design, fabrication and characterisation of rf-mems parte iireggiani/old-files/mems_parte_ii.pdf ·...

ARCES -Advanced Research Centre on Electronic Systems

University of Bologna - Italy

Thursday, 8th February 2006

Design, Fabrication and Characterisation of RF-MEMS

Parte II

Roberto Gaddi

Email: [email protected]

ARCES - University of Bologna

Strutture MEMS in un transceiver a radio frequenza

Potenziale applicativo dei MEMS include la sostituzionedi componenti tradizionali


Applicazione MEMS in sistemi wireless

Possibili elementi in un transceiver adatti a realizzazionein tecnologia MEMS:

Induttori ad alto fattore di qualità integratiCapacitori variabiliInterruttori accoppiati in DC o ACMicro-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 architetturaIn particolare: selezione di canale e riconfigurabilità…


Componenti passivi ad alto fattore di qualità

Induttori integrati isolati dal substrato semiconduttivohanno perdite ridotte ⇒ maggiore fattore di idealità (Q)


Interruttori MEMS accoppiati in DC o AC-RF

Deformazioni di strutture conduttive, tramite trasduzione elettrostatica o magnetica, si utilizza per implementareinterruttori


Capacitori variabili integrati

Tramite strutture deformabili e trasduzione elettrostaticaè possibile realizzare capacitori variabili MEMS integrati


Esempio: ricevitore a banco di switch


Strutture MEMS risonanti

Masse sospese elasticamente a punti di ancoraggioimplementano strutture risonantiTramite trasduzione elettrostatica si possono trasferirecaratteristiche di risonanza meccanica all’interno di un sistema elettricoUtilizzabili 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…)


Strutture risonante a trasduttore comb-drive

Strutture a trasduzione trasversale basate sulcomb-drive (pettine)Capacità variabilelinearmente con la deformazioneelettrostaticaTrasduzione lineareFrequenze di risonanzanon superiori alledecine di KHz


Micromechanical resonator FEM analysis

Micromechanical resonator: the mechanicalresonance frequency is transduced into the electrical domainTypical transduction mechanisms: electrostatic, piezoelectric, electrothermalA frequency selective electrical response is obtained, with a quality factor depending only on viscous damping and mechanical losses

losses

stored

WWQ =


Schematic analysis of an electrostatic resonator

Actuationelectrode

Sensingelectrode

Iout

Vin

Vbias


Resonator electromechanical behaviour

Fkxxbxm =++ &&&xAVεv F x

2

2

xAV

21F ε

=

t∂∂Q i

f

i/viv

f0

mkf0 ≅


Example: clamped-clamped resonator

Surface micromachining:1. Oxide as sacrificial layer2. Thick polysilicon as structural layer3. Deep Reactive Ion Etching (DRIE) typically needed for

thick polysilicon layers (up to 20 μm)


FEM simulation of mechanical resonance


Simulation approaches for MEMS

System Level

Sub-system / Circuit Level

Device / Physical LevelTOP-DOWN

BOTTOM-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


Sub-system / Circuit Level Modeling

This modeling level involves:Terminal characteristics description of a sub-systemMultiple physical domains phenomena and quantitiesHierarchy compatible model complexity

Reduced-order modelling approach:Starts from exact continuous 3D modelling; space discretisation and reduction of mechanical degrees of freedom are appliedUsually requires expertise and intuition to avoid loss of significant device behaviour descriptionLately some automated model reduction tools are available also from commercial CAD toolsSeems more appropriate to a bottom-up design methodology…


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 loopZero sum of through quantity into a node or network cut-set

Physical domain Flow quantity Difference quantityElectrical Current Voltage

Mechanical-trans Force Velocity / Displ.

Mechanical-rot Torque Ang. Velocity / Displ.

Pneumatic Volume Flow PressureThermal Heat Flow Temperature


Lumped element electrical equivalence

Different energy domains can have formally identical constituent relationships (implicit/explicit or differential)

extFxkxBxM =⋅+⋅+⋅ &&& ext

t

idvLR

vvC =⋅++⋅ ∫∞−

τ1&

geometry parameters

mech. model abstraction

energy domain equivalence:

force ↔ currentvelocity ↔ voltage

electrical simulation

NO DIRECT LINK WITH DESIGN PARAMETERS


Higher level electrical equivalent approach

Equivalent electrical network modelling is suitable to small-signal analysis of generalised dumped resonatorsElectrical equivalent extraction quickly looses track of geometrical and mechanical design parameters


MEMS component library in Cadence®


Prediction of beams eigenfrequencies

F1=173.9KHz

F2=1.088MHz

F3=3.039MHz


Resonance modes of a composite device (1)

res1=110kHz res2=225kHzres3=275kHz res4=350kHz


Resonance modes of a composite device (2)

Small-signal ac simulation of the device with a punctual force stim.

res1=109kHzres2=204kHzres3=278kHzres4=347kHz


Complete MEMS example: tunable capacitor

MEMS varactor with T-shaped spring suspensionsParasitic extraction from RF characterisation or electromagnetic simulations should be performed for accurate RF modellingHere only access resistancedue to finite conductivity of beams is accounted for


MEMS Varactor top-down design (1)

Critical specs for varactor as tuning element within an electronic circuit are: tuning ratio (Cmax/Cmin), nominal capacitance (Cnom) and pull-in voltage (VPI)

Vbias

Z-pos

Vbias

Z-posAll geometrical parameters are available for design: MEMS design tool based on Spectre simulatorParametric static (DC) simulations quickly allow for Pull-in voltage design



The tuning ratio is technology defined

A sweep from 200x200μm2 to 400x400μm2, at f=1.8GHz and bias voltage VNOM

ox

oxairox

ttg

CC +

=ε

min

max

Total plate area A and nominal voltage VNOM define the capacitance value Cnom

Small signal (ac) analysisperformed at given frequency and sweeping Aleads quickly to the desired nominal capacitance

AA ~=



Spring beams dimensions control the overall spring constant k, e.g. the pull-in voltageAccess resistance also depends on beams W/LPossible trade-off: tuning range vs. resistive losses

⇓ width: ⇑ tuning range ⇓ Q factor


Varactor transient behaviour

Transient simulationscan give insight to response time to VBIAS

Spectre® simulator does not show any convergence issues, even with added electronicsBoth electrical and mechanical quantities can be observed


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


Mixed-domain complete VCO simulation

Differential VCO: CMOS technology from UMC, 0.18μm channel lengthModel library based on BSIM3 modelSpectre achieves convergence in transient analysisPeriodic-steady-state (PSS) simulation for noise analysis still have issues…

time

Vout

time

Vout

design, fabrication and characterisation of rf-mems parte iireggiani/old-files/mems_parte_ii.pdf ·...

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