Acknowledgements
This venturous project - which originated by quitting a permanent position and thereby
sacrifice the associated benefits - in trade for a few new - has finally come to its end. And it
seems to be a happy ending.
First of all I would like to thank Ola Sveen, professor Aasmund Sudbø and professor
Terje Finstad for having confidence in me and giving me the opportunity to start with this
project after several years away from university. Most of all thank you to my main supervisor
Ola Sveen, who has always had his door wide open when I’ve come with my more or less
peculiar questions. He has helped me with numerous problems related to the measurement
setup, performed many hours with soldering work, and also been a good friend with an
impressive knowledge about minor and major things in the world. Thank you also to my cosupervisor Aasmund Sudbø for important comments on the papers, and thanks also to Terje
Finstad, who has not been my supervisor but nevertheless been open for discussions about a
wide range of physics matter. Principal Scientist Arthur van Rheenen at FFI deserves a special
thanks for introducing me into the field of noise in semiconductors and moreover performing
important measurements.
During this project I’ve been dependent on help from numerous people. The
acknowledgements following each of the papers are extensive and shows the real nature of a
MEMS project; it is impossible to do it all by yourself. Even if the acknowledgements are
extensive, there are still some people who have not received any thanks; all the people at the
Mechanical workshop at the Department of Physics deserve credit for their service and
helpfulness. Also people at the Electronic workshop have been indispensable. And I would, no
doubt, have had infinite troubles without the help form the library. A great many books and
papers have been found in the post shelf only short time after my enquiries.
i
I’ve had a great time at the University of Oslo. Not at least due to the presence of some
of my colleagues; Erik Marstein who - when I first arrived - worked as a self-appointed
mentor. Sean Erik Foss, Ulrike Grossner and Joachim Grillenberger, who have encouraged me
and strengthened my faith in completing this race and also shown true interest in my family.
Thank you to my parents for the inheritance of the “never-giving-up” gene, to stand
and to always incite a more or less hyperactive child and to sponsor my life when needed.
Most of all I will be everlasting indebted to my lovely family for their patience with
me. Thank you Martin, Mari and Gjermund for being so understanding when I had to
withdraw from the family and you, for some periods, had to live more or less without your
mum. And for your cheering “You’ll make it!” Tusen takk Martin, Mari og Gjermund for at
dere har vært så forståelsesfulle når jeg har måttet ”melde meg ut” og dere har vært nødt til å
klare dere uten meg. Og tusen takk for de stadig oppmuntrende heiaropene ”du skal klare det,
Mamma!” Not at least thank you to my dear husband Ståle for supporting me, even if your
workload at home has been considerable increased. Moreover, thank you for always keeping
my skis ready for use and allowing me the necessary timeouts for cross-country skiing even
during the busiest periods!
I also owe thanks to my future leader Anders Hanneborg at SINTEF, who trusted me
and credited me with a position long before I completed this work. The certainty of this happy
ending has given me the necessary peace of mind for the final work.
ii
Contents
Acknowledgements..................................................................................................................i
Contents ............................................................................................................................... iii
Preface...................................................................................................................................1
1 Introduction .......................................................................................................................3
1.1 The aim of the work ...............................................................................................................4
1.2 The structure of this thesis .....................................................................................................5
2 Medical motivation for development of a MEMS-based pressure measurement system ....9
2.1 A new era for pressure measurements in medical treatment................................................9
2.2 What is hydrocephalus? .......................................................................................................11
3 The physics of the polycrystalline silicon (polysilicon) piezoresistive pressure sensor .....15
3.1 The piezoresistive pressure sensor .......................................................................................15
3.2 Semiconductor materials and doping ..................................................................................16
3.3 Silicon ...................................................................................................................................17
3.3.1 Monocrystalline silicon................................................................................................................. 18
3.3.2 Polycrystalline silicon................................................................................................................... 19
3.4 Electrical properties of polysilicon.......................................................................................21
3.4.1 Segregation of impurity atoms ...................................................................................................... 21
3.4.2 The carrier trapping model ............................................................................................................ 21
3.5 Temperature dependence of resistivity................................................................................25
3.6 Piezoresistivity ......................................................................................................................27
3.7 Piezoresistive pressure sensors.............................................................................................30
3.7.1 Placement of piezoresistors........................................................................................................... 30
3.7.2 Temperature compensation ........................................................................................................... 31
4 MEMS as an interdisciplinary field .................................................................................33
4.1 Work allocation ....................................................................................................................33
iii
4.2 And then there were none.................................................................................................... 35
4.3 Assembly .............................................................................................................................. 36
4.4 Metrology ............................................................................................................................. 38
4.4.1 Pneumatics ................................................................................................................................... 39
4.4.2 “Subsea” technology..................................................................................................................... 39
4.5 Noise issues........................................................................................................................... 41
4.5.1 Investigation of the measurement setup......................................................................................... 42
4.5.2 Inherent sensor noise .................................................................................................................... 43
5 Paper I..............................................................................................................................51
6 Paper II ............................................................................................................................59
7 Paper III...........................................................................................................................83
8 Paper IV.........................................................................................................................101
9 Concluding remarks.......................................................................................................121
Appendix A.........................................................................................................................123
Bibliography.......................................................................................................................127
iv
Preface
This thesis is submitted in partial fulfillment of the requirements for the degree of Doctor
Scientiarum at the University of Oslo (UiO), Norway.
The work has been performed at the Electronics group, Department of Physics, at the
Faculty of Mathematics and Natural Sciences. The experimental work has mainly been carried
out in the new accommodations at the Norwegian Micro and Nano Laboratories hosted by
SINTEF and UiO. Noise analysis has been performed at the Norwegian Defence Research
Establishment.
The described work has been part of the Strategic University Research Program for
Micro Opto Electro Mechanical Systems (MOEMS) and Micro Electro Mechanical Systems
(MEMS) funded by the Norwegian Research Council. Fabrication of medical sensors for
implantation, based on MEMS, has been one of three research objectives.
The idea presented in this thesis was conceived by people from SINTEF,
Rikshospitalet University Hospital and UiO [1]. Two master students at the UiO had made
detailed plans for the general measurement system [2, 3], and a post doc fellow had designed
the sensor before the work being described in this thesis commenced.
1
1 Introduction
The cellular phone is small enough. Some will also say that the computers are small enough,
fast enough and powerful enough. Still the silicon technology is developing. Towards what? Is
there anything to be done that has not been done so far? One natural answer to this may be
that things can always be done better. Another answer may be found when looking for new
fields of applications. This is to a large extent what has happened to the growth of MEMS
technology, a technology that is more or less an outgrowth from the integrated circuit (IC)
industry.
So what is MEMS? MEMS is an acronym for Micro Electro Mechanical System, a
system not only involving electronic components but also involving mechanical action, of a
solid, a liquid, or a gas. MEMS technology is attractive for biochemical analysis, pressure
measurements and acceleration measurements, to mention only a few fields of application.
Silicon is an attractive material for making electronic components and is extensively
used in the microelectronics industry. Silicon is also very attractive for MEMS, both due to
the advantages of integrating the electronic circuitry and the mechanical sensor structure, and
also because silicon is an elastic and very robust material.
MEMS components can amongst others be found in ink-jet print heads, projector
displays, car air bags and DNA amplification systems. Future applications may be most
attractive where MEMS can enable a new mission due to reduced size or added functionality.
The medical field is maybe the area with the largest amount of unresolved tasks that can
utilize the MEMS technology. The MEMS application focused in this thesis is an outstanding
example in this respect.
MEMS technology started back in 1960s, when researchers worked to use the
integrated circuits technology to also form integrated sensors. Today the MEMS technology
is not longer only a promising technology; it has found its use in wide areas ranging from
3
automotive safety, mass data storage systems, and military applications, to systems for health
monitoring and control.
Working with MEMS usually starts with an idea. How to apply the technology? Or
how to find a solution to an existing problem? Or maybe the best; a starting point which is
both technology-driven (i.e. searching for new applications) and market-driven (i.e. searching
for new solutions). The next phase is to design the general application. For a measurement
system sensor design is one of the key issues. Knowing the desired application and given the
constraints from the end users, designers try to incorporate the different requirements into the
sensor design. Since the idea presented in this thesis was already conceived, and the sensor
designed, what was then left to be explored? Was the real work already done, with only some
characterization, calibration and packaging issues left? A question asked by Stephen. D.
Senturia [4] in his textbook about microsystem design may illustrate that this is not the case: If
the package, test, and calibration are so important and so expensive, why aren’t they a more
prominent part of the MEMS conferences and publications? He also gives an answer: It is not
because there are not significant intellectual and engineering challenges. Quite the contrary.
The author states that his experience is that packaging, test, and calibration are intrinsically
industrial and commercial fields and that it is difficult for university researchers to engage the
real intellectual core of these subjects because they depend on having access to large
quantities of manufactured devices and to specialized physical facilities. And furthermore;
And since successful execution of packaging, test, and calibration can determine the
commercial success or failure of an entire product line, detailed information critical to these
operations is typically kept extremely private by manufacturers.
In this landscape I have tried to maneuver during the past three years. It has been an
interesting, but hard journey as a quite lonely representative from a university.
1.1 The aim of the work
The aim of the work presented in this thesis has been to:
4
•
establish a measurement setup for characterization of micromachined pressure sensors
•
characterize an already fabricated pressure sensor prototype
•
evaluate the reliability of the sensor
•
propose and evaluate packaging solutions
•
perform in-vivo testing as “proof of concept”
The sensor design has not been a part of the thesis and a detailed explanation and justification
of the design are therefore not given.
1.2 The structure of this thesis
Four papers that constitute chapter five through eight of my thesis are included:
I. Clausen, I. Godovitsyn and O. Sveen,
MEMS-based permanently implanted Brain Pressure Measurement System. Proceedings of
the International Microelectronics And Packaging Society, 5th Topical Workshop on MEMS,
Related Microsystems & Nanopackaging.
This paper gives an overview of the application, the requirements for the
measurement system, and details about the sensor design. Results from
functionality tests of the sensors are also presented.
The first author performed the characterization and did all the writing.
The second author designed the sensor and performed the functionality
test.
I. Clausen, H. Karlsson, K.M. Johansen and O. Sveen
Characterization and evaluation of the reliability of a piezoresistive sensor for permanent
measurement of human brain pressure. Submitted to Sensors and Actuators A.
This paper gives a detailed description of the measurement setup and presents
results from characterization of sensor sensitivity, accuracy and stability. An
uncertainty analysis based on the Guide to Uncertainty in Measurements
(GUM) is used to evaluate if the medical needs introduced by the neurosurgical
end users are achieved.
The first author made the measurement setup, performed the
experimental work and did all the writing. The second author performed
5
the uncertainty analysis. The third author made the LabVIEW
programming for automatic measurements.
I. Clausen and O. Sveen
Die separation and packaging of a surface micromachined piezoresistive pressure sensor.
Submitted to Sensors and Actuators A.
The work described in this paper originated from preparatory works related to
in-vivo testing for “Proof of concept”. The several processing steps required to
obtain a useful single sensor assembly starting from the entire silicon wafer
with thousands of surface micromachined sensors, are described. Problems due
to the very small size of the sensor are discussed and proposals for
improvement in the sensor design are given. The pig intended for the in-vivo
testing is still alive, as the preparatory work is not yet fulfilled.
The first author did all the work.
I. Clausen, O. Sveen and A. Sudbø
Protective coating for a piezoresistive pressure sensor intended for permanent implantation
into the human brain. Submitted to Sensors and Actuators A.
This paper presents the requirements for a protective coating for the pressure
sensor. Potential shortcomings for the sensor design are identified. Arguments
for a suitable protective coating are put forward and the influence from the
coating on sensor sensitivity, offset, linearity and temperature dependence is
examined. Results after immersion in a fluid similar to the human blood plasma
are also presented.
The first author did all the work.
The acknowledgements following each paper are quite extensive and illustrate in an excellent
way the nature of a MEMS project; it is a highly multidisciplinary field which calls for
communication and cooperation with specialists within quite distinct areas. This is highlighted
in the forth chapter of the thesis:
6
MEMS as an interdisciplinary field
The need for combining knowledge from a number of disciplines to solve
multiple challenges is addressed. Useful experiences acquired during the work
are described, experiences that are lying beyond the scope of the included
papers but give a good illustration of the complexity related to practical
realization of MEMS projects. One section is dedicated to noise issues.
Arthur van Rheenen performed the measurements and did most of the writing
in section 4.5.2 Inherent sensor noise.
To put the described work in a larger context, the second chapter is dedicated to the medical
aspects:
Medical motivation for the development of a MEMS-based pressure measurement system
The advantages with use of MEMS in medicine are discussed and examples of
interesting applications are shown. A brief introduction to the diagnosis
hydrocephalus is given with special focus on the need for noninvasive pressure
measurement.
The basis of the described MEMS is solid state physics and electronic devices. The third
chapter is therefore dedicated to some theory about semiconductor physics:
The physics of the polycrystalline silicon (polysilicon) piezoresistive pressure sensor
This chapter goes into the basic principles of operation for a piezoresistive
pressure sensor. Polycrystalline silicon is the main sensing material in the
developed sensor. Piezoresistivity in polysilicon is described in particular, as it
is somewhat different from piezoresistivity in monocrystalline silicon.
And finally, some concluding remarks are given in the last chapter:
Concluding remarks and future prospects
A brief history of the abundant number of pressure units are given in Appendix A.
7
The work has been presented at the following conferences:
O. Sveen, T. Lundar, M. Berg, J. Due-Hansen, I. Godovitsyn, I. Clausen,
“MEMS-based Hydrocephalic Intracranial Pressure Measurement”. Final Program and Book
of Abstract, the 14th Annual Scientific Meeting of the Society for Medical Innovation and
Technology, Oslo, Norway, September 5-7, 2002, pp. 70.
I. Godovitsyn, I. Clausen, O. Sveen, T. Lange, A. A. Khan,
“Silicon Surface-Micromachined Pressure Sensors: features and applications, MEMS-based,
wireless measurement of brain pressure”, Poster at Micro Tech café; Oslo, Norway, April 3,
2003
I. Clausen, I. Godovitsyn, O. Sveen,
”MEMS-based permanently implanted Brain Pressure Measurement System”, Final Program
& Abstract Book, the International Microelectronics And Packaging Society, 5th Topical
Workshop on MEMS, Related Microsystems & Nanopackaging; Boston, MA, US, November
20-22, 2003
I. Clausen, O. Sveen, I. Godovitsyn,
“Permanently Implanted Piezoresistive Sensor for Brain Pressure Measurements” 15th
MicroMechanics Europe Workshop, Leuven, Belgium, September 5-7, 2004, pp. 25-28. Best
poster award
I. Clausen, O. Sveen, I. Godovitsyn,
”MEMS-based permanently implanted Brain Pressure Measurement System” Proceedings of
Society for Experimental Mechanics, 5th International Symposium on MEMS and
Nanotechnology, Costa Mesa, CA, US, June 7-10, 2004, Invited speaker
8
2 Medical motivation for development of a
MEMS-based pressure measurement system
2.1 A new era for pressure measurements in medical
treatment
Medical diagnostics is a rapidly developing application field for micromachined sensors.
MEMS obviously have their benefits when size is a crucial parameter. Low weight and low
power consumption are other obvious advantages for MEMS. Surface micromachining
technology1 is particular convenient for small and planar structures. Use of miniaturized,
implantable sensors in medical practice opens new avenues for patient diagnostics and
significantly improves health-care services.
With present IC technology, as used for instance in a Pentium processor, it is possible
to make conductor paths as small as 60 nm, approximately one hundredth of a human red
blood cell (Figure 1). Taking our pressure sensor as an example, the dimensions of the
conductor paths are about 3 µm (Figure 2), i.e. 50 times larger than the technological limit.
Even if existing technology opens up for even smaller sensors, there is a physical limit for
downscaling since the MEMS normally aims at detecting a physical quantity. Again taking
our pressure sensor as an example, where small changes in brain pressure are to be detected,
the pressure sensitive element needs to have a minimum size to react to applied pressure.
1
Surface micromachining technology make use of the wafer substrate and depose thin films on top, in contrary
to bulk micromachining technology which modifies the structure of the whole wafer by changing the properties
in some areas and etching away others
9
Figure 1. Human red blood cells with typical dimensions 7 µm.
Figure 2. Scanning electron microscopy of piezoresistor and conductor paths.
Research is in progress for several medical applications. A medicine pump inserted under the
skin can control medicine flow for cancer patients who need pain relief, and for patients with
diseases as cerebral palsy and diabetes [5, 6]. Permanently implantable blood pressure sensor
for monitoring of hypertension is another future application (Figure 3) [7, 8]. Implantable
intraocular pressure sensor for detection of glaucoma is another interesting field (Figure 4), [9,
10]. Work is going on to improve pacemakers [11].
Figure 3. Implantable transponder capsule containing blood pressure sensor [7].
10
Figure 4. Outline of a sensor system for monitoring of eye pressure [10].
Monitoring of pressures is in general highly important in medical practice. Blood pressure,
eye pressure, pressure inside the bladder and pressure within big joints are only some of the
pressures being routinely measured. Of special interest in this thesis is brain pressure, as this
is crucial for people with the diagnosis hydrocephalus as well as many other conditions inside
the skull.
2.2 What is hydrocephalus?
The brain pressure measurement system presented in this thesis is meant for people who have
undergone an operation for the condition hydrocephalus. A brief introduction to what
hydrocephalus is and how it is treated is given below. More detailed information about
hydrocephalus can be found in [12, 13].
The human brain produces about 500 ml brain fluid per day. Most brain fluid is
produced by the choroid plexus, a network of blood vessels covered by a tissue membrane.
Choroid plexus is found in water-filled cavities within the brain, called ventricles. The brain is
floating in the fluid, which therefore protects the brain from crushing under its own weight
and from blows. It also nourishes, cleans and acts as a volume buffer. Ordinarily, the brain
fluid is produced and drained at a constant rate so that its volume of 150 ml is replaced every
8 hours. However, if something obstructs the circulation between the production and drainage
sites, an abnormal accumulation of brain fluid may occur (Figure 5). This is the condition
called hydrocephalus, or more familiar water on the brain. In newborns, the resulting
11
increased brain pressure causes the head to enlarge since the skull bones are not yet fully
developed. Macrohead could in earlier days often be seen as a symptom of untreated
hydrocephalus. In adults, hydrocephalus is more likely to result in brain damage.
Hydrocephalus occurs in one out of 500 births [14] and may furthermore be acquired later in
life due to tumor, hemorrhage, meningitis etc. Hydrocephalus is treated by surgical insertion
of a ventricle shunt that drains off the excess fluid. A valve opens when the pressure exceeds a
preset limit, and the fluid is guided into for instance the abdomen or to other areas of the body
where it can be absorbed by the circulation system.
Figure 5. Ventricles before and after shunt surgery. The dark areas shown to the left are brain fluid and a
spectacular enlargement of the ventricles can be seen. To the right the ventricles are reduced to normal
size [12].
Hydrocephalus is a condition and not a disease. This is important because it means that the
individuals, after first having a surgery, can live a quite normal life. This has to be taken into
account when designing the measurement system, as described in chapter 5. After successful
shunt operation, however, maintenance problems may often occur. A survey at the
Rikshospitalet University Hospital, disclosed that maintenance problems are mainly related to
occlusion of the ventricle catheter as shown in Table 1 [15]. Increased brain pressure will
again be the result and repeated surgery will be necessary.
12
Table 1. Shunt system failures. From a survey at Rikshospitalet University Hospital in Oslo, Norway.
Complication
Incidence
Percent
Blockage of the tubes
119
35
Disconnected tube
48
14
Short abdomen catheter
45
13
Wrong placing
35
10
Over drain
22
6
Infection
20
6
Other
53
15
Total
342
100
Increased brain pressure will often manifest itself through commonplace symptoms as
headache and nausea, vomiting and stumbling when walking. These symptoms are too vague
for a repeated surgery. The neurosurgeon has to drill a hole in the skull and insert a pressure
sensor between the brain and the skull bone to evaluate if repeated surgery is necessary. On
average one person per day is hospitalized for brain pressure measurement at Rikshospitalet
University Hospital [16]. Both patients and medical staff would benefit on a permanently
installed pressure monitoring system. That is what our measurement system can offer.
It is possible to measure pressure in existing shunt systems, but only in the valve
outside the skull (inside the skin). These measurements may be misleading when the occlusion
of the shunt is deep within the brain. Existing systems for measuring brain pressure within the
skull are not meant for permanent installation [17]. Research on implantable pressure sensors
for measurement of brain pressure is in progress at other places than the University of Oslo
[18-21]. A new programmable shunt system with integrated pressure sensor is reported to be
under development, but the details are not known [22].
13
3 The physics of the polycrystalline silicon
(polysilicon) piezoresistive pressure sensor
The main outlines of the sensor are given in the included papers. The most important features
are also given below as a starting point for the discussion.
The material used for the sensing elements is polycrystalline silicon (polysilicon) and
not the more commonly used monocrystalline silicon. Basic properties of semiconductor
materials in general, included monocrystalline silicon will be addressed in the following, but
only to such an extent that the properties of the pressure sensor can be understood and the
special properties of polysilicon can be identified.
Semiconductor materials and monocrystalline silicon is thoroughly described in
textbooks and detailed information about structure and properties can be found there [4, 2325]. Some essential questions related to polysilicon will however be looked at; what is
polycrystalline silicon, how are the electrical (and mechanical) properties and how are the
piezoresistive properties. Methods for the fabrication of polysilicon material will not be
discussed.
3.1 The piezoresistive pressure sensor
The sensing structures of the sensor consist of a circular polycrystalline silicon diaphragm
with polysilicon piezoresistors on top of a sealed vacuum cavity (Figure 6). The diaphragm
deforms under applied pressure, the piezoresistors on top of the diaphragm sense the
deformation and the resulting changes in resistivity are measured as a voltage signal.
15
Figure 6. Scanning electron microscope (SEM) picture of the pressure sensor consisting of a circular
polycrystalline silicon diaphragm. Two active polycrystalline silicon piezoresistors (R1 and R3), are placed
on top of a sealed vacuum cavity. Two passive piezoresistors (R2 and R4) are placed on the substrate to
minimize the effect of temperature changes, but are not shown on the SEM picture. An outline of the
circuit configuration is drawn at the upper left corner. The diaphragm can be seen to be defective, with a
small crack on the right-hand side.
3.2 Semiconductor materials and doping
Semiconductors are a group of materials having electrical conductivity between insulators and
metals. Silicon (Si) is used for the majority of rectifiers, transistors and integrated circuits, and
is also used for the majority of wafers for manufacturing of MEMS. Other widely used
semiconductors are germanium (Ge) for transistors and diodes and compound semiconductors
as gallium arsenide (GaAs) and zinc sulfide (ZnS) for light-emitting diodes, to mention only a
few compounds and a few applications. The conductivity of the semiconductor materials can
be considerably affected by changes in temperature, optical excitation and by doping with
impurities.
Doping of a semiconductor is not very different from doping of athletes; you start with
an object with quite ordinary qualities, you manipulate the properties by adding some foreign
matter (dopants) and you get a material with greatly improved characteristics! The type and
amount of foreign matter or dopant are important for the end result for both semiconductors
and athletes. One major difference exists however; for semiconductors the manipulation is
both desirable and legal while this is not the case for the athletes.
16
The number of charge carriers contributing to the conductivity in a semiconductor
depends on the number of added dopants but also on the band gap; i.e. the amount of energy
needed to move carriers from the valence band to the conduction band where they can
contribute to the electric current.
Not so surprising, therefore, the resistivity of a material depends on the internal atoms’
positions and their motion. Mechanical strain changes these arrangements and hence the
resistivity. This phenomenon called piezoresistivity is of special interest for this thesis.
3.3 Silicon
Silicon provides both electrical and mechanical advantages. Electrical advantages are of
course related to the possibilities for precise modulation of the conductivity, but also to the
ease of forming an excellent oxide (SiO2). This oxide is amongst other widely used as an
insulator in active devices. Mechanically, silicon is an elastic and robust material and is
therefore highly attractive for MEMS structures.
Silicon exists in any of three forms
•
monocrystalline silicon
•
poly crystalline silicon, also called polysilicon or poly-Si
•
amorphous
The extent of regular structure varies from amorphous silicon, where the atoms do not even
have their nearest neighbors in definite positions, to monocrystalline silicon with atoms
organized in a perfect periodic structure (Figure 7).
17
Figure 7. Transmission electron microscope (TEM) picture of a Metal-Oxide Semiconductor Field-Effect
Transistor (MOSET) gate consisting of a 2 nm thick amorphous silicon oxide layer between crystalline
silicon (top) and polycrystalline silicon (bottom). Image by Reed electronics group/FEI Company.
Monocrystalline silicon is commonly used in silicon wafers for both integrated circuits and
MEMS. MEMS can be manufactured in two ways.
Bulk micromachining technology takes advantage of the different properties of the
different crystallographic planes. The structure of the wafer is modified by implanting
impurities or growing thin layers in some areas and removing substantial wafer volumes in
other places by etching.
In surface micromachining technology the two-dimensional IC technology is
converted to a tree-dimensional MEMS technology in order to form thin and planar structures.
Active structures are developed by depositing thin films on top of the monocrystalline silicon
wafer surface, and by removing one or more sacrificial layers through lateral etching.
Polysilicon is often used as thin film. Polysilicon has long been used as the conducting gate
material in metal-oxide-semiconductor (MOS) transistors (Figure 7), the most dominating
device in the IC industry. The material properties of polysilicon are therefore well known.
3.3.1 Monocrystalline silicon
Monocrystalline silicon has a diamond lattice crystal structure, i.e. the atoms are arranged in a
periodic structure where every atom is surrounded by four nearest neighbors. Every atom is
attached by covalent bonds to four neighbor atoms localized in the corners of a tetrahedron.
The smallest repeating unit of the lattice is cubic and silicon is therefore said to be a cubic
18
material. The three major coordinate axes as illustrated in Figure 8 are called the “principal
axes” and three crystallographic planes are related to these axes by the Miller indices [23].
The significant electrical and mechanical properties of silicon originate from this periodic
structure.
Figure 8. Illustration of the three principal axes and three lattice planes with their Miller indices in a
simple cubic lattice.
3.3.2 Polycrystalline silicon
In polycrystalline silicon, there is no such crystal orientation as in monocrystalline silicon.
That is; the polycrystalline structure is made up of small grains or crystallites (Figure 9), each
containing a large number of periodically arranged atoms with saturated bonds like in
monocrystalline silicon. In the boundaries that separate the grains the atoms do not have any
periodical arrangement, and the atoms have a lot of incomplete or dangling bonds that affect
the electrical properties (Figure 10). There is a close relationship between the mechanical and
electrical properties of a polysilicon film and the structure. The structure describes the size
of the crystallites and their preferred crystallographic orientation or texture. Polysilicon layers
are in general not isotropic, i.e. there is a preferential orientation for the crystallites [26].
19
Figure 9. Transmission electron microscope (TEM) picture (top/down) showing grain structure in a borondoped polycrystalline film (image by Accurel Inc.).
Figure 10. Outline of monocrystalline silicon with perfect periodical structure to the left and polysilicon
consisting of grains with periodical structure inside the grains but disordered grain boundaries with
incomplete bonds in between to the right.
The technological solution for manufacturing determines the structure and thereby the
electrical and mechanical properties. The mechanical properties are for the most part similar
to those of monocrystalline silicon, although differences exist concerning surface roughness
and fracture strength. Diffusion properties are also somewhat different. Some of these
properties are briefly discussed in chapter 4, 7 and 8. The electrical properties of polysilicon
differ substantially from those of monocrystalline silicon. A nice overview of the electrical
properties of polysilicon can be found in [27, 28]. The discussion below is for p-doped silicon,
i.e. where atoms having one less outer electron than silicon (such as boron) are added. The
charge carriers are then positively charged holes.
20
3.4 Electrical properties of polysilicon
The typical size of the grains is 100 – 200 nm. The size is mainly set by the deposition
temperature2. The thickness of the grain boundaries are of the order 1 to 3 nm [30]. The
electrical properties that distinguish polysilicon from monocrystalline silicon originate from
the grain boundaries. Two different mechanisms are known to affect the electrical properties;
a) segregation of impurity atoms and b) trapping of electrical carriers. It has been showed that
carrier trapping is the most dominant effect [31].
3.4.1 Segregation of impurity atoms
The unsaturated “dangling” bonds of the silicon atoms at the grain boundaries can be saturated
by atoms that segregate at the grain boundary [32]. Segregation of dopant atoms reduces the
amount of doping atoms inside the grains and thereby decreases the active carrier
concentration. Segregation of an atomic species at the grain boundary is determined by the
atom size, by the size of the grain and by the heat of sublimation [32]. Arsenic and phosphorus
are known to segregate at the grain boundaries, while boron is not. This is one reason why pdoping of polysilicon and not n-doping is most often used. Impurity atoms such as hydrogen,
oxygen and fluorine are also known to segregate at the grain boundaries [33, 34].
3.4.2 The carrier trapping model
The following is based on the carrier trapping model of Seto et al. [35] and the modified
model by Lu et al. [36]. A set of assumptions are made in this model; the polysilicon is
composed of identical crystallites all having a grain size L, the thickness δ of the grain
boundaries are negligible compared to L, there is only one type of impurity atoms present and
they are all ionized and uniformly distributed. The grain boundary contains a number of
Qt/cm2 traps (a surface charge density).
The unsaturated bonds in the grain boundaries can act like traps for charges and
thereby reduce the number of free carriers [35]. The number of traps is of the order of
1012 cm-2 [30, 35]. After trapping a carrier, the trap becomes electrically charged and a
2
Polysilicon films are mainly produced by a LPCVD production process [29]
21
depletion region of width W with no free carriers is formed on each side of the grain
boundary. The resulting potential barrier affects the motion of carriers from one grain to
another (Figure 11). The carriers can cross the potential barrier by tunneling or by thermionic
emission.
Figure 11. Schematic drawing of polysilicon grains separated by grain boundaries of width δ (not to scale).
Holes are trapped in the grain boundaries and a depletion region of width W is created (top). The carriers
have to cross the resulting potential barrier Vb to pass from one grain to another (bottom).
The potential barrier depends on the doping concentration (a volume charge density). If the
doping concentration is smaller than Qt/L all the carriers will be trapped and the grain will be
totally depleted. If the doping concentration is greater than Qt/L free carriers will, after all the
traps are filled, form an undepleted region in the middle of the grain. The two cases give two
different expressions for the potential barrier.
For doping concentrations smaller than Qt/L, a positive charge has to pass a potential barrier
given by
qNL2
Vb =
8ε
22
(1)
where q is the elementary charge, N is the doping concentration, ε is the permittivity and L is
the grain size.
For doping concentrations greater than Qt/L, the potential barrier can be calculated from
qQt2
Vb =
8εN
(2)
As the doping concentration is increased, the potential barrier at first increases linearly with N
(from (1)) and reaches a maximum at LN = Qt before it decreases as 1/N (from (2)). The
dependence of the potential carrier on the doping concentration is illustrated in Figure 12.
Figure 12. Variation of the grain-boundary potential barrier with doping concentration. For doping
concentrations smaller than Qt/L, the potential barrier is given by eq. (1) and for doping concentrations
larger than Qt/L it is given by eq. (2).
If all the traps are filled, a larger grain size gives a smaller potential barrier for similar doping
concentration, as can be seen from Figure 12.
A polysilicon resistor can be regarded as grain and grain-boundary resistors connected
in series [36].
ρ = ρ g (1 −
2W
2W
) + ρ gb
L
L
(3)
23
where ρ gb represents the grain-boundary resistivity and ρ g represents the grain resistivity
corresponding to the resistivity of monocrystalline silicon
ρg =
1
qµ p p 0
(4)
( µ p is the mobility of holes and p 0 is the equilibrium concentration of holes within the
undepleted grain regions).
A complete expression for the polysilicon resistivity are found in [28].
2πm *p kT
qV
1
2W
ρ=
(1 −
)+
exp( b )
2
gqµ p p0
L
kT
fLq p 0
(5)
with m *p as the effective mass for holes, k as Boltzmann's constant, T as the absolute
temperature and g and f are scaling or correction factors. A similar expression is found in [27]
but where g is omitted and f is interpreted as a physical factor related to tunneling and
scattering of carriers.
The doping concentration affects the resistivity through p 0 , the ration W/L and the
potential barrier Vb . For smaller doping concentrations (< 3·1018 cm-3) the exponential term
related to the grain-boundary resistivity is dominating, for larger doping concentrations
(> 2·1019 cm-3) the exponential term decreases and the term related to the grain resistivity
becomes the dominating one [27].
As can be seen from the above equation for the resistivity, a wide range of resistivities
can be obtained for polysilicon compared to monocrystalline silicon. This is illustrated in
Figure 13. This variety in resistivity makes polysilicon very attractive as resistor material in
the IC industry.
24
Figure 13. Resistivity of boron-doped LPCVD polysilicon as a function of the dopant concentration [28].
3.5 Temperature dependence of resistivity
The temperature coefficient of resistivity (TCR), normally represented by α (T ) , is used to
express the variation of resistivity with temperature
ρ = ρ 0 [1 + α (T − T0 )]
(6)
where ρ 0 is the resistivity at the reference temperature T0 .
The resistivity depends on the mobility through the relationship (4).
Two types of mechanisms influence the hole mobility; impurity scattering and phonon
scattering. Impurity scattering is most pronounced for lower temperatures, where slowly
moving carriers are influenced by Coulomb forces from the charged ions. At higher
temperatures, thermal agitation of the lattice becomes greater and phonon scattering, or lattice
scattering, becomes the most dominant mechanism, although the effect of impurity scattering
is evident for increased doping concentration also at higher temperatures (Figure 14). For
25
monocrystalline silicon the TCR is therefore typically positive for relevant doping
concentrations and for relevant temperature regions.
Figure 14. The carrier mobility decreases for increasing temperatures due to lattice scattering (to the left).
For higher temperatures increased impurity concentration also affects the mobility (to the right) [24].
For polysilicon the grain boundaries make a negative contribution to the TCR. As the
temperature increases, more carriers will be exited across the potential barriers around the
grain boundaries and so the resistivity will decrease.
This is why the TCR is known to be lower for polysilicon than for monocrystalline
silicon (0.04 % per °C compared to 0.14 % per °C) for doping levels approaching 10 20 cm-3 ,
and why it is even possible to change the sign of the TCR [25].
One expression for α (T ) for polysilicon can be found in [28] :
α (T ) =
1  ρ gb (T )  1 qVb  2W 
 2W
 −

 + α g ρ g (T )1 −

ρ 0  T  2 kT  L 
L




(7)
where ρ gb is as before the grain-boundary resistivity, ρ g is the resistivity of the grains and
α g is the temperature coefficient of the grains.
From the above equation and Figure 15 it is obvious that the TCR depends on the grain
size (through W/L) and on the carrier concentration (through Vb and the several resistivity
26
values). Negative TCR is particularly useful in compensating the temperature dependence of
the piezoresistivity which is always positive, as will be focused in the next section.
Figure 15. Temperature coefficient of the resistivity of boron-doped polysilicon around room temperature
[28].
3.6 Piezoresistivity
Piezo comes from the Greek word piezein which means to apply pressure. Piezoresistivity is a
phenomenon where the resistivity changes with the deformation ε of a material caused by an
applied force. The fractional change in resistivity can be related to the deformation or strain
through
dρ
ρ
= Gε
(8)
where G is known as the gauge factor.
27
Piezoresistivity originate from two different effects:
a) Changes in geometrical form of a resistor
b) Changes in the position of the energy bands
For metals, a) is the dominating effect. The resistance of a thin long rod is higher than for a
short, wide one made of the same material. If a thick short rod is strained so that it becomes
thinner and longer, the resistivity will consequently increase. The gauge factor of metals is
about 2.
For semiconductor materials, b) is the dominating effect. When mechanical stress is
applied the crystalline lattice is strained and conductivity is enhanced in some directions and
reduced in others because the number of carriers and their mobility changes. In polysilicon
(and amorphous silicon) all the crystal orientations are represented, and by intuition one might
think that the resulting piezoresistivity is small. It is certainly smaller than in monocrystalline
silicon, but it is still considerably larger than in metals. The gauge factor of monocrystalline
silicon varies from -100 to + 150 [37]. For polysilicon it is about five times smaller, with a
gauge factor typically between 20 and 40. Values up to 70 % of the gauge factor for
monocrystalline silicon have however been reported [38].
The axis of a resistor is defined according to the direction of the current flow through
the resistor. The longitudinal and transverse stress is defined with respect to the resistor axis
and not related to any specific crystal axes. The fractional change in resistivity is related to
(the applied) stress through
∆ρ
= π l σ l + π tσ t
ρ
(9)
where π l and π t are defined as the longitudinal and transverse piezoresistive coefficients and
σl and σt are the longitudinal and transverse stress.
For monocrystalline silicon the piezocoefficients are highly dependent on the crystal
orientation of the material, and for some dopants and some crystal directions the values of
longitudinal and transverse gauge factors are roughly equal in size but with opposite sign. This
can be utilized in monocrystalline pressure sensors.
28
For polysilicon, the piezoresistive coefficients loose sensitivity to crystalline direction
and average over all orientations. In spite of this, polysilicon still exhibits a strong
piezoresistivity. Several theoretical models for piezoresistivity in polysilicon exist, with
different approaches concerning grain size, texture, contributions from the grain and grain
boundaries etc. A discussion of the different models can be found in [28]. Mosser et al. also
describes a detailed procedure for averaging the piezocoefficients based on an approach where
the grain size is much smaller than the thickness of the polysilicon layer, but this is considered
to be well beyond the scope of this thesis. The main idea is, however, to find the angle
between the direction of the current flow and the principal axis for each grain and to calculate
the contribution to the gauge factor by summarizing over all grains. The conclusions of the
work are that the gauge factors are always larger for textured than isotropic material and that
the longitudinal gauge factor is always larger than the transverse one. A maximum ratio of
four between the two gauge factors was found for some specific orientations.
The piezoresistance effect depends on the dopant type (n or p) and concentration. The
piezoresistance decreases with increasing doping concentrations. Increasing temperature also
gives a lower piezoresistance effect (Figure 16). For higher doping concentrations
(> 1019 cm −3 ) the piezoresistance effect is low, but it is no longer dependent on temperature
variations.
Figure 16. Piezoresistance factor as a function of impurity concentration and temperature for p-type
monocrystalline silicon [24].
29
3.7 Piezoresistive pressure sensors
3.7.1 Placement of piezoresistors
For deflection-based pressure sensors the resistivity changes are commonly measured by a
Wheatstone bridge, as for the sensor investigated in this thesis. A Wheatstone bridge consists
of four resistors in a circuit, as shown in Figure 6. A voltage is applied across the circuit, the
bridge. A “bridge” consists of two arms, each arm with two resistors in series. An advantage
of this configuration is that the output voltage can be directly related to the resistivity changes.
The output voltage is almost independent of the absolute values of the piezoresistors, but
depends on the relative resistance change (and on the applied voltage).
One of the most common designs of a piezoresistive pressure sensor is to place four ptype monocrystalline piezoresistors on a diaphragm as in Figure 17. For this specific
configuration and type of dopants, the resistance increases with tensile stress applied in the
longitudinal direction while it decreases for the resistors oriented in the transverse direction.
This is not due to an elongation of the parallel resistor and increase in width of the transverse
one, as one might think by intuition, but it is due to a shift in the energy bands resulting in
redistribution of the carriers. The behavior is different for n-type piezoresistors and thereby
clearly indicates other reasons to the modified resistivity than geometrical changes. For a
configuration like the monocrystalline silicon sensor in Figure 17, the values of longitudinal
and transverse gauge factors are roughly equal in size and with opposite signs. Both the
longitudinal and transverse resistors can therefore contribute to the bridge sensitivity.
Figure 17. Schematic drawing of a deflection based pressure sensor with four p-type monocrystalline
piezoresistors on a diaphragm. (The piezoresistors are oriented in the <100> direction on a type {100}
wafer, see e.g. [4] for explanation.)
30
For polysilicon piezoresistors an averaging over all orientations occur as mentioned in the
previous section, but the longitudinal gauge factor is still found to reach 60 to 70 % of that of
monocrystalline silicon for optimal material parameters [38]. The longitudinal gauge factor is
always higher than the transverse one, and the longitudinal gauge factor therefore has to be
applied to achieve the best sensor sensitivity. For a Wheatstone bridge with four variable
polysilicon piezoresistors, compression is needed in two resistors together with tension in the
other two for maximum sensitivity. When the diaphragm deflects downwards under applied
pressure, maximum tension arises at the edge of the diaphragm while maximum compression
arises at the center of the diaphragm.
Only two active piezoresistors placed at the edge of the diaphragm are used in the
Wheatstone bridge for the sensor investigated in this thesis. The main reason for not placing
two additional piezoresistors at the center of the diaphragm was the challenges related to
electrical interconnection [39].
3.7.2 Temperature compensation
Self-heating of the piezoresistors will occur as the excitation current passes through the
resistors. Pressure sensors are preferred to be insensitive to temperature variations. The
temperature dependence of the piezoresistive coefficients has a great influence on the
sensitivity of the sensor. Different approaches for achieving high temperature stability for
silicon piezoresistive pressure sensors exist.
a) Figure 16 showed that temperature had low influence on the piezoresistive effect for
higher doping concentrations. One method to ensure low temperature sensitivity is
therefore to make piezoresistors with higher dopant concentrations. The disadvantage
is a lower sensitivity to pressure.
b) Another method is to use two of the piezoresistors in the Wheatstone bridge for
pressure sensing and two for temperature compensation, by for instance placing two of
the resistors at the substrate. The strain has little effect on the two resistors placed at
the substrate, but any changes in temperature will affect the two resistors at the
diaphragm and the two at the substrate in the same way. The temperature influence on
the output voltage is therefore minimized. This method is used for the sensor discussed
31
in this thesis. The disadvantage of this method is that only two piezoresistors are
sensitive to changes in strain.
c) The use of constant current instead of constant voltage excitation of the bridge is
another method. At constant bridge current, the bridge voltage increases with
temperature as a result of the positive TCR (from Ohm’s law). A higher bridge voltage
results in higher output signal from the bridge and compensates for the loss of
sensitivity due to the lower piezoresistance coefficient. At constant voltage this
“automatic” feedback does not occur. It may be difficult to design a constant current
source. A constant current source can also yield a lower output voltage and a reduced
signal-to-noise ratio [37]. For the discussed project, a constant voltage source has been
chosen.
32
4 MEMS as an interdisciplinary field
MEMS is to a great extent about downscaling; downscaling of size, weight, power
consumption etc. But challenges are indeed not downscaled! The downscaling causes a lot of
challenges itself. Furthermore the complex nature of a MEMS project, touching into very
different fields, represents many potential tribulations. The many aspects regarding MEMS
can be excellently demonstrated by the project discussed in this thesis; it simply covers it
“all”; small dimensions, strict demands to detectable quantities and the reliability of the
sensor, and very severe packaging challenges due to corrosive environment and long expected
lifetime. It touches into a broad spectrum of scientific and engineering areas as semiconductor
physics, thin film behavior, structural mechanics, chemistry, metrology, data analysis and
statistics, dicing, bonding and packaging. Medical aspects are also important. When working
with a project like this, knowledge is needed of at least some of the fields. But it is also
necessary to realize that you can’t be an expert in all of them. Cooperation with the true
experts within each field is required. It is however not possible to cope with the many
challenges only through experts. Success will also depend on people having a good overview
and being able to communicate with the experts.
This is exactly what chapter four is about. It shows a variety of fields not addressed in
the papers, or discusses fields in more detail than in the papers. Much knowledge can be
gained even from dead-ends, and some of them (but only some!) are being described.
4.1 Work allocation
As mentioned in the introductory chapter, the task for this thesis was characterization,
calibration, testing and packaging of already fabricated sensors. Sensor characterization in
laboratory was the obvious primary task. To be able to perform this work, a measurement
33
setup first had to be established. Further preparatory work can be classified as dicing and
assembly. Dicing should be self-explanatory; it is simply to divide the wafer with sensors
organized in fixed rows and columns, into smaller modules or chips containing only one or a
few sensors. The term assembly can have different meanings, but in this thesis it is used for
the process of mounting and attaching the sensor chip to a package, and furthermore to ensure
electrical interconnection between the chip and the package.
The above mentioned tasks were supposed to be preliminary work. Today, when the
concluding remarks are being written, it is clear that roughly two years have been spent on
strongly underestimated challenges related to these preliminary preparations. A rough
summary of the workload associated with the different fields and activities are given in Figure
18.
Figure 18. A rough estimate of the work load associated with the different activities.
As can be seen from above, dicing, assembly and metrology have occupied most of the
available time.
34
4.2 And then there were none
Six silicon wafers, each containing 31185 sensors, were the minimum amount that could be
ordered from the fabricating foundry in Singapore3. The work related to this thesis
commenced with these 6 wafers. Altogether 187110 sensors should be more than enough for
characterization, calibration, testing and packaging! It would be neither possible nor
interesting to characterize or assemble them all.
The Agatha Christie story And then there were none, became however highly relevant.
The Agatha Christie story is about 10 people gathered at an island. One by one disappears
under mysterious circumstances. This story is about 6 silicon wafers and one by one
disappears under partly mysterious circumstances (see chapter 7). Although the progression
was not as dramatic as in the Agatha Christie story, it was anyhow distressing. The foundry
tried to dice two of the wafers, but as they had experience only from dicing CMOS structures
and not delicate sensors with freestanding structures, the dicing was unsuccessful with lots of
broken diaphragms. The third wafer was diced by laser, but difficulties with handling single
sensors looking like “dust granules” made also this wafer a waste. The next attempt was to
involve people experienced with dicing hard silicon carbide wafers. This wafer was really
smashed up. Only two wafers were left and both wafers and time were running out. The
penultimate wafer was divided in four and luckily there were many intact sensors at a distance
from the cutting lines. One quarter was successfully diced in larger modules suitable for
testing in laboratory, by use of diamond saw and a protection tape. For in-vivo testing in
animals the larger modules were too big. The troublesome dicing process commenced once
more, but with the recently acquired experience, single sensors with unbroken diaphragms
were obtained from the last remaining wafer. Similar stories can be told about the flexible
printed card, about bonded sensors, about bumped sensors, about coated sensors and so on.
The knowledge to gain from this story is to start with a very high amount of samples to avoid
the conclusion And then there were none.
3
Institute of Microelectronics, Singapore
35
4.3 Assembly
Two different bonding techniques, both well established techniques in the IC industry, have
been applied in this project. Wire bonding has been used to electrically interconnect the sensor
chip to the ceramic package used for characterization in the laboratory (Figure 19). Flip-chip
bonding has been used to electrically interconnect a single sensor to a (flexible) printed circuit
board intended for in-vivo tests. The first method is only to some extent discussed in chapter 6
and more aspects will be addressed here. The latter method is discussed in detail in chapter 7
and will not be further discussed.
Figure 19. Wire-bonding of a sensor chip to a ceramic capsule for testing in the laboratory.
The methods for attaching wires, mostly gold or aluminum wires, from bond pads on the chip
to bond sites on the package or other interconnection substrates, can be divided in two.
Wedge bonding (Figure 20) utilizes ultrasonic energy and pressure to melt and press
one end of an aluminum wire to the bond pads on the chip and the other end to the terminals at
the package. A wide variety of wedges, the tool used for pressing the wire onto the sensor and
package, exist. The wedges vary with respect to material and geometry. The metallization
layer on both sensor contact pads and package terminals are decisive for selection of the
wedge to be used, and so is the geometry of the package or any other interconnecting
substrate. (For a package with a base cavity a sharper wedge is needed than for a flat base, as
only one example). The composition, thickness and elongation of the wire are dependent on
both sensor and package/substrate. Adjustment of ultrasonic energy and pressure are of course
also crucial for the result.
36
Figure 20. SEM picture showing wedge-bonding of aluminum wires.
Ball bonding (Figure 21) utilizes a combination of heat, pressure and ultrasonic energy
to bond one ball shaped end of a gold wire to the bond pads at the chip, and a stitch bond to
the terminals at the package. Adjustment of heat in addition to ultrasonic energy and pressure
are crucial for the result.
Figure 21. SEM picture of gold-bonding showing the ball bond at the sensor chip and the stitch bond at
the ceramic capsule.
After a few attempts of wedge-bonding it was soon realized that help from bonding
experts was unavoidable. This decision was further accelerated as the bonding machine at the
Physics Department was not made for left-handed people!
The preferred bonding technique naturally depends on the accessible bonding machine,
but also on the pitch between bond pads and whether heating is advisable or not. Both
techniques were used to bond sensors for characterization. For this purpose both methods
37
seemed to be suitable, although the stitch bond appeared to be larger than the bonding pads, as
can be seen from Figure 20.
4.4 Metrology
A detailed description of the measurement setup is given in chapter 6. A schematic outline of
the measurement setup (Figure 22) and some main features are also given her as a basis for the
matters pointed out below.
Figure 22. Illustration of the measurement setup used for pressure sensor characterization.
Sensors under test are placed inside a pressure chamber of stainless steel. The top of the
chamber is made of an acrylic glass called Perspex. The chamber is designed to withstand an
inner pressure between rough vacuum and 3 bars. Desired pressure is achieved by letting
nitrogen gas into the chamber and by monitoring the gas pressure by means of a combined
precision pressure controller and calibrator. Exact temperature conditions are ensured by
placing the chamber in an open bath circulator and by recording the temperature in the
38
proximity of the sensor by a PT100 temperature probe situated inside the pressure chamber.
The pressure chamber is immersed in water to a depth corresponding to 15 times the diameter
of the PT100 probe to ensure stable measurement conditions, in accordance with a
recommendation from experienced metrologists. Six sensors can be under test simultaneously.
Altogether 24 electrical conductors - 12 for bias voltage and 12 for registration - are connected
to a socket inside the chamber. Outside the chamber, each pair of wires is shielded separately.
The wire package is fed into the pressure chamber through a connector with 26 poles. Battery
is chosen as power source for the sensors and a low noise multimeter records output signals. A
software data acquisition system is developed for automatic instrument control as well as data
sampling.
4.4.1 Pneumatics
When establishing a measurement setup for characterization of pressure sensors, some insight
in pneumatics as tubes, fittings, press threads (links/rights, inner/outer) etc. is necessary. The
sensors had to be characterized over the operation range (500 – 1500 mbara corresponding to
± 0.5 atmosphere), but the behavior after overloading should also be examined. Overload tests
means a measurement setup able to withstand pressures up to 3 bar. For metrology reasons, as
well as security reasons, the connections need to be properly tightened. For a period the Dr.
Scient education in physics looked more like the education as a plumber!
4.4.2 “Subsea” technology
Much effort has been put into what can be denoted as subsea technology in connection with
submersion of the pressure chamber under water. Some might think that a complete
submersion was overkill, but the thoughts behind were quite clear;
•
observed output sensor signals were in the mV-range
•
observed signal-to-noise ratio was approximately 300
•
a resolution of 1 mbar, corresponding to 5 µV/V, was wanted by the neurosurgical end
users (ref. chapter 6)
Several conditions can influence the sensor signal. Ageing and temperature variations are
some. The effect of a protective coating is another. To be able to detect these changes, every
39
influence parameter from the test environments should be minimized. Temperature gradients
between the water in the circulator (35 - 42 °C), and the ambient temperature (20 °C), was one
such parameter that could be reduced by submersion of the pressure chamber. The decision
about submersion did however cause many challenges and resulted in knowledge in a variety
of fields. One experience gained was that metallic balloons are much stronger than ordinary
balloons and that white balloons are much more elastic than red ones (Figure 23). This was
realized when balloons were used as a water seal for the moisture resistant, but not watertight
connector. White, non-metallic balloons appeared to be most appropriate! The different
chemicals in the different balloon dyes obviously have an effect on the elastic properties of
balloons. (That dyeing chemicals do affect material properties is known from e.g. mechanical
testing of textiles.) Another observation that could be made was that balloons get completely
rotten after a couple of weeks soaking in water! The final and successful solution for keeping
water away from the electrical connector was heat-shrinkable tubing as used in off-shore
drilling.
Figure 23. Assortment of balloons used for keeping water away from the connector. The three metallic
balloons to the left were strong but non-flexible. The non-metallics were more elastic, the white one was
best suitable for the purpose. However, the white balloon got completely rotten after being immersed in
water for two weeks.
The several failures under water caused the cable/connector solderings to rotten, and repeated
soldering appeared to be a necessary but time consuming and error-prone activity.
Consequently repeated mounting of the connector into the pressure chamber perspex top was
40
also required. A thread sealant named Loctite® was used to seal the notches around the
screws. An undesired experience was then encountered; a chemical reaction between the
alcohol in Loctite® and the acrylic in perspex occurred and caused the perspex to crack. The
result can be seen in Figure 24.
Figure 24. Cracked perspex top due to chemical reaction between acrylic in the perspex and alcohol in the
thread sealant Loctite®.
4.5 Noise issues
Noise performance of the sensor is of particular interest due to the strong requirements for
measurement uncertainty as discussed in Chapter 6. Only signal voltages that are larger than
the noise voltage are reliable.
Instabilities in the sensor signal around 30-50 µV was observed for 10 repeated
measurements of a sensor at 1000 mbar absolute pressure and supplied with 3V bridge supply
voltage. Although not very sophisticated measurements, they showed that noise was present
either in the measurement setup, the sensor itself, or both. Further investigations were then
carried out to find the causes of the observed signal instabilities. The preliminary experiments
can presumably be classified as Physics at the kitchen bench.
41
4.5.1 Investigation of the measurement setup
Possible influence parameters could be cellular phone, fluorescent lamp, computer, circulator
bath etc., but no improvement was observed in signal stability when switching these devices
on or off. Influence from mechanical vibrations was investigated by knocking the table,
putting a shock absorber underneath the pressure chamber and by shouting (!). No effect could
be observed. Electromagnetic shielding, with a Faraday cage of aluminum foil or grounding
the pressure chamber and signal lead shields, did neither make any significant difference.
The Keithley 2010 multimeter was then configured to minimize the measurement
uncertainty; the repeating filter was enabled, taking the average of a number of readings. The
signal variation seemed to be partly reduced, but was still around 30 µV. The integration time,
i.e. the period of time the input signal was measured, was set to maximum. The integration
time is specified as a number of power line cycles, PLC. If any disturbances at the power line
influenced the sensor signals, the noise should be reduced by increasing the PLC. No
pronounced reduction in signal noise was observed.
Outside the chamber, each pair of the twelve powering and signal wires was shielded
separately. Inside the chamber the wires did not have any shield. To evaluate if current in the
wires affected the measurements, the main voltage source was disconnected and only one
sensor was powered and recorded directly through the connector. Changes in signal stability
were not observed.
The sensor was then replaced by a 20 kΩ resistor. The noise variations for the very
first measurements were as high as 5-15 µV before the signal stabilized around 2 µV, with
instability around 0.6 µV. The higher signals shortly after assembly indicate temperature
effects due to the recent assembly. As any Wheatstone bridge was no longer present, the
remaining small µV signals probably resulted from contact potentials at the solder terminals.
Thereafter, measurements were performed on a pressure sensor from Presens AS with
well known characteristics4. A temperature effect after assembly as mentioned for the resistor
above was observed. The signal instability thereafter stabilized around 2 µV. Repeated
measurements showed a maximum instability of 1.31 µV for the Presens sensor and 51 µV for
our sensor. (The sensor from Presens AS was later used as an extra reference standard and
control of the measurement setup.)
4
F320 from Presens with sensitivity of 10 mV/V for a pressure load of 10 bar and noise in the range 10 - 30 nV.
42
Throughout the experiments a much higher signal variation was observed in the
morning, after the gas inlet and supply voltage had been turned off during the night. The first
measurement series often showed instability of 45 µV for the Presens sensor and 310 µV for
our sensor. Three hours later the signal was stabilized at the earlier reported level. This can be
explained by temperature equilibrium between the initial cold pressure medium (the nitrogen
gas) and the ambient temperature, and also by the stabilized voltage source.
The strongly reduced signal variations when no sensor was present, and the much
lower variations for the Presens sensor than for our sensor, was taken as an indication of the
sensor being responsible for the higher instability and not the measurement setup.
The above experiments lead to the following conclusions:
•
Stabilized measurement conditions are crucial for the measurement results.
Temperature equilibrium after assembly and for the pressure medium is important.
•
The power source has direct impact on the results. A stabilized power source and
measurement of the real bridge supply voltage is important.
•
The greatest part of the remaining instability is most likely due to the sensor itself and
not due to the measurement setup.
•
Experts must be involved for further investigations of the noise behavior.
The latter was done and the results are presented in the next section.
4.5.2 Inherent sensor noise
Random noise in semiconductors is caused by several sources. Two of them exhibit a
frequency-independent spectrum: thermal noise and shot noise. Thermal noise is caused by the
random thermal motion (Brownian motion) of charge carriers. The source of shot noise is the
random excitation of charge carriers over a potential barrier. The first is typically observed in
resistors, and also in field-effect transistor (FET) channels. Shot noise is typically observed in
p-n junctions and Schottky junctions. A third source of noise is caused by the random capture
and successive emission of charge carriers by traps in the material. Traps may be associated
with local lattice imperfections (defects) or with impurities. The spectral signature of such a
43
generation-recombination noise contribution is 1/[1 + (f / f C)2]: constant at low frequencies
and falling off as f
-2
at high frequencies. The frequency fC is the typical frequency for capture
and release of a charge carrier by each specific trapping center. The fourth contribution to a
typical noise spectrum is called flicker noise or 1/f noise, named after its typical spectral
signature. The cause of 1/f noise is a still-debated issue in the literature. One possible
explanation is that this noise type is related to trapping noise. It is imagined that by
appropriately weighing generation-recombination noise contributions with a distribution of
trapping frequencies, a 1/f – shaped spectrum may be generated from several 1/[1 + (f / f C)2]like contributions. This model has been successful in explaining the 1/f noise in the channel of
MOSFETs [40].
Only signal voltages that are larger than the noise voltage are reliable. Measurements
of the spectral intensity of the voltage fluctuations (noise spectrum) provide a means to
quantify the noise voltage. The noise voltage is the square root of the integral of the noise
spectrum over the bandwidth (f2-f1) of the electronics:
VN =
f2
∫ S ( f ) df
V
[V]
(10)
f1
The spectral intensity of the thermal noise is:
SV ,th = 4kTR
[V2/Hz]
(11)
In this expression k is Boltzmann's constant, T the absolute temperature, and R the resistor
value. Typically, each bridge resistor has a value of 4.2 kΩ, resulting in SV,th ≈ 7 × 10-17
V2/Hz at room temperature. If it is further assumed that the electronics bandwidth (f2-f1) is
100 kHz, then VN = 2.6 µV. This contribution is independent of the applied bias over the
resistor and, as mentioned before, independent of frequency.
44
The spectral intensity of shot noise is:
S I , sh = 2qI
[A2/Hz]
(12)
Here, q is the unit of charge and I the bias current through the element. In crystalline,
homogeneous semiconductor resistors there are no potential barriers and the observation of
shot noise is not expected. In polycrystalline semiconductors the potential barriers at the grain
boundaries could give rise to shot noise. Quantifying how spatial distributions of potential
barriers contribute to the frequency-independent part of the noise spectrum is beyond the
scope of this thesis. However, it may be possible to distinguish between the two frequencyindependent noise sources based on their bias dependencies. Thermal noise in a resistor is
independent of bias, while shot noise is bias dependent.
To obtain the same units [V2/Hz] for shot noise as for thermal noise one may either
multiply the shot noise expression in (12) by the resistance squared, or divide the thermal
noise expression in (11) by the resistance squared.
A heuristic expression for 1/f noise is:
SV ,1/ f =
A
f
[V2/Hz]
(13)
In this expression A is a parameter that may be bias dependent. Mostly, in resistors, A scales
with the bias voltage squared ( A = βV2 ) or bias current squared. In diodes, the 1/f noise
intensity has a more complex bias dependence. The constant β is a measure for the noisiness
of the component.
A simple description of the observed noise spectrum may be:
SV ,total =
A
+ 4kTR
f
[V2/Hz]
(14)
45
where it is assumed that the observed spectrum consists of a 1/f-noise component and a
thermal noise contribution. Obviously, see (14), the 1/f noise will dominate at low frequencies
and the thermal noise will dominate at high frequencies. Plotted in a graph with double
logarithmic scales the spectrum may be thought off as consisting of two lines: one with a
slope of –1 (1/f noise) and one with a slope of 0 (thermal noise). For each operating condition
(bias) the parameter A may be determined from the measured noise spectrum. A plot of A as a
function of the bias will establish the bias dependence of the noise parameter A and possibly
establish the value of β, if that bias dependence is indeed quadratic.
Measurements of the noise were performed in a manner that is schematically depicted
in Figure 25. The bridge under test (R1 – R4) was biased with the help of a bias resistor
(82 kΩ) and a variable power supply based on a 12-V battery. A coupling capacitor coupled
the noise signal into the low-noise amplifier (LNA) and the noise spectrum was measured
with a spectrum analyzer (SA). The bias resistor is chosen to be much larger than the bridge
resistors that are 4.2 kΩ, typically. The applied total bias voltage could be varied between 0
and 12 V. Of this voltage 4.9% appears across the bridge, so that its voltage ranged between 0
and 580 mV. The LNA is necessary to amplify the otherwise small noise signal to measurable
levels for the spectrum analyzer. The spectrum analyzer is really a digital signal analyzer,
used in Fast Fourier Transform (FFT) mode.
Figure 25. Schematic outline of the noise measurement circuit. Resistors R1-R4 represents the Wheatstone
bridge. The bias voltage is a variable power supply. The low-noise amplifier (LNA) amplifies the small
noise signal to be measured by the spectrum analyzer (SA).
46
Measured spectra for different total applied bias (Vbias) voltages are presented in Figure 26.
As expected, the 1/f noise increases with applied bias and at zero bias the thermal noise level
(7 × 10-17 V2/Hz) is clearly observed. The small 1/f component (10 times weaker than for the
smallest applied non-zero bias) is probably due to the measurement setup.
Figure 26. Spectral intensity (calibrated) for the Wheatstone bridge configuration. The voltages specified
above are bias voltage for the total noise measurement circuit and not the bridge supply voltage.
Corresponding bridge supply voltages are between 0 and 540 mV.
By subtracting the thermal noise component from the measured spectra (Vbias = 1 – 11 V) the
1/f contributions are obtained. The parameter A is estimated by multiplying the “pure” 1/f
spectra by the frequency, essentially obtaining a frequency-independent set of data whose
average and standard deviation are easily calculated:
From (14): A =  SV ,total − 4kTR  × f
(15)
47
The extracted values for A and their standard deviations for the different bias voltages are
presented in Table 2.
Table 2. 1/f noise coefficient expressed by A and associated values for the standard deviation σA for
varying bias voltage. Corresponding bridge supply voltages are also listed.
Total
voltage Bridge voltage A
σA
(V)
(V)
(10-14 V2/Hz)
(10-14 V2/Hz)
0
0.000
0.78
0.57
1
0.049
5.4
11
2
0.097
8.7
10
3
0.146
14.6
14
4
0.195
23.6
18
5
0.244
29.3
32
6
0.292
36.2
18
7
0.341
49.5
23
8
0.390
64.6
26
9
0.439
89
52
11
0.536
156
54
The trend in Table 2 is clear: for increasing bias voltage the noise parameter A increases.
Especially at smaller biases the uncertainty in the extracted noise parameter is appreciable.
48
To further study the voltage dependence of the noise parameter A it is plotted as a function of
the square of the bridge voltage (second column in Table 2) in Figure 27.
Figure 27. Least square fit of 1/f noise coefficient A versus squared bridge voltage.
It was anticipated (see above) that A would have quadratic voltage dependence. A linear leastsquare fit to the experimental data yields:
A = (5.06 ± 0.19) × 10-12 V 2 + (4 ± 2) × 10-14
[V2]
In the least-squares fit the errors in the individual data points, as listed in Table 2, are not
considered. Judging from the error analysis the coefficient in front of the V2 term, called β
above, is relatively well determined. Somewhat surprisingly there is a voltage independent
term. This could be an artifact of the fit since the best fit was not forced to go through the
origin. On the other hand, possibly the measuring equipment produces some rudimentary 1/f
noise. The value of this contribution, 4 × 10-14, is only slightly larger than what is found for
the spectral value at 1 Hz for V = 0 V. Either way, for bridge voltages larger than 0.1 V the
bias independent contribution is much smaller than the bias dependent part.
49
In conclusion, the measured noise may be well described by the following expression:
SV ,total =
5.1× 10−12V 2
+ 7.0 × 10−17
f
[V2/Hz]
(16)
for bridge voltages V between 0 and 540 mV.
In the application, the bridge is operated at higher voltages, typically 3 V. If the assumption is
made that extrapolation is permitted, the total noise at that operating voltage is estimated to be
SV ,total ≈
45 × 10−12
+ 7.0 × 10−17
f
[V2/Hz]
(17)
Upon integrating this spectrum from 1 Hz out to 100 kHz and then taking the square root the
anticipated noise voltage is
VN = 45 × 10−12 ln (1× 105 ) + 7 × 10 −17 × 1× 105 = 23 µV
It is apparent that, under the assumption that extrapolation is legitimate, the 1/f noise
contributes much more to the noise voltage than the thermal noise.
During the measurements no bias dependence of the frequency-independent parts of the
spectra was observed suggesting that shot noise due to carriers passing grain boundaries was
smaller than the thermal noise. Even when shot noise was measurable, it would probably not
contribute to the overall noise voltage, which is completely dominated by the 1/f noise.
Models for low-frequency noise arising from the grain boundaries in polycrystalline silicon
can be found in literature, e.g. [41, 42], but further investigations of the noise sources are
beyond the scope of this thesis.
50
I
5 Paper I
I. Clausen, I. Godovitsyn and O. Sveen,
MEMS-based permanently implanted Brain Pressure Measurement System
Proceedings of the International Microelectronics and Packaging Society, 5th Topical
Workshop on MEMS, Related Microsystems & Nanopackaging
6 Paper II
II
I. Clausen, H. Karlsson, K.M. Johansen and O. Sveen
Characterization and evaluation of the reliability of a piezoresistive sensor for permanent
measurement of human brain pressure
Submitted to Sensors and Actuators A
.
7 Paper III
I. Clausen and O. Sveen
Die separation and packaging of a surface micromachined piezoresistive pressure sensor
Submitted to Sensors and Actuators A
III
8 Paper IV
I. Clausen, O. Sveen and A. Sudbø
Protective coating for a piezoresistive pressure sensor intended for permanent implantation
into the human brain
Submitted to Sensors and Actuators A
IV
9 Concluding remarks
The work presented in this thesis involves several specialized disciplines. In that respect the
thesis shows the true nature of a MEMS project. It has not been attempted to cover all aspects
of the project with equal analytical power.
A measurement setup for characterization of pressure sensors has been established.
The general setup can be used also for other MEMS based pressure measurement systems.
The solutions for dicing and assembly can be put to use for other MEMS structures as well.
There are many more things that could have been done and would have been done if time
allowed. With only limited time and man-years available, setting priorities for the work is
important. Different schools for testing and characterization exist and only one can be chosen.
One example is investigations of aging. Some people prefer accelerated test, others prefer
“burn in”. If accelerated tests should be entitled, they need to be properly designed for the
device under test, and the aging parameters must be temperature dependent. For this reason
the burn-in approach were chosen for the presented work. Similar arguments can be proposed
for the rest of the performed - or not performed - work.
Agree or disagree with the priorities, it is the hope that the established measurement
setup and the described work can be a platform for future effort related to the brain pressure
measurement project or other related work. Hopefully, this thesis gives a nice understanding
of MEMS. In any case I have learnt a lot during the work that has been carried out.
121
Appendix A
A brief history of the pressure units
Pressure is force per unit area. Historically a great variety of units have been used for
expressing pressure, depending on their suitability for the application. A table taken from
Bosch Kraftfahrtechnisches Taschenbuch [43] should illustrate the variety of pressure units
throughout the ages (Table 3). A more updated table for conversion of pressure units can be
found in Fraden's Handbook of Modern Sensors [37]. Originally mercury manometers were
used for measuring blood pressure, and mmHg is therefore the normal unit for expressing
blood pressure. Atmospheric pressure is usually expressed in mmHg for the same reason.
Another unit used for atmospheric pressure is simply atmosphere, corresponding to the
pressure from a column of water with height 10 meters, and having a temperature of +4°C, on
1 square centimeter.
123
Table 3. Conversion table for units of pressure taken from Bosch Kraftfahrtechnisches Taschenbuch, 1961
The derived SI unit Pascal was not defined before 1971 and is therefore not included in the
table above (1 Pa = 1 N/m² = 0.00750062 atm.). Even if Pascal is the scientific correct unit it
is rarely used in industry. In industry, specifications are often given in bar, as for the pressure
controllers acquired for the measurement setup. Bar is moreover normally used for sensor
specifications.
For a multidisciplinary project like the one discussed in this thesis, the related units are
not less confusing. As already mentioned, mmHg is often used in the medical world. Brain
pressure, however, is measured in mmH2O. One might think that this is due to the cause of
brain pressure – namely water (remember that hydrocephalus is often called “water on the
brain”). There are however historical, practical reasons even for this. Pressure exerted from a
column of water was from the beginning the preferred method, and was used for small
pressures like brain pressure. For higher pressures, like blood pressure, the height of the water
124
column would simply be too high, at least for indoor measurements. Mercury was then
applied instead, despite of harmful properties.
What would be the best to use for the project subject of this thesis? Being a physicist
communicating with doctors and metrologists, buying equipment from suppliers in industry,
characterizing sensors for measurement of brain pressure, and hoping to communicate results
to the scientific community within applied physics and medicine? A comfortable compromise
was to use mbar. The link to the scientific unit is ensured through the relationship 1 mbar =
100 Pa. Although deciding to use only one unit, this did not prevent the repeated toil related to
the different conversion factors.
125
Bibliography
1 O. Sveen, T. Lundar, A. Hanneborg, R. Bernstein, M. Berg and J. Due-Hansen, "Pressure
Measuring System, device and method," N. P. Office, Norway, 2003.
2 M. Berg, "Sensor og utlesningskrets for måling av intrakranielt trykk," in Department of
Physics, vol. Candidatus Scientiarum. Oslo: University of Oslo, 2002, pp. 192.
3 J. Due-Hansen, "Systemløsning for måling av intrakranielt trykk," in Department of Physics,
vol. Candidatus Scientiarum. Oslo: University of Oslo, 2002, pp. 129.
4 S. D. Senturia, Microsystem design, Kluwer Academic, Boston, 2001, p. 689.
5 http://www.sintef.no/content/page1____4279.aspx, "New micro instrument controls
medicine flows," 2005.
6 "http://www.mercola.com/2001/feb/14/diabetes_monitor.htm."
7 U. Schnakenberg, C. Kruger, J.-G. Pfeffer, W. Mokwa, G. vom Bogel, R. Gunther and T.
Schmitz-Rode, Intravascular pressure monitoring system, Sensors and Actuators A: Physical,
110 (2004) 61.
8 E. Cibula, D. Donlagic and C. Stropnik, Miniature fiber optic pressure sensor for medical
applications, First IEEE International Conference on Sensors, 2002, p. 711-714.
9 L. Rosengren, P. Rangsten, Y. Bäcklund, B. Hök, B. Svedbergh and G. Selen, A system for
passive implantable pressure sensors, Sensors and Actuators A, 43 (1994) 55-58.
10 U. Schnakenberg, P. Walter, G. Vom Bogel, C. Kruger, H. C. Ludtke Handjery, H. A.
Richter, W. Specht, P. Ruokonen and W. Mokwa, Initial investigations on systems for
measuring intraocular pressure, Sensors and actuators. A, Physical, A85 (2000) 287.
11 H. Joseph, B. Swafford and S. Terry, "MEMS in the Medical World," in Sensors Online
http://www.sensorsmag.com/articles/0497/medical/main.shtml, 1997.
12 C. Toporek and K. Robinson, Hydrocephalus, A Guide for Patients, Families, and Friends,
O'Reilly & Associates, Inc., Sebastopol, CA, 1st edn., 1999, p. 355.
13 R. M. Scott, "Hydrocephalus," in Concepts in neurosurgery, vol. 3, F. P. Wirth and R. A.
Ratcheson, Eds. Boston, MA: Williams & Wilkins, pp. 124.
14 University-of-Utah and Health-Sciences-Center, "High-risk newborn - Hydrocephalus,
http://www.uuhsc.utah.edu/healthinfo/pediatric/Hrnewborn/hcp.htm," 2005.
15 C. Tiller, S. Myrvold and T. Lundar, "Nevrokirurgisk shuntbehandling av barn med
hydrocephalus," in Tidsskrift for den Norske lægeforening, vol. 11, 2000, pp. 1298-1302.
127
16 T. Lundar, "Number of people being hospitalized for observation of hydrocephalus,"
Rikshospitalet, 2002, personal communication.
17 http://www.spiegelberg.de/home/index.html, "ICP Measurements," Spiegelberg, 2005.
18 H. J. Yoon, J. M. Jung, J. S. Jeong and S. S. Yang, Micro devices for a cerebrospinal fluid
(CSF) shunt system, Sensors and Actuators A: Physical, 110 (2004) 68.
19 C. Hierold, B. Clasbrummel, D. Behrend, T. Scheiter, M. Steger, K. Oppermann, H.
Kapels, E. Landgraf, D. Wenzel and D. Etzrodt, Low power integrated pressure sensor system
for medical applications, Sensors and Actuators A: Physical, 73 (1999) 58.
20 T. Eggers, C. Marschner, U. Marschner, B. Clasbrummel, R. Laur and J. Binder, Advanced
hybrid integrated low-power telemetric pressure monitoring system for biomedical
applications, IEEE Thirteenth Annual International Conference on Micro Electro Mechanical
Systems, 2000, p. 329.
21 FISO, "FOP-MIV Pressure Sensor," Technologies Fiber Optic Sensors Inc.,
http://www.globalspec.com/FeaturedProducts/Detail/FISOTechnologies/FOPMIV_Pressure_S
ensor/3215/1.
22 http://www.medicaldesign.com/articles/ID/12407, "Implantable sensor chip monitors
intracranial pressure," 2005.
23 N. W. Ashcroft and N. D. Mermin, Solid state physics, Saunders College, Philadelphia,
1976, p. 826.
24 B. G. Streetman and S. Banerjee, Solid state electronic devices, Prentice-Hall, Upper
Saddle River, N.J., 5th edn., 2000, p. 558.
25 N. Maluf, An introduction to microelectromechanical systems engineering, Artech House,
Boston, 2000, p. 265.
26 M. Hendriks, R. Delhez, T. H. de Keijser, S. Radelaar, F. H. P. M. Habraken, A. E. T.
Kuiper and P. R. Boudewijn, X-ray diffraction study and electrical characterization of boronimplanted low-pressure chemical vapor deposited polycrystalline silicon layers, Journal of
applied physics, 56 (1984) 2751.
27 M. Rydberg, "Electrical Properties of Polycrystalline Silicon," in Faculty of Science and
Technology. Uppsala: Uppsala University, 1999, pp. 49.
28 V. Mosser, J. Suski, J. Goss and E. Obermeier, Piezoresistive Pressure Sensors Based on
Polycrystalline Silicon, Sensors and Actuators A-Physical, 28 (1991) 113-132.
29 S. A. Campbell, The science and engineering of microelectronic fabrication, Oxford
University Press, New York, 2nd edn., 2001, p. 603.
128
30 N. C. C. Lu, L. Gerzberg, C. Y. Lu and J. D. Meindl, A conduction model for
semiconductor-grain-boundary-semiconductor barriers in polycrystalline-silicon films, IEEE
transactions on electron devices, ED-30 (1983) 137.
31 G. Baccarani, B. Ricco and G. Spadini, Transport properties of polycrystalline silicon
films, Journal of applied physics, 49 (1978) 5565.
32 M. M. Mandurah, K. C. Saraswat, C. R. Helms and T. I. Kamins, Dopant segregation in
polycrystalline silicon, Journal of applied physics, 51 (1980) 5755.
33 L. L. Kazmerski, Chemistry of hydrogen and arsenic interactions at silicon grain
boundaries, Journal of vacuum science & technology. A, An international journal devoted to
vacuum, surfaces, and films, 4 (1986) 1638.
34 D. S. Ginley, Modification of grain boundaries in polycrystalline silicon with fluorine and
oxygen, Applied physics letters, 39 (1981) 624.
35 J. Y. W. Seto, The electrical properties of polycrystalline silicon films, Journal of Applied
Physics, 46 (1975) 5247-5254.
36 N. C.-C. Lu, L. Gerzberg, C.-Y. Lu and J. D. Meindl, Modeling and optimization of
monolithic polycrystalline silicon resistors, IEEE transactions on electron devices, ED-28
(1981) 818.
37 J. Fraden, Handbook of modern sensors: physics, designs, and applications, Springer, New
York, 2nd edn., 1996, p. 556.
38 J. Suski, V. Mosser and J. Goss, Polysilicon SOI pressure sensor, Sensors and actuators,
17 (1989) 405.
39 I. Godovitsyn, "Sensor design", 2004, personal communication.
40 1 A. Van der Ziel, Noise in solid state devices and circuits, Wiley, New York, 1986
41 A. Il Ki Han and A. Young Ju Park, Noise sources in polycrystalline silicon thin-film
transistors, Progress in Semiconductors II Electronic and Optoelectronic Applications.
Symposium Mater., 2003, p. 481.
42 I. Han, J. Lee, A. Chovet and J. Brini, Barrier height dependence of low frequency noise in
poly-Si thin-film transistors, Proceedings of SPIE--the international society for optical
engineering, 2003, p. 552.
43 R. Bosch GMBH, Bosch Kraftfahrtechnisches Taschenbuch, VDI-Verlag GmbH, Stuttgart,
1961
129