Very High Frequency Nanoelectromechanica

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Very High Frequency Nanoelectromechanical Resonators and their Chemical Sensing Applications
Citation
Li, Mo
(2007)
Very High Frequency Nanoelectromechanical Resonators and their Chemical Sensing Applications.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/0KB4-H204.
Abstract
Nanoelectromechanical systems (NEMS) have been proven to be ultrasensitive sensors for a variety of physical variables with unprecedented sensitivity, including force, mass, electrical charge, magnetic field, pressure, and heat. This thesis is intended to discuss using NEMS devices as chemical gas sensors, in a portable and compact total chemical analysis system. An integrated transduction method using piezoresistive metallic thin film is described, which enables both fabrication and operation of nanoscale NEMS resonator devices with resonance frequency up to very high frequency (VHF). The advantages over using traditional doped semiconductor film as piezoresistive material is discussed. Performance and noise properties of the devices are carefully characterized. The dependence between quality factor, device dimension, and pressure is studied, and very high quality factor is obtained with devices at nanoscale dimensions, indicating advantages over their microscale counterparts. Subsequently, the resonator devices are employed as a mass sensor, demonstrating attogram scale mass sensitivity in ambient conditions. Application of these devices as detectors in a gas chromatographic (GC) system is then described, together with method of coating them with functional polymeric film. Detection of multiple analytes of nerve gas simulants with ultrahigh speed, superior sensitivity, and excellent selectivity is achieved. The replacement of conventional bulky detectors with an NEMS detector makes fully integrated microscale gas analysis system possible, which has promising potential applications in health care, medical science, and environmental science.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
gas sensing; NEMS; resonators
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Roukes, Michael Lee
Thesis Committee:
Roukes, Michael Lee (chair)
Vahala, Kerry J.
Bockrath, Marc William
Lewis, Nathan Saul
Defense Date:
11 May 2007
Non-Caltech Author Email:
moli96 (AT) ece.uw.edu
Record Number:
CaltechETD:etd-05212007-112803
Persistent URL:
DOI:
10.7907/0KB4-H204
ORCID:
Author
ORCID
Li, Mo
0000-0002-5500-0900
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17 Mar 2020 22:24
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VERY HIGH FREQUENCY
NANOELECTROMECHANICAL
RESONATORS AND THEIR
CHEMICAL SENSING
APPLICATIONS
Thesis by

Mo Li
In Partial Fulfillment of the Requirements for the
degree of
Doctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California
2007
(Defended May 11th, 2007)

Mo Li

iii

ACKNOWLEDGEMENTS
I want to thank all the people who have helped me throughout the research toward
this thesis. Firstly, I would like to acknowledge my advisor, Dr. Michael Roukes, who
took me on to his group since my first day at Caltech. During years in his group, he
generously provided me with support, inspiration, guidance, encouragement, and freedom
to pursue my research ideas. Secondly, I am very thankful to Dr. Hong Tang, who trained
me on many experiment skills, shared me with his research ideas and thoughts, and
mentored me on a day-to-day base. In fact, several research topics in this thesis began
with his original ideas. I am indebt to Prof. Nate Lewis, Prof. Marc Bockrath, and Prof.
Kerry Vahala, for serving in my exam committee. I am also privileged to work with Dr.
Edward Myers and Dr. Sequoyah Aldridge on the DARPA MGA project. We worked
very hard together, sometimes all day and all night, and successfully met several very
harsh milestones before the impending deadlines. The whole Roukes group has always
been a source of support and inspiration for me. My thanks go to Philip Feng, Sotiris
Masmanidis, Ben Gudlewski, Steve Stryer, Igor Bargatin, Inna Kozinsky, Blake Axelord,
Jessica Arlett, Renaud Richard, Wonhee Lee, Rassul Karabalin, and all the others in the
group. I am also very grateful to Dr. Joe Simonson and Dr. Joshua Whiting, our
collaborators at Sandia National Laboratories, for their help in building our GC systems
and numerous very helpful discussions.
Finally, I wish to thank my parents and my sister in China, for their endless love
and support to me during my more-than-twenty-year-long journey of study in schools.

To my wife

ABSTRACT
Nanoelectromechanical systems (NEMS) have been proven to be ultrasensitive
sensors for a variety of physical variables with unprecedented sensitivity, including force,
mass, electrical charge, magnetic field, pressure, and heat. This thesis is intended to
discuss using NEMS devices as chemical gas sensors, in a portable and compact total
chemical analysis system. An integrated transduction method using piezoresistive
metallic thin film is described, which enables both fabrication and operation of nanoscale
NEMS resonator devices with resonance frequency up to very high frequency (VHF).
The advantages over using traditional doped semiconductor film as piezoresistive
material is discussed. Performance and noise properties of the devices are carefully
characterized. The dependence between quality factor, device dimension, and pressure is
studied, and very high quality factor is obtained with devices at nanoscale dimensions,
indicating advantages over their microscale counterparts. Subsequently, the resonator
devices are employed as a mass sensor, demonstrating attogram scale mass sensitivity in
ambient conditions. Application of these devices as detectors in a gas chromatographic
(GC) system is then described, together with method of coating them with functional
polymeric film. Detection of multiple analytes of nerve gas simulants with ultrahigh
speed, superior sensitivity, and excellent selectivity is achieved. The replacement of
conventional bulky detectors with an NEMS detector makes fully integrated microscale
gas analysis system possible, which has promising potential applications in health care,
medical science, and environmental science.

Table of Contents
ACKNOWLEDGEMENTS ............................................................................................. iii
ABSTRACT........................................................................................................................ v
Table of Contents.......................................................................................................... vi
List of Figures .............................................................................................................. viii
List of tables................................................................................................................. xiii
Chapter 1

Overview: nanoelectromechanical systems (NEMS) for chemical sensing.. 1

1.1

Nanomechanical mass sensing............................................................................ 3

1.2

Micro- and nanomechanical chemical sensing ................................................... 5

1.3

Scaling metrics for mass and chemical concentration sensing ........................... 6

1.4

Reference ............................................................................................................ 9

Chapter 2

Self-sensing NEMS using metallic piezoresistive detection....................... 10

2.1

Introduction to piezoresistivity ......................................................................... 11

2.2

Rationale of using metallic piezoresistive detection on NEMS........................ 17

2.3

Cantilever design .............................................................................................. 21

2.4

Fabrication of nanocantilevers.......................................................................... 25

2.5

Low frequency cantilevers................................................................................ 29

2.6

HF/VHF cantilevers .......................................................................................... 34

2.7

Operation of high frequency nanocantilevers in ambient conditions ............... 38

2.8

Piezoresistive microcantilevers for AFM ......................................................... 45

vii
2.9

Reference .......................................................................................................... 54

Chapter 3
3.1

Measurement techniques........................................................................... 57

Noise measurement: thermomechanical noise, Johnson noise and 1/f noise.... 58

3.1.1

Johnson noise and thermomechanical noise measurements..................... 59

3.1.2

1/f noise..................................................................................................... 67

3.2

Frequency down-conversion measurement....................................................... 74

3.3

Phase-locked loop (PLL) .................................................................................. 78

1.8 Reference ................................................................................................................ 88
Chapter 4

Nanomechanical chemical gas analysis with gas chromatography (GC) 90

4.1

Introduction of gas chromatography: column and detectors............................. 91

4.2

NEMS mass sensor in ambient condition ......................................................... 96

4.3

Polymeric film functionalized NEMS detector in GC.................................... 101

4.4

Reference ........................................................................................................ 122

Chapter 5

Conclusion and future work.................................................................... 125

5.1

Conclusion ...................................................................................................... 125

5.2

Future work..................................................................................................... 127

5.3

Reference ........................................................................................................ 131

Appendix A Electrochemical deposition of nano-magnet tip on microscale scanning
probes.............................................................................................................................. 132
Reference .................................................................................................................... 138

viii

List of Figures
Figure 2-1 Electrical conductor deforms under mechanical force.................................... 12
Figure 2-2 Impedance matching from high-impedance nanoscale devices to radio
frequency electronics ................................................................................................ 19
Figure 2-3 Finite elements simulation of a Π shape cantilever under deformation.......... 22
Figure 2-4 Fabrication process flow ................................................................................. 26
Figure 2-5 SEM images of cantilevers made of 100 nm thick SiC and with 30 nm gold
film............................................................................................................................ 27
Figure 2-6 A doubly clamped beam with metalized bottom gate..................................... 28
Figure 2-7 A trampoline resonator with integrated heater and piezoresistive transducer. 28
Figure 2-8 Fundamental mode resonance response of cantilever from Figure 2-5a at
constant DC bias voltage and varying bias voltage. ................................................. 30
Figure 2-9 Fundamental mode resonance response of cantilever from Figure 2-5a at
constant actuation voltage and varying bias voltage................................................. 30
Figure 2-10 Second mode resonance response of cantilever from Figure 2-5a at constant
bias voltage and varying actuation voltage............................................................... 31
Figure 2-11 Second mode resonance response of cantilever from Figure 2-5a at constant
actuation voltage and varying bias voltage............................................................... 31
Figure 2-12 Fundamental mode resonance response of cantilever from Figure 2-5b at
constant bias voltage and varying actuation voltage. Dotted lines show cantilever’s
resonance response in air. ......................................................................................... 32
Figure 2-13 Second mode resonance response of cantilever b) at constant bias voltage
and varying actuation voltage. .................................................................................. 33

ix
Figure 2-14 Fundamental mode resonance response of cantilever from Figure 2-5c at
constant bias voltage and varying actuation voltage, plotted in log scale. ............... 35
Figure 2-15 Fundamental resonance mode of cantilever from Figure 2-5d, both in
vacuum (red) and at 1 atm (blue), with actuation voltage varying from 100 mV to
500 mV...................................................................................................................... 37
Figure 2-16 Resonance quality factor for cantilever from Figure 2-5b, c and d when
operated in air at various pressures. ........................................................................ 41
Figure 2-17 Knudsen number and air flow regime at varying pressure, for cantilever
beams with different width (2 μm, 400 nm, 8 nm, and 2 nm respectively) .............. 42
Figure 2-18 Quality factor and pressure dependence of nanocantilever in different
ambient gases ............................................................................................................ 44
Figure 2-19 Commercial AFM microcantilever coated with gold film and processed with
focused ion beam for piezoresistive detection .......................................................... 46
Figure 2-20 Piezoresistively detected resonance of commercial microcantilevers in air
and vacuum with varying actuation voltage ............................................................. 46
Figure 2-21 Frequency down mixing method detected resonance of commercial
microcantilever. ........................................................................................................ 47
Figure 2-22 Modified AFM probe head and electrical setup to measure piezoresistive
AFM signal ............................................................................................................... 48
Figure 2-23 Diagram of modified signal configuration for piezoresistive readout .......... 50
Figure 2-24 Images of silicon calibration grating sample, with 30 nm step height.......... 52
Figure 2-25 Scan trace of calibration grating step of 30 nm............................................. 53
Figure 3-1 Circuitry to measure NEMS thermomechanical noise.................................... 62

Figure 3-2 Thermomechanical noise spectrum measured on a low frequency cantilever.63
Figure 3-3 Thermomechanical noise spectrum measured on a VHF cantilever............... 64
Figure 3-4 Cantilever made of 30 nm silicon carbide, with very low force constant of 10
mN/m. ....................................................................................................................... 66
Figure 3-5 AC bridge setup to measure 1/f noise low resistance NEMS ......................... 69
Figure 3-6 Noise figure contours of Stanford Research SR 554 amplifier....................... 69
Figure 3-7 Low frequency noise spectrum of 1 kΩ metal film resistor............................ 71
Figure 3-8 Low frequency noise spectrum of two NEMS cantilever devices. ................. 73
Figure 3-9 Frequency down-conversion piezoresistive measurement.............................. 76
Figure 3-10 Amplitude and phase of a cantilever measured with DC bias and a network
analyzer ..................................................................................................................... 77
Figure 3-11 Amplitude and phase of a cantilever measured with the frequency downconversion method .................................................................................................... 77
Figure 3-12 Basic phase lock loop (reproduced as in Ref 11).......................................... 78
Figure 3-13 NEMS embedded in a phase-locked loop ..................................................... 79
Figure 3-14 Amplitude and phase response at resonance frequency of a typical cantilever
in air .......................................................................................................................... 80
Figure 3-15 Polar plot of a NEMS amplitude-phase frequency response ........................ 81
Figure 3-16 Piezoresistive frequency down-conversion NEMS phase-locked loop ........ 82
Figure 3-17 Y quadrature signal versus drive frequency of a typical NEMS cantilever... 83
Figure 3-18 Phase-locked loop gain measurement with loop gain value set by various
lock-in sensitivities ................................................................................................... 85
Figure 3-19 PLL Frequency stability versus loop gain K................................................. 86

xi
Figure 4-1 Schematic representation of the chromatographic process. ............................ 92
Figure 4-2 Instrument diagram of a GC (from www.practicingoilanalysis.com)............. 94
Figure 4-3 Coating cantilever resonators with polymer ................................................... 98
Figure 4-4 Frequency shift and quality factor reduction of the resonance response of the
cantilever before (red) and after (blue) coating ........................................................ 98
Figure 4-5 Real-time NEMS chemisorption measurements. .......................................... 100
Figure 4-6 Setup to test NEMS detector with commercial GC system with FID detector
connected in serial................................................................................................... 104
Figure 4-7 Gas chromatogram from NEMS detector (purple) and FID detector (blue),
showing peaks from five analytes (3MH, DMMP, DIMP, DEMP, MS) with similar
concentration........................................................................................................... 108
Figure 4-8 Gas chromatogram from NEMS detector (purple) and FID detector (blue),
showing peaks from ten analytes (C8, Toluene, 3MH, DMMP, DIMP, DEMP, DCH,
NAPTH, C11, MS) with similar concentration ...................................................... 109
Figure 4-9 Faster GC separation with 1 meter long column........................................... 109
Figure 4-10 Micro-machined flow chamber with microfluidic flow channel and the
assembly with NEMS device chip. ......................................................................... 110
Figure 4-11 Very fast GC chromatogram from both NEMS (red) and FID (blue) detectors,
obtained using nanoliter volume chamber. ............................................................. 113
Figure 4-12 Relative response of DKAP-coated NEMS and FID detectors to various
analytes ................................................................................................................... 114
Figure 4-13 Chromatogram of thirteen analytes from cantilever resonators coated with
DKPA and PCL polymer, respecitively.................................................................. 115

xii
Figure 4-14 Relative response of DKAP- and PCL-polymer coated NEMS to various
analytes ................................................................................................................... 115
Figure 4-15 Maximum NEMS detector frequency shift at various averaged DIMP
concentrations.. ....................................................................................................... 117
Figure 4-16 Relative response of the NEMS detector with 10 nm thick polymer coating.
................................................................................................................................. 119
Figure 4-17 The function of equation (4.8) can be approximated using the square root of t
when m(t)/mmax < 0.6............................................................................................... 120
Figure 4-18 Spatial (depth) distribution of gas molecule concentration inside the polymer
at various times (0.001, 0.01, 0.1, and 1 τ) ............................................................. 121
Figure 5-1 Differentially coated NEMS resonator array ................................................ 129

Figure A-1 Electrodeposition setup ................................................................................ 133
Figure A- 2 Deposition rate versus current density ........................................................ 134
Figure A-3 Patterning the PMMA e-beam resist on a seed layer for self-aligned
electrodeposition ..................................................................................................... 135
Figure A-4 Array of nanomagnets with dimension of 2 um high and 300 nm wide ...... 136
Figure A-5 A 500 nm by 2 μm permalloy nanomagnet on SiN membrane.................... 137
Figure A-6 A mushroom shaped overgrown nanomagnet on the tip of a release cantilever
................................................................................................................................. 137

xiii

List of tables
Table 1-1 Scaling metrics of various quantities of a rectangular beam.............................. 7
Table 2-1 Poisson's ratio, guage factor, and resistivity of typical metals (Data from
reference [1] and webelements.com) ........................................................................ 13
Table 2-2 Piezoresistive coefficients for n-type and p-type silicon and germanium7. .... 15
Table 2-3 Properties of gold and silicon carbide .............................................................. 24
Table 2-4 Geometrical parameters of typical cantilevers ................................................. 24
Table 2-5 Calculated and finite elements simulate results of cantilever parameters........ 24
Table 2-6 Parameters of typical cantilever devices as shown in Figure 2-5..................... 39
Table 2-7 Properties of different ambient gases ............................................................... 44
Table 3-1 Phase-locked loop parameters measured and calculated.................................. 85
Table 4-1 Comparison of areal mass sensitivity of various acoustic devices and NEMS
resonators. ............................................................................................................... 102
Table 4-2 List of tested chemicals and their formulas, densities, and molecular weights
(MW), including CWA simulants (*) and interferents ........................................... 107
Table A-1 Electrodeposition solution for permalloy (Fe20Ni80) electro-deposition ....... 133
Table A-2 Exposure dosage for hole patterns using on bilayer PMMA resist. .............. 135

Chapter 1
Overview: nanoelectromechanical systems
(NEMS) for chemical sensing
Modern advances in semiconductor fabrication technologies developed by the
microelectronics industry and research have enabled very large-scale integration (VLSI)
of billions of transistors onto a single chip. Nanotechnology, the technology based on
nanometer scale dimension, was envisioned decades ago by Richard Feynman in 1959,
emerged only after these fabrication technologies were rapidly developed after the 1980s.
Only a few years later after Feynman’s famous talk, microscale mechanical devices were
proposed as a means to improve the state-of-the-art transistors at that time1,2. The field of
microelectromechanical systems, or MEMS, debuted also only when enough
microfabrication techniques and tools were available, in the late 1980s. Then in the 1990s
a new research field crossing over both nanotechnology and MEMS emerged, as a result
of intensive and extensive research activities in both fields.

That field is

nanoelectromechanical systems or NEMS, which studies and develops electromechanical
devices with nanoscale dimensions3,4.

MEMS, the first wave of miniaturization of mechanical devices from macroscopic
to microscale, have demonstrated lots of fantastic success. Examples include the
accelerometer that is used to deploy the airbags in almost every modern automobiles, the
digital light processor (DLP) device in color projectors, and the printing head in advanced

inkjet printers, only to name a few. Although NEMS, further miniaturization of MEMS to
nanoscale, is still a nascent research field, many remarkable milestones have already been
demonstrated.

These

achievements

include

the

first

microwave

frequency

nanomechanical resonator5, detection of single electron spin6, measurement of zeptogram
scale mass7, mechanical motion detection near the quantum limit8, and so on. These
accomplishments demonstrate the capability of NEMS which stems from their unique
characteristics of their nanoscale dimensions. NEMS devices promise a variety of novel
applications with superior performance.

This thesis focuses on the application of NEMS resonator devices for mass
sensing and chemical gas sensing applications. In this overview, aspects of these
applications are discussed and explained. Scaling metrics of some important parameters
of the NEMS resonators related to mass and chemical gas sensing are derived. The results
indicate the improvement of performance by miniaturization of the device dimensions, as
demonstrated in the following chapters.

1.1

Nanomechanical mass sensing

A sensor that measures the mass change of itself is called a gravimetric sensor.
Types of gravimetric sensors include quartz crystal microbalance (QCM), surface
acoustic wave (SAW), bulk acoustic wave (BAW), and flexural plate wave (FPW)
devices and other microscale mechanical resonators based on MEMS technologies. All
these devices are operated at their characteristic resonance frequencies, and their
frequencies are measured in response to the change of additive mass on the sensors’
active surfaces. Since frequency measurement is regarded as the most precise of all
science measurements (for example, National Institute of Standard and Technology’s
cesium fountain atomic clocks), and given the excellent frequency stabilities of these
sensors, resonance-frequency-based gravimetric sensors provide mass sensing resolution
far superior to any other sensing methods.
NEMS resonators are also a type of gravimetric sensor. They have demonstrated
orders of magnitude improvement in mass sensing resolution than the above-mentioned
macroscopic sensors. This improvement stems from NEMS resonators’ miniature total
mass, very high resonance frequency, and remarkable frequency stability, as indicated
clearly from the expression of mass-frequency responsivity:
ℜ=

∂ω0
=− 0 .
∂ M eff
2 M eff

(1.1)

This equation is derived from the expression of the eigen-frequency of a simple harmonic
oscillator: ω0 = K eff / M eff , where ω0 is the angular frequency, M eff is the effective
mass, and K eff is the effective spring constant of the resonator. The minimum resolvable

mass change of the resonator is then determined by the minimum measurable frequency
change and the mass responsivity:

δm =

δ ω0

⎛δω ⎞
= ⎜ 0 ⎟ ⋅ 2 M eff .
⎝ ω0 ⎠

(1.2)

From equation (1.2), it is clear that the higher the frequency measurement
accuracy δ ω0 / ω0 ,

and the smaller the effective resonator mass, the lower is the

minimum resolvable mass δ m . NEMS resonators have demonstrated better or
comparable frequency stability with other microscale gravimetric sensors, in the range of
one part per million (10-6) to ten parts per billion (10-8). But the effective mass of NEMS
resonators is much smaller — at pictogram scale for typical high-frequency silicon or
silicon carbide cantilevers, and at femtogram scale for UHF/microwave frequency doubly
clamped beams and nanowires. So inherently, NEMS resonators will have unprecedented
mass sensing resolution. Recent progress has achieved zeptogram scale mass sensing on
an ultra-high-frequency NEMS resonator. The experiment demonstrated sensing physisorption of 100 zeptogram xenon atoms on the device surface at low temperature and in
vacuum, with noise level at only 7 zeptogram. This mass resolution corresponds to the
mass of one 4 kDa macromolecule or protein molecule, or 30 Xenon atoms. In this thesis,
experiments carried out at room temperature and atmosphere pressure instead,
demonstrating the sensing of single attogram gas molecules with 100 zeptogram noise
level, will be described in detail. This demonstrates another benchmark for mass sensing
in ambient conditions. With fast progresses in fabrication and measurement techniques,
the ultimate goal of mass sensing at single Dalton level should be within reach in the very
near future, so that mass spectroscopy can be implemented with these nanoscale devices

in an integrated and compact form which will have tremendous application opportunities
in chemical and biological science and technology.

1.2

Micro- and nanomechanical chemical sensing

Mechanical gravimetric sensors can be applied straightforwardly for chemical sensing
applications9. For that purpose, the mass of targeted chemical analytes of interest will be
measured when the analyte molecules adsorb (absorb) onto (into) the active surface of the
sensor. There are two types of radically different adsorption mechanisms between
adsorbate molecules and surfaces: chemi-sorption and physi-sorption. For chemi-sorption,
the adsorbate molecules form a direct chemical bond with the surface, while for physisorption, only weak physical forces (van der Waals force) hold adsorbate molecules on
the surface. These two adsorption mechanisms can be quantitatively discriminated
between by their adsorption energy. Typically, chemi-sorption energies are 80 – 400
kJ/mol, compared to physi-sorption which has adsorption energy less than 40 kJ/mol.
However, in many cases, the distinction between these two mechanisms is not that clear
and necessary. Details of the change and perturbation of molecular electron states, and
their interaction with surface atoms upon adsorption need to be taken into consideration.
Usually, a sorption process involves both physi-sorption and chemi-sorption processes.

To obtain both better chemical sensitivity and selectivity, modification of the sensor
surface with functional coating material is essential. Coating materials employed for
different sensing purpose include polymeric films, thiols, silanes, zeolites, metals, metal
oxides, zeolites, antibodies, enzymes, lipids, and ssDNAs, each tailored for specific
applications. For vapor-phase sensing of organic compounds, polymeric films are the

most often used coating material. Details of the vapor-phase sensing using polymeric
films on gravimetric sensors will be addressed in Chapter 4.

1.3

Scaling metrics for mass and chemical concentration
sensing

For vapor-phase chemical sensing, the purpose is to measure the concentration of the
analytes, usually at very low level, in the ambient gaseous environment. Thus, the
sensor’s sensitivity of concentration sensing is the main concern in this scenario. The
excellent mass sensitivity of a gravimetric sensor does not automatically transfer to good
concentration sensitivity, for the surface area of the sensor has to be taken into account.
Whether or not scaling down the dimensions of the sensor to nanoscale will improve
concentration sensitivity, as it does for mass sensitivity, is not clear at the first glance. It
is advisable to see qualitatively how scaling the dimensions will change the properties of
the device.

Take a beam with a rectangular cross section for example. Assume its length L, width
W, and thickness t, can be scaled down simultaneously. We can write L=al, W=bl, t=cl,
so that they all are proportional to a linear dimension l. In Table 1-1, expressions of
various important mechanical properties of the beam and theoretical sensitivities of the
beam as a sensor are listed, as well as how these expressions scale with dimension l. In
the table, Δf is the measurement bandwidth, Aeff is the effective surface area of the sensor,
DR is the linear dynamic range, s is the sticking coefficient of the gas molecules at the
sensor surface, and m0 is the molecular mass of the gas species. However, some

quantities, such as quality factor Q and dynamic range DR, are assumed to have no
dependence on the dimensions of the device, as suggested from reported experimental
results showing that no simple dependence of these quantities on dimension can be
found10. Yet this assumption holds only to a limited extent and remains to be checked in a
more complete, detailed modeling of each device.
Table 1-1 Scaling metrics of various quantities of a rectangular beam
Resonance
frequency

f0 =
2π

E t
ρ L2

l −1

k = βE

wt 3
L3

Force constant
Mass responsivity

f0
E 1
ℜ=
=α
2 M eff
ρ 3 wL3

Minimum resolvable
mass

δm =

Minimum resolvable
concentration

Areal mass
sensitivity

δc =

1 ω0
( Δf )1/ 210( − DR / 20)
ℜ Q

2.5
k BT ω0 3
Δf ⋅ 10− ( DR / 20)
Aeff ℜ ⋅ p0 ⋅ s m0 Q

Sm =

Aeff = − eff
f0
2 M eff

l −4

l 3.5

l 1.5

l −1

As discussed previously, both the resonance frequency and mass responsivity will
increase, while the force constant will decrease, as the dimension l is scaled down. The
thermomechanical noise limited minimum resolvable mass change decreases as l3.5 11. To

convert this mass resolution to concentration resolution, we use the equation of flux
dependent adsorption rate:
ra =

s.
5 mk BT

(1.3)

So within measurement time τ = 1/ Δf , the total mass of adsorbed gas molecules is

Δm = ( ra Aeff m0 ) ⋅τ . If Δm is replaced with the minimum resolvable mass, and the
concentration of the gas species is defined as the ratio of its partial pressure to ambient
pressure: c = p / p0 , we can define the minimum resolvable concentration of the sensor

δ c . Using the scaling method, it is found that δ c decreases with l as l1.5, indicating the
improved concentration sensitivity of the sensor when its dimensions are scaled
downward. Also, the areal sensitivity Sm is a frequently used quantity for gravimetric
sensors, and it also improves as l-1 when l decreases. (It will be noted in Chapter 4 that
the effective thickness of the sensor plays the major role here.)

All of the above discussions explicate the advantages of nanoscale mechanical
resonator sensors — they have both improved mass sensitivity and improved
concentration sensitivity. They are therefore very promising for chemical sensing
applications when relative concentration of vapor phase analytes is the objective of
measurement. The work described in this thesis is motivated by these findings, and
proves these predictions. Unprecedented sensitivity as well as substantially improved
sensing speed have been successfully demonstrated, and will be discussed in detail.

1.4

Reference

Nathanso, H., et al. Resonant gate transistor. IEEE Transactions on Electron
Devices Ed14, 117 (1967).

Newell, W. E. Miniaturization of tuning forks. Science 161, 1320-1326 (1968).

Roukes, M. Plenty of room indeed. Scientific American 285, 48 (2001).

Roukes, M. Nanoelectromechanical systems face the future. Phys. World 14, 2531 (2001).

Huang, X. M. H., et al. Nanodevice motion at microwave frequencies. Nature 421,
496-496 (2003).

Rugar, D., et al. Single spin detection by magnetic resonance force microscopy.
Nature 430, 329-332 (2004).

Yang, Y. T., et al. Zeptogram-scale nanomechanical mass sensing. Nano Lett. 6,
583-586 (2006).

LaHaye, M. D., et al. Approaching the quantum limit of a nanomechanical
resonator. Science 304, 74-77 (2004).

Hughes, R. C., et al. Chemical microsensors. Science 254, 74-80 (1991).

Yasumura, K. Y., et al. Quality factors in micron- and submicron-thick cantilevers.
J. Microelectromech. Syst. 9, 117-125 (2000).

Ekinci, K. L., Yang, Y. T., and Roukes, M. L. Ultimate limits to inertial mass
sensing based upon nanoelectromechanical systems. J. Appl. Phys. 95, 2682-2689
(2004).

Chapter 2
Self-sensing NEMS using metallic
piezoresistive detection
Measurement of nanoelectromechanical resonators with very high resonance
frequency is challenging because the signal generated from the mechanical motion of the
device is minuscule and buried in other parasitic or interference signals. Previously,
typical readout methods such as magnetomotive and optical interferometry have been
employed. However, these techniques require bulky setup, cryogenic temperatures or
optical instruments that are not integratible to the chip scale. An alternative readout
method is needed for efficient signal transduction from mechanical motion to electrical
signal that is suitable for a very wide frequency range. For the future of large-scale
integration of multiple NEMS devices with other micro- and nanoelectronics, this readout
scheme also needs to be capable of being both scaled down to allow a high level of
integration, and scaled up to allow large throughput fabrication and multiplexing of many
devices that can be operated in parallel. Room temperature and atmosphere operation is
also a prerequisite.

In this chapter, a method of utilizing the piezoresistivity of metallic film for
reading out NEMS devices is described. Self-sensing NEMS resonator devices from low
frequency up to very high frequency (VHF) is demonstrated. Noise and sensitivity

11
analysis is conducted based on measured data. Also, the dependence of resonance quality
factor on ambient pressure of devices with various dimensions is studied. The attributes
of metallic piezoresistive transduction scheme are manifested clearly by the measured
data and theoretical analysis. Further, self-sensing cantilevers for atomic force
microscopy (AFM) are also demonstrated, indicating promising application potential.

2.1

Introduction to piezoresistivity

Piezoresistivity is the effect that the resistance of an electrical conductor changes
when it deforms under mechanical strain. It was first discovered by Lord Kelvin (William
Thomson) in 1856. The geometrical deformation of a conductor implies that any
conductor is piezoresistive, including both metal and semiconductor. The resistancestrain relation of piezoresistive material can be characterized by a figure of merit called
gauge factor, defined as γ = (d R / R ) /(d L / L) — the relative change of resistance divided
by the applied strain. The DC resistance of a uniform conductor with length L, cross
section A, and electrical resistivity ρ is: R = ρ L / A . When the conductor is deformed, its
partial resistance change can be calculated:
dR dρ dL d A

(2.1)

If we know the Poisson’s ratio of the material that the conductor is made of, equation
(2.1) can be written as:
dR dρ
dL
dL
+ (1 + 2ν )
=γ

(2.2)

12
Thus we can find the expression for gauge factor is:

γ = (1 + 2ν ) +

dρ / ρ
dL/L

(2.3)

Figure 2-1 Electrical conductor deforms under mechanical force.
The first term in (2.3) derives solely from the geometrical deformation of the
conductor. This effect is illustrated in Figure 2-1. For most conductive materials,
Poisson’s ratio is less than 0.5. For example, typical cited values for metals are 0.33 for
aluminum, 0.42 for gold, 0.34 for copper, and 0.32 for titanium. So the contribution of
the first term to gauge factor is less than 2. The second term stems from the conductivity
change of the material under deformation. The value of this term can vary in three orders
of magnitude for different materials with different conducting mechanisms. In typical
metallic conductors (such as aluminum, copper, gold, platinum), this term is usually in
the range of 1–3 1. In metals, a possible mechanism of this conductivity change is the
modification of free electron path length caused by the elastic field generated by applied

13
stress2, or in some magnetic metals, by the coupling between magnetoresistive and
magnetostrictive effects. In general, including both terms, the gauge factor of bulk
metallic conductor is commonly in the range of 1–3. Bulk values of Poisson’s ratio,
gauge factor and resistivity of common metals are listed in Table 2-1.
Table 2-1 Poisson's ratio, gauge factor, and resistivity of typical metals
(Data from reference [1] and webelements.com)
Metal

Poisson’s ratio ν

Gauge factor γ

Electrical resistivity ρ ( μΩ⋅ cm )

0.35
0.42
0.34
0.39
0.39
0.30

1.96
3.03
2.17
2.23
2.54
1.88

1.7
2.2
2.65
10
10.6
7.0

Au
Al
Pd
Pt
Ni

Gauge factors of metallic thin films can be significantly different from the
corresponding bulk values. The gauge factor of a particular metal film depends on its
thickness, or the specific resistance of the film. This dependence can be divided into three
regimes according to the film thickness. For relatively thick films (typically > 100 nm),
their gauge factors approach the value of bulk. For the films of intermediate thickness (in
the range of 100 nm to 10 nm) when the film is still continuous, the gauge factor has a
lower value. This is due to the fact that for a two dimensional conductor, the translation
factor of longitudinal deformation d L / L to cross sectional deformation d A / A equals
only one Poisson ratioν , instead of 2ν in a three dimensional conductor. For very thin
films (less than 10 nm typically), it becomes discontinuous and approaches percolation
regime that the conduction in the film is mainly by thermally excited electron hopping or

14
tunneling between isolated metal islands or particles. Thus, the electrical conduction
becomes very sensitive to the strain which changes the separation between islands or
particles, and the gauge factor diverges 2,3. For example, 3 nm gold film with specific
resistance as high as 25 kΩ/□ shows a gauge factor of 24 to 484.

Piezoresistance effect was discovered in semiconductor materials such as silicon
and germanium in 1954 by Charles S. Smith5. The gauge factor of semiconductor
material is usually orders of magnitude higher than that of metallic material. Apparently,
the second term in (2.3) is dominant in this case. In simple explanation, this large gauge
factor in semiconductor materials arises from the modulation of band structures, the
redistribution of carriers in conducting valleys, and the subsequent change of carrier
mobility and effective mass as the material is under mechanical stress and strain6. As
with other electrical properties of a semiconductor, the gauge factor depends strongly on
the doping type (n- or p-type) and doping concentration. Because of the crystalline
structure of semiconductors, the piezoresistive coefficients of semiconductors have to be
described as a tensor, in a way similar to the modulus of elasticity tensor. To define the
tensor of piezoresistive coefficients, we start from Ohm’s law:
E = ρ ⋅ j = (1 +

dρ

) ⋅ ρ0 j

(2.4)

where the conductor is under strain and resistivity r changes by d ρ . Then, Ohm’s law
needs to be written in vector form to incorporate the strain tensor:
⎡ E1 ⎤ ⎡ j1 ⎤ ⎡ d11 d12
1 ⎢ ⎥ ⎢ ⎥ ⎢
E = j + d
ρ 0 ⎢ 2 ⎥ ⎢ 2 ⎥ ⎢ 21 22
⎢⎣ E3 ⎥⎦ ⎢⎣ j3 ⎥⎦ ⎢⎣ d 31 d 32

d13 ⎤ ⎡ j1 ⎤
d 23 ⎥ ⎢ j2 ⎥ .
⎥⎢ ⎥
d 33 ⎥⎦ ⎢⎣ j3 ⎥⎦

(2.5)

15
In cubic crystalline, (2.5) can be simplified using symmetry to:
⎡ E1 ⎤ ⎡ j1 ⎤ ⎡ d1
1 ⎢ ⎥ ⎢ ⎥ ⎢
E = j + d
ρ0 ⎢ 2 ⎥ ⎢ 2 ⎥ ⎢ 6
⎢⎣ E3 ⎥⎦ ⎢⎣ j3 ⎥⎦ ⎢⎣ d 5

d6
d2
d4

d 5 ⎤ ⎡ j1 ⎤
d 4 ⎥ ⎢ j2 ⎥ .
⎥⎢ ⎥
d 3 ⎥⎦ ⎢⎣ j3 ⎥⎦

(2.6)

The coefficient of d can be related to mechanical stress tensor with further simplification
by the symmetry in cubic crystalline as:
0 ⎤ ⎡σ 1 ⎤
⎡ d1 ⎤ ⎡π 11 π 12 π 12 0
⎢ d ⎥ ⎢π
π 11 π 12 0
0 ⎥ ⎢σ 2 ⎥
⎢ 2 ⎥ ⎢ 12
⎥⎢ ⎥
0 ⎥ ⎢σ 3 ⎥
d ρ ⎢ d 3 ⎥ ⎢π 12 π 12 π 11 0
=⎢ ⎥=⎢
⎥ ⎢ ⎥ = π ⋅σ .
0 π 44 0
0 ⎥ ⎢σ 4 ⎥
ρ ⎢d 4 ⎥ ⎢ 0
⎢d5 ⎥ ⎢ 0
0 π 44 0 ⎥ ⎢σ 5 ⎥
⎢ ⎥ ⎢
⎥⎢ ⎥
0 π 44 ⎦ ⎣σ 6 ⎦
⎣d 6 ⎦ ⎣ 0

(2.7)

Here tensor elements π 11 , π 12 , π 44 are called piezoresistive coefficients, and their values
for p-type and n-type silicon and germanium are given in Table 2-2.

Table 2-2 Piezoresistive coefficients for n-type and p-type silicon and germanium7

n-Si (11.7 Ω⋅ cm )
p-Si (7.87 Ω⋅ cm )
n-Ge (9.9 Ω⋅ cm )
p-Ge (15 Ω⋅ cm )

π 11 (100 GPa)

π 12 (100 GPa)

π 44 (100 GPa)

−102.2
6.6
−4.7
−10.6

53.4
−1.1
−5.0
5.0

−13.6
138.1
−137.9
46.5

To compare with metal, the typical value of gauge factor for p-type doped single
crystal silicon is in the range of 40–200, while n-type doped single crystal silicon has a
relatively lower and negative value of gauge factor in the range of −20–−100.
Polycrystalline silicon has a considerably lower gauge factor than single-crystal silicon,
in the range of 10–30, and it is strongly dependent on structure of the film.

16
Giant piezoresistivity was reported recently on silicon nanowire, showing
piezoresistance coefficient π 11 as high as − 3.55 × 10−8 Pa -1 at <111> direction8, a factor
of more than 30 higher than bulk silicon. This will correspond to a surprisingly high
gauge factor, at the order of 3000–5000. Further comprehensive investigation is
necessary to confirm and clarify this unexpectedly giant effect.

Piezoresistance effect in conducting materials has been widely used for sensing
applications. The most commonly used is metal foil strain gauge. A variety of pure
metals such as gold, chromium, silver, palladium, nickel, platinum, and alloys such as
gold-nickel, nickel-chromium (Constantan), copper-nickel, and platinum-nickel, are used
in commercial products. Although the gauge factors of metal films are two orders of
magnitude lower than semiconductor films, metal film strain gauge still dominates the
market. The reasons for this include low cost of fabrication, robustness, low temperature
coefficient, and the capability of using flexible substrates such as polyimide and other
polymeric materials. All of these enable much wider usages and applications for metal
film stain gauge devices than for semiconductor gauges. However, semiconductor gauges
are recently more often seen in applications requiring high precision and in cleaner
environments, such as pressure transducers and other MEMS-based devices.

2.2

Rationale of using metallic piezoresistive detection on
NEMS

To date, most self-sensing microcantilevers employ piezoresistive displacement
transduction 9-12. A sensor patterned from piezoresistive material, a piezoresistor, affixed
to moving parts of a mechanical device undergoes resistance change when the device is
in motion and strain is induced in the sensor. With current biasing, such a piezoresistor
converts the strain-induced resistance change into a measurable voltage. The integration
of such displacement sensors with the mechanical elements eliminates the need for device
alignment with an (otherwise) external readout, such as a laser. This brings immense
simplification to instrument design.

Even more important, however, is that, by

circumventing optics, piezoresistive transduction yields access to dimensions far below
the diffraction limit, where the substantial advantages of nanoscale sensors are available.
However several important issues must be addressed to make this possible.

Previous efforts to optimize piezoresistive sensors have largely focused upon the
use of doped semiconducting materials, since they can provide a very large gauge factor
γ. It is widely assumed that optimal transducer performance is obtained simply by using
materials offering maximal γ, for it provides the largest absolute signal level. However,
this assumption becomes profoundly incorrect for nanoscale sensors.

The commonly held assumption is that a large gauge factor will serve to
maximize a displacement sensor’s performance, but this is actually only one element in

18
optimizing its transduction efficiency.

There are three generic attributes of high- γ

materials that are always deleterious to high sensitivity displacement transduction. The
first is that high γ is generally achieved only with high resistivity materials and, hence,
large two-terminal resistances are quickly attained when the size of a piezoresistive
transducer patterned from such materials is scaled down to nanometer dimensions. This
can make noise matching between nanoscale piezoresistors and readout circuitry
extremely difficult to impossible, especially at high frequencies.

In fact, below a

particular size range set by the carrier depletion length, surface states in semiconducting
transducers can render them susceptible to freeze-out at reduced temperatures, or in the
worst case, non-conducting even at room temperature. A second issue, in fact related to
the first, is that high γ is typically associated with very low carrier densities and, hence,
often with highly disordered or percolative conduction. When such a piezoresistor is
scaled downward in size its resistance increase is accompanied by a very large increase in
low frequency 1/f noise, as described by Hooge’s relation13, S R(1/ f ) = 2πζ R 2 /( N ω ) .
This empirical relation describes how the spectral density of resistance fluctuations at
angular frequency ω grows when the number of carriers becomes small. Here N is the
number of carriers within the sample of resistance R, and ζ is a sample-specific materials
parameter (for p+ Si, ζ ~ 10−5 )14.

Finally, a third deleterious attribute of high- γ

materials is their large temperature coefficients. These, too, originate from the low
carrier density in the semiconducting (compared to metallic) regime, and the thermally
activated, defect-mediated transport that is involved.

Device

RF
Electronics

Figure 2-2 Impedance matching from high-impedance nanoscale devices to radio
frequency electronics
These issues become more problematic for nanoscale piezoresistors. We find
they may be circumvented, thereby enabling the immense advantages of self-sensing
detection in the nanoscale regime, by replacing the conventionally employed
semiconducting piezoresistive layer with a thin metal film. The underlying rationale for
this replacement elucidates the true figure of merit for piezoresistive displacement
transduction. It is not solely the gauge factor, but the output (voltage domain) signal-tonoise ratio (SNR), which also takes into account the coupling efficiency attained between
the displacement transducer and its subsequent readout electronics. Specifically, for a
nanoscale device, the loss of a factor of ~ 20 in γ that results upon transitioning from a
semiconducting to a metallic transducer, is amply compensated by a profound reduction
in the resistance of the latter, which can be a factor of ~ 104 or more. The latter arises
directly from the huge disparity between the carrier density in thin metal films (on the

20
order of 1022 cm-3) compared to that of doped semiconductor layers (on the order of 1018
cm-3 in the case of heavily doped semiconductors).
Use of metallic-density elements immensely simplifies impedance matching
between the transducer and its subsequent readout, whose quality we characterize by the
transmission coefficient, 1 − Γ ( Z L , Z 0 ) at their juncture. Here, Γ = ( Z L − Z 0 ) / ( Z L + Z 0 )
is the junction reflection coefficient and Z L and Z 0 are the impedances of the transducer
output and the readout input. Typically, Z 0 is 50 Ω for a low-noise, high frequency
amplifier. As depicted in Figure 2-2, invariably, for high-impedance semiconducting
devices of nanoscale dimensions Z L >> Z 0 ; consequently Γ~1 and most of the signal is
lost by reflection at readout’s input. With nanoscale, metallic-density transducers we can
engineer Z L ~ Z 0 , so that the transduced signal is optimally transmitted (Γ<<1). Further,
low transducer output impedances provide greatly reduced susceptibility to signal
degradation from the inevitable parasitic reactances, which otherwise will severely limit
the accessible readout bandwidth of the circuit. For example, typically seen parasitic
capacitance from the cabling and wiring of a readout circuit can be on the order of picofarad — with device impedance of 1 MΩ, the cut-off frequency given by 1/ 2π RC will
be less than 1 MHz. Signal above this frequency will be attenuated and accessible signal
to noise ratio drops.

Further, metallic materials permit immense simplification of fabrication given
their ease of deposition and patterning at the micro- and nanoscale. They can be
deposited on a wide range of different substrates, including flexible polymeric materials

21
which cannot sustain the semiconductor process, which requires high processing
temperature (deposition, doping, activation etc.). Their conductivity is robust against a
wide range of chemical and plasma-based process conditions —in stark contrast to the
well-known susceptibility of ultrathin low-density semiconducting layers to such
processes.

2.3

Cantilever design

The most employed design of piezoresistive NEMS devices described in this
thesis is cantilever. These piezoresistive cantilevers are designed with Π shape as
depicted in Figure 2-3. The design of two “legs” on the cantilevers has two purposes:
First, coated with metallic thin film, the legs form a conduction path for the
piezoresistance measurement of the device. Secondly, when the cantilever devices
displace, most of the mechanical strain will be concentrated at the leg area, thus
providing improved piezoresistive transduction efficiency. This is justified by the finite
elements simulation15 result in Figure 2-3, indicating the leg area has highest strain
energy density.

Figure 2-3 Finite elements simulation15 of a Π shape cantilever under deformation. The
colorization shows the strain energy density, indicating the concentration at the leg area.

When designing a cantilever with predetermined force constant and fundamental
mode resonance frequency, the following analytical equations derived from classical
beam theory are used in the calculation16. The results are further confirmed by finite
element simulation. Excellent agreement between two methods is usually obtained. In the
equations, l , b and t are the total length, width, and thickness of the cantilever; l1 and
w are the length and width of each leg.

The force constant, effective mass, and resonance frequency are given in
equations (2.8), (2.9), and (2.10) respectively:

Eeff t 3
4l 3
1 2
+ (2l13 − 6ll12 + 6l 2l1 )( − )
b w

meff =

(2.8)

ρ eff tl 7

⎡ 4l 3
w⎢
+ (2l13 − 6ll12 + 6l 2l1 )( − ) ⎥
b w ⎦
w 1 l1 5
1 l1 7 1 l1 6
72
)[
( ) − ( ) ]+
b 20 l
252 l
36 l
11
1 l1 1 l1 2 2 w
144[
2)
420 12 l 2 l
l1 3
l1 2 w
1 l1 5
1 l1 7 1 l1 6 ⎪
⎪ 1
⎪⎩144 [2( l ) − 3( l ) ]( b − 2) − 20 ( l ) − 252 ( l ) + 36 ( l ) ]⎪⎭

ω=

meff

(2.9)

(2.10)

Since the cantilevers are coated with metal film, the effective density and
Young’s modulus of the bi-layer structure have to be used in the calculation16. They are
given by equation (2.11) and (2.12):

ρ eff =

ρ1t1 + ρ 2t2
t1 + t2

⎛ t1 ⎞
t2 3
t1E1E2 ⎡
t1
E1 ⎛ t1 ⎞ E2t2 ⎤
Eeff =
⎢4 + 6 + 4 ⎜ ⎟ +
⎥.
⎜ ⎟ +
(t1 + t2 )3 t1E1 + t2 E2 ⎢
t2
t2 ⎠ E 2 ⎝ t2 ⎠
E1t1 ⎥

(2.11)

(2.12)

Here respectively t1 and t2 , ρ1 and ρ 2 , E1 and E2 are the thickness, density, and Young’s
modulus of each layer of materials.

24
Typical properties of the materials, the design parameter of the cantilevers, and
the results of calculation and simulation are listed in following tables, showing excellent
consistency.
Table 2-3 Properties of gold and silicon carbide
Material
Au
3C-SiC

Young’s modulus (GPa)
78
440

Density(g/cm3)
19.32
3.166

Thickness (nm)
30
70

Table 2-4 Geometrical parameters of typical cantilevers
Cantilever

l (mm)

w (mm)

l1 (mm)

w1 (mm)

t (mm)

33
10
2.7
0.7

0.8
0.4

1.5
0.5

0.3
0.5
0.2
0.1

0.1
0.1
0.1
0.1

Table 2-5 Calculated and finite elements simulate results of cantilever parameters
Cantilever

Measured
frequency
[Hz]

Calculated
frequency
[Hz]

FE
simulation
frequency
[Hz]

52 k
1.6 M
8M
127 M

48 k
1.2 M
7.6 M
125 M

51.2 k
1.3 M
8.4 M
128.4 M

Calculated
spring
constant from
Eq. (1)
[N/m]
0.006
0.12
1.16
32.2

FE
simulation
spring
constant
[N/m]
0.005
0.15
1.15
32.1

2.4

Fabrication of nanocantilevers

Nanocantilevers are fabricated with reactive plasma-etching-based surface
micromachining techniques. The starting material is epitaxial 3C silicon carbide (3C-SiC)
on silicon substrate, or PECVD grown silicon nitride (SiN) on silicon substrate. This
layer of material forms the supporting mechanical structure of the cantilever. Silicon
carbide and silicon nitride are selected for their excellent mechanical properties, easiness
of fabrication, and robustness to chemical and physical etching processes.

We then define cantilever structure using electron beam lithography. Typically
two layers of resist, 4% 495 K PMMA and 2% 950 K PMMA in anisole (Microchem,
MA) are spin coated on the substrate at 4000 rpm and baked at 180 °C. After the
exposure and development, 2–5 nm chromium and 30 nm gold films are thermally
evaporated and lifted off in acetone. These metal layers serve as both a self-aligned mask
in the subsequent etching process and as a piezoresistive transducer layer on the final
device. Then the SiC (SiN) /metal cantilever is released from the substrate with electron
cyclone etching (ECR) in two steps, using argon and nitrogen trifluoride (NF3) plasma.
In the first etching step, the chamber pressure is set at 20 mTorr and DC bias of −250 V is
applied to the plasma. At this condition, the etching process is highly anisotropic, and the
SiC or SiN layer is etched vertically toward the substrate. For 80 nm SiC and 100 nm SiN,
the etching time is about 45 seconds and 20 seconds, respectively. In the second etching
step, DC bias voltage is reduced to −100 V and the etching is thus changed to be more
isotropic, in order to etch the silicon substrate. In this way, the cantilever structure is
undercut and eventually released from the silicon substrate. The etching selectivity

26
between silicon and SiC (estimated to be larger than 70) is much larger than that between
silicon and SiN (less than 10). So SiN is less tolerant to the over-etching in the second
isotropic etching than SiC, and accurate timing is very important. Figure 2-4 illustrates
the etching process.

Figure 2-4 Fabrication process flow

In Figure 2-5, scanning electron microscope images of four typical devices made
of silicon carbide and gold are shown. Their lengths vary from 30 μm to 600 nm. The
geometry of the cantilever, especially the length and the width of the legs, is designed
with consideration of both wanted resonance frequency and low two-terminal resistance.
Completed devices have typical resistance below 100 Ohm. Their resonance frequencies
and force constants are listed in Table 2-5. The excellent etching selectivity of silicon
carbide to silicon can be clearly seen from the picture. For instance, in fabricating the
large cantilever (Figure 2-5a), the silicon substrate is undercut by more than 5 μm to
release the cantilever, while the 300 nm wide legs still remain, with negligible etching.

Figure 2-5 SEM images of cantilevers made of 100 nm thick SiC and with 30 nm gold
film. Their dimensions are: a) 33 μm x 5 μm; b) 10 μm x 2μm; c) 2.5 μm x 0.8 μm; d) 0.6
μm x 0.4μm

Structures other than cantilevers are also fabricated in a similar way, such as a
doubly clamped beam shown in Figure 2-6, and a trampoline resonator with integrated
heater and piezoresistive transducer shown in Figure 2-7.

Figure 2-6 A doubly clamped beam with metalized bottom gate

Figure 2-7 A trampoline resonator with integrated heater and piezoresistive transducer.
Gold layer is in yellow false color

2.5

Low frequency cantilevers

Low frequency cantilevers such as the one shown in Figure 2-5a have very low
force constants in the range of mN/m to μN/m (This cantilever has a force constant of 6
mN/m). As described in Chapter 3, this low force constant implies very high force
sensitivity, which is optimal for detection of small forces.

Figure 2-8 to Figure 2-11 show the measured piezoresistive response of

the

cantilever in Figure 2-5a at its both fundamental resonance mode of 52 kHz and second
resonance mode of 640 kHz, with varying actuation voltage, and bias voltage,
respectively. The response of the piezoresistive transducer shows excellent linearity with
both actuation and bias voltages, as expected for the metallic piezoresistivity. Resonance
quality factor of this low frequency cantilever is around 500 in vacuum.

amplitude [nV]

120
50uA dc Bias
Room Temperature

100

Amplitude [nV]

100
80
60
40
20

actuation amplitude [mV]
20mV
18mV
16mV
14mV
12mV
10mV
8mV
6mV
4mV
2mV

40
20
49

Frequency [kHz]

Figure 2-8 Fundamental mode resonance response of cantilever from Figure 2-5a at
constant DC bias voltage and varying bias voltage. Inset: response amplitude versus
actuation voltage amplitude

200

Amplitude [nV]

150

200

amplitude [nV]

20mV Actuation
Room Temperature

150

100

0 10 20 30 40 50 60 70 80 90

dc bias current [μA]

100
90uA
80uA
70uA
60uA
50uA
40uA
30uA
20uA
10uA

Frequency [kHz]

Figure 2-9 Fundamental mode resonance response of cantilever from Figure 2-5a at
constant actuation voltage and varying bias voltage. Inset: response amplitude versus bias
voltage amplitude

amplitude [nV]

150

Amplitude [nV]

50uA dc bias

100

ac actuation amplitude [mV]
20mV
18mV
16mV
14mV
12mV
10mV
8mV
6mV
4mV
2mV
1mV

634

636

638

640

642

644

Frequency [kHz]

Figure 2-10 Second mode resonance response of cantilever from Figure 2-5a at constant
bias voltage and varying actuation voltage. Inset: response amplitude versus actuation
voltage amplitude

300

Amplitude [nV]

250

20mV actuation

amplitude [nV]

300

350

250
200
150
100
50

200

100

dc bias current [μA]

150
90uA
80uA
70uA
60uA
50uA
40uA
30uA
20uA
10uA

100

633 634 635 636 637 638 639 640 641 642 643 644

Frequency [kHz]

Figure 2-11 Second mode resonance response of cantilever from Figure 2-5a at constant
actuation voltage and varying bias voltage. Inset: response amplitude versus bias voltage
amplitude

32
Resonance responses of cantilever from Figure 2-5b are shown in Figure 2-12 and
Figure 2-13. The second resonance mode has a frequency at about 15 MHz, into the high
frequency (HF) band. Both insets show the linear response to varying actuation voltage.
Also notable is that the cantilever from Figure 2-5b shows quality factor of 20 in

Voltage [μV]

a)
20mV
18mV
16mV
14mV
12mV
10mV
8mV
6mV
4mV
2mV
200mV in Air
100mV in Air

voltgae amplitude [μV]

atmospheric pressure, as shown with dotted lines in Figure 2-12.

15
10

10
15
20
actuation amplitude [mV]

1.57

1.58
1.59
Frequency [MHz]

1.60

1.61

Figure 2-12 Fundamental mode resonance response of cantilever from Figure 2-5b at
constant bias voltage and varying actuation voltage. Dotted lines show cantilever’s
resonance response in air. Inset: response amplitude versus actuation voltage amplitude

Amplitude [μV]

20mV
18mV
16mV
14mV
12mV
10mV
8mV
6mV
4mV
2mV

actuation amplitude [mV]

14.75

14.80

14.85

14.90

14.95

f [MHz]

Figure 2-13 Second mode resonance response of cantilever b) at constant bias voltage
and varying actuation voltage. Inset: response amplitude versus actuation voltage
amplitude

2.6

HF/VHF cantilevers

Further miniaturization of cantilever dimension will increase its resonance
frequency. Cantilevers such as the ones shown in Figure 2-5c and d have resonance
frequency well into the high frequency (HF, 3–30 MHz) and very high frequency (VHF,
30–300 MHz) bands. The advantages of low impedance metallic piezoresistive
transducers are manifested by the excellent responses and signal to noise ratios of the
resonant motion detection. No extra impedance-matching circuitry between the device
and pre-amplification stage are needed to readout the signal so that commercial 50 Ω
input impedance low-noise RF amplifiers (MITEQ AU-1442) can be conveniently used.
Details of direct resonance measurement of these HF cantilevers are described in Chapter
3.

Figure 2-14 shows the resonance response of the cantilever c in Figure 2-5 in
vacuum with varying actuation voltages, plotted in decibel units. Measured
thermomechanical noise spectrum is also shown as the black trace. Two resonance peaks
are observed because the usage of the frequency down conversion measurement scheme
which is also described in Chapter 3. This data demonstrates the remarkable linear
dynamic range (DR) of these cantilevers, on the order of 80 dB as measured from the
thermomechanical noise floor to the onset of nonlinearity. DR is an important figure-ofmerit for nanomechanical resonators, as it determines the largest signal to noise ratio that
can be achieved17,18. Also, when measuring the shift of the device’s resonance frequency,
it is crucial in determining the minimum resolvable frequency shift17. Nonlinear response
is observed at very high actuation amplitude, showing the resonance peak tilting toward

35
the lower frequency size19. This indicates the softening nonlinear behavior of the device,
possibly due to the bi-layer structure of the device20.

Amplitude [dBm]

80 dB

-20

-40

-60

-80
11.0

11.1

11.2

11.3

11.4

11.5

11.6

Frequency [MHz]
Figure 2-14 Fundamental mode resonance response of cantilever from Figure 2-5c at
constant bias voltage and varying actuation voltage, plotted in log scale. Nonlinear
response is observed with largest actuation. Black trace shows the thermomechanical
noise spectrum of the same cantilever using the frequency down conversion scheme as
described in Chapter 3. This data shows the excellent linear dynamic range (DR) of this
cantilever, at the order of 80 dB measured from thermomechanical noise floor to the
onset of nonlinearity.

36
The smallest cantilever of Figure 2-5d has a remarkably high resonance frequency
at 127 MHz, the first ever achieved in VHF band. This device has a length of only 600
nm and width only 400 nm. Figure 2-15 shows its measured fundamental mode resonance
response both in vacuum and at 1 ATM air. Very remarkably, a quality factor of 400, the
highest among all cantilevers, is observed in air. This avoidance of vacuum requirement
for operation makes these nanoscale cantilevers very promising for various applications
at ambient conditions, such as gas sensing, which will be described in details in later
chapters.
In terms of pushing the frequency limit of these cantilever devices, the highest
frequency that has been demonstrated is more than 180 MHz. However, the detection
bandwidth is not limited by metallic piezoresistive readout, but by the design of
cantilevers. By designing doubly clamped beams or other structures, detection of
nanomechanical motion at frequency higher than 1 GHz is possible. In fact, using the
same readout method, high-order modes of a complicated device at frequencies as high as
1.094 GHz have been observed by others21. Another limitation on operation frequency
here is the piezoelectric disk used to actuate. Even with the very high quality single
crystal (PMN-PT, TRS Technologies Inc.), the achievable actuation amplitude tails off at
above 100 MHz. An alternative high efficiency driving mechanism is necessary to
expand the operation frequency beyond the VHF band up to UHF and microwave
frequencies. One possible solution includes the integration of piezoelectric material such
as AlN, GaN, or PZT onto the NEMS device. There are many challenges to accomplish
with that, but it is certainly very worth exploring.

Figure 2-15 Fundamental resonance mode of cantilever from Figure 2-5d, both in
vacuum (red) and at 1 atm (blue), with actuation voltage varying from 100 mV to 500
mV. The inset shows that resonance amplitude is linearly proportional to the actuation
voltage.

2.7

Operation of high frequency nanocantilevers in ambient
conditions

Quality factor Q is very crucial for the performance of a mechanical resonator.
Fundamentally, quality factor characterizes the energy dissipation rate of the resonating
system into the surrounding environment, and, as elucidated by fluctuation-dissipation
theory, the noise induced by the environment to the system22. So far, the unprecedented
sensitivity and resolution of NEMS devices, such as zeptogram-scale mass sensing, are
only obtainable in a vacuum environment, which is required for NEMS resonators to
retain a very high resonance quality factor. Both signal to noise ratio and accuracy of
determining the resonance frequency of the NEMS resonators depend highly on high
quality factor17. This vacuum requirement is becoming a major inconvenient constraint
for wide application of NEMS, as most interesting sensing applications involving
chemical and biological samples are only viable in ambient environments, namely at
atmospheric pressure, or in liquid. Several methods to improve the quality factor of
mechanical resonators in heavily damping environments have been proposed and
implemented, including parametric amplification and active feedback control23,24.
However, successful demonstration of high Q at very high frequency in ambient
conditions is still rare.

In Figure 2-15, a noteworthy attribute of a very high frequency nanocantilever is
demonstrated. Even at atmospheric pressure, the quality factor of that cantilever still
remains at 400, decreased by only a factor of 2 from its value (900) in vacuum. This is

39
unlike larger cantilevers, whose quality factors usually drop by a factor of more than 10,
as shown in Table 2-6.
Table 2-6 Parameters of typical cantilever devices as shown in Figure 2-5

Cantilever

Dimension
(μm×μm×μ
m)

Frequency

Force
constant
(N/m)

33×5×0.1
10×2×0.1
2.7×0.8×0.1
0.6×0.4×0.1

52 kHz
1.6 MHz
8 MHz
127 MHz

5 × 10-3
0.15
1.15
32.1

at
.01 Torr
(300K)

at
1 Atm
(300K)

500

950
1000
900

20
90
400

This prompted us to carefully study the quality factor dependence on ambient
pressure of these cantilevers. Measured data is plotted in Figure 2-16. At low pressure,
these three cantilevers (b, c, d in Figure 2-5 and Table 2-6) have similar Q values, at
about 1000. As pressure increases, their Q values start to decrease. This initial decrease is
due the damping caused by momentum exchange between the ambient gas molecules and
the motional devices, and can be modeled using classical gas kinetic theory in free
molecular flow regime. Equation (2.13) gives the Q expression corresponding to this
damping mechanism for a simple “diving board” cantilever, showing an inverse
proportion to ambient pressure P 25. The total Q value is given by equation (2.14) — the
total damping to the device is the sum of intrinsic damping and the damping from gas
molecules. Here, r is the density of the material that the device is made of, d is the
thickness of the device, f0 is the resonance frequency, R0 is molar gas constant, T is

40
absolute temperature, M0 is the molar mass of the gas (M0 =29 g/mol for air), and P is
pressure.

π 3

Qm = ( ) 2 ρ d f 0

R0 T / M 0

Q Qi Qm

(2.13)

(2.14)

In Figure 2-16, measured data is fitted with equation (2.13) and (2.14). Deviation
of the data points from the fitting function happens at higher pressure, indicating the
breakdown of the free molecular flow modeling. It is also noticeable that the smaller the
cantilever, the higher pressure this deviation starts at. This is due to the size dependence
of fluid dynamics modeling regimes of devices with various dimensions. Generally,
smaller devices tend to have larger quality factor than larger devices at high pressure,
even though their intrinsic Q may not be higher.

Intrinsic quality factor as high as 100,000 has been observed on optimally
designed NEMS devices26. The relatively low Q value observed on these cantilever
devices is possibly due to the dominance of dissipation by the internal friction inside the
metal layer on the device27. Since much higher Q value is observed on devices without
metallization28, other intrinsic mechanisms — such as thermoelastic and surface states
damping — contribute only a little dissipation. To improve the Q of metalized devices,
optimized deposition methods and annealing processes need to be developed.

100

10000

Pressure [Torr]

Quality factor

1000

1000
100
10

0.1

Cantilever width [μm]

0.01

0.1

Pressure [Torr]

100

1000

Figure 2-16 Resonance quality factor for cantilever from Figure 2-5b, c and d when
operated in air at various pressures. Q factors at 1 Atm are 20, 90, and 400, respectively.
The measured cantilever Qs (symbols) deviate from predictions based upon molecular
flow (solid lines) at the crossover into the viscous flow regime (red arrows). This occurs
at 30, 300, and 1000 torr, for the 2 μm, 800 nm, and 400 nm wide cantilevers,
respectively. Inset: The relation between the pressure at crossover and cantilever width

Fluid dynamic modeling of the mechanical devices can be divided into three
different regimes, which can be demarcated by a dimensionless number — the Knudsen
number29. Knudsen number is defined as the ratio of mean free path of the ambient gas
lmfp to the characteristic dimension of the device structure. In the case of flexural mode of
cantilever devices, this characteristic dimension is the width w of the cantilever. At high
Knudsen number regime (Kn>10) with low pressure such that the mean free path of gas is
much larger than the width of the cantilevers, it is in the free molecular flow regime. At

42
low Knudsen number (Kn<0.01) with high pressure, the air flow is in a continuum regime.
A cross-over or Knudsen flow regime exists in between 0.01

Knudsen number Kn=lmfp/w

Molecular

Crossover
-2

Continuum
-4

0.01

0.1

100

1000

Pressure [Torr]

Figure 2-17 Knudsen number and air flow regime at varying pressure, for cantilever
beams with different width (2 μm, 400 nm, 8 nm, and 2 nm respectively)

In Figure 2-17, the Knudsen number for cantilever beams with different widths is
plotted against air pressure. What’s noteworthy is that for nanoscale cantilever beams, the
continuum flow limit can break down even at atmosphere pressure where the mean free
path of air is about 65 nm. For example, a beam with width of only 2 nm, such as a single
wall nanotube, is still in free molecular flow regime at atmospheric pressure. It can be
clearly seen in Figure 2-17 that for the smallest cantilever with width of 400 nm, it is in
the cross-over flow regime at atmospheric pressure. The data in Figure 2-16 shows the Q

43
value of the smallest cantilever drops substantially slower than larger cantilevers, for it
remains in the cross-over regime (or Knudsen flow) at high pressure. In continuous flow
regime, the viscous damping of air dominates and generally induces faster drop of the Q
value as pressure increases, as indicated by modeling. Detailed analysis of the damping
mechanisms and device design rationale to optimize the quality factor is beyond this
work’s scope and can be found in the literature30. Cross-over regime or Knudsen flow is
difficult to characterize analytically, but efforts have been made to approximate the
problem for nanoscale oscillating beams29. A straightforward conclusion is that nanoscale
mechanical devices tend to sustain high quality factors at high pressure, which enables
them to be operational with the same measurement accuracy and resolution as is
achievable by larger devices in vacuum conditions.

Quality factor and pressure dependence in different gases are also measured with
a nanocantilever having resonance frequency at 77 MHz. Nitrogen, helium, and
tetrafluoroethane (C2H2F4, hereafter TFE) are tested, and the quality factor and pressure
dependence is measured with different gases. Clearly, in heavier gases (such as TEF), the
quality factor of the cantilever drops faster with increasing pressure than it does in lighter
gases (such as helium), as indicated by equation (2.13). Their difference in viscosity must
also be considered to account for different viscous damping. These results demonstrate
the advantages of using hydrogen as the ambient gas for nanomechanical resonators (for
its lower molar mass and lower viscosity). In fact, as described in Chapter 4, for chemical
gas sensing in a gas chromatography system, hydrogen is commonly used as a carrier gas

44
because it provides the best separation speed. In a hydrogen environment,
nanocantilevers show the best quality factor at atmospheric pressure.

Table 2-7 Properties of different ambient gases

Gas

Molar mass

Density at
standard
conditions
(g/l)

hydrogen
helium
nitrogen
TFE

28
102

0.089
0.179
1.25
4.55

Absolute
viscosity
(10-6 Pa s)

Kinematic
viscosity
(10-6 m2/s)

8.76
18.6
17.81
unknown

98.43
103.9
14.25
unknown

100

1000

1000
800
600

400

μ_N2 =17.7 μPoise

200

μ_He =18.6 μPoise

N2
He
Tetrafluroethane C2H2F4
0.1

Pressure [torr]

Figure 2-18 Quality factor and pressure dependence of nanocantilever in different
ambient gases

2.8

Piezoresistive microcantilevers for AFM

In 1993, Tortonese et. al.9 first demonstrated using doped silicon piezoresistive
microcantilevers for atomic force microscopy (AFM). Atomic resolution was achieved
with their system. However, options for further improvement and wide usage of this type
of self-sensing cantilever are limited. Probable reasons for that include the high cost and
complex process of making those cantilevers, the high temperature coefficients of the
piezoresistive transducer, and most importantly, their limited resolution.

The success of making metallic piezoresistive cantilevers and their excellent
performance inspired us to use them for AFM applications. As demonstrated, these
cantilevers are fairly easy to fabricate, only requiring one more step of metallization. To
demonstrate, commercial AFM microcantilevers (μMash®, 15 series silicon cantilever,
typical resonance frequency 325 kHz, force constant 40 N/m) are used, and Cr/Au film is
evaporated onto one side of them. Focused ion beam was used to cut an opening on the
cantilevers to define a similar two-leg structure as in previous micro-machined
piezoresistive cantilevers. In Figure 2-19, an image of the microcantilever after the
processing is shown, and their resonance responses measured by piezoresistive detection
both in vacuum and in air are shown in Figure 2-20. The resonance frequency is lowered
from the original value after the process because of the cutting and mass loading of the
gold film. We hereafter can use these cantilevers for AFM in tapping mode. Frequency
down mixing method is used to reduce the capacitively coupled background signal, and
detected amplitude and phase of the resonance signal is shown in Figure 2-21. Details of
this technique are covered in Chapter 3.

Figure 2-19 Commercial AFM microcantilever coated with gold film and processed with
focused ion beam for piezoresistive detection

350

Vaccum

Amplitude [a.u]

300
Q=360

250

Air

200

Q=220

500mV
400mV
300mV
200mV
100mV

150
100

Shifted for better
visual inspection

50
230

240
250
Frequency [kHz]

260

Figure 2-20 Piezoresistively detected resonance of commercial microcantilevers in air
and vacuum with varying actuation voltage

Down mixed to 14Hz
3sec/point

500mV Drive
20mV Bias

150

100

30
50
20

10
238

Phase [deg]

Amplitude [mV]

200

239

240

241

242

243

-50
244

Frequency [kHz]

Figure 2-21 Frequency down mixing method detected resonance of commercial
microcantilever. Very low background signal can be obtained

Digital instruments 3100 AFM was used to test these modified microcantilevers.
The AFM probe head was also modified to connect the piezoresistor on the
microcantilever to an external pre-amplifier and lock-in amplifier. Signal access modulus
(SAM) was used to send the external driving signal to the piezoelectric actuator on the
probe head, and to reroute the piezoresistive readout signal output from the lock-in
amplifier’s auxiliary output port to the AFM controller and computer. Since the phase
signal channel from the extender electronics module to the controller is used, the
piezoresistive signal was recognized by the controller and computer as a phase signal.
Figure 2-22 shows the modified probe head and electronics used to measure the
piezoresistive signal from the cantilever.

Figure 2-22 Modified AFM probe head and electrical setup to measure piezoresistive
AFM signal

At tapping mode, the cantilever is driven at its resonance and its amplitude is read
by the photodiode detector via optical level setup. A feedback loop is used to keep this
amplitude constant and to move the height of the cantilever by a piezoelectric tube
element so that the cantilever tip is kept at a fixed distance above the local topographical
height of the sample surface. Thus this height adjustment feedback control signal is
proportional to the sample surface height relative to a reference plane, and is read by the
AFM controller as a height signal. However, in this mode, the cantilever is maintained at
constant oscillation amplitude so that the piezoresistive resonance signal will have no
change in response to the sample surface topography. The constant height feedback loop
has to be stopped to allow the change of cantilever tip and sample distance, and
consequently the cantilever oscillation amplitude. In this way, we can read the
piezoresistive resonance signal to reveal the height of the sample surface, because the
amplitude and frequency of the oscillating cantilever is affected by the tip-surface
distance, due to the van der Waals force between them. DI AFM system provides a very
convenient operation mode called “interleave” scan mode, designed for applications such

49
as magnetic force microscopy (MFM) and electric force microscopy (EFM). Briefly, in
this mode, each scan line is scanned twice by the cantilever tip. In the first scan, the
constant height feedback is on and the height profile of the trace is recorded. A mean
height value of the sample surface in this trace is then calculated and used to lift the
cantilever to a constant height above the mean value, large enough to avoid the tip
touching the surface. In the second scan of the same line, feedback control is turned off
and the signal from the second channel is recorded. Often it records the magnetic or
electrical force between the sample and cantilever, but in our case, piezoresistive
resonance signal is recorded. So by using this interleave mode, two images of the sample
are acquired: one from the height signal and one from the piezoresistive resonance signal
which should record the same surface height topography of the sample. A diagram of our
modified signal configuration using the signal access module is shown in Figure 2-23.

Figure 2-23 Diagram of modified signal configuration for piezoresistive readout
(Adapted from Veeco DI NanoscopeTM signal access module manual)
Preliminary scanning experiments on a silicon calibration grating sample obtained
decent images. Figure 2-24 shows two scanned images of the sample, one from the height
signal and one from piezoresistive resonance signal when the AFM is under interleave
mode. The piezoresistive signal is recognized by the AFM computer as a phase signal.
These two images show excellent consistence, except for extra noise in the second image
from un-optimized detection circuitry and open-loop operation during the second scan,
which lets in noises from system vibration and instability. Single scan traces from two
signals are displayed in Figure 2-25. Even without other higher-level feedback control, as
used in the constant height scanning mode, the piezoresistance resonance signal follows
the sample surface height profile very well.

51
These data first demonstrate the feasibility of using self-sensing metallic
piezoresistive read-out for AFM applications. This method has great potential as a highly
integrated and compact instrument by circumventing the need for laser optics and
consequent maintenance and alignment of components. The low impedance of the
transducer also allows high frequency cantilevers to be used for very high speed (> 1
MHz) and wide bandwidth scanning probe applications. Only one extra fabrication
process is needed to convert available commercial cantilevers to self-sensing cantilevers.
The attributes of low cost, easy fabrication, high sensitivity, and low temperature
coefficients enable these cantilevers to be the very promising next generation of scanning
probes.

Figure 2-24 Images of silicon calibration grating sample, with 30 nm step height. Left
image is from the height signal. Right image is from piezoresistive resonance signal. It is
recognized by the AFM control computer as a phase signal

Figure 2-25 Scan trace of calibration grating step of 30 nm. Top trace is from height
signal and bottom trace is from piezoresistive resonance signal. Again, the piezoresistive
signal is recognized as a phase signal by the system.

2.9

Reference

Kuczynski, G. C. Effect of elastic strain on the electrical resistance of metals.
Phys. Rev. 94, 61-64 (1954).

Parker, R. L. and Krinsky, A. Electrical resistance-strain characteristics of thin
evaporated metal films. J. Appl. Phys. 34, 2700-2708 (1963).

Jen, S. U., et al. Piezoresistance and electrical resistivity of pd, au, and cu films.
Thin Solid Films 434, 316-322 (2003).

Li, C. S., Hesketh, P. J., and Maclay, G. J. Thin gold film strain-gauges. J. Vac.
Sci. Technol. A 12, 813-819 (1994).

Smith, C. S. Piezoresistance effect in germanium and silicon. Phys. Rev. 94, 4249 (1954).

Kanda, Y. Piezoresistance effect of silicon. Sensors and Actuators a-Physical 28,
83-91 (1991).

Harris, C. M. and Crede, C. E., Shock and vibration handbook, 2d ed. (McGrawHill, New York, 1976).

He, R. and Yang, P. Giant piezoresistance effect in silicon nanowires. Nature
Nanotechnology 1, 42 (2006).

Tortonese, M., Barrett, R. C., and Quate, C. F. Atomic resolution with an atomic
force microscope using piezoresistive detection. App. Phys. Lett. 62, 834-836
(1993).

Harley, J. A. and Kenny, T. W. High-sensitivity piezoresistive cantilevers under
1000 angstrom thick. App. Phys. Lett. 75, 289-291 (1999).

55
11

Ried, R. P., et al. 6-mhz 2-n/m piezoresistive atomic-force-microscope cantilevers
with incisive tips. J. Microelectromech. Syst. 6, 294-302 (1997).

Takahashi, H., Ando, K., and Shirakawabe, Y. Self-sensing piezoresistive
cantilever and its magnetic force microscopy applications. Ultramicroscopy 91,
63-72 (2002).

Hooge, F. N. 1/f noise is no surface effect. Phys. Lett. A A 29, 139-140 (1969).

Arlett, J. L., et al. Self-sensing micro- and nanocantilevers with attonewton-scale
force resolution. Nano Lett. 6, 1000-1006 (2006).

Femlab 3.1 (Comsol AB, Burlington, MA, USA).

Roark, R. J., Young, W. C., and Budynas, R. G. Roark's formulas for stress and
strain, 7th ed. (McGraw-Hill, New York, 2002).

Ekinci, K. L., Yang, Y. T., and Roukes, M. L. Ultimate limits to inertial mass
sensing based upon nanoelectromechanical systems. J. Appl. Phys. 95, 2682-2689
(2004).

Postma, H. W. C., et al. Dynamic range of nanotube- and nanowire-based
electromechanical systems. App. Phys. Lett. 86, - (2005).

Husain, A., et al. Nanowire-based very-high-frequency electromechanical
resonator. App. Phys. Lett. 83, 1240-1242 (2003).

Kozinsky, I., et al. Tuning nonlinearity, dynamic range, and frequency of
nanomechanical resonators. App. Phys. Lett. 88, - (2006).

Bargatin, I., Kozinsky, I., and Roukes, M. L. Efficient electrothermal actuation of
multiple modes of high-frequency nanoelectromechanical resonators. App. Phys.
Lett. 90 (2007).

56
22

Callen, H. B. and Welton, T. A. Irreversibility and generalized noise. Phys. Rev.
83, 34-40 (1951).

Anczykowski, B., et al. Analysis of the interaction mechanisms in dynamic mode
sfm by means of experimental data and computer simulation. Applied Physics aMaterials Science and Processing 66, S885-S889 (1998).

Tamayo, J., et al. High-q dynamic force microscopy in liquid and its application
to living cells. Biophysical Journal 81, 526-537 (2001).

Newell, W. E. Miniaturization of tuning forks. Science 161, 1320-1326 (1968).

Harrington, D. A., Mohanty, P., and Roukes, M. L. Energy dissipation in
suspended micromechanical resonators at low temperatures. Physica B 284, 21452146 (2000).

Liu, X., et al. Low-temperature internal friction in metal films and in plastically
deformed bulk aluminum. Physical Review B 59, 11767 (1999).

Sekaric, L., et al. Nanomechanical resonant structures in silicon nitride:
Fabrication, operation and dissipation issues. Sensors and Actuators a-Physical
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Bhiladvala, R. B. and Wang, Z. J. Effect of fluids on the q factor and resonance
frequency of oscillating micrometer and nanometer scale beams. Phys. Rev. E 69,
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Cho, Y. H., Pisano, A. P., and Howe, R. T. Viscous damping model for laterally
oscillating microstructures. J. Microelectromech. Syst. 3, 81-87 (1994).

Chapter 3
Measurement techniques
In this chapter, detailed descriptions of measurement techniques, setup and
schematics are included. In the first section, the principles and the methods to
measure noise performance of the studied NEMS devices are described, including
Johnson noise, 1/f noise, and thermomechanical noise. Then measurement scheme
using frequency down-conversion in order to reduce the coupled background signal is
explained. Finally, phase-locked loop technique implemented to track and measure
the resonance frequency of the NEMS devices is described. Both theoretical analysis
and data acquired from NEMS devices measurement are discussed and compared.
Expectation for further improvement of frequency measurement accuracy is also
discussed.

3.1

Noise measurement: thermomechanical noise, Johnson
noise and 1/f noise

In order to analysis and optimize the device performance, it is necessary to
understand every source of noise. Quantitative measurement of every type of noise is
essential to determine the sensitivity and resolution of the device.

For piezoresistive transduction of mechanical devices, the main intrinsic noise
sources include the thermal noise of the resistive transducer itself, i.e., Johnson noise; the
low frequency 1/f noise, or Hooge’s noise; and the thermomechanical noise of the
mechanical device1. Johnson noise is also called white noise, as its spectral density is
constant over the frequency spectrum until extremely high frequencies are reached. The
spectrum of 1/f noise is as described by its name, having one over f dependence on
frequency. It is only noticeable at relatively low frequency below which it dominates over
Johnson noise. Thermomechanical noise is the mechanical analog of Johnson noise,
arising from the thermally actuated mechanical fluctuation of the device, and can be
better understood using fluctuation-dissipation theorem2. More detailed explanation can
be found elsewhere3. For a mechanical resonator device, the noise spectrum shows a
Lorentzian peak at the resonance frequency. The visibility of thermomechanical noise
peak is an indication of optimal transducer read-out noise performance such that the
thermal noise of the mechanical motion dominates the readout noise. All of these noises
are intrinsic and fundamental to the device, and can only be improved by means of the
design of the device and the selection of material. For a given device, there are no other
methods to reduce these noises except for reducing the temperature. Reduction of these

59
noises by proper selection of transducer material and device engineering to achieve
optimal sensitivity and resolution is one of the main goals of device researches.

To characterize each noise source, different measurement schemes must be
employed. Details of each of them and results measured from various piezoresistive
NEMS devices are discussed in the following sections.

3.1.1 Johnson noise and thermomechanical noise
measurements

The noise of a measurement system consists of two major parts, the noise from the
device itself and noise from the read-out amplifiers employed in the measurement. For
the amplifier noise in an appropriate cascade of multiple amplification stages, if the first
stage provides sufficient gain, subsequent stages will only contribute negligible noises
when referred to the input. So, most of the time, only the noise of the first amplifier
(preamplifier) needs to be considered.

The Johnson noise spectral density of a resistor R is given by
vnJ = 4k BTR

[v/ Hz ] ,

where:
k B = Boltzman constant = 1.38 × 10−23 J/K ,
T = absolute temperature of the resistor,

(3.1)

60
R = resistance of the resistor.

When the device is connected to an amplifier, contribution of the amplifier noise
to the total noise in the system can be calculated using the noise figure (NF) of the
amplifier. Noise figure (NF) is defined as:

NF = 20log10

total noise after amplification(referred to input)
[dB]
thermal noise of the device

(3.2)

So the total noise referred to input after the first amplification is:
vnT = total noise =10(NF/20) × thermal noise =10(NF/20) × 4k BTR

(3.3)

For a typical metallic piezoresistive NEMS device with DC resistance of 100 Ω,
using an amplifier with noise figure of 2 dB at the interested frequency range, the
expected total noise spectral density referred to input at that frequency range will be
1.6 nV/ Hz .

Thermomechanical noise of a mechanical device can be transduced into electrical
signal, as extra voltage noise appearing above the existing noise floor using various
transduction schemes, such as piezoresistive and optical detection methods1. Given
sufficient measurement sensitivity, thermomechanical motion of a high-Q mechanical
resonator device can be conveniently measured in the electrical domain, showing a
Lorentzian noise spectral peak centered at its resonance frequency.

Metallic

piezoresistive read-out has been demonstrated with superior sensitivity, such that
thermomechanical noise spectrum peaks at as high as 127 MHz can be observed with our
cantilevers.

It is also notable that measurement of thermomechanical noise spectra provides a
viable way to calibrate the displacement sensitivity. This technique has been proven to be
a reliable method and is widely used to calibrate scanning probes in the AFM
community4. An example of using this method is described in this section.

From fluctuation-dissipation theory, the thermomechanical noise arises from a
white equivalent noise force exerted on the device by the heat bath of the surrounding
environment, and its force spectral density is given as:

SthF =

4k BT K
ω0Q

(3.4)

Again here:
k is Boltzman constant,

T is absolute temperature,
K is the force constant of the device,
ω0 is the resonance frequency,
Q is the quality factor.
For a damped resonator, the displacement spectral density resulting from this
thermal driving force is:

Sthz (ω ) =

4ω0k BT
2 2
mQ (ω0 − ω ) + (ω0ω / Q )2

(3.5)

So at resonance frequency, the displacement spectral density is

Sthz 2 =

4k BTQ
ω0 K

(3.6)

By measuring the thermomechanical noise in the electrical domain, and
calibrating the spectral signal with the expected displacement spectral density, the
sensitivity of transduction from displacement to voltage can be calculated.
Agilent 4395A spectrum analyzer

Bias Tee

AU 1442
200MHz LNA

Figure 3-1 Circuitry to measure NEMS thermomechanical noise
Measurement circuitry shown in Figure 3-1 is used to measure the
thermomechanical noise spectra of piezoresistive cantilever devices. The cantilever
device is biased with a battery DC source via a bias tee to isolate the DC and AC parts of
the signal. A low noise RF preamplifier (Mitek®, AU1442, 0.02-200 MHz) with a noise
figure of 2dB is used for the first-stage amplification, and the output is fed to a spectrum
analyzer (Agilent 4395A). The thermomechanical motion of the device induces strain
fluctuation in the device’s piezoresistor and causes fluctuation of its resistance. Under
DC bias voltage, this resistance fluctuation is transferred into voltage noise, amplified,
and measured as electrical voltage noise on the spectrum analyzer.

63
Typical noise spectra measured with low frequency cantilevers, as shown in
Figure 2-5a and Figure 2-5b is displayed in Figure 3-2. Both the fundamental and second
resonance modes of the cantilever from Figure 2-5a can be seen in the plot. The
background noise floor varies with frequency due to different measurement conditions
and the noise from the amplifier.

Figure 3-2 Thermomechanical noise spectrum measured on a low frequency cantilever.
Noise spectral peak at first and second mechanical mode can be seen. Inset: Noise
spectrum measured with 1.5 MHz cantilever. All data are measured with 100 mV bias
voltage.

Metallic piezoresistive read-out is sensitive enough here to measure
thermomechanical noise up to the VHF band (30 MHz – 300 MHz) for the first time to

64
our knowledge. In Figure 3-3, a 127 MHz device as shown in Figure 2-5d is measured, at

1/2

1.65

1.60

1.55

40
39

1.50

124

125

126
127
128
Frequency [MHz]

Displacement Noise [fm/Hz

Voltage Noise [nV/Hz

1/2

room temperature and in 1 ATM pressure air. The displayed data is averaged by 200.

129

Figure 3-3 Thermomechanical noise spectrum measured on a VHF cantilever

We thus can use this measurement to calibrate the cantilever’s displacement
sensitivity. Its fundamental-mode force constant for end loading is K ~ 32 N/m, evaluated
both analytically and by finite element simulation. Considering Figure 3-3, the output
voltage noise floor near the 127 MHz resonance, vn0 = ( S T + SV )1 / 2 ~ 1.519 nV/ Hz ,
consists of the Johnson noise of the piezoresistive transducer ( R ~ 90 Ω,

S 1/T 2 = 4k B T R ~ 1.22 nV/ Hz ) and the readout amplifier’s noise referred to its input,

SV 1/ 2 ~ 0.92 nV/ Hz (NF~2dB at 50Ω). The measured voltage noise spectral density on
resonance is vn = (vn0 + vnm )1/ 2 ~1.644 nV/ Hz .

The contribution arising from the

65
cantilever’s thermomechanical motion is thus vnm ~0.63 nV/ Hz .

The displacement

noise floor on resonance for a 127 MHz cantilever, limited by thermal noise,
is S 1/z 2 = 4kbTQ /(2π f 0 K ) = 16 fm/ Hz .
responsivity

(transduction

“gain”)

Hence we deduce the displacement
of

this

self-sensing

device

Rvz = 0.63 nV/ Hz /16 fm/ Hz = 0.04 nV/fm . We further employ this responsivity to

evaluate the displacement resolution, imposed by the off-resonance output voltage noise
floor

referred

xn =

Sz ~

the

displacement

domain

using

this

responsivity,

SVout (ω ≠ ω0 ) / R T2 , which yields xn ~ 1.519 nV/ Hz / ( 0.04 nV/fm )

= 39 fm/ Hz . Thus, at 1 atm this displacement noise background, referred to the input
(displacement domain), corresponds to resolution of 39 fm/ Hz , which is comparable to
state-of-the-art optical detection via fiber-optic interferometry5.

As clearly seen in equation (3.6), cantilevers with a very high force constant K
can provide very good displacement sensitivity at very high frequencies. In other
circumstances, high force sensitivity is desired. From equation (3.4), a very low force
constant K is wanted for applications requiring sensing small forces. Such cantilevers will
have relatively large amplitude in thermomechanical motion. Figure 3-4 shows an
example. This cantilever is made with 30 nm silicon carbide material, having a force
constant of only 10 mN/m but a resonance frequency still around 1 MHz. The effect of its
thermomechanical motion can clearly be seen in the SEM picture as the blurring of the
cantilever tip. Its spectrum can be acquired by focusing the electron beam at the
cantilever tip and analyzing the spectrum from the secondary electron detector. Using

66
equation (3.4), we can calculate thermomechanical noise limited force sensitivity of this
cantilever as 144 aN/√Hz.

Figure 3-4 Cantilever made of 30 nm silicon carbide, with very low force constant of 10
mN/m. Its thermomechanical motion can be seen in this SEM picture, causing the
blurring at the tip in the image.

From the same thermomechanical noise spectrum in Figure 3-2, we can also try to
estimate the strain gauge factor of the gold film on cantilever. Equipartition principle also
applies to elastic energy of the system: Eeff Veff ε 2 = kbT , where Eeff and Veff are effective
Young's modulus and volume respectively6. Most of the strain energy is concentrated on
the legs, so that we can take the volume of them as effective volume. The mean squared
strain is transferred to mean square noise voltage power by v 2 = γ 2Vb2 ε 2 . Using
integrated voltage power and calculated value of mean squared strain, strain gauge factor

67
can be estimated. Finite element analysis also gives a numerical value for the ratio of
mean squared strain value in metal layer only and averaged value in the composite
cantilever leg structure. In this way, the gauge factor is estimated to be 2.38, which is
consistent with the measured value in literature7.

3.1.2 1/f noise
Another significant attribute of metallic piezoresistive NEMS devices is its low
1/f noise, as compared to conventional semiconductor devices. This is due to the fact that
metallic film has orders of magnitude higher carrier density (~ 1022 cm-3) than
semiconductors

(1018

1020

cm-3).

described

Hooge’s

relation8,

S R(1/ f ) = 2πζ R 2 /( N ω ) , metallic devices will have much larger the total number of

carriers N than a semiconductor device of the same dimension. Also, semiconductor
materials have a higher value of ζ, due to the doping atoms, defects, and combinationrecombination processes inside the material. This attribute of low 1/f noise will be
significantly advantageous for applications involving low frequency measurements, such
as contact mode AFM, and other static force measurements.

However, measuring the very low 1/f noise of metallic devices is challenging, as
most amplifiers using semiconductor transistors will have higher noise than the metallic
device at low frequency. An AC bridge method, invented by John Scofield in 1987 9, has
to be employed to enable successful measurement. With this method, the measurement of
device noise is super-heterodyned to the modulation frequency at which the preamplifier
has optimal noise performance and contributes negligible extra noise.

A diagram of the measurement setup is shown in Figure 3-5. The first
amplification stage uses transformer coupled amplifier (Stanford Research SR544). Its
noise figure contour is shown in Figure 3-6. It can be seen that the best noise
performance is at around 100 Hz and 50 Ω source resistance, corresponding to a noise
figure less than 0.2 dB or less than 2% of the total noise. So at this condition, noise from
the amplifier is truly negligible. The NEMS devices measured in the experiments
typically have a resistance less than 100 Ω. The devices under measurement are
connected in a Wheatstone bridge configuration with two high-precision metal wire
decade resistors. Those decade resistor can be tune with precision better than 0.01% to
null out any DC imbalance of the bridge, minimizing the loading to the amplifier
transformer. A Stanford research SR830 lock-in amplifier is used to provide an excitation
signal at 109 Hz with RMS amplitude of 10 mV. Demodulated signal output from the
lock-in is connected to a HP 35665A FFT spectrum analyzer. Varying lock-in time
constant (or measurement bandwidth) is used to measure different decades of frequency
spectrum.

Figure 3-5 AC bridge setup to measure 1/f noise low resistance NEMS

Figure 3-6 Noise figure contours of Stanford Research SR 554 amplifier

70
Another important and very useful attribute of this measurement method is that it
is a phase-sensitive detection (PSD). The dual phase lock-in amplifier can measure both
the amplitude and phase information in the noise spectrum. In fact, the measured
spectrum from the lock-in can be express as9:

Sv ( f ) = Sv0 ( f 0 − f ) + Svi ( f ) cos2 δ .

(3.7)

Here f 0 is the carrier frequency, and f is the sweeping frequency in the spectrum. Sv0 is
the phase-insensitive background noise power spectrum, including Johnson noise from
the device and amplifier noise. The significance of this AC bridge method is that the
measured low-frequency noise is Sv ( f = 0) = Sv0 ( f 0 ) . So if f 0 is selected to be at the
lowest noise point in the amplifier noise figure contours, amplifier noise is minimized.

Svi is the phase-sensitive part of the noise, in our case mostly including the 1/f noise of
the device. (It is actually due to the 1/f resistance fluctuation of the devices.) It only
appears as voltage noise when excitation current is flowed through the device, and can be
measured with different phase δ . Using lock-in amplifier, both in-phase ( δ = 0 ) and its
quadrature phase ( δ = 90o ) components of noise spectrum can be measured, and both
components of Sv0 and Svi can be decomposed with the measurements as described by
equation (3.8).

⎧⎪ Sv0 ( f 0 − f )
Sv ( f , δ ) = ⎨ 0
⎪⎩ Sv ( f 0 − f ) + Sv ( f )

,δ =0
,δ =90o

(3.8)

Figure 3-7 Low frequency noise spectrum of 1 kΩ metal film resistor. Both quadratures
of lock-in modulation are measured

An example of the phase-sensitive measurement is shown in Figure 3-7, measured
with a commercial metal film resistor. Both quadratures from the lock-in are plotted. The
spectrum for δ = 0 shows negligible frequency dependence over the measured frequency
band as predicted by equation (3.8), except for some increase at very low frequencies
(mainly due to the drift of measurement instruments), while the spectrum measured with

δ = 90o shows clear 1/f frequency dependence with a knee at around 100 mHz. This
demonstrates the capability of the heterodyne measurement method, and also the very
low 1/f noise of metal film devices.

Two NEMS cantilever devices, as shown Figure 2-5c and d are then measured,
and the result is displayed in Figure 3-8. The dimension of the cantilever from Figure
2-5c’s metallic piezoresistor is 3 μm long and 0.2 μm wide, while the cantilever from
Figure 2-5d’s piezoresistor is 1 μm long and 0.1 μm wide. Including the different
resistance of the two devices, from Hooge’s relation, the cantilever in Figure 2-5d is
expected to have larger 1/f noise than the cantilever in Figure 2-5c. This is exactly what
was observed from measured noise spectrum data, which shows higher noise from Figure
2-5d’s cantilever at low frequency, even though it has less noise at higher frequency. The
measured 1/f noise frequency knees are 8 Hz for Figure 2-5c’s cantilever and 100 Hz for
Figure 2-5d’s cantilever, respectively. The very low 1/f noise of these nanoscale devices
is very significant compared with measured data from semiconductor (doped silicon)
devices which shows 1/f noise at 100 nV/√Hz level with frequency knee at around 1–10
kHz10. When scaled to the same dimension and biasing conditions, the estimated 1/f noise
of metallic devices is more then two orders of magnitudes lower than that of devices
made of doped silicon, as expected from the previous discussion.

1/2

Voltage noise [nV/Hz ]

cantilever c)
cantilever d)

1m 10m100m 1 10 100 1k 10k 100k
Frequency [Hz]
Figure 3-8 Low frequency noise spectrum of two NEMS cantilever devices. Their 1/f
noise knees are measured to be at 8 Hz for cantilever Figure 2-5c and at 100 Hz for
cantilever Figure 2-5d respectively

3.2

Frequency down-conversion measurement

The piezoresistive detection enables convenient electrical measurement of the
devices’ mechanical motion with integrated transduction. But unlike optical detection
methods in which the actuation and detection circuits are isolated by laser beam,
piezoresistive detection method integrates both into one electrical circuit. Although the
impedance mismatching problem can be solved by using low resistivity metal film
transducers, other problems caused by this integration still remain. The major one is the
strong capacitively coupled background signal from the piezoelectric actuator to the
detection port when homodyne detection is used. This background signal can be many
orders of magnitude larger than the actual piezoresistive signal from the miniscule
mechanical motion of the device. It severely lowers the system’s dynamics range and
makes the cantilever useless for practical applications which require accurate
measurement of resonance frequency, amplitude and phase.

A heterodyne frequency down-conversion method was invented by Bargatin et. al.,
originally designed for solving impedance mismatching problems for their doped silicon
piezoresistive cantilevers with high resonance frequency. A diagram of the measurement
scheme is shown in Figure 3-9. Instead of using DC bias, an AC biasing signal is used,
and its frequency is kept at ω + Δω , a fixed intermediate frequency Δω higher than the
actuation frequency ω . So we can write the AC voltage signal generated across the
NEMS devices as:

v%o =

Rd 0
ΔR
Vb 0 cos[(ω + Δω )t ] × d 0 cos(ωt + φ )
Rd 0 + Rb
Rd 0

ΔRd 0
Vb 0 [cos( Δωt − φ ) + cos((2ω + Δω )t + φ )]
Rd 0 + Rb

(3.9)

Here Rd 0 and Rb are the DC resistance of the device and a bias resistor, ΔRd 0 is the
amplitude of the resistance change of the device when it is driven with the actuator at
frequency ω . An AC biasing signal Vb 0 cos[(ω + Δω )t ] is applied to the device. The bias
signal mixes with the mechanical motion of the piezoresistor, and generates signals at
beat frequencies Δω and 2ω + Δω . Since the intermediate frequency Δω can be set to be
much lower than ω , the higher frequency beat signal at 2ω + Δω can be easily filtered
with a low pass filter. Only the lower frequency signal at Δω is measured and the output
signal can be expressed as:

vo =

ΔRd 0
Vb 0 cos( Δωt − φ ) .
Rd 0 + Rb

(3.10)

Since this beat frequency signal can only be generated from the mechanical oscillation of
devices, and all other coupled signals at higher frequency from both the actuator and bias
signal source can be aggressively removed by filters, in principle no background signal
will be measured with this method. However, some nonlinear effects and interference still
exist in the system and produce some frequency components at Δω , but with much lower
amplitude compared to the wanted signal.

Figure 3-9 depicts the measurement setup. Two frequency sources are used to
generate actuation and bias signals. Their outputs are split and mixed with a commercial
mixer to provide the reference signal at intermediate frequency Δω for the lock-in

76
amplifier. Intermediate frequency in the range of 50 kHz to 100 kHz, is often used. The
signal from the device is filtered with a very sharp low-pass filter (cutoff frequency = 100
kHz), and measured with a lock-in amplifier after amplification.

Figure 3-9 Frequency down-conversion piezoresistive measurement

Example results of using homodyne measurement with DC bias and network
analyzers, and using frequency down-conversion methods are shown in Figure 3-10 and
Figure 3-11. In Figure 3-10, the resonance peak is on a relatively large background, and
the phase response is distorted and shifted. The greatly reduced signal background, and
preserved phase of the resonance is very remarkable in Figure 3-11. The resonance peak
amplitude to background ratio is higher than 100.

2.0
160
140
120
100
1.0

80
60

0.5

Phase [deg]

Amplitude [mV]

1.5

40
20

0.0

7.90

7.95

8.00

8.05

8.10

Frequency [MHz]
Figure 3-10 Amplitude and phase of a cantilever measured with DC bias and a network

analyzer
200
100
80
100
60

-50

-100

11.0

11.1

11.2

11.3

11.4

11.5

Phase [deg]

Amplitude [mV]

150

11.6

Frequency [MHz]
Figure 3-11 Amplitude and phase of a cantilever measured with the frequency down-

conversion method

3.3

Phase-locked loop (PLL)

Phase-locked loop (PLL) is a very widely used technique in both analog and
digital circuits, with applications for radio, telecommunications, and computers11. In our
nanomechanical resonator research, this technique is employed to track the resonance of
the resonator device in real time, and for mass sensing and chemical gas sensing
applications. It can provide frequency measurement at very high precision with large
applicable bandwidth.

A phase-locked loop is composed of three elementary components (Figure 3-12):
a phase detector, a loop filter and a voltage-controlled oscillator (VCO). In a nutshell, the
principle of the phase-lock loop can be explained as follows: The phase of a periodic
input signal is compared with the phase of a VCO signal at the phase detector and the
difference is output as an error signal. This error signal is fed back to the control port of
the VCO after a low-pass loop filter, and tunes the VCO frequency toward the input
signal’s frequency to reduce the error signal and close the loop. At locked state, the VCO
frequency will be exactly equal to the frequency of the input signal within the loop
bandwidth.

Figure 3-12 Basic phase lock loop (reproduced as in Ref 11)

79
When PLL is used to track the resonance frequency of a NEMS resonator, NEMS
is actuated by the actuation signal output from the VCO, as shown in the diagram of
Figure 3-13, in a way slightly different than the basic loop. The resonator response signal
is amplified, and compared against the VCO signal at the phase detector. The error signal
is fed back to control the VCO. Ideally, the resonator response signal should have the
same frequency as the actuation signal from the VCO, but with a shifted phase from the
resonator. It is clear from the displacement response function of a forced oscillator with
damping:

f /m
ω − ω + iωω0 / Q

(3.11)

f /m
[(ω − ω ) + ω 2ω02 / Q 2 ]1/ 2

(3.12)

z (ω ) =

Its amplitude and phase are:

A(ω ) =

2 2

(ω02 − ω 2 )
].
ω0ω / Q

Voltage

φ = arctan[−

Frequency

Figure 3-13 NEMS embedded in a phase-locked loop

(3.13)

120
90

200

60
30

150

100

-30
-60

Phase [degree]

Amplitude [mV]

250

-90

-120
7.9

8.0

8.1

8.2

8.3

Frequency [Hz]

Figure 3-14 Amplitude and phase response at resonance frequency of a typical cantilever

in air

As shown in Figure 3-14, at resonance ω = ω0 , the phase shift of the resonator is zero, and
so is the error signal from the phase detector. It is clearer to see when the response is
plotted in a polar coordinate, as in Figure 3-15. The circled point is the resonance and
tracked point of PLL. Usually, a tunable phase shifter can be inserted before the phase
detector to null out unwanted phase shift from the circuit components. The low pass filter
will filter out high frequency signal components and noise. Three important loop
parameters determining the loop gain and bandwidth are phase detector gain K d , loop
filter gain K1 , and VCO gain K o .

Amplitude-Phase polar plot
90
120

0.35

0.30
0.25
0.20

150

0.15
0.10
0.05
0.00
0.00

180

0.05
0.10
0.15
0.20

330

210

0.25
0.30
0.35

240

300
270

Figure 3-15 Polar plot of a NEMS amplitude-phase frequency response

Since the signal from the NEMS resonator using piezoresistive detection is often
coupled with some background signal, basic loop configuration has to be modified to
incorporate the frequency down-conversion method, similar to Figure 3-9 but without
computer control. A diagram of the actual circuitry is shown in Figure 3-16.

One signal generator (HP 8648B) with external frequency modulation input is
used as VCO. A signal at fixed intermediate frequency Δω is generated by another
generator, and split to the lock-in reference input and to mix with the actuation signal,
generating the biasing signal at beat frequency ω + Δω . A high pass filter after the mixer
is necessary to filter out leaked signal at frequency Δω . Signal from the NEMS resonator
is further filtered and amplified. Then the lock-in amplifier is used to demodulate the
signal at the intermediate frequency Δω . One quadrature (Y) from the lock-in analog

82
output is fed back to the frequency modulation port of the VCO and tunes its frequency.
This is because from equation (3.10) Y ∝ sin(θ ) . Since at resonance, θ = 0 , and Y = 0 ,
when the loop tracks the resonance of NEMS, the negative feedback forces the NEMS
signal’s phase to be zero so that VCO frequency follows the resonance frequency.

Figure 3-16 Piezoresistive frequency down-conversion NEMS phase-locked loop

If we plot quadrature Y versus frequency, when the phase shift from other circuit
components is compensated, Y equals zero when VCO frequency is at resonance
frequency. So the error signal (Y) can be approximated in linear relation to the frequency
as equation (3.14) for small error signal:
ve ≡ Y = K d ( f c − f PLL ) .

(3.14)

Here f c is the center frequency of the resonance, f PLL is the loop operating frequency or
the VCO output frequency, and K d is the feedback gain (V/Hz). Y quadrature data
measured from a typical cantilever resonator device is shown in Figure 3-17.

20
15
10

Y [mV]

slope= - 8.6mV/kHz
-5
-10
-15
7.080

7.085

7.090

7.095

Frequency [MHz]

Figure 3-17 Y quadrature signal versus drive frequency of a typical NEMS cantilever

The error signal (Y quadrature signal) tunes VCO frequency as described by
equation (3.15):
f PLL = fVCO + Ko ve

(3.15)

Here fVCO is the center frequency of the VCO with zero control voltage (free running
frequency), and K o is the VCO gain (Hz/V).
So the full closed loop can be described as:
f PLL = fVCO + Ko K d ( f c − f PLL )
f PLL =

Ko K d
fc +
fVCO .
1 + Ko K d
1 + K0 Kd

= f c0 +

Ko K d
Δf c
1 + Ko K d

(3.16)

84
Here we use f c = f c0 + Δf c and fVCO = f c0 , assuming that the VCO center frequency is set
the same as the resonator’s initial frequency. The final equation tells how the loop works.
When the resonance frequency changes by Δf c , the loop frequency changes by
Δf c K /(1 + K ) , where K = Ko K d is the total loop gain. So the higher the loop gain, the
more faithful the PLL tracks resonance frequency.

The VCO gain K o can be set by the frequency modulation amplitude of the signal
generator (HP 8648B). The actual loop feedback gain K d is determined by the NEMS
resonator (its frequency, quality factor, and signal amplitude), and the voltage gain of
subsequent amplifiers and the lock-in amplifier. The value of K d can be approximated
with the slope of the data at the vicinity of the resonance frequency. In Figure 3-17, the
measured slope is 8.6 mV/kHz. Knowing the value of K o , their product gives the total
loop feedback gain. We thus can calculate the total loop gain from the above parameters.

The loop gain can also be measured by changing the center frequency of the VCO
and reading the locked frequency of the loop. From equation (3.16), the later is
proportional to the VCO center frequency with coefficient of (1 + K ) −1 . From measured
data, we can determine the value of K. In the following, we use both methods to measure
and calculate the loop gain, and compare their results. Figure 3-18 shows the measured
data of loop gain, with various Kd and fixed Ko at 2 kHz/V, using a typical 7 MHz
cantilever resonator. Kd is changed by changing the sensitivity of the lock-in amplifier.

85
Then, both calculated and measured values of loop gain are listed in Table 3-1. Excellent
agreement can be found between the two methods.

7.0868

PLL frequency [MHz]

7.0866
7.0864
7.0862
7.0860
7.0858
7.0856

Sensitivity= 500mV Kloop=0.36
Sensitivity= 200mV Kloop=0.91

7.0854

Sensitivity= 100mV Kloop=1.79
Sensitivity= 50mV

7.0852
7.0845

7.0850

7.0855

7.0860

7.0865

Kloop=3.70

7.0870

7.0875

VCO center frequency [MHz]

Figure 3-18 Phase-locked loop gain measurement with loop gain value set by various

lock-in sensitivities

Table 3-1 Phase-locked loop parameters measured and calculated

VCO gain Ko (Hz/V)

2000

Lock-in sensitivity (mV)

100

200

500

Feedback gain Kd (V/kHz)

1.72

0.86

0.43

0.172

Calculated total loop gain

3.44

1.72

0.86

0.344

Measured total loop gain

3.70

1.79

0.91

0.36

86
Equation (3.16) tells us that the loop frequency changes with the resonator
frequency, with a coefficient of (K/K+1). So the loop frequency fluctuation is also scaled
by the factor of (K/K+1) from the frequency fluctuation of the resonator itself. This effect
can be clearly seen in Figure 3-19, the loop frequency fluctuation versus various loop
gain K, and the fitting to (K/K+1) functional form.
20

Frequency instability [Hz]

18
15
13
10
fitting δf = A K/(K+1)

Loop Gain K [unitless]

Figure 3-19 PLL Frequency stability versus loop gain K.

It is helpful to consider the minimum resolvable frequency shift limited by the
thermomechanical noise of the mechanical resonator. A simplified expression is given in
equation (3.17), where DR is the maximum dynamic range available to the resonator,
defined as the ratio of the critical amplitude at the onset of nonlinearity to the
thermomechanical displacement noise floor 12. BW is the measurement bandwidth.

δω = ( 0 ⋅ BW )1/ 210( − DR / 20)

[Hz/ Hz ]

(3.17)

87
For the cantilever measured in Figure 3-19, its resonance frequency is ω0 ~ 7 MHz, and
its quality factor is Q~ 500 in vacuum. Assuming measurement bandwidth of 10 Hz and
resonator dynamic range 60 dB, the minimum resolvable frequency shift is evaluated to
be 0.37 Hz, corresponding to a mass resolution of about 40 zeptogram. This is way below
the actual measured frequency fluctuation in Figure 3-19, even with very low loop gain.
Thus, it can be concluded that the frequency noise in the PLL measurement is not limited
by the intrinsic noise of the resonator, but mostly from the noise in the measurement
electrical circuits and environmental fluctuations, including temperature and pressure
variation13. These extra noise sources severely deteriorate the mass sensitivity of the
resonator. Detailed theoretical noise analysis can be found in Reference12. One order of
magnitude improvement in frequency noise performance can be expected upon
optimization of the system.

An alternative implementation of phase-locked loop is to use a microcomputer as
a feedback controller, such as the scheme shown in Figure 3-9. In such a scheme, the
frequency of the signal generator is not controlled by analog signal and using a VCO, but
is calculated and set by the computer software. Thus, there is no limit on the range of
traceable frequency by the resonator bandwidth (100 kHz to 1MHz for typical high
frequency resonators) or the modulation amplitude of the VCO (up to 100 kHz for model
HP 8648B). The drawback is that the loop bandwidth is limited by the speed of
communication between the computer and the instruments, which is about 10 Hz in our
setup, using the GPIB interface. This scheme is more often used for low bandwidth
measurement in this thesis, while the analog loop allows for much faster measurements.

1.8

Reference

Gabrielson, T. B. Mechanical-thermal noise in micromachined acoustic and

vibration sensors. IEEE Transactions on Electron Devices 40, 903-909 (1993).

Callen, H. B. and Welton, T. A. Irreversibility and generalized noise. Phys. Rev.
83, 34-40 (1951).

Cleland, A. N. and Roukes, M. L. Noise processes in nanomechanical resonators.
J. Appl. Phys. 92, 2758-2769 (2002).

Hutter, J. L. and Bechhoefer, J. Calibration of atomic-force microscope tips. Rev.
Sci. Instrum. 64, 1868-1873 (1993).

Rugar, D., Mamin, H. J., and Guethner, P. Improved fiber-optic interferometer for
atomic force microscopy. App. Phys. Lett. 55, 2588-2590 (1989).

Heer, C. V. Statistical mechanics, kinetic theory, and stochastic processes.
(Academic Press, New York, 1972).

Li, C. S., Hesketh, P. J., and Maclay, G. J. Thin gold film strain-gauges. J. Vac.
Sci. Technol. A 12, 813-819 (1994).

Hooge, F. N. 1/f noise is no surface effect. Phys. Lett. A A 29, 139-140 (1969).

Scofield, J. H. Ac method for measuring low-frequency resistance fluctuation
spectra. Rev. Sci. Instrum. 58, 985-993 (1987).

Harley, J. A. and Kenny, T. W. High-sensitivity piezoresistive cantilevers under
1000 angstrom thick. App. Phys. Lett. 75, 289-291 (1999).

Gardner, F. M. Phaselock techniques, 3rd ed. (John Wiley & Sons, Hoboken, NJ,
2005).

89
12

Ekinci, K. L., Yang, Y. T., and Roukes, M. L. Ultimate limits to inertial mass
sensing based upon nanoelectromechanical systems. J. Appl. Phys. 95, 2682-2689
(2004).

Robins, W. P. Phase noise in signal sources: Theory and applications. (Peter
Peregrinus on behalf of the Institution of Electrical Engineers, London, 1982).

Chapter 4
Nanomechanical chemical gas analysis
with gas chromatography (GC)
Microscale total analysis system (μTAS) has been of great research interest during
the last few decades1. The need for miniaturized, compact, portable, and high-speed
chemical and biological analysis systems is driven by applications both in chemical,
biological, and environmental sensing, and in homeland security2.

Both qualitative and quantitative measurement and detection of specific chemical
compounds provide important information for the above-mentioned application
circumstances. Separation-based chemical analysis methods, such as chromatography and
electrophoresis, are particularly suitable for those tasks. Particularly in chromatography,
separation of a complex chemical mixture is achieved by the different partition between a
mobile phase and a stationary phase of each composition. A non-specific or selective
detector can be used to detect the separated analytes, and provide quantitative analysis
information about the mixture3,4. Miniaturization of such a chromatographic system is
being pursued by several groups, and substantial progresses have been made5.

In this chapter, we describe the development of a polymer-coated NEMS
resonator detector in a miniaturized gas chromatographic system. After a brief

91
introduction of gas chromatography, cumulative improvements of device sensitivity,
speed, and analysis capability are described. Finally, a successful analysis of the mixture
of chemical warfare agent simulants and their interferents are discussed. Problems related
to the slow diffusion process of gas species into polymer phase are also discussed.

4.1

Introduction of gas chromatography: column and
detectors

Gas chromatography or GC is one of the most important instruments in modern
analytical chemistry. It can be used to analyze organic and inorganic materials, in gas,
liquid, and solid phase (after being dissolved in solvents). Quantitative analysis of
complicated samples with high precision is obtained routinely. For example, a gas
chromatography-mass spectroscopy or GC/MS system is considered the gold standard of
analytical chemistry. Modern instruments utilize high levels of automation so that
hundreds of samples can be analyzed per day6,7.

Figure 4-1 Schematic representation of the chromatographic process. (Reproduced from

Miller, J.M., Chromatography: Concepts and contrasts, 2nd edition, John Wiley & Sons,
Inc., 2005, p. 44.)
Chromatography is the method used to separate components of a mixture sample
by utilizing their different partition in stationary phase — in the case of capillary GC, the
coating of the column wall. Vaporized sample is carried by the mobile phase (the carrier
gas) through the separation column, and the components of the sample are separated
based on their different affinity to and partition coefficients in the stationary phase. At a
given operation temperature, when ideal separation is obtained, each component has its
own characteristic elution time at which it exits the column. The effluents from the
column are sensed by a detector whose signal is related to the quantity (the relative
concentration or total mass/volume) of the chemicals, showing peaks in its signal trace.

93
Such a trace is called a chromatogram. Then each component can be identified by its
corresponding peak’s position in the chromatogram. Quantitative analysis of each
composition of the sample can be achieved by further analysis of the height, shape, and
area of the peaks in the chromatogram.

The chromatographic process and the principle of a GC can be explained further
with Figure 4-1. The horizontal lines represent the length of the column, and the vertical
direction represents time. Each horizontal line is a stage of the process at different time.
The instantaneous signal of the detector is displayed in the boxes, and time trace of it is
plotted as the chromatogram in the right. So at the beginning, a sample consisting of two
components — A and B — is injected, vaporized and pushed through the column by
carrier gas. When they flow through the column, they can exist in two phases: mobile
phase in the carrier gas, shown as the peaks above the line, and a stationary phase inside
the column coating material, shown as the peaks below the line. Component B has a
larger partition coefficient in the stationary phase, which is represented as a larger portion
of the peak below the line than component A. Since the mobility in stationary phase is
lower than in mobile phase, component B moves at a slower migration speed down the
column than component A. Given enough column length and time of flow, the two
components will be separated from each other completely as they pass the column, as
shown in the third line. Eventually, components A and B will exit the column
sequentially, separated both spatially and temporally. They enter the detector and
generate two peaks shown on the chromatogram trace at their elution time.

94
A complete capillary column GC instrument consists of three major components:
an injector, a column, and a detector. A diagram of the configuration of a typical GC
system is shown in Figure 4-2. All of the three components are crucial for the
performance of a GC system, to achieve optimal analysis capacity, sensitivity, and speed.
The most often used carrier gases include nitrogen, hydrogen, and helium. In the case of
field application, air is also used. The injector is a section of heated tubing to vaporize the
injected liquid sample and let the carrier gas push the sample into the column. Various
injection modes such as split, splitless, and on-column injection, are applied on capillary
GC, using different configurations of flow paths. In order to obtain optimal analysis
result, the injection method has to be chosen according to the type and amount of sample
to be analyzed.

Figure 4-2 Instrument diagram of a GC (from www.practicingoilanalysis.com)

Two types of column are commonly used in modern GC systems: packed and
capillary. Pack columns are usually made of stainless steel or glass, filled tightly with
liquid stationary phase coated inert solid support material. They are easy and cheap to
make, and allow for a larger amount of sample to be injected. Capillary columns are most

95
often made of fused silica capillary tubes with an inner diameter typically of 100–250
microns. Unlike packed columns, capillary columns are not filled but are open tube with
liquid stationary phase coated on the tube walls. They can be made much longer than
pack columns, and have higher analysis efficiency and capability.

Frequently used detectors in GC include the flame ionization detector (FID),
thermal conductivity detector (TCD), photoionization detector (PID), electron capture
detector (ECD), and mass spectrometer (MS). FID and MS are the most widely used
among the total of more than 60 different detectors. Put briefly, FID uses a small oxyhydrogen flame to burn the column effluent, producing some ions in the process. The
amount of ions that can be generated in the flame is proportional to the carbon content of
the chemical, as quantified using effective carbon numbers (ECN) for various organic
compounds. The ions are collected by electrodes under a large bias voltage and form a
small current as the signal. Since all organic compound analytes are burnt in the detector,
FID is a destructive detector, detecting the total mass flow rate of the analytes.
All the experiments described in this thesis are conducted with a Hewlett-Packard
5890 GC system, using a 100 μm inner diameter capillary column and an FID detector.
Hydrogen is used as the carrier gas, because the best separation can be achieved at a
higher flow rate than helium or nitrogen so that a higher analysis speed can be obtained.

4.2

NEMS mass sensor in ambient condition

NEMS resonators have been demonstrated as a mass sensor with unprecedented
mass sensitivity when their resonance frequency is measured upon the change of their
inertial mass8,9. The frequency-mass responsivity of a resonating inertial mass sensor is
given by:
R=

1 ∂ω0
=− 0 .
2π ∂ M eff
2 M eff

(4.1)

This expression shows that the minuscule effective mass and high resonance frequency of
NEMS account for their very high mass sensitivity, orders of magnitude higher than
traditional gravimetric mass sensors such as quartz crystal microbalance (QCM), surface
acoustic wave (SAW) and flexural plate wave (FPW) devices. The recent mass sensing
milestone was achieved using ultrahigh frequency (UHF) NEMS resonators,
demonstrating 100 zeptogram scale mass with a resolution of only 7 zeptogram8. The
experiment was done at cryogenic temperatures and in an ultrahigh vacuum environment.
Physi-sorption of xenon gas on the NEMS surface at low temperature was utilized to
accrete the calibrated amount of mass onto the NEMS.

As described in Chapter 2, high frequency nanoscale cantilevers retain their
quality factor even at atmospheric pressure and room temperature, which allows high
precision measurement of their resonance frequency change. Thus, using them as mass
sensors at ambient conditions becomes possible, enabling many applications (such as
chemical gas sensing). Since physi-sorption is not possible at room temperature, chemisorption is needed to allow the accretion of mass on the device. The surface of NEMS

97
devices need to be functionalized with adsorptive materials to enable efficient adsorption
or absorption of interested chemical species.
As shown in Figure 4-5, we demonstrate attogram scale mass sensing with
nanocantilevers in ambient conditions, namely room temperature and atmospheric
pressure. We achieve this by functionalizing the device surface with a thin polymer film
having a high partition coefficient for the species of interest.

To maintain the

nanoresonator’s quality factor and frequency, this film must be extremely thin. For our
initial demonstration we employ polymethyl methacrylate (PMMA), which forms a very
thin, conformal layer without the need for elaborate surface treatments. The NEMS
devices are spin coated at 4000 rpm with a solution of 0.5 wt % 495 K PMMA in anisole.
The resulting polymer film thickness is approximately 10 nm, as is confirmed by both
atomic force microscopy and careful measurement of the change in resonance frequency
arising from mass loading by the coating after its application. A decrease of only 20–30%
in the resonance quality factor is typically observed after application of a layer of 1–10
nm coating. In Figure 4-3, such a coating process is illustrated, showing the cases of both
unsuccessful and successful coating. The frequency shift due to the added mass of
PMMA coating can be readily measured and used to calculate the film thickness. Figure
4-4 shows the resonance response of a typical cantilever before and after the coating
process. Atmospheric pressure mass sensing measurements are carried out on two typical
cantilevers operating at resonance frequencies of 8 and 127 MHz (Figure 2-5’s
cantilevers c and d). The mass responsivities of the two devices used in these experiments
are calibrated by separate low temperature physi-sorption experiments using a controlled

98
flux of xenon atoms. We obtain values of 7 Hz/ag and 0.68 Hz/zg respectively, in good
agreement with our predictions from finite element analysis.

Figure 4-3 Coating cantilever resonators with polymer: a) a too thick layer of polymer

glues the cantilever down to the substrate and prevents its oscillation; b) optimal coating
of the cantilever with very thin polymer

Amplitude [mV]

Δf=16 kHz

7.7

7.8

7.9

8.0

8.1

Frequency [MHz]

Figure 4-4 Frequency shift and quality factor reduction of the resonance response of the

cantilever before (red) and after (blue) coating

99
In separate experiments, these devices are exposed to a series of 1,1,difluoroethane (C2H4F2, , hereafter DFE) gas pulses at room temperature and atmospheric
pressure. These devices are read out using a computer-controlled phase-locked loop
(PLL), which allows us to excite and track the nanocantilevers’ resonance frequency in
real time. Our setup enables tracking the resonance frequency of cantilevers in air with a
precision better than 10-6 (1 ppm) using a time constant of 100 milliseconds. In response
to each pulse, the resonance frequency of the cantilevers first decreases rapidly during the
injection of gas, then recovers when the injection is completed, as the adsorbed gas
species slowly desorb from the coating (Figure 4-5).

This reversible adsorption-

desorption process carried out under ambient conditions yields temporal “dips” of
frequency shift, instead of the “steps” seen in the low temperature UHV physi-sorption
experiments. Increasing the DFE pulse length yields progressively higher peak mass
adsorption of DFE, as is reflected in the increasing mass response dips. Since the time
constant of the frequency tracking phase-locked loop (PLL) circuitry is set to be 100
milliseconds, the response and recovery time are limited only by the dead volume of the
testing chamber. With the 8 MHz cantilever, we are able to resolve mass accretion peaks
as small as 10 ag in real time, with mass noise floor ~ 1 ag. With the 127 MHz
cantilever, we achieve the highest mass resolution, estimated to be ~ 100 zg, allowing
mass peaks of 1 ag to be resolved (Figure 4-5).
Theoretically,

δ M ~ ( M eff / Q ) ⋅10− DR / 20 .

mass

resolution

given

the

expression

The 127 MHz cantilever has effective mass M eff = 100 fg ,

dynamic range DR=80 dB, and quality factor Q ~ 400 in air. Using these values, we
expect a mass resolution of ~ 25 zg at room temperature. Environmental fluctuations —

100
which include those of temperature, pressure, humidity, etc. — apparently degrade our
resolution to the observed value of ~ 100 zg, which is only a factor of four away from
ideal performance.

10 ag

17 ag

-200

35 ag

-300

50 ag

-1000

2 ag

-2000

1ag

Mass [attogram]

Frequency Shift [Hz]

-100

-3000

5 ag
-4000

2000

4000

6000

Time [seconds]

Figure 4-5 Real-time NEMS chemisorption measurements.

1,1-difluoroethane gas

molecules are chemisorbed onto the polymer-coated surfaces of two separate
nanocantilever devices. The measurements are carried out in air, at atmospheric pressure
and room temperature. The top and bottom traces are measured with 8 MHz and 127
MHz nanocantilevers(Figure 2-5’s cantilever c and d), respectively.
resolvable mass is below 1 ag (red arrows)

The minimum

101

4.3

Polymeric film functionalized NEMS detector in GC

When using gravimetric sensor for gas concentration sensing, instead of absolute
mass sensitivity, it is more sensible to use areal mass sensitivity, the mass sensitivity
normalized by available device area. This is necessary simply because a larger device has
larger surface area to adsorb more mass than a smaller device. The conversion from
unprecedented absolute mass sensitivity of the NEMS resonator to an equivalent
chemical sensing sensitivity can be justified by examining the Sauerbrey equation of
areal mass sensitivity:
Sm =

R Aeff
f0

(4.2)

Here R is the mass responsivity as defined in equation (4.2), Aeff is the effective surface
area of the device available for adsorption of mass, and f 0 is the resonance frequency. If
equation (4.1) is plugged into, it can be written as:
Sm =

Aeff
f0

(−

f0
) = − eff ∝
2 M eff
2 M eff
ρ teff

(4.3)

Here ρ is density of the device material and teff is the effective thickness of the device.
This relation shows that the areal mass sensitivity is inversely proportional to the
thickness of the device. It can be exemplified by the improvement of flexural plate wave
devices (FPW) from bulk acoustic wave (BAW) and surface acoustic wave (SAW)
devices. In BAW and SAW devices, the effective thickness is the operational acoustic
wave length in the devices, on the order of hundreds of microns. While in FPW, since the
thickness of the plate is thinner than the acoustic wave length, the actual device thickness,
which can be made below 100 micron, is taken as effective thickness. Thus better areal

102
mass sensitivity can be obtained with FPW. NEMS resonators have much lower thickness
than all of these acoustic wave devices. For example, the nanoscale cantilevers described
in this thesis have a typical thickness of only 100 nm. Thus, as indicated in Table 4-1,
several orders of magnitude of improvement in areal mass sensitivity can be achieved.

Table 4-1 Comparison of areal mass sensitivity of various acoustic devices and NEMS

resonators
Sensor

Theoretical Sm (cm2/g)

Typical Sm (cm2/g)

Bulk acoustic wave

−n / ρλ

−14

Surface acoustic wave

− K (σ ) / ρλ

−10 – −100

Flexural plate wave

−1/ 2ρ d

−400 – −1000

−1/ ρ t

−8000 – − 100000

NEMS – nanocantilever
8MHz ~ 127 MHz

Polymeric thin films have been widely used as adsorptive materials for various
gas sensing applications. Analyte gas molecules are absorbed and diffused into polymeric
film until equilibrium is reached. The different chemical interaction forces between
different types of gas molecules and the polymer gives the selectivity of a particular
polymer. This can be quantified using the partition coefficient K c . K c is a thermal
equilibrium constant, and is defined as the ratio of analyte volume concentration in gas
phase cgas to that inside the polymer film c poly :

103

Kc =

c poly
cgas

(4.4)

Typical values for K c for a particular polymer-gas combination can be in the range of
1000–1,000,000. The polymer film will have large selectivity for one analyte gas with
large K c over another analyte gas with low K c . K c is also a strong function of
temperature and the analyte vapor pressure. Thus, the polymer material can be chemically
engineered to target a specific chemical group of gas analytes, to achieve selective
sensing with a very low false-alarm rate. For example, a hydrogen-bond acid polymer
named DKAP is developed by the Sandia National Laboratory for detection of
phosphonate gas molecules, which are precursors and simulants of nerve gas agents. The
partition coefficient between DKAP and dimethyl methylphosphonate (DMMP) can
approach 1,000,000, while it is very small between DKAP and common alkenes. So
DKAP has excellent selectivity toward interested nerve gases.

We used solution evaporation method to coat the cantilever devices with DKPA
polymers. A droplet of DKAP solution in toluene with concentration of 0.05mg/ml is put
on the device chip. After the solvent evaporates, thin film of polymer with thickness
about 10 nm forms on the surface. This method has poor control of film uniformity, but is
very simple and still has very high yield. To improve the coating uniformity and prevent
coating the substrate, other novel methods with more complexity are possible, including
microspray, electrochemical methods, and self-assembly techniques.

104
An integrated microscale gas analyzer (MGA) includes a microscale injector/preconcentrator, separation column, and detector. The functionality of the first two
components has been demonstrated and is under development in many groups, including
the Sandia National Laboratory5,10-12. Before testing a fully integrated system, the
functionality of a NEMS-based detector is evaluated using a traditional GC system. We
thus set up a commercial GC system (Hewlett-Packard 5890), and tested the NEMS
detectors with it, at Sandia initially and later at Caltech. The device is housed in a flow
cell, and connected to the outlet of GC column. The original FID detector of the system is
connected in serial after the NEMS. A diagram of the experiment setup is shown in
Figure 4-6.

Figure 4-6 Setup to test NEMS detector with commercial GC system with FID detector

connected in serial
The minimized volume of the flow cell is crucial in order to reduce the dead
volume, or hold-up volume, of the whole system. Large dead volume can cause

105
broadening in the chromatographic peaks and deteriorate the analysis capability of the
system. This becomes more essential for a GC system working at a very fast spend such
as in the microscale gas analyzer, which requires total analysis time to be only a few
seconds. Thus, reducing the unnecessary dead volume of the system is crucial to
obtaining optimal analysis performance. For example, a benchmark of the microscale gas
analysis system requires 25 analysis channels (defined as the number of resolvable peaks
in predefined time) within 4 seconds, which is equivalent to a maximum peak width of
160 milliseconds. At a typical column flow rate of 1 ml/min, the hold-up volume of the
system needs to be smaller than 2.67 microliters.

Initially, a flow cell is designed with volume of 50 microliters. The NEMS device
is housed inside the cell. A 10 meter long column is used, GC oven temperature is at 50
°C, and inlet pressure is at 50 PSI. The device assembly is placed inside the oven.
Samples containing mixture of various analytes in carbon disulfide (CS2) solution are
tested. Tested chemical analytes include both chemical warfare agent simulants and some
interferents. Their names, formulas, densities, and molecular weights are listed in Table
4-2. In Figure 4-7 and Figure 4-8, the chromatograms obtained during this first successful
demonstration of the NEMS detector in a GC system are shown.

In Figure 4-7, 1 μl of sample containing equal concentration (1% v/v) of DMMP,
DIMP, DEMP and MS in CS2, together with ten times higher concentration (10% v/v) of
3-MH, is injected into the system. Chromatographic traces from both NEMS (purple) and
FID detector (blue) are displayed. Although 3-MH concentration is ten times higher than

106
other analytes, its corresponding peak only appears in the FID signal as the largest one
adjacent to the solvent peak (see inset). The large FID response to 3-MH is because of its
large equivalent carbon number (ECN). However, this peak is completely absent in the
NEMS signal trace. This indicates that the DKAP coating polymer has very low
adsorption of 3-MH. A more complicated mixture of all of the fifteen analytes is then
injected, and chromatogram traces are obtained as shown in Figure 4-8. Similar
selectivity of NEMS detector to other interferents can be observed. Successful separation
of typical CWA simulants including DMMP, DIMP, DEMP, DCP, and MS is achieved
and clearly visible as separated peaks on the NEMS frequency shift signal trace. However,
even with this 10 meter long column and an analysis time longer than 10 minutes, those
analytes are not baseline separated from each other. Each peak, both in NEMS and FID
traces, is severely broadened with extra long tailing. In fact, in an attempt to do faster
separation of only DMMP and solvent when using a one meter long column, poor
separation can be achieved within a 30 second analysis time, as shown in Figure 4-9.
Also, those NEMS traces show poor resolution with low signal to noise ratio, indicating a
reduced limit of detection. These problems are mainly caused by the substantially large
dead volume of the 50 microliter chamber used to house the NEMS chip. By reducing
the chamber volume further, both improved separation ability and limit of detection of
the system can be obtained.

107
Table 4-2 List of tested chemicals and their formulas, densities, and molecular weights

(MW), including CWA simulants (*) and interferents
No. Symbol

Formula

Density MW

Full name

(g/ml)

3MH

CH3CH2CH2CH(CH3)C
H2CH3

0.687

100.20 3-methylhexane

TOL

C6H5CH3

0.865

92.14

CH3(CH2)6CH3

0.703

114.23 Octane

DMMP*

CH3P(O)(OCH3)2

1.145

124.08 Dimethyl methylphosphonate

C7OH

CH3(CH2)5CHO

0.817

114.19 Heptanal

2-CEES*

ClCH2CH2SC2H5

1.07

124.63 2-Chloroethyl ethyl sulfide

C8OH

CH3(CH2)6CHO

0.82

128.21 Octanal

DEMP*

CH3P(O)(OC2H5)2

1.041

152.13 Diethyl methylphosphonate

DCP*

(C2H5O)2P(O)Cl

1.194

172.55 Diethyl chlorophosphate

DNBS*

CH3(CH2)3S(CH2)3CH3

0.838

146.29 di-n-butyl sulfide

DIMP*

(C3H7O)2P(O)CH3

0.976

180.18 Diisopropyl methylphosphonate

C11

CH3(CH2)9CH3

0.74

156.31 Undecane

DCH*

Cl(CH2)6Cl

1.068

155.07

NAPTH

C10H7OH

MS*

2-(HO)C6H4CO2CH3

Toluene

Dichlorohexane

144.17 1-Naphthol
1.174

152.15 Methyl salicylate

1000

Solvent
3MH

FID current [μA]

108

100

MS
DEMP

-500

DIMP

DMMP

Frequency shift [Hz]

100

-1000

100

200

300
400
Time [second]

500

600

Figure 4-7 Gas chromatogram from NEMS detector (purple) and FID detector (blue),

showing peaks from five analytes (3MH, DMMP, DIMP, DEMP, MS) with similar
concentration

3MH

Toluene

100
10

100

C11

100
NAPTH

FID current [μA]

1000

Solvent

109

-2 0 0

DCH
DEMP

-1 0 0

DIMP

DMMP

Frequency shift [Hz]

-3 0 0

100

200

300

400

500

600

T im e [s e c o n d ]

Figure 4-8 Gas chromatogram from NEMS detector (purple) and FID detector (blue),

showing peaks from ten analytes (C8, Toluene, 3MH, DMMP, DIMP, DEMP, DCH,
NAPTH, C11, MS) with similar concentration

Frequency Shift [Hz]

DMMP
-1000

-2000

CS2
-3000

Time [second]

Figure 4-9 Faster GC separation with 1 meter long column

110
To further reduce the dead volume of the system, a micro-machined flow chamber
using a microfluidic formation is designed and made. A 20 micrometer deep and 2.5
millimeter long channel is etched between inlet/outlet holes on a glass chip. Thus the
total volume of this flow cell is defined by the channel, which has a volume of only 15
nanoliters. Then, instead of the previous flow cell configuration which puts the device
chip inside the flow chamber, the glass lid/channel is assembled on top of the device chip
and sealed with vacuum epoxy. Two pieces of capillary tubing with 100 micron inner
diameter are inserted into the holes to allow inlet and outlet gas flow. A diagram and
photo of such an assembly is shown in Figure 4-10.

Figure 4-10 Micro-machined flow chamber with microfluidic flow channel and the

assembly with NEMS device chip. Total channel volume is only 15 nanoliters.
Remarkable improvement of the system performance is achieved immediately
after using the nanoliter volume assembly. Figure 4-11 shows chromatograms obtained at
very fast speed. A one meter long column is used, and fast temperature programming is
employed to further improve the speed and separation. To do that, an on-column heater

111
made of Ni-Cr wire, is wound around the column. The heater can provide a heating ramp
of about 20 °C/sec when 20 V heating voltage is applied at the moment when the sample
is injected. Very good separation can be achieved within the analysis time of only a few
seconds. To acquire the first chromatogram in Figure 4-11, 1 μl of sample containing a
solution of five simulants (DMMP, DEMP, DIMP, DCP, MS) in CS2 solvent is injected.
They can be successfully baseline separated as indicated by the individual sharp peaks in
both the NEMS and FID signal traces. In the second chromatogram, sample containing
thirteen analytes (excluding 3-MH and NAPTH in Table 4-2) is injected. Although
baseline separation of all analytes is not achieved, nine analytes can be clearly identified
from the chromatogram. Some analytes (CEES, DNBS and Undecane) are missing in the
chromatogram, due to the adjacent large peaks with broader width which cover the peak
from these analytes with smaller response. The fastest analyte peak (DMMP) shows a full
width at half maximum (FWHM) of less than 100 millisecond, indicating a channel
number of more than forty at this condition.

Another important feature of the polymer coated NEMS sensors is their chemical
selectivity to different analytes, as determined by the interaction of the analyte and the
coating polymer. In comparison, the FID detector is not very selective, with its response
proportional to the equivalent carbon number (ECN) of the analyte only. The DKAP
polymer (Figure 4-12) has a strong hydrogen bond and is designed to be selective to
organophosphonate chemicals, such as DMMP and DIMP. This selectivity can be clearly
seen from the second chromatogram in Figure 4-11, as the largest peaks corresponding to
toluene and octane in the FID signal are completely absent in the NEMS signal. But the

112
NEMS signal shows strong response to other organophosphonates. It indicates the strong
selective of DKAP polymer for orgnaophosphonates to alkenes and toluene. In Figure
4-12, the relative responses of DKAP-coated NEMS and FID detectors to all tested
analytes are plotted. The strong selectivity of DKAP to DMMP, DEMP, and DIMP is
clear as the protrusion point toward them; FID is not very selective showing a more
isotropic distribution of data points.
The selectivity of the detector is very important in improving the analytical
capability of the microscale analysis system, since at a very fast analysis speed and
microscale dimension, baseline separation of large number of analytes is challenging and
many analytes may co-elute. Using a selective detector relaxes the demand for separation,
as two overlapped analyte peaks that can not be resolved with a nonselective detector can
be detected by two detectors with strong selectivity for each of them respectively. Ideally,
two completely chemically orthogonal detectors will double the resolvable channel
number of the system. Although chemically orthogonal coating is difficult to realize, a set
of different coatings with less degree of chemical orthogonality still will improve the
analysis capability of the system by using some pattern recognition algorithm. Because of
the separation of the column, such an algorithm will be much simpler than those needed
for the proposed system using bare sensor arrays13,14.

113

1.0

-2000

frequency shift (Hz)

-6000

0.5

-8000
0.0

4 5

-2000

-4000

-6000

1.0

FID current (nA)

-4000

8 10
9,10
7 8

0.5

15
0.0

time (s)

Figure 4-11 Very fast GC chromatogram from both NEMS (red) and FID (blue)

detectors, obtained using nanoliter volume chamber. Top graph shows chromatogram
acquired from sample solution of five different analytes, and bottom chromatogram is
obtained from sample solution of thirteen different analytes. Each analyte peak is
identified with the number listed in Table 4-2.

114

Figure 4-12 Relative response of DKAP-coated NEMS and FID detectors to various

analytes
A different polymer, poly-caprolactone (PCL), is tested to determine the extent of
difference between its selectivity and that of DKAP polymer. Chromatograms are
acquired using cantilever resonators coated with DKAP and PCL respectively, as shown
in Figure 4-13. Their relative response of different analytes is plotted in Figure 4-14.
Apparently, the PCL polymer shows no difference in chemical selectivity from the
DKAP polymer. But it shows a different distribution of responses among test analytes,
which gives additional information that can be used to analyze the sample.
There are several dozen commonly used sensitive polymer coatings for gas
sensing. It still remains to find the optimal combination which provides the best
orthogonality for different applications involving different types of targeted analytes.

115

frequency shift (Hz)

DKAP
-2000

-4000

PCL
-2000
-4000
-6000

time (s)

Figure 4-13 Chromatogram of thirteen analytes from cantilever resonators coated with

DKPA and PCL polymer, respectively, acquired in different runs

Figure 4-14 Relative response of DKAP- and PCL-polymer coated NEMS to various

analytes

116
The limit of detect (LOD) of the NEMS detector can be determined by measuring
the response at various analyte concentrations, and then extrapolating to the frequency
readout noise floor to find out the corresponding lowest concentration. However, in a gas
chromatography measuring system, constant concentration cannot be generated; instead
the effluent of analytes in carrier gas with time-varying concentrations exits the column.
By using the mass concentration in injected sample solution, the flow rate in the column
and split line, and measuring the peak width, the averaged concentration within the peak
can be determined. In this way, by varying the concentration in the sample solution,
various averaged concentrations in the gas phase of the column effluent can be generated.
The NEMS detector response in frequency shift is then measured at various averaged
concentrations, as shown in Figure 4-15. Two sets of data of NEMS response to DIMP
are obtained using 10 meter and one meter long columns. When using the 10 meter long
column, the analyte peak shows a typical width of 600 seconds, while the 1 meter column
generates peaks with a width of about 1 second. At slow separation speed with longer
peak width, the LOD can be determined as better than one part-per-billion (ppb).
However, when the separation speed is increased with the 1 meter column, the sensitivity
of the NEMS detector is dramatically reduced. As shown in Figure 4-15, with a 1 second
peak width, the sensitivity is decreased by a factor of 300, giving a LOD of about 300
ppb. The concentration sensitivity of the NEMS detector is traded for improved speed.
This effect is due to the slower diffusion speed of the gas phase into the polymer phase,
so that the polymer coating film takes a relatively longer time to reach equilibrium with
the gas phase concentration and give the maximum possible response from the detector.
Thus, the faster the separation speed with the shorter peak width, the less response the

117
detector outputs. A similar problem was seen previously — large chamber size reduces
sensitivity too, but it can be improved by using a smaller chamber with a volume of only
nanoliters. But since the diffusion constant of gas molecules in the polymer phase is
orders of magnitude smaller than that in gas phase, the corresponding time constant is
much longer.

Figure 4-15 Maximum NEMS detector frequency shift at various DIMP concentrations.

Two sets of data obtained using slow and fast GC separation are plotted, showing
reduced sensitivity at high separation speed.

This diffusion problem can be manifested qualitatively by solving the diffusion
equation in polymer phase:
∂c
∂ 2c
=D 2.
∂t
∂x

(4.5)

118
Two boundary conditions are:

∂c / ∂t = 0 at x = 0 (i.e., no diffusion beyond the substrate)
and

c( L, t ) = c0 for t > 0
(i.e., concentration at the polymer-gas interface is constant)

(4.6)

(4.7)

If c0 is constant, Equation (4.5) can be solved to give an analytical solution for the total
amount of mass of absorbed gas molecules as15:

m(t ) = mmax [1 −

2 ∞ exp(

π 2 n =1

−π 2 ( n − 12 ) 2
Dt )
L2
],
(n − 12 )2

(4.8)

where D is the diffusion coefficient of the gas molecules inside the polymer, L is the
polymer film thickness and mmax is the maximum accumulated mass inside the polymer
film at t → ∞ (i.e., when equilibrium is reached). In Figure 4-16, solution (4.8) is plotted
against time with various assumed values of diffusion coefficient D. As clearly seen in
the plot, at a very low diffusion coefficient, a very long time is needed for the detector to
reach the maximum response. For example, for a diffusion coefficient of 10-16 cm2/s,
1000 seconds after the start of exposure to the analyte, the response of the detector only
reaches 36% of the maximum. After 1 second exposure, the detector only shows 1% of
the maximum response. When t is so small that m(t)/mmax < 0.6, equation (4.8) can be
very well approximated with the square root of t as shown in Figure 4-17. The spatial
concentration distribution of the gas molecules inside the polymer coating at various
times is plotted in Figure 4-18, further manifesting the absorption process of gas
molecules from gas phase to the polymer phase. Fourier number τ = t ⋅ D / L2 is used as
the unit of time. More complete solutions to the problem of chemical species diffusion
into a thin film can be found in the literature16.

119

Figure 4-16 Relative response of the NEMS detector with 10 nm thick polymer coating.

Various diffusion coefficients of the gas molecules in polymer phase are assumed.

120

Figure 4-17 The function of equation (4.8) can be approximated using the square root of

t when m(t)/mmax < 0.6.

121

Figure 4-18 Spatial (depth) distribution of gas molecule concentration inside the polymer
at various times (0.001, 0.01, 0.1, and 1 τ)
This slow diffusion puts major limitations on detection speed to acquire expected
sensitivity. It will be a universal problem for all polymer-coating-based chemical sensors
which rely on gas species diffusing into the polymer phase to be transduced to the sensor
response. Engineering the properties of the polymer coating to improve the diffusion
speed is possible by adding plasticizers into the polymer to turn the film more rubbery.
However, in the microscale fast gas analysis system, the application of a preconcentrating stage can also significantly compensate the loss of sensitivity at increased
analysis speed by pre-concentrating the analyte species and then quickly releasing them.
Such a system will have unprecedented detection and analysis speed and sensitivity, all
implemented at microscale and in integrated formation. Employing both the separation

122
column and chemically selective detectors, an extraordinary analysis capability of a very
complex sample can be achieved in almost real time. Applications in homeland security,
environmental monitoring, and disease diagnosis are within reach in the near term.

4.4

Reference

Dittrich, P. S., Tachikawa, K., and Manz, A. Micro total analysis systems. Latest
advancements and trends. Analytical Chemistry 78, 3887-3907 (2006).

Janasek, D., Franzke, J., and Manz, A. Scaling and the design of miniaturized
chemical-analysis systems. Nature 442, 374-380 (2006).

Thompson, M. and Stone, D. C. Surface acoustic-wave detector for screening
molecular recognition by gas-chromatography. Analytical Chemistry 62, 18951899 (1990).

Wohltjen, H. and Dessy, R. Surface acoustic-wave probes for chemicalanalysis .2. Gas-chromatography detector. Analytical Chemistry 51, 1465-1470
(1979).

Agah, M. et al. High-speed mems-based gas chromatography. Journal of
Microelectromechanical Systems 15, 1371-1378 (2006).

McNair, H. M. and Miller, J. M., Basic gas chromatography. (Wiley, New York,
1998).

Miller, J. M., Chromatography : Concepts and contrasts, 2nd ed. (Wiley,
Hoboken, N.J., 2005).

123

Yang, Y. T. et al. Zeptogram-scale nanomechanical mass sensing. Nano Lett. 6,
583-586 (2006).

Ekinci, K. L., Huang, X. M. H., and Roukes, M. L. Ultrasensitive
nanoelectromechanical mass detection. App. Phys. Lett. 84, 4469-4471 (2004).

Stadermann, M. et al. Ultrafast gas chromatography on single-wall carbon
nanotube stationary phases in microfabricated channels. Analytical Chemistry 78,
5639-5644 (2006).

Tian, W. C. et al. Multiple-stage microfabricated preconcentrator-focuser for
micro gas chromatography system. Journal of Microelectromechanical Systems
14, 498-507 (2005).

Lu, C. J. et al. First-generation hybrid mems gas chromatograph. Lab on a Chip 5,
1123-1131 (2005).

Park, J., Groves, W. A., and Zellers, E. T. Vapor recognition with small arrays of
polymer-coated microsensors. A comprehensive analysis. Analytical Chemistry
71, 3877-3886 (1999).

Burl, M. C. et al. Classification performance of carbon black-polymer composite
vapor detector arrays as a function of array size and detector composition. Sens.
Actuator B-Chem. 87, 130-149 (2002).

Frye, G. C. et al. Monitoring thin-film properties with surface acoustic-wave
devices - diffusion, surface-area, and pore-size distribution. Acs Symposium Series
403, 208-221 (1989).

Bartlett, P. N. and Gardner, J. W. Diffusion and binding of molecules to sites
within homogeneous thin films. Philosophical Transactions of the Royal Society

124
of London Series a-Mathematical Physical and Engineering Sciences 354, 35-57
(1996).

125

Chapter 5
Conclusion and future work
5.1

Conclusion

This thesis has described the development and application of self-sensing NEMS
resonator devices. The method of piezoresistive detection using thin metal film as the
sensing material is discussed in detail. For NEMS, the advantages of using metallic film
over conventional semiconductor materials are analyzed theoretically and demonstrated
experimentally. These advantages mostly stem from the low resistivity and high electron
density of metallic material. They include the low Johnson noise and 1/f noise, low
device impedance for optimal impedance matching with RF readout electronics, ease and
robustness of fabrication at nanoscale, and versatile selection of substrate. By using such
a method, nanoscale NEMS resonators (cantilevers) with resonance frequency up to the
very high frequency (VHF) band are demonstrated. The readout sensitivity is
thermomechanical

noise

limited,

verified

successful

measurement

thermomechanical noise at room temperature. The nanomechanical resonators also show
remarkable quality factor even at atmospheric pressures, due to their small dimensions
(which are close to the mean free path of air). Further theoretical discussion and
experimental study of this dimensional effect of damping in air are included. This high
quality factor makes these nanomechanical resonators readily operational at everyday
conditions, namely room temperature and atmospheric pressure. A successfully

126
demonstration using them for mass sensing in air is described. Mass sensing resolution
below 1 attogram is achieved.
These nanomechanical resonators become highly sensitive chemical gas sensors
after they are functionalized with chemically sensitive polymer films. The method of
coating is developed. As detectors in a gas-chromatography-based integrated system,
these nanomechanical resonators are proved superior in performance, including a very
good limit of detection and very high response speed. Successful demonstration of
separation and analysis of a complex mixture of various chemical compounds is achieved.
Particularly, chemical warfare agent (CWA) simulants and their interferents can be
clearly discriminated by the system. After optimization of the packaging of the system,
an analysis time for 13 different species in as short as 4 seconds is obtained. With the
sharpest peak width shorter than 100 milliseconds, the demonstrated optimal channel
number is more than 40. The polymer film functionalized NEMS resonators are also very
selective in that they are not responsive to interferents at orders of magnitude higher
concentration then targeted analytes, indicating an excellent false-alarm rate. Although
reduced sensitivity is observed when analysis speed is increased, due to the slow
diffusion process inside the polymer layer, this drawback can be compensated for by fast
pre-concentration of analyte before reaching the separation column.
In general, NEMS resonators have been demonstrated to be excellent chemical
gas sensors, particularly suitable for microscale total analysis systems that require
detection at high speed and high sensitivity. The use of the metallic film piezoresistive
self-sensing method is the critical element that enables the application of the NEMS
resonator in compact and convenient packages. Finally, the integration of NEMS

127
resonators with other microfabricated components, such as a pre-concentrator, GC
column, and valves, is a successful demonstration of the merging of NEMS and MEMS
technologies.

5.2

Future work

Integrated actuation
Operation of NEMS devices need both actuation or excitation and detection or
readout of the devices. (Only noise measurement does not need actuation.) The integrated
metallic piezoresistive detection method described in this thesis successfully makes the
NEMS device self-sensing. However, the actuation method employed in this research is
still not integrated — a piezoelectric disk is used to actuate or shake the whole device
chip. This method is not only bulky and inconvenient, but also inefficient. In addition, all
the devices on the same chip are actuated at the same time, but cannot be excited
individually at different frequencies. This lack of efficient integrated actuation is the
major hurdle to further implementation of NEMS, in multiplexed large-array devices, or
for feedback control of the devices.
Other traditional actuation methods include magnetomotive and optic-thermal
driving. The strong magnetic field and the optical system are not scalable. Alternative
methods need to be developed. One very promising candidate is to integrate piezoelectric
material at the device. Piezoelectric material can provide mechanical actuation when
electrical voltage is applied, just like the piezoelectric shaker disk that was used before.
Commonly seen strong piezoelectric materials are some ceramics with perovskite

128
structure, such as BaTiO3, SrTiO3, and PbZrTiO3 (PZT). Some polymeric materials such
as polymer polyvinylidene fluoride (PVDF) are also piezoelectric. III-V and II-VI
semiconductor materials, including aluminum nitride (AlN), gallium nitride (GaN), zinc
oxide (ZnO), and gallium arsenide (GaAs) are also piezoelectric. However, ceramic
materials are difficult to deposit as thin films at submicron thickness and maintain their
piezoelectricity, as are polymeric materials. The most promising materials are AlN and
ZnO, which show piezoelectricity in deposited thin film, or even in bottom-up grown
nanostructures. Further research into integration and application of these materials with
the NEMS structure are still ongoing in our group. Some other challenges still remains
with exciting possibilities. Problems such as the strong coupling and interference between
actuation and detection, when both are integrated at nanoscale need to be solved.

Array and multiplexing
There are interests in multiplexing or developing an array of a large number of
NEMS devices for many application purposes. For example, in chemical gas sensing,
differentially coating each NEMS resonator sensors with chemically selective polymeric
films, as shown conceptually in Figure 5-1, will enable classification and quantization of
known and unknown analytes in complex mixture1,2. Eventually, this sensor array
integrated with a microscale gas chromatography system, can realize an “electronic nose”
system with superior performance. Synchronized NEMS array can also improve the
sensitivity of individual devices, for the signal can be averaged within the array so that
the signal will be less susceptible to noise. As a concentration senor, the areal sensitivity
is also improved by a factor which equals the number of devices in the array, because the

129
frequency of each device remains, but the total surface area is the sum of all the devices
in the array. For RF signal processing applications, using an array of devices improves
the power-handling capability of the system. With reduced noise level, the dynamic range
of the system can be dramatically augmented.
However, although fabrication of a large number of devices in an array is
straightforward by lithography, operation of them collectively still remains a challenging
task. In order to achieve this, NEMS devices need to be addressed (actuate and detect)
individually or made to work synchronically and coherently3,4. Solving these problems
and understanding the operating principles will be critical to implementing the ideas.
Their collective behavior in a nonlinear regime is also an interesting research subject.

Figure 5-1 Differentially coated NEMS resonator array

130

Active feedback control
Feedback control is ubiquitous and a basic technique in electronic circuitry. It has
also been used very often in the measurement of NEMS. In fact, phase-locked loop is a
feedback controlled circuit where the signal from the NEMS resonator is used to control
the voltage controlled oscillator, thus the loop is stabilized and the frequency of the
NEMS resonator is tracked. Typical feedback control circuits use negative feedback.
Positive feedback can be used to make self-excited loops or oscillators. A ultrahigh
frequency oscillator has been demonstrated using NEMS as the frequency determining
element5. But magnetomotive actuation detection is used, which makes such an oscillator
not scalable. Given an integrated actuation technique, an integrated NEMS oscillator
circuit can be developed and will have more application potentials.
Using active feedback, the effective quality factor NEMS resonator can also be
improved. Such a technique applies a positive feedback that is proportional to the
resonator’s linear velocity, equivalently cancels out the damping forces and boosts the
effective Q of the resonator by orders of magnitude. This method has already been
applied to atomic force microscopy to achieve very high force resolutions even in
aqueous measurement conditions6. Active Q control has not been demonstrated with the
NEMS resonator yet. Potentially, the augmented Q will greatly improve the signal to
noise ratio and accuracy of frequency measurement in ambient or even aqueous
conditions. This will make liquid-phase chemical or biological sensing possible, and thus
promise tremendous application opportunities.

131

5.3

Reference

Burl, M. C. et al. Classification performance of carbon black-polymer composite
vapor detector arrays as a function of array size and detector composition. Sens.
Actuator B-Chem. 87, 130-149 (2002).

Park, J., Groves, W. A., and Zellers, E. T. Vapor recognition with small arrays of
polymer-coated microsensors. A comprehensive analysis. Analytical Chemistry
71, 3877-3886 (1999).

Sato, M. et al. Observation of locked intrinsic localized vibrational modes in a
micromechanical oscillator array. Phys. Rev. Lett. 90, - (2003).

Buks, E. and Roukes, M. L. Electrically tunable collective response in a coupled
micromechanical array. J. Microelectromech. Syst. 11, 802-807 (2002).

Feng, X. L., et. al. unpublished (2006).

Tamayo, J. et al. High-q dynamic force microscopy in liquid and its application to
living cells. Biophysical Journal 81, 526-537 (2001).

132

Appendix A
Electrochemical deposition of nano-magnet tip on
microscale scanning probes
In this appendix, a method to electrochemically deposit a high-aspect-ratio nanomagnet tip on scanning probes is described. Such a nano-magnet tip can provide high
vertical magnetic field gradients as needed for magnetic resonance force microscopy
(MRFM) and for magnetic actuation of a cantilever device. Electrochemical deposition is
a versatile and robust way to fabricate metallic and metal oxide micro- and
nanostructures. It is compatible with other integrated circuit fabrication processes. It is
also a self-aligned process, as deposition can only happen at the position where the seed
layer is exposed to solution. As described in the following, electrochemical deposition is
also advantageous in the fabrication of structures with high vertical aspect ratios, which is
rather challenging for other methods such as lithography, vacuum deposition, and lift-off.
Excellent magnetic properties of electrodeposited magnetic films are reported, including
nickel-iron, nickel-iron-copper, and cobalt-iron-copper alloys1-3.

The electrodeposition setup of the experiment is shown in Figure A-1. A cathode
plate made of copper and an anode plate made of nickel are connected to a DC power
supply, with both the current and voltage measured by meters. The substrate of the
sample is mounted on the cathode plate with a metallic clamp. It is crucial that the clamp
makes good electrical contact with the seed layer on the substrate so that current can flow

133
to the seed layer. The both cathode and anode plates are inserted in to a beaker filled with
electrodeposition solution. The composition of the solution for permalloy deposition is
listed in Table A-1.

Figure A-1 Electrodeposition setup
Table A-1 Electrodeposition solution for permalloy (Fe20Ni80) electro-deposition

NiSO4•6H2O FeSO4•7H2O NiCl2•6H2O
Amount
(g/L)

200

H3BO3

Saccharin

2.5~3.0

The deposition rate depends on the current density at the solution and seed layer
interface. And since the deposition rate is also critical in determining the formation and
stoichiometry of deposited film and structure, it’s important to optimize it. In Figure A- 2,
the deposition rate is measured with a different current level. The area current density is
also calculated using the total cathode plate area. It can be seen that the deposition rate

134
depends linearly on the current or current density as expected. Current density around
10–15 mA/cm2 is suggested by the literature to obtain the best stoichiometry of
permalloy3. Also, since very uniform agitation is hard to achieve in a small beaker, it is
crucial to avoid any agitation in order to obtain uniform and consistent deposition1.

Area Current Density (m A/cm )

200

250

300

350

600

Deposition rate

Deposition rate (nm/min)

500

400

300

200

100

150

I (mA)
Figure A- 2 Deposition rate versus current density

To electrodeposit microscale structure, a seed layer or a mask layer can be patterned to
allow deposition to only happen at the exposed area. Gold and copper are good seed
layers for permalloy deposition. Both blank coating (Au/Cr) and patterned seed layer
pads (Au/Cr) connected with conduction leads (Al) have been used successfully. A good
electrical connection is crucial for successful deposition. PMMA electron beam resist is
used as a mask layer on seed layers. A diagram shown in Figure A-3 explains the

135
patterning and deposition process. To acquire high aspect ratio, very thin PMMA layer is
used. We use bi-layer of PMMA to improve the patterning. The first layer is 200 K A3
PMMA, which has a thickness of about 200 nm after the spinning. The second layer is
495 K A11 PMMA, which has a thickness of about 2 μm.

Exposed area

Deposition
only happens
here

Seed layer

resist

Figure A-3 Patterning the PMMA e-beam resist on a seed layer for self-aligned

electrodeposition
Then the sample is patterned with electron beam lithography using JOEL 6400
SEM with 40 kV beam voltage. To fully expose the very thick PMMA layer, very large
exposure dosage has to be used. The the smaller pattern size, the larger the areal dosage is
needed. In Table A-2, typical exposure dosages for hole patterns with various sizes are
listed.
Table A-2 Exposure dosage for hole patterns using on bilayer PMMA resist.

Hole diameter (μm)

0.5

0.2~0.3

Dosage Setup(nC/cm2)

1600

2500~3000

4000~5000

136
The electrodeposition is conducted at current value of 120 mA–150 mA, which
gives a current density of about 15 mA/cm2 and a growth rate of about 150–200 nm/min.
Typical results are shown in Figure A-4 and Figure A-5. In Figure A-4, a blank gold seed
layer is used and an array of holes is patterned in PMMA. Then permalloy is
electrodeposited inside the PMMA holes and forms high-aspect-ratio nanomagnets. A
patterned seed layer can also be used to fabricate the nanomagnet at a specific site. In
Figure A-5, a pad of gold seed layer is patterned and it is connected to outer electrodes by
an aluminum line to allow electrical current to flow to the pad. This aluminum layer can
be removed by using KOH etching after the electrodeposition. After the deposition, the
PMMA layer can be dissolved in acetone with the nanomagnet staying firmly on the
substrate. In Figure A-6, a nanomagnet is fabricated to the tip of a cantilever, although it
is overgrown into the shape of a mushroom.

Figure A-4 Array of nanomagnets with dimension of 2 um high and 300 nm wide

137

Figure A-5 A 500 nm by 2 μm permalloy nanomagnet on SiN membrane. The

nanomagnet is grown on a gold seed layer pad. An aluminum line connects the pad to the
outer electrodes and will be removed by KOH etch in a later step.

Figure A-6 A mushroom shaped overgrown nanomagnet on the tip of a release cantilever

138

Reference

Lemehaut.C and Rocher, E. Electrodeposition of stress-insensitive ni-fe and ni-fecu magnetic alloys. Ibm Journal of Research and Development 9, 141 (1965).

Gao, L. J. et al. Characterization of permalloy thin films electrodeposited on
si(111) surfaces. J. Appl. Phys. 81, 7595-7599 (1997).

Park, J. Y. and Allen, M. G. Development of magnetic materials and processing
techniques applicable to integrated micromagnetic devices. Journal of
Micromechanics and Microengineering 8, 307-316 (1998).