:1... .3 i.
i 2.7.x 9. a.
x. « . 2.: 73
31:... 1.
In: .2

.s
. .cyirzf.
. ..
c: A”):
. .;
. .
$555.5»: . .
.a .1535} ~ 5
i5..;.? .,:
9 “1.3.: t

1.. .Vol..!
13.33.... c.
1} v.‘ In

, ..
, ..
. .3.“

arm” 9 ..

I

1
.3: I
:33. $519”)
D
' it»
{é :
u

G

3
‘I

5

1.

a.
A- 1,. .
I... 3.1.

”1:31 x
2...... .5 H 1
.s I .t.
(33.! 13.:
3.... .e

 

 

 

 

 

 

. .24.
43.7.5. 314 .11...A~QI.SI.: 3.... . . . T5
:ilefl .15.? 37:35 15“.. V .PIL..;.».J.. . «Hr-7.. 1”.

 

...|

Q. . .
,. l|

wt...
.

 

 

has: LIBRAFéY
2 Michigan tate
W _ University

 

This is to certify that the
dissertation entitled

Polycrystalline Diamond RF MEMS Resonator Technology and
Characterization

presented by

Nelson Sepulveda-Alancastro

has been accepted towards fulfillment
of the requirements for the

Doctoral degree in Electrical and Computer
EngineerinL

 

 

9/? flan»;

 

Major Professor’s Signature

December 8' 2005

 

Date

MSU is an Affirmative Action/Equal Opportunity Institution

 

n----4-v-----.—-----.--.-c----;—-c

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2/05 p:/CIRC/DateDue.indd-p.1

 

POLYCRYSTALLINE DIAMOND RF MEMS RESONATOR TECHNOLOGY AND
CHARACTERIZATION

By

Nelson Sepulveda-Alancastro

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Electrical Engineering

2005

ABSTRACT
POLYCRYSTALLINE DIAMOND RF MEMS RESONATOR TECHNOLOGY AND
CHARACTERIZATION
By
Nelson Sept'tlveda-Alancastro

Due to material limitations of polycrystalline silicon resonators, polycrystalline
diamond has been explored as a new RF MEMS resonator material. This work presents
the development of polycrystalline diamond micro and nano resonators with quality
factor (Q) values as high as 116,000.

Polycrystalline diamond resonator structures were tested using electrostatic and
piezoelectric actuation. Similar resonator structures were tested using both testing
methods, and their performance showed a difference in resonant frequency of about 3%,

while the measured Q values differed by approximately a factor of 10.

The resonant frequency shifts due to different testing temperatures was quantified

by the temperature coefficient (TCf) value, which ranged from -1.59x10'5 / °C to -2.56

x10’5 / °C for the different polycrystalline diamond structures. The Q values were not
limited by clamping losses, phonon-phonon interaction or thennoelastic dissipation and
they were measured as a function of temperature. The results showed an apparent
thermally activated relaxation process, with an activation energy of 1.9 eV responsible
for limiting the highest achievable Q value in the tested polycrystalline diamond
resonators.

The fabrication technology and the performance of polycrystalline diamond
resonators with dimensions in the nano scale are also presented. Polycrystalline diamond

resonator cantilevers and torsional resonators with dimensions in the nanometer range (as

small as 100 nm) have been fabricated and tested. The performance of these structures
shows resonant frequencies and Q values in the range of 23 KHZ — 805 KHZ and 2,800 —

103,600 respectively.

T 0 all those who defend peace

and happiness at the same time

iv

ACKNOWLEDGMENTS

First, I would like to thank my big and great family. My dad (Don Agustin
Sept'tlveda), who always motivated me to give the best of me. My mom (Dona Matilde
Alancastro) who has been part of the “big events” in my life (even watching me strike out
in a little league baseball game). My brothers (Isaias, Agustin, Ricardo, Jorge, “Cacho”,
and Javier) and sisters (Nelly and Tere), which I have always felt close even though most
of the time we have been physically distant. During my graduate school I married Laura,
the most beautiful and wonderful girl in the planet. She has been very patient and also
motivating during my career. Thanks also to “las malas compafiias" from “El Colegio”.
They showed me that friendship is a blessing.

This thesis would not have ever been written if it was not for those who inspired
and motivated me to begin this journey after my BS. degree. Thanks to Yuxing,
Xiangwei, and Yang who helped me in my research and with which I spend happy and
painful moments in the RCE.

Thanks also to Dr. John Sullivan for his knowledge and friendship, and to The

Bill and Melinda Gates Foundation for their financial support.

TABLE OF CONTENTS

LIST OF TABLES x
LIST OF FIGURES xi
CHAPTER I: Research Motivation and Goals ................................................ 1
1.1 Introduction ............................................................................... 1

1.2 Objective of this Work .................................................................. 2

1.3 Overview of this Thesis ................................................................. 3
CHAPTER I]: Background ....................................................................... 5
2.1 Introduction .............................................................................. 5

2.2 Resonator Theory and Operation ...................................................... 5

2.2.1 Resonance Frequency ....................................................... 5

2.2.2 Quality Factor ................................................................ 9

2.2.2.1 Lorentzian Fit .................................................... 11

2.2.3 Actuation and Detection Methods ....................................... 12

2.2.3.1 Electrostatic Actuation .......................................... 13

2.2.3.2 Piezoelectric actuation and Optical Detection ............... 19

2.2.3.3 Magnetomotive Actuation ...................................... 22

2.3 Energy Dissipation Mechanisms .................................................... 22

2.3.1 Extrinsic Mechanism ....................................................... 23

2.3.2 Intrinsic Mechanism ........................................... ‘ ............. 24

2.4 Micromechanical Resonator Structures and Limitations ......................... 28

2.4.1 Micromechanical Resonators ............................................. 28

vi

2.4.2 Resonator Geometry ........................................................ 28

2.4.3 Resonator Materials ........................................................ 33

2.4.4 Resistance Rx ............................................................... 35

2.5 Polycrystalline Diamond Material ................................................... 36
2.5.1 Why Diamond? ................................................................................. 36

2.5.2 Chemical Vapor Deposition (CVD) of Diamond Fihns ............... 38

2.5.3 Seeding ....................................................................... 40

2.5.4 Doping ........................................................................ 40

2.5.5 Patterning .................................................................... 41
CHAPTER III: Polycrystalline Diamond Film Technology ............................... 43
3.1 Introduction ............................................................................. 43
3.2 Seeding .................................................................................. 43
3.3 Film Growth Process ................................................................... 44
3.4 Doping ................................................................................... 46
3.5 Patterning ............................................................................... 48
3.6 Surface Roughness ..................................................................... 55
3.7 Microresonator Fabrication Process ................................................. 57
3.7.1 Fabrication Technology .................................................... 57

3.7.1.1 Samples for Electrostatic Testing ............................. 58

3.7.1.2 Samples for Piezoelectric/Optical Testing ................... 61

3.7.2 Post-Processing ............................................................. 63
CHAPTER IV: Resonator Testing Methods .................................................. 65
4.1 Introduction ............................................................................. 65

vii

4.2 Electrostatic Testing ................................................................... 65

4.2.1 Electrostatic Testing Equipment Set-Up ................................. 65

4.2.2 Electrostatic Testing Measurement Results ............................. 66

4.3 Piezoelectric Actuation with Optical Detection .................................... 69
4.3.1 Piezoelectric Actuation and Optical Detection Results ............... 69

4.4 Comparison of Results ................................................................ 73

CHAPTER V: Study of Q and Frequency Shifts in Polycrystalline Diamond

Resonators ....................................................................... 79

5.1 Introduction ............................................................................. 79
5.2 Quality Factor Limitations ............................................................ 79
5.3 Quality Factors in Polycrystalline Diamond Resonators ......................... 81
5.4 Polycrystalline Diamond Fihn Microstructure .................................... 85
5.4.1 Seeding Layer and Film Layer ............................................ 86

5.5 Temperature Dependence. .................................................................. .92

5.5.1 Young’s Modulus and Frequency Temperature Dependence. . . . . ....92

5.5.2 Quality factor temperature dependence.......................................94

 

 

CHAPTER VI: Polycrystalline Diamond Nanoresonators......... ....101
6.11ntroduction........... .................................................................................... 101

6.2 Fabrication of Nanoresonators. . . .. ............................................................... 101

6.3 Torsional Resonators. . . .. ........................................................................... 102

6.3.1 Testing of Torsional Resonators. ................................................ 104

6.4 Nanocantilevers. . . . . . .. ............................................................................... .105

6.4.1 Testing of Nanocantilevers.. ...................................................... 109

CHAPTER VII: Conclusions and Future Research... .............. 116

viii

7.1 Summary and Conclusions. ..................................................................... 116
7.2 Future Research. ................................................................................... 117

BIBLIOGRAPHY .............. 1 1 9

 

ix

2.1

2.2

2.3

2.4

3.1

4.1

4.2

5.1

5.2

6.1

6.2

LIST OF TABLES
Constant Kn for the first five flexural modes of a bridge structure .................... 7

Resonator structures fabricated from polycrystalline diamond. The

torsional resonator shown in the second row was patterned at Sandia

National Laboratories. The other structures were completely

fabricated at Michigan State University ................................................ 31

Properties of materials that can be used to fabricate micromechanical
resonators .................................................................................... 34

Most recent results for diamond resonators before the work reported
in this thesis ................................................................................. 35

Growth parameters for the three polycrystalline diamond samples studied and
dry etching parameters (superscript denotes the sample on which the value was
used) .......................................................................................... 46

Results for piezoelectically-actuated cantilever beams (first vibration mode)
madefromsample.............. ............................................................................. 70

Polycrystalline diamond growth parameters for the sample tested
electrostatically and piezoelectrically ................................................... 73

Polycrystalline diamond and polycrystalline silicon properties used for plotting

 

the dissipation curves in figure 5.1 ...................................................... 81
Ratio of seeding and film thickness to total thickness for each sample and the

average of the 15 higher measured Q values for each sample (Qtot )... . . .. ...88
Measurement results for single and double torsional resonators ................... 105

Results of polycrystalline diamond nanocantilevers fabricated from sample 1.
The resonant frequencies were calculated using the width as the resonator
thickness ( a), and the film thickness as the resonator thickness (b). M“
represents the number of measurements taken from each structure (the values
shown in the table correspond to the measurement with the highest

measured Q) ............................................................................... 114

1.1

2.1

2.2

2.3

2.4

2.5

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

LIST OF FIGURES
Thesis overview .............................................................................. 4

Bridge resonator diagram to be tested using electrostatic actuation [8]. . . .....6
Example of resonant peak obtained using electrostatic actuation. The resonant
frequency and Q are obtained directly from the measured data shown in the

spectrum ..................................................................................... 1 1

Schematic diagram for piezoelectric actuation and detection. The reflected laser
beam from the vibrating structure is sent to a photodetector. A network analyzer

uses the output of the photodetector to plot the resonance spectrum. . . . . . . . .....21

Schematic diagram for the magnetomotive actuation and detection ................ 22
a) HF CVD and b) MPCVD polycrystalline diamond deposition .................... 39
Raman spectra for the three samples studied ........................................... 48

Grass eflect diagram. The sputtering of aluminum during the dry etching of
diamond prevents the plasma from etching the diamond under the sputtered
aluminum .................................................................................... 51

Evidence of the grass eflect found on (a) the dry etching of the polycrystalline

diamond resonators reported in this thesis and (b) the DRIE of silicon-on-
insulator wafers [78] ....................................................................... 52

Released polycrystalline diamond structures (comb-drives and bridges) patterned
at Michigan State University. No grass eflect can be observed ..................... 53
a) Fabricated and patterned polycrystalline diamond resonators from [31] and b)

Michigan State University (reported in this thesis) ................................... 54

AF M images showing the polycrystalline diamond surface roughness of

Sample 3 (a) and Sample 2 (b). The difference in the film roughness is about

5 nm ........................................................................................... 56
Starting substrate for the fabrication of polycrystalline diamond resonators. . .....57

Fabrication process flow for electrostatically tested resonators ..................... 59

Fabrication process flow for resonators to be tested using piezoelectric actuation
and optical detection ....................................................................... 63

xi

4.1

4.2

4.3

4.4

4.5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

Connections to the resonator structure for electrostatic testing. In order to
measure only the change in current across the resonator, a bias tee is used
to isolate the dc- bias from the IN-port of the network analyzer ..................... 66

Electrostatic measurements on polycrystalline diamond resonators: a) bridge
structure, b) comb-drive. The resonant frequency (mwas calculated by finding

the frequency at maximum magnitude and the Q was calculated using thist

value and the 3dB bandwith (Af) ......................................................... 68

Young’s modulus of sample 1 was calculated from a linear fit done to the
measured data. .............................................................................. 72

Raman spectra for samples measured using different actuation methods: a)
piezoelectric b) electrostatic .............................................................. 74

Testing results on two similar polycrystalline diamond cantilevers using different
actuation and detection methods ......................................................... 76

Energy loss mechanism curves for a 1 pm thick poly-crystalline diamond and
polycrystalline silicon cantilever beam .................................................. 80

Q value limiting curves for a 0.6 pm polycrystalline diamond cantilever beam and
measured data for the three samples ..................................................... 82

Measured Q values as a function of frequency for the three studied samples.
Resonant peaks show the highest Q value for each sample ........................... 84

Cross section TEM images of the three studied polycrystalline diamond
samples ...................................................................................... 86

Plot of l/Qm, as a function of ts/ttot. The values for Qf and Q, are obtained fiom
the slope and intercept of the linear fit .................................................. 89

The approximation for the minimum space of solutions is determined by

the rectangle, which touches all the curves at least in one single point. . .. . . ....91

Young’s modulus temperature dependence for the three samples. The
three samples have very similar slopes and the sample 1 showed the

highest Young’s modulus at room temperature ......................................... 93
Frequency shift as a function of testing temperature for sample l............ . . . . ...95
Frequency shift as a function of testing temperature for sample 2 .................. 96

xii

5.10

5.11

5.12

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

Frequency shifi as a function of testing temperature for sample 3 .................. 97

Measured Q values vs. temperature a) Three samples plotted in the entire
testing temperature range; b) Sample 2 in the range of temperature
where a minimum in Q was observed ................................................... 99

Measured Q values vs. activation energy for the three samples. A
minimum in Q was observed for two of the three samples at an activation
energy around 1.9 eV ..................................................................... 100

SEM image of polycrystalline diamond single torsional resonator ................ 103

Excitation of torsional resonator. The offset of the paddle support from the
center of the paddle causes a torsional vibration mode .............................. 104

Smooth sidewalls of polycrystalline diamond nanocantilevers fabricated
using e-beam lithography ................................................................ 107

Use of piezoelectric actuation and optical detection for a cantilever with vibration
perpendicular to the substrate (a) and parallel to the substrate (b). The

vibration will be in the direction parallel to the smallest

dimension of the cantilever .............................................................. 108

100 nm wide polycrystalline diamond cantilever. The top view shows that
the width of the cantilever is in not uniform along the beam length. . . . . . . . . . 109

SEM image and performance of the nanocantilever with the highest measured
Q ............................................................................................. 1 10

SEM image and performance of a 100 nm wide polycrystalline diamond
nanocantilever ............................................................................. 1 1 1

Plot of measured Q values on cantilever beams made of silicon nitride [26], single

crystal silicon [26] and polycrystalline diamond (reported in this work). All the
cantilevers had a thickness between 170 nm and 200 nm ........................... 115

xiii

Chapter 1

Research Motivation and Goals

1.1 Introduction

Microsystems and Broadband/wireless communication systems need high
performance, low-cost, low-power and small-size components. Such components can
lead to single-chip transceivers and microsystems. However, the majority of the high-Q
bandpass filters commonly used in the radio frequency (RF) and intermediate frequency
(IF) stages of transceivers are realized using off-chip, mechanically resonant components,
such as crystal filters and surface acoustic wave (SAW) devices. These off-chip resonator
components can contribute to the substantial percentage (often up to 80%) of portable
transceiver area taken up by board-level passive components.

Recently, silicon-based low-power resonant micromechanical structures have
been fabricated. Microelectromechanical systems (MEMS) technologies that make it
possible to fabricate high quality factor (Q) on-chip micromechanical resonators [1,2]
now suggest a method for miniatruizing and integrating highly selective filters alongside
transistors leading to miniaturized transceivers. Among the RF MEMS components that
could replace conventional components in cellular and cordless applications are image
reject and IF filters with center frequencies in the ranges of 0.8 - 2.5 GHz and 0.455 - 254
MHz, respectively [1]. Some of the specific devices fabricated are tunable
micromachined capacitors, integrated high-Q inductors, low-loss micromechanical
switches, and micromechanical resonators with quality factors (Qs) above 10,000.

Microfabricated resonant structures for sensing pressure, acceleration, and vapor

concentration have been demonstrated [3]. Recent advances in IC-compatible MEMS
technologies suggest methods for board-less integration of wireless transceiver
components [4]. In fact, given the existence already of technologies that merge
micromechanics with transistor circuits onto single silicon chips [4-7], single-chip RF
MEMS transceivers are not a far goal anymore.

However, before one can take firll advantage of RF MEMS, a number of issues
need to be addressed including higher frequency, selectivity, vacuum encapsulation and
reliability. In order to solve these issues, researchers have tried to use different resonator

structures, designs and materials.

1.2 Objective of this Work

Polycrystalline silicon has been the material of choice for RF MEMS
micromechanical resonators. It is, however, found that reducing the resonator dimensions
(to achieve higher frequencies) close to or below 1 um for polycrystalline silicon
resonators is expected to lead to size related limitations due primarily to enhanced
adsorption properties of water-related species to the silicon surface. As diamond surfaces
are known to be chemically inert to such adsorption and diamond has the highest
Young’s Modulus (which allows higher resonant frequencies) among all the materials,
polycrystalline diamond micromechanical resonators are expected to be superior to
silicon based resonators.

The goal of this work is to study the polycrystalline diamond material for its use as a
structural material in RF MEMS micromechanical resonators. The major
accomplishments and/or contributions to the scientific community reported in this thesis

include the following:

1)

2)

3)

4)

5)

6)

1.3

The development of the fabrication technology for polycrystalline diamond RF
MEMS resonators.

The testing of polycrystalline diamond resonator using different techniques
showed similar resonant frequencies but differences in Q values by a factor of 10.
Achievement of the highest Q of 116,000 measured for any polycrystalline
diamond resonators structure or cantilever beams made of any polycrystalline
material.

Study of the energy dissipation mechanisms (which influence the Q) in
polycrystalline diamond micromechanical resonators and their relation to the film
microstructure.

Study of the temperature dependence of the resonant frequency and Q in
polycrystalline diamond resonators.

Fabrication and testing of polycrystalline diamond nanocantilevers with widths as

small as 100 nm.
Overview of this Thesis

This thesis presents the development and characterization of a polycrystalline

diamond microresonator fabrication technology capable of achieving high Q and nano-

sized polycrystalline diamond resonators. Chapter 2 explains the theory of the resonator

dynamic behavior and the different actuation and detection methods that can be used for

the testing of micromechanical resonators. It also discusses the energy dissipation

mechanisms, the micromechanical resonators limitations and the polycrystalline diamond

material. The third chapter on this thesis talks about the polycrystalline diamond

microresonator technology used for the fabricated and tested devices. The details for

polycrystalline diamond film growth and patterning are presented with some of the issues
faced and ways to avoid/solve them. The fourth chapter describes the measurement
techniques used and the equipment set up. It discusses the measurement results on the
two actuation and detection techniques used: 1) electrostatic actuation and detection and
2) piezoelectric actuation with optical detection. Then, in chapter five, the energy
dissipation mechanisms present in polycrystalline diamond micromechanical resonators
and the thermal stability of such devices are discussed. The last chapter shows the
technology for the fabrication of nano sized cantilever beams and the results obtained

from such structures. The following figure (figure 1.1) shows an overview of this thesis.

 

 

Polycrystalline Diamond RFMEMS
Resonator Technology and Characterization

 

 

 

 

 

 

Figure 1.1: Thesis Overview

Chapter 2

Background

2.1 Introduction

This chapter presents the theory necessary to understand the dynamic behavior of
micromechanical resonators and discusses the energy dissipation mechanisms, which are
responsible for limiting the Q. It also mentions the resonator geometries and materials
commonly used, their limitations and a summary of the latest results obtained for RF
MEMS resonators. Finally, the justification for using polycrystalline diamond and some
of the common techniques for the fabrication and processing of polycrystalline diamond

films are discussed.

2.2 Resonator Theory and Operation

For the understanding of the operation of an RF MEMS micromechanical
resonator there are important concepts and parameters such as resonance frequency and Q
that need to be clear. Some related concepts are the actuation and detection methods,
which help to understand the testing of such devices.

The following section describes the concept of resonant frequency assuming electrostatic

actuation and detection is used as the testing technique.
2.2.1 Resonance frequency

Figure 2.2 shows a typical clamped-clamped (bridge) structure [8]. It is clamped

at both ends, and a capacitance is formed between the beam and the underlying electrode.

Resonator Beam

 

 

 

 

Figure 2.1 Bridge resonator diagram to be tested using electrostatic
actuation [8].

An infinite number of resonance modes are possible for the structure presented in figure

2.1. The frequency of each mode is determined by the structural material properties and

resonator geometry. The resonance frequency fm of a given mode I: for the bridge in

figure 2.1 is given by the expression [9]

1 k
fm =7 _r (2-1)
7: m,

where k, and m, are the stiffness and mass of the beam respectively. The stiffness is given
by [9]:

k, = EW, — (2.2)

where E is the Young's modulus of the structural material; Lr, wt and h are the beam

length, width and thickness specified in figure 2.1 respectively. By substituting equation

(2.2) in equation (2.1) the following expression for the resonance frequency of a bridge

resonator is obtained:

1&2

fm

where p is the density of the structural material. Different modes are distinguished by a

constant Kn. If this constant is taken into consideration a more general expression for the

resonant frequency of a bridge or cantilever beam can be obtained [10]:

E h
fm =Kn ‘——2 (2-4)
P L,

The constant Kn will depend on the vibration mode the beam is operated and is tabulated

for the first five modes of a bridge structure in table 2.1.

Table 2.1 Constant Kn for the first five flexural modes of a bridge structure

 

 

 

 

 

 

Mode n Nodal Points Kn fnflo
Fundamental (fo) 1 2 1-03 1
15‘ Hmonic (f2) 2 3 2.83 2.76
nd .

2 Harmomc (f3) 3 4 5.55 5.4
3rd Hmonic (f4) 4 5 9.18 8.93
th .

 

 

 

 

 

 

 

Now, equation (2.4) is the mechanical resonance fiequency of the resonator if
there were no electrodes or applied voltages. The presence of electrostatic forces on the

vibrating beam seems to alter the stiffness of the beam [11]. Mathematically, it may be

appropriate to re-define the spring constant k,. If k,- is the spring constant in the absence

of electrostatic forces, then

k; =k, —ke (2.5)

where Ice is the electrostatic spring stiffness, which is subtracted fi’orn the spring constant

k, to give the “modified” spring constant k} . Thus equation (2.1) can be modified to:

_k_r_ _ z-kr ke __ £r_[1-£e_]y2 (2.6)
m, m, 27: k,

A good approximation for Ice, can be made to get [1 1]:

(MI/,3)

d3 (27)

 

e:

where A is the electrode overlap area, a is the permittivity of free space, V p is the dc bias

applied to the resonator and d is the electrode to resonator gap as shown in figure 2.1.

After substituting equation (2.2) and equation (2.7) in equation (2.6) and taking in

account the constant Kn discussed earlier the following equation is obtained:

2 3
E h aAV L 1
fm=Kn -——2[1— —” 1/2

3 3 (2.3)
pL, d EWh

It is important to remember that equation (2.8) adds the effect of electrostatic actuation

testing, and therefore it can only be used when this testing method is used. When testing

methods that do not affect the spring constant (k, ) of the resonator structure are used, the

resonant frequency can be calculated using equation 2.4. Due to the fact that the

polycrystalline diamond Young’s Modulus is about 6 times larger than that of

is about 6 times smaller for a

2 3
k EAV L
polycrystalline silicon, the ratio <—£> = ___3 P 3
r d E Wh

polycrystalline diamond beam when compared to a polycrystalline silicon. For a typical

bridge structure (100 um long, 10 um wide, 2 um thick) with a gap spacing of 0.2 pm, an

k
electrode beam overlap of 20 um and a DC bias (Vp) of 2V, the ratio <_e> is 0.06 for a
r

polycrystalline silicon beam and 0.01 for a polycrystalline diamond beam.
2.2.2 Quality factor

Another parameter that is important to study in order to characterize the
performance of a resonator is the Q. The Q is defined as the ratio between the energy
stored in the system to the energy lost per cycle. It describes the frequency selectivity of
the device (i.e. the device response to a specific frequency). Processes or mechanisms,
which increase the energy dissipated in the resonator are sources of Q degradation.
Section 2.3 explains in more detail the energy dissipation mechanisms for a
micromechanical resonator.

High Q resonators are necessary for sensor and RF MEMS applications. In sensor

applications, if a resonator is exposed to a chemical leading to a change in its mass, 3

shift in its resonant frequency could be used to detect the chemical. The shift in resonant
frequency needed for detection or sensing of a mass change is determined more precisely
if the resonator has a high Q. Thus, the sensitivity of a microresonator based sensor
increases with Q. Also, a high Q value is desirable for oscillators and filter applications,
where the frequency of operation needs to be carefully controlled.

The Q of a resonator can be obtained in different ways. When electrostatic
actuation and detection is used for testing the resonator, the measured output is the
magnitude of the 821 scattering parameter (y-axis) as a function of frequency (x-axis).
The scattering parameters are commonly used in RF circuits to measure the ratio of the
output power signal to the input power signal. When the resonator beam is vibrating, the
changes in the output current (which are discussed in section 2.2.3.1) are reflected on the
output power signal used to determine the scattering parameters. In most cases, the

magnitude of the 821 parameter is converted to decibels by using [521' dB = 20xlog(]521|).
The frequency at maximum magnitude is used as the resonant fiequency f0. The half

power points (1/J2 max Iszrl) [12] are determined on either side of the resonant

frequency and the difference of those frequency positions is the bandwidth Af If the |821|

value is in decibel units (ISzlde), then the half power points are located at the two points
of the curve which are 3dB apart from the maximum magnitude (20 x log (1/«/2 max

ISZII) = lszlldB — 3dB)-
Figure 2.2 shows an example of a resonant peak obtained using electrostatic

testing and the procedure for calculating the Q. This method relies solely on the measured

10

data. However, there is a more accurate method for calculating the resonator Q, which

uses a curve fit.

Af3dB

ISZI|
(dB)

 

 

 

 

 

 

 

 

FREQUENCY (Hz)

Figure 2.2 Example of resonant peak obtained using electrostatic actuation.
The resonant frequency and Q are obtained directly from the measured
data shown in the spectrum.

2.2.2.1 Lorentzian fit

The equation for a Lorentzian curve is given by [12]:

 

y = Ymax 2 (29)
J1+4Q2[i 4]
1‘0

where x0 is the x value that corresponds to ymax. It has been found that the most accurate
fit for the resonant curve of micromechanical resonators is a Lorentzian curve using
nonlinear least-squares fit using frequency in the x-axis and a variable directly

proportional to the resonator amplitude of motion (such as [321' or the voltage read from

11

a photodetector) in the y-axis [12]. Therefore, the data from which the resonant peak is

plotted can be fit with a Lorentzian curve, and the frequencny and Q parameters can be

extracted from the fit.
2.2.3 Actuation and detection methods

Different resonator actuation and detection methods have been described and used

[13,14,15]. The two techniques most commonly used for micromechanical resonator
measurement are the capacitive (electrostatic actuation and detection) and the
combination of mechanical actuation (piezoelectric actuation) with optical detection. The
electrostatic method measures the change in the scattering parameter S21 (caused by a
change in the output current) for the detection of motion and the mechanical method
measures the change in an optical (laser) signal reflected from the resonator surface for
motion detection. The change in output current for the electrostatic actuation is caused by
the change in charge across the vibrating resonator which behaves as a time varying
capacitor. However, as the structure gets smaller and its geometry more complicated, the
difficulty to use these two techniques for movement detection increases significantly.
The problem with optical detection is the minimum spot size of the laser. If the laser spot
size is larger than 1 pm, it would difficult to measure the reflected signal from the surface
of a resonator with dimensions smaller than 1 pm. Also, the laser induces noise such as
heating.

The capacitive method suffers from various drawbacks such as parasitic
capacitances (which are difficult to account for) [16]. Restrictions on the device design
and changes to the structural material (e. g. the stiffness of the material) are introduced

due to the current flow, which limits the material capabilities [17].

12

The third method for actuation and detection of a resonator is the magnetomotive
technique. This method makes use of the Lorentz force [18]. A drawback of this method
is that in order to prevent heating the structure has to have low resistance [19]. For a
polycrystalline diamond resonator this can only be accomplished with heavy doping or a
thick metal film on top of the resonator, which makes this method unsuitable if the
intrinsic characteristics of diamond are of interest. These three techniques are described

in more detail in the following sections.

2.2.3.1 Electrostatic actuation

When electrostatic force is used, a dc-bias Vp is applied to the suspended beam,

and an ac input voltage v,- = Vm sin cot (Vm is in the range of the mV) is applied to the

electrode under the beam (see figure 2.1). Therefore, the resulting electrostatic potential

across the beam is
v=vi+Vp. (2.10)
In a vibrating resonator, the capacitance formed between the bottom electrode and the

beam is changing with time. Therefore, the charge stored in the capacitor is also changing

with time, which implies a current flow. From equation (2.10) three different inputs can
be analyzed: 1) v = Vp (vi = 0), 2) v = v,- (Vp = 0) and 3) v = vi + Vp. Each one of these
cases is analyzed separately.

First, let the input to the system be purely dc (i.e. v = VP). The electrostatic force

will make the beam bend towards the bottom electrode, generating a change in

capacitance for a short period of time. However, once the system reaches its equilibrium,

l3

the beam stops moving, and the equivalent circuit can be represented by a dc voltage
source connected in series with a capacitor. The expression for the current flowing
through a capacitor is:

._6Cv_C6v+ ac

___ _. _ 2.11
’0 at at ya: ( )

From (2.11) it can be seen that if neither the voltage nor the capacitance varies with time,
the current will be zero. Therefore, in steady state, the current for a purely dc input would

be zero.

Now, let v=v,-. If the frequency of this input signal ( fi :31) is far from the
7:

natural frequency of the beam ( f0 = 2% ), the beam does not vibrate, and therefore the
72'

capacitance between the beam and the electrode does not change with time. The second

term in (2.11) becomes zero, and the total current becomes i0 = C 6vi/6t. As the

frequency of the ac signal approaches the natural frequency of the beam, it begins to

vibrate, creating a time varying capacitor. Then the current is given by (2.11) with v = vi.

The third input v = v,- + Vp results in a current given by

6(Vi + VP)

i0 =C 6t

+(Vi +Vp)%€ (2.12)

Since the magnitude of the ac signal (Vm) is in the range of mV and the dc signal is in the

range of Volts, the current is significantly increased when the dc signal is added to an ac

signal with frequency close to the natural frequency of the resonator.

l4

Knowing that the change of Vp with respect of time is zero (6Vp/6t = 0), equation (2. 12)
can be simplified to:

1'0 =C%—+(vi +Vp)%€— (2.13)

Now, in the second term in equation (2.13) Vp is added to v,- and since the magnitude of

the ac signal is in the mV range, it can be neglected and we get the following equation:

i0 =C%+Vp%€— (2.14)

The derivative of capacitance with respect of time (6C / at) can be expressed as:

66-2993

__ 2.15
61 6x61 ( )

where the derivative of capacitance with respect to the displacement x can be obtained
directly fi'om the plate capacitance formula:

80A
C =
(d - x)

 

(2.16)

where so is the permitivity of free space, A is the electrode area, d is the initial electrode

gap, and x is the beam displacement (see figure 2.1).
So, after taking the derivate of the capacitance with respect to displacement x we get;

6C EA

ax =(d_x)2

 

(2.17)

For a typical vibrating beam the beam displacement is very small when compared to the

gap spacing (x< <d). So, equation (2.17) can be simplified to:

15

Substituting equation (2.18) in equation (2.15) and the result in equation (2.14),

the following equation is obtained:

at d2 at
Defining the new variable I] to be:
V
n = —P—§A— (2.20)
d

Using this variable 7) (herein after referred as electromechanical transduction factor)

equation (2.19) can be simplified to:

. at" 6x . .
The first term is recognized as the normal ac-current through the capacitor and the second

term is the motional current imot = 71*6x/01, due to the time varying capacitance. Since

the current is proportional to the dc-bias, it is reasonable to think of the dc-bias as a

parameter to use for getting a more noticeable peak in the transmission spectrum.

However, when the dc-bias voltage Vp is sufficiently large, catastrophic failure of the

device ensues, in which the resonator beam is pulled down onto the electrode. This leads

to either destruction of the device due to excessive current passing through the now

shorted electrode to resonator path. The dc-bias voltage Vp at which this event occurs is

known as the pull-in voltage (ij). The pull-in voltage can be estimated to be [20]

3

8k (1
VP]: L (2.22)

2750

16

where

125 . koL,
[( 2 )Smh( 2 )1

 

(2.23)

 

L; (koir )SlI'lh(k—0211) + 20 — COSh(£0§LL))

In (2.23) 00, h and L, are the residual stress, thickness and length of the beam

respectively,

12
and k0 = I 00 .
Eh

Equation (2.22) yields a pull-in voltage, which captures the dependence of pull-in

 

voltage on beam dimensions, elastic modulus, and residual stress. However, since the gap
under the beam is not uniform, this approximation is off by about 20% [20]. Expressions
for the pull-in voltage of the beam have been developed by adding some adjustable
constants so that the pull-in voltage expression matches the calculated behavior based on
fiill non-linear simulations [20]. This has been done, with a factor added to account for

electrostatic fringing at the edges of the beam. The result is [20]

 

 

3
4 0’ hd

VP] = 2 71( 0 ) d (2.24)

80L D(}’23k03L)[1 + 73 W]

where
L
[1 - c0811(721‘0 3)]

D(72,k0,L)=1+2 (2.25)

 

. L
(72ko 3) Slnh(72ko -2-)

17

The values of the constants for a fixed-fixed beam with fully clamped boundary

conditions are 71:2.79, 72:0.97 and the fringing field correction term is y3=0.42 [20].

So far, the system has been described in the electrical domain. Now, let’s see how
the voltages applied to the resonator relate to the forces in the system. The application of
the voltage input to the resonator creates an electrostatic force between the electrode and
the beam. The energy stored in the parallel plate capacitor C formed by the beam and the

electrode is:
E = l Cv2 (2.26)
2
Then, by substituting the voltage given by equation (2. 10) into equation (2.26) we get
_ 1 2 2
E — EC(VP + 21)in + Vi ) (2.27)

The force is obtained from

F = 95 = -1—v2 9—C— (2.28)
6x 2 6x

and using the simplified derivative of capacitance with respect to distance obtained in

equation (2.18), and substituting it into equation (2.28) we get:

 

F = v2 :2 (2.29)
Now, substituting (2.10) into (2.29) we get:
F = (V17; + 21?in + v1.2)i (2.30)

2d2

18

28A

— ), a force
2d2

As can be seen in equation (2.30), there are three forces: a dc-force (Vp

at the excitation frequency f due to a combination of ac and dc (2vin -fl2-) and a force
2d
at twice the excitation frequency due to the square term (v.21). The v.2 M term is
2d2 ' 2d2

 

very small in comparison to the other two terms ( Vm in the mV range) so it can be

ignored. When the beam is vibrating, and the system has reached equilibrium, the pure

28A

dc-term (Vp —2-) has no effect on the device response. It is a purely dc-force that
2d

statically bends the beam but dynamically has no effect on the frequency response. In

28A
2d

other words, the pure dc-term (Vp

 

) is a constant term which does not influence

the force frequency. So, when the beam is actuated, and begins to vibrate, after reaching

equilibrium the frequency of the force acting on the beam can be calculated by:

= vinaA =

F
d2

77v,- (2.31)

where the variable t] is the electromechanical transduction factor defined in (2.20) and it
represents the connection between the mechanical and electrical domain in the system.
2.2.3.2 Piezoelectric actuation and optical detection

The basic idea behind the piezoelectric actuation method is to physically attach
the sample that contains the resonator structure to a piezo transducer. This piezo element
is driven to vibration at a frequency determined by the output of a spectrum analyzer. For

the laser detection, a laser is focused on the vibrating beam and the reflected signal is

19

used to determine the frequency of vibration. A schematic of the piezoelectric actuation
and detection set up is shown in figure 2.3.

The frequency of a light source changes with the speed of the light source
(Doppler effect). Since the reflective surface of the resonator can be considered as a point
source, this effect can be employed to detect the vibration of a resonator. A laser is
reflected off the point of the resonator structure where the amplitude of motion is
maximum (for a cantilever, this point would be the tip of the cantilever, for a bridge, this
point would be the beam midpoint along the length axis), and directed to a photodiode.
Depending on the angle between the surface of the cantilever and the incident laser beam,
the position of the reflected light at the detector changes. This is how the photodiode
detects when the device is vibrating.

In this technique, light from a laser was passed through a lens, which caused the
beam to diverge, and then it was sent through another lens to focus the light. The now
converged beam is reflected off a mirror, through the vacuum chamber window and
focused on the resonator structure of interest. The beam hits the sample and the reflected
light is sent to a split photodiode. The reflected light is positioned so that the light on the
two halves of the photodiode is about the same. Then the difference between the
photovoltages is the output from the photodetector, and this is then routed into the
spectrum analyzer that is simultaneously driving the piezo element that is driving the
resonator into vibration. When the beam is vibrating, the output from the photodetector is
maximum and a resonant peak is observed in the spectrum analyzer. This technique is

very similar to the one used in AFM’s.

20

 

Photodetector

r r ’V g ‘ ‘ or
A i 'i I T i i '

‘ Mirr
lens lens ‘\ Vacuum
Chamber

Window

 

 

 

 

To Vacuum
—‘ Incident Beam 5 '

/
Reflected Beams K 7 Cantilever Beam
\

l

I

1,

 

 

 

Figure 2.3 Schematic diagram for a the piezoelectric actuation and detection. The
reflected laser beam from the vibrating structure is sent to a photodetector. A
network analyzer uses the output of the photodetector to plot the resonance
spectrum

The force that drives the resonator comes from the piezo—transducer that
mechanically shakes the sample containing the resonator. The detection is done by
monitoring the reflected light from a laser that was focused on the resonator. This
technique does not involve any current flow through the resonator and therefore the

sample does not need to be conductive.

21

The optical detection scheme used in this work was light interferometry, which
has been described in detail by Czaplewski [13]. In this technique, a better resolution of
the cantilever displacement can be obtained, and therefore resonator structures with a
smaller displacement can be tested.
2.2.3.3 Magnetomotive actuation

If an ac current flows through a wire that is exposed to a perpendicular magnetic
field, a force acts on the current and the wire moves perpendicular to the magnetic field.
Since the current is oscillating the wire also oscillates and an electromotive force (emf),
having the same frequency, is induced in the wire. To pick up the vibration either the
reflected voltage can be measured with a network analyzer [18], or the electromagnetic
power that is absorbed by the motion of the beam can be measured [21]. To excite the
resonator, relatively large magnetic fields are required (up to 12 Tesla [21]). So, the idea
is to excite the resonator by applying a drive current through an electrode on its surface in
the presence of a magnetic field perpendicular to the length of the current carrying
- electrode, and motion is detected by measuring the induced emf in the electrode. Figure

2.4 shows a diagram of the parameters involved in this type of technique.

I

m Force

k;—l
Ve_.®®:®®3®l _ @163)
[lllHlllFL iContacts Flfl‘filea :1“
(X) (X)

Substrate Magnetic field

 

 

 

 

 

 

Figure 2.4 Schematic diagram for the magnetomotive actuation and detection
2.3 Energy Dissipation Mechanisms

As it was mentioned earlier, the Q of a microresonator can be improved by

22

minimizing the energy losses. The energy loss mechanisms can be divided in two
categories; extrinsic and intrinsic.
2.3.1 Extrinsic mechanisms

Extrinsic loss mechanisms have nothing to do with the material itself but are
influenced by the design of the microresonator structures. Intrinsic loss mechanisms, on
the other hand, are the loss mechanisms that come from the material properties, and will
limit the highest possible achievable Q. Two main extrinsic loss mechanisms are the
energy losses due to clamping and air damping.

Clamping losses originate from the fact that since no structure can be perfectly
rigid, energy can be dissipated from the resonator to the support structure, where local
deformations and nricroslip can occur. By increasing the rigidity of the anchor, the
movement in this area of the resonator is decreased. As a result of this decrease in
displacement, the anchor losses are reduced. It is often not possible to increase the
rigidity of the support, but energy losses can be reduced by optirrrizing the structure
design. In the case of a cantilever beam, if the support is considered as an infinitely large
elastic plate, the damping ratio of the radiation on the support was given by Hosaka et al.

and the maximum achievable Q can be estimated from the following equation [22]:

L3

champ = 34ng- (2.32)

where L and h are the length and thickness of the cantilever respectively.
Air damping arises from the transfer of mechanical energy to the gas surrounding

the structure [22]. Depending on the pressure level the microresonator is subjected while

it is being tested, air damping may affect its Q. At pressures below 10 mtorr, the air

23

damping is negligible compared to the intrinsic damping of the vibrating beam itself.
Since at this pressure level intrinsic mechanisms limit the Q, this pressure regime is
called the intrinsic damping region. When the pressure is between 4 torr and 10 mtorr

(molecular region), the Q is inversely proportional to P, following the relationship [22]:

_. 279%"19
Q - __ka (2.33)

where fn is the resonance fiequency of the nth vibrational mode, p is the density, P is the

1/2
gas pressure, and km = [ (3211/049an) ] , where M is the molecular weight of the gas,

R is the gas constant, and T is the temperature. At pressures above 4 torr (viscous region)
the air acts as a viscous fluid and air damping becomes a significant factor for limiting
the Q. In this region the Q is limited by the following expression [23]:

Q = 472199, (2.34)
6141+ —)

0'

where w and l are the beam width and length respectively, p is the dynamic viscosity of

the medium, a = fl and P,M,R, T and f" are the same parameters used for (2.33).
PM 279‘”

The maximum Q for a 100 (um long, 10 um wide, 1 pm thick polycrystalline diamond
cantilever beam, is in the order of 10,000 when it is operated at a pressure of 75 mtorr
(molecular region), and about 500 when it is operated at 7 torr (viscous region).
2.3.2 Intrinsic mechanisms

Intrinsic loss mechanisms, on the other hand, are the loss mechanisms that come

from the material properties, and will limit the highest possible achievable Q. Energy

24

losses due to thermoelastic dissipation (TED), phonon-phonon interaction, and internal
fiiction can be considered intrinsic loss mechanisms.

It is well known that a material that possesses a positive coefficient of thermal
expansion will experience a temperature increase when subjected to a compressive stress
and a decrease in temperature when subjected to a tensile stress. When a resonator
vibrates in a vibrational mode other than pure torsion, it experiences both tensile and
compressive stresses in the structure, leading to regions of elevated and reduced
temperatures. For example, when a cantilever beam is operated in its flexural mode, one
of its surfaces experiences a tensile stress while the other a compressive stress. As a
result, one side of the beam has a higher temperature than the other. Some of the
mechanical energy in the resonator is lost due to heat flow from the warmer to the cooler
side of the resonator, and this is known as thermoelastic dissipation. Following Roszhart
[24], the therrnoelastically limited Q value (QTED) can be obtained from the product of

two different functions I‘(T) and (1(f) in the following way:

1
= ——-—— 2.35
QTED 21‘(T)Q( f) ( )

The term HT) depends on temperature and contains the material dependencies of the

TED process. It can be expressed as [24]:

azTE

r(T) = 4pC
p

 

(2.36)

where T is the cantilever temperature a is the coefficient of thermal expansion and Cp is

the specific heat capacity. The term 00') depends on the cantilever resonant frequency

and it can be expressed as [24],

25

2f
00') = F0 (2.37)

”(W2

where f is the cantilever frequency and F0 is the frequency at which heat flows from the

 

warm side to the cool side. This F0 value can be calculated from [24],

717C

F0 = —
2,0Cph2

(2.38)

where K is the thermal conductivity of the cantilever. If the temperature is fixed, l"(T)

becomes a constant, leaving .Q(f) as the parameter to influence QTED. When the cantilever

frequency f matches the characteristic frequency F0, .(l(/) becomes unity and QTED gets to

its lowest value. The larger the difference between f and F 0, the smaller 0.0) gets, and the

larger QTED becomes.

When a beam is vibrating, the mechanical vibration of the structure (sound
waves) can interact with the thermal phonons changing the population distribution of
thermal phonons [25] . This process leads to a direct conversion of mechanical energy
into a temperature increase of the resonator and is the origin of the phonon-phonon
energy loss mechanism. The highest achievable Q limited by phonon-phonon interaction

is given by [25],

 

—1
2 (or h
Q h = p” p (2.39)
p CT72[1+(wr)zj

26

where v is the sound velocity, 7 is the Gruneisen’s constant, and rph is the phonon

relaxation time. The phonon relaxation time can be calculated from the longitudinal and
transverse velocities of sound in the material from the following equation [25],

rph = ——35— (2.40)
2
PC1001)

where UD is the Debye sound velocity, which is obtained fi'om [25],

(2.41)

 

Here in equation (2.41) U] and vt are the velocity of longitudinal and transverse sound

waves in the material, respectively.

Another energy loss mechanism can arise from internal friction. Such an energy
loss mechanism can be associated with defects (intrinsic or extrinsic) in the crystal lattice
[13]. Additionally, there are energy loss mechanisms related to the surface of the
resonator, which are not well understood. In many cases, a linear relationship between the
energy loss and the surface area to volume ratio has been observed [19,23,26], suggesting
that the Q is limited by surface losses. The reported studies on the origin of surface losses
point at either a thin film of a different material on the surface of the resonator [26] or the

resonator surface roughness [16].

27

2.4 Micromechanical Resonator Structures and Limitations

The three methods used for increasing the performance (i.e. resonant frequency
and Q) of a micromechanical resonator are:
l) The use of materials with superior elastic properties
2) The use of strategic resonator geometries
3) Decreasing resonator dimensions
Researchers have used combinations of these 3 techniques to achieve resonators with
unique performance [7,8,11,22,26,27]. However, these techniques have challenges that
need to be overcome. Every resonator geometry and material has some advantages and

some limitations.
2.4.1 Micromechanical resonators

The resonator structure stiffiress and mass depend on the resonator geometry and
size. Therefore, the natural mechanical frequency of the micromechanical resonator will
also depend on the type of structure (geometry). However, no matter which type of
geometry or operation mode (i.e. flexural, torsional or radial contour) is being analyzed;
the frequency will always depend on the elastic properties of the material the device is
made of. For example; a cantilever beam, comb-drive or bridge structure has a resonant
frequency that is dependent on the material’s Young’s modulus, and the torsional

resonator has a resonant frequency dependent on the material’s shear modulus.
2.4.2 Resonator geometry

As it was mentioned before, the modification of resonator geometry is one of the
tools used for increasing the fundamental frequency of the device, and also the Q. Table

2.2 shows pictures of some resonator structures fabricated form polycrystalline diamond.

28

The structures in this table have different advantages and disadvantages in their
performance.

The first resonator shown in table 2.2 is a comb-drive structure. Comb-drive
structures can be designed to get a Q higher than even fi'ee-free beams (i.e. 100,000 when
operated at 1m torr) [23]. However, these structures tend to have a low resonance
frequency (KHz range), since their dimensions and consequently their mass are much
larger than other strucutres. Due to the geometrical complexity of comb-drive structures,
it is harder to reduce the size of these devices than it is to reduce the size of a bridge
structure. Since the resonant frequency of a structure is inversely proportional to the
resonator mass, most comb-drive structures show a lower frequency than bridges or other
structures that can be fabricated in much smaller sizes.

The next structure in table 2.2 is a torsional resonator. Torsional resonators can be
operated in a torsional mode (instead of flexural as in the bridge, comb-drive, cantilever
and free-free structures), which makes the resonant frequency dependent on the shear
modulus instead of the Young’s modulus. When this type of resonator is excited in its
pure torsional mode, the structure does not experience the tensile and compressive stress
as in the case for other vibration modes. This eliminates the regions in the structure with
elevated and reduced temperatures. Therefore, there is no heat flow across the structure
and the losses due to thermoelastic dissipation (TED) are eliminated. Torsional resonators
have the limitation of having only one torsional vibration mode, limiting the number of
resonant frequencies for a specific device (when it is operated in their torsional modes) to

one.

29

The third row of table 2.2 shows an SEM picture of a 92MHz free-free beam flexural
mode micromechanical resonator with some of its dimensions. This device is comprised
of a free-free micromechanical beam supported at its flexural node points by four
torsional beams, each of which is anchored to the substrate by rigid contact anchors. The
free-free beam supports will be located at the nodal points of the beam. At these points
there is ideally no movement. As a result, anchor dissipation mechanisms normally found
in the bridge structure, are greatly suppressed (ideally zero), allowing much higher device

Q. It can be noticed from equations (2.4) and (2.32) that the resonant frequency increases

and that the champ decreases with decreasing beam length. Therefore, if the clamping

losses are the dominant energy dissipation mechanism on a cantilever beam, then the Q
values would decrease with increasing resonant frequency. However, since clamping

losses do not affect fi'ee-free beams; the Q does not drop with frequency.

30

Table 2.2 Resonator structures fabricated from polycrystalline diamond. The
torsional resonator shown in the second row was patterned at Sandia
National Laboratories. The other structures were completely fabricated at

Michigan State University.

 

 

 

 

 

 

 

 

 

Structure Picture Performance Frequency
1
3 2
2.41%]
l E Lfl’
f0 = ___. _
2” ’0 Vp + (1)” + (3)14;
. 4 35
-H1gh Qs due to
1 W Where Wfb and Lib are the width
Comb _ 0 aDChor losses and length of the folded beam
' - Low frequency suspensions; h is the thickness; and
Drlve due to large mass Vp, Vt and Vb are the shuttle
volume, the total combined
volumeof the folding trusses and
total combined volume of the
suspended beams respectively.
- Operated 1n _ .05220b3
torsronal mode. f0 r __3
T . I No dissipation WM
OISIOna due to Where G is the shear modulus, d and
thermo elastic w are the paddle's length and width
_ , , respectively, and b and L are the
dISSIPatlon paddle’s support length and width.
E h
fo = Kn — —
P L2
-No acnhor Free-Free barns share the same
Free Clamped Beam; therefore the
fiequency is the same given by
equation (2.4)
6x Jo@(5)= I — a
J 1
P x (I - 02)
6 = a) x R x
0 E
-Rad1al contour Where a id the disk radius; Do=21rfo
mode operation is its angular resonance frequency;
DISk - Jn(y) is the Bessel function of the
mStead 0f first kind of order n; and ‘1 ,1; and E
flexural are the density, poisson ratio, and
Young '5 modulus of the disk
structural material respectively.

 

 

 

 

 

31

 

70MHz bridges have been tested under 50 uTorr vacuum and the results have
been compared to a free-free beam with similar dimensions [1 1]. The results show a Q
difference by a factor of 28 between both structures with the same frequency. This shows
that free-flee beams can operate at the same frequency of a bridge with similar
dimensions but a much larger Q.

In a disk structure (last row of table 2.2), if the position of the anchor (at the
middle of the disk) is carefirlly controlled, and the anchor is made from a different
material than the disk, the anchor losses can also be suppressed. These advantages allow
this type of structure to have a high frequency and Q as it was shown for polycrystalline
silicon [7]. The disk resonator shown in table 2.2 has achieved the highest resonance
frequency (1.51GHz when operated in its second radial-contour mode) while maintaining
relatively large dimensions (20pm diameter) and a decent Q (17,458 for first mode,
11,555 for the second one). The device consists of a 2 rim-thick nanocrystalline diamond
disk suspended by a stem located at its center and enclosed by polycrystalline silicon
electrodes spaced less than 1,000A from the disk perimeter. Such tiny lateral electrode-to
resonator gaps were achieved using a recent lateral sub-um gap process technology that
combines surface micromachining technologies with a sacrificial sidewall technique to
achieve sub-micron (sub-um) lateral gaps without the need for aggressive lithography or
etching [27]. Since the center of the disk corresponds to a node location for the radial
contour vibration mode shape, anchor losses through the supporting stem are greatly
suppressed, allowing this design to retain a very high Q.

The fourth column in Table 2.2 shows the equation for determining the resonant

frequency of each device. Either the Young’s or shear moduli (E or G) is present in all

32

these equations. Since diamond is the hardest material known, the use of polycrystalline
diamond in small strategic resonator geometries is the best alternative for achieving high

frequency RF MEMS resonators.
2.4.3 Resonator materials

So far, polycrystalline silicon has been the preferred material for RF MEMS
resonators [27,28,29]. This is mainly due to the fact that silicon technologies have been
deeply studied, and are well known. However, the electrical and mechanical properties of
polycrystalline silicon begin to rapidly degrade at elevated temperatures (>350 °C),
making it increasingly unsuitable for high temperature applications [30]. Materials with
higher Young’s and shear moduli will provide a larger resonant frequency as the
equations in the fourth column of table 2.2 show. That is why polycrystalline silicon
carbide and polycrystalline diamond materials are being studied for use in RF MEMS
devices. Both materials have a larger Young’s and shear moduli than polycrystalline
silicon (see table 2.3). Early results on polycrystalline silicon carbide [30] and
polycrystalline diamond [31,32] show that indeed devices made of these two materials
show a higher resonance frequency than that of equivalently sized polycrystalline silicon
versions. Polycrystalline diamond folded beam comb-drive nricromechanical resonators
have now been measured with resonance frequencies 1.77 times higher than that of
identical polycrystalline silicon counterparts, 1.20 times higher than achievable by
polycrystalline SiC, and 1.53 times higher than a previous attempt at using CVD
polycrystalline diamond as a resonator structural material [32]. Also, polycrystalline
diamond cantilever beams have shown the highest Q for cantilevers made of any

polycrystalline material [33]. Table 2.4 shows the most recent and outstanding results

33

(prior to the work shown in this thesis) for diamond resonators tested using different

actuation methods.

Table 2.3 Properties of crystalline materials that can be used to fabricate
micromechanical resonators

 

 

 

 

 

 

many/Mm... haggline figggggflggg sec on.
Density, p 2300 3300 3500 Kg/m3
Young’s Modulus, E 150 448 1200 GPa
Shear Modulus, G 52 160 478 GPa
Acoustic Velocity, «1(B1p) 8075 11652 18516 m/s
Normalized Acoustic Velocity l 1.44 2.29 --

 

 

 

 

 

 

 

34

Table 2.4 Most recent results for diamond resonators before the work reported in
this thesis

 

 

 

 

 

 

 

 

 

 

 

Actuation
Method Structure f0 Q
Disk* [7] 1.51GHz 11,555
Electrostatic Bridge [31] 2.938 MHz 6,225
Comb-Drive [32] 27.35 KHz 36,460
Doubly-Clamped
Paddle * [34] 640 MHz 3,000
Piezoelectric
Doubly-Clamped
Paddle * [14] 157 MHz 9,000
Magnetomotive 13:23:13.3?)ng 157 MHz ~9,000
* These structures (Doubly-Clamped Paddle and Disks) were made of nanocrystalline
diamond

 

 

 

2.4.4 Resistance Rx

Now that the GHz frequency range has been reached, micromechanical resonators
are emerging as viable candidates for on-chip versions of the high-Q resonator used in
wireless communication systems for frequency generation and filtering. Among the more
important of the remaining issues that still hinder development of these devices in RF

front ends is their larger-than-conventional impedance. In particular, it is their large

impedance (commonly called motional resistance, Rx) that presently prevents

micromechanical resonator devices in the VHF and UHF ranges from directly coupling to
antennas in wireless cormnunication applications, where matching impedances in the

range of 500 and 3300 are often required [35].

35

The most direct methods for lowering the motional resistance Rx of

electrostatically actuated micromechanical resonators are [36]: 1) decrease the electrode-
to-resonator gap; 2) raising the dc-bias voltage; and 3) summing together the outputs of

an array of identical resonators. Each of these methods comes with drawbacks. The first

two methods are very effective in lowering Rx, with exponential dependences. However,

they do so at the cost of linearity [37]. On the other hand the third method improves

linearity while lowering Rx. Unfortrmately, the third method is difficult to implement,

since resonators with identical responses are required. This is even harder for large Q

devices.

2.5 Polycrystalline Diamond Material

In this thesis, the polycrystalline diamond material is studied for its use as a
structural material for RF MEMS resonators. The following sections show the
justification for the use of polycrystalline diamond and a summary of the reported

properties and techniques for the processing of this material.
2.5.1 Why diamond?

The use of strategic geometries, and alternative materials, are the two methods of
choice for increasing the resonance of the device. Going for smaller dimensions (sub-um
range) on polycrystalline silicon resonator structures is not practical due to enhanced

adsorption properties of water-related species to the silicon surface. Diamond, with the

. . -1 . .
highest acoustic velocrty of 18,076 ms [38] and chemrcal inertness, seems to be the

36

most superior among the new materials including polycrystalline silicon carbide. The

3 . . . . .
carbon-carbon sp bonds in tetrahedral configuration, crucral for the formation of srngle

crystal diamond (SCD), are responsible for a unique combination of diamond properties.
However, SCD is too expensive for most applications in wireless systems. Furthermore
SCD technology is not compatible with the conventional silicon technologies.
Fortunately, the polycrystalline diamond, with physical properties approaching those of
SCD, can be fabricated on silicon substrates using the chemical vapor deposition (CVD)
techniques and its cost is comparable to that of polycrystalline silicon for film thicknesses
in the range of l — 2 pm. Table 2.3 shows a comparison of properties of the three
structural materials that have been studied for RF MEMS applications. Polycrystalline

diamond films with the same acoustic velocity of SCD can be obtained by controlling the

sp3/sp2 ratio during its growth [38].

As the polycrystalline diamond films contain sp and sp2 carbon-carbon bonds
leading to non-diamond phases at the grain boundaries, their properties, such as acoustic
velocity can be affected adversely if the polycrystalline diamond quality, indicated by the
sp3/sp2 ratio as measured by Raman spectroscopy, is not carefully controlled. As
mentioned earlier, reducing the resonator dimensions close to or below 1 pm for
polycrystalline silicon resonators is expected to lead to size related limitations due
primarily to enhanced adsorption properties of water-related species to the silicon
surface. The diamond surfaces are known to be chemically inert to such adsorption,
which makes this material more suitable and reliable for resonators with dimensions

below 1 pm.

37

2.5.2 Chemical Vapor Deposition (CVD) of diamond films

Therrnodynamically, graphite, not diamond, is the stable form of solid carbon at
ambient pressures and temperatures.

The CVD technique is based on decomposition of carbon-containing precursor

molecules (typically CH4) diluted in H2 gas. This generally involves thermal (i.e. hot

filament) or plasma (DC, RF, or microwave) activation, or use of a combustion flame

(oxyacetylene or plasma torches). The fact that polycrystalline diamond films can be

formed by CVD techniques is linked to the presence of H2 and hydrocarbon molecules.

The H2 atoms are believed to play a number of crucial roles in the CVD process [39].

There are several techniques for the deposition of polycrystalline diamond
including microwave plasma CVD (MPCVD), hot filament CVD, radio frequency CVD,
and dc-arc jet CVD. MPCVD is the most widely used technique due to its efficacy to
produce high film quality, large substrate size, less contamination and better
controllability [40]. Figure 2.5 includes schematics of HFCVD and MPCVD techniques.
These processes have been described in the past [41, 42, 43, 44].

All the deposition techniques rely on the ability to set up a dynamic non-
equilibrium system, in which only sp3 carbon bonding can survive. This is achieved by
the presence of hydrocarbon radicals, and more importantly, by large quantities of atomic
hydrogen in the deposition gas. The hydrocarbon radicals provide the vapor source of
carbon for diamond deposition. The atomic hydrogen is believed to play two important
roles: it eliminates sp2 bonded carbon (graphite), while establishing the dangling bonds of

the tetrahedrally bonded carbon sp3. By creating a plasma system where atomic hydrogen

38

predominates, any graphitic bonding is etched away. Atomic hydrogen etches both

diamond and graphite out, but under typical CVD conditions, the rate of diamond growth

exceeds its etch rate, while this is the opposite for other forms of carbon (graphite).

a)

—hydv8m

 

 

 

— methane

 

lPC power swirl

 

 

 

.11.;

pyrometer

 

 

 

 

pump

 

heating element

\ thermocouple

 

 

 

 

b)
microwave 10de
generator 333"“ urethane
8‘; : m...
. -———substrate
Wesmde: heater
pimp

Figure 2.5 a) HFCVD and b) MPCVD polycrystalline diamond deposition

When the sample is ready for diamond growth it is loaded into the chamber and

taken to a low pressure level. A mixture of gases (gases and their quantities depend on

the type of polycrystalline diamond film that needs to be deposited) is then introduced

into the chamber. The energy, provided by either DC. power supply or microwave

generator, helps creating the conditions inside the chamber for creating the plasma

(ionized gas). The sample is heated by the plasma and usually monitored with a

pyrometer.

39

2.5.3 Seeding

One of the most crucial steps in CVD growth of polycrystalline diamond films is
generating seeds on the substrate (seeding) before the growth begins. In order to
guarantee a continuous polycrystalline diamond film, a high nucleation density of
diamond particles is necessary. Some of the techniques for this seeding step, are the
abrasive polishing of the substrate with various grain sizes of diamond [45,46] and the
ultrasonic agitation of the substrate with a diamond powder suspension [47,48,49,50].
Bias enhanced nucleation (BEN) has also been reported for effectively creating
nucleation sites on silicon substrates [51] and preparing highly oriented diamond films
[52,53].

An IC-compatible nucleation technique which does not cause surface damage [54]
is the use of Diamond Powder Loaded Fluids (DPLF) with different carrier fluids, mean
powder sizes and densities. The idea of this method is to spread diamond crystals,
suspended in carrier fluids, on the substrate surface. During the diamond deposition
process, the carrier fluids are evaporated at initial stages leaving behind the diamond
particles which act as seeds for diamond growth. There are different ways to apply the

DPLF to the substrate such as direct writing, spinning, spraying or brush painting.
2.5.4 Doping

As a wide band gap semiconductor material (Eg = 5.5 eV), CVD diamond films
deposited without intentional doping are usually good insulators. Since the
micromechanical resonators which are meant to replace oscillating components in
transceivers need to be conductive, the diamond fihns used for the fabrication of such

devices, need to be doped. Because the 2000 K temperature necessary for effective

40

diffusion in diamond is too high [55], diamond doping is performed either during growth,
or by subsequent ion-implantation. Boron, aluminum, phosphorous, lithium and nitrogen
have been tested as dopants for diamond [56].

Polycrystalline diamond film doping (p-type) during the CVD process is usually

achieved by using pure boron powder [57], boron trioxide (8203) [5 8], diborane (B2H6)

[59,60], or trymethylboron [61]. IR measurements have confirmed that boron atoms
occupy substitutional sites [62]. Diamond quality, grain size, growth rate, hydrogen and
oxygen contents, dislocation and planar defect densities are affected by boron doping
[63-66]. The changes in polycrystalline diamond resistivity as a function of doping

concentration have been reported by [40].
2.5.5 Patterning

Due to diamond’s chemical inertrress, standard wet etching techniques are not
possible. Two patterning techniques can be applied: selective deposition and selective dry

etching. Selective deposition is achieved by selective nucleation or by masking the areas

where diamond growth is not desired. SiOz was successfully used as a masking layer by

Masood et al. [54], Roppel et al. [66] and Davidson et al. [67]. A nucleation technique,
which consists of spinning a layer of photoresist pre-mixed with diamond powder and

lithographically patterning it, was developed at Michigan State University [54].

Selective etching of CVD diamond with SiOz or Si3N4 as a mask, was performed at

atmospheric pressure, in oxygen environment at 700 °C, in a rapid thermal processor

[54].

41

The dry etching of polycrystalline diamond, which uses different active gas
species such as oxygen, argon, CR; and SF6 with metal or SiOz masks [69-71] seems to
be an excellent choice for polycrystalline diamond patterning. Most researchers have
used conventional reactive ion etching (RIE) methods where the gas species are excited
by RF power [71-72]. Dry etching using ECR assisted microwave plasma at low substrate
temperatures and pressures has led to very clean structures with small feature sizes and

sharp edges [73-74].

42

Chapter 3

Polycrystalline Diamond Film Technology

3.1 Introduction

The work reported in this thesis focuses on the use of polycrystalline diamond as
a micromechanical resonator structural material. This chapter explains the polycrystalline
diamond film technology used for the fabrication of such devices as well as the

fabrication process flow.

3.2 Seeding

The seeding process influences the grain sizes in the polycrystalline diamond film
and is the fabrication step responsible for guaranteeing a continuous film. The seeding
technique used for the polycrystalline diamond fihns reported in this thesis consists of the
use of a diamond powder loaded water suspension, commonly known as diamond in
water (DW). This suspension is prepared by mixing of 25 carats of diamond powder, with
an average particle size of 25 nm, in 1000 ml of deionized (DI) water and a suspension
reagent. The DW suspension is placed in an ultrasonic bath for 30 nrinutes before it is
intended to use.

For the fabrication of the resonators reported in this work, the surface over which

the seeding will be done is mainly SiOz. The starting substrate depends on the fabrication

process that will be used, which are discussed in section 3.7.
The first step is to clean the substrate, which was done using RCA cleaning [74].

Then, before the DW was poured over the substrate a quick dip of the sample in a diluted

43

HF solution (1% HF in H20) for 10-20 seconds was done to clean the SiOz layer. It was

observed that this HF dip step improved the DW suspension surface coverage over the
sample. After the HF dip, the sample was rinsed in DI water for 5 nrinutes, and then
blown dried with nitrogen. Now the samples are ready to be seeded. The DW suspension
is taken out from the ultrasonic bath and it is poured over the substrate. The sample,
which is now covered with the DW suspension, was loaded in a conventional spinner,
and was spun for 30 seconds at 1000 rpm. For improving the seeding density, the

spinning process was repeated more than once. This seeding method is particularly

suitable for clean hydrophilic surfaces [75] such as SiOz or Si3N4. A nucleation density

of 1011 cm-z, and an average surface area of film grains of 0.06 pm2 has been obtained
by using this seeding method [76].
3.3 Film Growth Process

All the CVD polycrystalline diamond films reported in this work were grown in a

bell jar type MPCVD chamber (WavematTM MPDR 313EHP) with a 9 inch chamber

diameter and a 5 inch quartz bell jar diameter. A 2.45 GHz, 5 kW microwave power

TM . .
supply (Sairem GMP60KSM) and a large chamber size ensured the uniformity of the

plasma. The sample wafer was heated by the plasma and its temperature was monitored
by a pyrometer. The gas mixture introduced to the chamber depended on the properties
needed for the diamond film. Since the polycrystalline diamond film quality increases
with lower methane concentrations [77], the methane concentration was never above 2%

of the total gas mixture.

As it will be seen in later chapters, a comparative study between different
diamond films was made to identify the growth parameters that affect the diamond
microstructure and consequently the Q. More precisely, the parameters varied in order to
get diamond films with different microstructures were the growth temperature (600 °C -
780°C) and the gas percentage of tri-methyl-boron (TMB) in the MPCVD chamber
during growth .

The following samples are referred to in the rest of the thesis.

0 Sample 1: Undoped film grown 780 °C (66 measurements)

0 Sample 2: Highly doped film grown at 780 °C (69 measurements)

0 Sample 3: Undoped film grown at 600 °C (62 measurements)
Each sample represents one specific type of polycrystalline diamond fihn from which
different resonator structures were tested at different vibration modes and temperatures.
Table 3.1 shows the polycrystalline diamond growth parameters used for each one of the

films.

45

Table 3.1 Growth parameters for the three polycrystalline diamond samples studied
and dry etching parameters (superscript denotes the sample on which the value was
used)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Polycrystalline Diamond Film Growth
H2 1001,213
Gas(I;lcocv;1 Rate CH4 11,25
TMB 42; 0"3
Temperature (°C) 780”2 ; 6003
Microwave Plasma Power (kW) 2.01’2'3
MPCVD Gas Pressure (torr) 35i’2’3
Seeding Diamond Powder Size (nm) 251’2’3
Dry Etching Parameters
Gas Flow Rate CE. 1’"3
(seem) 02 30"”3
Chamber pressure (mbar) 41110'2 1’2’3
DC Power (W) 400 W

 

 

Figure 3.1 shows the Raman spectra for three representative polycrystalline

diamond films. It can be noticed that from the three samples, sample 1 has the best

-1 .
looking Raman peak at ~1332 cm . It has been reported how the doping of

polycrystalline diamond films and the low temperature synthesis affect adversely the

sp3to spzratio in polycrystalline diamond films [77]. This can also be seen from figure
3.1, where the sharpest diamond (sp3 carbon-carbon bonding) peak corresponds to sample
1, which is the undoped film grown at the highest temperature (780°C).
3.4 Doping

If the micromechanical resonator is intended to be used in oscillator or filter

applications, the resonator structural material needs to be conductive. The doping

technique used in this work is done in situ using TMB. The boron doping of

46

polycrystalline diamond films using TMB has been investigated in the past as a function

of TMB/CH4 gas ratio, growth temperature and post growth anneal [40].

In this work, the diamond films that were heavily doped (e. g. sample 2) had a hole

. 1 -3 . . . .
concentration around 1 x 10 cm and a resrst1v1ty of 0.15 Q-cm. Thrs came as a result

of a diamond growth gas mixture of 100:1 :4 (szCH4zTMB).

47

Raman Spectra

 

   
 
 

  

 

 

6000‘ 1 1 z 1 1 *i
l g s s 3 3 .
1 i
5000 e .....................................................................
DZ
3; 4000 1 ...................................................................................
3‘ ,
17:
c
3C3 3000 . """"""" """"""""""""""""""""""
"" ; Sample 2
2000 L ............. ............. ...... .............. .............. ............ ..
l Sample 3
1000 ' 1 i 1 1
1000 1100 1200 1300 1400 1500 1600
Wavenumber (cm'1)
Figure 3.1 Raman spectra for the three samples studied
3.5 Patterning

As it was mentioned in the last chapter, due to chemical inertness of diamond, it
can not be patterned using wet etching. The polycrystalline diamond patterning technique
used in this work was dry etching using electron cyclotron resonance (ECR) assisted

microwave plasma for the samples that were patterned at Michigan State University. For

48

the samples that were patterned at Sandia National Laboratories the dry etching was done
using RF plasma. The dry etching system at Michigan State University etched
polycrystalline diamond at an approximate rate of 0.05 11ml rrrinute, while the
polycrystalline diamond etch rate for the system at Sandia National Laboratories was
about 0.03 urn/minute. Aluminum was used as a hard mask material in both cases for the
selective dry etching of polycrystalline diamond. The etch rate for aluminum in both dry
etching systems is much slower than the etch rate of polycrystalline diamond. For the dry
etching system at Michigan State University, the aluminum was etched around 13 times
slower than polycrystalline diamond [40], whereas for the system at Sandia National
Laboratories the aluminum was etched around 4 times slower [13].

Some of the recipes for dry etching of polycrystalline diamond can cause
aluminum sputtering over some areas of the diamond surface. When this happens, the
plasma can not attack the diamond under the sputtered aluminum. As a result, one might
end up getting “spikes” around the patterned structure after the dry etching of diamond is
completed in the rest of the sample. This is called the grass eflect (process shown in
figure 3.2) and it has been reported in the past when deep reactive ion etching (DRIE)
was used to pattern silicon-on-insulator wafers [78]. Figure 3.3-a shows SEM images of
the grass effect noticed in the polycrystalline diamond structures patterned at Michigan
State University with the spikes created by the grass eflect. These spikes are likely to be

polycrystalline diamond. Since the fabricated polycrystalline diamond resonator

structures lie on top of the $102 layer, when the structures are released, the spikes that are

not attached to the structure are released as well. Figure 3.3-3 shows areas where the

spikes are still attached to the structure, and some of the released spikes. In order to

49

obtain these SEM images with the released diamond spikes, the samples did not go
through the cleaning process after the release step, and they were loaded into the SEM
right after release. Figure 3.3-b shows an SEM image of a patterned silicon structure
showing also the spikes generated by the grass eflect [78].

For the dry etching done at Sandia National Laboratories the gas mixture was a

combination of oxygen plasma with CF4 (02:CF4 ; 30:1). This recipe etches A1 at a

faster rate and eliminated the grass effect by etching the sputtered aluminum which
caused the diamond spikes. The samples that were patterned at Michigan State University
had to go through a more vigorous rinsing process in order to eliminate the released
diamond spikes from the sample.

Figure 3.4 shows SEM images of released polycrystalline diamond structures
patterned at Michigan State University. Very clean surfaces and smooth sidewalls can be
observed and the spikes discussed earlier are not noticed in these SEM images. For the
patterning of these structures, the temperature inside the dry etching chamber was kept
below 100 °C and the dry etching process was done for only 3 minutes. Since 3 minutes
was not enough for etching the polycrystalline diamond fihn, the dry etching process was
repeated until the polycrystalline diamond fihn was entirely removed. The dry etching
system was not used for 30 minutes between each run. This suggests that a careful
cleaning of the released samples together with a low temperature and short dry-etching
intervals can also help reduce the sidewall roughness and lower the grass eflect.

Figure 3.5 shows a comparison of the structures fabricated and patterned at

Michigan State University and the very first set of results for polycrystalline diamond

50

resonators reported by [31]. The close up views of the structures show a comparable

sidewall roughness.

 

Aluminum
Sputtering

 

 

 

 

A!

 

P-type Silicon (substrate) Cross Section View A-A’
Aluminum
1:] Diamond

Silicon Dioxide

Sputtered
Aluminum

 

 

 

 

Figure 3.2 Grass effect diagram. The sputtering of aluminum during the dry
etching of diamond prevents the plasma from etching the diamond under
the sputtered aluminum.

51

 

 

 

 

 

 

| Silicon Spikes]

 

Figure 3.3 Evidence of the grass efi'ect found on (a) the dry etching of the
polycrystalline diamond resonators reported in this thesis and (b) the
DRIE of silicon-on-insulator wafers [78].

52

Anchors
\

. 5011111

Corjib

‘ \
Anchors\§~

10 11111

 

Figure 3.4 Released polycrystalline diamond structures (comb-drives and bridges)
patterned at Michigan State University. N o grass effect can be observed.

53

 

Figure 3.5 a) Fabricated and patterned polycrystalline diamond resonators
from [31] and b) Michigan State University (reported in this thesis)

54

3.6 Surface Roughness

As it was mentioned in the previous chapter, researchers have found the surface
roughness of a micromechanical resonator to influence the Q [19,23,26]. Randomly
oriented polycrystalline diamond films (which are the ones used for this work), show
very rough surfaces when compared to polycrystalline silicon fihns [79]. It is therefore
important to have some control over the surface roughness in polycrystalline diamond
fihns which are going to be used for micromechanical resonators. The results obtained in
this work, show similar surface roughness for undoped films grown at 600 °C, and highly
doped films grown at 780 °C (sample 2 and sample 3). Figure 3.6 shows AFM images of

these two samples. The difference in surface roughness was only about 5 nm.

55

   
 
  
 

/

/
Img Rms (Rq) 57.52 nm
X scale 2p./div
Z scale lit/div

b)

Img Rms (Rq)
62.35 nm
X scale 2p./div
Z scale lu/div

Figure 3.6 AFM images showing the polycrystalline diamond surface
roughness of Sample 3 (a) and Sample 2 (b). The difference in the film
roughness is about 5 nm.

56

 

u. -..

1.810. f

I. . ...—...,

 

Silicon Substrate

 

 

 

Figure 3.7 Starting substrate for the fabrication of polycrystalline diamond
resonators

3.7 Microresonator Fabrication Process

The following section describes the fabrication process steps for the resonators

used in this work.
3.7.1 Fabrication technology

In this work, two testing methods were used: 1) the electrostatic actuation and
detection and 2) the piezoelectric actuation with optical detection. Depending on the
testing method that will be used, micromechanical resonators can go through different
fabrication steps. A device that has been fabricated for electrostatic actuation can be
tested using either electrostatic or piezoelectric actuation with optical detection.
However, if the device is going to be tested using only piezoelectric actuation with
optical detection, the fabrication process can be simplified significantly. Both fabrication

processes, begin with the same substrate which is shown in figure 3.7. It consists of a

commercially available silicon wafer with a 2 pm thick thermal SiOz (wet grown) layer

on top. The doping and orientation of the silicon wafer is not critical. In this thesis, a p-

type (100) silicon wafer was used.

57

3.7.1.1 Samples for electrostatic testing

Figure 3.8 shows the fabrication process flow for a micromechanical resonator

which is meant to be tested using electrostatic actuation and detection. The thermally

grown SiOz layer that comes with the starting substrate is necessary to electrically isolate

the devices from the substrate. The fabrication of these devices consists of a 3 mask
fabrication process.

The first step for the fabrication of a micromechanical resonator that will be tested using
electrostatic actuation and detection (after the starting substrate was cleaned using

standard RCA cleaning process [74]) is the deposition of a thin (~ 300 nm) layer of

silicon nitride (Si3N4). The deposition of this layer prevents the etching of the underlying

Si02 layer at the time of release. The justification of this Si3N4 layer is explained in

more detail later on, when the releasing of the structure is discussed. Since the purpose of

this layer is to simply isolate the underlying $102 layer from the future wet processing of

the sample, the details about its deposition are not critical.

The second step is the deposition and patterning of the layer that will serve for
making the electrical connections for testing (mask #1). Highly doped polycrystalline
silicon has been used for this layer in the past. However, a metal had to be deposited over
it, in order to decrease the contact resistivity [80]. In the work reported in this thesis, a
single layer of chromium (100 nm thick) was deposited and patterned for electrical

connections.

58

 

 

 

 

 

 

 

 

q MATERIALNTEROSS SECT'OMROCESSING STEP“

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VIEW
Chromium
SisN4 3102 * a) Metal deposition
Silicon Substrate ‘
PECVD S'O
' 2 b) Metal patterning and
PECVD Si02 deposition

Pogprystalcljine c) PECVD Si02

\ 'amO" j ‘ Patterning and diamond

 

deposition

d) Diamond patterning

e) Release (PECVD

@2 removal) /

Figure 3.8 Fabrication process flow for electrostatically tested resonators

 

 

 

 

 

 

After this metal layer was deposited and patterned, it follows to deposit the

material that will serve as a sacrificial layer. In this work, SiOz was deposited via

PECVD and used as the sacrificial layer.

59

This layer will be removed entirely at the last step of the process (releasing step).
The thickness of this layer will dictate the electrode to resonator gap. The gap value used
in this work is 200 +/- 100nm. This range of values is very crucial for the electrostatic
operation of polycrystalline resonators. As the gap increases, the electromechanical
transduction factor (n) discussed in chapter 2 decreases. When this factor decreases, the
output current also decreases, limiting the detection capability. If it is too thin, it can get
completely etched away by the plasma in the diamond growth step, leaving a short circuit
between the beam and the bottom electrode. A thickness around 200 nm has been
successfully used in the past [81]. After this sacrificial layer has been deposited, it has to
be patterned to create the contact areas where the resonator will be in contact with the
metal layer underneath (mask #2). These areas are commonly called “anchors”. Once the
anchors are patterned, the sample is ready for diamond seeding and growth (sections 3.3
and 3.3). A device that will be tested using electrostatic techniques needs to be
conductive. For achieving this, in situ doping was done (section 3.4). For patterning the

diamond (mask #3), dry etching was used (section 3.5). After the diamond film has been

patterned, the exposed areas of the sample are SiOz and diamond. Now the devices are

ready for releasing. In the release step, the purpose is to remove the entire sacrificial SiOz

layer. This is done by submerging the sample in a 5:1 BHF solution (5 40% NH4F :l

49% HF). This solution typically etches the PECVD SiOz at a rate between 250 nm/min

and 500 nm/min [82]. The time that it will take for the solution to remove entirely the

sacrificial layer depends on how large is the area under the resonator structures. This

60

etching solution (5:1 BHF) is isotropic. Therefore, if a 10 um wide cantilever needs to be
released, it will take the solution at least 20 minutes to etch 5 am from each side and
completely release the structure. If a faster releasing is desired, a solution with higher HF
concentration can be used or even pure HF (49% by weight, remainder water). Both

etching solutions remove the aluminum that was used to mask the diamond.

If the Si3N4 layer was not deposited, the SiOz etching solution (BHF or HF) will

etch parts of the 2 um thick thermal SiOz that came with the starting substrate. If this

happens, the corner areas of the metal interconnect layer, which in this case would be

over the thermally grown SiOz layer, would be partially released as well. This could lead

to metal peeling off. Also, the undercutting of this metal layer will affect the resonator Q

since the rigidity of the anchor can be affected. The Si3N4 isolates the thermally grown

SiOz from the sacrificial PECVD SiOz in the release step, which avoids this problem and

also gives more flexibility for the releasing time.

3.7.1.2 Samples for piezoelectric/optical testing

The fabrication process for a micromechanical resonator that is going to be tested
using piezoelectric actuation and optical detection is much simpler. There are fewer
processing steps and restrictions on the design. These include:

1) The underlying electrode required by the electrostatic method is not necessary.
2) The material does not need to be doped

3) The resonator gap is not critical.

61

Figure 3.9 shows the fabrication process flow for devices to be used using
piezoelectric actuation and optical detection. Since there will be no current flow across
the resonator and no time varying capacitance needs to be formed, metal electrodes are
not necessary and the resonator does not need to be conductive. Since there is no

capacitance formed or electromechanical transduction factor (n) to keep high, the gap

between the beam and the substrate is not critical. In this work, the 2 pm thick SiOz layer

that comes with the commercially available sample (figure 3.7) was used as the sacrificial
layer. This would lead to a resonator to substrate gap of 2 am.

The fabrication consists of a two mask fabrication process. The processing for a
micromechanical resonator that will be tested using piezoelectric actuation and optical

detection starts with the standard RCA cleaning of the substrate. Then mask #1 is used to

pattern the thermally grown SiOz layer that comes with the starting substrate and form

the anchors. Now the sample is ready for diamond seeding and growth (sections 3.2 and
3.3). The second and final mask is used to pattern the material (aluminum for purposes of
this thesis) that will be used to mask and pattern the diamond (section 3.5).

The releasing step is the same used for the releasing of devices for electrostatic

testing. The difference is that now the sacrificial thermal SiOz (wet grown) etches at a

much slower rate in the BHF solution (100 nm/min) than the PECV D SiOz. Therefore,

the releasing time will be longer. It will now take at least 50 minutes to completely

release a 10 um wide cantilever beam.

62

 

 

 

 

 

 

 

 

VIEW

q MATERIAL PFROSS SECT'OFI‘4ROCESSING STEPI\

 

 

 

 

$102

 

 

 

 

Silicon Substrate :

 

 

 

 

 

Polycrystalline
Diamond

a)Si02 patterning and
k 1‘

diamond deposition

 

 

 

 

b) Diamond patterning

c) Release (PECVD

SiO removal)
U /

Figure 3.9 Fabrication process flow for resonators to be tested using piezoelectric
actuation and optical detection

 

 

 

 

 

3.7.2 Post-processing

After the samples are released, some cleaning and drying steps were made. The
samples that were tested at Michigan State University (tested electrostatically) could not
go through standard RCA cleaning or any other cleaning process that involved hydrogen
peroxide (piranha cleaning for example). This is because the metal layers present in such
samples could suffer oxidation or be removed. After the sample was released, it was
submerged in acetone for 5 minutes, then rinsed in a beaker with running DI water for 5
minutes and then submerged in methanol for 5 minutes. Since there might be released

diamond spikes to be removed, the sample was then rinsed again with running DI water

63

for about 10 minutes. Finally, the sample was then heated in a hot plate to 100 °C and
then annealed to 500 °C in a nitrogen environment for removing any moisture.

The samples that were processed and tested at Sandia National Laboratories
(piezoelectric actuation and optical detection) went through a different post processing.
After the sample was released, it was taken into an ultraviolet ozone cleaning system to
remove the organic residues, and finally it was heated to 800 °C in an argon atmosphere

using rapid thermal annealing to remove any residual moisture.

64

Chapter 4

Resonator Testing Methods

4.1 Introduction

As it was explained in chapter 2, there are several methods for testing
micromechanical resonators. In this thesis, two different techniques were used to test
similar resonator structures. The two methods used are the electrostatic testing and the

piezoelectric actuation with optical detection.

4.2 Electrostatic Testing

This section describes the equipment set-up for the electrostatic testing system
and the measurement results of polycrystalline diamond resonator structures. The
equipment for electrostatic actuation was set-up at Michigan State University for the first

time.
4.2.1 Electrostatic testing equipment set-up

Figure 4.1 shows a diagram of the testing system and the connections to the
resonator structure. The system consists of a Low Temperature Microprobe vacuum
chamber supplied by MMR Technologies capable of reaching a vacuum level of 10
mtorr. The chamber had four probes with electrical connections to the outside of the
chamber by SMA (Sub-Miniature A) connectors. By using these SMA connectors, the
network analyzer and the dc-voltage supply were connected to the probes inside the

chamber and consequently to the resonator structure. The network analyzer was used to

65

supply the input ac signal and to constantly monitor the output current. A bias tee was
used to isolate the dc-bias from the network analyzer. As soon as the beam starts
vibrating, a change in the output current flow will be detected by the spectrum analyzer
and it will show a maximum value at the resonant frequency. For purposes of this work a
Hewlett-Packard/Agilent 8753B Network Analyzer (300KHz —- 3GHz) was used. The dc-
voltage supply was used to apply the dc-bias needed in order to increase the output
current and get a more noticeable peak. A more detailed explanation of the theory

involved in electrostatic testing can be found in section 2.2.3. 1.

Bias Tee

 

POI-III’

Vacuum Chamber (100 mtorr)

 

 

 

 

 

 

 

 

 

Network Analyzer

 

 

Figure 4.1 Connections to the resonator structure for electrostatic testing. In order
to measure only the change in current across the resonator, a bias tee is used to
isolate the dc- bias from the IN-port of the network analyzer.

4.2.2 Electrostatic testing measurement results

Different resonator structures were tested electrostatically. The results obtained

were on bridge, comb—drive and cantilever resonator structures tested at a vacuum level

66

of 100 mtorr. Figure 4.2 shows the measurement results for a bridge and comb-drive
structure tested using a dc-bias voltage of 30 V and SEM images of the tested structures.

It can be noticed how the resonant peak shows a slight non-symmetry with respect to the
resonant frequency point. This could be due to a non-linear effect caused by over driving

the resonator structure. This problem has been found in the past by Kaaj akari [83].

1

67

V‘
LII): 5011111 _

‘U/I,

\Q/ ,

f/rr.

 

Figure 4.2 Electrostatic measurements on polycrystalline diamond resonators: a)
bridge structure, b) comb-drive. The resonant frequency (f,) was calculated by
finding the frequency at maximum magnitude and the Q was calculated using this f,
value and the 3dB bandwith (Af)

68

4.3 Piezoelectric actuation with optical detection

The piezoelectric actuation and optical detection was done using the measurement
system that was already built at Sandia National Laboratories. The basic idea of the
piezoelectric actuation method is to drive the resonator into vibration by using a
piezoelectric transducer, which is in contact with the sample that contains the resonator
structure. This piezoelectric transducer is driven into vibration at a frequency determined
by the output of a network analyzer. For the optical detection, a laser is focused on the
vibrating beam and the reflected signal is used to determine the frequency of vibration. A

more detailed explanation is given in section 2.2.3.2.
4.3.1 Piezoelectric actuation and optical detection results

The tested structures were cantilevers and torsional resonators. The cantilevers
reported in this section had lengths ranging from 50 pm to 100 um, and they all had a
width of 10 pm. The thickness varied from 0.45 um to 0.7 pm. The table 4.1 summarizes
the set of results obtained for these cantilevers made from the sample 1 described in
chapter 3.

Researchers have found different values for the Young’s modulus of
polycrystalline diamond at room temperature [84]. The Young’s modulus of the
polycrystalline diamond resonators fabricated and tested was checked using the data
shown in Table 4.1 and the following equation for the resonant frequency of a cantilever

[10].

f0 =O.1615 51 (4.1)

PL;

69

Table 4.1 Results for piezoelectically-actuated cantilever beams (first vibration
mode) made from sample 1.

 

 

 

 

 

 

 

 

 

 

 

 

Cantilever Performance
Length (um) f0 (HZ) Q
100 258,900 9,970
95 276,400 7,540
90 325,500 14,470
85 346,300 10,070
80 384,900 15,260
75 443,500 8,240
70 503,800 6,390
65 570,900 3,550
60 654,300 5,390
50 856,500 6,726

 

 

 

 

 

where E and p are the Young's modulus and density of polycrystalline diamond

respectively. The constants L,- and h are the beam length and thickness respectively.

Figure 4.3 shows a plot of the data shown in table 4.1. Since the plot in figure 4.3 shows
1

the fiequency ( f0) on the y-axis and the inverse of the cantilever length squared ( 2
Lr

)in

70

the x-axis, equation (46) can be fit with a linear equation by takingx ___;2’ y = f0
Lr

andm = 0.1615J—E—h. This would lead to:
p

 

f0 = 0.1615 -E—h[—12-] (4-2)
7 L a p J L,
W—/
m x

The Young’s modulus can be calculated by using the expression for the slope

m=0.l615\/§h.
p

The linear fit to the data shown in figure 4.3 shows a slope (m) of 0.002 Hz-umz.
The value for the film thickness (h) can be approximated from the SEM images to be 0.7

pm and the value for p is commonly know to be 3520 kg-m-3. Since the variables h, p,

and m are known, the Young’s modulus for the polycrystalline diamond film (E) was
calculated to be 1,000 GPa. This value is close to the accepted value of the Young’s
modulus for bulk single crystal diamond, which is about 1,050 GPa [85]. The inset in

figure 4.3 shows the resonant peak of the 95 um long cantilever beam.

71

 

 

Data for 95 um long cantilever
Lorentzian Fit

 

 

  
    
 

 

f,,=276,400 Hz —-— Data
Q=7.540 Linear Fit

 

5.
9x10 ‘

(Normalized Amplitude) 2

   
 
  

276,200 276.400 276.600

8x1 05-
. Frequency (Hz)

7x105-

6x105-

5x105-

4x105:

3x105.-
5.

9.00x107 1.80 x108 2.70 x108 3.60 x108

1/L2

Figure 4.3 Young’s modulus of sample 1 was calculated from a linear fit done
to the measured data.

~<OZmCIOm7U~r1

E

Slope = 0.002 (Hz -,rm2)
E = 1,000 GPa

 

2x10

 

72

4.4 Comparison of results

Polycrystalline diamond cantilever beams were tested using both methods in order
to compare the resonator performance. The cantilever beams that were tested using both
methods came from polycrystalline diamond films grown at 780 °C. The sample tested
electrostatically came from a highly doped (5x1019 cm'3) polycrystalline diamond fihn.
Table 4.2 shows the polycrystalline diamond fihn growth parameters for the sample

tested using electrostatic and piezoelectric actuation.

Table 4.2 Polycrystalline diamond growth parameters for the sample tested
electrostatically and piezoelectrically

 

 

 

 

 

 

 

 

 

 

 

 

 

Polycrystalline Diamond Film Growth
Gas Flow Rate Sample
(sccm) Electrostatic Piezoelectric
H2 100 100
CH4 1 1
TMB 4 0
Temperature (°C) 780 780
Microwave Plasma
Power (kW) 2.0 2.0
MPCVD Gas
Pressure (torr) 35 35
Seeding Diamond
Powder Size (nm) 25 25

 

 

The seeding process was the same for both samples. For the sample used in
electrostatic actuation, the gap between the structure and the bottom electrode was 0.2
run, while for the piezoelectrically actuated the gap spacing was 2 11m. Figure 4.4 shows
the Raman spectra of both samples. It can be seen that the doped sample has a higher

background at higher wavenumber. This probably is due to fluorescence noise [86].

73

 

 

    

INTENSITY A.U.

 

INTENSITY A.U.

WAVE NUMBER (cm'l) WAVE NUMBER (cm'l)

Figure 4.4 Raman spectra for samples measured using different actuation
methods: a) piezoelectric b) electrostatic

74

Figure 4.5 shows the comparison of two cantilevers with the same length (90 um)
and tested using the two different testing methods. Although the difference in resonant
frequencies of the two samples is on the order of 3%, the Q for piezoelectric actuation is
8 times higher than that for electrostatic actuation. The most likely reason for the

decrease in resonance frequency for the electrostatically actuated beam could be the

effect of an electrical spring constant ke that subtracts from the mechanical spring

constant of the beam, km, lowering the overall spring stiffness kr=km-ke [1 l]. The dc-

bias voltage used for this measurement was 5 volts. The gap spacing was 0.2 am, the
electrode and beam overlap was 20 um and the beam length and width were 90 um and
10 pm respectively. This gives rise to a <1]:_e_> ratio of 0.045. This ratio means that the
r
measured resonant frequency of this device using electrostatic actuation will be
(theoretically) 95.5% of the resonant frequency that would be measured using a testing
method which does not affect the resonator spring constant. The resonant frequency
measured using electrostatic actuation was 315,240 Hz which is 96% the resonant
frequency measured using piezoelectric actuation and optical detection (325,560 Hz).
Another possible reason for the difference in frequency is a film thickness difference
between the two polycrystalline diamond films from which the resonators were

fabricated.

75

3) Electrostatic Actuation

 

_.v' -'~):v...'
, ~,_.. --. .

J

,/
rv' /

1‘ I
_,, ,.. i . .._-' i" ‘I

i. ’5’/ ."J i: i . ‘ ; -. ' J

l

“a ‘ f“ ‘ ' ”L i 4“;

 

"A f =315,240 Hz
8 1 0
g Q=1,902
g. -
< 0.5 1
' i
g :
v 0

 

 

314,900 315,200 315,500

Resonant Frequency (Hz)

b) Piezoelectric Actuation

 

N 1 ]
g ‘ f0=325,560 Hz
i I Q=l4,469
g 0.5 1
g 1
Z .
v 0 i

 

 

 

325,300 325,600 325,900
Resonant Frequency (Hz)

Figure 4.5 Testing results on two similar polycrystalline diamond cantilevers using
different actuation and detection methods.

76

Also, although both films were fabricated under similar conditions (table 4.2),
their thickness could still be slightly different due to possible fluctuations in temperature
at the polycrystalline diamond grth step.

The difference in Q is likely not related to the method of actuation or the
properties of the polycrystalline diamond film, but rather due to the different
measurement pressures used in the two methods, 100 and 0.001 mtorr for electrostatic
and piezoelectric actuations, respectively. The pressure of 100 mtorr reflects a low
vacuum and, thus, represents what would be readily achievable in a packaged device
[87]. At 0.001 mtorr there should be negligible air damping, and the Q should reflect the
true mechanical Q of the structure. The effect of air damping on Q can be readily
estimated. At 100 mtorr, the Q is limited by the exchange of energy between the
mechanical structure and gas molecules. This is in the molecular flow regime, and the

magnitude of Q can be calculated according to the following equation [22]:

_ 271nm?
Q - _km P (43)

where f" is the resonance frequency of the 11th vibrational mode, p is the density, P is the

1/2
gas pressure, and km = [(32M)/(92r.R7)] , where M is the molecular weight of the gas,

R is the gas constant, and T is the temperature.

The molecular flow regime extends down to about 10 mtorr, and below this point
air damping is negligible. Therefore, decreasing the pressure item 100 mtorr to pressures
less than 10 mtorr should result in an increase in Q of about a factor of 10. For the
cantilever structures tested using electrostatic and piezoelectric actuation, the measured Q

values were in the range of 1,000-2,000 and 3,550-15,260 respectively. The low quality

77

factors of the electrostatically structures are consistent with the Q being limited by air
damping, and the quality factors of these structures are representative of what can be
achieved for structures of these dimensions in a low vacuum package [87]. The
piezoelectrically-actuated structures in high vacuum should not be limited by air
damping.

Similar resonator structures also made from polycrystalline diamond were tested
electrostatically under 50 mtorr by Wang [31]. Their reported Q values range from 2,000
— 6,000. Later results, also on similar polycrystalline diamond resonators tested
electrostatically under 50 utorr [32], showed Q values in the range of 6,225 — 36,460.
Since the molecular flow regime extends down to about 10 mtorr, and below this point air
damping is negligible, a decrease in pressure from 50 mtorr to any pressure below 10
mtorr would represent an increase of Q by a factor of 5. The results obtained in [31] and
[32] show an improvement of Q close to a factor of 5 when the pressure in the chamber is
lowered from 50 mtorr to 50 utorr.

Based on the measured resonant frequencies and the dimensions of the structures,

an acoustic velocity of 16,100 ms.1 was found for the doped fihn and 15,900 for the

. . -3 .
undoped one. Assuming a densrty of 3,500 kg-m , the resulting Young’s modulus for

the polycrystalline diamond films are 883 GPa for the doped sample and 907 GPa for the
undoped one. The slightly lower moduli found here could be due to a slightly lower
density for the polycrystalline diamond films or an error in the estimation in the

polycrystalline diamond film thickness.

78

Chapter 5

Study of Q and Frequency Shifts in Poly-

crystalline Diamond Resonators

5.1 Introduction

Two very important characteristics of micromechanical resonators are resonant
frequency and Q. This chapter discusses the Q and resonant frequency shifts due to
varying testing temperature for polycrystalline diamond resonators. The data obtained
during this study showed the measurement of the highest quality factor (116,000) for
polycrystalline diamond resonators and for cantilever beams made of any polycrystalline

material [33].
5.2 Quality Factor Limitations

As it was discussed in chapter 2, there are different mechanisms that can limit the
Q. Figure 5.1 shows the effect of different energy loss mechanisms as a function of
resonant frequency for polycrystalline silicon and polycrystalline diamond computed for
a 1 um thick cantilever beam. The corresponding cantilever beam length for each
frequency and material appears on the top axis. The parameters used for plotting the
dissipation curves [25] in figure 5.1 are shown in the Table 5.1. It is interesting to note
that the increase of resonant frequency achieved by reducing the length of the beam leads
to a substantial decrease in Q because the anchor losses are dominant mechanisms in the
whole frequency range. In other words, Q can be substantially increased by minimizing

anchor losses. However, in that case, the maximum achievable Q will be determined by

79

other energy loss mechanisms as shown in figure 5.1. As most applications require a Q of
at least 10,000, the anchor losses will limit the frequencies to less than 10 MHz. Thus, for
applications requiring frequencies above 10 MHz, if the clamping losses can be

minimized, the losses due to other mechanisms will allow Q values of 10,000 as seen in

figure 5.1.

 

 

 

 

Quality Factor

 

 

   

— Diamond
1_' Silicon

 

Resonant Frequency (Hz)

Figure 5.1 Energy loss mechanism curves for a 1 pm thick poly-
crystalline diamond and polycrystalline silicon cantilever beam

80

Table 5.1 Polycrystalline diamond and polycrystalline silicon properties used for
plotting the dissipation curves in figure 5.1

 

Polycrystalline Polycrystalline

 

 

 

 

 

 

 

 

 

 

 

 

Parameter Silicon Diamond
Thermal Expansion Coefficient, a( x 10'6 "C’1 ) 2-67 1-1
Yorgg’s Modulus, E (GPa) 170 41050
Density, p ( kg m'3) 2329 3520
-l -1
Specific Heat Capacity, C9 ( J kg K ) 700 502
Heat Capacity per Unit Volume, C (J mn3K-1 ) L63 1.767
Thermal Conductivity, 1c( W Ill-l K.l ) 130 1500
Gruneisen’s Constant, y l 1
Velocity of longitudinal and transverse sound
. . 3 -1 9; 5.5 18; 13.1
waves in the material 0| ; 0t (l x 10 ms )

 

5.3 Quality Factors in Polycrystalline Diamond Resonators

This section shows the results obtained for polycrystalline diamond cantilever
beams with widths of 10 um, and lengths and thicknesses varying from 100 um - 500 um,
and 0.45 pm - 0.8 pm respectively. Piezoelectric actuation and optical detection was used
as the testing method for all the results reported in this chapter. The samples were tested
at a vacuum level of 1x10" torr. The performance of the resonators (frequency and Q)
was obtained from the Lorentzian fits done to the obtained data. The frequencies of the
tested resonators were all in the KHz range (8 KHz — 800 KHz), and the Q values varied
significantly from sample 1, where a Q of 116,000 was obtained, to the other two samples
(sample 2 and 3), where the Q values did not exceed 50,100.

Figure 5.2 shows some of the Q limiting curves in polycrystalline diamond
resonators (solid lines) and the measured data (experimental points) on all the samples.
These curves apply to a 0.7 pm thick polycrystalline diamond cantilever beam. The

clamping curve does not depend on the cantilever temperature, and this is why figure 5.2

81

shows only one curve for clamping losses. The curves for erao and Qpi, will be shifted

in the y-axis by the cantilever temperature. Figure 5.2 shows 2 curves for each of these

temperature dependent dissipation mechanisms. They are plotted to include the lowest

and highest temperature at which the samples were tested (30 °C and 400 °C).

 

 

 

 

 

 

 

 

 

 

1X108 v- ooc' _1 1
leO7 I P CTy2 1+(wrph? [ f 2
FopCp 1+[-——)
1... F0
O 6 r QTED=
3 1x10 fazm‘
a: w a
. dish 1 =O.34x \ .5
3, 1x105 8 Ogegn y r 30°C
:1 n n 2 gg '800 400
g 1 104 Eng ° 0
x i P
o F 3%, ° [3 Samplet .
0 o O 0 .
1x103 , o 0 Samplaz 1:
O Sample3 1
1x104 1x105 1x106 1x107 1x108 1x109
Frequency (Hz)

Figure 5.2 Q value limiting curves for a 0.6 pm polycrystalline diamond
cantilever beam and measured data for the three samples.

82

All the Q factors measured in this work are below any of the dissipation curves,
suggesting that the Q values are not limited by any of these mechanisms. The most likely
mechanisms for limiting Q values in polycrystalline diamond are mechanical relaxation
processes at defects in the films, such as vacancy or impurity motion, grain boundary
sliding, etc [13]. A study of the temperature dependence of Q in polycrystalline diamond
resonators together with the study of the polycrystalline diamond microstructure will
allow a better understanding of these mechanisms.

Figure 5.3 shows a plot of the obtained Q values for the three samples (same
experimantal points shown in figure 5.2) in a range of frequency where the data can be
observed clearly. It also shows the resonant peak with the highest Q value for each

sample.

83

 

1.6

0.5

 

(Normalized Amplitude)

0.

fo= 318.183 Hz
Q=116,400

Sample}

 

318.180

 

318.190

 

\.

 

 

 

 

_ 318,170
g 12 k Frequency (Hz) J : l a
‘;< 10» U Sample1 a u
1: _ 0 Samplez :
L 8 0 Sample3 3 II '5 5'
.9 . ' -
0 _ a B
(U
1.1. , 6
3‘ ~ .
'r-B 4 .-
3 O
O 2* a a

 

 

 

 

Frequency (Hz)

Figure 5.3 Measured Q values as

 

(g Sample 3\ (a Sample 2
r3. 1. g ...l
g f fo = 89.030 Hz g fo = 120, 970 Hz
E ' Q = 50,100 ”g °"
2 2

 

Frequency (Hz)

 

 

j ”1 Q: 47, 900
0.0

120.940 120.960 120.980 121.000
Frequency (Hz)

 

 

 

 

J

a function of frequency for the three studied

samples. Resonant peaks show the highest Q value for each sample.

84

5.4 Polycrystalline Diamond Film Microstructure

In order to characterize the different polycrystalline diamond films, TEM images
of the cross sections from one piece of each sample were taken. The cross sections were
obtained by using the focused ion beam (FIB) technique, which uses an ion beam to
raster over the surface allowing the milling of small holes in the sample at well localized
sites, so that cross—sectional images of the structure can be obtained. From the TEM
images, the polycrystalline diamond fihn can be studied in more detail including the
nucleation layer (seeding layer) that is necessary for polycrystalline diamond growth.
This nucleation layer is typically formed of small grains (~30 nm in diameter).

Figure 5.4 shows how the grain sizes fiom the studied polycrystalline diamond
films increases from the nucleation layer up, showing a larger percentage of the fihn
composed of small grains for the sample 2. As the polycrystalline diamond fihns contain
sp and sp2 carbon-carbon bonds leading to non-diamond phases at the grain boundaries,
their properties can be affected adversely in this nucleation layer. According to figure 5.3
the Q values are larger for the polycrystalline diamond film with less percentage of the
film composed by the seeding layer (sample 1). This preliminary result suggests a
relation between Q and the nucleation layer in polycrystalline diamond resonators. The
characteristics of this nucleation layer (thickness, grain sizes, nucleation density, etc.) can
be controlled by the growth process.

Polycrystalline diamond films can be divided into two layers: 1) The seeding

layer and 2) The film layer.

85

 

SAMPLE 1

       
  

SAMPLE 2

 

   

Film Percentage
Occupied by Nucleation
Layer:

~Sample 1 ~ 10%
-Sample 2 ~ 18%
08ample 3 ~ 13%

»|

Figure 5.4 Cross section TEM images of the three studied polycrystalline
diamond samples.

5.4.1 Seeding Layer vs. Film Layer

If a cantilever beam is treated as a two layer structure across its thickness [88],
where the two layers are the seeding and film layer, the total dissipation can also be
thought of as the combination of the dissipation in these two layers. In other words, the
total dissipation in the cantilever beam would be partially due to the seeding layer, and
partially due to the film layer. The total dissipation can then be expressed as [89]:

.,/ tf/
1 t tot ttot

=___+— (5.1)

Qtot Qs Q f

86

where ts, and tf, are the thicknesses of the seeding and film layer respectively and

ttot 2 ts + t f' The values HQ, and I/Qf, are the dissipation due to the seeding and film

layer respectively, and I/Qtot is the total dissipation in the cantilever structure. The

purpose of this analysis is to find if there is a common dissipation among all the

polycrystalline diamond films (Samples 1, 2 and 3) due to the seeding layer HQ, and
another due to the film I/Qf.
For this analysis, the values for ts, and tfwere obtained directly from the TEM

images. For estimating the Qtot for each fihn, the arithmetic average of the 15 higher

measured Q values of each sample was calculated. The 15 higher Q values for each
sample were in the following ranges for each sample:

1) Sample 1: 76,560 - 116,000

2) Sample 2: 31,596 - 47,900

3) Sample 3: 23,544 - 50,100

The obtained values for ts / ttotr tf ”tot and the average of the 15 higher Q values for each

sample (Qtot) are shown in table 5.2. Now that these variables are known, they can be

substituted in equation (5.1) for each of the three films. The result of this substitution is

shown in equations (5.2), (5.3), and (5.4).

87

Table 5.2 Ratio of seeding and film thickness to total thickness for each sample and
the average of the 15 higher measured Q values for each sample (Qtot ).

 

 

 

 

 

 

 

 

 

 

 

 

Sample/Parameter ts/ttot tf/ttot Qtot
Sample 1 0.1 0.9 96,000
Sample 2 0.18 0.82 35,000
Sample 3 0.13 0.87 30,000

1 _ 0.1 0.9

 

— + =>S l 1
96,000 QS Q f amp 8* (5'2)

1 _O.18+0.82
35,000 Q3 Qf

1 _O.13+O.87
30,000 QS Qf

:> Sample_ 2 (5-3)

 

 

 

 

:> Sample _ 3 (5.4)

Now, if equation 5.1 is rearranged in the following way

 

1 = 1 + t s 1 _ l (5.5)
Qtot Q f ttot Qs Q f
the values for the Qtot can be plotted as a function of tS/tm, and from the slope of a linear

fit and the intercept in the y-axis, the values for Q5 and chan be obtained. The resulting
plot is shown in figure 5.5. From the slope an intercept values, the calculated Qf and Q,

values are: Qj=66,000 and QS=4,737

88

    

3.5‘
1
3 _.
1 25-i
/Qtot ' .
(10-5) 2 -
1.5 Slope = 1.961x104
, Intercept = 1.5x10'5
1 _ I

 

 

I ' I ' I ' I ' I

0.1 0.12 0.14 0.16 0.18

ty
‘tot

Figure 5.5 Plot of 1/Qm as a function of tS/ttop The values for Q; and Q, are
obtained from the slope and intercept of the linear fit.

Another way to find the range of values for Qf and Q3, would be to plot the Qfas
a function of Q, by using the functions shown in equations 5.2-5.4 and then approximate

the minimum space which contains a set of values for Qfand Q5 which satisfy each of the

equations in the system. One possible way and find this minimum area or space of

solution is to find a rectangle that contains at least one set of values for Qfand Q5, which

belong to each of the curves. This is similar to what was done by [90] and [91]. The

horizontal line that would describe this rectangle (HOR) is the difference in Q, from

89

sample 1 and sample 3. The vertical line that would describe this rectangle (VER) is the

difference in forom sample 1 and sample 3. Using equations (5.2) and (5.4), these lines

can be taken as:

_ 9,600Q f 3,900Qf
- Q f — 86,400 — Q f — 26,100 (5.6)

__ 86,400Qs _ 26,100QS
Q3 —9,600 QS -3,900

 

VER

 

(5.7)

In order to minimize the area of the rectangle, it would be necessary to minimize the

product of equations (5.6) and (5.7). An approximation of this minimization was obtained

graphically by plotting the product of equations (5.6) and (5.7) in terms of Q3 and Qfand
obtaining the values for Q3 and Qfat which the area of the rectangle is minimum. Fig 5.6

shows a plot of the obtained rectangle. The range of values for Qfand Qs that are defined

by the rectangle are:

Q f = 70,500 i 30,000

5.8
93 =30,250:19,750 ( )

These values suggest that the Q of a polycrystalline diamond film consisting
entirely of the seeding layer would be about 30,000 +/- 20,000 whereas a polycrystalline
diamond film having no seeding layer would have a Q of about 70,000 +/- 30,000. The Q
of a polycrystalline diamond film containing both a seeding layer and a film layer can be

estimated using equation 5.1.

90

 

   
    
     

 

 

 

 

 

 

 

 

 

 

20~-[--E-? ------------- F ------ i ------ Qs=50,000

1 g : g ; Qf=106,930 5
15—-1-4.-:r-—---—-a-- ------- i -----

Qf l a 2 . : a
4 10-- ~17? ------ E ------- i ------- i ----- \— - ----- i ----- 1‘
(1x10) i\ ‘i: (Qs=30,250 01:70.500) : :
a =- a a a

‘ £1 5 e i

 

 

Qs=11,223 1 104
Qf=40,000| Qs(x )

Figure 5.6 The approximation for the minimum space of solutions is determined
by the rectangle, which touches all the curves at least in one single point.

91

5.5 Temperature dependence

It is important to guarantee the micromechanical resonator thermal stability in
order to make the device suitable for high temperature applications. Since the elastic
properties of most polycrystalline materials change at different temperatures, the
performance of resonators made from such films also varies with temperature. Also, it is
important to be able to predict the shift in resonant frequency of a mechanical resonator

when the ambient pressure changes.
5.5.1 Young’s modulus and frequency temperature dependence

As it has been pointed out earlier, for most resonators the frequency depends on
the Young’s modulus of the material the resonator is made of. Most polycrystalline
materials have a temperature dependent Young’s modulus. Consequently, there is a
frequency shift on polycrystalline resonators when they are operated at different
temperatures. The Young’s Modulus of polycrystalline diamond decreases with
temperature [92] and so does the frequency of resonators made of polycrystalline
diamond.

In this work, cantilever beams made from the three different polycrystalline
diamond films (described in section 3.3) were tested at different temperatures. The
temperature dependence of the polycrystalline diamond Young’s modulus was obtained
from the measured frequency values at different temperatures and using a linear fit
analysis similar to the one used in section 4.3.1. Figure 5.7 shows the variation of the
Young’s modulus for the three polycrystalline diamond films. In the studied temperature
range (30 °C — 400 °C) the samples show a Young’s modulus decrease of 2.5% (sample

1), 3.8% (sample 2) and 2.6% (sample 3).

92

Young's Modulus (GPa)

1050 —

 

 

 

 

 

 

 

 

 

 

 

 

 

1000 -, ____ Sample 1: Undoped, 780 °C _____ _
F A k 4
950 - ————-~— ,__ —— ~
900 ~ —— ~
S I 2: 5 1019 '3, 780°C
850 fig ___} ampe x :n'\'
800 Sample 3- Undoped 600°C
750 -___.__.h ._ +. i J_.
700 I r I I
100 200 300 400

Tom perature (C)

Figure 5.7 Young’s modulus temperature dependence for the three samples. The
three samples have very similar slopes and the sample 1 showed the highest
Young’s modulus at room temperature.

This decrease in Young’s modulus is reflected in a resonant frequency shift of

resonators made from these films. The shifts in resonant frequency due to changes in
temperatures are measured by the temperature coefficient (T Cf). This temperature

coefficient represents the resonant frequency shift in relation to the room temperature

resonant frequency (A%0 ) by degree centi grade.

Figures 5.8 - 5.10 shows the frequency shift Af f0 for 300 um and 400 um long

cantilever beams made from the three different samples when operated in their first two
flexural modes. The resonant frequency shift by degree centigrade was obtained by

calculating the slopes of linear fits done to the measured data. The range of the obtained

93

temperature coefficients (TCf) for the three types of polycrystalline diamond structures go
from -1.59x10'5 °C’1 to -2.56x10'5 °C'1 (-15.9 ppm/°C to -25.6 ppm/°C). These ranges are
comparable to those obtained for poly-Si structures (-12.5 ppm/°C to -l6.7 ppm/°C ) in a
shorter temperature range (30 °C — 247 °C) [11], but are far from values obtained for
geometrically compensated poly-Si structures (~2.5 ppm/°C to -0.24 ppm/°C) [93,94] in a
shorter temperature range (30 °C — 107 °C).

5.5.2 Quality factor temperature dependence

Most of the extrinsic internal dissipation mechanisms that cause Q degradation in
polycrystalline materials are associated with atomic motion or with structural
reconfiguration. The motion of vacancies or substitutional impurities, interstitial motions,
dislocation, grain boundary sliding cause a resonant Debye-like relaxation, which limits

the Q value according to the following equation [25]:

. ’1 (s 9)
Qdefect = A x [Jr—)2] .

l + (tor *
where A is known as the “intensity” of the relaxation process, 1* is the relaxation time for

the defect motion and a) is the resonator vibrational angular frequency (w=2nf0). It can be

noticed from (5.9) that when a defect is limiting the Q, then its value (Qddea) will be
minimum at arr * = 1. Since there is atomic motion involved, 1* is thermally activated

and has the following functional form [25]:

94

0.002

-0.002

-0. 004

-0.006

Frequency Shift (A f / f0)

-0.008

-0.01

 

 

I

Torrie 5\3

 

Freq. Shift =

 

B

..-...-...o-.~. ...........

 

TC’ -2.5659 x 105

0
0.0013235 2 ER
0

 

 

 

 

 

R

0.99335

0 £300 pm 1st mode

3 5 1:1 E300 pm 281 mode

—"'““\ """ """"""""" """"""" <>"'§'400'pm"1fist'mod‘e‘r
x 5400 pm 2st mode

 

 

O

100

200 300
Temperature (C)

Figure 5.8 Frequency shift as a function of testing temperature for sample 1

95

Frequency Shift (A f / f0)

0.001

-0.001
-0.002
-0.003
-0.004
-0.005
-0.006
-0.007

Sample 2

 

 

 

 

 

 

 

 

i . ! i
\ o 300 pm 151 mode
”a """" ; 3:2 """"""""" f """" film'300'firfi'23trfibdéfl
_. ................ 8K ________ <.>.-...4QQ-ym-..1.s;t.mod.e.-_
= \ g x 400 pm Zst mode
“' """""""""""""""" \ """""""" “
_35 ..... x ................. .............. _
\é O
_ .................................................... --\. ............... E ............... 4
= - if] N o ci>
__ Freq.Shift=TCf*T+B [3‘ "1:1 _______________ __
8 0.0010015 g; g
_ TC’ -1.5915x10'5 ............. 99 ............... a
R 0.98262 5 9 if:
i i

 

 

 

 

0

100

i
200 300 400
Temperature (C)

Figure 5.9 Frequency shift as a function of testing temperature for sample 2

96

Frequency Shift (A f / f0)

0.002

-0.002

-0.004

-0.006

-0.008

-0.01

 

 

   

Sample 3

 

 

 

 

 

 

 

 

  
 

 

 

o 300 pm 13}: mode
_ -.g ..................................... :1-..300.pm.23§t-mode._
0 400 pm 1st mode
_ .......................................... 8--..49980293m999L
~— ------ Fre.Shift=TCfx T.+B .......... .............. —
B 0.0011124 : [5
TC" -1.8677 x 10'5 k S)
” '''' R 0.97822 """""""""""""" 5 """""""
i i 1 L
0 100 200 300 400 500

Temperature (C)

Figure 5.10 Frequency shift as a function of testing temperature for sample 3

 

97

(5.10)

. . . . . 13
where l/‘to is the characteristic atomic Vibration frequency (on the order of 10 Hz), EA

is the activation energy for the relaxation process, and k3 is the Boltzmann’s constant. If

a single defect type dominates, then there will be a maximum in internal dissipation (a
minimum in Q) at the frequency in which on * =

The Q values of a resonator can be measured as a function of temperature. Then
the activation energy for the relaxation process can be identified by finding the
temperature at which the Q degradation is maximum and using equation (5.10). Figure
5.11 (a) shows the Q values as a fiJnction of temperature for the three samples. It can be
noticed in figure 5.11 (b) how the Q values for the sample 2 reached a minimum value at
around 350 °C. This suggests the presence of a thermally activated relaxation mechanism
responsible to limit the Q in highly doped polycrystalline diamond resonators or at least
the existence of a higher concentration of defects having an activation energy
corresponding to the measurement temperature of 350 °C.

The data for the 3 samples was then plotted as a function of the activation energy
by using (5.10). The activation energy axis was divided in ranges of 0.2 eV and the
measured Q values for each polycrystalline diamond film that were inside each
subdivision were averaged and represented by one single point. Figure 5.12 shows the
results fiom this analysis, where it can be noticed — in addition to the higher Q values for
sample 1 - the minimum in Q value for two of the three samples at an activation energy

around 1.9 eV.

98

 

. Sample1
I Sample2
O Sample3

0)
v

 

 

 

 

120

100 -. ......... ........... ...... ............ __________ a

Quality Factor (1x103)

 

 

 

 

0 100 200 300 400 500 600 700
b) Temperatur (C)

 

IlSample
35

 

 

30 .......... .......... i
25 _ ........... . ............ .......... -

20 .... ....... i ............ --g. ...... -.. .......... __J

Quality Factor (1x1 03)

15 _ ........... ............ .......... _

10 ... ....... .. ......... -.- ........ ...: ............

 

 

5 1 : 1 1 1
280 300 320 340 360 380 400 420

Temperature (C)

 

Figure 5.11 Measured Q values vs. temperature a) Three samples plotted in the
entire testing temperature range; b) Sample 2 in the range of temperature where a
minimum in Q was observed.

99

 

YTrjrfrTIfitfrfFfrlrITIIIIFTIVVT
.O- ; Z 3 ' '

 

0 Sample 1
D Sample 2
0 Sample 3

     
   

Quality Factor (1x104)
-¥ N 0° -h (11 O) \l (D
i

in-
839

 

 

1111111111111lllillillllliillll

(0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Activation Energy (eV)

 

Figure 5.12 Measured Q values vs. activation energy for the three
samples. A minimum in Q was observed for two of the three
samples at an activation energy around 1.9 eV.

The data suggests there are some defects or a higher concentration of defects that
give rise to mechanical relaxation that have an activation energy for defect relaxation
around 1.9 eV. This activation energy can be compared to the activation energies for
self-interstitial or vacancy diffusion in crystalline diamond (about 1.3 eV and 2.3 eV,
respectively). A comparison to diffusional activation energies was made because many
defect relaxation processes, e.g. grain boundary sliding, are limited by diffusional

processes.

100

Chapter 6

Polycrystalline Diamond Nanoresonators

6.1 Introduction

This chapter reports on the fabrication technology and testing of polycrystalline
diamond resonators with dimensions in the nanometer range (nanoresonators). These are
the first fabricated and measured structures of this type reported. The fabricated and

tested nanoresonators include torsional and cantilever structures.

6.2 Fabrication of Nanoresonators

Electron beam (e-beam) lithography has been used in the past to fabricate
nanoresonators in single crystal silicon [95]. E-beam lithography is also used in this work
to pattern polycrystalline diamond nanoresonators. The fabrication process of the
polycrystalline diamond nanoresonators was the same used for the fabrication of the
cantilevers reported in chapter 5 up to the polycrystalline diamond deposition step. A
special high resolution photoresist commonly used in e-beam patterning called “PMMA”
(Poly Methyl MethAcrylate) was deposited (200 nm thick) on top of the polycrystalline
diamond film. After this photoresist has been patterned, a 100 nm thick Al film was
deposited and patterned via lift-off. This aluminum film was used as a hard mask to
pattern the polycrystalline diamond film using dry etching to form the torsional
resonators and nanocantilevers.

The fabricated nanoresonator structures included cantilever structures patterned to

have widths as small as 100 nm, and torsional paddle resonators with a support beam

101

width of 0.5 pm. The performance of these structures shows resonant frequencies and Q
values in the range of 23 KHz - 805 KHz and 9,500 — 103,600 respectively. All the
torsional resonators were fabricated from the the 3 types of polycrystalline diamond
samples described in chapter 3, whereas the nanocantilevers were fabricated from the

sample 1.
6.3 Torsional Resonators

The torsional paddle resonator structures consisted of a proof mass (paddle) with
a mass close to 6.16x10’13 kg in a rectangular shape suspended by a 0.5 pm wide, 20 pm
long polycrystalline diamond beam. The paddles were supported perpendicular to the
largest side of the paddle in either one side (single) or both (double). Figure 6.1 shows an
SEM image of a single torsional paddle with its dimensions. The resonant fiequency of
this type of resonator structure (when it is operated in its torsional vibration mode) can be

calculated using the following equation [96]:

0.0522 xGx 53
f0 = 3 (6-1)
pxwaxd

where the variables b, w, L and d are the resonator dimensions shown in figure 6.1. The

 

 

variable p and G are the polycrystalline diamond density (3520 Kg-m-3) and shear

modulus (480 GPa) respectively. Equation (6.1) applies to a single torsional resonator.
For a double torsional resonator, the equation differs only on the constant inside the
radical (0.1 is used instead of 0.0522) [96].

In order to excite a torsional movement, the paddle support had to be ofi‘ the

center of the paddle. Otherwise, the beam would vibrate in a flexural mode similar to a

102

cantilever beam. Figure 6.2 shows a diagram of this structure and the excitation mode of

vibration.

d=20 um 2_£Lnl

 

Figure 6.1 SEM image of polycrystalline diamond single torsional resonator

103

 

Figure 6.2 Excitation of torsional resonator. The offset of the paddle support
from the center of the paddle causes a torsional vibration mode.

The patterning of the torsional resonators had to be done using e-bcam
lithography since the thin support (0.5 pm wide) of the torsional paddle would have been
hard to produce using optical lithography. The tested torsional resonators had a fixed
width (w) of 5 um, and their lengths (d) varied from 50 um to 20 pm.

6.3.1 Testing of torsional resonators

The measurement results from the torsional resonator structures are shown in
Table 6.1. As it can be noticed from the testing results, the measured Q values did not
show a dependence on the number of supports of the torsional resonator, or paddle length
(d). However, sample 1 shows higher Q values than the other 2 samples. This result

suggests a dependence of resonator Q on the type of polycrystalline diamond film. This

104

same observation was made on the results shown in chapter 5 of this thesis. The
measured resonant frequencies for the torsional resonators ranged from 269,645 Hz —
805,415 Hz and the Q values ranged from 17,152 — 86,603. The range of obtained
frequencies are lower than those obtained on torsional paddles made of nanocrystalline
diamond (13 MHz — 640 MHz) [14,34], but the measured Q values are much larger

(2,500 — 10,000) [14,34].

Table 6.1 Measurement results for single and double torsional resonators

 

Torsional Paddles
Single
Length (um)
30 4O 50
Samnle fo(sz Q fofly Q @072) Q
1 490,446 68,498 361,632 78,106 269,645 65,132
2 506,005 17,152 364,146 17,815 295,844 19,387
3 529,678 35,311 353,149 28,388 274,199 31,553
Double
Length (um)
30 40 50
Sample fo(HZ) Q fo(HZ) Q fa (HZ) Q
1 805,415 86,603 527,934 76,958 384,070 7051
2 706,756 23,796 462,139 32,209 329,973 25,382
3 752,627 22,953 461,704 46,170 327,282 27,273

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.4 Nanocantilevers

For the first time, polycrystalline diamond resonators have been successfully
patterned using e-beam lithography to have dimensions as small as 100 nm. The results
of the patterning show sharp and smooth sidewalls as can be noticed from figure 6.3.

The mask used for the e—beam patterning was designed to include cantilevers with widths

and lengths ranging from 100 nm - 1 pm and 500 nm - 200 um respectively.

105

The cantilevers reported in chapter 5 had a thickness of 0.7 pm, which was much
smaller than the resonator width (10 um). Consequently the cantilever spring constant for
a vibration perpendicular to the substrate is smaller than that for a vibration parallel to the
substrate. This is why the cantilever vibration was perpendicular to the substrate for the
cantilevers reported in chapter 5. However, for the nanocantilevers reported in this
chapter, the width (100 nm — 500 nm) is smaller than the fihn thickness (~ 0.7 am). In
this case, the cantilever spring constant for a vibration parallel to the substrate is smaller
than that for a vibration perpendicular to the film substrate. As a result, the
nanocantilevers reported in this chapter vibrate parallel to the substrate. The vibration
detection is done by monitoring the change in the reflected beam for both cases.

Figure 6.4 shows a diagram of the vibration mode of cantilevers with a width
larger (figure 6.4-a) or smaller (figure 6.4-b) than the film thickness. Figure 6.5 shows

SEM images of a 100 nm wide polycrystalline diamond cantilever.

106

Patterned
Diamond
Grain

 

Figure 6.3 Smooth sidewalls of polycrystalline diamond nanocantilevers
fabricated using e-beam lithography.

107

8)

  
 
     

Incident
Laser

ANCHOR Reso Beam

b)

Reflected
Laser

   

ThIckness Width

Length

Figure 6.4 Use of Piezoelectric actuation and optical detection for a cantilever
with vibration perpendicular to the substrate (a) and parallel to the substrate
(b). The vibration will be in the direction parallel to the smallest dimension of
the cantilever.

108

 

Figure 6.5 100 nm wide polycrystalline diamond cantilever. The top view
shows that the width of the cantilever is in not uniform along the beam length

6.4.1 Testing of nanocantilevers

The most noticeable result was the measurement of the highest Q value (103,000)
found for a nanoresonator made from any polycrystalline material. (Higher Q values
(~250,000) have been found in nanoresonators made of single crystal silicon [22]). This
value was found for a 500 mm wide, 50 um long cantilever. Figure 6.6 shows an SEM
image of this structure and the resonant peak obtained. The tested cantilever with the
smallest width was a 100 nm wide, 25 mm long cantilever beam. This structure had a
resonant frequency of 475 KHz and a Q of 14,600. SEM images of this cantilever and the

testing results are shown in figure 6.7.

109

 

Data

 
  
 

 

,3 _— LorentzianFit

'5 1.01

£08

£0.61 fo=536,050 Hz
7;, Q=103,600

:1 0.4

E05

° 1

50.0

 

 

536,020 536,040 536,060 536,080
Frequency (Hz)

Figure 6.6 SEM image and performance of the nanocantilever with
the highest measured 0.

110

[0:183 kHz
.. Q=3,()33

 

    
 
 

g 10' H EzigntzianFit

E .8

EDS] f0=183,214 Hz
8 0- . Q=3,033

g 0.4-

m .

E 0.2

o .

50.0

 

 

183,000 183,200 183,400
Frequency (Hz)

Figure 6.7 SEM image and performance of a 100 nm wide polycrystalline
diamond nanocantilever

111

Table 6.2 shows some of the measurements of nanocantilevers. The resonant

frequencies for the nanocantilevers were calculated using the equation:

fo=0.1615 ii (6.2)

p L?
where E and p are the film Young’s modulus and density respectively, h is the resonator
thickness, L, is the beam length and j}, is the resonant fiequency. The values for the

nanocantilever width and film thickness were used as the resonator thickness in equation
(6.2) to calculate the resonant frequency of the nanocantilevers. The results are shown in
table 6.2. The measured resonant frequencies are closer to the calculated values using the
resonator width as the resonator thickness, which indicates that the cantilevers are
moving parallel to the substrate as it was expected since the beam width was smaller than
the film thickness. The difference between the measured and calculated frequency values
could be due to the non-uniformity of the nanocantilevers width along the beam direction
as shown in figure 6.5.

Figure 6.8 shows a plot of the measured Q values on 200 nm thick cantilever
beams made of single crystal silicon [26], silicon nitride [26], and polycrystalline
diamond (reported in this work). The testing method for all these samples consisted of
piezoelectric actuation with optical detection. A direct relationship between the measured
Q values and the beam length can not be observed for any of the samples. This suggests
that the dominant energy dissipation mechanism is not related to clamping losses, since
the clamping losses are directly proportional to the beam length (see equation 2.32). The
measured Q values for polycrystalline diamond seem to vary much more with beam

length than the measured Q values for silicon nitride and single crystal silicon. One of the

112

possible reasons for the larger variations in Q for polycrystalline diamond could be
related to the material itself. The single crystal silicon and silicon nitride nanocantilevers
consist of only one uniform fihn. On the other hand, as it was pointed out in chapter 5,
polycrystalline diamond consists of a seeding layer composed mainly by small diamond
grains ( ~ 30 nm in diameter) and a film layer composed by much larger grains (~ 0.5
pm). The measured Q values on a structure made of two layers will depend on the
thickness of each layer [14,89]. The seeding and film layer could vary in their thickness
among different polycrystalline diamond nanocantilevers structures, leading to
differences in Q. Another possible reason for this large variation could be the low yield
that was obtained in the fabrication process of the polycrystalline diamond
nanocantilevers. Due to this low yield, the number of measurements on a nanocantilever
with specific dimensions was not larger than two. Although the yield was never
mentioned in [26], it is possible that several measurements were taken on each
nanocantilever, and the reported results was the one with the highest Q. This technique is
completely valid since there are many processes that can decrease the Q, and the
measurement with the highest Q would be the closest to the real Q of the device.

It is interesting to notice how the average of the measured Q values for the
polycrystalline diamond nanoresonators plotted in figure 6.8 (~ 21,000) is larger than that

of single crystal silicon (~ 17,000) and silicon nitride (~ 11,500).

113

Table 6.2 Results of polycrystalline diamond nanocantilevers fabricated from
sample 1. The resonant frequencies were calculated using the width as the resonator
thickness (a), and the film thickness as the resonator thickness ( b). M* represents
the number of measurements taken from each structure (the values shown in the
table correspond to the measurement with the highest measured Q).

NAN OCANTILEVERS

Meas. Calc. ” Meas. Calc. "

f0 (Hz) Q f0 (Hz) f0 (Hz) Q f0 (Hz)

210,023 1,003 219,640
77 97 7

 

114

Q Factor (1x 103)

 

0 50 100 150 200 250 300
Beam Length (nm)

Figure 6.8 Plot of measured Q values on cantilever beams made of silicon
nitride [26], single crystal silicon [26] and polycrystalline diamond (reported
in this work). All the cantilevers had a thickness between 170 nm and 200 nm

115

Chapter 7

Conclusions and Future Research

7.1 Summary and Conclusions

0 Testing of polycrystalline diamond RF MEMS resonators using

different methods

Polycrystalline diamond resonators have been tested using different actuation methods,
and the results have been compared. The results showed similar resonant fi'equencies, and
a significant difference in Q (by a factor close to 10) was attributed to the resonator

testing pressure.

0 Measured the highest Q values

A Q of 116,000 has been measured on a cantilever beam made of an undoped
polycrystalline diamond film grown at 780°C. Highly doped (5x10'9 cm'3) polycrystalline
diamond films grown at 780 °C and undoped polycrystalline diamond films grown at 600
°C had about half the Q values obtained from undoped polycrystalline diamond flms

grown at 780 °C.

0 Study of frequency thermal stability of polycrystalline diamond

resonators.

116

The performance of polycrystalline diamond resonators at elevated temperatures showed
thermal coefficient values ranging from -l.59x10'5 / °C to -2.56 x10'5 / °C. for different

polycrystalline diamond films.

0 Study of energy dissipation mechanisms in polycrystalline diamond

resonators.

The measured Q values on different polycrystalline diamond films were not limited by
clamping losses, thermoelastic dissipation or phonon-phonon interaction. In order to
identify the mechanism responsible for limiting the highest possible achievable Q, the Q
values were measured as a function of temperature and an apparent thermally activated

relaxation mechanism was identified with an activation energy around 1.9 eV.

0 Design, fabrication and testing of polycrystalline diamond

nanoresonators

Polycrystalline diamond films have been patterned to fabricate cantilever structures with
widths as small as 100 nm. The measured data does not show a relationship between the

Q values and the cantilever beam length.

7.2 Future Research

Some areas of future research are:

117

1.

Polished polycrystalline diamond films: This film can be used to produce
polycrystalline diamond resonator structures with smooth surfaces. This would be

very significant for the fabrication of polycrystalline diamond nanoresonators.

Improvement of the yield in the fabrication of polycrystalline diamond
nanoresonators: Modifications to the fabrication process of polycrystalline
diamond resonators could lead to an increase in the yield of such devices. By
increasing the yield, the characterization and the performance of polycrystalline

diamond nanoresonators can be studied in more detail.

118

BIBLIOGRAPHY

119

BIBLIOGRAPHY:

[1] C. T.-C. Nguyen, “Microelectromechanical devices for wireless communications
(invited),” Proceedings, 1998 IEEE International Micro Electro Mechanical Systems
Workshop, Heidelberg, Germany, Jan. 25-29, 1998, pp. 1-7.

[2] C. T.C. Nguyen, “Transceiver front-end architectures using vibrating
micromechanical signal processors (invited),” Dig. 0f Papers, Topical Meeting on
Silicon Monolithic Integrated Circuits in RF Systems, Sept. 12-14, 2001, pp.23-32

[3] R. T. Howe and R. S. Muller, “Resonant microbridge vapor sensor,” IEEE Trans.
Electron Devices, vol. ED-33, pp. 499-506, 1986.

[4]N. M. Nguyen and R. G. Meyer, “Si IC-compatible inductors and LC passive filters,”
IEEE J. of Solid-State Circuits, vol.SC-25, no. 4, pp. 1028-1031, Aug. 1990.

[5]N. M. Nguyen and R. G. Meyer, “A 1.8-GHz monolithic LC voltage-controlled
oscillator,” IEEE J. of Solid-State Circuits, vol. SC-27, no. 3, pp. 444-450.

[6]S. V. Krishnaswarny, J. Rosenbaum, S. Horwitz, C. Yale, and R. A. Moore, “Compact
FBAR filters offer low-loss performance,” Microwaves & RF, pp. 127-136, Sept. 1991.

[7] Jing Wang, James E. Butler, Tatyana F eygelsonand Clark T.-C. Nguyen “1.51-GHz
Nanocrystalline diamond micromechanical disk resonator with material-mismatched
isolating support” To be published in IEEE Transducers '04.

[8] Clark T.-C. Nguyen, “Vibrating RF MEMS for low power wireless communications
(invited)”, Proceedings, 2000 Int. MEMS Workshop (iMEMS’Ol), Singapore, July 4-6,
pp.2 1 -34

[9] L. Meirovitch, Analytical Methods in Vibrations. New York: Macmillirnan
Publishing Co, Inc. 1967

[10] W. Weaver, S. P. Timoshenko, and D. H. Young, Vibration Problems in
Engineering, 5th ed: Wiley Publishers, 1990

[11] Kun Wang, Ark-Chew Wong, Clark T.-C. Nguyen “VHF Free-Free Beam High-Q
Micromechanical Resonators” IEEE Journal of Microelectromechanical Systems, Vol 9.
No.3 (2000) pp. 347-360

[12] P. J. Petersan and S. M. Anlage, “Measurement of resonant frequency and quality
factor of microwave resonators: Comparison of methods” Journal of Applied Physics,

vol. 84, pp. 3392-3402, 1998

[13] D. Czaplewski, J.P. Sullivan, T.A. Friedmann, D.W. Carr, B.E.N. Keeler and J .R.
Wendt; J. Appl. Phys. 97, 023517 (2005).

120

[14]A.B. Hutchinson, P.A. Truitt and KC. Schwab, L. Sekaric, J .M. Parpia, H.G.
Craighead and J .E. Butler; Appl. Phys. Lett 84 (6) 2004, 972

[15] J. R. Clark, W.-T. Hsu, and C. T.-C. Nguyen, “Measurement techniques for
capacitively—transduced VHF -to-UHF micromechanical resonators” Digest of Technical
Papers, the 11th Int. Conf. on Solid-State Sensors & Actuators (Transducers’Ol),
Munich, Germany, June 10-14, 2001, pp. 1118-1121.

[16] P. Mohanty, D. A. Harrington, K. L. Ekinci, Y. T. Yang, M. J. Murphy, and M. L.
Roukes, "Intrinsic dissipation in high-frequency micromechanical resonators," Physical
Review B, vol. 66, pp. 085416 1-15, 2002.

[17] RM. Osterberg and SD. Senturia, “M-Test: A test chip for MEMS material property
measurement using electrostatically actuated test structures” J. Microelectromechanical
Systems, vol. 6 pp. 107-118, 1997.

[18] R. H. Blick, A. Erbe, H. Krémmer, A. Kraus, J. P. Kotthaus, Phys. E 6, 821 (2000)

[19] D. W. Carr, Nanoelectomechanical Resonators, Ph.D. thesis Cornell University
2000

[20] Stephen D. Senturia Microsystem Design; Kluwer Academic Publishers 2001

[21] E. Buks, M.L. Roukes, Europhys. Lett. 54, 2220 (2001) and E. Buks, M.L.
Roukes, Phys. Rev. B. 63, 033402 (2001)

[22] J. Yang, T. Ono and M. Esashi, IEEE J. Microelectromech. Sys. 11(6) Dec. 2002,
775

[23] FR. Blom, S. Bowstra, M. Elwenspoek, J .H.J Fluitrnan “Dependence of the quality
factor of micromachined silicon beam resonators on pressure and geometry” J. Vac. Sci.
Technol. B 10(1), Jan/Feb 1992.

[24] T. V. Roszhart, “The effect of thermoelastic internal friction on the Q of
micromachined silicon resonators,” in Tech. Dig. Solid-State Sens. Actuator Workshop,
Hilton Head, SC, 1990, pp. 13—16.

[25] V. B. Braginsky, V. P. Mitrofanov, V. I. Panov, K. S. Thorpe, Systems with Small
Dissipation, The University of Chicago Press, 1985

[26] K.Y. Yasumura, T.D. Stowe, E.M. Chow, T. Pfafman, T.W. Kenny, B.C. Stipe and
D. Rugar, J. Microelectromech. Sys. 9(1) Mar. 2000, 117

[27]W.-T. Hsu, J. R. Clark, and C. T.-C. Nguyen, “A sub-micron capacitive gap process
for multiple-metal-electrode lateral micromechanical resonators,” Technical Digest, 14th
Int. IEEE Micro Electro Mechanical Systems Conference, Interlaken, Switzerland, Jan.

121

21—25, 2001, pp. 349-352.

[28] RM. Osterberg and SD. Senturia, “M-Test: A test chip for MEMS material property
measurement using electrostatically actuated test structures” J. Microelectromechanical
Systems, vol. 6 pp. 107-118, 1997.

[29] G. Pearson,W. Read, Jr., andW. F eldman, “Deformation and fracture of small Si
crystals,” Acta Metall, vol. 5, p. 181, 1957.

[30] Shuvo Roy, Russell G. DeAnna, Christian A. Zorman and Mehran Mehregany
“Fabrication and Characterization of Polycrystalline SiC Resonators” IEEE Transactions
on Electron Devices, vol. 49, No.12 December 2002.

[31] Jing Wang, James E. Butler, D.S.Y. Hsu and Clark T.-C. Nguyen “CVD
Polycrystalline diamond high-Q micromechanical resonators” IEEE International
Conference Micro Electro Mechanical Systems, 2002. pp. 657-660

[32] J. Wang, J. E. Butler, D.S.Y. Hsu, and C. T. —C. Nguyen, “High-Q
Micromechanical resonators in CH4-reactant optimized high acoustic velocity CVD
polydiamond” Tech. Digest, 2002 Solid-State Sensor, Actuator and Microsystems
Workshop, Hilton Head Island, South Carolina, June 2-6, 2002, pp. 61-62.

[33] N. Sepulveda, D.M. Aslam, J .P. Sullivan, “Polycrystalline diamond RF MEMS
resonators with the highest quality factors” to be presented at IEEE MEMS’O6.

[34] L. Sekarik, J .M. Parpia, H.G. Craighead, T. Feygelson, B.H. Houston, J .E. Butler, J.
Appl. Phys. 81, 23 pp.4455 (2002).

[35] Mustafa U. Demirci, Mohamed A. Abdehnoneum and Clark T.-C. Nguyen
“Mecanically comer-coupled square microresonator array for reduced series motional
resistance”, IEEE Transducers, Solid-State Sensors, Actuators and Microsystems, 12th
International Conference, vol.2 June9-12, 2003

[36] F. Bannon 111, Clark, John R., Clark T.-C. Nguyen “High Q HF Micromechanical
Filters”., IEEE J SSC, pp.512-526, April 2000

[37] Navid, K; Clark J .R.; Demirci, M; Nguyen, C.T.-C. “Third-order intermodulation
distortion in capacitively-driven CC-beam micromechanical resonators” IEEE
International Conference on Micro Electro Mechanical Systems, 2001. pp.228-231

[38] Cohn M Flannery, Michael D Whitfield and Richard B Jackrnan “Acoustic wave
properties of CVD diamond” Institute of Physics Publishing. Semicond. Sci. Technol. 18
(2003) $86-$95

[39] K. Iakoubovskii, Optical Study of Defects in Diamond, PhD thesis, Katholieke
Universiteit Leuven, 2000.

122

[40]Y. Tang and D. M. Aslam “Technology of polycrystalline diamond thin films for
microsystems applications” J. Vac. Sci. Technol. B 23(3), May/Jun 2005

[41] S. Matsumoto, Y. Sato, M. Kamo, and N. Setaka, Jpn. J. Appl. Phys, Part 1 21, 183
(1982)

[42] R. C. Hyer, M. Green, K. K. Mishra, and S. C. Sharma, J. Mater. Sci. Lett. 10, 515
(1991)

[43] A. Lettington and J. W. Steeds, Thin Film Diamond _Chapman and Hall, London,
(1994)

[44] J. Stiegler, Y. vonKaenel, M. Cans, and E. Blank, J. Mater. Res. 11, 716 (1996).

[45] LA. Chernozatonskii, Z. Ya. Kosakovskaya, Yu. V. Gulyaev, N.I. Sinitsyn, G.V.
Torgashov, and Yu. F. F. Zakharchenko, “Influence of external factors on electron field
emission from thin-filrn nanofilament carbon structures” J. Vac Sci Technol. B 14(3), p.
2080, 1996.

[46] T. Xie, W.A. Mackie and RR. Davis, “Field emission from ZrC films on SSi and
Mo single emitters and emitter arrays”, J. Vac Sci. Technol. B 14(3), p.2090, 1996.

[47] J .S. Ma, H. Kawarda, T. Yonehara, J .I. Suzuki, J. Wei, Y. Yokota and A Hiraki
“Selective Nucelation and Growth of Diamond Particles by Plasma-assisted Chemical
Vapor Deposition” App. Phys. Lett., vol. 55 no.11, pp.1071-1073, 1989.

[48] MP. Everson and MA. Tamor :Studies of Nucleation and Growth Morphology of
Boron-doped Diamond Microcrystals by Scanning Tunnelling Microscopy” J. Vac. Sci.
Technol. B, vol.9 no.3 pp. 1570-1575, 1991.

[49]S. Ijima, Y. Aikawa, and K. Baba, “Early Formation of Cernical Vapor Deposition
Diamond Films” Appl. Phys. Lett., vol.57, no.25, pp. 2646-2648, 1990.

[50] K. Hirabayashi, Y. Taniguchi, O. Takamatsu, T. Ikeda, K. lkoma and N. Iwasaki-
Kurihara. “Selective Deposition of Diamond Crystals by Chemcial Vapor Deposition
Using a Tungsten-filament Method” Appl. Phys. Lett., vol. 53 no.19 pp. 1815-1871,

1 988.

[51] B.W. Sheldon, R. Csencstis, J. Rankin, and RE. Boekenhauer, “Bias-enhanced
Nucleation of Diamond During Microwave-assisted Chemical Vapor Deposition” J.
Appl. Phys, vol. 75, no.10, pp.5001-5008, 1994.

[52]B.R. Stoner, G.H. Ma, S.D. Wolter, and J .T. Glass, “Characterization of Bias-

enhanced Nucleation of Diamond on Silicon by in vacuo Surface Analysis and
Transmission Electron Microscopy” Phys Rev. B. vol.45, pp.11067-11084, 1992.

123

[53]X. Jiang, C.P. Klages, R. Zachai, M. Hartweg and HI. Fusser, “Epitaial Diamond
Thin Films on (001) Silicon Substrates” Appl. Phys Lett., vol. 62, pp.3438-3440, (1993).

[54] A. Massod, M. Aslam, M.A. Tamor and T.J. Potter, “Techniques for Patterning
CVD Diamodn Films on Non-diamond substrates,” J. Electrochem. Soc., vol 138.
no.11pp. L67-L68, 1991.

[55] RV. Spitsyn, G. Popovic and M.A. Prelas, “Problems of Diamond Film Doping” 2nd
Int Conf. on the Application of Diamond F ihns and Related Materials, Ed. M.
Yoshikawa, M.Murakawa, Y.Tzeng and W.A. Yarbrough, MY, Tokyo., pp. 57-64, 1993.

[56] Gennady SH. Gildneblat, Stephen A. Grot, and Andrzej Badzian, “The electrical
properties and Device Applications of Homoepitaxial and Polycrystalline Diamond
Films” in Proc. Of the IEEE, vol. 79, pp647-667, 1991.

[57] T. Takada, T. Fukunaga, K. Hayashi, and Y. Yokota, Sens. Actuators, A 82, 97
(2000)

[58] J. Cifre, J. Puigdollers, M. C. Polo, and J. Esteve, Diamond Relat. Mater.
3, 628 (1994).

[59] J .F. Prins, Thin Solid Films 212, 11 (1992)
[60] J .F. Prins, Diamond Related Materials. 11, 612 (2002)

[61] F. Zhang, B. Xie, B. Yang, Y. Cai and G. Chen, “Synthesis and Infrared Absorption
Characteristics of Boron-Doped Serniconducting Diamond Thin Films”. Materials
Letters, vol. 19, pp.115-118, 1994

[62] X. J iang, M. Paul, P. Willich, E. Bottger and C.-P. Klages, “Controlled Boron
Doping in Chemical Vapor Deposited Diamond Films”, Diamond 96, Tours, France,
Sept. 8-13, poster 11.051, 1996

[63] E. Colineau, et.al. “Minimization of Defects Concentration fiom Boron
Incorporation in Polycrystalline Diamond Fihns”, Diamond 96, Tours, France, Sept. 8-
13, poster 11.0512, 1996.

[64] X.Z. Liao, et al. “The influence of Boron Doping on the Structure and
Characteristics of Diamond Thin Films,” Diamond 96, Tours, France, Sept. 8-13, poster
8.060, 1996

[65] K. Miyata, K. Kumagai, K. Nishimura and K.Kobashi, “Morphology of heavily B-
Doped Diamond Films,” J. Mat. Res., vol.8, pp. 2845-2857, 1997.

124

[66] T. Roppel, R. Ramesham and S.Y. Lee, “Thin Film Diamond Microstructures” Thin
Solid Films, vol. 212, pp.56-62, 1992.

[67] J .L. Davidson, C. Ellis and R. Rarnesham, “Selective Deposition of Diamond
Films,” New Diamond, vol.6, pp.29-32, 1990.
[68] O. Dorsch, M. Werner, and E. Oberrneier, Diamond Relat. Mater. 4, 456 (1995).

[69] M. Bernard, A. Deneuville, T. Lagarde, and E. Treboux, Diamond Relat. Mater. 11,
828 (2002).

[70] C. Vivensang, L. F erlazzoManin, M. F. Ravet, and G. Turban, Diamond Relat.
Mater. 5, 840 (1996).

[71] R. Otterbach and U. Hilleringrnann, Diamond Relat. Mater. 11, 841(2002).
[72] H. Shiomi, Jpn. J. Appl. Phys., Part 1 36, 7745 (1997).

[73] F. Silva, R. S. Sussrnann, F. Benedic, and A. Gicquel, Diamond Relat.
Mater. 12, 369 (2003).

[74] W. Kern and D. A. Puotinen, RCA Rev. 31, 187 (1970).

[75] R. R. Thomas, F. B. Kaufman, J. T. Kirleis, and R. A. Belsky, J. Electrochem.
Soc. 143, 643 (1996).

[76] N. Sepulveda-Alancastro and D. M. Aslam, “Polycrystalline diamond technology for
RF MEMS Resonators” Microelectron. Eng. 73-74, 435 (2004).

[77] H. Windischmann, Glenn F. Epps, Yue Cong and R. W. Collins, “Intrinsic stress in
diamond fihns prepared my microwave plasma CVD” J. Appl. Phys. 69 (4) Feb. 1991,
pp. 2231-2237.

[78]P T Docker, P K Kinnell and M C L Ward, “Development of the one-step DRIE dry
process for unconstrained fabrication of released MEMS devices” J. Micromech.
Microeng. 14 pp. 941—944 (2004)

[79] L M Phinney , G Lin, J Welhnan and A Garcia, “Surface roughness measurements
of micromachined polycrystalline silicon films” J. of Micromechanics and
Microengineering 14, 927-93, 2004

[80] John R. Clark, Wan-Thai Hsu, and Clark T.-C. Nguyen, “High-Q VHF

Micromechanical Contour-Mode Disk Resonator” IEEE Int. Electron Devices Meeting ,
Dec 11-13, 2000 pp. 493-496.

125

[81] N. Sepulveda, D.M. Aslam, J .P. Sullivan, “Polycrystalline Diamond MEMS
Resonator Technology for Sensor Applications” Diamond and Related Materials,
Currently in press.

[82]Kirt R. Williams, Kishan Gupta, Mathew Wasilik, “Etch rates for micromachining
process-Part 11” IEEE J. Micro Electrom. Sys. Vol.12 no.6 Dec 2003.

[83] Ville Kaajakari, Tomi Mattila, Antti Lipsanen, and Aame Oja, “Nonlinear
Mechanical Effects in Silicon Longitudinal Mode Beam Resonators”, Sensors and
Actuators A: Physical vol. 120(1), pp.64-70, 2005

[84] E. S. Zouboulis, M. Grimsditch, A. K. Ramdas and S. Rodriguez, “Temperature
dependence of the elastic moduli of diamond: A Brillouin-scattering study” Physical
Review B, vol. 57, pp. 2889-2896, 1998.

[85] F. Szuecs, M. Werner, R. S. Sussrnann, C. S. J. Pickles and H. J. Fecht, “
Temperature dependence of Young’s modulus and degradation of chemical vapor
deposited diamond” Jouranl of Applied Physics vo. 86, pp.6010-6017, 1999

[86] J. O. Orwa, K. W. Nugent, D. N. Jarnieson, and S. Prawer, “Raman investigation of
damage caused by deep ion implantation in diamond”, Physical Review B, vol. 62,
pp.5461-5472, 2000.

[87] Liwei Lin, "MEMS Post-Packaging by Localized Heating and
Bonding", IEEE TRANSACTIONS ON ADVANCED PACKAGING, VOL. 23, NO. 4,
PP. 608-616, NOVEMBER 2000

[88] X. Liu, D.M. Photiadis, J .A. Bucaro, J .F. Vignola, B.H. Houston, H.-D. Wu, D.B.
Chrisey, “Low temperature internal friction of diamond-like carbon films” Material
Science and Engineering A, 5 July 2002.

[89] BE. White, Jr., R.O. Pohl, Materials Research Symposium Proc. 356 (1995) 567.
[90] Victor J. Milenkovic, “Rotational polygon contaimnent and minimum enclosure

using only robust 2D constructions” Computational Geometry, Theory and Aplications
(13)pp.3-19 1999

[91] H. Freeman and R. Shapira, “Determining the Minimum-Area Encasing Rectangle
and Arbitrary Closed Curve”, Communications of the ACM, vol. 18 pp.409-413, 1975

[92] H. J. McSkimin and P. Andreatch Jr, “Elastic Moduli of Diamond as a Function of

Pressure and Temperature” Journal of Applied Physics, vol. 43, pp. 2944-2948, July
1972.

126

[93] W. T. Hsu; C.T.-C. Nguyen, “Stiffiress-compensated temperature-insensitive
micromechanical resonators” IEEE Int. Conference on MEMS, pp.73l — 734, Jan 20-24
2002

[94] . T. Hsu; J .R Clark,.; C.T.-C Nguyen,.; “Mechanically temperature-compensated
flexural-mode micromechanical resonators” Electron Devices Meeting, International pp.
399 - 402, Dec 10-13 2000

[95] J. Yang, T. Ono, and M. Esashi, “Mechanical behavior of ultrathin micro-
cantilever,” Sens. Actuators, vol. 82, pp. 102—107, 2000

[96] DA. Czaplewski, J.P. Sullivan, T.A. Friedmann and JR. Wendt, “Mechanical

dissipation at elevated temperatures in tetrahedral amorphous carbon oscillators”
Diamond and Related Materials, Currently in press.

127