Wave Vector Conservation Research Articles

Long-Lived 1D Excitons in Bright CdTe Quantum Wires

Time-resolved photoluminescence (PL) intensity decay profiles were recorded for room-temperature ensemble samples of CdTe quantum wires (QWs) with varying PL quantum yields (ΦPL). The PL lifetimes for samples with ΦPL > 4% are nearly an order of magnitude greater than the radiative lifetime of CdTe QDs, ≥200 versus ∼25 ns. The photogenerated electron–hole pairs relax to the lowest exciton state, correlating with the 1Σe and 1Σ3/2h quantum-confinement states, and are bound together as one-dimensional (1D) excitons. These 1D excitons have a thermal distribution of translational kinetic energy along the long, unconfined dimension of the QWs. The extended lifetimes are justified via the constraints imposed by the conservation of wave vector (or momentum) and the large mismatch between the wave vector of the moving 1D excitons and of the photons emitted during radiative relaxation. The long charge-carrier lifetimes and the dimensionality of these high-quality semiconductor QWs offer distinct advantages for use...

Simulating Tunneling Electron Transport in the Semiconductor–Crystalline Insulator–Si(111) System

Tunneling carrier transport through a thin insulator (e.g., CaF2) layer between a Si(111) substrate and a semiconductor gate is theoretically investigated. Along with the conservation of a large transverse wave vector of tunneling particles, the limitation imposed on the availability of states in the gate is taken into account. Due to this limitation, the tunneling currents at low insulator bias are weaker than in an analogous structure with a metal gate electrode. The same feature leads to a change in the shape of the energy distribution of tunneling electrons, both in transport between the substrate and gate conduction bands and during the Si(111) conduction band–gate valence band transfer.

Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover

Simulations (e.g. Zhou et al., Phys. Rev. B 79, 115201 (2009)) show nonlocal effects of the ballistic/diffusive crossover. The local temperature has nonlinear spatial variation not contained in the local Fourier law $\vec{j}(\vec{r})=-\kappa\vec{\nabla}T(\vec{r})$. The heat current $\vec{j}(\vec{r})$ depends not just on the local temperature gradient $\vec{\nabla}T(\vec{r})$, but also on temperatures at points $\vec{r}^{ \ \prime}$ within phonon mean free paths, which can be micrometers long. This paper uses the Peierls-Boltzmann transport theory in non-local form to analyze the spatial variation $\Delta T(\vec{r})$. The relaxation-time approximation (RTA) is used because full solution is very challenging. Improved methods of extrapolation to obtain the bulk thermal conductivity $\kappa$ are proposed. Callaway invented an approximate method of correcting RTA for the $\vec{q}$ (phonon wavevector or crystal momentum) conservation of N (normal as opposed to Umklapp) anharmonic collisions This method is generalized to the non-local case where $\kappa(\vec{k})$ depends on wavevector of the current $\vec{j}(\vec{k})$ and temperature gradient $i\vec{k}\Delta T(\vec{k})$.

Моделирование туннельного переноса электронов в системе полупроводник-кристаллический диэлектрик-Si(111)

AbstractTunneling carrier transport through a thin insulator (e.g., CaF_2) layer between a Si(111) substrate and a semiconductor gate is theoretically investigated. Along with the conservation of a large transverse wave vector of tunneling particles, the limitation imposed on the availability of states in the gate is taken into account. Due to this limitation, the tunneling currents at low insulator bias are weaker than in an analogous structure with a metal gate electrode. The same feature leads to a change in the shape of the energy distribution of tunneling electrons, both in transport between the substrate and gate conduction bands and during the Si(111) conduction band–gate valence band transfer.

Insight into boron-doped diamond Raman spectra characteristic features

Characteristic Raman features of boron-doped diamond layers with metallic conduction are studied experimentally and discussed in comparison with an extensive selection of literature data. Despite evidence that the main Raman bands are mostly characteristic features of carbon atom vibration modes, their position is found to be proportional to boron concentration. While the origin of the Raman bands located at c.a. 500 cm−1 remains unclear, the band centred at c.a. 1200 cm−1 is attributed to a maximum of phonon density of states due to softening of the Raman wave vector conservation rule. The downshift and broadening of the diamond line are attributed, primarily, to the domain size effect caused by scattering on boron impurities, secondly to the Fano effect due to electronic Raman interaction, and finally to lattice expansion due to the boron doping.

An amorphous-to-crystalline phase transition within thin silicon films grown by ultra-high-vacuum evaporation and its impact on the optical response

A number of thin silicon films are deposited on crystalline silicon, native oxidized crystalline silicon, and optical quality fused quartz substrates through the use of ultra-high-vacuum evaporation at growth temperatures ranging from 98 to 572 °C. An analysis of their grazing incidence X-ray diffraction and Raman spectra indicates that a phase transition, from amorphous-to-crystalline, occurs as the growth temperature is increased. Through a peak decomposition process, applied to the Raman spectroscopy results, the crystalline volume fractions associated with these samples are plotted as a function of the growth temperature for the different substrates considered. It is noted that the samples grown on the crystalline silicon substrates have the lowest crystallanity onset temperature, whereas those grown on the optical quality fused quartz substrates have the highest crystallanity onset temperature; the samples grown on the native oxidized crystalline silicon substrates have a crystallanity onset temperature between these two limits. These resultant dependencies on the growth temperature provide a quantitative means of characterizing the amorphous-to-crystalline phase transition within these thin silicon films. It is noted that the thin silicon film grown on an optical quality fused quartz substrate at 572 °C, possessing an 83% crystalline volume fraction, exhibits an optical absorption spectrum which is quite distinct from that associated with the other thin silicon films. We suggest that this is due to the onset of sufficient long-range order in the film for wave-vector conservation to apply, at least partially. Finally, we use a semi-classical optical absorption analysis to study how this phase transition, from amorphous-to-crystalline, impacts the spectral dependence of the optical absorption coefficient.

Model calculation of thermal conductivity in antiferromagnets

A theoretical study is given of thermal conductivity in antiferromagnetic materials. The study has the advantage that the three-phonon interactions as well as the magnon phonon interactions have been represented by model operators that preserve the important properties of the exact collision operators. A new expression for thermal conductivity has been derived that involves the same terms obtained in our previous work in addition to two new terms. These two terms represent the conservation and quasi-conservation of wavevector that occur in the three-phonon Normal and Umklapp processes respectively. They gave appreciable contributions to the thermal conductivity and have led to an excellent quantitative agreement with the experimental measurements of the antiferromagnet FeCl2.

Low-dimensional CdS/CdTe multiple-quantum well heterostructure for optical refrigeration

The major challenge for semiconductors to achieve temperatures below 10 K by luminescence upconversion, is that at these lattice temperatures the acoustic phonon component dominates and the scattering rate becomes comparable to the band-to-band radiative transition rate. This problem can be significantly alleviated by employing quantum-confined systems, where relaxation of wave-vector conservation in the confined direction reduces material conductivity by nearly three orders of magnitude. Although previous studies have reported theoretical and experimental analyses of cooling characteristics for bulk semiconductors, the electron band-to-band transition due to photon absorption or photon emission under cooling conditions in quantum-confined semiconductor systems which exhibit quantum effects at the dimensions of several nanometers have not been completely analyzed in conventional theoretical studies. We realized a numerical investigation of optical cooling conditions for a low-dimensional CdS/CdTe multiple-quantum well heterostructure where injected carriers in the active region are quantum mechanically confined in one dimension. Effects of such quantum mechanically confined carriers on photon absorption and photoluminescence (PL) were analyzed under cooling conditions. Most importantly, the CdS/CdTe heterostructure absorption and PL spectra for cooling conditions were defined in terms of the active layer width and number of quantum wells in the complete heterostructure.

Investigation on nanotube-metal contacts under different contact types

The contacts of the metallic or semiconducting carbon nanotubes (CNTs) and the Ti (side-contacted type) or TiC (end-contacted type) have been investigated by non-equilibrium Green׳s function approach. The transmission coefficient and resistance of the contacts are calculated. The study shows the contact resistance between TiC and metallic or semiconducting CNT is 2 and 4 orders of magnitude lower than that between Ti and metallic or semiconducting CNT, respectively. The contact resistance between TiC and metallic CNT can be low down to ~6.8kΩ. The contact characteristics are illustrated by the wave-vector conservation of electron transportation between CNT and metal.

Quantum Theory of Surface Plasmon Polaritons: Planar and Spherical Geometries

A quantum theory of retarded surface plasmons on a metal–vacuum interface is formulated, by analogy with the well-known and widely exploited theory of exciton-polaritons. The Hamiltonian for mutually interacting instantaneous surface plasmons and transverse electromagnetic modes is diagonalized with recourse to a Hopfield–Bogoljubov transformation, in order to obtain a new family of modes, to be identified with retarded plasmons. The interaction with nearby dipolar emitters is treated with a full quantum formalism based on a general definition of modal effective volumes. The illustrative cases of a planar surface and of a spherical nanoparticle are considered in detail. In the ideal situation of absence of dissipation, as an effect of the conservation of in-plane wavevector, retarded plasmons on a planar surface represent true stationary states (which are usually called surface plasmon polaritons), whereas retarded plasmons in a spherical nanoparticle, characterized by frequencies that overlap with the transverse electromagnetic continuum, become resonances with a finite radiative broadening. The theory presented constitutes a suitable full quantum framework for the study of nonperturbative and nonlinear effects in plasmonic nanosystems.

Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study

Second-order perturbation theory based on multiple time scale analysis is used to illuminate three-phonon scattering processes in the one-dimensional anharmonic monoatomic crystal. Molecular dynamics simulation techniques in conjunction with spectral energy density analyses are used to quantify phonon mode lifetime in (1) the monoatomic crystal and (2) a series of superlattice configurations. It is found that the lifetime of vibrational modes in the monoatomic crystal is inherently long, because the conditions for conservation of wave vector and frequency are pathologically difficult to satisfy. Superlattice configurations, however, offer band-folding effects, whereby the availability of phonon decay channels decreases the lifetime of the vibrational modes supported by the medium.

Study of the Correlation of Plasma Resonance and the Refractive Index to Dielectric Dispersion in the Complex Plane

Based on the dispersive feature of the dielectric function of noble metals and the wave vector conservation in physics, both the plasma effect and the complex refractive index, which are profoundly correlated to the complex dielectric function and permeability, have been studied and analyzed. The condition to induce a bulk or a surface plasma in the visible region will not be satisfied, and there will be one solution for the real and the imaginary parts of the refractive index, restricting it only to region I of the complex plane. The results given in this work will aid in understanding the properties of light transmission at the metal/dielectric interface as characterized by the law of refraction in nature.

Temperature dependence of the Raman spectrum in Ge1−ySnyand Ge1−x−ySixSnyalloys

The temperature dependence of the Raman spectrum of Ge-rich Ge${}_{1\ensuremath{-}y}$Sn${}_{y}$ and Ge${}_{1\ensuremath{-}x\ensuremath{-}y}$Si${}_{x}$Sn${}_{y}$ alloys has been determined in the 10- to 400-K range. The Raman line shift and width changes as a function of temperature are found to be virtually identical to those observed in bulk Ge. This result shows that the anharmonic decay process responsible for the temperature dependence is extremely robust against the alloy perturbation, so that the expected relaxation of the wave vector conservation rule does not affect the decay in any noticeable way.

Determination of the photoelectron reference plane in nanostructured surfaces

In angle-resolved photoemission (ARPES) from crystalline solids, wave-vector conservation applies to the two-dimensional (2D) surface, which may thus be defined as the reference plane in ARPES. We investigate whether such reference varies for photoemitted electrons in nanometer-sized systems that expose different crystal planes. To this aim, we exploit the structural tunability of the Ag/Cu(223) system which is capable of offering surfaces with periodic arrays of nanofacets of varying size and orientation. A thorough, photon-energy-dependent analysis of the surface states confined to such nanostructures is performed comparing different reference planes for photoemitted electrons. Assuming the premise that k|| must be a good quantum number for 2D states, we conclude that the (final state) photoelectron reference direction is not the average optical direction but the local facet that confines the (initial state) surface electrons. Moreover, in the general case of nanostructured systems with uneven surfaces, we show how the photoelectron reference plane can be empirically determined through such a photon-energy-dependent ARPES analysis.

Probing bulk electronic structure with hard X-ray angle-resolved photoemission

Traditional ultraviolet/soft X-ray angle-resolved photoemission spectroscopy (ARPES) may in some cases be too strongly influenced by surface effects to be a useful probe of bulk electronic structure. Going to hard X-ray photon energies and thus larger electron inelastic mean-free paths should provide a more accurate picture of bulk electronic structure. We present experimental data for hard X-ray ARPES (HARPES) at energies of 3.2 and 6.0 keV. The systems discussed are W, as a model transition-metal system to illustrate basic principles, and GaAs, as a technologically-relevant material to illustrate the potential broad applicability of this new technique. We have investigated the effects of photon wave vector on wave vector conservation, and assessed methods for the removal of phonon-associated smearing of features and photoelectron diffraction effects. The experimental results are compared to free-electron final-state model calculations and to more precise one-step photoemission theory including matrix element effects.

Tunneling of electrons with conservation of the transverse wave vector in the Au/CaF2/Si(111) system

Epitaxial layers of calcium fluoride on silicon(111) have been prepared, in which tunneling transfer of electrons with conservation of the transverse momentum component has been observed. A good agreement between the results of simulation and the experimental data has been achieved. The procedure underlying the calculations has been described in detail. The obtained films are suitable for the use as barrier layers in various solid-state electronic devices.

The phototransistor action of a reverse-biased Au/CaF2[3–7 ML]/n-Si(1 1 1) structure

Metal–ultra-thin insulator–semiconductor (MIS) tunnel structures with a high-quality ultra-thin epitaxial fluoride layer have been fabricated on n-Si wafers. Under the reverse bias, these structures have been experimentally shown to amplify photocurrent. They can therefore be treated as MIS tunnel emitter bipolar phototransistors. The gain value reaches 102–103, and is due to the asymmetry between conduction-band and valence-band tunneling. The importance of the valence-band component has been elucidated. The experimental data have been well reproduced by simulations considering the conservation of the transverse wave vector of tunneling particles. The current multiplication effect was observed within the voltage range up to the structure overload. After the insulator damage, the structure ceased to exhibit gain rendering a photodiode.

Ray splitting in the reflection and refraction of surface acoustic waves in anisotropic solids

This paper examines the conditions for, and provides examples of, ray splitting in the reflection and refraction of surface acoustic waves (SAW) in elastically anisotropic solids at straight obstacles such as edges, surface breaking cracks, and interfaces between different solids. The concern here is not with the partial scattering of an incident SAW's energy into bulk waves, but with the occurrence of more than one SAW ray in the reflected and/or transmitted wave fields, by analogy with birefringence in optics and mode conversion of bulk elastic waves at interfaces. SAW ray splitting is dependent on the SAW slowness curve possessing concave regions, which within the constraint of wave vector conservation parallel to the obstacle allows multiple outgoing SAW modes for certain directions of incidence and orientation of obstacle. The existence of pseudo-SAW for a given surface provides a further channel for ray splitting. This paper discusses some typical material configurations for which SAW ray splitting occurs. An example is provided of mode conversion entailing backward reflection or negative refraction. Experimental demonstration of ray splitting in the reflection of a laser generated SAW in GaAs(111) is provided. The calculation of SAW mode conversion amplitudes lies outside the scope of this paper.

Azimuthal dispersion and energy mode condensation of grating-coupled surface plasmon polaritons

The excitation conditions for surface plasmon polaritons (SPPs) on a silver-gold bilayer coated sinusoidal grating can be varied over a wide range by tuning the azimuthal grating orientation $(\ensuremath{\alpha})$. Grating coupling induces rotation of the SPP wave vector which, for specific conditions, can be directed perpendicular to the exciting light direction. Certain $\ensuremath{\alpha}$ orientations allow the excitation of two SPPs with the same frequency but different propagation directions. Other azimuthal orientations allow excitation of many SPP modes characterized by propagation over a large angular range. The kinematics of SPP propagation can be described by a model based on the wave-vector conservation law. Using this model, SPP dispersion relation, propagation direction, and mode density have been computed and shown to be in agreement with experimental measurements. The wave-vector dispersion is characterized by an energy threshold for the SPP excitation that increases as $\ensuremath{\alpha}$ increases. The angular spread is accompanied by an energy condensation of the SPP modes in correspondence to the energy threshold.

The Magnetic Manipulation of Surface Plasmons --- Consideration of Possible Technologies

An as yet unexploited mechanism for producing controlled shifts in the frequency of lightwaves via their temporary conversion to surface plasmons propagating on a ferromagnetic surface or under the action of applied magnetic flelds is introduced. Indirect evidence of the observation of this phenomena is presented and the technological possibilities it might ofier are explored and discussed. Interfaces between dielectric and metallic media possessing negative permittivity () can support electromagnetic waves propagating as longitudinal density oscillations in the free-electron plasma at the metallic surface. Like photons, the quanta of these collective excitations remain bosons and are known as surface plasmons. Moreover, under conditions satisfying the relevant conservation laws, photons and plasmons are mutually transformable. Photons incident on a metallic surface may for example be temporarily induced to convert to plasmons that propagate on the surface for a while before their subsequent recovery as photons emitted back into the incident medium. The most exciting and complete conflrmation of the nature of this process is evidenced in the work of Altewischer etal. (1) which demonstrated that a photon, having followed a path that includes its conversion to a plasmon and back to a photon, retains entanglement with the twin with which it was originally created in a down-conversion process. The objective here is to draw attention to the potential to exploit this two way conversion process to operate on photons in ways not previously considered. More than 30 years ago Chiu and Quinn (2) and Nakamura and Paranjape (3) flrst described theoretically how propagating plasmons undergo frequency shifts when subject to in∞uence by ap- propriately orientated dc magnetic flelds (H) applied orthogonal to the plasmon ∞ux. In more recent times Smolyaninov etal. (4) have interpreted the equations of Chiu and Quinn (2) and Naka- mura and Paranjape (3) as describing a second-order mixing process between the ac plasmon fleld (Ep) and any applied dc magnetic fleld (H). If ´ (2) is a generalised susceptibility then such mixing processes generate terms of the form ´ (2) E 2 p H in the plasmon fleld energy density and the break- ing of inversion symmetry at the interfaces requisite for the very existence of surface plasmons determines that terms such as ´ (2) E 2 p will always be present. The plasmon energy and hence frequency consequently acquire a contribution linear in the applied fleld H which is real and in light of the results of Altewischer etal. (1) transposable to a photon emission fleld when the plasmon is intercepted by a grating out-coupler. We have obtained strong indirect evidence of the reality of this position by studying plasmon propagation on a nickel surface on which a linear grating with a period of 1.13m and depth of 0.7m is modulated, as shown schematically in Figure 1, by a shallower structure with an order of magnitude greater periodicity of about 12.5m (5). When this structured surface is illuminated at an angle of incidence (µi) of exactly 19.85 - by optical radiation with a wavelength of 800nm and conservation of wavevector is satisfled by the addition of that associated with the 1.13m structural periodicity to that of the incident photons, a deep absorption trough is observed as shown on the left of Figure 1 indicating the resonant gen- eration of a ∞ux of forward propagating surface plasmons. Because of the flnite spectral width of the incident optical beam, its residual divergence and the inherent error in the periodicity of the 1.13m coupling structure this ∞ux consists of plasmons with a narrow spectrum of wavevectors rather than a single identical wavevector and the population of this spectrum is primarily deter- mined by the Gaussian intensity proflle of the incident beam. The width of the plasmon spectrum at full width half maximum ¢Ksp(FWHM) may be estimated by examination and analysis of the form of the re∞ectivity trough in Figure 1 to be of the order of 0:35£10 i3 nm i1 . This plasmon ∞ux subsequently interacts in a much weaker fashion with the longer and shallower periodic structure which re-couples it back to an emissive optical fleld emerging from the surface at an angle of 77 -