Quality Factor in Trench-Refilled Polysilicon Beam Resonators

Abdolvand, Reza; Johari, Houri; Ho, G.K.; Erbil, A.; Ayazi, Farrokh

doi:10.1109/jmems.2006.876662

Cited by 80 publications

(28 citation statements)

References 15 publications

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“…More recently, Zener's analysis of homogenous, isotropic beams has been extended in multiple directions and there are now over 350 significant publications on this topic. A selection of the literature includes models to account for the effects of structural boundaries [47,48]; polycrystalline grain structure [49,50]; layered composite architecture [51][52][53]; electrostatic actuation [54]; and geometry (plates [54,55], slotted, channeled, and hollow beams [56][57][58], double-paddle oscillators [63], and bulk-mode, ring-mode, and disc-mode resonators [59]). Using these models, the design space can be explored to formulate detailed guidelines for selecting geometries, structures, modes, materials, and frequencies to minimize thermoelastic damping.…”

Section: Thermoelastic Dampingmentioning

confidence: 99%

Design strategies for controlling damping in micromechanical and nanomechanical resonators

2014

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Damping is a critical design parameter for miniaturized mechanical resonators usedin microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS),optomechanical systems, and atomic force microscopy for a large and diverse set ofapplications ranging from sensing, timing, and signal processing to precisionmeasurements for fundamental studies of materials science and quantum mechanics.This paper presents an overview of recent advances in damping from the viewpointof device design. The primary goal is to collect and organize methods, tools, andtechniques for the rational and effective control of linear damping in miniaturizedmechanical resonators. After reviewing some fundamental links between dynamicsand dissipation for systems with small linear damping, we explore the space ofdesign and operating parameters for micromechanical and nanomechanicalresonators; classify the mechanisms of dissipation into fluid–structure interactions(viscous damping, squeezed-film damping, and acoustic radiation), boundarydamping (stress-wave radiation, microsliding, and viscoelasticity), and materialdamping (thermoelastic damping, dissipation mediated by phonons and electrons,and internal friction due to crystallographic defects); discuss strategies for minimizingeach source using a combination of models for dissipation and measurements of material properties; and formulate design principles for low-loss micromechanical and nanomechanical resonators

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Section: Thermoelastic Dampingmentioning

confidence: 99%

Design strategies for controlling damping in micromechanical and nanomechanical resonators

2014

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“…In this case, s was determined by the FE results in Fig. 10 for the nominal shell parameters by Q TED = Im{λ} 2Re{λ} [29], and s was found to be 0.126.…”

Section: F Scaling Law Of Bulk Ted In μHsrsmentioning

confidence: 95%

Bulk and Surface Thermoelastic Dissipation in Micro-Hemispherical Shell Resonators

Sorenson

Shao

Ayazi

2015

J. Microelectromech. Syst.

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Thermoelastic dissipation (TED) is a fundamental energy loss process, which bears concern in all microelectromechanical resonators. High aspect ratio (R/h) 3-D microhemispherical shell resonators (µHSRs) have exceptionally low stiffness and are sensitive to dissipation forces both internally and at their surfaces. TED in µHSRs originating in the bulk of the shell and near its surfaces due to asperities (roughness) is investigated. Rayleigh's inextensional solutions for the lowest frequency vibration modes of µHSRs in the isothermal quasistatic limit result in zero contributions to energy loss from bulk TED since no volumetric strain is generated in this approximation. After relaxing Rayleigh's inextensional assumption, perturbational undulations of the shell's neutral surface are found to cause non-zero bulk TED. The resulting quasiinextensional vibration modes force the shell into an approximately anti-biaxial strain state, which stretch surface asperities along one axis and compress them along the other, generating thermal flux around the base of each asperity. Closed-form approximate analytical models are developed from the geometrical and material dependencies to predict the quality factor associated with bulk and surface TED, enabling examination of these effects across scale. Fully-coupled thermoelastic finite element models verify the above results. Finally, experimental results from fabricated µHSRs are compared with the developed models.[ 2013-0229]Index Terms-Micro-hemispherical shell resonator, µHSR, 3D silicon micromachining, silicon micromolding, quality factor, Q, thermoelastic dissipation, TED, surface roughness, asperities, surface loss.

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“…3 In addition, for MEMS device manufacturing, trenches must be completely filled 4,5 without internal voids. 6 Gas-phase methods are capable of delivering a precursor molecule to a surface without line-of-sight transport and afford good control of the reaction kinetics. Filling of high aspect ratio recessed features, however, is difficult because the internal surface area is very large compared to the area of the opening, and because transport is limited by molecular diffusion.…”

Section: Introductionmentioning

confidence: 99%

“…Such shapes are a common, but not inevitable, result of reactive ion etching or assembly processes. 6 In addition, even in features that have parallel walls, conformality tends to degrade as filling proceeds. As coatings build up on the opposite sides of the feature, the remaining opening becomes narrower and narrower, and eventually the aspect ratio becomes extremely large and the transport rate of the precursor shrinks to tiny values.…”

Section: Introductionmentioning

confidence: 99%

“…This seam is undesirable or unacceptable in many applications because it leads to a degradation of performance, such as reducing the electrical conductivity of copper lines in ULSI circuits, and reducing thermal transport in MEMS devices. 6,[8][9][10] A different result holds when the feature width decreases steadily with depth, which we will refer to as a "V" shape. In this case, highly conformal coating produces high quality filling: as the deposit on the walls thickens, the angle at the bottom of the V remains constant and the position of the bottom point moves progressively toward the opening.…”

Section: Introductionmentioning

confidence: 99%

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Superconformal chemical vapor deposition of thin films in deep features

Wang

Chang

Codding

et al. 2014

Journal of Vacuum Science &Amp; Technology A: Vacuum, Surfaces, and Films

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The authors report a new and potentially widely applicable method for the chemical vapor deposition (CVD) of films with a superconformal thickness profile in recessed features, i.e., the rate of growth increases with depth away from the opening. Provided that the aspect ratio of the feature is not too large, deposition initially affords a “V” shaped profile; continued deposition eventually fills the feature without leaving a void or seam of low-density material along the centerline. Superconformal deposition occurs under the following set of conditions: (1) growth involves two coreactants; (2) the deposition rate depends directly on the surface concentrations of both coreactants; (3) the molecular diffusivities of the coreactants are different; and (4) the partial pressures of the coreactants are chosen such that the surface coverage of the more rapidly diffusing coreactant is relatively small, and therefore rate-limiting, near the opening. The latter condition can be fulfilled if the more slowly diffusing coreactant is employed in excess or has an intrinsically higher sticking coefficient. Under these circumstances, the deposition rate will increase deeper in the feature for the following reason: the pressure of the slowly diffusing coreactant necessarily drops more quickly with depth than that of the rapidly diffusing coreactant, which increases the fractional surface coverage of the fast-diffusing coreactant and with it the growth rate. At sufficiently large depths, eventually the surface concentration of the more slowly diffusing coreactant will become rate limiting and the growth rate will begin to fall; to obtain superconformal growth, therefore, conditions must be chosen so that the growth rate does not surpass its peak value. As a specific example of how this new approach can be implemented, MgO is deposited at 220 °C using the aminodiboranate precursor Mg(DMADB)2 and H2O. Under properly chosen conditions, the growth rate increases from 1.0 nm/min at the trench opening to 1.8 nm/min at a depth/width ratio of 18. The authors propose a kinetic model that quantitatively explains these observations and, more generally, predicts the film profile as a function of the partial pressures of the coreactants in the gas feed, the molecular diffusivities, and the aspect ratio of the feature. An additional benefit of the model is that it can be used to predict conditions under which perfectly conformal CVD depositions will result. The present method should enable the fabrication of nanoscale devices in which high aspect ratio recessed features need to be completely filled. The method is intrinsic in nature and does not require special surface preparation, the use of a catalyst, or cycles of deposition and etching.

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Quality Factor in Trench-Refilled Polysilicon Beam Resonators

Cited by 80 publications

References 15 publications

Design strategies for controlling damping in micromechanical and nanomechanical resonators

Design strategies for controlling damping in micromechanical and nanomechanical resonators

Bulk and Surface Thermoelastic Dissipation in Micro-Hemispherical Shell Resonators

Superconformal chemical vapor deposition of thin films in deep features

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