In the recent years, the interest for miniature structures has considerably increased in different engineering and scientific application fields. The main reason is found in the growing need for accurate ultrasmall instruments and equipment characterized by very diminutive size, low power consumption, high precision and reliability. These systems can be successfully employed in manipulators, tweezers, resonators, sensors, actuators and memory devices. Introducing the fundamental concepts for modelling and designing of miniature structures such as micro- or nanoelectromechanical systems (MEMS/NEMS), the main purpose of this thesis is to provide an analytical method to accurately estimate the pull-in parameters of micro- and nanostructures with particular attention to the electrostatically actuators under intermolecular surface forces. Then, accurate models are essential for reliable analytical predictions and crucial to avoid or partially reduce the high cost and complexity of experimental tests and fabrication processes. An in-depth knowledge of the physical conditions and a complete analysis of the interactions between the system and external forces are then required for a correct formulation of the pull-in instability problem. Micro- or nanobeams are used to model the structures of many MEMS and NEMS devices. Typically, in actuators, a mobile electrode is suspended above a conductive substrate and actuated by a voltage difference. Under the action of the electrostatic force and intermolecular surface forces of Casimir and van der Waals that become relevant in nanoscale and very miniature microscale, the movable electrode deflects toward to the substrate. Reducing the separation distance between the electrodes, the magnitude of the attractive forces increases until at a critical voltage, named the pull-in voltage, where the flexible electrode collapses onto the substrate. Devices with small gap distance require small actuation voltage then low power consumption, but if the gap is small enough the structure might unexpectedly collapse onto the ground substrate even in the absence of electrostatic actuation, due to the effect of intermolecular forces. Then, determining the operation voltage and power dissipation, the pull-in voltage and deflection are considered as the most important parameters of pull-in instability. The Euler-Bernoulli beam deflection is described by a fourth-order nonlinear boundary value problem where the nonlinearity is accentuated by the distributed forces acting on the beam that are proportional to inverse integer powers of the distance between the two electrodes. In the present thesis an accurate analytical approach is proposed for estimating from both sides the pull-in characteristics of MEMS/NEMS actuators subject to electrostatic actuation by considering various effects such as fringing field effect, intermolecular surface force, flexible boundary conditions, buckling in compressed nanocantilever, tip-charge concentration in carbon nanotube devices, size effects considering the surface elasticity and nanocantilever immersed in liquid electrolytes. Following the analytical approach, the differential BVP is equivalently formulated in terms of a nonlinear integral equation. Then by using a priori estimates on the deflection from both sides, lower and upper bounds for the pull-in parameters are given, with no need of solving the complex nonlinear BVP. The analytical estimates turn out to be in excellent agreement with the numerical results provided by the shooting method. Finally, simple closed-form relations are proposed for the pull-in parameters providing useful tools for a fast and safe design of MEMS/NEMS devices.

L’interesse per le strutture miniaturizzate è aumentato considerevolmente in diversi campi di applicazione dall’ingegneria alla scienza. La ragione principale sta nella necessità crescente di accurati strumenti ultrapiccoli ovvero dispositivi dalle dimensioni ridotte, basso consumo di potenza, elevata precisione e affidabilità. Questi sistemi possono essere impiegati con successo in sensori, attuatori e dispositivi di memoria. Introducendo i concetti fondamentali per la modellazione e progettazione delle strutture miniaturizzate come i micro- nanoelectromechanical systems MEMS/NEMS, lo scopo principale di questa tesi è quello di fornire un metodo analitico per stimare accuratamente i parametri di pull-in delle micro- nanostrutture con particolare attenzione agli attuatori elettrostatici soggetti alle forze intermolecolari di superficie. Modelli accurati sono essenziali per ottenere stime analitiche affidabili ed evitare o ridurre parzialmente i costi elevati e la complessità dei test sperimentali e dei processi di fabbricazione. Un’approfondita conoscenza dei fenomeni fisici e un’analisi completa delle interazioni tra sistema e forze esterne sono quindi richieste per una corretta formulazione del problema dell’instabilità di pull-in. Micro- e nanotravi sono utilizzate per modellare le strutture di molti dispositive MEMS e NEMS. Tipicamente, negli attuatori, un elettrodo mobile è sospeso su un substrato conduttivo e attuato da una differenza di tensione. Sotto l’azione della forza elettrostatica e delle forze intermolecolari di superficie di Casimir e van der Waals che diventano rilevanti alla nanoscala e alla microscala più ridotta, l’elettrodo mobile deflette verso il substrato. Riducendosi la distanza fra gli elettrodi, l’intensità delle forze di attrazione cresce fino a un valore critico di tensione, ovvero la tensione di pull-in, dove l’elettrodo flessibile collassa su quello fisso. I dispositivi con una piccola distanza tra gli elettrodi richiedono una piccola tensione di attuazione, quindi presentano basso consumo di energia, ma se il gap è sufficientemente piccolo la struttura può collassare improvvisamente sul substrato anche in assenza dell’attuazione elettrostatica, a causa delle forze intermolecolari. Quindi, condizionando la tensione operativa e la dissipazione di energia, la tensione e la deflessione di pull-in sono considerati come i parametri più importante dell’instabilità di pull-in. La deflessione della trave di Eulero-Bernoulli è descritta da un problema ai valori al contorno nonlineare del quart’ordine dove la nonlinearità è accentuata dalle forze distribuite sulla trave che sono proporzionali all’inverso di potenze intere della distanza tra gli elettrodi. Nella presente tesi è proposto un accurato metodo analitico per stimare inferiormente e superiormente i parametri di pull-in degli attuatori MEMS/NEMS soggetti ad attuazione elettrostatica, considerando diversi effetti come quello di bordo, le forze intermolecolari di superficie, supporti flessibili, buckling in nanotravi compresse, concentrazione della carica di punta nei dispositivi CNT, effetti dimensionali considerando l’elasticità di superficie e dispositivi immersi in soluzioni elettrolitiche. Seguendo l’approccio analitico, il BVP differenziale è formulato come un’equazione integrale equivalente. Quindi utilizzando stime a priori sulla deflessione, si ottengono limiti inferiori e superiori sui parametri di pull-in, senza bisogno di risolvere il complesso BVP nonlineare. Le stime analitiche si mostrano in perfetto accordo con i risultati numerici forniti dal metodo di shooting. Infine, semplici relazioni in forma chiusa sono proposte per i parametri di pull-in fornendo utili strumenti per una progettazione rapida e sicura dei dispositivi MEMS/NEMS.

Sviluppo di un metodo analitico per lo studio dell’instabilità di pull-in di micro- o nanoattuatori MEMS/NEMS soggetti a forze elettrostatiche e intermolecolari di superficie / Giovanni Bianchi , 2021 Apr 21. 33. ciclo, Anno Accademico 2019/2020.

Sviluppo di un metodo analitico per lo studio dell’instabilità di pull-in di micro- o nanoattuatori MEMS/NEMS soggetti a forze elettrostatiche e intermolecolari di superficie

BIANCHI, GIOVANNI
2021

Abstract

In the recent years, the interest for miniature structures has considerably increased in different engineering and scientific application fields. The main reason is found in the growing need for accurate ultrasmall instruments and equipment characterized by very diminutive size, low power consumption, high precision and reliability. These systems can be successfully employed in manipulators, tweezers, resonators, sensors, actuators and memory devices. Introducing the fundamental concepts for modelling and designing of miniature structures such as micro- or nanoelectromechanical systems (MEMS/NEMS), the main purpose of this thesis is to provide an analytical method to accurately estimate the pull-in parameters of micro- and nanostructures with particular attention to the electrostatically actuators under intermolecular surface forces. Then, accurate models are essential for reliable analytical predictions and crucial to avoid or partially reduce the high cost and complexity of experimental tests and fabrication processes. An in-depth knowledge of the physical conditions and a complete analysis of the interactions between the system and external forces are then required for a correct formulation of the pull-in instability problem. Micro- or nanobeams are used to model the structures of many MEMS and NEMS devices. Typically, in actuators, a mobile electrode is suspended above a conductive substrate and actuated by a voltage difference. Under the action of the electrostatic force and intermolecular surface forces of Casimir and van der Waals that become relevant in nanoscale and very miniature microscale, the movable electrode deflects toward to the substrate. Reducing the separation distance between the electrodes, the magnitude of the attractive forces increases until at a critical voltage, named the pull-in voltage, where the flexible electrode collapses onto the substrate. Devices with small gap distance require small actuation voltage then low power consumption, but if the gap is small enough the structure might unexpectedly collapse onto the ground substrate even in the absence of electrostatic actuation, due to the effect of intermolecular forces. Then, determining the operation voltage and power dissipation, the pull-in voltage and deflection are considered as the most important parameters of pull-in instability. The Euler-Bernoulli beam deflection is described by a fourth-order nonlinear boundary value problem where the nonlinearity is accentuated by the distributed forces acting on the beam that are proportional to inverse integer powers of the distance between the two electrodes. In the present thesis an accurate analytical approach is proposed for estimating from both sides the pull-in characteristics of MEMS/NEMS actuators subject to electrostatic actuation by considering various effects such as fringing field effect, intermolecular surface force, flexible boundary conditions, buckling in compressed nanocantilever, tip-charge concentration in carbon nanotube devices, size effects considering the surface elasticity and nanocantilever immersed in liquid electrolytes. Following the analytical approach, the differential BVP is equivalently formulated in terms of a nonlinear integral equation. Then by using a priori estimates on the deflection from both sides, lower and upper bounds for the pull-in parameters are given, with no need of solving the complex nonlinear BVP. The analytical estimates turn out to be in excellent agreement with the numerical results provided by the shooting method. Finally, simple closed-form relations are proposed for the pull-in parameters providing useful tools for a fast and safe design of MEMS/NEMS devices.
Implementation of an analytical method for the pull-in instability investigation of micro- or nanoactuators MEMS/NEMS under electrostatic and intermolecular surface forces
21-apr-2021
RADI, Enrico
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1244335
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