunable way. We calculate the weak localization correction to the Casimir force as a function of magnetic field and temperature and demonstrate that the quantum interference suppression of the Casimir force is a strong, observable effect. The coexistence of weak localization suppression in electronic transport and Casimir pressure would lend credence to the Drude theory of the Casimir effect, while the lack of such correlation would indicate a fundamental problem with the existing theory. We also study mesoscopic disorder fluctuations in the Casimir effect and estimate the width of the distribution of Casmir energies due to disorder fluctuations.

Time dependent changes in Schottky barrier mapping of the W/Si(001) interface utilizing ballistic electron emission microscopy

The W/Si(001) Schottky barrier height is mapped to nanoscale dimensions using ballistic electron emission microscopy (BEEM) over a period of 21 days to observe changes in the interface electrostatics. Initially, the average spectrum is fit to a Schottky barrier height of 0.71 eV, and the map is uniform with 98% of the spectra able to be fit. After 21 days, the average spectrum is fit to a Schottky barrier height of 0.62 eV, and the spatial map changes dramatically with only 27% of the spectra able to be fit. Transmission electron microscopy shows the formation of an ultra-thin tungsten silicide at the interface, which increases in thickness over the 21 days. This increase is attributed to an increase in electron scattering and the changes are observed in the BEEM measurements. Interestingly, little to no change is observed in the I-V measurements throughout the 21 day period.

Study on the frequency characteristics of nanogap electron devices

Ballistic electron transport in the nanogap devices will make it practical to combine the advantages of solid-state devices and vacuum electron devices including high integration and high frequency characteristics. Although a number of experiments have been exploited on frequency characteristic in nanogap, less modeling or calculations were investigated at such scale yet. In this paper, the concept of mean flight time is proposed in order to theoretically determine the frequency in nanoscale. Traditionally, we have to first determine the frequency response diagram and then deduce the cut-off frequency. This work presents a new method for exploring the frequency characteristics of electron transport in a nanogap structure by calculations and numerical simulations. A double-gate structure was applied in the simulations, and the results suggest that the nanogap structure can perform in the THz range. Additionally, an equivalent circuit model was adopted to demonstrate the validity of this method. Our results provide a model for the intrinsic ballistic transportation of electrons inside the nanogap electron devices.

Penn Algorithm Including Damping for Calculating the Electron Inelastic Mean Free Path

We present an approach for introducing damping into the Penn algorithm by using the Mermin dielectric function instead of the Lindhard dielectric function. We find that for a damping of 1.5 eV, the electron inelastic mean free path calculated by the present algorithm for Al is in excellent agreement with experimental values in the energy range 5–9 eV. Meanwhile, for a damping of 2.0 eV, our result for Au is consistent with the GW+T ab initio calculation at several electronvolts. In particular, at an energy of 1 eV, our result for Au is 297 A and lies within the range 220–330 A obtained from measurements by ballistic electron emission microscopy.

Deposition of thin Si and Ge films by ballistic hot electron reduction in a solution-dripping mode and its application to the growth of thin SiGe films

To enhance the usefulness of ballistic hot electron injection into solutions for depositing thin group-IV films, a dripping scheme is proposed. A very small amount of SiCl4 or GeCl4 solution was dripped onto the surface of a nanocrystalline Si (nc-Si) electron emitter, and then the emitter is driven without using any counter electrodes. It is shown that thin Si and Ge films are deposited onto the emitting surface. Spectroscopic surface and compositional analyses showed no extrinsic carbon contaminations in deposited thin films, in contrast to the results of a previous study using the dipping scheme. The availability of this technique for depositing thin SiGe films is also demonstrated using a mixture SiCl4+GeCl4 solution. Ballistic hot electrons injected into solutions with appropriate kinetic energies promote preferential reduction of target ions with no by-products leading to nuclei formation for the thin film growth. Specific advantageous features of this clean, room-temperature, and power-effective process is discussed in comparison with the conventional dry and wet processes.

Reduction of the effect of electron relaxation behavior on the femtosecond laser-induced response of copper thin film by ballistic energy transfer

The thermomechanical response of a copper thin film to ultrafast laser with the pulse durations from 10 to 100 fs is investigated by the methods integrating the parabolic and hyperbolic two-temperature models with the molecular dynamics. It is found that there is an insignificant discrepancy in the results obtained by the two different two-temperature models for all the considered pulse durations, indicating the trivial effect of electron relaxation behavior on the response of the heated copper film. Further study suggests that the electron relaxation effect on the material response could be offset by the energy transport due to the ballistic electron motion.

Electron injection barrier and energy-level alignment at the Au/PDI8-CN2 interface via current–voltage measurements and ballistic emission microscopy

We probe electron transport across the Au/organic interface based on oriented thin films of the high-performance n-type perylene diimide semiconductor PDI8-CN2. To this purpose, we prepared organic-on-inorganic Schottky diodes, with Au directly evaporated onto PDI8-CN2 grown on n-Si. Temperature-dependent current–voltage characteristics and complementary ballistic electron emission microscopy studies reveal that rectification at the Au/PDI8-CN2 interface is controlled by a spatially inhomogeneous injection barrier, that varies on a length scale of tens of nanometers according to a Gaussian distribution with mean value ∼0.94eV and standard deviation ∼100meV. The former gradually shifts to ∼1.04eV on increasing PDI8-CN2 thickness from 5nm to 50nm. Experimental evidences and general arguments further allow to establish the energetics at the Au/PDI8-CN2 interface. Our work indicates injection-limited current flow in PDI8-CN2-based devices with evaporated Au electrodes. Furthermore, it suggests chemical reactivity of PDI8-CN2 with both Au and Si, driven by the lateral isocyano groups.

Tuning the ballistic electron transport of spatial graphene–metal sandwich electrode on a vacuum-silicon-based device

Future high-speed electronic devices rely on the integration of hot-carrier generation and short transit time. The combination of a graphene–metal electrode can enable an extremely high ballistic electron emission bias to the graphene mesh at ambient conditions.

Electric- and exchange-field controlled transport through silicene barriers: Conductance gap and near-perfect spin polarization

We study ballistic electron transport through silicene barriers, of width d and height U, in the presence of an exchange field M and a normal electric field Ez. Away from the Dirac point (DP), the spin- and valley-resolved conductances, as functions of U, exhibit resonances while close to it there is a pronounced dip that can be transformed into a transport gap by varying Ez. The charge conductance gc changes from oscillatory to a monotonically decreasing function of d beyond a critical Ez and this can be used to realize electric-field-controlled switching. Further, the field M splits each resonance of gc into two spin-resolved peaks. The spin polarization near the DP increases with Ez or M and becomes nearly perfect above certain of their values. Similar results hold for double barriers.

Partitioning of on-demand electron pairs.

The on-demand generation and separation of entangled photon pairs are key components of quantum information processing in quantum optics. In an electronic analogue, the decomposition of electron pairs represents an essential building block for using the quantum state of ballistic electrons in electron quantum optics. The scattering of electrons has been used to probe the particle statistics of stochastic sources in Hanbury Brown and Twiss experiments and the recent advent of on-demand sources further offers the possibility to achieve indistinguishability between multiple sources in Hong-Ou-Mandel experiments. Cooper pairs impinging stochastically at a mesoscopic beamsplitter have been successfully partitioned, as verified by measuring the coincidence of arrival. Here, we demonstrate the splitting of electron pairs generated on demand. Coincidence correlation measurements allow the reconstruction of the full counting statistics, revealing regimes of statistically independent, distinguishable or correlated partitioning, and have been envisioned as a source of information on the quantum state of the electron pair. The high pair-splitting fidelity opens a path to future on-demand generation of spin-entangled electron pairs from a suitably prepared two-electron quantum-dot ground state.

Atomistic features in the electrochemical potential drop across a graphene grain boundary

A recent publication presents a new computational approach to the local electrochemical potential in the vicinity of a graphene grain boundary subject to an in-plane electric current []. The local electrochemical potential can be measured using scanning tunneling potentiometry, a method related to scanning tunneling microscopy. The paper predicts that atomistic features should be measurable. These features reflect the local electrochemical potential drop caused by the opaque grain boundary which is non-transparent to ballistic electrons. The paper has implications not only for scanning tunneling potentiometry, but also for Kelvin probe-force microscopy which can also measure the local electrochemical potential. In addition it could help to understand electronic transport across metallic nanocontacts.

Electronically transparent graphene barriers against unwanted doping of silicon.

Diffusion barriers prevent materials from intermixing (e.g., undesired doping) in electronic devices. Most diffusion barrier materials are often very specific for a certain combination of materials and/or change the energetics of the interface because they are insulating or add to the contact resistances. This paper presents graphene (Gr) as an electronically transparent, without adding significant resistance to the interface, diffusion barrier in metal/semiconductor devices, where Gr prevents Au and Cu from diffusion into the Si, and unintentionally dope the Si. We studied the electronic properties of the n-Si(111)/Gr/M Schottky barriers (with and without Gr and M=Au or Cu) by I(V) measurements and at the nanoscale by ballistic electron emission spectroscopy (BEEM). The layer of Gr does not change the Schottky barrier of these junctions. The Gr barrier was stable at 300 °C for 1 h and prevented the diffusion of Cu into n-Si(111) and the formation of Cu3Si. Thus, we conclude that the Gr is mechanically and chemically stable enough to withstand the harsh fabrication methods typically encountered in clean room processes (e.g., deposition of metals in high vacuum conditions at high temperatures), it is electronically transparent (it does not change the energetics of the Si/Au or Si/Cu Schottky barriers), and effectively prevented diffusion of the Cu or Au into the Si at elevated temperatures and vice versa.

Ultra-short channel GaN high electron mobility transistor-like Gunn diode with composite contact

We present a numerical analysis on an ultra-short channel AlGaN/GaN HEMT-like planar Gunn diode based on the velocity-field dependence of two-dimensional electron gas (2-DEG) channel accounting for the ballistic electron acceleration and the inter-valley transfer. In particular, we propose a Schottky-ohmic composite contact instead of traditional ohmic contact for the Gunn diode in order to significantly suppress the impact ionization at the anode side and shorten the “dead zone” at the cathode side, which is beneficial to the formation and propagation of dipole domain in the ultra-short 2-DEG channel and the promotion of conversion efficiency. The influence of the surface donor-like traps on the electron domain in the 2-DEG channel is also included in the simulation.

Low-Temperature Deposition of Thin Si, Ge, and SiGe Films Using Reducing Activity of Ballistic Hot Electrons

It is shown that a wet process for thin Si and Ge films deposition based on the ballistic electron injection into solutions is available for SiGe. A nanocrystalline silicon (nc-Si) diode is composed of a thin Au (10 nm)/Ti (1 nm) film surface electrode, nc-Si layer (~1 µm), n+-Si substrate, and back contact. The electrochemical effect of ballistic hot electrons was confirmed by cyclic voltammetry analyses. Electrons are emitted from the nc-Si device on which a very small amount of SiCl4+GeCl4 solutions is dripped. After the emitter operation, thin SiGe films are deposited on the emitting surface with neither byproducts nor contaminations as in the case of thin Si and Ge films deposition. Based on the structural and compositional characterizations of deposited SiGe films, the specific features of this reduction-induced deposition mode are discussed in comparison with the conventional processes.

Low-Temperature Deposition of Thin Si, Ge, and SiGe Films Using Reducing Activity of Ballistic Hot Electrons

Quantum-sized nanocrystalline Si (nc-Si) dots behave as a drift layer which efficiently generates ballistic hot electrons. This is due to little phonon scattering losses in nc-Si at the early stage of injection and subsequent multiple-tunneling cascade through nc-Si dots chain interconnected with thin oxides [1]. At a sufficient electric field, generated ballistic hot electrons are ejected through the surface electrode. In solutions, the nc-Si emitter operates as an active electrode supplying highly reducing electrons. This is applicable to deposition of thin films of metals [2], Si [3], and Ge [4]. Details of this thin film deposition scheme based on the ballistic reduction effects is discussed here including the availability for the deposition of thin Ge and SiGe films.The nc-Si emitter is a kind of MIS diode consisting of a thin film surface electrode, a nanosilicon layer (~1 μm thick), a crystalline silicon wafer substrate, and a back contact. The nc-Si layer includes parallel chains of quantum-sized nanosilicon dots (~3 nm in mean diameter) interconnected with tunnel oxides. When a positive voltage is applied to the surface electrode, electrons injected from the substrate into the nc-Si layer are accelerated toward the outer surface, and then some of them are emitted from the surface electrode as ballistic hot electrons [5]. This planar cold cathode emits energetic and directional electrons. The kinetic energy of electrons can be controlled by the applied voltage. At applied voltages of 15-20 V, for instance, the mean energy of output electrons varies from 5 to 7 eV.Besides in vacuum, the nc-Si emitter operates in atmospheric-pressure gases and even in solutions. Since electrons with an extremely high and electrochemical activity are supplied at relatively low applied voltage, positive ion species are directly reduced. Following the experimental confirmation of the usefulness in aqueous solutions as means for H2 generation and pH control, it has been demonstrated that the ballistic hot electron injection into metal-salt solutions leads to the deposition of thin metal (Cu, Ni, Co, Zn, and so on) films without using any counter electrodes.After the device is mounted in a N2 gas filled glove box, a small amount (5~10 μl) of SiCl4, GeCl4, or their mixture (1:1 in volume) was dripped onto the emission surface, and then the emitter was driven at V b=10-15 V. After the emitter operation for several min without using any counter electrodes, thin films were uniformly deposited on the emitting area in the same way as the previous dipping method. The structure and composition of the deposited films were investigated by transmission electron microscope (TEM), scanning electron microscope (SEM), atomic force microscope (AFM), energy dispersive X-ray (EDX) spectra, X-ray photoelectron spectroscopy (XPS), and secondary ion mass spectroscopy (SIMS).In accordance with TEM analyses, the deposited films are amorphous. The observed EDX spectra indicate that the respective deposited films are composed of Si, Ge, and SiGe. The contamination signals of Cl were below the detection limit of XPS measurements. The result of SIMS of thin SiGe films, the compositional ratio of Si to Ge was about 0.9:0.1. This can be controlled by changing the mixture ratio of SiCl4+GeCl4 solution.In contrast to the electro-plating based on exchange of thermalized electrons, the ballistic electro-reduction proceeds with neither Cl2 evolution nor byproducts generation at the counter electrode. Despite a significantly large electrochemical window between the reduction (Si/Si4+) and oxidation (Cl2/Cl-) potentials, injected electrons have energies sufficient enough for unilateral reduction. Being a low-temperature and clean process, this ballistic electro-reduction mode is attractive as an alternative approach for fabrication of group-IV thin-films, multilayered nanostructures, and devices. This work was partially supported by the JSPS through a Grant-in-Aid for Scientific Research and the FIRST Program and by the NEDO through the R&D Project.

Optical conductivity of the R-Cd quasicrystals and approximants

Recently, a new family of R-Cd binary icosahedral quasicrystals has been discovered [1]. Using optical reflectance spectroscopy, we have examined the quasicrystal GdCd7.98and the approximants GdCd6and YCd6. To explain the unique behaviour of electrons in a quasiperiodic lattice Mayou [2] created a model of electron transport due to anomalous diffusion of wave packets scattering from the quasiperiodic lattice. We have determined the optical conductivity of the above-mentioned materials from 7.5 meV to 5.5 eV and have used Mayou's model of optical conductivity for approximants and quasicrystals, σ1∝ Re[ (1/(γ-iω))^(2β-1) ], to describe the low frequency behaviour. Despite the concern of Mayou of not being able to differentiate experimentally between normal metallic conductivity of ballistic electrons, β=1, and sub-ballistic conductivity, 1/2<β<1, we clearly see β≍3/4 in the intraband peak of the icosahedral approximants, which has not been observed before. Before this work, the only unambiguously Drude-like peak seen in any quasicrystal or their approximant occurred in the decagonal approximant γ-brass, which was fit with exactly β=1 [3]. However, unlike the approximants in our study, this sample of γ-brass was admittedly not a good approximant to a quasicrystal with its small lattice constant. In the GdCd7.98quasicrystal, we observe low frequency behaviour that lacks a Drude peak but is not nearly perfectly linear as seen by others. In this case, the low frequency behaviour is qualitatively similar to the diffusive regime, 0<β<1/2, that is often seen. However, it is not adequately modelled by Mayou's generalized Drude model. With these results, unlike in previous optical conductivity studies, we have a striking difference in the low frequency conductivity that suggests that there is a difference in the physics of the optical conductivity of periodic and quasiperiodic lattices that needs to be explored.

Manipulation of electron flow using near-zero index semiconductor metamaterials

We study the possibility of controlling the propagation of ballistic electrons using an electronic metamaterial with zero quantum index of refraction. This is obtained by tailoring the band structure of a semiconductor superlattice to exhibit a Dirac cone at the center of the Brillouin zone, creating an artificial quantum medium with zero refractive index for electrons. We demonstrate attractive functionalities, such as anomalous tunneling, ideal matching, electronic routing, cloaking, and focusing. We envision applications in nanoelectronics and sensing.