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ARCES - University of Bologna Strutture MEMS in un transceiver a radio frequenza Potenziale applicativo dei MEMS include la sostituzione di componenti tradizionali

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ARCES - University of Bologna Applicazione MEMS in sistemi wireless Possibili elementi in un transceiver adatti a realizzazione MEMS: Induttori ad alto fattore di qualità integrati Capacitori variabili Interruttori accoppiati in DC o AC Micro-risonatori, per filtri o tank per oscillatori locali Caratteristiche favorevoli dei nuovi componenti MEMS permettono di rivedere anche la descrizione del sistema a livello di architettura In particolare: selezione di canale e riconfigurabilità…

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ARCES - University of Bologna Componenti passivi ad alto fattore di qualità Induttori integrati isolati dal substrato semiconduttivo hanno perdite ridotte maggiore fattore di idealità (Q)

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ARCES - University of Bologna Interruttori MEMS accoppiati in DC o AC-RF Deformazioni di strutture conduttive, tramite trasduzione elettrostatica od magnetica, si utilizza per implementare interruttori

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ARCES - University of Bologna Strutture MEMS risonanti Masse sospese elasticamente a punti di ancoraggio implementano strutture risonanti Tramite trasduzione elettrostatica si possono trasferire caratteristiche di risonanza meccanica allinterno di un sistema elettrico Utilizzabili a diversi range di frequenza, dai pochi KHz fino alle centinaia di MHz (GHz?..) Filtri alle frequenze intermedie (IF in supereterodyne) fino alla selezione di canale (HF) o tank per LO… Tipicamente alti fattori di qualità raggiungibili (~10000), grazie alle ridotte perdite meccaniche (in vuoto…)

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ARCES - University of Bologna Strutture risonante a trasduttore comb-drive Strutture a trasduzione trasversale basate sul comb-drive (pettine) Capacità variabile linearmente con la deformazione elettrostatica Trasduzione lineare

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ARCES - University of Bologna Capacitori variabili integrati Tramite strutture deformabili e trasduzione elettrostatica è possibile realizzare capacitori variabili MEMS integrati

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ARCES - University of Bologna Esempio: ricevitore a banco di switch

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ARCES - University of Bologna Simulation approaches for MEMS System Level Sub-system / Circuit Level Device / Physical Level TOP-DOWNBOTTOM-UP System modeling Behavioral analysis of complete MEMS devices Reduced order modeling Electrical equivalent Lumped elements Modified nodal analysis 3D modeling FEM / FVM / BEM field solvers Coupled domains

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ARCES - University of Bologna Sub-system / Circuit Level Modeling This modeling level involves: Terminal characteristics description of a sub-system Multiple physical domains phenomena and quantities Hierarchy compatible model complexity Reduced-order modelling approach: Starts from exact continuous 3D modelling; space discretisation and reduction of mechanical degrees of freedom are applied Usually requires expertise and intuition to avoid loss of significant device behaviour description Lately some automated model reduction tools are available also from commercial CAD tools Seems more appropriate to a bottom-up design methodology…

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ARCES - University of Bologna Generalized Kirkhoffian networks Kirkhoffian network theory is applicable to diverse energy domains, provided that: Flow (through) and difference (across) quantities can be identified, with relationships between them given as implicit/explicit equations or differential equations depending only on terminal quantities and internal states. Conservation laws apply: Zero sum of across quantity along a closed network loop Zero sum of through quantity into a node or network cut-set Physical domainFlow quantityDifference quantity ElectricalCurrentVoltage Mechanical-transForceVelocity / Displ. Mechanical-rotTorque Ang. Velocity / Displ. PneumaticVolume FlowPressure ThermalHeat FlowTemperature

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ARCES - University of Bologna Lumped element electrical equivalence Different energy domains can have formally identical constituent relationships (implicit/explicit or differential) geometry parameters mech. model abstraction energy domain equivalence: force current velocity voltage electrical simulation NO DIRECT LINK WITH DESIGN PARAMETERS

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ARCES - University of Bologna Higher level electrical equivalent approach Equivalent electrical network modelling is suitable to small-signal analysis of generalised dumped resonators Electrical equivalent extraction quickly looses track of geometrical and mechanical design parameters

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ARCES - University of Bologna Hierarchical structural analysis approach MEMS devices are made of basic shapes and elementary components, i.e. plate masses, beam springs, electrostatic air-gaps… A number of connectivity points (nodes) and degrees of freedom (dof) established for each component A global reference system allows for relative placement between components forming complete devices Geometrical and mechanical design parameters are maintained visible throughout the modeling and simulation cycle

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ARCES - University of Bologna Matrix-based structural analysis Each component has a total complexity of m=n·d, where n equals the number of nodes and d the dofs Two vectors of dimension m are created for the through and for the across quantities: In general, any linear physical behaviour of a component can be described by an m x m matrix, relating the forces/torques vector to the displacements vector or any of its derivatives, in the local reference system: The three main physical descriptions are: i) Elasticity (structural analysis) stiffness matrix k ii) Inertia (virtual works principle) mass matrix M iii) Damping (viscosity) damping matrix B

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ARCES - University of Bologna Assumption of thin uniform cross-section, i.e. L>>w,t with L being the length of the beam Homogeneous material: Young modulus E and Poisson ratio Two connectivity nodes at the two beams ends, each one given six degrees of freedom: total model complexity of 12 Indexes are: axial (1,7); shear (2,3,8,9); bending (5,6,11,12); twisting (4,10) Linear Euler beam – Definitions Area Polar 2 nd moment Bending moments

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ARCES - University of Bologna Linear Euler beam – Stiffness matrix [k] The result is the complete stiffness matrix:

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ARCES - University of Bologna Linear Euler beam – Mass matrix M Analysis limited to translational inertia leads to:

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ARCES - University of Bologna Spectre-HDL ® language for MEMS simulation (1) Model interface at schematic level through nodes and parameters, e.g. beam dimensions, orientation angles, … SpectreHDL model structure: Declarations of nodes, parameters (internal and external) and variables init: initialization performed once before simulation analog: model core, iterated at every simulation step post: final computations after simulation converged

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ARCES - University of Bologna Spectre-HDL ® language for MEMS simulation (2) SpectreHDL allows for the definition of across and through quantities, adopting a Cartesian reference system: across displacements (x,y,z) and rotations ( x, y, z ) through forces (F x,F y,F z ) and torques ( x, y, z ) Two key simulation parameters must be properly adjusted due to several orders of magnitude differences among electrical and mechanical quantities: abstol : absolute tolerance during simulation blowup : critical value that defines a diverging simulation On top of them also velocity and acceleration, both translational and angular, are declared as across quantities

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ARCES - University of Bologna MEMS component library in Cadence ® Basic components implemented so far: Straight beam 12 degrees-of-freedom, elasticity, viscous damping, inertia, electric conductivity Rigid plate mass 6 degrees-of-freedom, viscous damping, inertia, contact detection Suspended plate capacitor 4 degrees-of-freedom, electrostatic force, charge storage, viscous damping, inertia, contact forces Rigid comb-drive actuator 4 degrees-of-freedom, electrostatic force, charge storage, viscous damping, inertia Anchor points – Stimulus forces 6 degrees-of-freedom, stimuli for large and small signal static and dynamic analysis

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ARCES - University of Bologna MEMS component library in Cadence ®

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ARCES - University of Bologna Prediction of beams eigenfrequencies F 1 =173.9KHz F 2 =1.088MHz F 3 =3.039MHz

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ARCES - University of Bologna Resonance modes of a composite device (1) res 1 =110kHz res 2 =225kHz res 3 =275kHz res 4 =350kHz

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ARCES - University of Bologna Resonance modes of a composite device (2) Small-signal ac simulation of the device with a punctual force stim. res 1 =109kHz res 2 =204kHz res 3 =278kHz res 4 =347kHz

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ARCES - University of Bologna Complete MEMS example: tunable capacitor MEMS varactor with T-shaped spring suspensions Parasitic extraction from RF characterisation or electromagnetic simulations should be performed for accurate RF modelling Here only access resistance due to finite conductivity of beams is accounted for

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ARCES - University of Bologna MEMS Varactor top-down design (1) Critical specs for varactor as tuning element within an electronic circuit are: tuning ratio (C max /C min ), nominal capacitance (C nom ) and pull-in voltage (V PI ) All geometrical parameters are available for design: MEMS design tool based on Spectre simulator Parametric static (DC) simulations quickly allow for Pull-in voltage design

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ARCES - University of Bologna MEMS Varactor top-down design (2) The tuning ratio is technology defined A sweep from 200x200 m 2 to 400x400 m 2, at f=1.8GHz and bias voltage V NOM Total plate area A and nominal voltage V NOM define the capacitance value C nom Small signal (ac) analysis performed at given frequency and sweeping A leads quickly to the desired nominal capacitance

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ARCES - University of Bologna MEMS Varactor top-down design (3) Spring beams dimensions control the overall spring constant k, e.g. the pull-in voltage Access resistance also depends on beams W/L Possible trade-off: tuning range vs. resistive losses width: tuning range Q factor

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ARCES - University of Bologna Varactor transient behaviour Transient simulations can give insight to response time to V BIAS Spectre ® simulator does not show any convergence issues, even with added electronics Both electrical and mechanical quantities can be observed

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ARCES - University of Bologna Varactor insertion within an LC tank Typical application can be the tuning element within an LC tank for an RF voltage controlled oscillator (VCO) LC network includes two varactors that provide isolation from controlling voltage

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ARCES - University of Bologna Mixed-domain complete VCO simulation Differential VCO: CMOS technology from UMC, 0.18 m channel length Model library based on BSIM3 model Spectre achieves convergence in transient analysis Periodic-steady-state (PSS) simulation for noise analysis still have issues…

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