Semiconductor materials are the foundation of modern electronics, and their functionality is dictated by the interactions between fundamental excitations occurring on (sub‐)picosecond timescales. Using time‐resolved Raman spectroscopy and transient reflectivity measurements, the ultrafast dynamics in germanium are elucidated. An increase in the optical phonon temperature is observed in the first few picoseconds, driven by the energy transfer from photoexcited holes, and the subsequent decay into acoustic phonons through anharmonic coupling. Moreover, the temperature, Raman frequency, and linewidth of this phonon mode show strikingly different decay dynamics. This difference is ascribed to the local thermal strain generated by the ultrafast excitation. Brillouin oscillations are also observed, given by a strain pulse traveling through germanium, whose damping is correlated to the optical phonon mode. These findings, supported by density functional theory and molecular dynamics simulations, provide a better understanding of the energy dissipation mechanisms in semiconductors.
Thermoelectric transport in silicon nanofilms is investigated using a self-consistent electro-thermal Monte Carlo simulator that couples electron dynamics to a phonon bath with spatially varying temperature. A key novelty of this work is the explicit inclusion of the phonon-drag contribution, implemented by modifying the electron-phonon momentum exchange based on the local deviation of the phonon distribution from equilibrium. The method is validated against bulk silicon data and extended to incorporate rough boundary scattering for both electrons and phonons, yielding excellent agreement with experimental measurements on nanofilms. We also analyze the transient regime and show that a temperature bias produces a slower current response than a voltage bias, although the phonon-drag effect itself tends to accelerate the response. These results demonstrate that the proposed framework provides a powerful tool for predicting both steady-state and time-dependent thermoelectric behavior in semiconductor nanostructures.
In recent years, computational approaches which couple density functional theory (DFT)-based description of the electron–phonon and phonon–phonon scattering rates with the Boltzmann transport equation have been shown to obtain the electron and thermal transport characteristics of many 3D and 2D semiconductors in excellent agreement with experimental measurements. At the same time, progress in the DFT-based description of the electron–phonon scattering has also allowed to describe the non-equilibrium relaxation dynamics of hot or photo-excited electrons in several materials, in very good agreement with time-resolved spectroscopy experiments. In the latter case, as the time-resolved spectroscopy techniques provide the possibility to monitor transient material characteristics evolving on the femtosecond and attosecond time scales, the time evolution of photo-excited, nonthermal carrier distributions has to be described. Similarly, reliable theoretical approaches are needed to describe the transient transport properties of devices involving high energy carriers. In this review, we aim to discuss recent progress in coupling the ab initio description of materials, especially that of the electron–phonon scattering, with the time-dependent approaches describing the time evolution of the out-of-equilibrium carrier distributions, in the context of time-resolved spectroscopy experiments as well as in the context of transport simulations. We point out the computational limitations common to all numerical approaches, which describe time propagation of strongly out-of-equilibrium carrier distributions in 3D materials, and discuss the methods used to overcome them.
Boron-rich compounds within the B-C-N-O and B-C-Si systems exhibit exceptional functional properties, making them highly attractive for industrial applications such as those requiring superhardness, nuclear technologies, or thermoelectricity. High-pressure, high-temperature (HPHT) conditions allow obtaining the ingots of ceramics with best physical properties, as well as to explore advanced materials by means of in situ crystallography, high-pressure chemistry, and nanoscience. This review summarizes recent experimental and theoretical advances on high-pressure, high-temperature (HPHT) phase equilibria up to 20 GPa and 3000 K, focusing on boron carbide (B4C), boron suboxide (B6O), boron subnitride (B13N2), boron silicides, and some of their solid solutions. Emphasis is placed on in situ X-ray diffraction (XRD), density functional theory (DFT) calculations, and CALPHAD thermodynamic modeling. Despite recent progress, significant methodological challenges remain, requiring enhanced experimental accuracy and refined theoretical approaches. Future work should address these gaps to fully leverage the potential of these superhard materials.
EPIq (Electron-Phonon wannier Interpolation over k and q-points) is an open-source software for the calculation of electron-phonon interaction related properties from first principles.Acting as a post-processing tool for a density-functional perturbation theory code ( Quantum ESPRESSO ) and wannier90, EPIq exploits the localization of the deformation potential in the Wannier function basis and the stationary properties of a force-constant functional with respect to the first-order perturbation of the electronic charge density to calculate many electron-phonon related properties with high accuracy and free from convergence issues related to Brillouin zone sampling. EPIq features includes: the adiabatic and non-adiabatic phonon dispersion, superconducting properties (including the superconducting band gap in the Migdal-Eliashberg formulation), double-resonant Raman spectra and lifetime of excited carriers. The possibility to customize most of its input makes EPIq a versatile and interoperable tool. Particularly relevant is the interaction with the Stochastic Self-Consistent Harmonic Approximation (SSCHA) allowing anharmonic effects to be included in the calculation of electron-properties. The scalability offered by the Wannier representation combined with a straightforward workflow and easy-to-read input and output files make EPIq accessible to the wide condensed matter and material science communities.
We report an exhaustive study of the formation enthalpy and charge states of carbon-based defects in rhombohedral α boron within the density functional theory (DFT) that enables us to derive rules about the formation of complex carbon defects. We have accounted for one and two interstitial carbon atoms, eventually combined with one substitutional carbon atom and/or one interstitial boron atom and varied several geometric parameters. We find that when positioned in the plane perpendicular to the [111] rhombohedral axis, two carbon atoms turn out to preferentially form a graphite-like hexagon with four boron atoms. When positioned instead along the [111] axis, the distance between them strongly affects the defect thermodynamic stability, and we find in particular that additional negative charges strongly stabilize the diatomic carbon–carbon chains.
In this work, we discuss the possibility of reaching the Ziman conditions for collective heat transport in cubic bulk semiconductors, such as Si, Ge, AlAs and AlP. In natural and enriched silicon and germanium, the collective heat transport limit is impossible to reach due to strong isotopic scattering. However, we show that in hyperenriched silicon and germanium, as well as in materials with one single stable isotope like AlAs and AlP, at low temperatures, normal scattering plays an important role, making the observation of the collective heat transport possible. We further discuss the effects of sample sizes, and analyse our results for cubic materials by comparing them to bulk bismuth, in which second sound has been detected at cryogenic temperatures. We find that collective heat transport in cubic semiconductors studied in this work is expected to occur at temperatures between 10 and 20 K.
The progress in DFT-based description of the electron-phonon scattering allowed to describe the relaxation dynamics of hot or photoexcited electrons in several materials, in very good agreement with time-resolved spectroscopy experiments. As hot carriers also start to attract attention in the context of emerging concepts for energy conversion, here we present our first results related to the coupling of ab initio data with device-oriented Monte Carlo simulation methods. We show that DFT-based description of the electron-phonon intervalley scattering in GaAs, coupled with the stochastic Monte Carlo method, allows to describe the energy transfer from electrons to phonons in transient regime, in good agreement with previous time-resolved photoemission experiments.
With the advance of materials fabrication techniques and increase of computational power during the past two decades, the research aiming to enhance the efficiency of thermoelectric devices, with the search of new materials and manipulation of materials properties at the nanoscale, has attracted significant interest. In general, the efficiency of thermoelectric materials, measured by the figure of merit ZT, directly depends on the Seebeck coefficient of the material. In the present work, we have studied, by combining the density functional theory calculations of the electron-phonon [1], [2] and phonon-phonon [3] interactions, the enhancement of the Seebeck coefficient due to electron-phonon coupling, known as the “phonon-drag” effect [4]. To account for this effect, we have solved the linearized Boltzmann equation for electronic transport in presence of non-equilibrium phonon populations introduced by a temperature gradient [5]. In order to understand the phonon drag effect at the nanoscale, we have studied the effect of direction-dependent nano-structuring effect on the Seebeck coefficient of silicon. We will present our recent results related to phonon and/or impurity limited carrier mobility, as well as the variation of the Seebeck coefficient of bulk and nanostructured silicon with temperature and carrier concentrations. Our results for $n$ -doped silicon not only show a good agreement with the experimental data in both bulk samples [6] and nanostructures [7] but also pave the way to further understand the contribution of phonon-drag in other semiconductor nanostructures [8], which still remain largely unexplored.
In this theoretical study, we examine the influence of dimensionality, size reduction, and heat-transport direction on the phonon-drag contribution to the Seebeck coefficient of silicon nanostructures. Phonon-drag contribution, which arises from the momentum transfer between out-of-equilibrium phonon populations and charge carriers, significantly enhances the thermoelectric coefficient. Our implementation of the phonon drag term accounts for the anisotropy of nanostructures, such as thin films and nanowires, through the boundary- and momentum-resolved phonon lifetime. Our approach also takes into account the spin-orbit coupling which turns out to be crucial for hole transport. We reliably quantify the phonon drag contribution at various doping levels, temperatures, and nanostructure geometries for both electrons and holes in silicon nanostructures. Our results support the recent experimental findings, showing that a part of phonon drag contribution survives in 100 nm silicon nanostructures.
The role of carbon in the formation of alpha boron at high pressure and high temperature (HPHT) has been investigated by combining HPHT experiments and density functional theory (DFT) calculations. Starting from beta rhombohedral or amorphous boron and amorphous carbon at 5 GPa, the alpha boron phase has been repeatedly observed between 1473 K and 2273 K, at temperatures that are much higher than those reported in the phase diagram of boron. The DFT investigation of the effect of carbon insertion into the alpha rhombohedral boron atomic structure on the formation enthalpy, volume and optical properties shows that only the (B11C) substituted icosahedron defect accounts for the slight volume contraction observed in alpha boron. It is also compatible with the observed red colour of alpha boron crystals, and consistently has a very low formation energy. Our calculations also provide a calibration tool to evaluate the carbon concentration in the samples. Finally, the synthesis temperature is found to be an easy means to tune the carbon concentration on demand.
The most striking features of the Raman spectrum of boron carbide under pressure are explained theoretically by computing the Raman tensor using density functional perturbation theory and the second-order response. While the observed pressure-induced changes in frequencies and intensities of all of the peaks above 450 cm−1 are convincingly explained by the vibrations of (B11C) icosahedra and C-B-C chains – that have been identified for long as the two main components of the atomic structure of pristine B4C –, the puzzling non-monotonic behavior of a broad Raman band at low frequency, whose intensity increases under pressure up to 44 GPa, decreases and then vanishes, was so far unexplained. We find that the behavior under pressure of both the frequency and intensity of this band turns out to be remarkably accounted for, in the calculations, by the activation of the chain bending mode in atypically flexured chains. We show that the flexion of the chain occurs at high pressure in presence of interstitial B atoms that, at ambient pressure, sit in the prolongation of standard C-B-C chains. We propose the ambient-P mode observed at 270 cm−1 as a fingerprint for the identification of both such B-C-B-C chain-defects in boron carbide and local deviations from the rhombohedral symmetry.
In this work, we revisit the DFT-based results for the electron-phonon scattering in highly excited silicon. Using state-of-the-art ab initio methods, we examine the main scattering channels which contribute to the total electron-phonon scattering rate and to the energy loss rate of photoexcited electrons in silicon as well as their temperature dependence. Both temperature dependence and the main scattering channels are shown to strongly differ for the total electron-phonon scattering rate and for the energy loss rate of photoexcited electrons. Whereas the total electron-phonon scattering rate increases strongly with temperature, the temperature dependence of the energy loss rate is negligible. Also, while acoustic phonons dominate the total electron-phonon scattering rate at 300 K, the main contribution to the energy loss rate comes from optical modes.
We report a combined experimental and theoretical study of boron carbide under stress/deformation. A special rotating anvil press, the rotating tomography Paris Edinburgh cell (RotoPEC), has been used to apply torsional deformation to boron carbide under a pressure of 5~GPa at ambient temperature. Subsequent damages and point defects have been analysed at ambient pressure by energy dispersive X-ray microdiffraction at the synchrotron and by Raman spectroscopy, combined with calculations based on the density functional theory (DFT). We show that apart from the signals due to B$_4$C, new peaks appear in both characterisation methods. The DFT calculations of atomic structures and phonon frequencies enable us to attribute most of the new peaks to boron vacancies in the intericosahedral chains of boron carbide. Some of the Raman spectra also show three peaks that have been attributed to amorphous boron carbide in the literature. Deformed boron carbide thus shows small inclusions of clusters of boron carbide with chain vacancies, and/or small zones interpreted as amorphous zones.
Significance Two-dimensional electron gases are an essential building block of today’s technology and attract broad interest in the context of material science or nanoengineering. Their widespread applications in many strategical sectors call for a direct visualization of hot electrons relaxation in an accumulation layer. In this work, we make use of time-resolved photoelectron spectroscopy to acquire snapshots of the electronic distribution after a strong and impulsive drive. We identified and quantified the remote coupling of the confined electrons to phonon modes of the adjacent polar material. The far-reaching outcomes provide insights on the screening of electron–phonon coupling in constrained dimensions and will be of high relevance for the development of aggressively downscaled circuits.
In this work we present our recent results of the ab initio calculations of anharmonic coupling in cubic semiconductors and bismuth. Our results allow us to explain the anomalous behavior of the attenuation of the longitudinal acoustic phonon in GaAs as a function of the phonon energy in the subterahertz domain, which shows a plateau between 0.6 and 1 THz at low temperatures. The plateau is explained by the competition between different phonon-phonon scattering processes such as Herring's mechanism, which dominates at low frequencies, saturates, and disappears at higher frequencies. We found an excellent agreement between measurements performed by some of us, and new ab initio calculations of third-order anharmonic processes. We predict that the same phenomenon should occur in other cubic semiconductors. In the case of bismuth, we discuss the occurrence of the hydrodynamic heat transport regime at low temperatures, in consistency with the experimental observations. Bismuth is one of the rare materials in which second sound has been experimentally observed. Our calculations predict the occurrence of the Poiseuille phonon flow in Bi between 1.5 K and 3.5 K for sample size of 3.86 mm and 9.06 mm, in consistency with the experimental observations. We will also discuss a Gedanken experiment allowing to assess the occurrence of the hydrodynamic regime in any bulk material.