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Recent Advances in Microelectromechanical Systems and Their Applications 269

Fig. 30. OELIM measurements of a vibrating MEMS cantilever – resonating at 261,400 Hz

corresponding to a complex third flexure mode: (a) time-average fringe pattern, (b) mode

shape based on the fringe pattern of part (a) exhibiting maximum deformation of 870 nm.

Quantitative interpretation of these fringe patterns shows mode shapes included

as part (b) of Figs 28 to 30. The corresponding frequencies of the three modes

displayed show good correlation with the frequencies determined analytically,

well within the uncertainty limits [43]. More specifically, fundamental resonance

frequencies for the first three bending modes of the microcantilevers considered

herein can be expressed as 14.57±1.72 kHz, 92.57±10.72 kHz, and 261.40±30.02

kHz, for the results displayed in Figs 28 to 30, respectively.

Following procedures used to obtain representative results shown in this

Section, displacements, deformations, and motions of other MEMS and structures

can be determined.

5 Conclusions and Future Work

An optoelectronic methodology for micro- and nano-scale measurements was

presented. Suitability of this methodology in experimental mechanics on the

micro/nanoscale was demonstrated by applications to representative MEMS

[23,44], deformations of the maximum magnitude ranging from pm to hundreds of

μm were measured on MEMS samples that were considered.

The methodology is applicable under static and dynamic conditions. In this

paper, its applicability was illustrated by use of four representative MEMS

samples: microengine, microgyroscope, pressure sensor, and a cantilever-type

Ohmic-microswitch. Deformations of these representative MEMS samples were

from picometers to a few hundred μm, depending on the specific operating

conditions and nature of the MEMS considered. Theoretical results correlated

with the experimental results well within the criteria specified by the uncertainty

analysis. Validated correlations will lead to establishment of “design by analysis”

methodology for efficient and effective developments of structures, which is

becoming more and more necessary especially as consequences of MEMS

reliability assessments are being considered/resolved [45,46].

All in all, representative results presented in this paper indicate that the

optoelectronic methodology is a viable tool for micro- and nano-scale measurements,

(b)

(a)

270 R.J. Pryputniewicz

as such it is particularly useful for development of MEMS, especially while

considering MEMS reliability assessment. In fact, this author strongly believes that

this methodology may become a differentiating factor in developments of reliable

and durable MEMS for high-performance applications to satisfy ever increasing

requirements especially those relating to the Q-factor [21] discrimination.

Based on a recent publication [47] we should expect to witness an increasing

activity in the field of microsystems technology. More specifically, MEMS-based

products made in 2005 had an estimated value of about $8 billion, 40% of which

was in microsensors while the balance was for products that include

micromachined features such as ink jet printers, catheters, and RF IC chips.

Currently, the MEMS related activities, judging by global distribution of MEMS

fabrication facilities, shown in Fig. 31, are approximately 40% in North America,

40% in Europe, and about 20% in Asia.

Fig. 31. Global distribution of MEMS fabrication facilities.

Growth projections for MEMS-based products follow an exponential curve [47]

with value of products rising to $40 billion in 2015 and to $200 billion in 2025.

This is a projected 25-fold growth of MEMS products during the 20-year period

from 2005 to 2025!

Acknowledgments

The authors gratefully acknowledge support by all sponsors and thank them for

their permissions to present the results, of their projects, in this paper. This work

was also supported by the NEST Program at WPI-ME/CHSLT.

Recent Advances in Microelectromechanical Systems and Their Applications 271

References

1. Pryputniewicz, R.J.: Integrated approach to teaching of design, analysis, and

characterization in micromechatronics. In: Paper No. IMECE2000/DE-13, ASME -

Am. Soc. Mech. Eng., New York, NY (2000)

2. Pryputniewicz, R.J.: MEMS design education by case studies, Paper No.

IMECE2001/DE-23292, ASME - Am. Soc. Mech. Eng., New York, NY (2001)

3. Pryputniewicz, R.J.: Progress in MEMS. Strain 43, 1–13 (2007)

4. Pryputniewicz, D.R.: ACES approach to the development of microcomponents, MS

Thesis, Worcester Polytechnic Institute, Worcester, MA (1997)

5. Pryputniewicz, R.J.: A hybrid approach to deformation analysis. In: Proc. SPIE,

vol. 2342, pp. 282–296 (1994)

6. Furlong, C., Pryputniewicz, R.J.: Hybrid computational and experimental approach for

the study and optimization of mechanical components. Opt. Eng. 37, 1448–1455

(1998)

7. Furlong, C.: Hybrid, experimental and computational, approach for the efficient study

and optimization of mechanical and electro-mechanical components, Ph.D.

Dissertation, Worcester Polytechnic Institute, Worcester, MA (1999)

8. Pryputniewicz, E.J.: ACES approach to the study of electrostatically driven MEMS

microengines, MS Thesis, Worcester Polytechnic Institute, Worcester, MA (2000)

9. Pryputniewicz, R.J., Galambos, P., Brown, G.C., Furlong, C., Pryputniewicz, E.J.:

ACES characterization of surface micromachined microfluidic devices. Internat. J. of

Microelectronics and Electronic Packaging (IJMEP) 24, 30–36 (2001)

10. Pryputniewicz, D. R., Furlong, and Pryputniewicz, R. J. (2001) “ACES approach to the

study of material properties of MEMS,” Proc. Internat. Symp. on MEMS: Mechanics

and Measurements, Portland, OR, pp. 80-83.

11. Pryputniewicz, R.J.: Engineering experimentation, Worcester Polytechnic Institute,

Worcester, MA (1993)

12. Pryputniewicz, R.J., Furlong, C., Pryputniewicz, E.J.: Optimization of contact

dynamics for an RF MEMS switch. In: Paper No. IMECE2002-39504, Am. Soc.

Mech. Eng., New York, NY (2002)

13. Pryputniewicz, R.J., Furlong, C.: Novel optoelectronic methodology for testing of

MOEMS. In: Proc. Internat. Symp. on MOEMS and Miniaturized Systems III. SPIE,

vol. 4983, pp. 11–25 (2003)

14. Rogers, M.S., Miller, S.L., Sniegowski, J.J., LaVigne, G.F.: Designing and operating

electrostatically driven microengines. In: Proc. 44th Internat. Instrumentation Symp.,

Reno, NV, pp. 56–65 (1998)

15. Pryputniewicz, R.J., Tan, X.G., Przekwas, A.J.: Modeling and measurements of

MEMS gyroscopes. In: Proc. IEEE-PLANS 2004, Monterey, CA, pp. 111–119 (2004)

16. Rowe, J.R.: Advanced sensor technology key to new multivariable transmitter. In:

Proc. Instr. Soc. Am.

17. Pryputniewicz, R.J., Angelosanto, J.P., Furlong, C., Brown, G.C., Pryputniewicz, E.J.:

Analysis and measurements of high pressure response of MEMS sensors. In: Proc.

Internat. Symp. on MEMS: Mechanics and Measurements, Portland, OR, pp. 76–79

(2001)

18. Pryputniewicz, R.J.: Thermal management in RF MEMS Ohmic switches. In: Paper

No. IPACK 2007-33502, ASME – Am. Soc. Mech. Eng., New York, NY (2007)

272 R.J. Pryputniewicz

19. Pryputniewicz, R.J., Wilkerson, P.W., Przekwas, A.J., Furlong, C.: RF MEMS:

modeling and simulation of switch dynamics. In: Proc. 35th Internat. Symp. on

Microelectronics, Denver, CO, pp. 267–272 (2002)

20. Furlong, C., Pryputniewicz, R.J.: Integrated approach to development of microelectronic

contacts. In: Paper No. IPACK 2007-33345, ASME – Am. Soc. Mech. Eng., New York,

NY (2007)

21. Pryputniewicz, R.J., Pryputniewicz, D.R., Pryputniewicz, E.J.: Effect of process

parameters on TED-based Q-factor of MEMS. In: Paper No. IPACK 2007-33094,

ASME – Am. Soc. Mech. Eng., New York, NY (2007)

22. Klempner, A.R., Marinis, R.T., Hefti, P., Pryputniewicz, R.J.: Experimental

determination of the Q-factors of microcantilevers coated with thin metal films.

Strain 45, 295–300 (2009)

23. Pryputniewicz, R.J., Furlong, C.: MEMS and nanotechnology, Worcester Polytechnic

Institute, Worcester, MA (2002)

24. Pryputniewicz, R.J.: Recent advances in optoelectronic methodologies: from milli-

through micro- to even ...smaller applications. In: Proc. Workshop on Optical

Methodology, Worpswede, Germany (2007)

25. Stout, P.: CFD-ACE+ a CAD system for simulation and modeling of MEMS. In: Proc.

SPIE, Paris, France (1999)

26. Wilkerson, P.W., Kranz, M., Przekwas, A.J.: Flip-chip hermetic packaging of RF

MEMS. In: MEMS4 Conference, Berkeley, CA, August 24-26 (2001)

27. Przekwas, A.J., Turowski, M., Furmanczyk, M., Hieke, A., Pryputniewicz, R.J.:

Multiphysics design and simulation environment for microelectromechanical systems.

In: Proc. Symp. on MEMS: Mechanics and Measurements, Portland, OR, pp. 84–89

(2001)

28. CFDRC, “CFD-ACE+ Multiphysics software” (2004), http://www.cfdrc.com

29. SRAC, “COSMOS/M user’s guide”, Structural Research and Analysis Corporation,

Santa Monica, CA (1998)

30. Brown, G.C.: Laser interferometric methodologies for characterizing static and

dynamic behavior of MEMS, Ph.D. Dissertation, Worcester Polytechnic Institute,

Worcester, MA (1999)

31. Pryputniewicz, R.J.: Quantitative determination of displacements and strains from

holograms. In: Holographic interferometry. Springer Series in Sciences, ch. 3, vol. 68,

pp. 33–72. Springer, Berlin (1995)

32. Pryputniewicz, R.J.: High precision hologrammetry. Internat. Arch. Photogramm. 24,

377–386 (1981)

33. Pryputniewicz, E.J., Miller, S.L., de Boer, M.P., Brown, G.C., Biederman, R.R.,

Pryputniewicz, R.J.: Experimental and analytical characterization of dynamic effects in

electrostatic microengines. In: Proc. Internat. Symp. on Microscale Systems, Orlando,

FL, pp. 80–83 (2000)

34. Pryputniewicz, R.J.: Hologram interferometry from silver halide to silicon and

...beyond. In: Proc. SPIE, vol. 2545, pp. 405–427 (1995)

35. Pryputniewicz, R.J., Shepherd, E., Allen, J.J., Furlong, C.: University – National

Laboratory alliance for MEMS education. In: Proc. 4th Internat. Symp. on MEMS and

Nanotechnology (4th-ISMAN), Charlotte, NC, pp. 364–371 (2003)

36. Brown, G.C., Pryputniewicz, R.J.: Holographic microscope for measuring

displacements of vibrating microbeams using time-average electro-optic holography.

Opt. Eng. 37, 1398–1405 (1998)

Recent Advances in Microelectromechanical Systems and Their Applications 273

37. Klempner, A.R., Hefti, P., Marinis, R.T., Pryputniewicz, R.J.: Development of a high

stability optoelectronic laser interferometric microscope for characterization and

optimization of MEMS. In: Proc. 15th Internat. Invitational UACEM Symp.,

Springfield, MA, pp. 275–285 (2004)

38. Pryputniewicz, R.J., Marinis, R.T., Klempner, A.R., Hefti, P.: Hybrid methodology for

development of MEMS. In: Proc. IEEE-PLANS 2004, San Diego, CA, vol. 6 (2006)

39. Marinis, T.F., Soucy, J.W., Hanson, D.S., Pryputniewicz, R.J., Marinis, R.T.,

Klempner, A.R.: Isolation of MEMS devices from package stresses by use of

compliant metal interposers. In: Proc. 56th IEEE Electronic Components &

Technology Conf (56th-IEEE-ECTC), paper No. P1S25-MEMS, San Diego, CA

(2006)

40. Pryputniewicz, R.J., Champagne, R.P., Angelosanto, J.P., Brown, G.C., Furlong, C.,

Pryputniewicz, E.J.: Multivariable MEMS polysilicon piezoresistive sensor: analysis

and measurements. In: Proc. Internat. Symp. on Microscale Systems, Orlando, FL, pp.

72–75 (2000)

41. Pryputniewicz, R.J.: Thermomechanics of high-pressure MEMS sensors. In: Paper No.

IPACK 2007-33507, ASME – Am. Soc. Mech. Eng., New York, NY (2007)

42. Mihailovich, R.E., Kim, M., Hacker, J.B.H., Sovero, A., Studer, J., Higgins, J.A.,

DeNatale, J.F.: MEM relay for reconfigurable RF circuits. IEEE Microwave Wireless

Components Lett. 11, 53–55 (2001)

43. Pryputniewicz, R.J., Pryputniewicz, E.J.: Quantitative characterization of microsystem

dynamics. In: Paper No. IPACK 2007-33503, ASME – Am. Soc. Mech. Eng., New

York, NY (2007)

44. Pryputniewicz, R.J.: Advances in optoelectronic metrology: from milliscale to

nanoscale applications. In: Proc. 7th Internat. Symp. on MEMS and Nanotechnology

(7-ISAMAN), St. Louis, MO, pp. 1–17 (2006)

45. Zunino III, J.L., Skelton, D.R., Han, W., Pryputniewicz, R.J.: Hybrid approach to

MEMS reliability assessment. In: Paper No. SPIE6563-03, Proc. Internat. Symp., on

MOEMS-MEMS 2007: Reliability, Packaging, and Characterization of MEMS, San

Jose, CA (2007)

46. Skelton, D.R., Zunino III, J.L., Han, W., Pryputniewicz, R.J.: MEMS reliability

assessment: preliminary results. In: Paper No. 318, Proc.8th Internat. Symp., on

MEMS and Nanotechnology (8-ISMAN), Springfield, MA (2007)

47. Marinis, T.F.: The future of microelectromechanical systems (MEMS). Strain 45, 208–

220 (2009)

Experimental Mechanics in Nano-engineering

Cesar A. Sciammarella

, Federico M. Sciammarella

, and Luciano Lamberti

College of Engineering & Engineering Technology

Northern Illinois University, DeKalb, USA

Dipartimento di Ingegneria Meccanica e Gestionale,

Politecnico di Bari, Bari, Italy

csciammarella@niu.edu, sciammarella@niu.edu,

lamberti@poliba.it

Abstract. A new renaissance in the field of Experimental Mechanics is well

underway because of the recent technologies developed for Nano-Engineering.

There are many challenges to face and overcome when going from the macro

world to the manipulation of nano-objects. In the macro world, with the

experience gained in the last century and the development of numerical

techniques, Experimental Mechanics has changed its initial role of an analogical

tool to solve difficult differential equations to a complementary methodology to

support numerical techniques in handling complex boundary condition effects in

static or dynamic problems. Experimental Mechanics is also a very important tool

in materials science research. With the introduction of Nano-Engineering,

Experimental Mechanics has experienced a vast expansion in its applications to

understand an almost completely new field where both basic physical properties

that have a well established statistical meaning in the macro world and

fundamental formulations require a revision and in many cases new theoretical

developments.

Since theories must be supported by experimental evidence, Experimental

Mechanics represents a necessary basic tool to lay the foundations to

understanding properties and behavior of materials at the nano-level. There are

well established tools that allow events at the nano-level to be observed: for

example, X-rays with new developments in holographic interferometry done with

X-rays. Electron microscopy also has been extended to the field of holographic

interferometry. Optics with its versatile photons appears also as a promising tool

in many cases where X-rays or electron microscopy become difficult or

impossible to apply. However, the classical resolution limitations confined for a

long while optics to be used in the range of hundreds of nanometers. New recent

developments have opened a new window of opportunity for optical techniques to

be applied in the nano-range. This chapter will cover these recent developments.

The essential theoretical aspects that make it possible to go beyond the classical

resolution limits as well as their application in engineering problems such as

metrology, surface topography and strain determinations will be presented.

276 C.A. Sciammarella, F.M. Sciammarella, and L. Lamberti

1 Introduction and Theoretical Background

This paper is devoted to the description of methods developed to apply visible

radiation optics at the nanometric level and to the procedures of data analysis to

retrieve the information contained in the images. Classical optics has limitations

on the resolution that can be achieved utilizing optical microscopy in the

observation of events taking place at the sub-micron level, i.e. to a few hundreds

of nanometers. To overcome this limitation, a new methodology was developed.

The adopted solution is to apply non conventional methods of illumination. These

new methods are made possible by the emission of coherent light by the objects

that are under analysis. This is done through the phenomenon of light generation

produced by electromagnetic resonance. Object self-luminosity is the consequence

of electromagnetic resonance. Why self-luminosity may help us to increase

resolution? The light generated in this way has particular properties that are not

present in the light sent by an object that results from external illumination. The

produced wave fronts can travel long distances or go through an optical system

without the diffraction changes experienced by ordinary wave fronts [1-3].

1.1 Properties of Evanescent Waves

The self generation of light is achieved through the use of total internal reflection

(TIR). At the interface between two media such that the index of refraction of

medium 1 is larger than the index of refraction of medium 2 (i.e.

nn > ), if a

light beam is incident with an angle

crit,ii

θ>θ , a total reflection of the beam, in

which essentially all of the light is reflected back into the first medium, takes place

(Fig. 1a). Even though the light no longer propagates into the second medium, there

is a small amount of penetration of the electromagnetic field across the interface

between the two media. In the vector form solution of the Maxwell equations, it is

possible to show that under the condition of total reflection the electromagnetic field

does not disappear in the second medium [4]. However, there is no energy exchange

with the second medium. The components of the electromagnetic field transmitted in

the second medium, vectors E and H, depend on [4]:

⎥

⎦

⎤

⎢

⎣

⎡

−

− 1

sin

iexp

(1)

where the relative index of refraction is defined as

1212

n/nn = .

The intensity of the field decays by 1/e at the distance from the interface equal to:

sin

−

(2)

Experimental Mechanics in Nano-engineering 277

Under this condition a particular type of waves are produced in the interface

(Fig. 1a). These waves are called evanescent waves and travel at the interface

decaying exponentially in the second medium at a depth that is a fraction of the

wavelength of the utilized light as shown by Eq. (2). The decay of electromagnetic

field is sketched in Fig. 1a.

i,crit

Incident beam

Totally reflected beam

Evanescent

wave

i,crit

Incident beam

Totally reflected beam

E(z)/E

Scatte

ed waves

Fig. 1. a) Principle of formation and characteristics of evanescent waves; b) Propagation in

a dielectric medium.

As was said before, the electromagnetic field of the evanescent waves does not

propagate light in the second medium. However, if a dielectric medium or a

conducting medium comes in contact with the evanescent field, light is emitted by

the medium itself. This interaction depends on the properties, size and geometry of

the medium. In the case of a dielectric medium, through Rayleigh molecular

scattering, light is emitted in all directions as illustrated in Fig. 1b. The light

emission is a function of the electronic configuration of the medium. If the

medium is a metal, the Fermi’s layer electrons produce resonances called

plasmons. The effect is reversible, photons can generate plasmons, and the

decaying plasmons generate photons. In the case of very small dielectric objects,

the resonance takes place at the level of the bound electrons. The actual

dimensions of the crystal determine the different resonances and light at

frequencies different from the frequency of illuminating light is generated.

According to the Quantum Mechanics principle of preservation of momentum

for the photons, some of the energy of the incident beam continues in the second

medium (the direction indicated by the blue arrow in Fig. 1b).

1.2 Super-Resolution

In the preceding paragraphs there were outlined the basic physical processes

required for light generation in an object that is within the region of influence of

evanescent fields. Now the effect of self illumination in the generation of super-

resolution images has to be considered. In general, the possibility of getting higher

resolutions depends on the energy available and on the detector spatial frequency

capability. This result was foreseen by Toraldo di Francia [5] when he postulated

that the resolution of an optical system could be increased almost continuously

beyond the classical Rayleigh’s diffraction limit, provided that the necessary

energy to achieve these results is available. When Toraldo di Francia [6] presented

278 C.A. Sciammarella, F.M. Sciammarella, and L. Lamberti

this original work it was argued that his proposed super-resolution approach

violated the Heisenberg uncertainty principle. In the discussion presented in [6]

the arguments using the Heisenberg principle, arguments that are included in

many text books of Optics, can be easily dismissed because they are based on the

wave function of a single photon while one is dealing with the wave function of

millions of photons. The question can be summarized in the following way [7]. If

ΔE is the amount of energy invested in an observation and Δx is a distance to be

measured, the Heisenberg principle can be stated as follows:

xE ≥ΔΔ

(3)

where h is the Planck’s constant, c is the speed of light. This equation tells us that

by increasing the energy there is no limit to the smallness of the distance that can

be measured. From the practical point of view, it implies that increases in

smallness of the distance that one wants to obtain will require enormous increases

in the energy that has to be invested. This is because in Eq. (3) there is a large

factor: the speed of the light c. From a more direct type of approach, one can say

that information is encoded in the interference patterns of the evanescent wave

fronts transformed into propagating wave fronts. Whatever signal can be

recovered above the noise level, it will contain some type of information that may

be extracted within certain practical limits that have been analyzed. This is a

general argument that applies to all types of electromagnetic radiation.

There is another important application of the Heisenberg principle that is more

relevant to the topic of this chapter and has been pointed out by Vigoureux [8].

This relationship is:

πΔΔ 2kx

(4)

The wave propagation vector has two components

and

. In Eq. (4),

the wave vector component in the x-direction. Vigoureux shows that for waves

propagating in the vacuum Eq. (4) leads to the Rayleigh limit of λ/2. In order to go

beyond the λ/2 limit, one must have values of

falling in the field of evanescent

waves. Therefore, to capture evanescent waves is an effective approach to getting

super-resolution. This conclusion is in agreement with the conjecture made by

Toraldo di Francia in 1952.

A further mathematical argument can be made by resorting to a Fourier

expansion of the solution of Maxwell equations. In the classical optics scheme of

plane-wave solutions of the Maxwell equations, monochromatic waves with

definite frequencies and wave numbers are considered. This idealized condition

does not apply in the present case. One can start from the Fourier solution of the

Maxwell equations in the vector field (time-space):

∫

∞+

∞−

τω

=τ dke)k(A

),x(E

)k(i

ikx

(5)