Surface Polar Phonons Research Articles

Crosstalk analysis of multilayer graphene nanoribbon interconnects in GHz regime: Unraveling scattering induced effects

This paper analyzes the impact of high-frequency phenomena on the operational characteristics of intercalation-doped horizontal top-contact multilayer graphene nanoribbon (D-HTC-MLGNR) interconnects. The purpose is to explore their viability for utilization in high-frequency circuit design. A methodology incorporating the scattering-limited realistic mean free path and a finite thickness-dependent skin effect model is proposed for extracting the frequency-dependent impedance of MLGNR interconnects. By employing the proposed methodology, the frequency-dependent characteristics of scattering-limited impedance parameters and crosstalk effects in d-HTC-MLGNR interconnects are examined and compared with undoped MLGNR (viz. HTC and vertical top-contact) and copper (Cu) counterparts (smooth and rough). The findings indicate that Cu variants outperform scattering-limited MLGNR variants placed on SiO2 substrate in terms of crosstalk effects. However, Li-doped HTC-MLGNR without surface polar phonons (SPPs) and edge roughness (ER) placed on SiC and BN substrates demonstrates superior crosstalk-induced performance than Cu counterparts. Furthermore, in the absence of SPPs and ER, Li-D HTC-MLGNR placed on SiC has a minimum average percentage increase in overshoot peak amplitude, overshoot width, and delay of 6.6%, 0.18%, and 15.6%, respectively, for the entire frequency range, implying minimum impact of frequency variations and skin effect.

A Theoretical Study of the Electron-Surface Optical Phonon Interaction in Monolayer Transition Metal Dichalcogenides Deposited on SiC and hexagonal BN Dielectric Substrates in the Vicinity of the Points K+(K-) of the Brillouin Zone.

We theoretically investigated the electron-surface optical phonon interaction across the long-range Fröhlich coupling in monolayer transition metal dichalcogenides, such as WS2, WSe2, MoS2, and MoSe2 monolayers, on SiC and hexagonal BN dielectric substrates. We employed the effective Hamiltonian in the K+(K-) valley of the hexagonal Brillouin zone to assess the electronic energy shifts induced by the interaction between electronic states and surface polar optical phonons. Our results indicate that the interaction between electrons and surface optical phonons depends upon the polar nature of the substrate. We have also calculated the polaronic oscillator strength, as well as the polaronic scattering rate of the lower polaron state in monolayer WS2, WSe2, MoS2, and MoSe2 on SiC and hexagonal BN dielectric substrates. As a result, we have theoretically proved the following: firstly, the enhancement of the polaronic scattering rate with temperature, and secondly, the notable influence of the careful selection of surrounding dielectrics on both the polaronic oscillator strength and the polaronic scattering rate. Thus, optimal dielectrics would be those exhibiting both elevated optical phonon energy and a high static dielectric constant.

2D MoS2 under switching field conditions: Study of high-frequency noise velocity fluctuations

The transient high-frequency noise response of two-dimensional MoS2 under abrupt large signal switching field conditions is studied by means of an ensemble Monte Carlo simulator. Low-to-high and high-to-low transitions are analyzed at low (77 K) and room temperature, considering several underlying substrates. The incorporation of stochastic individual scattering events allows capturing the transient collective phonon–electron coupling, which is shown to be responsible for the appearance of an oscillatory behavior in the average velocity and energy at low temperature in the case of MoS2 on SiO2, hBN, and Al2O3. Activation and deactivation of surface polar phonon emissions in the low-to-high field switching process yield the appearance of a relevant peak in the power spectral density of velocity fluctuations in the THz range. The results show the important influence of the substrate type in the noise behavior of MoS2 at very high frequencies, which is critical for the design of future FET devices based on 2D TMD technology.

Polaronic Effects on the Electron Raman Scattering in a Spherical Anisotropic Quantum Dot

We study the polaronic effect on the differential cross section (DCS) for an electron Raman scattering process in a spherical anisotropic semiconductor quantum dot in the presence of a homogeneous external electric field. The Fröhlich coupling of electrons with confined and surface polar optical phonon modes for resonance Raman scattering is considered. The influence of electron-phonon coupling on the energy spectrum is taken into account in the framework of perturbation theory. The emission spectra are discussed for different anisotropy cases. Resonant peaks in the spectra are found and interpreted.

Semiempirical modeling of the effects of the intrinsic and extrinsic optical phonons on the performance of the graphene-based devices

Surface plasmons in graphene have mainly been affected by intrinsic optical phonons due to the vibrations of the carbon atoms and surface polar optical phonons (S-POPs) of the underlying dielectric surface. This plasmon hybridization dramatically changes the features of the plasmonic devices. However, a complete theoretical model for the graphene impedance to consider the optical phonons effects is yet remained to be developed. Here, we show how to derive a model for graphene impedance to include such impacts on graphene surface plasmons. Earlier models suffer from two limitations—i.e., the inability to show (i) the transformation of a single pure plasmonic mode into multiple hybrid plasmon–phonon excitations and (ii) the damping effect for energies beyond that of the intrinsic optical phonons due to the phonon emission. Our new model overcomes these two limitations. Then, we calculate the extinction spectra for a one-dimensional periodic array of graphene ribbons obtained through the impedance boundary condition method, addressing these obstacles. These spectra are directly related to graphene impedance, modeled using the dielectric function we developed in our earlier work. The extinction spectra show the presented model overcoming the limitations, firmly fitting the experimental data reported by others. Furthermore, we introduce our developed model for graphene to the CST Studio software to verify the accuracy of our extinction relation and impedance model. This study can be a step forward correctly predicting the behavior of graphene-based plasmonic devices.

Phonon-Limited Mobility in h-BN Encapsulated AB-Stacked Bilayer Graphene.

The weak acoustic phonon scattering in graphene monolayer leads to high mobilities even at room temperatures. We identify the dominant role of the shear phonon mode scattering on the carrier mobility in AB-stacked graphene bilayer, which is absent in monolayer graphene. Using a microscopic tight-binding model, we reproduce experimental temperature dependence of mobilities in high-quality boron nitride encapsulated bilayer samples at temperatures up to ∼200 K. At elevated temperatures, the surface polar phonon scattering from boron nitride substrate contributes significantly to the measured mobilities of 15 000 to 20000 cm^{2}/Vs at room temperature and carrier concentration n∼10^{12} cm^{-2}. A screened surface polar phonon potential for a dual-encapsulated bilayer and transferable tight-binding model allows us to predict mobility scaling with temperature and band gap for both electrons and holes in agreement with the experiment.

Hot carrier dynamics and electron-optical phonon coupling in photoexcited graphene via time-resolved ultrabroadband terahertz spectroscopy

Electron-electron (e-e) interaction is known as a source of logarithmic renormalizations for Dirac fermions in quantum field theory. The renormalization of electron-optical phonon coupling (EPC) by e-e interaction, which plays a pivotal role in hot carrier and phonon dynamics, has been discussed since the discovery of graphene. We investigate hot carrier dynamics and EPC strength using time-resolved ultrabroadband terahertz (THz) spectroscopy combined with numerical simulation based on the Boltzmann transport equation and a comprehensive temperature model. The numerical simulation demonstrates that the extrinsic carrier scatterings by the Coulomb potential of the charged impurity and surface polar phonons are significantly suppressed by the carrier screening effect and have negligible contributions to the THz photoconductivity in heavily doped graphene on polyethylene terephthalate (PET) substrate. The large negative photoconductivity and the non-Drude behavior of THz conductivity spectra appear under high pump fluence and can be attributed to the temporal variation of the hot carrier distribution and scattering rate. The transient reflectivity well reflects the EPC strength and temporal evolution of the hot carrier and optical phonon dynamics. We successfully estimate the EPC matrix element of the ${A}_{1}^{\ensuremath{'}}$ optical phonon mode near the $\mathbf{K}$ point as ${\ensuremath{\langle}{D}_{\mathbf{K}}^{2}\ensuremath{\rangle}}_{\mathrm{F}}\ensuremath{\approx}450$ ${(\mathrm{eV}/\AA{})}^{2}$ from the fitting of THz conductivity spectra and temporal evolution of transient THz reflectivity. The corresponding dimensionless EPC constant ${\ensuremath{\lambda}}_{\mathbf{K}}\ensuremath{\approx}0.09$ at Fermi energy ${\ensuremath{\varepsilon}}_{\mathrm{F}}=0.43\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ is slightly larger than the prediction of the renormalization group approach including the dielectric screening effect of the PET substrate. This leads to a significant difference in hot carrier and phonon dynamics compared with those without the renormalization effect by the e-e interaction. This approach can provide a quantitative understanding of hot carrier and optical phonon dynamics and support the development of future graphene optoelectronic devices.

Tunable Plasmons in Large-Area WTe2 Thin Films

The observation of the electrically tunable and highly confined plasmons in graphene has stimulated the exploration of interesting properties of plasmons in other two dimensional materials. Recently, hyperbolic plasmon resonance modes are observed in exfoliated WTe2 films, a type-II Weyl semimetal with layered structure, providing a platform for the assembly of plasmons with hyperbolicity and exotic topological properties. However, the plasmon modes were observed in relatively thick and small-area films, which restrict the tunability and application for plasmons. Here, large-area (~ cm) WTe2 films with different thickness are grown by chemical vapor deposition method, in which plasmon resonance modes are observed in films with different thickness down to about 8 nm. Hybridization of plasmon and surface polar phonons of the substrate is revealed by mapping the plasmon dispersion. The plasmon frequency is demonstrated to be tunable by changing the temperature and film thickness. Our results facilitate the development of a tunable and scalable WTe2 plasmonic system for revealing topological properties and towards various applications in sensing, imaging and light modulation.

Inelastic scattering and cooling of photoexcited electrons through coupling with acoustic, optic, and surface polar optic phonons in graphene

The acoustic, optic, and surface polar optic phonons are the three important intrinsic and extrinsic phononic modes that increasingly populate graphene on a substrate with rising temperatures; the coupling of the three phononic modes with photoexcited hot carriers in the equipartition regime provides significant pathways for electron-phonon relaxation. In this paper, we theoretically investigate the relative significance of the three phononic modes in electron scattering and cooling phenomena in single layer graphene, including their comparison with supercollision driven power loss, and obtain analytical formulas on the energy dependence of electron–phonon scattering rates and cooling power in the Boltzmann transport formalism. The obtained analytical solutions not only closely reproduce the results for scattering rates and cooling power, as that obtained from the earlier reported numerically tractable integral forms, but also enable us to derive closed-form formulas of the cooling time and thermal conductance. The important role of Pauli blocking that prevents transition to filled energy states has also been elucidated in the estimation of the scattering rate and cooling power density for all three modes. The obtained formulas provide better insight into the dynamics of hot electron phenomena giving an explicit view of the interplay of the different variables that affect the transport quantities under investigation. The formulas can also be potentially useful for performance optimization of transport quantities in numerical optimization methods since the first and second-order derivatives are easily deducible from these formulas.

Tunable Graphene Split-Ring Resonators

A split-ring resonator is a prototype of meta-atom in metamaterials. Though noble metal-based split-ring resonators have been extensively studied, up to date, there is no experimental demonstration of split-ring resonators made from graphene, an emerging intriguing plasmonic material. Here, we experimentally demonstrate graphene split-ring resonators with deep subwavelength (about one hundredth of the excitation wavelength) magnetic dipole response in the terahertz regime. Meanwhile, the quadrupole and electric dipole are observed,depending on the incident light polarization. All modes can be tuned via chemical doping or stacking multiple graphene layers. The strong interaction with surface polar phonons of the SiO2 substrate also significantly modifies the response. Finite-element frequency domain simulations nicely reproduce experimental results. Our study moves one stride forward toward the multi-functional graphene metamaterials, beyond simple graphene ribbon or disk arrays with electrical dipole resonances only.

Electron transport properties of silicene: Intrinsic and dirty cases with screening effects

The electronic transport characteristics of silicene sheets are studied by an Ensemble Monte Carlo (EMC) technique in the presence of phonon (acoustic, non-polar optic, surface polar optic), surface roughness and ionized impurity scattering mechanisms. Both intrinsic and silicene on an Al2O3 substrate are considered. Screening is also considered for both ionized impurity and surface polar optic phonon scattering of electrons. The velocity-applied field characteristics are obtained for both cases. A negative differential resistance (NDR) behaviour is observed for intrinsic case only. The mobility of carriers are calculated as a function of temperature for both cases and the results are compatible with existing experimental results and theoretical predictions. The effects of screening and flexural phonons on mobility are also studied.

High-speed and on-chip graphene blackbody emitters for optical communications by remote heat transfer

High-speed light emitters integrated on silicon chips can enable novel architectures for silicon-based optoelectronics, such as on-chip optical interconnects, and silicon photonics. However, conventional light sources based on compound semiconductors face major challenges for their integration with a silicon-based platform because of their difficulty of direct growth on a silicon substrate. Here we report ultra-high-speed (100-ps response time), highly integrated graphene-based on-silicon-chip blackbody emitters in the near-infrared region including telecommunication wavelength. Their emission responses are strongly affected by the graphene contact with the substrate depending on the number of graphene layers. The ultra-high-speed emission can be understood by remote quantum thermal transport via surface polar phonons of the substrates. We demonstrated real-time optical communications, integrated two-dimensional array emitters, capped emitters operable in air, and the direct coupling of optical fibers to the emitters. These emitters can open new routes to on-Si-chip, small footprint, and high-speed emitters for highly integrated optoelectronics and silicon photonics.

Interplay of out-of-equilibrium phonons and self-heating under high field transport conditions in graphene

The interaction between out-of-equilibrium phonons and Joule heating in the static electron transport properties of monolayer graphene supported on is investigated. An ensemble Monte Carlo electronic transport engine with a self-consistent out-of-equilibrium phonon population is coupled to a thermal resistive model describing the heat dissipation, so experimental velocity-field curves are successfully reproduced for samples 7 μm wide and 4 μm long. The separate effect of self-heating and hot phonons is analyzed in depth, showing that neglecting the hot phonon effect yields to an overestimation of the lattice temperature and drift velocity. In particular, the lowest energy surface polar phonon mode is found to present a strong coupling between both effects, which need to be considered together in a consistent manner to correctly describe the heating of graphene samples at high fields.

A balance equations approach for the study of the dynamic response and electronic noise in graphene

A computationally efficient modelling approach for the study of the small-signal and high-frequency noise properties of graphene is presented. The method combines stationary Monte Carlo particle simulations and analytical balance equations. Relevant parameters, like energy and velocity relaxation rates, are determined as a function of the applied electric field for graphene on several substrates of interest. The results show that transport in graphene is characterized by a streaming motion regime governed by the interplay between the applied field and the interactions with surface polar phonons. The dynamic behavior is analyzed by means of the response matrix, the time dependent velocity response functions, and the spectra and cut-off frequency of the differential mobility. It is shown that the negative differential mobility intrinsic of pure graphene could be exploited up to the THz in graphene on h-BN, SiC, SiO2, and even HfO2, with values approaching those of III-V nitrides, thus opening the possibility of graphene-based frequency multipliers, fast switches, or high frequency oscillators based on this effect. The correlation functions of velocity fluctuations and their power spectral density are also computed in order to determine the noise temperature, which shows a good agreement with complete Monte Carlo simulations, thus assuring the reliability of the proposed approach.

Substrate influence on the early relaxation stages of photoexcited carriers in monolayer graphene

The influence of different substrates on the photocarrier relaxation dynamics in monolayer graphene during the early stages of thermalization and cooling is explored and analyzed by means of ensemble Monte Carlo simulations. In addition, phonon dynamics of both intrinsic and surface polar modes associated to the interface between graphene and the underlying substrate are investigated. Suspended graphene and graphene on four of the most common substrates used for nanoelectronics will be studied, showing that depending on the case, carrier relaxation can be accelerated due to the leading role that the surface polar phonon modes take under such out-of-equilibrium situations. Among the considered cases, graphene on Al2O3 shows the highest relaxation rates, while the results of graphene on h-BN, SiO2 and SiC are quite similar. On its behalf, photocarriers in suspended graphene take longer to thermalize than any of the substrate supported cases.

Drag of electrons in graphene by substrate surface polar phonons

It is known that electron scattering by surface polar phonons (SPPs) of the substrate reduces their mobility in supported graphene. However, there is no experimental evidence for contribution of drag of electrons by SPP to thermoelectric phenomena in graphene: graphene thermopower exhibits good agreement with Mott's law, which means that the diffusion contribution to the thermopower is dominant in a wide range of carrier densities and temperatures. Here we develop a complete theory of drag of electrons in graphene by SPP. By solving Boltzmann transport equation for electrons scattered by SPPs we derive SPP drag contribution to the thermopower in graphene. Compared to diffusion thermopower, obtained values appear to be one order of magnitude lower for various substrates. This can be explained by low occupation number of the SPPs and short mean free path of such phonons stemming from their small group velocity. We conclude that experiments on thermopower in graphene can be treated within the framework of Mott's law.

Transport Properties of Graphene and Suspended Graphene with EMC: The Role of Various Scattering Mechanisms

The electronic transport properties of graphene and suspended (intrinsic) graphene sheets are studied using an ensemble Monte Carlo (EMC) technique. The combined scattering mechanisms that are taken into account for both cases are nonpolar optic and acoustic phonons, ionized impurity, interface roughness, and surface polar phonon scatterings. The effect of screening is also considered in the ionized impurity and surface polar phonon scatterings of electrons. A rejection technique is used in EMC simulations to account for the occupancy of the final states. Velocity-field characteristics of graphene and suspended graphene sheets are obtained using various values of acoustic deformation potential constants. The variation of electron mobility of graphene is studied as a function of electron concentration and its variation as a function of temperature are investigated for the case of suspended graphene. For the former case, the mobility increases with electron concentration first and after a certain value of electron concentration it begins to decrease, while for the latter case the mobility decreases almost linearly with temperature. The mobility results from EMC simulations are compatible with the existing experimental studies for the unsuspended graphene case.

Effect of charged impurity scattering on the electron diffusivity and mobility in graphene

The influence of charged impurities on the transport properties of graphene, including the diffusion coefficient at low and high electric fields, is investigated by means of an ensemble Monte Carlo simulator. Three different possible substrates are considered, h-BN, SiC and SiO2. The results show the importance of impurity scattering in degrading the diffusion coefficient, electronic mobility and drift velocity, particularly at low and intermediate electric fields. The influence of the substrate dielectric constant in relation to impurities and surface polar phonon scattering is also evidenced; this turns SiC into the most suitable substrate of choice from this point of view.

Screening-induced surface polar optical phonon scattering in dual-gated graphene field effect transistors

The effect of surface polar optical phonons (SOs) from the dielectric layers on electron mobility in dual-gated graphene field effect transistors (GFETs) is studied theoretically. By taking into account SO scattering of electron as a main scattering mechanism, the electron mobility is calculated by the iterative solution of Boltzmann transport equation. In treating scattering with the SO modes, the dynamic dielectric screening is included and compared to the static dielectric screening and the dielectric screening in the static limit. It is found that the dynamic dielectric screening effect plays an important role in the range of low net carrier density. More importantly, in-plane acoustic phonon scattering and charged impurity scattering are also included in the total mobility for SiO2-supported GFETs with various high-κ top-gate dielectric layers considered. The calculated total mobility results suggest both Al2O3 and AlN are the promising candidate dielectric layers for the enhancement in room temperature mobility of graphene in the future.

Theoretical interpretation of the electron mobility behavior in InAs nanowires

This work studies the electron mobility in InAs nanowires (NWs), by solving the Boltzmann Transport Equation under the Momentum Relaxation Time approximation. The numerical solver takes into account the contribution of the main scattering mechanisms present in III-V compound semiconductors. It is validated against experimental field effect-mobility results, showing a very good agreement. The mobility dependence on the nanowire diameter and carrier density is analyzed. It is found that surface roughness and polar optical phonons are the scattering mechanisms that mainly limit the mobility behavior. Finally, we explain the origin of the oscillations observed in the mobility of small NWs at high electric fields.