ARCES - University of Bologna Strutture MEMS in un transceiver a radio frequenza Potenziale applicativo dei MEMS include la sostituzione di componenti tradizionali
Mar 27, 2015
ARCES - University of Bologna
Strutture MEMS in un transceiver a radio frequenza
Potenziale applicativo dei MEMS include la sostituzione di componenti tradizionali
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…
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)
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
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 all’interno 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…)
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
ARCES - University of Bologna
Capacitori variabili integrati
Tramite strutture deformabili e trasduzione elettrostatica è possibile realizzare capacitori variabili MEMS integrati
ARCES - University of Bologna
Esempio: ricevitore a banco di switch
ARCES - University of Bologna
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
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…
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 domain Flow quantity Difference quantity
Electrical Current Voltage
Mechanical-trans Force Velocity / Displ.
Mechanical-rot TorqueAng. Velocity /
Displ.
Pneumatic Volume Flow Pressure
Thermal Heat Flow Temperature
ARCES - University of Bologna
Lumped element electrical equivalence
Different energy domains can have formally identical constituent relationships (implicit/explicit or differential)
extFxkxBxM ext
t
idvLR
vvC
1
geometry parameters
mech. model abstraction
energy domain equivalence:
force currentvelocity voltage
electrical simulation
NO DIRECT LINK WITH DESIGN PARAMETERS
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
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
N1 N2
Nn N3
x1
x2xd…
x1
x2xd…
x1
x2xd…
x1
x2xd…
N1 N2
Nn N3
x1
x2xd…
x1
x2xd…
x1
x2xd…
x1
x2xd…
x1
x2xd…
x1
x2xd…
x1
x2xd…
x1
x2xd…
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 dof’s
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 mxm 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 kii) Inertia (virtual works principle) mass matrix Miii) Damping (viscosity) damping matrix B
,...,,~~
UUUUUAS
UkUBUMS
mm UUSS 11 US
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 beam’s 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
twA
12;
12
33 twI
twI zy
22
3
7
2
tw
twJ
Area
Polar 2nd moment
Bending moments
ARCES - University of Bologna
Linear Euler beam – Stiffness matrix [k]
21 kkkukS
L
EI
L
EIL
EI
L
EIL
GJL
EI
L
EIL
EI
L
EIL
AEL
EI
L
EIL
EI
L
EIL
GJL
EI
L
EIL
EI
L
EIL
AE
zz
yy
x
yy
zz
zz
yy
x
yy
zz
2000
60
02
06
00
00000
06
012
00
6000
120
00000
4000
60
04
06
00
00000
06
012
00
6000
120
00000
2
2
23
23
2
2
23
23
1k
L
EI
L
EIL
EI
L
EIL
GJL
EI
L
EIL
EI
L
EIL
AEL
EI
L
EIL
EI
L
EIL
GJL
EI
L
EIL
EI
L
EIL
AE
zz
yy
x
yy
zz
zz
yy
x
yy
zz
4000
60
04
06
00
00000
06
012
00
6000
120
00000
2000
60
02
06
00
00000
06
012
00
6000
120
00000
2
2
23
23
2
2
23
23
2k
The result is the complete stiffness matrix:
ARCES - University of Bologna
Linear Euler beam – Mass matrix M
Analysis limited to translational inertia leads to:
140000
420
130
0140
0420
1300
006
000
0420
130
70
900
420
13000
70
90
000006
1105
000210
110
0105
0210
1100
003
000
0210
110
35
1300
210
11000
35
130
000003
1
2
2
2
2
LL
LLA
J
L
L
LL
LLA
J
L
L
AL
x
x
2M
105000
210
110
0105
0210
1100
003
000
0210
110
35
1300
210
11000
35
130
000003
1140
000420
130
0140
0420
1300
006
000
0420
130
70
900
420
13000
70
90
000006
1
2
2
2
2
LL
LLA
J
L
L
LL
LLA
J
L
L
AL
x
x
2M
21 MMM
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, …
symbol
spectreHDL
declarations
init
analog
post
schematic
externalparametersand nodes
internalparametersand nodes
symbol
spectreHDL
declarations
init
analog
post
schematic
externalparametersand nodes
externalparametersand nodes
internalparametersand nodes
internalparametersand nodes
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
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 (Fx,Fy,Fz) and torques (x,y,z)// Structural analysis implementation within SpectreHDL
// Roberto Gaddi, 29/01/2002// Quantity definitions for the mechanical signals// For each signal, name, units and absolute tolerance is given
displacement quantity name="disp" units="m" abstol=1pforce quantity name="frc" units="N" abstol=1pvelocity quantity name="vel" units="m/s" abstol=1n blowup=1e12angular_velocity quantity name="avel" units="rad/s" abstol=1n blowup=1e12angle quantity name="ang" units="rad" abstol=1ptorque quantity name="trq" units="Nm" abstol=1pacceleration quantity name="acc" units="m/s2" abstol=1u blowup=1e15angular_acceleration quantity name="aacc" units="rad/s2" abstol=1u blowup=1e15voltage_derivative quantity name="DV" units="V/s" abstol=1p blowup=1e15
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
ARCES - University of Bologna
MEMS component library in Cadence®
Basic components implemented so far:
Straight beam12 degrees-of-freedom, elasticity, viscous
damping, inertia, electric conductivity
Rigid plate mass6 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
ARCES - University of Bologna
MEMS component library in Cadence®
ARCES - University of Bologna
Prediction of beams eigenfrequencies
F1=173.9KHz
F2=1.088MHz
F3=3.039MHz
ARCES - University of Bologna
Resonance modes of a composite device (1)
res1=110kHz res2=225kHz
res3=275kHz res4=350kHz
ARCES - University of Bologna
Resonance modes of a composite device (2)
Small-signal ac simulation of the device with a punctual force stim.
res1=109kHz
res2=204kHz
res3=278kHz
res4=347kHz
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
ARCES - University of Bologna
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-pos 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
ARCES - University of Bologna
MEMS Varactor top-down design (2)
The tuning ratio is technology defined
A sweep from 200x200m2 to 400x400m2, at f=1.8GHz and bias voltage VNOM
ox
oxairox
t
tg
C
C
min
max
Total plate area A and nominal voltage VNOM define the capacitance value Cnom
Small signal (ac) analysis performed at given frequency and sweeping A leads quickly to the desired nominal capacitance
AA~
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
ARCES - University of Bologna
Varactor transient behaviour
Transient simulations can give insight to response time to VBIAS
Spectre® simulator does not show any convergence issues, even with added electronics
Both electrical and mechanical quantities can be observed
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
ARCES - University of Bologna
Mixed-domain complete VCO simulation
Differential VCO: CMOS technology from UMC, 0.18m 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…
time
Vout
time
Vout