Waitz, Reimar
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Quantitative signal extraction in the dynamic range of nanomechanical systems by free and constrained fitting
We present a free and a constrained fitting procedure for determining the intrinsic response of a nanomechanical systems subject to noise and other environmental influences. We demonstrate that applying the free fitting procedure to the measured frequency response of amorphous silicon nitride (SiN) nanomembranes at varying pressure enables us to disentangle the intrinsic membrane vibration properties from the system response. This approach gives quantitative access to the eigenfrequency, quality factor, coupling strength to the excitation system as well as to system noise. The validity of physical models for quantities such as excitation, fluctuations, and damping can be verified with the help of the constrained fitting procedure that implies additional mathematical relationships between the fit parameters. We verify the performance of the constrained fitting procedure for amorphous SiN membrane resonators tested in various experimental setups.
Vibrational modes of ultrathin carbon nanomembrane mechanical resonators
We report measurements of vibrational mode shapes of mechanical resonators made from ultrathin carbon nanomembranes (CNMs) with a thickness of approximately 1 nm. CNMs are prepared from electron irradiation induced cross-linking of aromatic self-assembled monolayers and the variation of membrane thickness and/or density can be achieved by varying the precursor molecule. Single- and triple-layer freestanding CNMs were made by transferring them onto Si substrates with square/rectangular orifices. The vibration of the membrane was actuated by applying a sinusoidal voltage to a piezoelectric disk on which the sample was glued. The vibrational mode shapes were visualized with an imaging Mirau interferometer using a stroboscopic light source. Several mode shapes of a square membrane can be readily identified and their dynamic behavior can be well described by linear response theory of a membrane with negligible bending rigidity. By applying Fourier transformations to the time-dependent surface profiles, the dispersion relation of the transverse membrane waves can be obtained and its linear behavior verifies the membrane model. By comparing the dispersion relation to an analytical model, the static stress of the membranes was determined and found to be caused by the fabrication process.
Lateral and Temporal Dependence of the Transport through an Atomic Gold Contact under Light Irradiation : Signature of Propagating Surface Plasmon Polaritons
Metallic point contacts (MPCs) with dimensions comparable to the Fermi wavelength of conduction electrons act as electronic waveguides and might operate as plasmon transmitters. Here we present a correlated study of optical and conductance response of MPCs under irradiation with laser light. For elucidating the role of surface plasmon polaritons (SPPs), we integrate line gratings into the leads that increase the SPP excitation efficiency. By analyzing spatial, polarization, and time dependence, we identify two SPP contributions that we attribute to transmitted and decaying SPPs, respectively. The results demonstrate the role of SPPs for optically controlling the transport in metallic nanostructures and are important for designing opto-nanoelectronic devices.
Mode shape and dispersion relation of bending waves in thin silicon membranes
We study the vibrational behavior of silicon membranes with a thickness of a few hundred nanometers and macroscopic lateral size. A piezo is used to couple in transverse vibrations, which we monitor with a phase-shift interferometer using stroboscopic light. The observed wave pattern of the membrane deflection is a superposition of the mode corresponding to the excitation frequency and several higher harmonics. Using a Fourier transformation in time, we separate these contributions and image up to the eighth harmonic of the excitation frequency. With this method we determine the dispersion relation of membrane oscillations in a frequency range up to 12 MHz. We develop a simple analytical model combining stress of a membrane and bending of a thin plate that describes both the experimental data and finite-elements simulations very well. We derive correction terms to account for a finite curvature of the membrane and for the inertia of the surrounding atmosphere. A simple criterion for the transition between stressed membrane and thin plate behavior is presented.
Fast quantitative optical detection of heat dissipation by surface plasmon polaritons
Heat management at the nanoscale is an issue of increasing importance. In optoelectronic devices the transport and decay of plasmons contribute to the dissipation of heat. By comparison of experimental data and simulations we demonstrate that it is possible to gain quantitative information about excitation, propagation and decay of surface plasmon polaritons (SPPs) in a thin gold stripe supported by a silicon membrane. The temperature-dependent optical transmissivity of the membrane is used to determine the temperature distribution around the metal stripe with high spatial and temporal resolution. This method is complementary to techniques where the propagation of SPPs is monitored optically, and provides additional information which is not readily accessible by other means. In particular, we demonstrate that the thermal conductivity of the membrane can also be derived from our analysis. The results presented here show the high potential of this tool for heat management studies in nanoscale devices.
Time-resolved detection of propagating Lamb waves in thin silicon membranes with frequencies up to 197 GHz
Guided acoustic waves are generated in nanopatterned silicon membranes with aluminum gratings by optical excitation with a femtosecond laser. The spatial modulation of the photoacoustic excitation leads to Lamb waves with wavelengths determined by the grating period. The excited Lamb waves are optically detected for different grating periods and at distances up to several μm between pump and probe spot. The measured frequencies are compared to the theoretical dispersion relation for Lamb waves in thin silicon membranes. Compared to surface acoustic waves in bulk silicon twice higher frequencies for Lamb waves (197 GHz with a 100 nm grating) are generated in a membrane at equal grating periods.
Time-resolved optical measurement of thermal transport by surface plasmon polaritons in thin metal stripes
We investigate the thermal transport originating from the propagation of surface plasmon polaritons (SPPs) in a thin gold stripe. The SPPs are excited by a grating coupler on the Au stripe which was patterned onto a silicon membrane. The transmissivity changes of the Si membrane due to temperature-induced changes of the interference conditions enable measuring the temperature distribution with temporal and spatial resolution better than 1 μs and 1 μm. With this setup, we demonstrate that SPP excitation, propagation, and decay are accompanied by considerable heating and heat transport.
Quantitative Determination of the Mechanical Properties of Nanomembrane Resonators by Vibrometry In Continuous Light
We present an experimental study of the bending waves of freestanding Si3N4 nanomembranes using optical profilometry in varying environments such as pressure and temperature. We introduce a method, named Vibrometry in Continuous Light (VICL) that enables us to disentangle the response of the membrane from the one of the excitation system, thereby giving access to the eigenfrequency and the quality (Q) factor of the membrane by fitting a model of a damped driven harmonic oscillator to the experimental data. The validity of particular assumptions or aspects of the model such as damping mechanisms, can be tested by imposing additional constraints on the fitting procedure. We verify the performance of the method by studying two modes of a 478 nm thick Si3N4 freestanding membrane and find Q factors of 2 x 104 for both modes at room temperature. Finally, we observe a linear increase of the resonance frequency of the ground mode with temperature which amounts to 550 Hz=/°C for a ground mode frequency of 0:447 MHz. This makes the nanomembrane resonators suitable as high-sensitive temperature sensors.
Spatially Resolved Measurement of the Stress Tensor in Thin Membranes Using Bending Waves
The mode shape of bending waves in thin silicon and silicon-carbide membranes is measured as a function of space and time, using a phase-shift interferometer with stroboscopic light. The mode shapes hold information about all the relevant mechanical parameters of the samples, including the spatial distribution of static prestress. We present a simple algorithm to obtain a map of the lateral tensor components of the prestress, with a spatial resolution much better than the wavelength of the bending waves. The method is not limited to measuring the stress of bending waves. It is applicable in almost any situation, where the fields determining the state of the system can be measured as a function of space and time.
Femtosecond spectroscopy of acoustic frequency combs in the 100-GHz frequency range in Al/Si membranes
Acoustic frequency combs are optically excited and detected in silicon membranes covered with thin aluminum layers by femtosecond pump-probe spectroscopy. The various frequency combs consist of 11 up to 45 modes ranging in frequency from 10 up to 500 GHz. Evaluating the different modes of the combs allows us to quantify the dynamic properties of this two-layer system with great precision. Deviations of the frequencies of higher modes from a linear relation can be quantitatively understood. The time domain traces show clearly defined pulses which are detected in regular time intervals after each roundtrip in the acoustic cavity formed by the membrane and the metal film. By analyzing the individual reflected pulses and their evolution in time, damping times for the whole frequency range are determined. We analytically derive a deviation of the individual comb modes from integer values of the fundamental frequency which is corroborated by the experiments.