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]
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Strutture MEMS in un transceiver a radio frequenza
Potenziale applicativo dei MEMS include la sostituzionedi componenti tradizionali
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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…
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Componenti passivi ad alto fattore di qualità
Induttori integrati isolati dal substrato semiconduttivohanno perdite ridotte ⇒ maggiore fattore di idealità (Q)
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Interruttori MEMS accoppiati in DC o AC-RF
Deformazioni di strutture conduttive, tramite trasduzione elettrostatica o magnetica, si utilizza per implementareinterruttori
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Capacitori variabili integrati
Tramite strutture deformabili e trasduzione elettrostaticaè possibile realizzare capacitori variabili MEMS integrati
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Esempio: ricevitore a banco di switch
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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…)
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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
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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 =
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Schematic analysis of an electrostatic resonator
Actuationelectrode
Sensingelectrode
Iout
Vin
Vbias
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Resonator electromechanical behaviour
Fkxxbxm =++ &&&xAVεv F x
2
2
xAV
21F ε
=
t∂∂Q i
f
i/viv
f0
mkf0 ≅
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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)
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FEM simulation of mechanical resonance
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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
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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…
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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
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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
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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
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MEMS component library in Cadence®
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Prediction of beams eigenfrequencies
F1=173.9KHz
F2=1.088MHz
F3=3.039MHz
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Resonance modes of a composite device (1)
res1=110kHz res2=225kHzres3=275kHz res4=350kHz
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Resonance modes of a composite device (2)
Small-signal ac simulation of the device with a punctual force stim.
res1=109kHzres2=204kHzres3=278kHzres4=347kHz
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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
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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
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MEMS Varactor top-down design (2)
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 ~=
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MEMS Varactor top-down design (3)
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
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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
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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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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