mems-based force sensor: design and applications

20
MEMS-Based Force Sensor: Design and Applications Daniel López, Ricardo S. Decca, Ephraim Fischbach, and Dennis E. Krause Micromachined force detectors are extremely sensitive instruments capable of measuring forces as small as 10 15 N. We describe one such instrument that combines a novel micromachined torsional oscillator with an interferometric position-sensing mechanism that allows fine control of vertical scans. The design, fabrication, and operation of MEMS-based force sensors are described. The sensitivity and unique features of micromachined torsional oscillators allow us to undertake experiments that set new constraints on corrections to Newtonian gravitational forces at separations below 1 mm. Moreover, the measurements provide the most precise characterization of quantum vacuum fluctuation forces to date. © 2005 Lucent Technologies Inc. mechanical systems (MEMS) is used to describe miniature devices with characteristic dimensions on the order of 1 mm that are fabricated using integrated- circuit-like techniques. Industries as different as automaking, aeronautics, cellular communications, chemistry, acoustics, and lightwave systems are exploring the potential capabilities of these micron- sized machines. Similarly, high-sensitivity MEMS-based sensors are being used and developed in all areas of science [4, 11, 13]. Perhaps the most ubiquitous example of their use is as micromachined tips of atomic force microscopes (AFMs) [2, 24, 44]. These micro- machined cantilevers are very popular and are being used extensively as physical, biological, and chemical transducers [35]. The attractiveness of this structure resides in its simple design, its reliability and low-cost fabrication process, and its flexibility, which allows it to be used in a variety of conditions (e.g., in liquid or gaseous environments, in low or high temperatures, Introduction The development of high-sensitivity force sensors has always been associated with progress in science and technology. In science, the ability to sense small forces is of fundamental importance for the discov- ery and complete characterization of new phenom- ena. In technology, sensitive force sensors are continually used in mature and novel applications that have a profound impact on economies and on societies in general. In the late 1960s, engineers and scientists began to realize that silicon and other semiconductors could be used to fabricate not only discrete and integrated electronic circuits, but also sensors with increased per- formance and sensitivity. More recently, thanks to the development of widely available lithographic and etching technologies, the miniaturization of force sen- sors has become increasingly popular. In particular, the use of silicon micromachines as miniaturized sen- sors is just beginning to impact the most diverse areas in science and technology [3]. The term microelectro- Bell Labs Technical Journal 10(3), 61–80 (2005) © 2005 Lucent Technologies Inc. Published by Wiley Periodicals, Inc. Published online in Wiley InterScience (www.interscience.wiley.com). • DOI: 10.1002/bltj.20104

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Page 1: MEMS-based force sensor: Design and applications

MEMS-Based Force Sensor: Design and ApplicationsDaniel López, Ricardo S. Decca, Ephraim Fischbach, and Dennis E. Krause

Micromachined force detectors are extremely sensitive instruments capableof measuring forces as small as 1015 N. We describe one such instrumentthat combines a novel micromachined torsional oscillator with aninterferometric position-sensing mechanism that allows fine control ofvertical scans. The design, fabrication, and operation of MEMS-based forcesensors are described. The sensitivity and unique features of micromachinedtorsional oscillators allow us to undertake experiments that set newconstraints on corrections to Newtonian gravitational forces at separationsbelow 1 mm. Moreover, the measurements provide the most precisecharacterization of quantum vacuum fluctuation forces to date.© 2005 Lucent Technologies Inc.

mechanical systems (MEMS) is used to describe

miniature devices with characteristic dimensions on

the order of 1 mm that are fabricated using integrated-

circuit-like techniques. Industries as different as

automaking, aeronautics, cellular communications,

chemistry, acoustics, and lightwave systems are

exploring the potential capabilities of these micron-

sized machines.

Similarly, high-sensitivity MEMS-based sensors

are being used and developed in all areas of science

[4, 11, 13]. Perhaps the most ubiquitous example

of their use is as micromachined tips of atomic

force microscopes (AFMs) [2, 24, 44]. These micro-

machined cantilevers are very popular and are being

used extensively as physical, biological, and chemical

transducers [35]. The attractiveness of this structure

resides in its simple design, its reliability and low-cost

fabrication process, and its flexibility, which allows it

to be used in a variety of conditions (e.g., in liquid or

gaseous environments, in low or high temperatures,

IntroductionThe development of high-sensitivity force sensors

has always been associated with progress in science

and technology. In science, the ability to sense small

forces is of fundamental importance for the discov-

ery and complete characterization of new phenom-

ena. In technology, sensitive force sensors are

continually used in mature and novel applications

that have a profound impact on economies and on

societies in general.

In the late 1960s, engineers and scientists began

to realize that silicon and other semiconductors could

be used to fabricate not only discrete and integrated

electronic circuits, but also sensors with increased per-

formance and sensitivity. More recently, thanks to the

development of widely available lithographic and

etching technologies, the miniaturization of force sen-

sors has become increasingly popular. In particular,

the use of silicon micromachines as miniaturized sen-

sors is just beginning to impact the most diverse areas

in science and technology [3]. The term microelectro-

Bell Labs Technical Journal 10(3), 61–80 (2005) © 2005 Lucent Technologies Inc. Published by Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com). • DOI: 10.1002/bltj.20104

Page 2: MEMS-based force sensor: Design and applications

62 Bell Labs Technical Journal

from the axis of rotation (see Figure 1). When

torsional motion is induced in the suspended plate by

the action of an external force, the oscillator plate will

rotate an angle u that can be quantified by using one

or both of these electrodes.

The restoring torque associated with uniform and

small rotations of the plane around the axis defined

by the springs is given by

(1)

Assuming the structure has uniform thickness,

(2)

Here u is the angle of rotation in radians, G is the

modulus of rigidity, l is the length of the torsional

element (see Figure 1) and K is a geometrical factor

that takes into account the geometry of the torsional

elements.

If the torsional springs have a rectangular cross

section with then K is given by [40]

(3)

If the torsional springs have a rectangular cross section

with w t, then K is given by [40]

(4)

For the particular case of torsional springs with square

cross section (i.e., w t),

The spring constant of a straight rod under bend-

ing motion (i.e., a cantilever) is governed by [40]

(5)

where I is the moment of inertia, which in our case

is proportional to wt3. Notice that for devices with

the beam bending is in the “hard” direction.w 6 t

kbending 3EI

l3,

K Ksquare t4.

K t3w

3c1 0.63

t

wa1

t4

12w4b d .

K w3t

3c1 0.63

w

ta1

w4

12t4b d .

w t,

ktorsion aKG

lb.

T ktorsion u.

Panel 1. Abbreviations, Acronyms, and Terms

AFM—Atomic force microscopeFET—Field effect transistorLPCVD—Low-pressure chemical vapor

depositionMEMS—Microelectromechanical systemsRIE—Reactive ion etchSEM—Scanning electron microscope

in the presence of high magnetic fields, and in high-

radiation settings).

In this paper, we describe the fundamentals and

applications of alternative micromachined force sen-

sors that have advantages over cantilever transduc-

ers. The MEMS-based force sensors described in this

paper are micromachined torsional oscillators. These

sensors present a low coupling with the environment

while maintaining a large quality factor Q. The effect

of external vibrations is considerably reduced, when

compared to cantilever oscillators, due to the intrin-

sically lower coupling of a torsional oscillator to modes

that involve a displacement of the center of mass.

Moreover, these sensors can be designed to have

extremely high force sensitivity. Indeed, they are so

precise that their sensitivity is limited by fundamental

limits like the thermomechanical noise limit.

The sensitivity and unique features of microma-

chined torsional oscillators allow us to undertake ex-

periments that set new constraints on corrections to

Newtonian gravitational forces at separations below

1 mm. In order to investigate the nature and charac-

teristics of these forces, we need a force sensor that

allows measuring the interaction between two bodies

when the distance between them is reduced below

1 mm. In this paper, we describe a torsional MEMS

sensor that achieves a force resolution of 1015 N at

room temperature with a quality factor Q of several

thousands.

We show in this paper that MEMS-based force

sensors are ideal force detectors and that the force

sensitivity they provide is orders of magnitude better

than that previously achieved.

MEMS DesignIn this section, we discuss the design of a simple

micromachined torsional structure that can be used as

the sensor element in a MEMS-based force sensor.

A typical micromachined oscillator (see Figure 1)

consists of a micromachined plate suspended by tor-

sional elements above a substrate. These torsional

elements are springs in the form of either straight rods

of uniform cross section or serpentines. Serpentines

are advantageous because, for the same sensitivity,

they can be arranged in a more compact structure. In

addition, a couple of electrodes used for sensing and

actuation are located underneath the plate and away

Page 3: MEMS-based force sensor: Design and applications

Oscillatorplate

Oscillatorplate

Electrode

Torsion rod

l

L

w

The SEM image is from a micromachined oscillator with dimensions 500 m 500 m 3.5 m.

W

Figure 1.Torsional structure with rectangular plate and electrodes below.

Bell Labs Technical Journal 63

In order to optimize the mechanical behavior of

the oscillator, the torsional springs should have the

right compliance with respect to the rotation of the

plate about the appropriate axis and they must also

exhibit sufficient stiffness to limit the excitations of

other modes of motion. Both longitudinal and trans-

versal serpentine springs (see Figure 2) have sections

that are mainly in torsion and sections that are mainly

in bending. In the transversal serpentine spring bend-

ing dominates, while in the longitudinal configura-

tion most of the structure is in torsion.

The factor G is related to the physical properties of

the materials used in the torsional elements. G is

connected to the Young’s modulus E and Poisson’s

ratio n by

For silicon, E 130 GPa and n 0.22; consequently

MPa.

The torsional resonant frequency of the oscilla-

tor is given by

(6)

In equation 6, I is the moment of inertia of the oscil-

lator. For a thin rectangular plate [40]

I mW2

12

LW3tr

12,

frestorsion fo

1

2p Bktorsion

I.

G 50

G E

2(1 n).

Page 4: MEMS-based force sensor: Design and applications

Torsion

L

L

L

Torsion

Bending Bending

Figure 2.Basic spring types suitable for use in MEMS oscillators.

64 Bell Labs Technical Journal

where m is the oscillator’s mass, r is its density and L,

W and t are, respectively, the length, width, and thick-

ness of the oscillator plate.

MEMS FabricationThe most standard processes for MEMS fabrica-

tion are bulk and surface micromachining. A detailed

description of these processes can be found in [32]

and [45]. In order to make clear the basic structure of

our oscillators, we present a short description of the

process used to fabricate them. The MEMS oscillators

used in our experiments were fabricated using a

three-layer monolithic surface micromachining

process. A sketch of the microfabrication process flow

is shown in Figure 3.

The process begins with 100 mm n-type (100) sil-

icon wafers of 1–2 cm resistivity. The surface of the

wafers is first heavily doped with phosphorus in a

standard diffusion furnace using POCl as the dopant

source. This reduces or prevents charge feed through

to the substrate from electrostatic devices on the sur-

face. Next, a 0.6 mm low-stress low-pressure chemical

vapor deposition (LPCVD) silicon nitride layer is de-

posited on the wafers as an electrical isolation layer.

This is followed directly by the deposition of a 0.5 mm

LPCVD polysilicon film, Poly 0. Poly 0 is then pat-

terned by photolithography, a process that includes

coating the wafers with photoresist, exposing the pho-

toresist with the appropriate mask, and developing

the exposed photoresist to create the desired etch

mask for subsequent pattern transfer into the under-

lying layer. After the photoresist has been patterned,

the Poly 0 layer is etched in a reactive ion etch (RIE)

system. This polysilicon level is used to define the

electrodes, wiring, and ground contacts.

A 2 mm silicon oxide sacrificial layer is then de-

posited by LPCVD and annealed at 1050 °C for 1 hour

in argon. This layer of SiO2, known as first oxide, is re-

moved at the end of the process to free the first me-

chanical layer of polysilicon. The sacrificial layer is

lithographically patterned with the “dimples” mask

and the dimples are transferred into the sacrificial SiO2

layer by RIE. The nominal depth of the dimples is

750 nm.

The wafers are then patterned with the third

mask layer, ANCHOR1, and reactive ion etched. This

step provides anchor holes that will be filled by the

Poly 1 layer. After ANCHOR1 has been etched, the

first structural layer of polysilicon (Poly 1) is deposited

at a thickness of 2.0 mm.

Page 5: MEMS-based force sensor: Design and applications

Wafer/SiN/Poly0 Etching of Poly11. 6.

2. 7.

3. 8.

4. 9.

5. 10.

Etching of Poly0 to defineelectrodes and ground

Deposition and etchingof second oxide

Etching of oxide to definedimples and anchors

Deposition of metal

Deposition of Poly1 HF release

Deposition of first oxide Deposition and etchingof Poly2

Figure 3.Sketch of a typical three-layer surface micromachining process.

Bell Labs Technical Journal 65

Subsequently, this layer of polysilicon is litho-

graphically patterned and etched using RIE tech-

niques. Once again, another film of SiO2 is deposited,

patterned, and etched, and this is followed by the

deposition, patterning, and etching of the second

structural polysilicon film.

To reduce stress in the structural films, the wafer

is annealed at high temperatures. Then, a 0.5 mm

Page 6: MEMS-based force sensor: Design and applications

Figure 4.Schematic of the experimental setup showing its main components: micromachined oscillator and metallic sphere.

66 Bell Labs Technical Journal

thick metal layer (Cr/Au) is deposited to create bond

pads and electrical connections.

Finally, the devices are immersed in HF acid to

selectively dissolve the SiO2 (i.e., the sacrificial lay-

ers) without etching the polysilicon (i.e., the struc-

tural layer).

A CO2 critical-point chamber is used to release

the devices without stiction problems. In a critical-

point dryer chamber, the temperature and pressure

of the liquid containing the MEMS devices is in-

creased beyond the CO2 critical point and, as a con-

sequence, the liquid transforms into a gas in a

continuous way, avoiding the presence of the liquid-

gas interfaces characteristic of a phase transition [32].

Experimental SetupWhen using mechanical oscillators to measure

forces, one has to confront the coupling of the oscil-

lator with environmental vibrations. Compared with

cantilever oscillators, torsional oscillators are less

sensitive to mechanical vibrations that induce a

motion of the center of mass. Moreover, the minia-

turization of the oscillators yields an improvement in

their quality factor and sensitivity [41]. Consequently,

it is advantageous to use microelectromechanical tor-

sional oscillators to measure small forces. The exper-

imental arrangement used in our experiments is

shown schematically in Figure 4. This arrangement is

general enough to be of use in any situation in which

the forces acting between two different materials must

be measured as a function of the distance separating

them. The dimensions and spring of the MEMS os-

cillator is designed to take into account the magni-

tude of the forces to be measured. The remainder of

the assembly consists of a sphere that can be brought

in close proximity to the oscillator plate (see Figure 4).

In the most general case, the sphere is evaporated

with one material and the oscillator is coated with

another. As the sphere approaches the oscillator plate,

the acting forces between the different materials

Page 7: MEMS-based force sensor: Design and applications

Bell Labs Technical Journal 67

induces a torque in the plate, forcing it to rotate

around the torsional axis. The induced angular dis-

placement of the plate can be measured using the

electrodes located below it.

The sphere used in the experiments is glued with

conductive epoxy to the side of an Au-coated optical

fiber, establishing an electrical connection between

them. The entire setup (i.e., the MEMS oscillator and

the fiber-sphere) is rigidly mounted into a can, where

low pressure (e.g., 105 Torr) can be maintained. The

can has built-in magnetic damping vibration isolation

and is mounted onto an air table. This combination of

vibration isolation systems yielded base vibrations

with zrms 0.05 nm for frequencies above 100 Hz.

The fiber-sphere assembly can be moved verti-

cally by the combination of a micrometer-driven and

a piezo-driven stage. The micromachined oscillator is

mounted on a piezoelectric-driven xyz stage which,

in turn, is mounted on a micrometer-controlled xy

stage. This combination allows positioning the coated

sphere over specific positions on the coated plate. The

separation zi between the sphere and the Si-plate is

controlled by the z axis of the xyz stage. A two-color

fiber interferometer-based closed-loop system is used

to keep zi constant. The error in the interferometric

measurements is found to be zirms 0.25 nm; it is

dominated by the overall stability of the closed-loop

feedback system. Because this error is much greater

than the actual mechanical vibrations of the system,

the closed loop is turned off while data acquisition is

in progress.

A force F(z) acting between the sphere and the

plate produces a torque

(7)

where b is the lever arm between the sphere and the

torsional axis of the micromachined oscillator (see

Figure 4). In all the cases reported in this paper,

u 105 rad 1. Under these circumstances,

(8)

where Cright (Cleft) is the capacitance between the right

(left) electrode and the plate (see Figure 4).

Consequently, the force between the two metallic sur-

faces separated by a distance z is F(z) kC, where k

is the proportionality constant.

u r ¢C Cright Cleft,

V

T bF(z) ktorsionu,

To provide a calibration of the proportionality

constant k between F and C, it is very useful to apply

a known potential difference between the coated

sphere and the MEMS oscillator. Of course, this cali-

bration needs to be done at a sphere-plate distance

that is large enough to ensure that the dominant

interaction is electrostatic in nature. In this case, the

net force can be approximated by the electrostatic

force Fe between a sphere and an infinite plane [47],

(9)

Here eo is the permittivity of free space, Vsphere is the

voltage applied to the sphere, Vo is the residual po-

tential difference between the materials when they

are both grounded, and cosh u (1 zR), where

z zmetal 2do, R is the radius of the sphere, and do is

the average separation between the layers when the

test bodies come in contact (so that zmetal 0) and is

primarily determined by the roughness of the films.

By measuring, at constant z, the angular deflec-

tion u (and hence the electrostatic force) as a func-

tion of the applied voltage difference, the minimum

in Fe can be experimentally determined. Once

the value Vo is found, the equation (9) can be used to

determine three different parameters:

• The proportionality constant k between the

sphere-plate force and the measured difference

in capacitances,

• The radius R of the coated sphere, and

• The parameter do.

By performing a dynamic measurement, we di-

rectly use the high-quality factor of the micromachined

oscillator to increase the force sensitivity [11, 19]. In

this approach, the separation between the sphere and

the oscillator plate is varied as z A cos(wres t), where

wres is the resonant angular frequency of the oscillator

and A its amplitude. The solution for the oscillatory

motion yields [11, 19],

, (10)

where for for and Fx is the

force acting between the sphere and the oscillator

plate.

QW 1vo 2ktorsionI

v2res v2

o c1 b2

Iv20

0Fx

0zd

a

n1

coth(u) n coth(nu)

sinh(nu).Fe 2peo(Vsphere Vo)

2

Page 8: MEMS-based force sensor: Design and applications

+

+–

––

––10kHz 1K 1K

560k+15V 1k

Resistors values are in Ω, capacitors are in F, and inductors are in H.

MEMST

470n

470n

470u470100

18p2V

5u

5u

10M

10M

Cright

Cleft

V1

V2

1u

20k

–15V

To lock-inamplifier

14u

14u

__

++OP2710n

AD8292SK152

2SK152

1u 2k

10k100k

100k

10n

10G 10G10

1.5k 100u 100n

10n

10n20M–

++

Bridge Amplifier

Figure 5.Schematic of the electronic circuit used to measure the difference in capacitance between the two sides of theMEMS oscillator plate.

68 Bell Labs Technical Journal

Unlike the static regime where forces are mea-

sured, in the dynamic regime the force gradient

is measured by observing the change in the resonant

frequency as the sphere-plate separation changes.

The circuit used to measure the capacitance is

schematically shown in Figure 5 [1].

The field effect transistor (FET) of the amplifier

stage is placed as close as possible to the oscillator to

minimize the effect of parasitic capacitances. The

smallest angular deviation that can be detected in this

configuration is given by

(11)

where dC is the minimum detectable change in C,

Co ≈ (eoww )dg is the capacitance between the oscil-

lator and each electrode when no forces are present

(w and w are the dimensions of the electrodes), CT

20 pF Co is the parasitic capacitance of the mea-

surement circuit (determined by the capacitance of

the FET transistor plus parasitic capacitances to

ground), dV 10 nV/Hz12 is the input noise of the

amplifier, and Vi (i 1, 2) 1 V is the DC potential

used to correct for initial asymmetries in the circuit

and linearize its response. In obtaining equation (11),

we have assumed that the plates are infinite and we

W

du dC

Co

2dg

w dV

Vi

CT

Co

2dg

w ,

0Fx0zhave used the fact that the maximum angular devia-

tion umax 1.

The effect of du on the force dFelectronic is given by

(12)

where A(v) is the frequency response of the micro-

machined oscillator for a harmonic torque with con-

stant amplitude. When taking into account the white

thermal noise dFthermal, the total noise in the force is

.

We note that, by performing a measurement at reso-

nance, dFelectronic is reduced by a factor Q. Because the

Q of micromachined oscillators in vacuum can be

quite large (i.e., several thousands), the total noise in

the force can be approximated by

(13)

where kB is Boltzmann’s constant and T is the tem-

perature. It is evident from this equation that, work-

ing at resonance, an improvement of the sensitivity

on the order of Q12 can be achieved. Moreover, the

noise in the force can be reduced by designing a

MEMS sensor with optimum ktorsion and vo.

dF(v) dFthermal 1

bB4ktorsionkBT

voQ,

dF(v) 2(dFthermal)2 (dFelectronic(v))2

dFelectronic(v) ktorsiondu

bA(v),

V

Page 9: MEMS-based force sensor: Design and applications

Spring detail

Figure 6.Scanning electron micrograph showing the MEMS oscillators and a detail of the springs used.

Bell Labs Technical Journal 69

In the particular case of the experiments described

in the next section, we have used a micromachined

oscillator 3.5 mm thick with a 500 500 mm2 heavily

doped polysilicon plate suspended at two opposite

points by serpentine springs, as shown in Figure 6.

The springs are anchored to a silicon nitride (SiNx)-

covered Si platform. When no torques are applied,

the plate is separated from the platform by a gap

mm. Two independently contacted polysilicon

electrodes located under the plate are used to measure

the capacitance between the electrodes and the plate.

For the oscillator used in these experiments, we cal-

culated the torsion spring ktorsion 9.5 1010 Nm/rad.

In our case, w 2 mm (the width of the spring), t

2 mm (the thickness of the spring), Lspring 500 mm

(the length of the spring), and ESi 130 GPa (Young’s

modulus for Si). This value is in good agreement with

2

the measured value ktorsion 8.6 1010 Nm/rad.

We used Al2O3 spheres, with nominal diameters rang-

ing from 100 mm to 600 mm. The spheres were coated

with a 1 nm layer of Cr, followed by a 200 nm

thick layer of gold. The sphericity of the Al2O3 spheres,

as measured on a scanning electron microscope

(SEM), was found to be within the specifications of

the manufacturer. As an example, a 600 mm diameter

ball was found to have an ellipsoidal shape with

major and minor semi-axes of (298 2) mm and

(294 0.5) mm, respectively. Deposition-induced

asymmetries were found to be smaller than 10 nm,

the resolution of the SEM.

The separation zmetal between the two metallic sur-

faces (see Figure 4) is given by

(14)zmetal zi zo zgap bu,

Page 10: MEMS-based force sensor: Design and applications

70 Bell Labs Technical Journal

where b is the lever arm between the sphere and the

axis of the oscillator, zo is the distance the bottom of

the sphere protrudes from the end of the cleaved fiber,

and zgap includes the gap between the platform and

the plate, the thickness of the plate, and the thick-

ness of the metal layer. An initial characterization of

zo, obtained by alternately gently touching the

platform with the sphere and the bare fiber, yielded

zo (55.07 0.07) mm. Using an AFM, we deter-

mined that zgap (5.73 0.08) mm.

ApplicationsIn this section, we describe two experiments that

show the advantages of using MEMS-based force sen-

sors. In both cases, the measurements obtained with

the MEMS sensors were superior in sensitivity to pre-

vious measurements obtained with state-of-the-art

sensors; thus, MEMS sensors appear to be a promising

technology with which to detect unexplored proper-

ties of new forces.

Considerable attention has been devoted recently

to experimental searches for new forces over ultra-

short distances [18, 22, 26, 27, 28, 31, 37]. These

experimental searches have been prompted by theo-

retical propositions suggesting that deviations from

the inverse-square law, a characteristic of Newtonian

gravity, should be evident in measurements of

gravitational forces in the sub-mm range.

Gravity was the first of the fundamental forces

(i.e., gravity, electromagnetism, the strong force, and

the weak force) to be described mathematically, but it

is still the worst characterized. The main reason

for this is that gravity is the weakest of all the funda-

mental forces. Only recently has the validity of

Newtonian gravity for objects separated by distances

500 mm been experimentally confirmed [29].

These data are extremely important in constraining

any deviation of Newtonian forces in the particular

range of distances studied. A variety of experimental

studies have been trying to measure gravitational

forces at distances smaller than 100 mm [35, 36, 46],

but they all have been limited by experimental

resolution and by background forces of a quantum

nature.

The deviations from Newtonian gravity are

characterized [23, 30] by a Yukawa-modified potential

V(r),

(15)

where VN (r) is the Newtonian gravitational potential

for two point masses m1 and m2 separated by a dis-

tance r, G is Newton’s constant, and a and l are con-

stants. The strength (relative to Newtonian) of any

new interaction is characterized by the constant a and

the range of the interaction is characterized by l. The

non-Newtonian effects are generally constrained in

the phase space a a (l).

At short distances (i.e., small l), the forces arising

from a Yukawa-modified potential are relatively

weak, because the effective interacting masses are

themselves small. Moreover, background disturbances

play a more important role than a larger distance,

making it more difficult to search for new forces over

short separations. For experiments with typical

dimensions 1 mm, the dominant background arises

from the Casimir force [8, 10], which is dominant at

short distances and has not been completely charac-

terized with the required level of precision [15]. At

separations of 100 nm, the Casimir force between

an infinite 5 mm thick Au slab and a 300 mm radius

gold sphere is about 7 orders of magnitude larger than

the Newtonian gravitational force.

In the first experiment, we measured and charac-

terized the Casimir force between two different metals

with a precision 100 times better than previous meas-

urements [11]. These experiments are useful to un-

derstand the origin and behavior of the Casimir force.

By comparing the measured Casimir force to that pre-

dicted by theory, it is possible to impose new limits on

hypothetical corrections to Newtonian gravity [15].

Since the Casimir force is much stronger than gravity

at short distances, a very precise comparison between

theory and experiments is required. Unfortunately,

the uncertainty in the dielectric properties of the sam-

ples used prevents the calculation of the Casimir force

between real bodies to an accuracy of better than a

V(r) VN(r)[1 aerl] Gm1m2

r[1 aerl],

Page 11: MEMS-based force sensor: Design and applications

0.000

The data were obtained at two different separations zbetween the metallic layers.

0.575 0.600 0.625 0.650 0.675 0.700 0.725

0.001

0.002

0.003

0.004

0.005

0.006

0.007

(m

rad

)

VAu (V)

z 3 mz 5 m

Figure 7.Dependence of the angular variation u as a function ofthe applied voltage to the sphere.

Bell Labs Technical Journal 71

few percent. In the second experiment, we used the

isoelectronic technique [33] to set limits on new forces

over the 0.1 1 mm distance scale. In this experi-

ment, we used a configuration in which the Casimir

background is minimized, allowing us to compare the-

ory with experiments more readily.

Casimir ForceThe Casimir effect is a true quantum effect. In its

simpler form, it represents the attraction between two

parallel, neutral metallic layers in a vacuum [38]. The

interaction is the direct manifestation of the zero-

point energy fluctuations modified by the presence

of boundary layers. No such interaction exists within

the field of classical electrodynamics. H.B.G. Casimir,

who published his results in 1948 (see [10]), was the

first one to deal with the infinite energy of the

vacuum fluctuations. He found that for two perfect

metallic layers separated by a distance z the Casimir

force is attractive and is given by [10, 38]

(16)

where c is the speed of light, is the Planck constant

divided by , and S is the area of the layers.

Due to the experimental difficulties of maintaining

the alignment of two parallel planes, the setup used to

measure this force is similar to the one defined in the

section “Experimental Setup,” in which one of the in-

teracting surfaces is chosen to be spherical. In this case,

using the proximity force approximation, the attrac-

tive Casimir force is given by [11, 19]

(17)

with R being the radius of the sphere.

Using the experimental configuration shown in

Figure 6, we measured, for the first time, the Casimir

force between two different metals: copper and gold.

The sphere was coated with Au, as described in the

section “Experimental Setup,” and the MEMS oscilla-

tor with 200 nm of Cu. The force between the

two metals was determined by measuring the angle u

FCsphere

p3c R

360 z3 ,

2p

FC p2Uc S240 z

4,

(proportional to C) as a function of the separation

between the layers.

The proportionality constant between F and C

was found by applying a known potential difference

between the layers, which were separated by 3 mm

and 5 mm, as described in “Experimental Setup.” The

measurements are shown in Figure 7, which illus-

trates the dependence of u and, hence, of the electro-

static force, on the applied voltage VAu.

The force between the two metals is F(z) = kC,

where C is measured to one part in 5 105 using the

bridge circuit shown in Figure 5 [1]. The constant k is

determined by equation (9) to be k 50280 6 N/F.

The electronic noise of the amplifier stage used (i.e.,

10 nV/Hz12) is equivalent to an angular deviation

109 rad/Hz12. This noise level is much smaller

than the thermodynamic noise at the measuring fre-

quency kHz fo 687.23 Hz [41]:

(18)

In equation (18), we used T 300K and the quality

factor of our oscillator Q 8000. Using these values,

a force sensitivity of dF (dtorsionSu1/2)b

1.4pN/(Hz)12 is obtained.

Su12 c 2KBTQ

p foktorsion

a fo

fb2 d 12

3 107 radHz12

Wf 10

du

Page 12: MEMS-based force sensor: Design and applications

80

60

40

20

01000800600400200

F C (

pN

)

z (nm)

(a)

z (nm)

(b)

2

1

0

1

21000800600400200

F Cth

F Cex

p (

pN

)

R 100 mR 50 m

R 150 mR 300 m

(a) Casimir force between an Au-coated sphere and a Cu-coated plate as a function of the separation z. Data fordifferent nominal radii are shown.(b) Difference between theory and experimental data for the 300 m radius sphere.

Figure 8.Casimir force: theory and experiment.

72 Bell Labs Technical Journal

Figure 7 shows that the minimum in the electro-

static force occurs for Vo 0.6325V, which reflects the

difference in the work function of the Au and Cu lay-

ers. This value was observed to be constant for z in the

range 0.2 mm to 5 mm, and it did not vary when

measured over different locations in the Cu layer.

Once the value Vo was determined, we set Vsphere

VAu Vo 0.6325V to ensure that the electrostatic

force is identically zero and that the Casimir force be-

tween the Au-coated sphere and the Cu-coated mi-

cromachined oscillator can be measured. The results

obtained are shown in Figure 8.Figure 8a shows the Casimir force for spheres of

different radii. As expected, the Casimir force decays

very rapidly with z and is strongly dependent on the

radius of the sphere. In order to compare the data

with the theoretical predictions, the expression of the

force has to be modified to include the finite conduc-

tivity of the metals and the specific roughness of the

layers [15]. A detailed description of the Casimir force

is presented in [15]. The difference between theory

and data (including roughness and finite conductivity

corrections) is shown in Figure 8b for the case of

R 300 mm. The agreement between theory and data

is extremely good over the whole range of distance.

The experimental relative uncertainty at 188 nm is

0.27%, several times lower than the most precise

experiments reported [25, 34, 39, 42, 43].

To improve the sensitivity of our experiments, we

implemented the dynamic approach described in

“Experimental Setup.” In the dynamic approach, the

vertical separation between the sphere and the MEMS

is periodically changed as z zmetal A cos(wres t).

In the current experiment, the force acting be-

tween the sphere and the oscillator plate is the

Casimir force, so, in equation (10), Fx FC. Our

MEMS oscillator has a moment of inertia I ≈ 4.6

1017 kgm2, and A was adjusted between 3 nm and

35 nm for values of zmetal between 0.2 and 1.2 mm,

respectively. We foundvo 2p (687.23 Hz) and b22I

6.489 108 kg1. With an integration time of 10s,

using a phase-lock loop circuit [14], changes in the

resonant frequency of 10 mHz were detectable [15].

This allows the force to be detected with a sensitivity

of dF 6 fN/Hz12, a factor of 3 larger than the ther-

modynamic noise. However, unlike the static regime

where forces are measured, in the dynamic regime

the force gradient is measured using the relation

shown in equation (10). The gradient is

quantified by detecting the change in the resonant

0FC0z

Page 13: MEMS-based force sensor: Design and applications

200

250

150

100

50

01000800600400

P C (

mPa

)

z (nm)

(a)

z (nm)

(b)

1.0

0.5

0.0

0.5

1.0

1000800600400

P Cth

P C

exp (

mPa

)

R 150 mR 300 m

(a) Casimir pressure between an Au-coated sphere and a Cu-coated plate as a function of the separation z. Data from twodifferent spheres are shown.(b) Difference between theory and experiment for the data obtained with the 300 m radius sphere.

Figure 9.Casimir pressure: theory and experiment.

Bell Labs Technical Journal 73

frequency as the sphere-MEMS separation changes.

Differentiating equation (17) with respect to z, one

obtains

, (19)

where is the force per unit area be-

tween two infinite metallic plates.

The experimental distance-dependence of PC (see

Figure 9) is shown in 9a for two different spheres.

Because, for all the spheres, the dynamic measurement

yields the pressure between parallel plates, all mea-

surements are expected to give the same results. The

small deviations observed arise from an incomplete

characterization of the roughness of each sphere, which

is equivalent to a shift in the separation sphere-MEMS.

This shift has been observed to be in the range of 5 nm

to 10 nm. In [15] and [19], a theoretical analysis of the

dynamic interaction, including roughness and finite

conductivity, is presented. In Figure 9b, we compared

our data with the theory for a 300 mm sphere. The ex-

perimental uncertainty at 260 nm is 0.26%, a marked

improvement on previous models [9], implying a 15%

agreement between data and theory.

Given the improved sensitivity of our measure-

ments of the Casimir interaction, we can set more

PC(z) (FCS)

0FC

0z 2p RPC(z)

strict limits on new forces acting over short separa-

tions. Using the difference between theory and ex-

periment shown in Figure 8b, we obtained [19] al

200 nm, 1013, which represents an improvement by

a factor of 4 over previously reported limits [21]. The

new results are summarized in Figure 10.In Figure 10, constraints from previous experi-

ments are also shown. Curve 1 was obtained by

Mohideen’s group [39], curve 2 was determined by

Lamoreaux [34], curve 3 was extracted from data

taken by Kapitulnik’s group [13], and curve 4 was ob-

tained by Price’s group [37]. In all cases, the region in

the (a, l) plane above the curve is excluded, and the

region below the curve is allowed by the experimental

results. As can be seen from Figure 10, the experiment

with a MEMS-based force sensor leads to the strongest

constraints in a wide interaction range (i.e., 56 nm

330 nm). The largest improvement, by a factor

of 11, is achieved at l 150 nm. We note that the

constraints obtained here almost completely fill in the

gap between those obtained by AFM measurements

and those obtained using a torsion pendulum. Within

this gap, the best previous restrictions were obtained

from old measurements of the Casimir force between

dielectrics, which were not as precise or reliable as

Page 14: MEMS-based force sensor: Design and applications

MEMS—Microelectromechanical systems

(meters)

Excludedby

experiments

MEMS force sensor

1

2

3

4

1020

1016

1012

108

104

100

107 106 105 104

Figure 10.Constraints on the Yukawa interaction constant aversus interaction range l obtained from Casimir forcemeasurements.

74 Bell Labs Technical Journal

those reported here for the Casimir pressure measure-

ments between metals using a micromachined oscilla-

tor [15].

Reduced Casimir BackgroundIn the experiments previously described, we

showed that, by using a very sensitive force sensor

and a detailed theoretical model of the Casimir force

[15], it is possible to infer new constraints on Yukawa

corrections to Newton’s law of gravity. Our experi-

ments produced the most precise comparison of the-

ory and experiment to date and yielded the limit

a 1013 for l 100 nm [15]. In order to improve

even further the limits on a a(l) without develop-

ing more precise theoretical calculations, it is essential

to perform experiments in which the enormous

Casimir background is suppressed.

Recently, an alternative approach that uses the

fact that Casimir forces depend mainly on the elec-

tronic properties of materials has been proposed [20,

33]. Since gravitational forces, and virtually all pro-

posed new forces, involve coupling to both electrons

and nucleons, experiments measuring force differ-

ences between materials with very similar electronic

properties (i.e., isotopes of the same element) should

be very sensitive to new interactions [33]. By measur-

ing force differences between iso-electronic materials,

the Casimir background is subtracted and detailed

modeling of the Casimir force is not required. Hence,

by comparing the force between a probe (the sphere)

and a substrate (the oscillator plate) containing two

materials with identical electronic properties, any dif-

ference in the force experienced by the two substrates

can be attributed to a force other than the Casimir.

An experiment like this can be performed with the

experimental setup described in “Experimental Setup”

by coating the plate of the micromachined oscillator

with the two different iso-electronic materials.

In the experiments reported below, rather than

using two isotopes of the same element, we compare

the force produced by two dissimilar materials like

Au and Ge covered by a thick layer of Au.

Figure 11 shows the details of the setup and the

sample used in the experiments. The left panel shows

a SEM picture of the micromachined oscillator with

the two metals evaporated symmetrically around the

rotation axis. A cross section of the metals used in

this “Casimir-less” experiment is also shown. By cov-

ering the bottom Au and Ge films with a thick layer of

Au (larger than its plasma wavelength, which is

135 nm), we can be confident that the Au-coated

sphere will “feel” the same Casimir force on both sides

of the sample. On the other hand, the gravitational

force acting on the Au sphere will change when the

probe is displaced from the Ge-covered side to the Au-

covered side. Thus, by directly comparing the forces

measured on the Au-and-Ge-coated substrate, a limit

on a a(l) can be obtained without using detailed

theories of the Casimir interaction.

Within the experimental configuration, and using

a Yukawa-like correction, as in equation 15, to the

Newtonian gravitational attraction, the difference in

force that the sphere will experience is given by [16, 17]

(20)

where G is the gravitational constant and the func-

tions KS and KP are associated with the layered struc-

ture of the sphere (S) and oscillator plate (P). These

functions are given by [16, 17]

KP [(rAu rGe)e(dPAudTi)l(1 edGel)].

KS [rAu (rAu rCr)ed SAul (rCr rS)e(dS

AudCr)l]

¢Fhyp(z) 4p2Gal3ezl RKS KP

Page 15: MEMS-based force sensor: Design and applications

Bell Labs Technical Journal 75

The densities of the materials used in our multilayer

are represented by ri and the thicknesses of the dif-

ferent materials are di.

The right panel of Figure 11 shows a SEM picture

of the MEMS oscillator with the multilayer sample de-

posited on top. In our experiment, we used a bottom

layer of Au and Ge because it gives a large mass density

difference: rGe 5.32 103 kg/m3 and rAu 19.28

103 kg/m3. This bottom layer is capped by a homoge-

neous Au layer 150 nm thick. The fact that the thick-

ness of this layer is greater than the plasma length for

Au is sufficient to ensure that the underlying Au/Ge

composite has a negligible Casimir interaction with

the Au-coated spherical probe [15]. The MEMS oscil-

lator is similar to the one we used for the Casimir

measurements described in the previous section.

During the microfabrication process, we have si-

multaneously fabricated the MEMS oscillator and the

evaporation masks that allow us to deposit metals on

selected regions of the plate (see Figure 11). Once the

micromachined oscillator is released, we flip the cor-

responding mask over the oscillator plate and the

metals are evaporated without venting the chamber.

In the first evaporation, we deposited the following

multilayer: dTi 10 nm, dGe 200 nm, dPt 10 nm,

and 50 nm of Au. The Ti layer is used to increase the

adhesion of Ge to Si and the Pt layer is used to avoid

inter-diffusion of Au and Ge. The oscillator is then re-

moved from the evaporation chamber, the mask used

for the first evaporation is returned to its original po-

sition, and the second evaporation mask is flipped

over. The second evaporation is similar, the only dif-

ference being that an Au layer replaces the Ge layer:

dTi 10 nm, dAu 200 nm, dPt 10 nm, and 50 nm

of Au.

Once the second evaporation is done, a final

evaporation consisting only of Au is performed on top

of the previous multilayers. This last Au layer and the

final 50 nm of Au of the multilayers constitute .

In order to obtain maximum sensitivity to the

force, we used a dynamic technique in our measure-

ment of the force difference between the sphere and

the two sides of the oscillator. It would be desirable to

move the sphere parallel to the rotation axis of the os-

cillator plate, while keeping z constant, at a frequency

coincident with the resonant frequency of the oscilla-

tor. The problem with this approach is that the reso-

nant frequency of our MEMS device ( fo 700 Hz) is

dPAu

A cross section of the multilayer sample used is shown in the upper middle panel.

Pt

Ti

Figure 11.Scanning electron micrograph and schematic of the MEMS torsional oscillator used in the Casimir-less experiment.

Page 16: MEMS-based force sensor: Design and applications

76 Bell Labs Technical Journal

too large and moving the sphere over several tens of

microns at this frequency is experimentally compli-

cated. An analysis of equation (20) provides a solution

to this problem: the sphere is harmonically moved over

the interface at a frequency fx such that it will see an ef-

fective mass density described by a square-wave func-

tion with a characteristic angular frequency wx. In

practice, we used the electrodes under the oscillator

to induce an oscillation such that the separation be-

tween the sphere and the plate changes as zm zmo

dz cos(wz t) with zmo dz. Simultaneously, we moved

the micromachined oscillator’s stage along a direction

parallel to its axis (x-axis) such that the effective mass

density under the sphere is

(21)

where r (rAy rGe)2 and is the square-

wave function with characteristic angular frequency

wx. Introducing the above expressions in equation

(20), we find the time dependence of the force dif-

ference detected by the sphere

(22) a

k0

1

k!c (dz cos(wzt))

ld k,

¢Fhyp(zm, t) ¢Fhyp(zmo) ¢r ¢r(t)

2¢r

(t)

reff ¢r ¢r (t),

W

By selecting wz wx wr, the Fourier component at

wr of equation (22) is the only one providing a

significant signal-to-noise ratio. By using this hetero-

dyne technique, the signal to detect is at fr even

though no parts in the system are moving at this fre-

quency. For our experiment, we select fx (wx2p)

(wr140p) fr70 10 Hz. The signal at fz fr fx is

used to excite the oscillator plate, while the signal fx is

used to move it laterally along the x-axis.

In our experiments, the lateral displacement was

varied between 50 mm and 150 mm and the vertical

amplitude was 5 nm. The minimum detectable force

measured with this heterodyne technique (see

Figure 12) is shown in 12a.

We determined the root mean square value of the

force for integration times t ranging from 0.1 to

2000 sec. As is evident in Figure 12a, the results ob-

tained for are well described by the thermo-

dynamic limit in conjunction with the electronic

noise. For integration times larger than 3 seconds, the

root mean square value of the force starts to deviate

from this limit and for the measured force

becomes independent of the integration time t. The z

dependence of this integration-time-independent

force is shown in Figure 12b. Although the experi-

mental data show a finite force forF (t 200s, z)

t 7 200s

t 6 3s

F

(a) Minimum detectable force as a function of the integration time. Data are shown for a 50 m radiussphere at different separations of the sphere and the multilayered sample z.(b) Dependence of F

– measured at 100s as a function of the separation of z.

F– (N

)

1E-14

1E-15

1E-160.1 1 10

(s)

(a)

100 1000

F– (fN

)

6

1

2

3

4

5

100 200 300

z (nm)

(b)

400 500

z 300 nmz 500 nm

z 150 nm

Figure 12.Force as a function of integration time and sample separation.

Page 17: MEMS-based force sensor: Design and applications

Bell Labs Technical Journal 77

finite separations z, several experimental facts and un-

certainties prevent us from concluding that it origi-

nated from new physics. The large magnitude and

strong distance-dependence of this force indicate that

its origin is not Newtonian in nature. For the geome-

try used in our experiment, the Newtonian force

should have a magnitude of N and should be

independent of the separation sphere-plate. is not

associated with magnetic impurities in the materials,

because these forces are much smaller than the sen-

sitivity of our apparatus [13]. Moreover, it is not in-

duced by vibrations, because it takes a constant value

at a fixed separation, independent of t.

Some possible experimental errors that may have

an effect on the force detection are listed below:

• A geometrically induced background arises if the

motion of the probe is not parallel to the x-axis or

if the motion across the interface does not occur

at constant zmo. These effects can be sorted out

experimentally by performing the same mea-

surement, but only over one side of the sample.

The maximum force observed when doing the

experiment on one side of the sample showed a

residual force more than one order of magnitude

smaller than . Hence, we conclude that the re-

sults shown in Figure 12b are not caused by lack

of parallelism between the probe direction and

the torsional axis of the oscillator [16, 17].

• Differences in local roughness. This will have a

huge impact when the separation between bodies

is comparable to the characteristic root mean

square roughness dr. The magnitude of this ef-

fects will decay as (drzmo)2 when zmo dr [23].

In our case, dr 4 nm, so, for zmo 200 nm, the

effect of roughness differences on the detected

force is 0.02%.

• The existence of patch potentials (i.e., local vari-

ations of the work function [12] of the metals)

can produce unwanted electrostatic forces. In our

samples [15, 17], the patch potential has a lateral

dimension of 0.3 mm and produces a maximum

force dFep(200 nm) 1 fN (ref).

In spite of all the experimental uncertainties listed

above, we can use the data of Figure 12b to impose

more strict limits on hypothetical forces. Using these

experimental values and assuming that any new force

W

F

F

1019

MEMS—Microelectromechanical systems

Curve 1 was obtained by Mohideen’s group [39], curve 2was determined by Lamoreaux [34], curve 3 was extractedfrom data taken by Kapitulnik’s group [13], and curve 4 wasobtained by Price’s group [37].

(meters)

Excludedby

experiments

MEMS force sensor

Casimir-lessconfiguration

1

2

3

4

1020

1016

1012

108

104

100

107 106 105 104

Figure 13.Values in the (a, l) phase space excluded by theexperiment.

should have an amplitude less than or equal to that of

the observed force, we obtained the a a(l) diagram

shown in Figure 13 [17].

Our experimental setup, in which the Casimir

background has been dramatically reduced, improves

by an order of magnitude the current limits for

Yukawa-like corrections to Newtonian gravity [19].

ConclusionsIn conclusion, we have described a MEMS-based

force sensor with ultra-high sensitivity for measuring

the interaction between different bodies. Currently,

resolution of fN is easily achievable at room tem-

perature. By changing the dimensions of the torsional

springs, improvement in the force resolution should

be possible. The sensitivity of our micromachined sen-

sor allows measurements that would be extremely

complicated using any other technique, such as the

observation of the Casimir effect and deviation of the

Newtonian gravity at distances below 1 mm.

Our primary objective with the reported mea-

surements has been to impose new constraints on

hypothetical corrections to Newtonian gravity. We

Page 18: MEMS-based force sensor: Design and applications

78 Bell Labs Technical Journal

have done so by using Casimir force measurements

between a sphere and a plate separated by 0.2 to

1.2 mm. These experimental results, along with a de-

tailed theoretical analysis, lead to new constraints on

Yukawa modifications of Newtonian gravity at short

distances. The MEMS-based force sensor we used al-

lowed us to measure the Casimir force between two

metallic surfaces with a resolution two orders of mag-

nitude better than previous experiments. Moreover,

we presented an experimental configuration in which

the Casimir background was suppressed, allowing us

to set new limits in the 10 to 100 nm distance scale.

By not having to resort to detailed theoretical de-

scriptions of the Casimir interaction and by using soft

micromachined force sensors, the experimental sen-

sitivity is greatly improved. The results reported here

are the first experiments done at these separations. We

found that for nm, which represents

an improvement of one order of magnitude over

previous limits.

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(Manuscript approved June 2005)

DANIEL LÓPEZ is a member of technical staff inthe Nanofabrication Research Group at BellLabs in Murray Hill, New Jersey; he is also amember of the New Jersey NanotechnologyConsortium. He received his B.Sc. degree(with honors) in physics from the University

of San Luis in Argentina and his Ph.D. degree, also inphysics, from the Institutio Balseiro in Bariloche,Argentina. At Bell Labs, he has worked onsuperconductors, MEMS-based devices for opticalcommunications, acoustics, and basic physics research.He was a member of the team that received the 2000Bell Labs President’s Gold Award for the outstandinglevel of innovation and technical excellencedemonstrated in the WaveStar® LambdaRouter project.Dr. López has co-authored over 100 papers in the fieldsof superconductivity, and he has been invited to givelectures at several international conferences anduniversities and research institutes worldwide. In thefield of micro- and nano-mechanical devices, he has co-authored several patents. He is a member of theAmerican Physical Society and has also been a panelistin technology-related conferences. His researchinterests include design and fabrication of MEMSdevices for communication networks, acousticalsystems, medical devices, and high-sensitivity forcedetectors.

RICARDO S. DECCA is an assistant professor of physicsat Indiana University-Purdue UniversityIndianapolis in Indiana. He received hisLicenciatura and Ph.D. degrees in physics atthe Instituto Balseiro in Bariloche,Argentina. His dissertation dealt with the

granular behavior of the recently discovered highcritical temperature LaSrCuO superconductor. For atime, he worked at Bell Labs, where he investigatedthe optical properties of highly correlated GaAs/AlGaAsdouble quantum wells. Dr. Decca has developed newways of using near-field scanning microscopy and iscurrently studying the interaction (i.e., resonantenergy transfer) between single quantum dots, theorganization of lipid bilayers, and the use of MEMS infundamental physics. He has authored and coauthoredmore than 60 journal and professional conference

papers and is a member of the APS, the AAAS, and theAAPT.

EPHRAIM FISCHBACH is a professor of physics at PurdueUniversity in West Lafayette, Indiana. Hehas a B.A. degree in physics from ColumbiaCollege in New York City and M.S. and Ph.D.degrees in physics from the University ofPennsylvania in Philadelphia. His research

interests include searching for new gravity-like forces.Dr. Fischbach is a fellow of the American PhysicalSociety.

DENNIS E. KRAUSE is an associate professor of physicsand Physics Department chair at WabashCollege in Crawfordsville, Indiana. Hereceived his B.A. degree in physics fromSaint Olaf College in Northfield, Minnesota,his M.S. degree in physics from the

University of Wisconsin-Milwaukee, and his Ph.D. inphysics from Purdue University in West Lafayette,Indiana. Before going to Wabash, he was a visitingassistant professor in physics at Williams College inWilliamstown, Massachusetts. Dr. Krause’s primaryresearch interests include the search for new Yukawaand inverse power law forces at sub-micron separationsand the theoretical investigation of the Casimir forceusing novel materials.