Optical Phonon Population Research Articles

Characterization of local non-equilibrium phonons in bulk MoS2 probed by temperature-dependent Raman scattering

This study presents an experimental implementation to determine the temperature dependence of Raman spectra of bulk 2H-MoS2 in the temperature range of 300–650 K. In addition, we have measured according to the anti-Stokes to Stokes integrated intensity ratio (). The results indicate that Raman shift of both the vibration modes and exhibits a linear temperature-dependent behavior in the heating and cooling processes. It is confirmed that the sample did not deteriorate by oxidization and decomposition at high temperatures. However, above 500 K, the measured phonon temperature deviated from the heat bath temperature. It is suggested that the does not correspond to the equilibrium population of optical phonons, thus indicating that the measurement was not in thermal equilibrium but in a thermal steady state under laser irradiation. We conclude that this is caused by the difference in relaxation times in the thermal steady state.

Competition Pathways of Energy Relaxation of Hot Electrons through Coupling with Optical, Surface, and Acoustic Phonons

The hot electrons in carbon-based materials exhibit interesting ballistic transport behaviors for designing high-performance single-electron transistors. However, the cooling of such hot electrons back to the equilibrium state may be slowed down by the excessively populated optical phonons, thus limiting their ballistic transport. Therefore, a thorough understanding of the coupling between hot electrons and optical phonons is of critical importance. Here, by varying the thickness of a multilayer graphene film on a supporting substrate, we investigated the competition pathways of the energy relaxation of the photoinduced hot electrons through coupling with the optical, surface, and acoustic phonons. The difference in the τ2 values indicates that thickness plays an important role in the optical phonon population. For the multilayer graphene film thickness less than 3 nm, the super-collision model describes the hot electron cooling dynamics that is strongly affected by the surface phonons from the supporting substrate. As the multilayer graphene film thickness increases from 3 to 20 nm, the accumulation of the optical phonons induces a hot optical phonon effect, resulting in a bottleneck of cooling of the hot electrons. As the multilayer graphene film thickness further increases from 20 to 40 nm, a direct coupling between the hot electrons and acoustic phonons starts to dominate. The surface states of the interfaces at the inner layers of the multilayer graphene film contribute to this direct coupling as an additional cooling channel. The quantitative understanding of the energy relaxation pathways of the hot electrons offers insights into designing high-performance single-electron transistors.

Atomic-Level, Energy-Conversion Heat Transfer

Abstract Heat is stored in quanta of kinetic and potential energies in matter. The temperature represents the equilibrium and excited occupation (boson) of these energy conditions. Temporal and spatial temperature variations and heat transfer are associated with the kinetics of these equilibrium excitations. During energy-conversion (between electron and phonon systems), the occupancies deviate from equilibria, while holding atomic-scale, inelastic spectral energy transfer kinetics. Heat transfer physics reaches nonequilibrium energy excitations and kinetics among the principal carriers, phonon, electron (and holes and ions), fluid particle, and photon. This allows atomic-level tailoring of energetic materials and energy-conversion processes and their efficiencies. For example, modern thermal-electric harvesters have transformed broad-spectrum, high-entropy heat into a narrow spectrum of low-entropy emissions to efficiently generate thermal electricity. Phonoelectricity, in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes a high-entropy heat. In particular, the suggested phonovoltaic cell generates phonoelectricity by employing the nonequilibrium, low-entropy, and elevated temperature optical-phonon produced population—for example, by relaxing electrons, excited by an electric field. A phonovoltaic material has an ultranarrow electronic bandgap, such that the hot optical-phonon population can relax by producing electron-hole pairs (and power) instead of multiple acoustic phonons (and entropy). Examples of these quanta and spectral heat transfer are reviewed, contemplating a prospect for education and research in this field.

Two-colour Three-pulse Spectrally Resolved Nonlinear Spectroscopy for Studies of Dynamics in Semiconductor Si Quantum Dots

We demonstrate that a two-colour three-pulsenonlinear spectroscopy can be used to study the dynamics of excited carriers inSi quantum dot structures embedded in SiN. Decays of the transverse optical phonon population and the transverse acoustic phonon population are measured and discussed. A simple theoretical modelis also used to support interpretation of our experimental observations.

Hot-Carrier Relaxation in CdSe/CdS Core/Shell Nanoplatelets

We present time-resolved photoluminescence (PL) spectroscopy of a series of colloidal CdSe/CdS core/shell nanoplatelets with different core and shell thicknesses. Exciton numbers are determined from the integrated PL intensities, and carrier temperatures are determined from the high-energy exponential tail of the PL spectra. For times between 10 and 1000 ps, the measured carrier relaxation dynamics are well described by a simple model of Auger reheating: biexcitonic Auger recombination continually increases the average energy of the carriers (while decreasing their number), and this reheating sets a bottleneck to cooling through electron–phonon coupling. For times between 1 and 10 ps, the relaxation dynamics are consistent with electron–phonon coupling, where the bottleneck is now the decay of the longitudinal optical phonon population. Comparison of relaxation dynamics to recombination dynamics reveals changes in the carrier–phonon coupling for shell thicknesses greater than 4 monolayers.

From thermoelectricity to phonoelectricity

Here, we review the history and progress of solid-state heat harvesting. Efficiency models, material metrics, and current research are discussed for thermoelectrics, thermionics, laser-coolers, and modern technologies. Then, we discuss nonequilibrium optical phonon harvest in the phonovoltaic cell. We make an effort to distinguish between the harvest of equilibrium heat, or thermal-electricity, and the targetted harvest of a particular nonequilibrium phonon mode, or phonoelectricity. We survey the state of phonovoltaic research, focusing on phonovoltaic materials, the electron-phonon coupling, and entropy production in a phonovoltaic cell. Throughout this review, discussions are connected to the electron and phonon structures, interactions, and transport. The modern thermal-electric harvesters are shown to reshape broad-spectrum, high-entropy heat into a narrow-spectrum of low-entropy emissions in order to efficiently generate thermal-electricity. Phonoelectricity, in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes high-entropy heat. In particular, the phonovoltaic cell generates phonoelectricity by utilizing the nonequilibrium, low-entropy, and high temperature optical phonon population produced by, e.g., the relaxation of electrons excited by an electric field. A phonovoltaic material has an ultranarrow electronic bandgap, such that the hot optical phonon population can relax by producing electron-hole pairs (and power) instead of multiple acoustic phonons (and entropy). The phonovoltaic device has an electric diode, e.g., a p-n junction, such that the internal electric field of the diode splits the electrons and holes in order to produce an electric current, and thus, power. The low entropy and high-temperature of the nonequilibrium optical phonon population enable efficient, in-situ heat harvesting. Bilayer graphene, for example, can theoretically convert the nonequilibrium population of optical phonons generated in a field-effect transistor into electricity with an efficiency exceeding 70% of the Carnot limit. The thermal-electric devices, in contrast, are either inefficient or restricted to ex-situ power generation. Furthermore, as the phonoelectric Carnot limit is defined by the local nonequilibrium between electron and optical phonon populations, rather than the spatial nonequilibrium across the device, the Carnot limit can be very large without inducing melting.Here, we review the history and progress of solid-state heat harvesting. Efficiency models, material metrics, and current research are discussed for thermoelectrics, thermionics, laser-coolers, and modern technologies. Then, we discuss nonequilibrium optical phonon harvest in the phonovoltaic cell. We make an effort to distinguish between the harvest of equilibrium heat, or thermal-electricity, and the targetted harvest of a particular nonequilibrium phonon mode, or phonoelectricity. We survey the state of phonovoltaic research, focusing on phonovoltaic materials, the electron-phonon coupling, and entropy production in a phonovoltaic cell. Throughout this review, discussions are connected to the electron and phonon structures, interactions, and transport. The modern thermal-electric harvesters are shown to reshape broad-spectrum, high-entropy heat into a narrow-spectrum of low-entropy emissions in order to efficiently generate thermal-electricity. Phonoelectricity, in contrast, intervenes before a low-ent...

Exciton and phonon dynamics in highly aligned 7-atom wide armchair graphene nanoribbons as seen by time-resolved spontaneous Raman scattering.

The opening of a band gap in graphene nanoribbons induces novel optical and electronic properties, strongly enhancing their application potential in nanoscale devices. Knowledge of the optical excitations and associated relaxation dynamics are essential for developing and optimizing device designs and functionality. Here we report on the optical excitations and associated relaxation dynamics in surface aligned 7-atom wide armchair graphene nanoribbons as seen by time-resolved spontaneous Stokes and anti-Stokes Raman scattering spectroscopy. On the anti-Stokes side we observe an optically induced increase of the scattering intensity of the Raman active optical phonons which we assign to changes in the optical phonon populations. The optical phonon population decays with a lifetime of ∼2 ps, indicating an efficient optical-acoustic phonon cooling mechanism. On the Stokes side we observe a substantial decrease of the phonon peak intensities which we relate to the dynamics of the optically induced exciton population. The exciton population shows a multi-exponential relaxation on the hundreds of ps time scale and is independent of the excitation intensity, indicating that exciton-exciton annihilation processes are not important and the exsistence of dark and trapped exciton states. Our results shed light on the optically induced phonon and exciton dynamics in surface aligned armchair graphene nanoribbons and demonstrate that time-resolved spontaneous Raman scattering spectroscopy is a powerful method for exploring quasi-particle dynamics in low dimensional materials.

Observing non-equilibrium state of transport through graphene channel at the nano-second time-scale

Electrical performance of a graphene FET is drastically affected by electron-phonon inelastic scattering. At high electric fields, the out-of-equilibrium population of optical phonons equilibrates by emitting acoustic phonons, which dissipate the energy to heat sinks. The equilibration time of the process is governed by thermal diffusion time, which is few nano-seconds for a typical graphene FET. The nano-second time-scale of the process keeps it elusive to conventional steady-state or DC measurement systems. Here, we employ a time-domain reflectometry-based technique to electrically probe the device for few nano-seconds and investigate the non-equilibrium state. For the first time, the transient nature of electrical transport through graphene FET is revealed. A maximum change of 35% in current and 50% in contact resistance is recorded over a time span of 8 ns, while operating graphene FET at a current density of 1 mA/μm. The study highlights the role of intrinsic heating (scattering) in deciding metal-graphene contact resistance and transport through the graphene channel.

Bilayer graphene phonovoltaic-FET:In situphonon recycling

A new heat harvester, the phonovoltaic (pV) cell, was recently proposed. The device converts optical phonons into power before they become heat. Due to the low entropy of a typical hot optical phonon population, the phonovoltaic can operate at high fractions of the Carnot limit and harvest heat more efficiently than conventional heat harvesting technologies such as the thermoelectric generator. Previously, the optical phonon source was presumed to produce optical phonons with a single polarization and momentum. Here, we examine a realistic optical phonon source in a potential pV application and the effects this has on pV operation. Supplementing this work is our investigation of bilayer graphene as a new pV material. Our ab initio calculations show that bilayer graphene has a figure of merit exceeding 0.9, well above previously investigated materials. This allows a room-temperature pV to recycle 65% of a highly nonequilibrium, minimum entropy population of phonons. However, full-band Monte Carlo simulations of the electron and phonon dynamics in a bilayer graphene field-effect transistor (FET) show that the optical phonons emitted by field-accelerated electrons can only be recycled in situ with an efficiency of 50%, and this efficiency falls as the field strength grows. Still, an appropriately designed FET-pV can recycle the phonons produced therein in situ with a much higher efficiency than a thermoelectric generator can harvest heat produced by a FET ex situ.

Molecular dynamics study of phonon transport in graphyne nanotubes

We determine the thermal conductivities of α, β, and γ graphyne nanotubes (GNTs) as well as of carbon nanotubes (CNTs) using molecular dynamics simulations and the Green-Kubo relationship over the temperature range 50–400 K. We find that GNTs demonstrate considerably lower thermal conductivity than CNTs with the same diameter and length. Among α, β, and γ-GNTs, γ-GNT has the highest thermal conductivity at all temperatures. By comparing the phonon transport properties of GNTs with CNTs, we find that as the fraction of acetylene bonds in the atomic network increases, the population of high-energy optical phonons increases. This enhances phonon-phonon scattering, and reduces the mean free path, adversely affecting the thermal conductivity of GNTs relative to CNTs. Also reducing the thermal conductivity of GNTs relative to CNTs is the considerably lower acoustic phonon group velocities for the former as well as the lower volumetric heat capacity of GNTs. Optical phonons in α-GNT are high in energy (0.26 eV) with a high population number, making them more energetic than the electronic direct band gap and significantly more energetic than the thermal energy at room temperature. Therefore, we suggest α-GNT as a potential candidate for phonovoltaic energy conversion applications.

Light-induced nonthermal population of optical phonons in nanocrystals

Raman spectroscopy is widely used to study bulk and nanomaterials, where information is frequently obtained from spectral line positions and intensities. In this study, we monitored the Raman spectrum of ensembles of semiconductor nanocrystals (NCs) as a function of optical excitation intensity (optical excitation experiments). We observe that in NCs the red-shift of the Raman peak position with increasing light power density is much steeper than that recorded for the corresponding bulk material. The increase in optical excitation intensity results also in an increasingly higher temperature of the NCs as obtained with Raman thermometry through the commonly used Stokes/anti-Stokes intensity ratio. More significantly, the obtained dependence of the Raman peak position on temperature in optical excitation experiments is markedly different from that observed when the same NCs are excited only thermally (thermal excitation experiments). This difference is not observed for the control bulk material. The inefficient diffusion of photogenerated charges in nanoparticulate systems, due to their inherently low electrical conductivity, results in a higher steady-state density of photoexcited charges and, consequently, also in a stronger excitation of optical phonons that cannot decay quickly enough into acoustic phonons. This results in a nonthermal population of optical phonons and thus the Raman spectrum deviates from that expected for the temperature of the system. Our study has major consequences to the general application of Raman spectroscopy to nanomaterials.

Encapsulated nanowires: Boosting electronic transport in carbon nanotubes

The electrical conductivity of metallic carbon nanotubes (CNTs) quickly saturates with respect to bias voltage due to scattering from a large population of optical phonons. Decay of these dominant scatterers in pristine CNTs is too slow to offset an increased generation rate at high voltage bias. We demonstrate from first principles that encapsulation of 1D atomic chains within a single-walled CNT can enhance decay of "hot" phonons by providing additional channels for thermalisation. Pacification of the phonon population growth reduces electrical resistivity of metallic CNTs by 51% for an example system with encapsulated beryllium.

Phonovoltaic. I. Harvesting hot optical phonons in a nanoscalep−njunction

The phonovoltaic (pV) cell is similar to the photovoltaic. It harvests nonequilibrium (hot) optical phonons $({E}_{p,\mathrm{O}})$ more energetic than the band gap $(\mathrm{\ensuremath{\Delta}}{E}_{e,g})$ to generate power in a p-n junction. We examine the theoretical electron-phonon and phonon-phonon scattering rates, the Boltzmann transport of electrons, and the diode equation and hydrodynamic simulations to describe the operation of a pV cell and develop an analytic model predicting its efficiency. Our findings indicate that a pV material with ${E}_{p,\mathrm{O}}\ensuremath{\simeq}\mathrm{\ensuremath{\Delta}}{E}_{e,g}\ensuremath{\gg}{k}_{\mathrm{B}}T$, where ${k}_{\mathrm{B}}T$ is the thermal energy, and a strong interband electron-phonon coupling surpasses the thermoelectric limit, provided the optical phonon population is excited in a nanoscale cell, enabling the ensuing local nonequilibrium. Finding and tuning a material with these properties is challenging. In Paper II [C. Melnick and M. Kaviany, Phys. Rev. B 93, 125203 (2016)], we tune the band gap of graphite within density functional theory through hydrogenation and the application of isotropic strains. The band gap is tuned to resonate with its energetic optical phonon modes and calculate the ab initio electron-phonon and phonon-phonon scattering rates. While hydrogenation degrades the strong electron-phonon coupling in graphene such that the figure of merit vanishes, we outline the methodology for a continued material search.

Electronic transport in carbon nanotubes: Diffusive and localized regimes

A fully self-consistent analysis of Boltzmann's equations for electrons and phonons is used to study how the resistance of single-walled carbon nanotubes evolves as a function of its length. We demonstrate that the population of hot optical phonons controls the electronic transport of short nanotubes, whereas acoustical phonons take the leading role when the nanotube is very long. In this limit of long tubes, we also analyze the interplay between the diffusive and localized transport regimes when the electron mean-free path and the localization length due to impurities are comparable.

Numerical analysis of the relaxation of photoexcited carriers and the hot-phonon effect in GaN

The ultrafast relaxation kinetics of the photo-injected plasma in polar semiconductors has been analyzed with certain details resorting to a first-principles quantum theory based on a nonequilibrium ensemble formalism (the non-equilibrium statistical operator method). Particular attention was given to the so-called hot-phonon effect that accompanies the rapid relaxation processes in the photo-injected plasma. This is done by studying the process of generation and decay of the nonequilibrium longitudinal optical (LO) phonon population per mode. Numerical calculations are presented for the GaN, particular attention being paid to the influence of the carriers effective mass and the time relaxation of the LO-phonons population in the process.

Relaxation dynamics of hot carriers and phonons in semiconductors: Influence of the excitation conditions

The so-called hot-phonon effect that accompanies the rapid relaxation processes in the photoinjected plasma in semiconductors is analyzed, resorting to a nonlinear quantum kinetic theory based on a nonequilibrium ensemble formalism. We concentrate the study on the process of generation and decay of the nonequilibrium longitudinal optical phonon population per mode. Particular attention is paid to the question of the influence of the conditions of excitation imposed on the system, which determine the occurrence of different regimes of relaxation by means of carrier–phonon interactions. Comparison of the relaxation dynamics in the case of several semiconductors with different polar strengths is done.

Optical Phonon Coherence and Population Decays in III–V Semiconductors

Investigations of optical phonon coherence and population decays in bulk III–V semiconductors are discussed. The results are compared to our lifetime determinations using a non phonon-mode selective technique based on precise measurement of electron-lattice thermalization dynamics. The measured LO phonon lifetimes were found to be consistent with the dephasing times measured in intrinsic samples. In the presence of carriers (for the density range 1016–1017 cm -3), due to LO phonon-plasmon hybridization, the dephasing time is strongly reduced and becomes much smaller than the lifetime which is almost not altered. The roles of pure dephasing and population decay mechanisms in optical phonon relaxation are discussed for various carrier environment.

Probing optical-phonon propagation in GaAs/AlxGa1-xAs quantum-well samples via their nonequilibrium population.

We develop a theoretical model to analyze a nonequilibrium optical- (LO-) phonon population by Raman scattering in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells. With the assumption of bulklike hot-electron relaxation, the effect of LO-phonon confinement on a nonequilibrium optical-phonon population (NOP) is isolated. Our analysis shows that the decrease in spatial extent or coherence length of LO phonons is reflected by a decrease in NOP. This is because the contributions from large q wave vectors with small occupation numbers dominate as the spatial extent decreases. Our method is applied to explain picosecond Raman-scattering experiments on GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As. The increasing NOP with decreasing x is interpreted as the result of an increase in the coherence length of LO phonons, since for smaller x, the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As barrier is no longer effective in localizing GaAs LO phonons within the well. Using this model, we also deduce coherence length of LO phonons as a function of x. Our results show that for values of x between 0.2 and 0.4, the GaAs LO phonon in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells changes from a bulklike propagating mode to one localized within the wells. \textcopyright{} 1996 The American Physical Society.

Ultrafast dynamics of optic phonons in a 2D electron gas

Absorption of ultrafast laser pulses in a III–V semiconductor heterostructure is used to excite a coherent optical phonon population. The dephasing and decay of the phonon wavepacket is directly monitored on a femtosecond timescale. Localised injection of phonons within a 2D electron gas is shown to reveal strong interactions whose strength can be tuned using the laser wavelength. Experiments utilizing this source of high-wavevector acoustic phonons are discussed.

Role of interface optical phonons in cooling hot carriers in GaAs-AlAs quantum wells.

We present an experimental study of the nonequilibrium phonon population generated by the relaxation of hot carriers photoexcited in GaAs-AlAs quantum wells. The optical phonon population is measured by anti-Stokes Raman scattering performed in the plane of the layers. The measured occupation numbers suggest that interface phonon modes contribute significantly to the relaxation dynamics over the lifetime of an electron-hole pair. These results are explained on the basis of the interplay between emission and reabsorption of hot phonons, which leads to a large population of interface phonons under steady-state conditions.