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.