Phonons and fluctuations in low dimensional structures

Resume : The experimental discovery of thermal rectification in asymmetrically mass-loaded carbon nanotubes in 2006 boosted the search for thermal analogs of electronic devices. However, the realization of efficient thermal rectifiers based on simple materials, such as Si or SiGe, remains a challenge. In this work, we provide experimental evidence of outstanding heat flow asymmetries in two remarkably different systems: trapezoidal Si nanowires and compositionally graded SiGe superlattices. The structure of the trapezoidal nanowires is asymmetrically defined between suspended heater/sensors by Focus Ion Beam. The origin of the heat flow asymmetry is related to the presence of Ga ions at the outer shell of the nanowire that produces a mass–damping of the oscillations with a strong influence in the atoms located at the narrow outer edge of the structure. On the other hand, specific Si1-xGex/Si SLs superlattices with well-defined compositional gradients across the SiGe layer show a strong reduction of the cross plane thermal conductivity and an outstanding difference of around 40% in its value depending if the heat flow is parallel or antiparallel to the concentration gradient.

Resume : Semiconducting nanowires (NWs) have attracted a growing interest in recent years and are recognized as important building blocks for emerging applications in nanoelectronics [1-3]. The understanding of thermal transport has lately acquired a great importance as well, because NWs have been proposed to be a pathway for the engineering of efficient thermoelectric materials. Here we study thermal transport in SiGe nanowires across a Si/Ge axial interface by means of non-equilibrium molecular dynamics simulations. We calculate the interface thermal resistance (ITR) of realistic models of axial SiGe heterojunctions, whose morphology depends strongly on the different experimental conditions [4-7]. We also investigate if these asymmetric junctions can yield thermal resistances that depend on the applied thermal gradient, i.e. thermal rectification. We find that diffuse interfaces result in larger ITR, while sharp junctions yield a small, but non-negligible thermal rectification, favoring heat transport from Si to Ge. [1] D. K. Ferry, Science 319, 579 (2008) [2] R. Rurali, Rev. Mod. Phys. 82, 427 (2010) [3] M. Amato, M. Palummo, R. Rurali, and S. Ossicini, Chem. Rev., doi:10.1021/cr400261y [4] Clark et al., Nano Lett. 8, 1246 (2008) [5] Wen et al., Science 326, 1247 (2009) [6] Perea et al., Nano Lett. 11, 3117 (2011) [7] Geaney et al., Nano Lett. 13, 1675 (2013)

Resume : The understanding of the transport of hot electrons and their interactions with the bulk lattice and the interface is of prime importance for the improvement of advanced nanoscale devices. In this communication, we show that supersonic hot electrons are responsible for the emission of coherent acoustic phonons deeply beneath the free surface where they are optically excited consistently with previous experiments [1-3]. Moreover, these hot electrons can also travel enough far at room temperature to interact with a buried interface (Cu-Ti in our case) located at 220 nm beneath the free surface. In particular, we evidence that this interaction leads to coherent acoustic phonon emission. Such phenomenon has been reported only one time up to now in the case of aluminum [4]. In order to go deeper in the experimental investigations and to discuss in more details the underlying physics, several ultrafast optical pump-probe configurations been used [2]. In particular, we have performed different experiments where the time of flight of hot electrons and coherent acoustic phonons have been characterized. From an original probe wavelength dependence study of the optical detection process, we clearly establish the signature of superdiffusive hot transport within the copper film and the link with the acoustic phonon emission. These results and observations are important to quantify the mechanism of electron-phonon interaction at materials interfaces. [1] O. B. Wright, “Ultrafast nonequilibrium stress generation in gold and silver,” Phys. Rev. B 49, 9985–9988 (1994). [2] O. B. Wright and V. Gusev, “Ultrafast generation of acoustic waves in copper,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 331–338 (1995). [3] G. Tas and H. J. Maris, “Electron diffusion in metals studied by picosecond ultrasonics,” Phys. Rev. B 49, 15046–15054 (1994). [4] M. Lejman, V. Shalagatskyi, O. Kovalenko, T. Pezeril, V. Temnov, P. Ruello “Ultrafast optical detection of coherent acoustic phonons emission driven by superdiffusive hot electrons”, J. Opt. Soc. Am. B, to be published in Feb 2014.

Resume : We describe the use of an AlGaAs p-i-n diode to monitor the output of a single pass phonon amplification device. The optical resonance of quantum wells, incorporated in the intrinsic region of the diode, strongly depend on the strain associated with acoustic waves. This can be exploited to create an optically-gated detector with picosecond resolution by monitoring changes in induced photocurrent caused by acoustic waves [1]. In the current scheme, the p-i-n detector is fabricated on one side of a 150µm GaAs substrate, and two GaAs/AlAs superlattices (SLs), the lower of which can be placed under an electrical bias, are grown on the other side. The lower, SASER gain, SL was grown to specifications which have been previously shown, using an incoherent bolometric detection technique, to provide phonon amplification [2]. Femtosecond optical pumping of the top SL generates quasi-monochromatic sub-Terahertz phonons which propagate through the gain SL and the substrate to the p-i-n diode. This is gated by a time-delayed femtosecond pulse providing a high resolution coherent detection, this shows evidence of coherent amplification in the SASER device. [1] Moss, D et al. Phys. Rev. B 83, 245303 (2011) [2] Beardsley, R. P. et al. New J. Phys. 13, 073007 (2011)

Resume : We report the characterization of a thermoelectric microgenerator build up using standard CMOS technologies. As a thermoelectric active material we use ultrathin single-crystalline Si membranes, 100 nm in thickness, with embedded n and p-type doped regions. The planar design, with the n-p couples electrically connected in series and thermally in parallel, includes a central heater/sensor that permits to impose several small temperature gradients and then characterize the average thermoelectric lumped parameters. Finite element modeling is used to derive, from the experimental data, the intensive parameters for the thin film couples, and thus evaluate ZT in the full range measured from 50 to 350K. A 3-fold reduction in thermal conductivity due to the phonon boundary scattering with the thin film surfaces supposes an effective improvement in ZT respect to bulk values since resistivity and Seebeck coefficients are respected. The ZT obtained grows monotonically in the measured range. As a test of the maximum output power density produced, we imposed a 200K temperature gradient with the frame at 350K obtaining 250 µW/cm^2.

Resume : The understanding of coupled particles and heat transport in complex systems is a fundamental problem, also of practical interest in connection with the challenging task of developing high-performance thermoelectric heat engines and refrigerators. Recently discovered general mechanisms of optimizing the figure of merit of thermoelectric efficiency are discussed, also in connection to momentum-conserving interacting systems [1.2], to the breaking of time-reversal symmetry by an applied magnetic field [3-6], and to multiterminal steady-state quantum thermal machines [7]. [1] G. Benenti, G. Casati and W. Jiao, Conservation laws and thermodynamic efficiencies, Phys. Rev. Lett. 110, 070604 (2013). [2] G. Benenti, G. Casati and C. Mejia-Monasterio, Thermoelectric efficiency in momentum-conserving systems, New J. Phys. 16, 015014 (2014). [3] G. Benenti, K. Saito and G. Casati, Thermodynamic bounds on efficiency for systems with broken time-reversal symmetry, Phys. Rev. Lett. 106, 230602 (2011). [4] K. Saito, G. Benenti, G. Casati and T. Prosen, Thermopower with broken time-reversal symmetry, Phys. Rev. B 84, 201306(R) (2011). [5] M. Horvat, T. Prosen, G. Benenti and G. Casati, Railway switch transport model, Phys. Rev. E 86, 052102 (2012). [6] V. Balachandran, G. Benenti and G. Casati, Efficiency of three-terminal thermoelectric transport under broken time-reversal symmetry, Phys. Rev. B 87, 165419 (2013). [7] F. Mazza, R. Bosisio, G. Benenti, V. Giovannetti, R. Fazio and F. Taddei, Thermoelectric efficiency of three-terminal quantum thermal machines, preprint.

Resume : The mutual coupling of optical and mechanical degrees of freedom via radiation pressure has been a subject of interest in the context of quantum limited displacements measurements for Gravity Wave detection for many decades. Over the past years these radiation pressure “backaction” phenomena have been observed – starting from observations in in high Q optical microresonators(1) – in a variety of micro and nanoscale opto and electro-mechanical systems. The high Q of the microresonators, not only enhances nonlinear phenomena - such as optical frequency comb generation(2) via the Kerr nonlinearity – but also enhances the radiation pressure interaction. This has allowed the observation of radiation pressure phenomena in an experimental setting and constitute the fast developing research field of cavity quantum optomechanics(3, 4). I will describe a range of optomechanical phenomena studied using on-chip optical microresonators, that combine both optical and mechanical degrees of freedom in one and the same device. Radiation pressure back-action of photons is shown to lead to effective cooling(5-8) of the mechanical oscillator mode using dynamical backaction. Cooling to the quantum regime is possible using sideband resolved cooling, with passive of cryogenic precooling to ca. 700 mK, which enables cooling the oscillators such that it resides in the quantum ground state more than 1/3 of its time(9). Increasing the mutual coupling further, it is possible in this regime to observe quantum coherent coupling(9) in which the mechanical and optical mode hybridize and the coupling rate exceeds the mechanical and optical decoherence rate (7). In this regime the mechanical and optical mode form an optomechanical ‘polariton’. This enables a range of quantum optical experiments, including state transfer from light to mechanics using the phenomenon of optomechanically induced transparency(10). In addition experiments are described that utilized the optomechanical coupling for highly efficient force measurements using nanomechanical oscillators(11), as well as elements enabling switching, slowing or advancing of radiation(12). References: 1. T. J. Kippenberg et al., Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity. Physical Review Letters 95, 033901 (2005). 2. T. J. Kippenberg, R. Holzwarth, S. A. Diddams, Microresonator-based optical frequency combs. Science 332, 555 (Apr 29, 2011). 3. T. J. Kippenberg, K. J. Vahala, Cavity Optomechanics: Backaction at the mesoscale. Science 321, 1172 (2008, 2008). 4. M. Aspelmeyer, T. J. Kippenberg, F. M. Marquardt, Cavity Optomechanics. http://arxiv.org/abs/1303.0733, (2012). 5. V. B. Braginsky, S. P. Vyatchanin, Low quantum noise tranquilizer for Fabry-Perot interferometer. Physics Letters A 293, 228 (Feb 4, 2002). 6. V. B. Braginsky, Measurement of Weak Forces in Physics Experiments. (University of Chicago Press, Chicago, 1977). 7. A. Schliesser et al., Radiation pressure cooling of a micromechanical oscillator using dynamical backaction. Physical Review Letters 97, 243905 (Dec 15, 2006). 8. A. Schliesser et al., Resolved-sideband cooling of a micromechanical oscillator. Nature Physics 4, 415 (2008). 9. E. Verhagen et al., Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63 (Feb 2, 2012). 10. S. Weis et al., Optomechanically induced transparency. Science 330, 1520 (Dec 10, 2010). 11. E. Gavartin, P. Verlot, T. J. Kippenberg, A hybrid on-chip optomechanical transducer for ultrasensitive force measurements. Nature nanotechnology 7, 509 (Aug, 2012). 12. X. Zhou et al., Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics. Nature Physics 9, 179 (2013).

Resume : Silicon is considered as a reference material both for its crystalline and amorphous phases. While each phase separately has been investigated extensively, less attention is given to nanostructures involving both phases and especially their interfaces. Yet, almost all silicon devices contain such interfaces and the transport for both electrons and phonons through them is a crucial issue. In this study, we model amorphous/crystalline interfaces for nanowires and superlattices. The aim is to predict the thermal properties of these nanostructured materials, and explain the trends with the phonon density of states and the Kapitza resistance. The calculations have been done with molecular dynamics method, using a realistic interatomic potential. The thermal conductivity of both nanostructures is found to be close to the bulk amorphous one and almost independent the temperature. In bulk amorphous silicon, the vibrational features of the crystalline phase are present but smoothed out, due to the lack of periodicity. The localized modes and the large depression of the high frequency phonons, which have been proved to carry heat even if they are nonpropagating diffusive modes, contribute to the reduction of the thermal conductivity. We will present also the local phonon density of states at different locations on both sides of a planar interface. The phonons feel the interfaces in a distance of roughly 4Å away from them.

Resume : Suspended structures are widely used to measure thermal conductivity (k) on nanowires and thin films. Here we present a detailed analysis of the uncertainties in the measurement of thermal conductivity using suspended structures. These structures are often modeled using a 1D heat diffusion equation in order to extract the thermal conductivity of the sample under test. As we illustrate, the use of a 1D simplified model may give incorrect values of the thermal conductivity. To show this, we first calculate in a 1D approximation the uncertainty of the measured k value of the nanostructure for a wide range of thermal conductances. We prove the existence of a plateau with low uncertainties depending on the properties of the structure. Tuning these properties allows the fabrication of structures intended for the measurement of samples with specific thermal conductance. We have also carried out finite element modeling of the structure in 3D, to account for some inaccuracies that appear when k is calculated using the 1D equation for highly-conductive samples. In this framework, correct solutions of the thermal conductivity can be obtained for any geometry and/or thermal conductance.

Resume : The aim of this work was on the one hand the development of theoretical models ( mathematical) to numerically simulate the experimental results of variations in the electrical conductivity as a function of various parameters, and on the other hand, the study of boundary conditions necessary for the numerical resolution of the heat propagation equation. Note that all obtained theoretical models are of the linear or sigmoidal form, Boltzmann type. Most obtained models allowed finding relationships more or less simple between the different parameters with an acceptable relative error of calculation, which allowed us to calculate theoretical values very close to the experimental values for the physical variables studied. Some of our models have given incorrect values , this can be explained by the fact that our calculation method is not reliable for this kind of data (values in small intervals). Note that this type of calculation can be improved by using other interpolation methods in particular the method of cubic splines. The model we have developed for solving the heat propagation equation, can serve in the research on the estimation of the isomerization temperature of PA by laser effect, which is widely used in current studies on the polyacetylene. Finally, it should be noted that our model for solving the heat propagation equation can be more efficient when the semi -empirical method is used to set the condition at the lower boundary of the domain.

Resume : properties of materials over a very wide range, and give access to physical phenomena that would not occur in three-dimensional systems. This is especially true for the vibrational porperties and the lattice thermal conductivity of materials. In this talk I will illustrate case studies of atomistic calculations of phonon transport in two-dimensional materials, namely graphene and ultrathin silicon membranes, in which the thermal conductivity can be modified over several orders of magnitude with respect to the respective bulk counterparts. In particular, non-Fourier thermal transport in graphene at non-equilibrium conditions, and how heat conduction may be affected by mechanical strain will be discussed. Whereas in the case of graphene dimensionality reduction leads to extremely high thermal conductivity, it will be also shown how modulating thickness and surface structure turn silicon nano-membranes into low-thermal conductivity systems, attractive for thermoelectric applications.

Resume : Good thermoelectric materials require high electron power factor and low thermal conductivity. Recent theoretical predictions and observations have provided evidence that inhomogeneities can favor the thermoelectric properties of nanowires. Enhanced thermoelectric power factor has been observed in InAs nanowires at low temperatures and has been attributed to quantum effects in the presence of inhomogeneities. The thermal conductivity of nanowires is reduced by inhomogeneities. In an earlier work, we showed theoretically that the thermal conductivity of a nanowire can be more significantly reduced by diameter modulation than by diameter decrease. The calculations were done using a kinetic theory model based on the Boltzmann transport equation and the relaxation time approximation. The mean free path was estimated using the Matthiessen rule with the bulk mean free path and an average phonon-boundary scattering length. Here, we use a method earlier proposed to study the thermal conductivity of a nanostructure with arbitrary geometry through Monte Carlo sampling of the free paths associated with phonon-phonon and phonon-boundary scattering. The two methods are compared for various nanowire dimensions and geometry modulations.