This master thesis is realized in STMicroelectronics thanks to a collaboration between the com- pany and Politecnico di Milano. The activity is aimed at modelling and experimentally character- izing a Piezoelectric Micro-machined Ultrasound Transducer (PMUT). This is a new generation MEMS (Micro Electro Mechanical System) able to send and receive ultrasound waves by ex- ploiting the piezoelectric effect: here the attention will be focused on the sending mode only. Throughout all the activity a continuous comparison between numerical simulation and exper- imental results is proposed. This approach is the typical workflow to launch a product into the market. The design modelling is done by using the finite element software COMSOL Mul- tiphysics 5.6 while the laboratory campaign is carried out through Polytec MSA500 and other electronic equipment. The analysis performed are mainly focused on investigating the static and dynamic mechanical behavior of the device and only as a closing section the emitted acoustic field has been considered. Concerning the mechanical characterization, the main fields of investigation are the deformed configurations both of the single membrane and the whole device, the resonance frequencies of the membranes, the dynamic oscillation and the cross-talk phenomena through which the membranes within the same die can interact. Starting from the distorted geometry of the membranes, this is due to the fabrication process which introduces residual stresses and in turn causes a non flat configuration of the membrane: it is noted that the initial upward deformation flattens by applying an increasing DC voltage. Similarly, even the deformation of the die is caused by the presence of residual stresses. Going on, the modal analysis is performed: the first six modes are evaluated to have a complete characterization but the only one exploited in applications is the first one, having a frequency equal to 140kHz. Once the frequency is known, a dynamic analysis is carried out. The membranes are activated by means of a single sinusoidal voltage signal at the resonance frequency and the oscillation ring down is analyzed. Thanks to these measurements, it has been possible to measure the damping of the device by computing the Q factor. This is carried out in presence of Air and Vacuum and the values obtained are respectively 22 and 182: in this way the fluid and mechanic contributions to the damping are divided. Furthermore, by studying the oscillation ring down it appears the need to develop a non linear hysterical piezoelectric model to simulate the dynamic behavior of PZT layer: it will be part of the future activity. Subsequently, the presence of the undesired phenomena of cross-talk has been experimentally investigated. Because of this effect, the membranes can interact each other and the oscillation of one membrane can put in motion the close ones. The analysis has been performed in vacuum and air: it is noted that the acoustic contribution to the cross-talk has a higher influence and in particular the communication occurs through the back cavities. The last part of the thesis is devoted to the acoustic measurements of the emitted field in terms of directionality and sound pressure level. The radiation pattern of the emitted acoustic field by the membrane is simulated by means of a 2D axysimmetric model. Moreover, the pressure intensity has been evaluated at 2cm over the membrane both through simulation and experimentally: a mismatch is noted and it is due to the inability of the model to consider the oscillation cross-talk of the other membranes. From here comes the second future development to be investigated: the emitted acoustic field considering the oscillation of the other membranes or avoid the cross-talk by changing the design of the device, i.e closing the cavity at the bottom of the membranes. This thesis is the starting point of future activities aimed at modelling the non linear hysterical piezoelectric behavior to better match the dynamic response and studying the cross-talk effect in the acoustic emission.
Questa tesi di Laurea Magistrale `e realizzata in Stmicroelectronics grazie ad una collaborazione tra l’azienda e il Politecnico di Milano. L’attivit`a `e finalizzata alla modellazione e alla caratter- izzazione sperimentale di un micro trasduttore ad ultrasuoni piezoelettrico (PMUT). Si tratta di un MEMS (Micro Electro Mechanical System) di nuova generazione in grado di inviare e rice- vere onde ultrasoniche sfruttando l’effetto piezoelettrico: qui l’attenzione `e focalizzata sulla sola modalit`a di invio. Durante tutta l’attivit`a viene proposto un confronto continuo tra simulazione numerica e risultati sperimentali. Questo approccio `e il tipico flusso di lavoro per introdurre un prodotto nel mercato. La modellazione numerica viene effettuata utilizzando il software ad elementi finiti COMSOL Multiphysics 5.6 mentre la campagna sperimentale di laboratorio viene effettuata tramite Polytec MSA500 insime ad altre apparecchiature elettroniche. L’analisi effettuata `e principalmente focalizzata sullo studio del comportamento meccanico statico e di- namico del dispositivo e solo nel capitolo di chiusura `e stato analizzato il campo acustico emesso. Per quanto riguarda la caratterizzazione meccanica, i principali campi d’indagine sono le configu- razioni deformate sia della singola membrana che dell’intero dispositivo, le frequenze di risonanza delle membrane, l’oscillazione dinamica e i fenomeni di cross-talk attraverso i quali le membrane all’interno dello stesso die possono interagire tra loro. A partire dalla geometria distorta delle membrane, questa `e dovuta al processo di fabbricazione che introduce tensioni residue e a sua volta provoca una configurazione non piatta della membrana: si nota che la deformazione in- iziale verso l’alto si appiattisce applicando una tensione CC crescente. Allo stesso modo, anche la deformazione dell’intero dispositivo `e causata dalle tensioni residue. Proseguendo, l’analisi modale viene eseguita per conoscere le frequenze di risonanza: primi sei modi di vibrazione sono valutati per avere una caratterizzazione completa ma l’unico sfruttato in applicazione `e il primo, con una frequenza pari a 140 kHz. Una volta che la frequenza `e nota, viene effettuata un’analisi dinamica. Le membrane vengono attivate mediante un singolo impulso sinusoidale di tensione alla frequenza di risonanza e a seguire viene analizzato lo smorzamento dell’oscillazione. Grazie a queste analisi `e stato possibile misurare lo smorzamento del dispositivo calcolando il fattore Q. La misura viene effettuata sia in presenza di aria che in vuoto: in tal modo vengono divisi i contributi fluidi e meccanici dello smorzamento. I valori ottenuti di Q per aria e vuoto sono rispettivamente 22 e 182. Inoltre, studiando lo smorzamento della vibrazione appare la necessit`a di sviluppare un modello piezoelettrico isteretico non lineare per simulare il comportamento dinamico dello strato di PZT: questo sar`a parte dell’attivit`a futura. Successivamente, la presenza di fenomeni indesiderati di cross-talk `e stata analizzata sperimentalmente. A causa di questo effetto, le mem- brane possono interagire tra loro e l’oscillazione di una membrana pu`o mettere in movimento quelle vicine. Anche in questo caso, l’analisi `e stata eseguita in vuoto e nell’aria: si `e notato che il contributo acustico ha un’influenza maggiore e in particolare la comunicazione avviene attraverso le cavit`a posteriori. L’ultima parte della tesi `e dedicata alle misurazioni acustiche del campo emesso in termini di direzionalit`a e livello di pressione sonora. Il radiation pattern del campo acustico emesso dalla membrana viene simulato mediante un modello assial-simmetrico 2D. Inoltre, l’intensit`a della pressione in funzione del tempo `e stata valutata a 2 cm sopra la membrana sia attraverso simulazione che sperimentalmente: si osserva un disallineamento che `e dovuto all’incapacit`a del modello di considerare il fenomeno di cross-talk. Da qui nasce il secondo sviluppo futuro, il quale dovr`a investigare il campo acustico emesso tenendo in considerazione l’oscillazione delle altre membrane o annullarlo cambiando design del dispositivo, i.e chiudendo la cavit`a inferiore delle membrane. Questa tesi `e il punto di partenza di attivit`a future volte a modellare il comportamento piezoelettrico isteretico non lineare e studiare l’effetto del cross-talk nell’emissione acustica.
Design modelling and mechanical/acoustic experimental characterization of piezoelectric micro-ultrasound transducers
Colosio, Matteo
2020/2021
Abstract
This master thesis is realized in STMicroelectronics thanks to a collaboration between the com- pany and Politecnico di Milano. The activity is aimed at modelling and experimentally character- izing a Piezoelectric Micro-machined Ultrasound Transducer (PMUT). This is a new generation MEMS (Micro Electro Mechanical System) able to send and receive ultrasound waves by ex- ploiting the piezoelectric effect: here the attention will be focused on the sending mode only. Throughout all the activity a continuous comparison between numerical simulation and exper- imental results is proposed. This approach is the typical workflow to launch a product into the market. The design modelling is done by using the finite element software COMSOL Mul- tiphysics 5.6 while the laboratory campaign is carried out through Polytec MSA500 and other electronic equipment. The analysis performed are mainly focused on investigating the static and dynamic mechanical behavior of the device and only as a closing section the emitted acoustic field has been considered. Concerning the mechanical characterization, the main fields of investigation are the deformed configurations both of the single membrane and the whole device, the resonance frequencies of the membranes, the dynamic oscillation and the cross-talk phenomena through which the membranes within the same die can interact. Starting from the distorted geometry of the membranes, this is due to the fabrication process which introduces residual stresses and in turn causes a non flat configuration of the membrane: it is noted that the initial upward deformation flattens by applying an increasing DC voltage. Similarly, even the deformation of the die is caused by the presence of residual stresses. Going on, the modal analysis is performed: the first six modes are evaluated to have a complete characterization but the only one exploited in applications is the first one, having a frequency equal to 140kHz. Once the frequency is known, a dynamic analysis is carried out. The membranes are activated by means of a single sinusoidal voltage signal at the resonance frequency and the oscillation ring down is analyzed. Thanks to these measurements, it has been possible to measure the damping of the device by computing the Q factor. This is carried out in presence of Air and Vacuum and the values obtained are respectively 22 and 182: in this way the fluid and mechanic contributions to the damping are divided. Furthermore, by studying the oscillation ring down it appears the need to develop a non linear hysterical piezoelectric model to simulate the dynamic behavior of PZT layer: it will be part of the future activity. Subsequently, the presence of the undesired phenomena of cross-talk has been experimentally investigated. Because of this effect, the membranes can interact each other and the oscillation of one membrane can put in motion the close ones. The analysis has been performed in vacuum and air: it is noted that the acoustic contribution to the cross-talk has a higher influence and in particular the communication occurs through the back cavities. The last part of the thesis is devoted to the acoustic measurements of the emitted field in terms of directionality and sound pressure level. The radiation pattern of the emitted acoustic field by the membrane is simulated by means of a 2D axysimmetric model. Moreover, the pressure intensity has been evaluated at 2cm over the membrane both through simulation and experimentally: a mismatch is noted and it is due to the inability of the model to consider the oscillation cross-talk of the other membranes. From here comes the second future development to be investigated: the emitted acoustic field considering the oscillation of the other membranes or avoid the cross-talk by changing the design of the device, i.e closing the cavity at the bottom of the membranes. This thesis is the starting point of future activities aimed at modelling the non linear hysterical piezoelectric behavior to better match the dynamic response and studying the cross-talk effect in the acoustic emission.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/183485