In this Rapid Communication we report the first time-resolved measurements of confined acoustic phonon modes in free-standing Si membranes excited by fs laser pulses. Pump-probe experiments using asynchronous optical sampling reveal the impulsive excitation of discrete acoustic modes up to the 19th harmonic order for membranes of two different thicknesses. The modulation of the membrane thickness is measured with fm resolution. The experimental results are compared with a theoretical model including the electronic deformation potential and thermal stress for the generation mechanism. The detection is modeled by the photoelastic effect and the thickness modulation of the membrane, which is shown to dominate the detection process. The lifetime of the acoustic modes is found to be at least a factor of 4 larger than that expected for bulk Si.Free-standing thin semiconductor membranes have a wide range of applications, for example, as key elements in nanomechanical systems, 1 sensors, 2 or optomechanical systems. 3 Thorough understanding of the mechanical and elastic properties in these structures is crucial for the design and engineering of the desired performance of these potential devices. 4 When the dimension of these structures is reduced to the order of magnitude of the phonon wavelength, the confinement of acoustic modes leads to a discretization of the acoustic spectrum. These effects have been studied via continuous wave light scattering techniques such as Brillouin and Raman scattering in supported and free-standing thin films. 5-9 Recently time-resolved experiments have contributed significantly to the understanding of phonon dynamics in nanoscale systems and nanoparticles. 4,[10][11][12][13] In this Rapid Communication we present results of femtosecond time-resolved pump-probe experiments performed on free-standing Si membranes with a thickness of a few hundred nanometers. A superposition of oscillations corresponding to frequencies of a fundamental mode and its higher odd harmonics up to the 19th order with lifetimes exceeding 1 ns is observed in the time domain. The results are successfully modeled using a combined elastic and electromagnetic model. It is shown that the detection process is dominated by the dynamic change in the membrane thickness. Our analysis demonstrates that free-standing Si membranes are a model system, which allows disentanglement of basic phonon-photon interaction processes.The pump-probe experiments were performed using highspeed asynchronous optical sampling ͑ASOPS͒ described in detail before. 14 Two femtosecond Ti:Sapphire oscillators are used to generate the pump and probe pulses with a duration of less than 100 fs. The repetition rates f rep of about 800MHz are stabilized in order to fix the difference of the repetition rates at ⌬f rep = 10 kHz. This offset allows for an automatic scan of the measurement window ͑f rep −1 = 1.2 ns͒ by the probe pulse in ⌬f rep −1 = 100 s without mechanical delay line. The time resolution achieved by this technique lies below 150 fs. Experiment...

We propose sub-harmonic resonant optical excitation with femtosecond lasers as a new method for the characterization of phononic and nanomechanical systems in the gigahertz to terahertz frequency range. This method is applied for the investigation of confined acoustic modes in a free-standing semiconductor membrane. By tuning the repetition rate of a femtosecond laser through a subharmonic of a mechanical resonance we amplify the mechanical amplitude, directly measure the linewidth with megahertz resolution, infer the lifetime of the coherently excited vibrational states, accurately determine the system's quality factor, and determine the amplitude of the mechanical motion with femtometer resolution.In recent years, nanophononic and nanomechanical systems have emerged as intriguing subjects for studying mechanics, heat transfer and opto-mechanical coupling on a nanometer scale [1][2][3]. From a fundamental point of view, they provide a route to study mechanical excitations and their interactions with other elementary excitations [1,4]. ¿From an applied perspective they have opened a pathway for high sensitivity sensors in the zeptogram mass range and in the attonewton force range [5,6]. In established experimental methods these systems are driven electrically, magnetically, thermoelastically [7], via radiation pressure from continuous wave lasers [8], or via other optical non-radiation-pressurebased schemes [9,10]. The frequencies of typical systems investigated so far are in the megahertz to gigahertz frequency range [7]. The investigation of higher frequencies is strongly restricted by the driving and detection methods. Here, we report a new method for the investigation of a vibrational system by sub-harmonic resonant excitation with a high-repetition rate femtosecond laser. This excitation scheme can be regarded as tuning the separation of modes of the frequency comb of a femtosecond laser [11] to a commensurable of the frequency of the phononic system. By sweeping the comb spacing of the femtosecond laser, resonant impulsive excitation of the mechanical oscillator can be achieved, which allows the determination of its quality factor in the gigahertz to terahertz frequency range with femtometer sensitivity for the mechanical amplitude. We demonstrate the amplification of the fundamental eigenmode of a free-standing silicon membrane at 19 GHz by a factor of 20 compared to the off-resonant case and determine its quality factor.The dynamical properties of the free-standing silicon membranes were investigated by performing fs resolution pump-probe experiments using the recently developed high-speed asynchronous optical sampling (ASOPS) method [12,13]. This method is based on two asynchronously linked femtosecond Ti:sapphire ring lasers of repetition rate f R ∼ 1 GHz. One laser provides the pump beam and the second laser the probe beam. In this technique the time delay between pump-/probepulse pairs of the two pulse trains is realized through an actively stabilized 10 kHz repetition-rate-offset ∆f R between the tw...

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Nanostructured semiconductors open the opportunity to independently tailor electric and thermal conductivity by manipulation of the phonon transport. Nanostructuring of materials is a highly promising strategy for engineering thermoelectric devices with improved efficiency. The concept of reducing the thermal conductivity without degrading the electrical conductivity is most ideally realized by controlled isotope doping. This work reports on experimental and theoretical investigations on the thermal conductivity of isotopically modulated silicon nanostructures. State-of-the-art pump-and-probe experiments are conducted to determine the thermal conductivity of the different nanostructures of isotopically enriched silicon layers epitaxially grown on natural silicon substrates. Concomitant molecular dynamics calculations are performed to study the impact of the silicon isotope mass, isotope interfaces, and of the isotope layer ordering and thickness on the thermal conductivity. Engineering the isotope distribution is a striking concept to reduce the thermal 6 New J. Phys. 16 (2014) 015021 H Bracht et al conductivity of silicon without affecting its electronic properties. This approach, using isotopically engineered silicon, might pave the way for future commercial thermoelectric devices.

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