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2.5
S. Ouenzerfi1,2,3, H.A.C Tilmans2, S. El-Borgi3 and X. Rottenberg2
1KACST-Intel Consortium Center of Excellence in Nano-manufacturing Applications (CENA), Riyadh, KSA 2 IMEC, Leuven, Belgium
3 Applied Mechanics and Systems Research Laboratory, Tunisia Polytechnic School, University of Carthage, B.P. 743, La Marsa 2078, Tunisia
Novel Simulation of a Voltage-Driven Electro-Thermo-Mechanical MEMS Self-Oscillator
. .
ABSTRACT ANALYTICAL MODEL
Quantity
governing the
condition of
oscillation
Threshold value
DC current 𝐈𝐝𝐜𝟐 > −
𝟏
𝐑𝐝𝐜𝐐𝐦
𝟏 + 𝛚𝟎𝟐𝐂𝐭𝐡
𝟐 𝐑𝐭𝐡𝟐
𝐂𝐭𝐡𝐑𝐭𝐡𝟐 𝛚𝟎𝛂𝐆𝐩𝐫
DC voltage 𝐕𝐝𝐜𝟐 >
𝐑𝐝𝐜
𝐐𝐦
𝟏 + 𝛚𝟎𝟐𝐂𝐭𝐡
𝟐 𝐑𝐭𝐡𝟐
𝐂𝐭𝐡𝐑𝐭𝐡𝟐 𝛚𝟎𝛂𝐆𝐩𝐫
Power
𝐏𝐝𝐜 >𝟏
𝐐𝐦
𝟏 + 𝛚𝟎𝟐𝐂𝐭𝐡
𝟐 𝐑𝐭𝐡𝟐
𝐂𝐭𝐡𝐑𝐭𝐡𝟐 𝛚𝟎𝛂 𝐆𝐩𝐫
where 𝑃𝑑𝑐 = 𝐼𝑑𝑐2 𝑅𝑑𝑐 for the I-drive 𝑃𝑑𝑐 =
𝑉𝑑𝑐2
𝑅𝑑𝑐
for the V-driven
Methodology : Direct application of
Barkhaussen criteria
Block model of the voltage driven
electro-thermo-mechanical oscillator
representing the transfer functions The
“loop gain” should be equal to one for
satisfying the Barkhausen criterion [2].
|A(ω)(ω)|=1 and the
phase [A(ω)β(ω)]=2πn ,
n ϵ 0,1,2,..
Summary the threshold limit
oscillation condition for
current, voltage cases and the
general power expression [2].
This paper presents the modeling and simulation of electro-thermo-mechanical self-
oscillators, an emerging type of M/NEMS-enabled timing devices in which sustaining
electronic amplifiers are not required for their operation. Indeed, they realize
amplification in the mechanical domain and feedback by crossing three physical
domains: electrical, thermal and mechanical [1]. In a previous work [2], we proposed a
new model to study such kind of MEMS oscillator. We demonstrated also the possible
self-oscillation in case of the more attractive and practical direct voltage pumping for
devices with a positive piezoresistive coefficient.
In this poster, we present a novel COMSOL Multiphysics® finite element model for an
electro-thermo-mechanic self-oscillator and according simulations that support our
theoretical developments.
GEOMETRY AND DESIGN
PRINCIPAL OF OPERATION
The resulting asymmetric temperature
distribution generates thermal expansion
forces that drive the mechanical structure
mainly in bending.
Given the piezoresistive character of
silicon, the strain results in a change of
electrical resistance, and thus of the Joule heating power, closing the loop.
Dis
pla
cem
en
t (m
)
Time(s)
SELF-OSCILLATOR SIMULATION
Simulation without piezoresistivity presenting thermally
resonator aspect inducing ringing . Time dependent
study was involved in this simulation adjusting boundary
conditions in Joule Heating and Thermal expansion
module
COMSOL simulation of the heating and the
cooling part of a cycle. The colors indicate
total displacement (blue=high motion and
red is low motion).
Run implanting the piezoresistivity effect and presenting the growth oscillation aspect. (Time dependent simulation)
Piezoresisivity effect: electrical conductivity expression of the
material as a function of the stress due to the piezoresistivity
property of silicon.
Simulation time optimization: Stationary study as initial values for the
complete Time dependent study.
Simulation “stabilization”: Hyper elastic material to accentuate
the nonlinearity effect of the material.
Start oscillation Oscillation established Steady state (numerical noise)
The current driven through
the structure heats it up
through Joule heating mainly
concentrated in the thin and
thick supporting beams.
VERIFICATION OF THEORETICAL CONDITIONS
Parametric sweep simulation to check the threshold limit voltage condition
CONCLUSIONS Novel study of the electro-thermo-mechanical self oscillator based on direct
application of Barkhaussen criteria was verified via COMSOL.
New simulation of the complete behavior oscillation (voltage driven case).
Nonlinearity option in COMSOL was integrated to identify the stability of oscillation
[1] J. T. M. van Beek and R. Puers, “A review of MEMS oscillators for frequency reference and timing applications,” J. Micromech. Eng., vol. 22, no. 1, Jan. 2012, pp. 013001-1–013001-35 [2] S. Ouenzerfi H.A.C Tilmans, S. El-Borgi and X. Rottenberg ,”Voltage driven electro-thermo-mechanical self-oscillator” in Proc. 24th MME Conference, ESPOO, 2013.