The temperature dependence of the first-order phonon mode of single crystal of Silicon (Si) is determined by Raman scattering in a broad temperature range of 4-623 K. Our studies reveal the anomalous red-shift of the Raman active phonon mode at temperature (~ 50 K) attributed to the anomalous expansion of Si in the low temperature region. Silicon shows negative thermal expansion below 120 K, however, odd behaviour is also observed at very low temperatures i.e., softening of the Si crystal is detected below 40 K. This peculiar behaviour of Si is described by the anomalous phonon anharmonicity observed at low temperature.
Renormalization of the electronic band gap due to electron-phonon coupling in the tetrahedral semiconductors diamond, silicon and cubic silicon carbide is studied from first principles. There is a marked difference between the coupling of the vibrational state to the valence band maximum and to the conduction band minimum. The strength of phonon coupling to the valence band maximum is similar between the three systems and is dominated by vibrations that change the bond length. The coupling strength to the conduction band minimum differs significantly in diamond, silicon carbide and silicon. In…
A theory for the relation between the spin polarization and luminescence in silicon is presented. The theory provides intuitive relations for phonon-assisted optical transitions between the conduction and valence band edges. It is shown that an opposite behavior of longitudinal and transverse optical phonon-assisted transitions is responsible to recent experimental results of spin injection into silicon. The effects of spin-orbit coupling and doping are studied in detail.
We perform molecular dynamics simulations to investigate the reduction of the thermal conductivity by kinks in silicon nanowires. The reduction percentage can be as high as 70% at room temperature. The temperature dependence of the reduction is also calculated. By calculating phonon polarization vectors, two mechanisms are found to be responsible for the reduced thermal conductivity: (1) the interchanging effect between the longitudinal and transverse phonon modes and (2) the pinching effect, i.e a new type of localization, for the twisting and transverse phonon modes in the kinked silicon nan…
Electron-phonon interaction has been well known to create major resistance to electron transport in metals and semiconductors, whereas less studies were directed to its effect on the phonon transport, especially in semiconductors. We calculate the phonon lifetimes due to scattering with electrons (or holes), combine them with the intrinsic lifetimes due to the anharmonic phonon-phonon interaction, all from first-principles, and evaluate the effect of the electron-phonon interaction on the lattice thermal conductivity of silicon. Unexpectedly, we find a significant reduction of the lattice ther…
Compared with direct-gap semiconductors, the valley degeneracy of silicon and germanium opens up new channels for spin relaxation that counteract the spin degeneracy of the inversion-symmetric system. Here the symmetries of the electron-phonon interaction for silicon and germanium are identified and the resulting spin lifetimes are calculated. Room-temperature spin lifetimes of electrons in silicon are found to be comparable to those in gallium arsenide, however, the spin lifetimes in silicon or germanium can be tuned by reducing the valley degeneracy through strain or quantum confinement. The…
The phonon-assisted interband optical absorption spectrum of silicon is calculated at the quasiparticle level entirely from first principles. We make use of the Wannier interpolation formalism to determine the quasiparticle energies, as well as the optical transition and electron-phonon coupling matrix elements, on fine grids in the Brillouin zone. The calculated spectrum near the onset of indirect absorption is in very good agreement with experimental measurements for a range of temperatures. Moreover, our method can accurately determine the optical absorption spectrum of silicon in the visib…
We study all of the leading-order contributions to spin relaxation of \textit{conduction} electrons in silicon due to the electron-phonon interaction. Using group theory, $k\cdot p$ perturbation method and rigid-ion model, we derive an extensive set of matrix element expressions for all of the important spin-flip transitions in the multi-valley conduction band. The scattering angle has an explicit dependence on the electron wavevectors, phonon polarization, valley position and spin orientation of the electron. Comparison of the derived analytical expressions with results of empirical pseudopot…
Time-resolved two color pump-probe polarization spectroscopy was performed at room temperature on SrTiO3 films grown directly on Si with film thickness varying from 2 nm to 7.8 nm. The E soft mode with a characteristic frequency of 0.2 THz is impulsively generated and measured in these coherently strained tetragonal phase SrTiO3 thin films. Another over-damped signal observed indicates the possible relaxational hopping of Ti ion between double potential wells. The dependence of the coherent phonon signal on pump and probe laser polarization helps to identify the phonon modes.
We present a new interpretation of measured Raman frequencies of a high-pressure structure of Silicon which was assigned previously to the beta-tin phase. Our results show that the beta-tin->Imma->sh phase transitions have been already indicated in this experiment which was performed before the discovery of the Imma phase. We have calculated phonon-dispersion curves for the beta-tin, Imma, and sh phases of silicon using the plane-wave pseudopotential approach to the density-functional theory and the density-functional perturbation theory within the local density approximation. With the new ass…
Confined acoustic and optical phonons in Si nanoclusters embedded in sapphire, synthesized using ion-beam implantation are investigated using Raman spectroscopy. The l = 0 and l = 2 confined acoustic phonons, found at low Raman shift, are analyzed using complex frequency model and the size of the nanoparticles are estimated as 4 and 6 nm. For the confined optical phonon, in contrast to expected red shift, the Raman line shape shows a substantial blue shift, which is attributed to size dependent compressive stress in the nanoparticles. The calculated Raman line shape for the stressed nanopartic…
Despite recent progress in the first-principles calculations and measurements of phonon mean-free-paths (MFPs), contribution of low-energy phonons to heat conduction in silicon is still inconclusive, as exemplified by the discrepancies between different first-principles calculations. Here we investigate the contribution of low-energy phonons with MFP>0.8 um by accurately measuring the cross-plane thermal conductivity of crystalline silicon films by time-domain thermoreflectance (TDTR), over a wide range of film thickness 1-10 um and temperature 100-300 K. We employ a dual-frequency TDTR approa…
Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well-understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100-1500K on a single-crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmoni…
In nanostructures phonon transport behaviour is distinctly different to transport in bulk materials such that materials with ultra low thermal conductivities and enhanced thermoelectric performance can be realized. Low thermal conductivities have been achieved in nanocrystalline materials that include hierarchical sizes of inclusions and pores. Nanoporous structures present a promising set of material properties and structures which allow for ultra-low thermal conductivity, even below the amorphous limit. In this paper we outline a semiclassical Monte Carlo code for the study of phonon transpo…
The mean-free-paths (MFPs) of energy carriers are of critical importance to the nano-engineering of better thermoelectric materials. Despite significant progress in the first-principles-based understanding of the spectral distribution of phonon MFPs in recent years, the spectral distribution of electron MFPs remains unclear. In this work, we compute the energy dependent electron scatterings and MFPs in silicon from first-principles. The electrical conductivity accumulation with respect to electron MFPs is compared to that of the phonon thermal conductivity accumulation to illustrate the quanti…
We develop a theory for the electron-phonon interaction effects on the electronic properties of graphene. We analytically calculate the electron self-energy, spectral function and band velocity renormalization due to phonon-mediated electron-electron interaction. We find that phonon-mediated electron-electron coupling has a large effect on the graphene band structure renormalization, and our analytic theory successfully captures the essential features of the observed graphene electron spectra in the ARPES experiments, predicting a kink at $\sim 200\mathrm{meV}$ below the Fermi level and a redu…
We measure the temperature dependence of the Raman spectra of metallic and semiconducting nanotubes. We show that the different trend in metallic tubes is due to phonon re-normalization induced by the variation in electronic temperature, which is modeled including non-adiabatic contributions to account for the dynamic, time dependent nature
The physics of mutual interaction of phonon quasiparticles with electronic spin degrees of freedom, leading to unusual transport phenomena of spin and heat, has been a subject of continuing interests for decades. Despite its pivotal role in transport processes, the effect of spin-phonon coupling on the phonon system, especially acoustic phonon properties, has so far been elusive. By means of inelastic neutron scattering and first-principles calculations, anomalous scattering spectral intensity from acoustic phonons was identified in the exemplary collinear antiferromagnetic nickel (II) oxide, …
The renormalization of the band structure at zero temperature due to electron-phonon coupling is investigated in diamond, BN, LiF and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasiparticle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40%. Anharmonic effects in the renormalized eigenvalues at finite …
We report a detailed experimental and theoretical investigation of the effect of residual strain, and strain relaxation, which manifests itself at the Si/SiO$_{2}$ interfaces in commercial silicon-on-insulator (SOI) wafers. SOI material is made of a single-crystal silicon overlayer (SOL) on top of an insulator (buried SiO$_{2}$ layer) sitting on a handle silicon wafer. Infrared reflectivity spectra show that the buried SiO$_{2}$ layer relaxes continuously when thinning the SOL. At the same time the SOL surface roughness and the linewidth of optical phonons in Si near the Si/SiO$_2$ interface (…
Porous materials provide a large surface to volume ratio, thereby providing a knob to alter fundamental properties in unprecedented ways. In thermal transport, porous nanomaterials can reduce thermal conductivity by not only enhancing phonon scattering from the boundaries of the pores and therefore decreasing the phonon mean free path, but also by reducing the phonon group velocity. Here we establish a structure-property relationship by measuring the porosity and thermal conductivity of individual electrolessly etched single crystalline silicon nanowires using a novel electron beam heating tec…
Ion beam irradiation has recently emerged as a versatile approach to functional materials design. We show in this work that patterned defective regions generated by ion beam irradiation of silicon can create a phonon glass electron crystal (PGEC), a longstanding goal of thermoelectrics. By controlling the effective diameter of and spacing between the defective regions, molecular dynamics simulations suggest a reduction of the thermal conductivity by a factor of $\approx$20 is achievable. Boltzmann theory shows that the thermoelectric power factor remains largely intact in the damaged material.…
The decay of the optical phonon into the two phonons of smaller energy is calculated for Si nanocrystals. The rate of the process is in the range of 1 to 10 ps. Such anharmonic phonon decay may control the energy relaxation rate of excited carriers in Si/SiO$_2$ nanocrystals. Relevance of the phonon decay to the experimentally observed hot carrier photoluminescence is discussed.
A detailed understanding of the relation between microscopic structure and phonon propagation at the nan oscale is essential to design materials with desired phononic and thermal properties.Here we uncover a new mechanism of phonon interaction in surface oxidized membranes, i.e., native oxide layers interact with phonons in ultra-thin silicon membranes through local resonances. The local resonances reduce the low frequency phonon group velocities and shorten their mean free path. This effect opens up a new strategy for ultralow thermal conductivity design as it complements the scattering mecha…
Thermal transport across interfaces is an important issue for microelectronics, photonics, and thermoelectric devices and has been studied both experimentally and theoretically in the past. In this paper, thermal interface resistance (1/G) between aluminum and silicon with nanoscale vacancies was calculated using non-equilibrium molecular dynamics (NEMD). Both phonon-phonon coupling and electron-phonon coupling are considered in calculations. The results showed that thermal interface resistance increased largely due to vacancies. The effect of both the size and the type of vacancies is studied…
Silicon carbide (SiC) is a wide band gap semiconductor with a variety of industrial applications. Among its many useful properties is its high thermal conductivity, which makes it advantageous for thermal management applications. In this paper we present \textit{ab initio} calculations of the in-plane and cross-plane thermal conductivities, $κ_{\text{in}}$ and $κ_{\text{out}}$, of three common hexagonal polytypes of SiC: 2H, 4H and 6H. The phonon Boltzmann transport equation is solved iteratively using as input interatomic force constants determined from density functional theory. Both $κ_{\te…
Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope it is of interest to explore whether defects such as dislocations or grain boundaries will result in measurable changes of the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. Since these boundaries are modeled by supercells with up to 160 atoms, the density of states was calculated by taking the Fourier transform of the velocity-velocity autocorrelation function from molecular dynamics simulations based on new supercells doubled in each …
We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation theory we show how the standard approaches for studying vibronic effects in molecules and those for addressing electron-phonon interactions in solids correspond to slightly different choices for the non-interacting Hamiltonian. Our present approach naturally leads to the Allen-Heine theory of temperature-dependent energy levels, the Franck-Condon principle, the …
Anisotropic phonon transport along different lattice directions of two-dimensional (2D) materials has been observed, however, the effect decreases with increasing the thickness beyond a few atomic layers. Here we establish a novel mechanism to induce anisotropic phonon transport in quasi-2D materials with isotropic symmetry. The phonon propagation is guided by resonance hybridization with surface nanostructures. We demonstrate that the thermal conductivity of 3 nm-thick silicon membrane with surface nanofins is greater by $\sim50\%$ parallel to the fins than that perpendicular to the fins.
Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limi…
SrTiO$_3$ has been extensively investigated owing to its abundant degrees of freedom for modulation. However, the microscopic mechanism of thermal transport especially the relationship between phonon scattering and lattice distortion during the phase transition are missing and unclear. Based on deep-potential molecular dynamics and self-consistent \textit{ab initio} lattice dynamics, we explore the lattice anharmonicity-induced tetragonal-to-cubic phase transition and explain this anomalous behavior during the phase transition. Our results indicate the significant role of the renormalization o…
Experimental phonon imaging in diamond anvils cell is demonstrated to be an adequate tool to extract the complete set of elastic constants of single-crystalline silicon up to the ZB$\rightarrow β-$Sn transition (10 GPa). Contrary to what was commonly admitted, we demonstrate that the development of the strain-energy density in terms of strains cannot be stopped, for silicon, after the terms containing the third-order elastic constants. Nonlinear elasticity, degree of anisotropy and pressure-induced mechanical stability of the cubic silicon structure are thus revisited and investigated in more …
Research on topological physics of phonons has attracted enormous interest but demands appropriate model materials. Our {\it ab initio} calculations identify silicon as an ideal candidate material containing extraordinarily rich topological phonon states. In silicon, we identify various topological nodal lines protected by glide mirror or mirror symmetries and characterized by quantized Berry phase $π$, which gives drumhead surface states observable from any surface orientations. Remarkably, a novel type of topological nexus phonon is discovered, which is featured by double Fermi-arc-like surf…
Silicon carbide (SiC) is an essential material for next generation semiconductors and components for nuclear plants. It's applications are strongly dependent on its thermal conductivity, which is highly sensitive to microstructures. Molecular dynamics (MD) simulation is the most used methods to address thermal transportation mechanisms in devices or microstructures of nano-meters. However, the implementation of MD is limited in SiC because of lacking accurate inter-atomic potentials. In this work, using the Deep Potential (DP) methodology, we developed two inter-atomic potentials (DP-IAPs) for…
The thermoelectric properties of nanostructured silicon are not fully understood despite their initial promise. While the anomalously low thermal conductivity has attracted much work, the impact of nanostructuring on the power factor has mostly escaped attention. While initial reports did not find any significant changes to the power factor compared to the bulk, subsequent detailed measurements on p-type silicon nanowires showed a stark reduction in the Seebeck coefficient when compared to similarly doped bulk. The reduction is consistent with the disappearance of the phonon drag contribution,…
First-principles theory of phonon renormalization from nonlinear electron-phonon interactions
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Theory of Quantum Systems and Complex Systems, Universiteit Antwerpen（安特卫普大学量子系统与复杂系统理论）；Faculty of Physics, Computational Materials Physics, University of Vienna（维也纳大学物理学院计算材料物理系）；Department of Physics and Astronomy “Augusto Righi”, Alma Mater Studiorum - Università di Bologna（博洛尼亚大学阿ugusto Righi物理与天文学系）
We present a novel approach to electron-lattice interaction beyond the linear-coupling regime. Based on the solution of a Holstein-Peierls-type model, we derive explicit analytical expressions for the eigenvalue spectrum of the Hamiltonian, resulting in a narrowing of bands as a function of temperature. Our approach enables the intuitive interpretation in terms of quasiparticles, i.e. polaron bands and dressed-phonon frequencies. Being nonperturbative, the formalism also applies in the strong-coupling case. We apply it to the organic crystal naphthalene, with the coupling strengths obtained by…
Direct observation of temperature dependence of individual bands of semiconductors for a wide temperature region is not straightforward, in particular. However, this fundamental property is a prerequisite in understanding the electron-phonon coupling of semiconductors. Here we apply \emph{ab initio} many body perturbation theory to the electron-phonon coupling on hexagonal silicon carbide (SiC) crystals and determine the temperature dependence of the bands. We find a significant electron-phonon renormalization of the band gap at 0~K. Both the conduction and valence bands shift at elevated temp…
Vacancy centers in diamond have proven to be a viable solid-state platform for quantum coherent opto-electronic applications. Among the variety of vacancy centers, silicon-vacancy (SiV) centers have recently attracted much attention as an inversion-symmetric system that is less susceptible to electron-phonon interactions. Nevertheless, phonon-mediated processes still degrade the coherent properties of SiV centers, however characterizing their electron-phonon coupling is extremely challenging due to their weak spectroscopic signatures and remains an open experimental problem. In this paper we t…
We present a first-principles investigation of the phonon-induced electron self-energy in graphene. The energy dependence of the self-energy reflects the peculiar linear bandstructure of graphene and deviates substantially from the usual metallic behavior. The effective band velocity of the Dirac fermions is found to be reduced by 4-8%, depending on doping, by the interaction with lattice vibrations. Our results are consistent with the observed linear dependence of the electronic linewidth on the binding energy in photoemission spectra.
In the past five years enormous progress has been made in the ab initio calculations of the optical response of electrons in semiconductors. The calculations include the Coulomb interaction between the excited electron and the hole left behind, as well as local field effects. However, they are performed under the assumption that the atoms occupy fixed equilibrium positions and do not include effects of the interaction of the lattice vibrations with the electronic states (electron-phonon interaction). This interaction shifts and broadens the energies at which structure in the optical spectra is…
The thermal interface conductance between Al and Si was simulated by a non-equilibrium molecular dynamics method. In the simulations, the coupling between electrons and phonons in Al are considered by using a stochastic force. The results show the size dependence of the interface thermal conductance and the effect of electron-phonon coupling on the interface thermal conductance. To understand the mechanism of interface resistance, the vibration power spectra are calculated. We find that the atomic level disorder near the interface is an important aspect of interfacial phonon transport, which l…
Developing a microscopic understanding of spin decoherence is essential to advancing quantum technologies. Electron spin decoherence due to atomic vibrations (phonons) plays a special role as it sets an intrinsic limit to the performance of spin-based quantum devices. Two main sources of phonon-induced spin decoherence - the Elliott-Yafet (EY) and Dyakonov-Perel (DP) mechanisms - have distinct physical origins and theoretical treatments. Here we show calculations that unify their modeling and enable accurate predictions of spin relaxation and precession in semiconductors. We compute the phonon…
Coherent phonon (CP) generation in an undoped Si crystal is theoretically investigated to shed light on unexplored quantum-mechanical effects in the early-time region immediately after the irradiation of ultrashort laser pulse. One examines time signals attributed to an induced charge density of an ionic core, placing the focus on the effects of the Rabi frequency $Ω_{0cv}$ on the signals; this frequency corresponds to the peak electric-field of the pulse. It is found that at specific $Ω_{0cv}$'s where the energy of plasmon caused by photoexcited carriers coincides with the longitudinal-optica…
We report first evidence for a 1.0 terahertz (THz) self-starting mirrorless acoustic phonon parametric oscillator (MAPPO) produced from acousto-optic phase-conjugate degenerate four-wave (D4WM) mixing in a THz laser-pumped silicon doping superlattice (DSL). The DSL was grown by molecular beam epitaxy on a (100) boron-doped silicon substrate. A superconducting NbTiN subwavelength grating was used to couple the THz laser radiation into the DSL. Superconducting granular aluminum bolometric detection, coupled with Si:B piezophonon spectroscopy, revealed excitation of THz coherent compressional and…
Acoustic and Optical Phonon Frequencies and Acoustic Phonon Velocities in Silicon-Doped Aluminum Nitride Thin Films
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute, University of California, Los Angeles（加州大学洛杉矶分校加利福尼亚纳米系统研究所）；Arizona State University（亚利桑那州立大学）；Auburn University（奥本大学）
Transverse acoustic waves in an inhomogeneous medium are analogues to electromagnetic waves and will exhibit topological behavior due to the Berry gauge potential in the momentum space due to inhomogeneity. The inhomogeneous (or gradient) medium can be created using an applied strain gradient in a semiconductor thin film (silicon) since the phonon frequency and dispersion will be a function of the local strain along the strain gradient direction. As a consequence, topological phonon mediated spin and heat transport can be engineered in the semiconductor thin films. Here, we present evidence of…
We investigate the effects of electron and acoustic-phonon confinement on the low-field electron mobility of thin square silicon nanowires (SiNWs) that are surrounded by SiO$_2$ and gated. We employ a self-consistent Poisson-Schrödinger-Monte Carlo solver that accounts for scattering due to acoustic phonons (confined and bulk), intervalley phonons, and the Si/SiO$_2$ surface roughness. The wires considered have cross sections between 3 $\times$ 3 nm$^2$ and 8 $\times$ 8 nm$^2$. For larger wires, as expected, the dependence of the mobility on the transverse field from the gate is pronounced. At…
Phonon reflection and transmission at the interfaces plays a fundamental role in cryogenic particle detectors, in which the optimization of the phonon signal at the sensor (in case of phonon-mediated detectors) or the minimization of the heat transmission (when the detection occurs in the sensor itself) is of primary importance to improve sensitivity. Nevertheless, the mechanisms governing the phonon physics at the interfaces are still not completely understood. The two more successful models, the acoustic mismatch model (AMM) and diffuse mismatch model (DMM) are not able to explain all the ac…
