Kounadis A.N., Gdoutos E.E. (Eds.) Recent Advances in Mechanics

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Recent Advances in Microelectromechanical Systems and Their Applications 259

such, is critical to implementation of this methodology for development of MEMS

as discussed herein.

Therefore, to minimize this influence, a number of algorithms for determination

of Ω were developed. Some of these algorithms require multiple recordings of

each of the two states, in the case of double-exposure method, of the object being

investigated with introduction of a discrete phase step between the recordings

[3,33]. For example, the intensity patterns of the first and the second exposures,

(x,y) and I’

(x,y), respectively, in the double-exposure sequence, can be

represented by the following equations [7]:

() ()()

()

[]

()

[]

{}()

[]

{}

nro

ron

yxyxIyxI

yxIyxIyxI

θϕ

+Δ+

++=

,cos,,2

,,,

2/1

(6)

and

() ()() ()

[]

()

[]

{}

()

[]

(){}

,,,cos

,,2,,,

2/1

yxyx

yxIyxIyxIyxIyxI

roron

Ω++Δ×

×++=

θϕ

(7)

where I

(x,y) and I

(x,y) denote the object and the reference beam intensities,

respectively, with (x,y) representing spatial coordinates, Δφ(x,y) = φ

(x,y)- φ

(x,y)

is the optical phase difference based on φ

(x,y), denoting random phase of the light

reflected from an object, and φ

(x,y), denoting the phase of the reference beam, θ

represents the discrete applied n

phase step, and Ω(x,y) is the fringe-locus

function relating to the displacements/deformations that an object incurred

between the first and the second exposures; Ω is what we need to determine.

When Ω is known, it is used in Eq. 2 to find L.

In the case of the 5-phase-steps algorithm with θ

=0, π/2, π, 3π/2, and 2π, the

distribution of the values of Ω(x,y) can be determined using [7]

()

() ()

[]

()()()

,,,2

,,2

tan,

513

⎭

⎬

⎫

⎩

⎨

⎧

−−

−

=Ω

−

yxIyxIyxI

yxIyxI

(8)

Results produced by Eq. 8 depend on capabilities of the illuminating, the

imaging, and the processing subsystems of the OEH system used in a specific

application. Developments in laser, fiber optic, CCD camera, and computer

technologies have led to advances in the OEH methodology; in the past, these

advances have almost paralleled the advances in the image recording media [34].

These developments resulted in educational procedures [2] and led to MEMS

education alliance [35].

In response to the needs of the emerging MEMS technology, an optoelectronic

laser interferometric microscope (OELIM) system for studies of objects with

micron size features was developed [36,37], Fig. 12.

260 R.J. Pryputniewicz

Fig. 12. OELIM configuration used herein.

3.3.1 OELIM System

In the OELIM system, Fig. 12, light beam produced by a laser illuminator is

directed into a directional beam splitter cube, which produces an object beam that

is sent into an interferometric objective with PZT phase stepper controlled

microscope lens. The lens, in turn, illuminates MEMS being investigated. The

particular characteristic of the configuration shown is that its specially designed

interferometric objective has a long working distance providing ample space for

installation of an environmental chamber and/or other loading device(s), as

needed to characterize various MEMS.

It should be noted that in the implementation of the OELIM system used in this

study, the environmental chamber permitted simultaneous control of pressure/

vacuum, temperature (heating and cooling), as well as dynamic excitation (needed

for vibrations) of the test samples being characterized/developed.

In the configuration of Fig. 12 the object beam reflected by the MEMS passes

back through the objective to the beam splitter cube where it is combined with a

reference beam. The two beams, recombined at the beam splitter, are imaged onto

the sensing element of a CCD camera, which digitally records intensity

distributions of the resulting interference patterns. These patterns are transferred

to the system computer for subsequent quantitative processing to determine Ω(x,y)

according to Eq. 8, which is needed to determine L based on the use of Eq. 2.

Recent Advances in Microelectromechanical Systems and Their Applications 261

4 Representative Results

The optoelectronic methodology described in the preceding Section was used to

determine displacements and deformations of the MEMS samples described in the

Section 2. Results of these determinations are summarized in Sections 4.1 to 4.4,

respectively.

4.1 Motions of HRS Microengine

Using the analytical model [8,13,32], forces acting on the microengine during its

operation were calculated to be a nonlinear function of rpm indicating that the

force increases at an increasing rate as the rotational speed of a microengine

increases; for example this function indicates that at 6,000 rpm magnitude of the

force acting on a connecting pin is 4 nN while at 500,000 rpm it is 27 μN.

Forces generated during operation of a microengine, load the drive gear and make

it wobble as it rotates around its shaft. A unique capability to measure this wobble is

provided by the OELIM methodology. Typical results obtained for two different

positions in a rotation cycle of the drive gear are shown in Fig. 13, where fringe

patterns vividly display changes in magnitude and direction of the displacements of

the microgears. These displacements, based on the fringe patterns of Fig. 13 vary in

magnitude from 0.8 μm to 1.7 μm, respectively; it should be noted that, in

comparison with these displacements, thickness of gears is about 2 μm. These

variations in displacements are due to kinematics and kinetics caused by impulsive

loading forces generated by the input signals during rotational/operational cycle. In

addition, the experimental results show that the wobble depends on the angular

position in the rotation cycle, which can be related to the forces exerted on the drive

gear by the pin during a typical operational cycle.

Fig. 13. Representative OELIM fringe patterns recorded during the study of dynamic

characteristics of microengines, at two different positions in a rotation cycle. White lines

indicate locations (a) and (b) where measurements of displacements, quoted in the text,

were made.

Operational functionality of a micromirror system depends also on the quality

of motions of section AB of the hinged micromirror, Fig. 14. OELIM was used to

measure these motions by recording fringe patterns, Fig. 15, which were, in turn,

interpreted to determine deformations/motions of the section AB of the

micromirror, Fig. 16.

(a) (b)

262 R.J. Pryputniewicz

100 µm

Fig. 14. Measurements were made on the

AB section, 100 μm wide and about 400 μm

long, of a hinged micromirror.

Fig. 15. Representative OELIM fringe pattern

of the AB section of a hinged micromirror,

shown in Fig. 14.

Fig. 16. Wireframe representation of absolute shape and deformations/motions of the

section AB of a hinged micromirror, corresponding to the upright position displayed in Fig.

3. Measurements show that the micromirror displacements range from 0 μm at hinge B to

113 μm at hinge A at which there is also a tilt of 18 mrad, based on results of Fig. 17.

Using Fig. 16, detailed information about deformations/motions of a

micromirror can be obtained, Fig. 17. This figure displays traces that were made

parallel to the long edges of section AB of the micromirror. Noticeable

differences between the two traces were measured and led to estimate of a tilt of

18 mrad at the hinge A.

100

120

0 50 100 150 200 250 300 350 400

X- P O S I TIO N, µ m

Z-POSITION, µ

y=4 µm

y=95 µm

Fig. 17. Vertical displacements (Z-POSITION) of section AB as a function of position

along the length (X-POSITION) of a micromirror as determined from traces parallel to the

long edges of the wireframe display of Fig. 16, resulting tilt of 18 mrad was determined at

hinge A (on the left side) of section AB shown in Fig. 14.

Recent Advances in Microelectromechanical Systems and Their Applications 263

4.2 Deformations of a Microgyroscope

Deformations of proof masses/shuttles were measured during operation of a

microgyroscope. In this application, interferograms were recorded stroboscopically

while microgyros were driven at their operating frequencies. To facilitate these

recordings, the optoelectronic system was set up to be sensitive to the out-of-plane

motions. Representative interferograms, corresponding to deformations of the left

shuttle, while a microgyro was operating at 10.1 kHz are shown in Fig. 18.

Observation of the fringe patterns of this figure clearly indicates asymmetry in

deformations of the proof mass(es) of a microgyroscope. This can be related to

structural design and suspension of the shuttles as well as to the way that

electrostatic forces affect their motions and deformations. A representative

display of deformations of the left shuttle of a microgyro operating at 10.1 kHz,

during a specific instant in a vibration cycle, is given in Fig. 19, indicating

deformations ranging up to 212 nm, which ideally should not exist. However, the

deformations/motions were measured, in this case, to be orders of magnitude

greater than typical (magnitudes of) motions of the proof masses due to the

Coriolis forces.

Fig. 18. Representative OELIM fringe patterns of the

left shuttle, at different times in a vibration cycle,

while a microgyro is operating at 10.1 kHz.

Fig. 19. The out-of-plane 212 nm

deformation component of the left

shuttle, based on Fig. 18.

Accuracy and precision of a microgyro depends on the quality of its

suspension. This suspension is provided by folded springs attached, at one end, to

proof masse/shuttle and, at the other end, to a post forming a part of a substrate,

Fig. 20a. Any deformations of the springs that are not in response to functional

operation of a sensor will cause an incorrect (i.e., erroneous) output. For example,

thermomechanical distortions of a package affect shape of posts and these, in turn,

lead to undesired deformations of the springs and erroneous results produced by a

sensor supported by these springs [3]. Because of the nanoscale of these

deformations and microsize objects over which they take place, it was not until the

advancement of optoelectronic metrology that such deformations were quantified

in the FFV, Fig. 20. This figure shows that the thermomechanical deformations of

a post are on the order of 40 nm [37].

Functional operation of MEMS microgyros (usually) depends on motion of a

proof mass in response to an applied load. The proof masses of a microgyro are

(typically) suspended by folded springs: one spring in each corner of a proof

264 R.J. Pryputniewicz

Fig. 20. OELIM measurements of thermomechanical deformations of a post in a

microgyro: (a) dual shuttle configuration with the rectangle indicating one of the posts, (b)

interference fringe pattern over the post section selected in part (a), (c) contour

representation of deformations corresponding to the fringe pattern shown in part (b) -

horizontal line HH indicates the trace along which deformations of the post were

determined, (d) deformations determined along the line HH of part (c).

mass/shuttle, Fig. 5. Because of advances in design, suspension springs that have

several folds (or turns) were implemented. These multi-fold spring configurations

allow compact design of MEMS, which facilitates a fast response. Figure 21

displays representative deformations of the upper-right folded spring supporting

the left proof mass of a microgyro, as measured using the OELIM methodology

[38]. These deformations are about 300 nm, over the section of the microgyro

displayed in the figure. More specifically, the folded spring, shown in Fig. 21,

deforms approximately 126 nm between the point where it is attached to the post

and the point of its attachment to the proof mass. The proof mass itself has the

deformation of about 174 nm. To mitigate adverse effects of packaging, new

design/fabrication approaches are being developed [39].

Fig. 21. OELIM measured thermomechanical deformations of the upper-right section of the

left proof mass of a MEMS gyroscope, Fig. 5, maximum deformation is 300 nm: 2D

contour representation.

Recent Advances in Microelectromechanical Systems and Their Applications 265

4.3 Deformations of a Pressure Sensor

Using the specially designed test fixture, the MEMS PPSs were subjected to high

pressure side (HPS) and low pressure side (LPS) loads [17,40]. These loads

ranged from the rest (i.e., reference) pressure, set at atmospheric, up to 100 psig

[41]. Representative OELIM fringe patterns, corresponding to deformations of the

diaphragms subjected to these loads, are shown in Figs 22 and 23.

It should be noted that the absolute shapes of the diaphragms at rest, Figs 22a

and 23a, influence their response to the applied pressures. That is, deformed

shapes of a specific diaphragm are different under HPS and LPS loads of the same

magnitude as, e.g., can be seen comparing Figs 22b and 23b. Both of these figures

show OELIM fringe patterns of the diaphragms subjected to the loads having the

magnitude of 10 psig. Based on previous studies [17], deformations of the

diaphragms due to HPS and LPS loads of this magnitude are unobstructed. Yet,

the fringe patterns vividly indicate different deformation patterns because of

influence that the initial shape, due to the residual stresses that developed while

fabricating these MEMS, has on their operational performance.

Clearly, as the load magnitudes increase so do the deformations of the diaphragms.

)

Fig. 22. Representative OELIM fringe patterns

corresponding to the HPS loadings of: (a) 0

psig (rest state), (b) 10 psig, (c) 20 psig, (d) 40

psig, (e) 80 psig, and (f) 100 psig.

Fig. 23. Representative OELIM fringe patterns

corresponding to the LPS loadings of: (a) 0

psig (rest state), (b) 10 psig, (c) 20 psig, (d) 40

psig, (e) 80 psig, and (f) 100 psig.

266 R.J. Pryputniewicz

Figure 22c shows that at the HPS load of 20 psig the diaphragm has already

reached the bottom of the cavity and rests on it. Increasing pressure beyond 20

psig flattens the diaphragm and makes its sides steeper as displayed by

corresponding fringe patterns. Also, the diaphragm begins to fill the etch holes

located at the bottom of the cavity, as can be seen from the fringe patterns. This is

also illustrated in Fig. 24 showing deformations measured along the longitudinal

line LL through the center of the diaphragm subjected to the HPS load of 100 psig,

for which the OELIM fringe pattern is displayed in Fig. 22f.

Examination of Fig. 23 shows that, because there is no mechanical stop on the

LPS, the diaphragm deforms without any obstructions reaching maximum

deformation/displacement of 3.458 μm at the LPS load of 100 psig (Fig. 23f).

This result is in good correlation with the maximum deformation/displacement of

3.724 μm determined computationally using the FEM model, Fig. 25;

representative von Mises stress field, based on the FEM half-model, is displayed

in Fig. 26.

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0 50 100 150 200 250 300 350 400 450 500 550 600 650

POSITION ALONG THE DIAPHRAGM, µm

DEFORMATION, µm

Fig. 24. Deformations of a DP diaphragm along the longitudinal line LL through the center

of a diaphragm, corresponding to the HPS load of 100 psig (see Fig. 22f).

Fig. 25. Representative 3D deformations of

a DP diaphragm subjected to the LPS load

of 100 psig, based on the FEM analysis,

half-model representation was used because

of the design symmetry of the sensor.

Fig. 26. Representative von Mises stress field

of a multilayer DP diaphragm subjected to

the pressure of +10 psig, based on the FEM

analysis, half-model representation was used

because of the design symmetry of the

sensor.

Recent Advances in Microelectromechanical Systems and Their Applications 267

Previous results, determined along the longitudinal lines through the center of

the diaphragm, indicate that the deformations at rest range from –20 nm to +90

nm, for the PPSs considered [40]. Furthermore, at the positive and the negative

differential pressures of the magnitude of 10 psig, these deformations are +813 nm

and –792 nm, respectively, i.e., they display a 21 nm difference, although

(according to the fundamental theories) they should be identical, i.e., the

difference should be 0. This data is essential for proper quantitative interpretation

of the signals produced by a MEMS PPS.

Using OELIM methodology, deformations of a PPS diaphragm can be

measured as a function of increments in pressure, both, along the longitudinal and

transverse lines, LL and TT, respectively, to facilitate their correlation [40].

FEM model of a MEMS PPS was developed in this study [40]. This model

incorporates the multilayer structure of a diaphragm and accounts for material

properties of each layer. It also incorporates the strain gages and their operational

characteristics. Because of the design symmetry of the sensor, half-model of the

diaphragm was used to facilitate/speed up the solution of cases considered.

The FEM model was used to determine response of a PPS to a variety of the

applied pressure and temperature conditions. It was also used to study the

structure of a diaphragm and the effects that the strain gauges have on its response

to the applied pressure and temperature loads [41]. Comparison of the

computational and experimental results on MEMS PPSs shows good correlation,

well within the uncertainty limits.

4.4 Deformations of a Cantilever Microcontact

MEMS RF switches present a promising technology for high-performance

reconfigurable microwave and millimeter wave circuits [42]. Low insertion loss,

high isolation, and excellent linearity provided by MEMS switches offer

significant improvements over an electrical performance provided by conventional

p-i-n diode and metal-oxide semiconductor field-effect transistor (MOSFET)

switching technologies. These superior electrical characteristics permit design of

MEMS switched high-frequency circuits not feasible with semiconductor

switches, such as high-efficiency broadband amplifiers and quasi-optic beam

steering arrays. In addition, operational benefits arise from low power

consumption, small size and weight, and integration capability of modern RF

MEMS switches.

Effective computational simulation of an RF MEMS switch must

simultaneously combine different loads including, but not limited to, the

following: electromagnetic, electrostatic, thermal, mechanical, and aeroelastic

[19]. A representative result of such computational multiphysics modeling is

shown in Fig. 27, which indicates damping effects of air “surrounding” a

microswitch in its package.

In some applications, the damping effects displayed in Fig. 27 help control

switch dynamics and enhance tribological characteristics of the microcontacts; in

others, they adversely affect performance of the microcontacts [23].

268 R.J. Pryputniewicz

Fig. 27. Computational multiphysics simulation of an RF MEMS contact closure at

atmospheric conditions: 3D representation of air damping.

Prototype microcantilever beams were fabricated and their dynamic

characteristics were determined in real-time using optoelectronic methodology

[22]. For example, results were obtained for the 350 μm long microcantilevers.

Representative fringe patterns, corresponding to the first three flexure/bending

modes are shown in parts (a) displayed in Figs 28 to 30, respectively; these figures

exhibit maximum deformations ranging from about 3 μm down to 870 nm as

frequency increases from 14.57 kHz to 261.4 kHz; however using different

samples deformations of picometer (pm) magnitudes were recorded in a previous

study [24].

Fig. 28. OELIM measurements of a vibrating MEMS cantilever – resonating at 14,570 Hz

corresponding to the first flexure mode: (a) time-average fringe pattern, (b) mode shape

based on the fringe pattern of part (a) exhibiting maximum deformation of 2.96 μm.

Fig. 29. OELIM measurements of a vibrating MEMS cantilever – resonating at 92,570 Hz

corresponding to the second flexure mode: (a) time-average fringe pattern, (b) mode shape

based on the fringe pattern of part (a) exhibiting maximum deformation of 1.68 μm.

(b)

(a)

(b)

(a)