Douglas M. Photiadis

Thermoelastic loss in microscale oscillators

A simple model of thermoelastic dissipation is proposed for general, free standing microelectromechanical (MEMS) and nanoelectromechanical (NEMS) oscillators. The theory defines a flexural modal participation factor, the fraction of potential energy stored in flexure, and approximates the internal friction by assuming the energy loss to occur solely via classical thermoelastic dissipation of this component of the motion. The theory is compared to the measured internal friction of a high Q mode of a single-crystal silicon double paddle oscillator. The loss at high temperature (above 150 K) is found to be in good agreement with the theoretical prediction. The importance of this dissipation mechanism as a function of scale is briefly discussed. We find that the relative importance of this mechanism scales with the size of the structure, and that for nanoscale structures it is less important than intrinsic phonon–phonon scattering.

Attachment losses of high Q oscillators

Attachment losses can play a role in limiting the quality factors of micro/nanomechanical oscillators. The existing theoretical results in this regard are applicable to highly idealized scenarios. The theory has been extended in two important directions: the width of the cantilever is considered to be small relative to a wavelength as opposed to large, and the base is allowed to have finite thickness. These extensions result in significant, in many cases order of magnitude, changes in the estimates of attachment loss. Simple formulas for Q−1 covering most of the parameter range are given.

Attachment loss of micromechanical and nanomechanical resonators in the limits of thick and thin support structures

Analytical expressions are provided for the energy loss from vibrating mechanical resonators into their support structures for two limiting cases: supports that can be treated as plates, and supports that act as semi-infinite elastic media, with effectively infinite thickness. The former case is applicable to many microscale resonators, while the latter is appropriate for nanoscale devices. General formulations are given, applicable to a wide range of resonator geometries. These formulations are then applied to two geometries commonly used in microelectromechanical systems and nanelectromechanical systems applications: cantilevered beams and doubly fixed beams. Experimental data are presented to validate the finite-thickness support theory, and the predictions of the theory are also compared to data from existing literature for a microscale rectangular paddle oscillator.

A loss mechanism study of a very high Q silicon micromechanical oscillator

The room-temperature quality factors of silicon micromechanical oscillators have been investigated by scanning laser vibrometry. One of the flexural modes has very little attachment loss to its environment, which enables us to study internal loss mechanisms. After several consecutive annealing steps up to 800°C, the quality factor Q has increased from 8×104 to 6.0×105. However, the Q decays to 1.4×105 over six months in air. We conclude that near-surface lattice defects caused by reactive-ion etching and surface adsorbates are the main source of internal loss while surface adsorbates are responsible for the time dependence. We also discuss the thermoelastic limit in terms of Zener’s theory and flexural modal components of thin plates with vibratory volume change, and compare it with our results.

On the modes and loss mechanisms of a high Q mechanical oscillator

We have performed laser-Doppler vibrometry measurements of the vibration of a double-paddle oscillator. Seven modes with principally out-of-plane motion have been identified. Their resonance frequencies and mode shapes are in excellent agreement with three-dimensional finite element simulations. We have found that the second antisymmetric torsional mode has exceptionally good vibration isolation of its mode shape. This explains its extremely small low temperature internal friction below 10 K (2×10−8). By correlating the internal friction of each mode with features of their mode shapes, a criterion has been established to develop high Q oscillators.

Broadband acoustic scattering from a ribbed shell

Monostatic acoustic scattering measurements have been made on a large aspect ratio (L/D=6.2) ribbed cylindrical shell over the frequency range 0.8<ω/ωr<12 (where ωr is the ring frequency for the shell). The ribs are arranged in a near periodic array with small random deviations in the rib locations of magnitude da/a=0.05. The physical processes that give rise to peaks in the scattering cross section are discussed and the ability of various theoretical models to predict the locations of the highlights is examined. The measurements provide further confirmation that the principle sources of scattering for typical ribbed shells in this frequency range are specular reflection, phase matching to fast membrane waves, phase matching to flexural Bloch waves, and Bragg scattering from the ribs. They also reveal that the scattered spectrum of the flexural Bloch waves can be more complicated than originally thought.

Ultrathin single crystal diamond nanomechanical dome resonators.

We present the first nanomechanical resonators microfabricated in single-crystal diamond. Shell-type resonators only 70 nm thick, the thinnest single crystal diamond structures produced to date, demonstrate a high-quality factor (Q ≈ 1000 at room temperature, Q ≈ 20 000 at 10 K) at radio frequencies (50-600 MHz). Quality factor dependence on temperature and frequency suggests an extrinsic origin to the dominant dissipation mechanism and methods to further enhance resonator performance.

Characterization of Silicon Micro-Oscillators by Scanning Laser Vibrometry

The dynamics of single-crystal silicon ∼100 μm size rectangular paddle oscillators at room temperature have been studied using a recently developed high-resolution scanning laser vibrometer. The dynamic mechanical behavior is determined by scans of the entire device, providing both amplitude and phase spatial maps of the vibratory response. These reveal more than 16 normal modes below 500 kHz. In addition to simple translation and torsional motion, flexural modes of the paddle plate are observed. Quality factors ranging from 1×103 to 2×104 are measured and are found to be significantly lower than those expected from well-known intrinsic absorption mechanisms. The measurements reveal that there exists significant modification of the expected eigenfrequencies and mode shapes. It is speculated that this is caused by excessive undercutting of the support structure, and that the resulting energy flow into the support leads to increased oscillator loss. Indeed, some correlation is found between observed loss an...

Scattering from flexural waves on a ribbed cylindrical shell

Monostatic scattering measurements over a ka range 2–30 made on two cylindrical shell structures, one with regular internal frames and one without, clearly demonstrate that the periodic discontinuities in the framed shell give rise to distinctive features in the scattering patterns at frequencies much lower than those at which Bragg scattering peaks can exist. These features are found to be even more dominant than those associated with the now well‐known scattering from supersonic shear and compressional helical shell waves. When the measured scattering levels are displayed as a function of frequency and aspect, these features manifest themselves as curves suggestive of folded‐over dispersion curves of flexural waves. It will be shown that these effects are, in fact, due to scattering from Bloch or Floquet wave packets arising from the frame‐induced multiple scattering of the subsonic flexural waves. The measured scattering functions are compared with predictions based on phase matching of the acoustic wa...

Thermoelastic relaxation in elastic structures, with applications to thin plates

A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined with the Kirchhoff assumption to obtain a new equation for the flexural vibration of thin plates incorporating thermoelastic loss as a damping term. The thermal relaxation loss is inhomogeneous and depends upon the local state of vibrating flexure, specifically, the principal curvatures at a given point on the plate. Thermal loss is zero at points where the principal curvatures are equal and opposite, that is, saddle shaped or pure anticlastic deformation. Conversely, loss is maximal at points where the curvatures are equal, that is, synclastic or spherical flexure. The influence of modal curvature on the thermoelastic damping is described through a modal participation factor. The effect of transverse thermal diffusion on plane wave propagation is also examined. It is shown that transverse diffusion effects are always small provided the plate thickness is far greater than the thermal phonon mean free path, a requirement for the validity of the classical theory of heat transport. These results generalize Zeners theory of thermoelastic loss in beams and are useful in predicting mode widths in micro- and nano-electromechanics systems oscillators.