![Micromachining 3
at a relativistic speed where a significant effect may be expected (a substantial
fraction of the speed of light).
A good engineering course teaches not only the models that the student needs
to employ, and how to employ them, but also the limitations of those models.
The knowledge that models are limited is of significance in microengineering
because the discipline is still compiling a family of models and list of pitfalls.
Despite the vast body of literature on the subject, there is still far more anecdotal
knowledge available than written information. This is evidenced by the substantial
traffic that MEMS mailing lists and discussion groups receive. There is only so
much that can be achieved by reading and modeling, and even a little experience
of the practice is of great benefit.
I.1.2 WHY IS MICROENGINEERING IMPORTANT?
The inspiration for nanotechnology, particularly molecular nanotechnology, is usu-
ally traced back to Richard Feynman’s presentation entitled “There’s Plenty of Room
at the Bottom” in 1959 [1]. A few people cite this presentation as the inspiration for
the field of microengineering, but it is more likely that it was the seminal paper by
Kurt Petersen, “Silicon as a Mechanical Material,” published in 1982 [2].
The micromachining of silicon for purposes other than the creation of elec-
tronic components was certainly being carried out at least a decade before
Petersen published this work, which compiled a variety of disparate threads and
technologies into something that was starting to look like a new technology. Not
only was silicon micromachining in existence at this time, but many of the other
techniques that will be discussed in later chapters of this volume were also being
used for specialized precision engineering work. However, despite the appearance
of some early devices, it was not until the end of that decade that commercial
exploitation of microengineering, as evidenced by the number of patents issued [3],
started to take off.
At the beginning of the 1990s, microengineering was presented as a revolu-
tionary technology that would have as great an impact as the microchip. It
promised miniaturized intelligent devices that would offer unprecedented accu-
racy and resolution and negligible power consumption. Batch fabrication would
provide us with these devices at negligible costs: few dollars, or even just a few
cents, for a silicon chip. The technology would permeate all areas of life: the
more adventurous projects proposed micromachines that would enter the blood-
stream and effect repairs, or examine the interior of nuclear reactors in minute
detail for the telltale signs of impending failure. As with many emerging tech-
nologies, some of the early predictions were wildly optimistic. Although some
of the adventurous projects proposed during this period remain inspirational for
technological development, the market has tended to be dominated by a few
applications — notably IT applications such as inkjet printer heads and hard disk
drive read–write heads. Pressure measurement appears next on the list; some may
intuitively feel that these devices, rather than inkjet printer heads, are more in
tune with the spirit of microengineering.
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![4 Microengineering, MEMS, and Interfacing: A Practical Guide
Nonetheless, microengineered devices have significant advantages and poten-
tial advantages over other solutions. Although the road to mass production and
low-cost devices is long and expensive, the destination can be reached; examine,
for example, the plethora of mass-produced silicon accelerometers and pressure
sensors. Beyond the direct advantages of miniaturization, integrating more intel-
ligence into a single component brings with it improved reliability: the fewer
components that need to be assembled into a system, the less chance there is that
it can go wrong. One great advantage of microengineering is that new tools
providing solutions to problems that have never been addressed before are still
to be fully exploited. The technology is still relatively new, and innovative think-
ing can potentially bring some startling results.
There is, however, a reason for the aforementioned cautious historical pre-
amble: market surveys are often conducted by groups with a particular interest
in the technology or by those interested in showing the economy in a positive
light. Evidence is often collected from people working in the field or companies
that have invested a lot of R&D dollars into the technology. The preamble thus
sets the following data in context.
It is undeniable that microengineering has had a substantial impact beyond
disk drives and printers. The sensors and transducers section of any commercial
electronics catalog reveals a dozen or so microengineered devices including
accelerometers, air-mass-flow sensors, and pressure transducers. (Surprisingly,
however, the electronics engineer may not be aware of the technological
advances that have gone into these devices). The molecular biologist cannot
help but be aware of the plethora of DNA chip technologies, and the material
scientist cannot have missed the micromachined atomic force microscope
(AFM) probe.
In the mid 1990s a number of different organizations compiled market growth
projections for the following few years. These were conveniently collected and
summarized by Detlefs and Pisano [3]. The European NEXUS (Network of
Excellence for Multifunctional Microsystems) has been particularly active in this
respect, publishing a report in 1998 [4] with a follow-up study appearing in 2002
[5]. Also, in 2002, the U.S.-based MEMS Industry Group published its own report
[6]. The absolute numbers for the global market in such reports vary depending
on how that market is defined. The NEXUS task force included all products with
a MEMS component, whereas the other groups only considered the individual
components themselves. The NEXUS 2002 report estimated the world market to
MEMS Advantages
• Suitable for high-volume and low-cost production
• Reduced size, mass, and power consumption
• High functionality
• Improved reliability
• Novel solutions and new applications
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![Photolithography 15
to depend on the chemistry and nature of the photoresist or the lithography system.
Table 1.1 summarizes the features of contact and projection lithography systems.
1.2.1.2 UV Light Sources
For most micromachining processes involving contact lithography, the UV light
source will be a broad-spectrum mercury arc lamp with a filter placed to restrict
illumination to one of the spectral lines (i or g). Photoresist manufacturers supply
data sheets that provide information about recommended exposure times and
wavelengths. Note that whereas some resists must be exposed to light within a
fairly strict spectrum in order to function correctly, others are available that also
work outside the range of UV wavelengths commonly used.
For very small feature sizes, in particular, the submicrometer feature sizes
typical of the most advanced IC technologies in use today, the excimer laser is
used as the UV source. This is a UV laser with a torch-like beam. This means
that it has to be employed in step-and-repeat processes as it cannot be used to
illuminate the entire substrate at once. The excimer laser has its own place in
micromachining and is discussed in more detail in Chapter 3.
Photoresists and photolithography systems are commonly referenced by the
nature of the UV source: g-line, the 436-nm band of the mercury arc lamp, i line,
the 365-nm band, and deep ultraviolet (DUV) at 248-nm and 193-nm wave-
lengths, in which excimer laser sources are preferred (Table 1.2).
1.2.1.3 Optical Systems
The resolution of an optical system is generally determined by considering its
ability to distinguish between two point sources of light [1,2,3]. This work by
Rayleigh in the 19th century gave rise to the Rayleigh criterion. Roughly stated,
the minimum resolved distance between two peaks depends on the wavelength of
light and the numerical aperture of the focusing optics:
(1.1)
TABLE 1.1
Advantages and Disadvantages of Contact
and Projection Systems
Contact vs. Projection Lithography Systems
Contact Projection
Single exposure
Multiple devices per wafer
Double-sided alignment
Low cost
More uniform light intensity
Small feature sizes
Grayscale masks
Longer mask life
d
NA
= 0 61
.
λ
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![16 Microengineering, MEMS, and Interfacing: A Practical Guide
Where λ is the wavelength of the light, and NA the numerical aperture of the lens.
This equation was derived from optical considerations alone and based on a
consideration of point light sources. In photolithography, the achievable
resolution (minimum feature size) is also related to other aspects, such as the
chemistry of the photoresist. Additionally, one is generally more interested in
lines than point sources. Considerations for contact, proximity, and projection
systems are outlined in the following subsections.
Also of interest is the depth of focus, the distance along the optical axis over
which the optics produce an image of suitable quality. The Rayleigh criterion for
depth of focus gives [1,2]:
(1.2)
As with considerations of resolution, this pure equation is not directly applicable
to photolithography.
1.2.1.3.1 Contact and Proximity Printing
In contact and proximity printing, the optical limits to minimum feature sizes are
due primarily to diffraction effects. In this case, the mathematics analyzes the
image of a slit in a grating. This gives rise to a resolution related to the wavelength
of light and the separation, s, between the mask plate and the substrate [2,4]:
(1.3)
In practice, because of the dependence on process parameters, this is normally
written as:
(1.4)
where k3 is empirically derived for the process and facility. Peckerar et al. give a
practical value of k3 as 1.6, whereas Reche suggests that it can be as low as 1.5.
TABLE 1.2
UV Sources and Wavelengths
Wavelength (nm) Source Region of Spectrum
436 Mercury arc lamp g line
405 Mercury arc lamp h line
365 Mercury arc lamp i line
248 Mercury arc lamp or
Excimer laser
Deep ultraviolet
193 Excimer laser
δ
λ
= 0 35 2
.
NA
d s
= 1 4
. λ
d k s
= 3 λ
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![Photolithography 17
In the case of contact printing, the distance s will be half the thickness of the
photoresist. Note that this can be quite substantial in micromachining applications
(tens of micrometers) and that raised and indented micromachined features can
mean that the surface of the resist may be considerably more rippled or featured
than one normally finds. In the case of proximity printing, one may assume that
the distance between mask and substrate is significantly greater than the thickness
of the resist, so s will take this value, and the thickness of the resist may be
neglected. Once again, beware of assumptions that may be invalidated by the
unusual nature of MEMS processing.
As mentioned previously, one of the advantages of contact or proximity
printing is that the entire area of the substrate can be exposed in a single-process
step. Unfortunately UV sources such as the mercury arc lamp appear somewhat
point-like. These, therefore, require special optics to expand and homogenize
(make the intensity uniform across the area of the substrate that is being exposed)
the beam. Somewhat unintuitively, the best results are not provided by collimated
light; a divergence of a few degrees will smooth out peaks that appear in the
intensity towards the edge of the pattern [3]. The optics for a contact aligner are
shown schematically in Figure 1.4.
1.2.1.3.2 Projection Printing
The key parameters for projection printing are derived from the Rayleigh criteria for
resolution and depth of focus (Equation 1.1 and Equation 1.2, respectively; [1,2,4]):
(1.5)
(1.6)
Once again, k1 and k2 are empirically derived for the process in question. In
practice, k1 will be between 0.5 and 1, typically, about 0.7 [1,4], and k2 will be
somewhere about 0.5 ([4]; Peckerar et al. suggest that is closer to 1). Reche also
FIGURE 1.4 Contact aligner exposure optics schematic. Alignment is usually performed
through a binocular microscope system, not shown, which focuses at two points near the
center of the wafer. The relative position of the mask and wafer are adjusted, and the
optical components of the aligner are moved out of the way during exposure.
d k
NA
= 1
λ
δ
λ
= k
NA
2 2
Source
Homogenizer
Optics
Mask
Substrate
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![18 Microengineering, MEMS, and Interfacing: A Practical Guide
gives the economically practical value of a numerical aperture as being no more than
0.5 for one-to-one projection printing. With reduction optics, it may be increased to
0.6 [1], although economically this would amount to using a production line stepper
around the clock. The optics of a projection system are shown in outline in Figure 1.5.
1.2.1.3.3 Projection and Contact Printing Compared
Working with Equation 1.4, Equation 1.5, and Equation 1.6 and taking values of
0.7, 1, and 1.6 for k1, k2, and k3, respectively, we find, with g-line (436 nm)
exposure for a 1:1 projection system with a numerical aperture of 0.5, the
achievable resolution will be approximately 0.61 µm with a depth of field of
1.7 µm. This would be adequate for many applications, but consider the situation
in which a 10-µm thick resist is required. A trade-off between depth of field and
resolution can be seen by examining Equation 1.5 and Equation 1.6. For a 10-µm
depth of field (greater, preferably, to accommodate positioning and other errors),
the resolution goes up to about 1.53 µm. Note that projection printing would
typically be used for high-resolution printing on thin films of resist.
Using the same numbers, contact printing would give a 3.34-µm resolution
with the 10-µm resist. In this case, we have considered the entire thickness of
the resist film as the separation distance, which will give a worst-case estimate
of resolution. For thin resists, the separation distance can be set to half the
thickness of the resist (implying that the resolution, in this case, is unlikely to be
better than 2.36 µm).
If we consider proximity printing with a 50-µm total separation, our achiev-
able resolution increases to 7.47 µm, which will be adequate for many microengi-
neering applications.
Typically, thick resists are used as structural elements in MEMS. They may
also be desirable in deep-etching applications, in which a thick resist is required
to withstand long periods spent in the etching apparatus. In the latter situation,
high resolutions can be achieved by the use of a hard mask. A thin layer of resist
can be used to pattern an underlying layer of more resilient material for the
etching of the next process stem: a metal film, for instance. This is the hard mask;
the pattern in this would then be transferred to the underlying material during a
long etch process before the hard mask (etch mask) is stripped.
FIGURE 1.5 Schematic outline of a projection printing system.
Source
Homogenizer
Condenser
Mask
Projection lens
Substrate on
movable stage
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![every son of Adam with faith as well as Adam himself. He wants not
a virtue superior to the greatest resistance of his creature; a
victorious beam of light might be shot into their understandings, and
a flood of grace might overspread their wills with one word of his
mouth, without putting forth the utmost of his power. What
hindrance could there be in any created spirit, which cannot be
easily pierced into and new moulded by the Father of spirits? Yet he
only breathes this efficacious virtue into some, and leaves others
under that insensibility and hardness which they love, and suffer
them to continue in their benighting ignorance, and consume
themselves in the embraces of their dear, though deceitful Delilahs.
He could have conquered the resistance of the Jews, as well as
chased away the darkness and ignorance of the Gentiles. No doubt
but he could overpower the heart of the most malicious devil, as well
as that of the simplest and weakest man. But the breath of the
Almighty Spirit is in his own power, to breathe “where he lists” (John
iii. 8). It is at his liberty whether he will give to any the feelings of
the invincible efficacy of his grace; he did not want strength to have
kept man as firm as a rock against the temptation of Satan, and
poured in such fortifying grace, as to have made him impregnable
against the powers of hell, as well as he did secure the standing of
the angels against the sedition of their fellows: but it was his will to
permit it to be otherwise.
(2.) Nor is it from any prerogative in the creature. He converts
not any for their natural perfection, because he seizeth upon the
most ignorant; nor for their moral perfection, because he converts
the most sinful; nor for their civil perfection, because he turns the
most despicable.
[1.] Not for their natural perfection of knowledge. He opened
the minds and hearts of the more ignorant. Were the nature of the
Gentiles better manured than that of the Jews, or did the tapers of
their understandings burn clearer? No; the one were skilled in the
prophecies of the Messiah, and might have compared the predictions
they owned with the actions and sufferings of Christ, which they](https://image.slidesharecdn.com/52005-250226073940-364a6036/85/Microengineering-MEMS-and-Interfacing-A-Practical-Guide-1st-Edition-Danny-Banks-58-320.jpg)
![were spectators of. He let alone those that had expectations of the
Messiah, and expectations about the time of Christ’s appearance,
both grounded upon the oracles wherewith he had entrusted them.
The Gentiles were unacquainted with the prophets, and therefore
destitute of the expectations of the Messiah (Eph. ii. 12): they were
“without Christ;” without any revelation of Christ, because “aliens
from the commonwealth of Israel, and strangers to the covenant of
promise, having no hope, and without God in the world,” without any
knowledge of God, or promises of Christ. The Jews might sooner, in
a way of reason, have been wrought upon than the Gentiles, who
were ignorant of the prophets, by whose writings they might have
examined the truth of the apostles’ declarations. Thus are they
refused that were the kindred of Christ, according to the flesh, and
the Gentiles, that were at a greater distance from him, brought in by
God; thus he catcheth not at the subtle and mighty devils, who had
an original in spiritual nature more like to him, but at weak and
simple man.
[2.] Not for any moral perfection, because he converts the most
sinful: the Gentiles, steeped in idolatry and superstition. He sowed
more faith among the Romans than in Jerusalem; more faith in a city
that was the common sewer of all the idolatry of the nations
conquered by them, than in that city which had so signally been
owned by him, and had not practised any idolatry since the
Babylonish captivity. He planted saintship at Corinth, a place
notorious for the infamous worship of Venus, a superstition attended
with the grossest uncleanness; at Ephesus, that presented the whole
world with a cup of fornication in their temple of Diana; among the
Colossians, votaries to Cybele in a manner of worship attended with
beastly and lascivious ceremonies. And what character had the
Cretians from one of their own poets, mentioned by the apostle to
Titus, whom he had placed among them to further the progress of
the gospel, but the vilest and most abominable? (Titus i. 12): “liars,”
not to be credited; “evil beasts,” not to be associated with; “slow
bellies,” fit for no service. What prerogative was there in the nature
of such putrefaction? as much as in that of a toad to be elevated to](https://image.slidesharecdn.com/52005-250226073940-364a6036/85/Microengineering-MEMS-and-Interfacing-A-Practical-Guide-1st-Edition-Danny-Banks-59-320.jpg)
![the dignity of an angel. What steam from such dunghills could be
welcome to him, and move him to cast his eye on them, and
sweeten them from heaven? What treasures of worth were here to
open the treasures of his grace! Were such filthy snuffs fit of
themselves to be kindled by, and become a lodging for, a gospel
beam? What invitements could he have from lying, beastliness,
gluttony, but only from his own sovereignty? By this he plucked
firebrands out of the fire, while he left straighter and more comely
sticks to consume to ashes.
[3.] Not for any civil perfection, because he turns the most
despicable. He elevates not nature to grace upon the account of
wealth, honor, or any civil station in the world: he dispenseth not
ordinarily those treasures to those that the mistaken world foolishly
admire and dote upon (1 Cor. i. 26); “Not many mighty, not many
noble:” a purple robe is not usually decked with this jewel; he takes
more of mouldy clay than refined dust to cast into his image, and
lodges his treasures more in the earthly vessels than in the world’s
golden ones; he gives out his richest doles to those that are the
scorn and reproach of the world. Should he impart his grace most to
those that abound in wealth or honor, it had been some foundation
for a conception that he had been moved by those vulgarly
esteemed excellencies to indulge them more than others. But such a
conceit languisheth when we behold the subjects of his grace as
void originally of any allurements, as they are full of provocations.
Hereby he declares himself free from all created engagements, and
that he is not led by any external motives in the object.
[4.] It is not from any obligation which lies upon him. He is
indebted to none: disobliged by all. No man deserves from him any
act of grace, but every man deserves what the most deplorable are
left to suffer. He is obliged by the children of wrath to nothing else
but showers of wrath; owes no more a debt to fallen man, than to
fallen devils, to restore them to their first station by a superlative
grace. How was he more bound to restore them, than he was to
preserve them; to catch them after they fell, than to put a bar in the](https://image.slidesharecdn.com/52005-250226073940-364a6036/85/Microengineering-MEMS-and-Interfacing-A-Practical-Guide-1st-Edition-Danny-Banks-60-320.jpg)
![sovereign right; and if he would by his largess make any of them
capable to fulfil the condition, by sending them presently a sufficient
sum to pay the fine, he acted as proprietor of his own goods, to
dispose of them in such a quantity to those to whom he was not
obliged to bestow a mite.
[5.] It must therefore be an act of his mere sovereignty. This
can only sit arbitrator in every gracious act. Why did he give grace to
Abel and not to Cain, since they both lay in the same womb, and
equally derived from their parents a taint in their nature; but that he
would show a standing example of his sovereignty to the future ages
of the world in the first posterity of man? Why did he give grace to
Abraham, and separate him from his idolatrous kindred, to dignify
him to be the root of the Messiah? Why did he confine his promise
to Isaac, and not extend it to Ishmael, the seed of the same
Abraham by Hagar, or to the children he had by Keturah after
Sarah’s death? What reason can be alleged for this but his sovereign
will? Why did he not give the fallen angels a moment of repentance
after their sin, but condemned them to irrevocable pains? Is it not as
free for him to give grace to whom he please, as create what worlds
he please; to form this corrupted clay into his own image, as to take
such a parcel of dust from all the rest of the creation whereof to
compact Adam’s body? Hath he not as much jurisdiction over the
sinful mass of his creatures in a new creation, as he had over the
chaos in the old? And what reason can be rendered, of his advancing
this part of matter to the nobler dignity of a star, and leaving that
other part to make up the dark body of the earth; to compact one
part into a glorious sun, and another part into a hard rock, but his
royal prerogative? What is the reason a prince subjects one
malefactor to punishment, and lifts up another to a place of trust
and profit? that Pharaoh honored the butler with an attendance on
his person, and remitted the baker to the hands of the executioner?
It was his pleasure. And is not as great right due to God, as is
allowed to the worms of the earth? What is the reason he hardens a
Pharaoh, by a denying him that grace which should mollify him, and
allows it to another? It is because he will. “Whom he will he](https://image.slidesharecdn.com/52005-250226073940-364a6036/85/Microengineering-MEMS-and-Interfacing-A-Practical-Guide-1st-Edition-Danny-Banks-62-320.jpg)
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- 5. Microengineering MEMS and Interfacing A Practical Guide 1st Edition Danny Banks Digital Instant Download Author(s): Danny Banks ISBN(s): 9781420015416, 1420015419 Edition: 1 File Details: PDF, 8.65 MB Year: 2006 Language: english
- 6. DK3182_half 1/18/06 11:31 AM Page 1 Microengineering,MEMS, andInterfacing APracticalGuide Copyright © 2006 Taylor & Francis Group, LLC
- 7. MECHANICAL ENGINEERING A Series of Textbooks and Reference Books Founding Editor L. L. Faulkner Columbus Division, Battelle Memorial Institute and Department of Mechanical Engineering The Ohio State University Columbus, Ohio 1. Spring Designer’s Handbook, Harold Carlson 2. Computer-Aided Graphics and Design, Daniel L. Ryan 3. Lubrication Fundamentals, J. George Wills 4. Solar Engineering for Domestic Buildings, William A. Himmelman 5. Applied Engineering Mechanics: Statics and Dynamics, G. Boothroyd and C. Poli 6. Centrifugal Pump Clinic, Igor J. Karassik 7. Computer-Aided Kinetics for Machine Design, Daniel L. Ryan 8. Plastics Products Design Handbook, Part A: Materials and Components; Part B: Processes and Design for Processes, edited by Edward Miller 9. Turbomachinery: Basic Theory and Applications, Earl Logan, Jr. 10. Vibrations of Shells and Plates, Werner Soedel 11. Flat and Corrugated Diaphragm Design Handbook, Mario Di Giovanni 12. Practical Stress Analysis in Engineering Design, Alexander Blake 13. An Introduction to the Design and Behavior of Bolted Joints, John H. Bickford 14. Optimal Engineering Design: Principles and Applications, James N. Siddall 15. Spring Manufacturing Handbook, Harold Carlson 16. Industrial Noise Control: Fundamentals and Applications, edited by Lewis H. Bell 17. Gears and Their Vibration: A Basic Approach to Understanding Gear Noise, J. Derek Smith 18. Chains for Power Transmission and Material Handling: Design and Applications Handbook, American Chain Association 19. Corrosion and Corrosion Protection Handbook, edited by Philip A. Schweitzer 20. Gear Drive Systems: Design and Application, Peter Lynwander 21. Controlling In-Plant Airborne Contaminants: Systems Design and Calculations, John D. Constance 22. CAD/CAM Systems Planning and Implementation, Charles S. Knox 23. Probabilistic Engineering Design: Principles and Applications, James N. Siddall DK3182_series.qxd 1/19/06 8:35 AM Page 1 Copyright © 2006 Taylor & Francis Group, LLC
- 8. 24. Traction Drives: Selection and Application, Frederick W. Heilich III and Eugene E. Shube 25. Finite Element Methods: An Introduction, Ronald L. Huston and Chris E. Passerello 26. Mechanical Fastening of Plastics: An Engineering Handbook, Brayton Lincoln, Kenneth J. Gomes, and James F. Braden 27. Lubrication in Practice: Second Edition, edited by W. S. Robertson 28. Principles of Automated Drafting, Daniel L. Ryan 29. Practical Seal Design, edited by Leonard J. Martini 30. Engineering Documentation for CAD/CAM Applications, Charles S. Knox 31. Design Dimensioning with Computer Graphics Applications, Jerome C. Lange 32. Mechanism Analysis: Simplified Graphical and Analytical Techniques, Lyndon O. Barton 33. CAD/CAM Systems: Justification, Implementation, Productivity Measurement, Edward J. Preston, George W. Crawford, and Mark E. Coticchia 34. Steam Plant Calculations Manual, V. Ganapathy 35. Design Assurance for Engineers and Managers, John A. Burgess 36. Heat Transfer Fluids and Systems for Process and Energy Applications, Jasbir Singh 37. Potential Flows: Computer Graphic Solutions, Robert H. Kirchhoff 38. Computer-Aided Graphics and Design: Second Edition, Daniel L. Ryan 39. Electronically Controlled Proportional Valves: Selection and Application, Michael J. Tonyan, edited by Tobi Goldoftas 40. Pressure Gauge Handbook, AMETEK, U.S. Gauge Division, edited by Philip W. Harland 41. Fabric Filtration for Combustion Sources: Fundamentals and Basic Technology, R. P. Donovan 42. Design of Mechanical Joints, Alexander Blake 43. CAD/CAM Dictionary, Edward J. Preston, George W. Crawford, and Mark E. Coticchia 44. Machinery Adhesives for Locking, Retaining, and Sealing, Girard S. Haviland 45. Couplings and Joints: Design, Selection, and Application, Jon R. Mancuso 46. Shaft Alignment Handbook, John Piotrowski 47. BASIC Programs for Steam Plant Engineers: Boilers, Combustion, Fluid Flow, and Heat Transfer, V. Ganapathy 48. Solving Mechanical Design Problems with Computer Graphics, Jerome C. Lange 49. Plastics Gearing: Selection and Application, Clifford E. Adams 50. Clutches and Brakes: Design and Selection, William C. Orthwein 51. Transducers in Mechanical and Electronic Design, Harry L. Trietley 52. Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, edited by Lawrence E. Murr, Karl P. Staudhammer, and Marc A. Meyers 53. Magnesium Products Design, Robert S. Busk 54. How to Integrate CAD/CAM Systems: Management and Technology, William D. Engelke DK3182_series.qxd 1/19/06 8:35 AM Page 2 Copyright © 2006 Taylor & Francis Group, LLC
- 9. 55. Cam Design and Manufacture: Second Edition; with cam design software for the IBM PC and compatibles, disk included, Preben W. Jensen 56. Solid-State AC Motor Controls: Selection and Application, Sylvester Campbell 57. Fundamentals of Robotics, David D. Ardayfio 58. Belt Selection and Application for Engineers, edited by Wallace D. Erickson 59. Developing Three-Dimensional CAD Software with the IBM PC, C. Stan Wei 60. Organizing Data for CIM Applications, Charles S. Knox, with contributions by Thomas C. Boos, Ross S. Culverhouse, and Paul F. Muchnicki 61. Computer-Aided Simulation in Railway Dynamics, by Rao V. Dukkipati and Joseph R. Amyot 62. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, P. K. Mallick 63. Photoelectric Sensors and Controls: Selection and Application, Scott M. Juds 64. Finite Element Analysis with Personal Computers, Edward R. Champion, Jr. and J. Michael Ensminger 65. Ultrasonics: Fundamentals, Technology, Applications: Second Edition, Revised and Expanded, Dale Ensminger 66. Applied Finite Element Modeling: Practical Problem Solving for Engineers, Jeffrey M. Steele 67. Measurement and Instrumentation in Engineering: Principles and Basic Laboratory Experiments, Francis S. Tse and Ivan E. Morse 68. Centrifugal Pump Clinic: Second Edition, Revised and Expanded, Igor J. Karassik 69. Practical Stress Analysis in Engineering Design: Second Edition, Revised and Expanded, Alexander Blake 70. An Introduction to the Design and Behavior of Bolted Joints: Second Edition, Revised and Expanded, John H. Bickford 71. High Vacuum Technology: A Practical Guide, Marsbed H. Hablanian 72. Pressure Sensors: Selection and Application, Duane Tandeske 73. Zinc Handbook: Properties, Processing, and Use in Design, Frank Porter 74. Thermal Fatigue of Metals, Andrzej Weronski and Tadeusz Hejwowski 75. Classical and Modern Mechanisms for Engineers and Inventors, Preben W. Jensen 76. Handbook of Electronic Package Design, edited by Michael Pecht 77. Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by Marc A. Meyers, Lawrence E. Murr, and Karl P. Staudhammer 78. Industrial Refrigeration: Principles, Design and Applications, P. C. Koelet 79. Applied Combustion, Eugene L. Keating 80. Engine Oils and Automotive Lubrication, edited by Wilfried J. Bartz 81. Mechanism Analysis: Simplified and Graphical Techniques, Second Edition, Revised and Expanded, Lyndon O. Barton 82. Fundamental Fluid Mechanics for the Practicing Engineer, James W. Murdock 83. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Revised and Expanded, P. K. Mallick DK3182_series.qxd 1/19/06 8:35 AM Page 3 Copyright © 2006 Taylor & Francis Group, LLC
- 10. 84. Numerical Methods for Engineering Applications, Edward R. Champion, Jr. 85. Turbomachinery: Basic Theory and Applications, Second Edition, Revised and Expanded, Earl Logan, Jr. 86. Vibrations of Shells and Plates: Second Edition, Revised and Expanded, Werner Soedel 87. Steam Plant Calculations Manual: Second Edition, Revised and Expanded, V. Ganapathy 88. Industrial Noise Control: Fundamentals and Applications, Second Edition, Revised and Expanded, Lewis H. Bell and Douglas H. Bell 89. Finite Elements: Their Design and Performance, Richard H. MacNeal 90. Mechanical Properties of Polymers and Composites: Second Edition, Revised and Expanded, Lawrence E. Nielsen and Robert F. Landel 91. Mechanical Wear Prediction and Prevention, Raymond G. Bayer 92. Mechanical Power Transmission Components, edited by David W. South and Jon R. Mancuso 93. Handbook of Turbomachinery, edited by Earl Logan, Jr. 94. Engineering Documentation Control Practices and Procedures, Ray E. Monahan 95. Refractory Linings Thermomechanical Design and Applications, Charles A. Schacht 96. Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufacturing, and Inspection, James D. Meadows 97. An Introduction to the Design and Behavior of Bolted Joints: Third Edition, Revised and Expanded, John H. Bickford 98. Shaft Alignment Handbook: Second Edition, Revised and Expanded, John Piotrowski 99. Computer-Aided Design of Polymer-Matrix Composite Structures, edited by Suong Van Hoa 100. Friction Science and Technology, Peter J. Blau 101. Introduction to Plastics and Composites: Mechanical Properties and Engineering Applications, Edward Miller 102. Practical Fracture Mechanics in Design, Alexander Blake 103. Pump Characteristics and Applications, Michael W. Volk 104. Optical Principles and Technology for Engineers, James E. Stewart 105. Optimizing the Shape of Mechanical Elements and Structures, A. A. Seireg and Jorge Rodriguez 106. Kinematics and Dynamics of Machinery, Vladimír Stejskal and Michael Valásek 107. Shaft Seals for Dynamic Applications, Les Horve 108. Reliability-Based Mechanical Design, edited by Thomas A. Cruse 109. Mechanical Fastening, Joining, and Assembly, James A. Speck 110. Turbomachinery Fluid Dynamics and Heat Transfer, edited by Chunill Hah 111. High-Vacuum Technology: A Practical Guide, Second Edition, Revised and Expanded, Marsbed H. Hablanian 112. Geometric Dimensioning and Tolerancing: Workbook and Answerbook, James D. Meadows DK3182_series.qxd 1/19/06 8:35 AM Page 4 Copyright © 2006 Taylor & Francis Group, LLC
- 11. 113. Handbook of Materials Selection for Engineering Applications, edited by G. T. Murray 114. Handbook of Thermoplastic Piping System Design, Thomas Sixsmith and Reinhard Hanselka 115. Practical Guide to Finite Elements: A Solid Mechanics Approach, Steven M. Lepi 116. Applied Computational Fluid Dynamics, edited by Vijay K. Garg 117. Fluid Sealing Technology, Heinz K. Muller and Bernard S. Nau 118. Friction and Lubrication in Mechanical Design, A. A. Seireg 119. Influence Functions and Matrices, Yuri A. Melnikov 120. Mechanical Analysis of Electronic Packaging Systems, Stephen A. McKeown 121. Couplings and Joints: Design, Selection, and Application, Second Edition, Revised and Expanded, Jon R. Mancuso 122. Thermodynamics: Processes and Applications, Earl Logan, Jr. 123. Gear Noise and Vibration, J. Derek Smith 124. Practical Fluid Mechanics for Engineering Applications, John J. Bloomer 125. Handbook of Hydraulic Fluid Technology, edited by George E. Totten 126. Heat Exchanger Design Handbook, T. Kuppan 127. Designing for Product Sound Quality, Richard H. Lyon 128. Probability Applications in Mechanical Design, Franklin E. Fisher and Joy R. Fisher 129. Nickel Alloys, edited by Ulrich Heubner 130. Rotating Machinery Vibration: Problem Analysis and Troubleshooting, Maurice L. Adams, Jr. 131. Formulas for Dynamic Analysis, Ronald L. Huston and C. Q. Liu 132. Handbook of Machinery Dynamics, Lynn L. Faulkner and Earl Logan, Jr. 133. Rapid Prototyping Technology: Selection and Application, Kenneth G. Cooper 134. Reciprocating Machinery Dynamics: Design and Analysis, Abdulla S. Rangwala 135. Maintenance Excellence: Optimizing Equipment Life-Cycle Decisions, edited by John D. Campbell and Andrew K. S. Jardine 136. Practical Guide to Industrial Boiler Systems, Ralph L. Vandagriff 137. Lubrication Fundamentals: Second Edition, Revised and Expanded, D. M. Pirro and A. A. Wessol 138. Mechanical Life Cycle Handbook: Good Environmental Design and Manufacturing, edited by Mahendra S. Hundal 139. Micromachining of Engineering Materials, edited by Joseph McGeough 140. Control Strategies for Dynamic Systems: Design and Implementation, John H. Lumkes, Jr. 141. Practical Guide to Pressure Vessel Manufacturing, Sunil Pullarcot 142. Nondestructive Evaluation: Theory, Techniques, and Applications, edited by Peter J. Shull 143. Diesel Engine Engineering: Thermodynamics, Dynamics, Design, and Control, Andrei Makartchouk 144. Handbook of Machine Tool Analysis, Ioan D. Marinescu, Constantin Ispas, and Dan Boboc DK3182_series.qxd 1/19/06 8:35 AM Page 5 Copyright © 2006 Taylor & Francis Group, LLC
- 12. 145. Implementing Concurrent Engineering in Small Companies, Susan Carlson Skalak 146. Practical Guide to the Packaging of Electronics: Thermal and Mechanical Design and Analysis, Ali Jamnia 147. Bearing Design in Machinery: Engineering Tribology and Lubrication, Avraham Harnoy 148. Mechanical Reliability Improvement: Probability and Statistics for Experimental Testing, R. E. Little 149. Industrial Boilers and Heat Recovery Steam Generators: Design, Applications, and Calculations, V. Ganapathy 150. The CAD Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design, Stephen J. Schoonmaker 151. Industrial Noise Control and Acoustics, Randall F. Barron 152. Mechanical Properties of Engineered Materials, Wolé Soboyejo 153. Reliability Verification, Testing, and Analysis in Engineering Design, Gary S. Wasserman 154. Fundamental Mechanics of Fluids: Third Edition, I. G. Currie 155. Intermediate Heat Transfer, Kau-Fui Vincent Wong 156. HVAC Water Chillers and Cooling Towers: Fundamentals, Application, and Operation, Herbert W. Stanford III 157. Gear Noise and Vibration: Second Edition, Revised and Expanded, J. Derek Smith 158. Handbook of Turbomachinery: Second Edition, Revised and Expanded, edited by Earl Logan, Jr. and Ramendra Roy 159. Piping and Pipeline Engineering: Design, Construction, Maintenance, Integrity, and Repair, George A. Antaki 160. Turbomachinery: Design and Theory, Rama S. R. Gorla and Aijaz Ahmed Khan 161. Target Costing: Market-Driven Product Design, M. Bradford Clifton, Henry M. B. Bird, Robert E. Albano, and Wesley P. Townsend 162. Fluidized Bed Combustion, Simeon N. Oka 163. Theory of Dimensioning: An Introduction to Parameterizing Geometric Models, Vijay Srinivasan 164. Handbook of Mechanical Alloy Design, edited by George E. Totten, Lin Xie, and Kiyoshi Funatani 165. Structural Analysis of Polymeric Composite Materials, Mark E. Tuttle 166. Modeling and Simulation for Material Selection and Mechanical Design, edited by George E. Totten, Lin Xie, and Kiyoshi Funatani 167. Handbook of Pneumatic Conveying Engineering, David Mills, Mark G. Jones, and Vijay K. Agarwal 168. Clutches and Brakes: Design and Selection, Second Edition, William C. Orthwein 169. Fundamentals of Fluid Film Lubrication: Second Edition, Bernard J. Hamrock, Steven R. Schmid, and Bo O. Jacobson 170. Handbook of Lead-Free Solder Technology for Microelectronic Assemblies, edited by Karl J. Puttlitz and Kathleen A. Stalter 171. Vehicle Stability, Dean Karnopp 172. Mechanical Wear Fundamentals and Testing: Second Edition, Revised and Expanded, Raymond G. Bayer 173. Liquid Pipeline Hydraulics, E. Shashi Menon DK3182_series.qxd 1/19/06 8:35 AM Page 6 Copyright © 2006 Taylor & Francis Group, LLC
- 13. 174. Solid Fuels Combustion and Gasification, Marcio L. de Souza-Santos 175. Mechanical Tolerance Stackup and Analysis, Bryan R. Fischer 176. Engineering Design for Wear, Raymond G. Bayer 177. Vibrations of Shells and Plates: Third Edition, Revised and Expanded, Werner Soedel 178. Refractories Handbook, edited by Charles A. Schacht 179. Practical Engineering Failure Analysis, Hani M. Tawancy, Anwar Ul-Hamid, and Nureddin M. Abbas 180. Mechanical Alloying and Milling, C. Suryanarayana 181. Mechanical Vibration: Analysis, Uncertainties, and Control, Second Edition, Revised and Expanded, Haym Benaroya 182. Design of Automatic Machinery, Stephen J. Derby 183. Practical Fracture Mechanics in Design: Second Edition, Revised and Expanded, Arun Shukla 184. Practical Guide to Designed Experiments, Paul D. Funkenbusch 185. Gigacycle Fatigue in Mechanical Practive, Claude Bathias and Paul C. Paris 186. Selection of Engineering Materials and Adhesives, Lawrence W. Fisher 187. Boundary Methods: Elements, Contours, and Nodes, Subrata Mukherjee and Yu Xie Mukherjee 188. Rotordynamics, Agnieszka (Agnes) Muszńyska 189. Pump Characteristics and Applications: Second Edition, Michael W. Volk 190. Reliability Engineering: Probability Models and Maintenance Methods, Joel A. Nachlas 191. Industrial Heating: Principles, Techniques, Materials, Applications, and Design, Yeshvant V. Deshmukh 192. Micro Electro Mechanical System Design, James J. Allen 193. Probability Models in Engineering and Science, Haym Benaroya and Seon Han 194. Damage Mechanics, George Z. Voyiadjis and Peter I. Kattan 195. Standard Handbook of Chains: Chains for Power Transmission and Material Handling, Second Edition, American Chain Association and John L. Wright, Technical Consultant 196. Standards for Engineering Design and Manufacturing, Wasim Ahmed Khan and Abdul Raouf S.I. 197. Maintenance, Replacement, and Reliability: Theory and Applications, Andrew K. S. Jardine and Albert H. C. Tsang 198. Finite Element Method: Applications in Solids, Structures, and Heat Transfer, Michael R. Gosz 199. Microengineering, MEMS, and Interfacing: A Practical Guide, Danny Banks DK3182_series.qxd 1/19/06 8:35 AM Page 7 Copyright © 2006 Taylor & Francis Group, LLC
- 14. DK3182_title 1/19/06 8:35 AM Page 1 Microengineering,MEMS, andInterfacing APracticalGuide DannyBanks Monisys Ltd. Birmingham, England A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc. Boca Raton London New York Copyright © 2006 Taylor & Francis Group, LLC
- 15. Published in 2006 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2006 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8247-2305-8 (Hardcover) International Standard Book Number-13: 978-0-8247-2305-7 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Taylor & Francis Group is the Academic Division of Informa plc. DK3182_Discl.fm Page 1 Monday, January 23, 2006 2:10 PM Copyright © 2006 Taylor & Francis Group, LLC
- 16. Dedication To Amanda Lamb DK3182_C000.fm Page v Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 17. Acknowledgments I would like to thank everyone who has contributed material and assistance. Material contributions should be acknowledged in the text, and I can only apologize if any of these have been accidentally omitted. To you, and everyone else, many thanks. DK3182_C000.fm Page vii Monday, February 13, 2006 10:25 AM Copyright © 2006 Taylor & Francis Group, LLC
- 18. The Author Danny Banks first studied electronic engineering at Leicester Polytechnic (now DeMontfort University), U.K., graduating in 1990 with a B.Eng. (Hons). He then joined the University of Surrey, U.K., as a Ph.D. student. His research involved modeling and experimental investigation of micromachined microelectrodes for recording neural signals from peripheral nerve trunks. He was awarded his Ph.D. in 1995. Subsequently, he was employed as a postdoctoral research fellow in the biomedical engineering group and was able to spend a further three years on this research. From 1997 to 1999, he was employed as a postdoctoral fellow at the European Molecular Biology Laboratory in Heidelberg, Germany. His work involved the investigation of microfabricated devices for biochemical analysis of single cells. He was also involved in the promotion of artificial microstructures for applications in molecular biology. Since 1999 Dr. Banks has been employed at Monisys, a small company specializing in embedded systems, sensors, and instrumentation R&D, located in Birmingham, U.K. He is presently technical director. Dr. Banks is a member of the Institute of Electrical Engineers (IEE), the Society for Experimental Biology of the Institute of Electrical and Electronics Engineers (IEEE) and Euroscience. DK3182_C000.fm Page ix Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 19. Table of Contents Part 1 Micromachining.......................................................1 I.1 Introduction..................................................................................................1 I.1.1 What Is Microengineering?.............................................................1 I.1.2 Why Is Microengineering Important?.............................................3 I.1.3 How Can I Make Money out of Microengineering?......................5 References .............................................................................................................7 Chapter 1 Photolithography..............................................................................9 1.1 Introduction..................................................................................................9 1.2 UV Photolithography.................................................................................10 1.2.1 UV Exposure Systems...................................................................11 1.2.1.1 Mask Aligners .................................................................12 1.2.1.2 UV Light Sources ...........................................................15 1.2.1.3 Optical Systems...............................................................15 1.2.1.3.1 Contact and Proximity Printing .....................16 1.2.1.3.2 Projection Printing..........................................17 1.2.1.3.3 Projection and Contact Printing Compared...18 1.2.1.4 Optical Oddities ..............................................................19 1.2.1.4.1 The Difference between Negative and Positive Resists........................................19 1.2.1.4.2 Optical Aberrations and Distortions ..............19 1.2.1.4.3 Optical Proximity Effects...............................20 1.2.1.4.4 Reflection from the Substrate ........................20 1.2.2 Shadow Masks...............................................................................21 1.2.3 Photoresists and Resist Processing ...............................................21 1.2.3.1 Photoresists......................................................................22 1.2.3.2 Photoresist Processing.....................................................24 1.2.3.2.1 Cleaning the Substrate ...................................25 1.2.3.2.2 Applying Photoresists ....................................27 1.2.3.2.3 Postexposure Processing ................................28 1.3 X-Ray Lithography....................................................................................28 1.3.1 Masks for X-Ray Lithography......................................................29 1.4 Direct-Write (E-Beam) Lithography.........................................................30 1.5 Low-Cost Photolithography ......................................................................32 1.6 Photolithography — Key Points ...............................................................34 References ...........................................................................................................35 DK3182_C000.fm Page xi Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 20. Chapter 2 Silicon Micromachining................................................................37 2.1 Introduction................................................................................................37 2.2 Silicon........................................................................................................37 2.2.1 Miller Indices.................................................................................39 2.3 Crystal Growth ..........................................................................................39 2.4 Doping .......................................................................................................40 2.4.1 Thermal Diffusion .........................................................................41 2.4.2 Ion Implantation ............................................................................41 2.5 Wafer Specifications..................................................................................42 2.6 Thin Films .................................................................................................45 2.6.1 Materials and Deposition ..............................................................45 2.6.1.1 Depositing Thin Films ....................................................47 2.6.1.1.1 Thermal Oxidation .........................................47 2.6.1.1.2 Chemical Vapor Deposition ...........................47 2.6.1.1.3 Sputter Deposition..........................................49 2.6.1.1.4 Evaporation.....................................................50 2.6.1.1.5 Spinning..........................................................50 2.6.1.1.6 Summary.........................................................50 2.6.2 Wet Etching ...................................................................................52 2.6.3 Dry Etching ...................................................................................56 2.6.3.1 Relative Ion Etching .......................................................56 2.6.3.2 Ion-Beam Milling............................................................57 2.6.4 Liftoff.............................................................................................58 2.7 Structures in Silicon ..................................................................................59 2.7.1 Bulk Silicon Micromachining.......................................................59 2.7.1.1 Pits, Mesas, Bridges, Beams, and Membranes with KOH........................................................................59 2.7.1.2 Fine Points through Wet and Dry Etching .....................63 2.7.1.3 RIE Pattern Transfer .......................................................64 2.7.1.4 Reflow .............................................................................64 2.7.2 Surface Micromachining ...............................................................64 2.7.3 Electrochemical Etching of Silicon ..............................................67 2.7.4 Porous Silicon................................................................................67 2.7.5 Wafer Bonding...............................................................................67 2.8 Wafer Dicing .............................................................................................68 2.8.1 The Dicing Saw.............................................................................68 2.8.2 Diamond and Laser Scribe............................................................69 2.8.3 Releasing Structures by KOH Etching .........................................70 References ...........................................................................................................72 Chapter 3 Nonsilicon Processes.....................................................................73 3.1 Introduction................................................................................................73 3.2 Chemical–Mechanical Polishing...............................................................73 3.3 LIGA and Electroplating...........................................................................74 DK3182_C000.fm Page xii Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 21. 3.4 Photochemical Machining.........................................................................75 3.5 Laser Machining........................................................................................75 3.5.1 IR Lasers........................................................................................76 3.5.2 Excimer Laser Micromachining....................................................77 3.6 Polymer Microforming..............................................................................79 3.6.1 Polyimides .....................................................................................80 3.6.2 Photoformable Epoxies (SU-8).....................................................80 3.6.3 Parylene and PTFE........................................................................81 3.6.4 Dry Film Resists............................................................................81 3.6.5 Embossing......................................................................................82 3.6.6 PDMS Casting...............................................................................83 3.6.7 Microcontact Printing....................................................................86 3.6.8 Microstereolithography..................................................................87 3.7 Electrical Discharge Machining................................................................89 3.8 Photostructurable Glasses..........................................................................90 3.9 Precision Engineering................................................................................91 3.9.1 Roughness Measurements .............................................................92 3.10 Other Processes .........................................................................................93 References ...........................................................................................................94 Chapter 4 Mask Design..................................................................................95 4.1 Introduction................................................................................................95 4.2 Minimum Feature Size..............................................................................95 4.3 Layout Software ........................................................................................95 4.3.1 File Formats...................................................................................97 4.3.1.1 Technology Files.............................................................98 4.3.1.1.1 Units ...............................................................99 4.3.1.2 Further Caveats .............................................................100 4.3.2 Graphics.......................................................................................100 4.3.3 Grid..............................................................................................101 4.3.4 Text ..............................................................................................101 4.3.5 Other Features .............................................................................102 4.3.6 Manhattan Geometry...................................................................102 4.4 Design......................................................................................................103 4.4.1 The Frame and Alignment Marks...............................................104 4.4.1.1 Scribe Lane ...................................................................104 4.4.1.2 Alignment Marks ..........................................................105 4.4.1.3 Test Structures...............................................................107 4.4.1.4 Layer and Mask Set Identification Marks....................108 4.4.1.5 Putting It All Together ..................................................108 4.4.1.6 Another Way to Place Alignment Marks......................111 4.4.2 The Device...................................................................................111 4.5 Design Rules............................................................................................117 4.5.1 Developing Design Rules............................................................120 DK3182_C000.fm Page xiii Monday, February 13, 2006 10:25 AM Copyright © 2006 Taylor & Francis Group, LLC
- 22. 4.6 Getting the Masks Produced ...................................................................122 4.6.1 Mask Plate Details.......................................................................122 4.6.2 Design File Details......................................................................123 4.6.3 Mask Set Details .........................................................................123 4.6.4 Step and Repeat...........................................................................124 4.6.5 Placement Requirements .............................................................124 4.7 Generating Gerber Files ..........................................................................124 4.8 Mask Design — Key Points....................................................................126 Part II Microsystems .......................................................127 II.1 Introduction..............................................................................................127 II.1.1 Microsystem Components...........................................................128 Chapter 5 Microsensors................................................................................131 5.1 Introduction..............................................................................................131 5.2 Thermal Sensors......................................................................................131 5.2.1 Thermocouples ............................................................................131 5.2.2 Thermoresistors ...........................................................................132 5.2.3 Thermal Flow-Rate Sensors........................................................133 5.3 Radiation Sensors....................................................................................134 5.3.1 Photodiodes..................................................................................134 5.3.2 Phototransistors............................................................................135 5.3.3 Charge-Coupled Devices.............................................................135 5.3.4 Pyroelectric Sensors ....................................................................136 5.4 Magnetic Sensors.....................................................................................137 5.5 Chemical Sensors and Biosensors ..........................................................138 5.5.1 ISFET Sensors.............................................................................138 5.5.2 Enzyme-Based Biosensors ..........................................................140 5.6 Microelectrodes for Neurophysiology ....................................................141 5.7 Mechanical Sensors.................................................................................143 5.7.1 Piezoresistors...............................................................................143 5.7.2 Piezoelectric Sensors...................................................................144 5.7.3 Capacitive Sensors.......................................................................144 5.7.4 Optical Sensors............................................................................145 5.7.5 Resonant Sensors.........................................................................145 5.7.6 Accelerometers ............................................................................146 5.7.7 Pressure Sensors..........................................................................146 Chapter 6 Microactuators.............................................................................147 6.1 Introduction..............................................................................................147 6.2 Electrostatic Actuators.............................................................................147 DK3182_C000.fm Page xiv Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 23. 6.2.1 Comb Drives................................................................................148 6.2.2 Wobble Motors ............................................................................149 6.3 Magnetic Actuators..................................................................................150 6.4 Piezoelectric Actuators............................................................................151 6.5 Thermal Actuators ...................................................................................151 6.6 Hydraulic Actuators.................................................................................152 6.7 Multilayer Bonded Devices.....................................................................153 6.8 Microstimulators......................................................................................153 Chapter 7 Micro Total Analysis Systems.....................................................155 7.1 Introduction..............................................................................................155 7.2 Basic Chemistry.......................................................................................156 7.2.1 Inorganic Chemistry ....................................................................157 7.2.1.1 Bond Formation ............................................................159 7.2.1.2 pH..................................................................................161 7.2.2 Organic Chemistry.......................................................................162 7.2.2.1 Polymers........................................................................164 7.2.2.2 Silicones ........................................................................166 7.2.3 Biochemistry................................................................................167 7.2.3.1 Proteins..........................................................................168 7.2.3.2 Nucleic Acids ................................................................170 7.2.3.3 Lipids.............................................................................172 7.2.3.3.1 Fats ...............................................................173 7.2.3.3.2 Phospholipids ...............................................173 7.2.3.3.3 Cholesterol....................................................174 7.2.3.4 Carbohydrates................................................................175 7.3 Applications of Microengineered Devices in Chemistry and Biochemistry.....................................................................................176 7.3.1 Chemistry.....................................................................................177 7.3.1.1 Synthesis........................................................................177 7.3.1.2 Process and Environmental Monitoring .......................177 7.3.2 Biochemistry................................................................................177 7.3.3 Biology ........................................................................................178 7.3.3.1 Microscopy....................................................................178 7.3.3.2 Radioactive Labeling ....................................................179 7.3.3.3 Chromatography............................................................180 7.3.3.4 Electrophoresis..............................................................181 7.3.3.5 Mass Spectrometry........................................................182 7.3.3.6 X-Ray Crystallography and NMR................................182 7.3.3.7 Other Processes and Advantages ..................................183 7.4 Micro Total Analysis Systems.................................................................183 7.4.1 Microfluidic Chips.......................................................................183 7.4.2 Laminar Flow and Surface Tension ............................................184 7.4.3 Electroosmotic Flow....................................................................185 DK3182_C000.fm Page xv Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 24. 7.4.4 Sample Injection..........................................................................186 7.4.5 Microchannel Electrophoresis.....................................................186 7.4.6 Detection......................................................................................190 7.4.6.1 Laser-Induced Fluorescence (LIF)................................190 7.4.6.1.1 Derivatization ...............................................190 7.4.6.1.2 Advantages and Disadvantages of LIF Detection...........................................190 7.4.6.2 Ultraviolet (UV) Absorbance........................................191 7.4.6.2.1 Advantages and Disadvantages of UV Absorption.........................................191 7.4.6.3 Electrochemical Detection ............................................192 7.4.6.3.1 Cyclic Voltammetry......................................193 7.4.6.3.2 Advantages and Disadvantages of Cyclic Voltammetry .................................194 7.4.6.4 Radioactive Labeling ....................................................194 7.4.6.5 Mass Spectrometry........................................................194 7.4.6.6 Nuclear Magnetic Resonance .......................................195 7.4.6.7 Other Sensors ................................................................195 7.5 DNA Chips ..............................................................................................196 7.5.1 DNA Chip Fabrication ................................................................196 7.6 The Polymerase Chain Reaction (PCR) .................................................197 7.7 Conducting Polymers and Hydrogels .....................................................197 7.7.1 Conducting Polymers ..................................................................198 7.7.2 Hydrogels.....................................................................................198 References .........................................................................................................199 Chapter 8 Integrated Optics .........................................................................201 8.1 Introduction..............................................................................................201 8.2 Waveguides..............................................................................................201 8.2.1 Optical Fiber Waveguides ...........................................................201 8.2.1.1 Fabrication of Optical Fibers........................................202 8.2.2 Planar Waveguides.......................................................................204 8.3 Integrated Optics Components................................................................204 8.4 Fiber Coupling.........................................................................................205 8.5 Other Applications...................................................................................205 8.5.1 Lenses ..........................................................................................205 8.5.2 Displays .......................................................................................206 8.5.3 Fiber-Optic Cross-Point Switches...............................................206 8.5.4 Tunable Optical Cavities.............................................................206 Chapter 9 Assembly and Packaging ............................................................209 9.1 Introduction..............................................................................................209 9.2 Assembly .................................................................................................209 DK3182_C000.fm Page xvi Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 25. 9.2.1 Design for Assembly...................................................................209 9.2.1.1 Auto- or Self-Alignment and Self-Assembly ........................................................210 9.2.1.2 Future Possibilities........................................................211 9.3 Passivation ...............................................................................................211 9.4 Prepackage Testing .................................................................................212 9.5 Packaging.................................................................................................212 9.5.1 Conventional IC Packaging.........................................................213 9.5.2 Multichip Modules ......................................................................214 9.6 Wire Bonding ..........................................................................................214 9.6.1 Thermocompression Bonding .....................................................214 9.6.2 Ultrasonic Bonding......................................................................214 9.6.3 Flip-Chip Bonding.......................................................................215 9.7 Materials for Prototype Assembly and Packaging..................................215 Chapter 10 Nanotechnology..........................................................................217 10.1 Introduction............................................................................................217 10.2 The Scanning Electron Microscope ......................................................217 10.3 Scanning Probe Microscopy..................................................................219 10.3.1 Scanning Tunneling Electron Microscope...............................219 10.3.2 Atomic Force Microscope .......................................................220 10.3.3 Scanning Near-Field Optical Microscope ...............................221 10.3.4 Scanning Probe Microscope: Control of the Stage.................................................................221 10.3.5 Artifacts and Calibration..........................................................221 10.4 Nanoelectromechanical Systems ...........................................................222 10.4.1 Nanolithography.......................................................................222 10.4.1.1 UV Photolithography for Nanostructures.........................................................222 10.4.1.1.1 Phase-Shift Masks................................223 10.4.1.2 SPM “Pens”.............................................................224 10.4.2 Silicon Micromachining and Nanostructures ..........................224 10.4.3 Ion-Beam Milling.....................................................................225 10.5 Langmuir–Blodgett Films......................................................................227 10.6 Bionanotechnology ................................................................................228 10.6.1 Cell Membranes .......................................................................229 10.6.2 The Cytoskeleton .....................................................................230 10.6.3 Molecular Motors.....................................................................230 10.6.4 DNA-Associated Molecular Machines....................................232 10.6.5 Protein and DNA Engineering.................................................233 10.7 Molecular Nanotechnology....................................................................233 10.7.1 Buckminsterfullerene ...............................................................234 10.7.2 Dendrimers...............................................................................234 References .........................................................................................................235 DK3182_C000.fm Page xvii Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 26. Part III Interfacing ...........................................................237 III.1 Introduction..............................................................................................237 References .........................................................................................................238 Chapter 11 Amplifiers and Filtering..............................................................239 11.1 Introduction............................................................................................239 11.1.1 Quick Introduction to Electronics............................................239 11.1.1.1 Voltage and Current Conventions ...........................239 11.1.1.2 The Ideal Conductor and Insulator .........................241 11.1.1.3 The Ideal Resistor ...................................................241 11.1.1.4 The Ideal Capacitor.................................................242 11.1.1.5 The Ideal Inductor...................................................242 11.1.1.6 The Ideal Voltage Source ........................................243 11.1.1.7 The Ideal Current Source........................................243 11.1.1.8 Controlled Sources ..................................................243 11.1.1.9 Power Calculations..................................................244 11.1.1.9.1 Switching Losses..................................244 11.1.1.10 Components in Series and Parallel .........................245 11.1.1.11 Kirchoff’s Laws.......................................................246 11.2 Op-Amp .................................................................................................247 11.2.1 The Ideal Op-Amp...................................................................248 11.2.1.1 Nonideal Sources, Inverting, and Noninverting Op-Amp Configurations..........................................251 11.2.2 Nonideal Op-Amps ..................................................................253 11.2.2.1 Bandwidth Limitations and Slew Rate ...................254 11.2.2.2 Input Impedance and Bias Currents........................255 11.2.2.3 Common-Mode Rejection Ratio and Power Supply Rejection Ratio ...........................................256 11.2.3 Noise.........................................................................................257 11.2.3.1 Combining White Noise Sources............................257 11.2.3.2 Thermal Noise .........................................................258 11.2.4 Op-Amp Applications ..............................................................258 11.2.4.1 The Unity-Gain Buffer Amplifier ...........................258 11.2.4.2 AC-Coupled Amplifiers...........................................260 11.2.4.3 Summing Amplifiers................................................261 11.2.4.4 Integrators and Differentiators ................................261 11.2.4.5 Other Functions .......................................................263 11.3 Instrumentation Amplifiers ....................................................................263 11.4 Wheatstone Bridge.................................................................................265 11.4.1 The Capacitor Bridge...............................................................266 11.5 Filtering..................................................................................................268 11.5.1 RC Filters.................................................................................268 DK3182_C000.fm Page xviii Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 27. 11.5.2 Butterworth Filters ...................................................................273 11.5.2.1 Synthesizing Butterworth Active Filters.................276 11.5.2.2 Approximating the Frequency Response of a Butterworth Filter ............................................278 11.5.3 Switched-Capacitor Filters.......................................................279 References .........................................................................................................280 Chapter 12 Computer Interfacing ..................................................................281 12.1 Introduction............................................................................................281 12.1.1 Number Representation............................................................281 12.2 Driving Analog Devices from Digital Sources .....................................282 12.2.1 Pulse-Width Modulation (PWM).............................................283 12.2.1.1 Estimating the PWM Frequency.............................284 12.2.1.2 Digital Implementation and Quantization...............285 12.2.1.3 Reproducing Complex Signals with PWM.............286 12.2.2 R-2R Ladder Digital-to-Analog Converter (DAC)..................286 12.2.3 Current Output DAC................................................................287 12.2.4 Reproducing Complex Signals with Voltage Output DACs............................................................................288 12.3 Analog-to-Digital Convearsion..............................................................288 12.3.1 Sample Raate ...........................................................................289 12.3.1.1 Antialiasing Filters ..................................................290 12.3.2 Resolution.................................................................................290 12.3.3 Signal Reconstruction: Sampling Rate and Resolution Effects.............................................................291 12.3.4 Other ADC Errors....................................................................292 12.3.4.1 Missing Codes .........................................................292 12.3.4.2 Full-Scale Error .......................................................292 12.3.5 Companding .............................................................................292 12.4 Analog-to-Digital Converters ................................................................292 12.4.1 Sample-and-Hold Circuit .........................................................293 12.4.2 PWM Output ADCs.................................................................293 12.4.2.1 Integrating ADC ......................................................293 12.4.2.2 Conversion Time......................................................294 12.4.3 Successive Approximation.......................................................294 12.4.4 Flash ADC................................................................................295 12.4.5 Sigma-Delta Converter.............................................................295 12.5 Converter Summary ...............................................................................296 References .........................................................................................................296 Chapter 13 Output Drivers.............................................................................297 13.1 Introduction............................................................................................297 13.2 Controlling Currents and Voltages with Op-Amps...............................297 13.2.1 Op-Amp Current Control.........................................................297 DK3182_C000.fm Page xix Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 28. 13.2.1.1 Four-Electrode Configuration..................................298 13.2.2 Op-Amp Voltage Control.........................................................299 13.3 Transistors..............................................................................................300 13.3.1 The BJT....................................................................................300 13.3.2 The MOSFET...........................................................................303 13.4 Relays.....................................................................................................306 13.4.1 Relay Characteristics................................................................307 13.4.2 Relay Types..............................................................................307 13.5 BJT Output Boost for Op-Amps ...........................................................308 13.6 Optoisolators ..........................................................................................309 DK3182_C000.fm Page xx Thursday, February 2, 2006 4:41 PM Copyright © 2006 Taylor & Francis Group, LLC
- 29. 1 Part I Micromachining I.1. INTRODUCTION I.1.1 WHAT IS MICROENGINEERING? Microengineering and Microelectromechanical systems (MEMS) have very few watertight definitions regarding their subjects and technologies. Microengineering can be described as the techniques, technologies, and practices involved in the realization of structures and devices with dimensions on the order of micrometers. MEMS often refer to mechanical devices with dimensions on the order of micrometers fabricated using techniques originating in the integrated circuit (IC) industry, with emphasis on silicon-based structures and integrated microelectronic circuitry. However, the term is now used to refer to a much wider range of microengineered devices and technologies. There are other terms in common use that cover the same subject with slightly different emphasis. Microsystems technology (MST) is a term that is commonly used in Europe. The emphasis tends towards the development of systems, and the use of different technologies to fabricate components that are then combined into a system or device is more of a feature of MST than MEMS, where the emphasis tends towards silicon technologies. In Japan, particularly, the term micromachines is employed. There is a ten- dency toward miniaturization of machines, with less emphasis on the technologies or materials employed. This should not be confused with micromachining, the processes of fabricating microdevices. The most rigorous definition available was proposed by the British govern- ment, which defined the term microengineering as working to micrometer tolerances. An analogous definition for nanotechnology was advanced. Although these definitions can be used effectively for policy setting, for exam- ple, they tend to lead to some anomalies: very large precision-engineered components that one would not normally consider to be MEMS were being classified as such. For this reason, the definition tends to be used with qualifi- cations in technical literature. DK3182_S001.fm Page 1 Friday, January 13, 2006 11:03 AM Copyright © 2006 Taylor & Francis Group, LLC
- 30. 2 Microengineering, MEMS, and Interfacing: A Practical Guide This volume will attempt to standardize the definitions for this technology given in the glossary for microengineering and MEMS: Microengineering: The techniques, technologies, and practices involved in the realization of structures and devices with dimensions on the order of micrometers MEMS: Microengineered devices that convert between electrical and any other form of energy and rely principally on their three-dimensional mechanical structure for their operation In this way, microengineering is a very broad term, as one may expect. It not only covers MEMS but also IC fabrication and more conventional microelectron- ics. As a rule of thumb, devices in which most of the features (gap or line width, step height, etc.) are at or below 100 µm fulfill the “dimensions in the order of micrometers” criteria. The definition of MEMS as transducers means that the term can be used a little more generally than other definitions would allow. For instance, infrared displays that use suspended structures to thermally isolate each pixel fit nicely into this definition as their operation relies on the three-dimensional suspended structure even though there is no moving mechanical element to the device. It does, however, exclude devices such as Hall effect sensors or photodiodes, which rely principally on their electrical (or chemical) structure for their oper- ation. It also tends to exclude semiconductor lasers for similar reasons, and components such as power MOSFET transistors that are formed by etching V grooves into the silicon substrate are also excluded as they are purely electrical devices. Once one is happy with the term microengineering, one can create all the relevant subdisciplines that one requires simply by taking the conventional dis- cipline name and adding the prefix micro to it. Thus, we have microfluidics, micromechanics, microlithography, micromachining, etc., and, of course, micro- electronics. This flippant comment does not mean that these disciplines are simply the macroscale discipline with smaller numbers entered into the equations. In many cases this can be done, but in others this can cause erroneous results. It is intended to point out that there are relatively few surprises in the nomenclature. At this point, it is worth highlighting the difference between science and engineering as it is of considerable import to the microengineer. Science aims to understand the universe and build a body of knowledge that describes how the universe operates. Engineering is the practical application of science to the benefit of humankind. The description of the universe compiled by scientists is often so complex that it is too unwieldy to be practically applied. Engineers, therefore, take more convenient chunks of this knowledge that apply to the situation with which they are concerned. Specifically, engineers employ models that are limited. For example, when calculating the trajectory of a thrown ball, Newton’s laws of motion would normally be used, and no one would bother to consider how Einstein’s relativity would affect the trajectory: the ball is unlikely to be traveling DK3182_S001.fm Page 2 Friday, January 13, 2006 11:03 AM Copyright © 2006 Taylor & Francis Group, LLC
- 31. Micromachining 3 at a relativistic speed where a significant effect may be expected (a substantial fraction of the speed of light). A good engineering course teaches not only the models that the student needs to employ, and how to employ them, but also the limitations of those models. The knowledge that models are limited is of significance in microengineering because the discipline is still compiling a family of models and list of pitfalls. Despite the vast body of literature on the subject, there is still far more anecdotal knowledge available than written information. This is evidenced by the substantial traffic that MEMS mailing lists and discussion groups receive. There is only so much that can be achieved by reading and modeling, and even a little experience of the practice is of great benefit. I.1.2 WHY IS MICROENGINEERING IMPORTANT? The inspiration for nanotechnology, particularly molecular nanotechnology, is usu- ally traced back to Richard Feynman’s presentation entitled “There’s Plenty of Room at the Bottom” in 1959 [1]. A few people cite this presentation as the inspiration for the field of microengineering, but it is more likely that it was the seminal paper by Kurt Petersen, “Silicon as a Mechanical Material,” published in 1982 [2]. The micromachining of silicon for purposes other than the creation of elec- tronic components was certainly being carried out at least a decade before Petersen published this work, which compiled a variety of disparate threads and technologies into something that was starting to look like a new technology. Not only was silicon micromachining in existence at this time, but many of the other techniques that will be discussed in later chapters of this volume were also being used for specialized precision engineering work. However, despite the appearance of some early devices, it was not until the end of that decade that commercial exploitation of microengineering, as evidenced by the number of patents issued [3], started to take off. At the beginning of the 1990s, microengineering was presented as a revolu- tionary technology that would have as great an impact as the microchip. It promised miniaturized intelligent devices that would offer unprecedented accu- racy and resolution and negligible power consumption. Batch fabrication would provide us with these devices at negligible costs: few dollars, or even just a few cents, for a silicon chip. The technology would permeate all areas of life: the more adventurous projects proposed micromachines that would enter the blood- stream and effect repairs, or examine the interior of nuclear reactors in minute detail for the telltale signs of impending failure. As with many emerging tech- nologies, some of the early predictions were wildly optimistic. Although some of the adventurous projects proposed during this period remain inspirational for technological development, the market has tended to be dominated by a few applications — notably IT applications such as inkjet printer heads and hard disk drive read–write heads. Pressure measurement appears next on the list; some may intuitively feel that these devices, rather than inkjet printer heads, are more in tune with the spirit of microengineering. DK3182_S001.fm Page 3 Friday, January 13, 2006 11:03 AM Copyright © 2006 Taylor & Francis Group, LLC
- 32. 4 Microengineering, MEMS, and Interfacing: A Practical Guide Nonetheless, microengineered devices have significant advantages and poten- tial advantages over other solutions. Although the road to mass production and low-cost devices is long and expensive, the destination can be reached; examine, for example, the plethora of mass-produced silicon accelerometers and pressure sensors. Beyond the direct advantages of miniaturization, integrating more intel- ligence into a single component brings with it improved reliability: the fewer components that need to be assembled into a system, the less chance there is that it can go wrong. One great advantage of microengineering is that new tools providing solutions to problems that have never been addressed before are still to be fully exploited. The technology is still relatively new, and innovative think- ing can potentially bring some startling results. There is, however, a reason for the aforementioned cautious historical pre- amble: market surveys are often conducted by groups with a particular interest in the technology or by those interested in showing the economy in a positive light. Evidence is often collected from people working in the field or companies that have invested a lot of R&D dollars into the technology. The preamble thus sets the following data in context. It is undeniable that microengineering has had a substantial impact beyond disk drives and printers. The sensors and transducers section of any commercial electronics catalog reveals a dozen or so microengineered devices including accelerometers, air-mass-flow sensors, and pressure transducers. (Surprisingly, however, the electronics engineer may not be aware of the technological advances that have gone into these devices). The molecular biologist cannot help but be aware of the plethora of DNA chip technologies, and the material scientist cannot have missed the micromachined atomic force microscope (AFM) probe. In the mid 1990s a number of different organizations compiled market growth projections for the following few years. These were conveniently collected and summarized by Detlefs and Pisano [3]. The European NEXUS (Network of Excellence for Multifunctional Microsystems) has been particularly active in this respect, publishing a report in 1998 [4] with a follow-up study appearing in 2002 [5]. Also, in 2002, the U.S.-based MEMS Industry Group published its own report [6]. The absolute numbers for the global market in such reports vary depending on how that market is defined. The NEXUS task force included all products with a MEMS component, whereas the other groups only considered the individual components themselves. The NEXUS 2002 report estimated the world market to MEMS Advantages • Suitable for high-volume and low-cost production • Reduced size, mass, and power consumption • High functionality • Improved reliability • Novel solutions and new applications DK3182_S001.fm Page 4 Friday, January 13, 2006 11:03 AM Copyright © 2006 Taylor & Francis Group, LLC
- 33. Micromachining 5 have been worth approximately $30 billions in 2000, whereas the U.S.-based MEMS Industry Group estimated it to be in the region of $2 billions to $5 billions. From the published summaries, it would appear that a growth of 20% per annum would be a conservative estimate for the coming few years. It should be noted, however, that many of these estimates are based on the highly volatile optical communications and IT markets, where optical MEMS in particular are expected to make a significant impact. Detlefs and Pisano highlight microfluidics and RF MEMS, apart from optical MEMS, as having significant potential for growth. This being in contrast to the 10 to 20% growth that they ascribe to more established microengineered sensors (pressure, acceleration, etc.). This assessment is in concordance with the NEXUS 2002 findings, where IT peripherals and biomedical areas are identified as having the most significant growth potential. I.1.3 HOW CAN I MAKE MONEY OUT OF MICROENGINEERING? This is not a book that intends to give financial business or other moneymaking advice. It was inspired, in part at least, by the recognition that there is a growing market and opportunities for microengineered products, and in order to exploit these it is necessary to have some understanding of the technology. This book deals with the technologies involved in microengineering, so pithy observations about their potential exploitation are restricted to the introduction. Firstly, nearly all the processes involved in micromachining involve a signif- icant capital outlay in terms of clean rooms, processing equipment, and hazardous chemicals. In the past this has restricted novel developments to those that had or could afford the facilities or to those using lower-cost micromachining technol- ogies. Multiproject processes, where designs from several different groups are fabricated on the same substrate (wafer) using the same process, are now avail- able. This cuts the cost, but limits you to a specific fabrication sequence. One other option, if you happen to be in an area with a high density of small (R&D) clean room facilities, is to try out your designs by shipping your batch of wafers to as many laboratories as possible. R&D, however, has not tended to be the bottleneck in commercial exploita- tion. The main bottleneck has been in scaling up from prototype volumes to mass production volumes. Much of the processing equipment is quite idiosyncratic and needs to be characterized and monitored to ensure that the vast majority of the devices coming off the line meet the specifications (process monitoring). Furthermore, parameters that are required for good electrical performance may result in undesirable mechanical characteristics. In short, it is highly likely that Microengineering and Money • Global market of billions of dollars • 20% annual growth rate to 2005 • Significant areas: IT, optical and RF components, and microfluidics DK3182_S001.fm Page 5 Friday, January 13, 2006 11:03 AM Copyright © 2006 Taylor & Francis Group, LLC
- 34. 6 Microengineering, MEMS, and Interfacing: A Practical Guide a new line will have to be set up and characterized for the product, and unlike IC foundries, it is difficult to adapt the line for the production of different devices. Additionally, if a silicon device is required with integrated electronic circuitry, the micromachining and circuit fabrication processes must be fully compatible and may be intertwined. If you are really serious about getting your microengineered device into the market, and have the money to set up a fabrication facility (fab), one of your best options is probably to work with a company (or organization) that has its own facility and is willing to work with others (a MEMS foundry). Usually these will be companies that already produce a few microengineered products of their own, rather than companies set up for the sole purpose of providing micromachining facilities to other parties. At the time of publication, there were a few (but a growing number of) these companies that were genuinely willing to collaborate in product development. Even if you have your own small R&D facility and are serious about producing marketable devices, it would probably be a good idea to find a few of these companies at an early stage in development and align your R&D with their processes. Also, make use of their expertise — this will almost certainly save you a lot of headaches. Packaging is another area that has often been neglected during device R&D. Most microengineered devices will need to interface with the outside world in a way beyond the simple electrical connections of integrated circuits. This will typically require the development of some specialized packages with appropriate tubes, ports, or lenses. The device itself will be exposed to the environment, which can contain all sorts of nasty surprises that are not found within a research laboratory. These surprises include obvious problems, such as dust, bubbles, or other contaminants in microfluidic systems, and the less obvious problems, such as air (many resonant devices are first tested in an electron microscope under vacuum — air can damp them sufficiently to prevent their working and packaging devices under vacuum can be problematical). Other unexpected problems include mechanical or other interactions with the package. Differential coefficients of thermal expansion between device and package can put transducers under strain, leading to erroneous results. Once again, resonant sensors are particularly sensi- tive to the mechanical properties of the package and to the mounting of dies within it. Exploitation Problems • Large initial capital outlay • Process monitoring • Potential incompatibility with integrated microelectronics • Dedicated foundries • Packaging • Is there a market for this product? DK3182_S001.fm Page 6 Friday, January 13, 2006 11:03 AM Copyright © 2006 Taylor & Francis Group, LLC
- 35. Micromachining 7 Packaging and associated assembly stages are easily the most expensive of any fabrication process. At this stage, each die must be handled individually, as opposed to a hundred or more devices on each wafer during the earlier micro- machining stages. Thus, the time spent handling individual dies should be kept to a minimum and automated as much as possible. A thing to note is that although mass production of microengineered devices can potentially reduce their cost, the amount of R&D effort involved will probably make it necessary to sell early versions at a premium in order to recover costs. It pays, therefore, to be well aware of your market before investing in R&D. The ideal thing to do is treat a microengineering technology as any other technology: first identify the problem and then select the most appropriate tech- nology to solve it. Of course, identifying the most appropriate technology does assume awareness of the technologies that are available. REFERENCES 1. Feynman, R., There’s Plenty of Room at the Bottom: An Invitation to Enter a New Field of Physics, presentation given on 29 December 1959 at the annual meeting of the APS at Caltech. 2. Petersen, K., Silicon as a mechanical material, Proc. IEEE, 70(5), 427–457, 1982. 3. Detlefs and Pisano, US MEMS Review, 5th World Micromachine Summit, 1999. 4. NEXUS! Task Force, Market Analysis for Microsystems 1996–2002, October 1998. The document can be ordered from the NEXUS web site, www.nexus- emsto.com, and an executive summary is freely available. 5. Wechsung, R., Market Analysis for Microsystems 2000–2005 — A Report from the NEXUS Task Force, summary in MST News, April 2002, 43–44. 6. MEMS Industry Group report released at MEMS 2002, Las Vegas. A brief sum- mary can be found at Small Times: J Fried, MEMS Market Continues to Grow, Says Industry Group’s New Report, January 21, 2002. www.smalltimes.com/ document_display.cfm?document_id=2949. Incorporating Microengineering into Your Business • Develop a novel solution to a new existing problem or gap in the market. • Develop new products to complement your existing product line or as upgrades. • Gain competitive advantage by incorporating new technology into your products. • Gain competitive advantage by using the new technology in new- product development. DK3182_S001.fm Page 7 Friday, January 13, 2006 11:03 AM Copyright © 2006 Taylor & Francis Group, LLC
- 36. 9 1 Photolithography 1.1 INTRODUCTION The fundamental aim of microengineering — to take a design from a computer aided design (CAD) software package and manifest it in a physical manner — may be achieved through one of a number of different fabrication or micromachining technologies. Many of these technologies employ a process known generally as photolithography, or a variation of this process, to transfer a two-dimensional pattern from a mask into the structural material. The mask is created from the data held by the CAD package, and the structure is built up by a series of steps that involve the deposition (addition of material to the structure) and etching (removing material from the structure) of patterned layers. The term photolithography refers to a process that uses light or optical techniques to transfer the pattern from the mask to the structural material. Typ- ically, it will refer to a process that employs ultraviolet (UV) light, but it may informally be employed to refer to other lithographic processes or lithography, generally, within the context of microelectromechanical systems (MEMS) and micromachining. Other processes may employ electrons or x-rays. The purpose of this chapter is to introduce the common forms of lithography, focusing on UV photolithography. Electron-beam (e-beam) and x-ray lithography, as well as some key design matters and processes related to photolithography, are introduced. This chapter is complemented by the matters discussed in Chapter 4 pertaining to mask design. Features of Photolithography for MEMS There are a number of features common in MEMS fabrication processes but that are not as common in integrated circuit (IC) fabrication; these are: • Nonplanar substrate (i.e., relatively large three-dimensional features, such as pits) • The use of thick resist layers (for structural purposes or for long etching times) • Relatively high-aspect-ratio structures (in resists as well as sub- strates) • Relatively large feature sizes (cf. IC processes) • Unusual processing steps • Unusual materials (particularly important in terms of adhesion) DK3182_C001.fm Page 9 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 37. 10 Microengineering, MEMS, and Interfacing: A Practical Guide 1.2 UV PHOTOLITHOGRAPHY UV photolithography is the workhorse of many micromachining processes and nearly all semiconductor IC manufacturing processes. With the continual demand for reduced transistor sizes and line widths from IC designers and manufacturers, UV lithography is being pushed to its physical limit to achieve features (line widths or gaps) with submicrometer dimensions. Generally, MEMS employ relatively large structures with dimensions ranging from a few micrometers to about 100 µm. Therefore, the techniques required to produce such small dimensions will not be mentioned here but will be touched on in Part III of this volume. The basic principle of photolithography is illustrated in Figure 1.1. The aim is to transfer a two-dimensional pattern that is formed on a mask (aka reticle, especially when exposure systems are discussed) into a three-dimensional or two- and-a-half-dimensional pattern in a structural material. The description “two-and- a-half-dimensional” is used because, as you will see, although it is possible to produce structures with complex curves in the xy plane, many micromachining techniques only provide limited control of shapes in the vertical z dimension. In the example in Figure 1.1, a thin film of silicon dioxide has been deposited on the surface of a silicon wafer. It is desired that this film be selectively removed FIGURE 1.1 Basic principle of photolithography (not to scale): (a) silicon substrate with oxide coating, (b) photoresist spun on, (c) exposed to UV light through mask, (d) devel- oped, (e) etching of underlying film, (f) photoresist stripped, leaving patterned film. Positive resist. Negative resist. (a) (b) (c) (d) (e) (f) DK3182_C001.fm Page 10 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 38. Photolithography 11 from certain areas of the wafer to expose the underlying silicon. To do this, a mask is produced. This will typically be a chromium pattern on a glass (quartz) plate, chromium being opaque to UV light and quartz being transparent. The wafer is cleaned and coated with a material that is sensitive to UV light, known as photoresist. The photoresist is exposed to UV light through the mask and then developed, transferring the pattern from the mask into the photoresist. There are two basic types of photoresists: positive resists and negative resists. (These are also known, respectively, as light-field resists and dark-field resists, although this terminology can cause some confusion when several different fab- rication facilities are involved in one process.) With positive resists, the chemical bonds within the resist are weakened when exposed to UV light, whereas they are strengthened in negative resists. As a result, after developing, positive resists take up a positive image of the mask (the resist remains on the mask where the chrome was) and negative resists take up a negative image, as seen in Figure 1.1. The next step involves the selective removal of the silicon dioxide film, through an etching process. A typical example would be to immerse the wafer in a bath of hydrofluoric acid. This will react with the exposed silicon dioxide, but not that protected by the photoresist, which is, as its name implies, resistant to chemical attack by the acid. Once the thin film of silicon dioxide has been etched through, the unwanted photoresist is removed with a solvent, leaving the wafer with the patterned silicon dioxide layer. 1.2.1 UV EXPOSURE SYSTEMS The structural dimensions that can be achieved in a photolithographic process are related to the wavelength of the light employed. When light is incident upon a narrow aperture, it will be diffracted. As the dimensions of the aperture approach the wavelength of the incident light, this diffraction becomes significant. Therefore, for smaller structures, smaller-wavelength light must be used. UV light has therefore been one of the most convenient forms of illumination to employ in photolithography. It conveniently interacts with chemical bonds in various compounds, is relatively easily generated (at longer wavelengths, at least), and has a relatively small wavelength compared to visible or infrared light Terminology Photoetching and photoengraving are terms that have also been used to refer to photolithographic processes, although they are not commonly used today. Although photolithography strictly refers to a process that involves light (pho- tons), it is sometimes used in casual conversation to refer to the general sweep of lithographic processes. It would be more correct to use the terms microli- thography, nanolithography, or simply lithography (or lithographic) in such cases. The term lithography itself refers to printing from a design onto a flat surface. In addition to UV photolithography, x-ray lithography and e-beam lithography will also be discussed. DK3182_C001.fm Page 11 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 39. 12 Microengineering, MEMS, and Interfacing: A Practical Guide (from about 400 nm down to 10 nm, where it merges into the soft x-ray region of the spectrum). Also, in the upper reaches of the UV spectrum, optics can be relatively easily fabricated from quartz. UV wavelengths from 426 nm down to about 248 nm are fairly common. 1.2.1.1 Mask Aligners Microstructures are typically built up through a series of steps in which thin films of materials are deposited and selectively etched (patterned), each photolithographic step, i.e., each pattern, requiring a different mask and each pattern having to be precisely aligned to the preceding ones. Alignment marks are placed on each layer of the design in an out-of-the-way area of the mask (i.e., somewhere where they can easily be found and can fulfill their function but will not interfere with the function of the finished device). The mask aligner is the tool used to align the marks on the mask with those existing on the substrate in order to ensure accurate registration of each layer of the design with the others, as well as to expose the photoresist through the mask to UV light. Exposure may be through a contact aligner or a step-and-repeat system. The contact mask aligner is the system most commonly used in microma- chining processes because they do not normally need the very small feature sizes that can be achieved at greater expense and complexity by step-and-repeat sys- tems. For the contact alignment system, the mask is produced at a 1:1 scale to the finished design. This will invariably be a single large mask plate with many, usually several hundred, individual chip designs on it. The photoresist-coated substrate (silicon wafer, glass sheet, or whatever is being micromachined) is placed in the aligner and adjusted so that the alignment marks can be located within the viewer. The mask is introduced into the machine, and the chrome-patterned face is brought into close approximation with the photoresist-coated face of the substrate, typically only micrometers apart. The alignment marks on the mask are located, and the position of the mask is adjusted so that they register with the alignment marks etched into the substrate. The mask is then brought into contact with the substrate, final alignment is checked, and the photoresist is then exposed to a pulse of UV light. The main advantage of contact photolithography is that relatively inexpensive mask aligners and optics are required. Furthermore, the entire area of the substrate is exposed in a single exposure. One advantage of micromachining is that a number of different devices, or different versions of one device, can be placed on the same mask for fabrication on the same substrate. This is of considerable assistance, as MEMS require far more trial-and-error experiments than micro- electronic circuits. Another advantage of micromachining is that the process of aligning both sides of the substrate (front and back) is a little easier; specialist double-sided alignment tools are also available. Double-sided alignment, in which micromachining is performed on both sides of a flat silicon substrate, is one feature of MEMS fabrication that is not used in conventional IC manufacture. Contact photolithography suffers more from wear and tear of the masks than does step-and-repeat, which uses a projection system to reduce the image of the mask on the substrate. Additionally, any small damage or irregularities on the DK3182_C001.fm Page 12 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 40. Photolithography 13 mask are reproduced in the developed photoresist structure. Although the single exposure tends to reduce the time required for photolithography, the UV intensity across the substrate may not be uniform if the system is not set up correctly. In this case, the developed image in the photoresist will not be different across the wafer, and the process yield will be affected. Finally, one does not have the option of using grayscale masks when employing contact lithographic techniques. The wear and tear of masks can be reduced by using contact alignment’s close relation, proximity alignment (or proximity printing). This proceeds in almost exactly the same manner as contact alignment, except that the mask is held at a very small distance from the photoresist. In consequence, the achievable minimum feature size is less than that possible with contact alignment methods. Contact photolithography is contrasted with the step-and-repeat process in Figure 1.2. Note that the mask face bearing the chrome pattern is the one that is brought into contact with the photoresist during contact lithography. The mask plate itself is relatively thick, typically, a few millimeters. If the chrome were not A Quick Way to Calibrate the Exposure Time in Your Contact Aligner This method is especially useful when trying out an old system for experi- mental purposes or trying out new resists, but not of much use if you hit problems with a calibrated setup. Work out the likely minimum and maximum exposure times. Then, subtract a bit from the one, and add a bit to the other. Apply resist to a spare wafer. Now, take a suitable mask with a slot in it (it need not be a quartz mask, but just something that will fit in the aligner). Starting at one end of the wafer (near a flat would be a good idea), put your makeshift mask in and expose it for your minimum exposure time. Now, move the strip up a bit and expose for a little longer (making sure that you note down each exposure time used and any other relevant settings). Repeat. Now, develop and examine the results under a microscope. This is not going to get you very high quality results but may be sufficient to get you started if you are just trying things out. FIGURE 1.2 (a) Contact printing exposes the entire wafer at once, whereas (b) in projection printing a single mask holds the pattern for a single device. This is reduced and projected onto the coated wafer, which is stepped beneath it and receives a series of exposures. y x (b) (a) DK3182_C001.fm Page 13 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 41. 14 Microengineering, MEMS, and Interfacing: A Practical Guide directly in contact with the photoresist, the optical effects due to the passage of UV light through the glass plate, divergence of the source, etc., would reduce the quality of the image formed in the resist. The step-and-repeat approach involves the use of a mask that bears a larger image of the desired pattern — usually the design for only one chip. This is placed in an optical system that reduces and projects an image of the mask onto the substrate. After each exposure, the substrate is moved (stepped) to expose the next section. Reduction will typically be a factor of about ten. In this case, note that a 1-µm blemish in the mask pattern will be reduced to a 0.1-µm blemish in the photoresist when using the step-and-repeat system but will remain as a 1-µm structure if a contact system is used. The step-and-repeat system’s main strength is that it can be used to produce devices with smaller feature sizes than in the case of the contact approach, mainly due to the advantages provided by the projection system. First, because the mask is made at a larger scale than that of the structure to be produced, it does not necessarily need to be made using a very-high-resolution technique. That is, for contact lithography with a 1-µm minimum structural feature size, the mask would have to be made using a process capable of producing 0.1-µm, or better, features in order to get a reasonable reproduction. If the same structure were to be created using a mask for 10:1 reduction in a projection system, then the minimum structural feature on the mask would be of 10-µm size.A process with better than a 1-µm minimum feature size would produce a result of the same quality as would the contact mask made using the 0.1-µm process. Furthermore, this gives the designer a chance to control the intensity of the UV light to specific areas of the photoresist which are exposed by creating grayscale masks (Figure 1.3). These essentially incorporate meshes of small apertures in the mask design, such that when the image is reduced, the image of the aperture is beyond the resolving capacity of the photolithographic system. Thus, instead of producing a series of islands or gaps in the imaged photoresist, a reduction in the average intensity of the UV light over the area in proportion to the relative opaque area of the mask is seen. The exact implications of this and the use it can be put FIGURE 1.3 An example of a grayscale mask. If the openings in the mask are sufficiently small, a variation in intensity rather than distinct lines will be produced when UV light is projected onto the substrate through reducing optics. Intensity DK3182_C001.fm Page 14 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 42. Photolithography 15 to depend on the chemistry and nature of the photoresist or the lithography system. Table 1.1 summarizes the features of contact and projection lithography systems. 1.2.1.2 UV Light Sources For most micromachining processes involving contact lithography, the UV light source will be a broad-spectrum mercury arc lamp with a filter placed to restrict illumination to one of the spectral lines (i or g). Photoresist manufacturers supply data sheets that provide information about recommended exposure times and wavelengths. Note that whereas some resists must be exposed to light within a fairly strict spectrum in order to function correctly, others are available that also work outside the range of UV wavelengths commonly used. For very small feature sizes, in particular, the submicrometer feature sizes typical of the most advanced IC technologies in use today, the excimer laser is used as the UV source. This is a UV laser with a torch-like beam. This means that it has to be employed in step-and-repeat processes as it cannot be used to illuminate the entire substrate at once. The excimer laser has its own place in micromachining and is discussed in more detail in Chapter 3. Photoresists and photolithography systems are commonly referenced by the nature of the UV source: g-line, the 436-nm band of the mercury arc lamp, i line, the 365-nm band, and deep ultraviolet (DUV) at 248-nm and 193-nm wave- lengths, in which excimer laser sources are preferred (Table 1.2). 1.2.1.3 Optical Systems The resolution of an optical system is generally determined by considering its ability to distinguish between two point sources of light [1,2,3]. This work by Rayleigh in the 19th century gave rise to the Rayleigh criterion. Roughly stated, the minimum resolved distance between two peaks depends on the wavelength of light and the numerical aperture of the focusing optics: (1.1) TABLE 1.1 Advantages and Disadvantages of Contact and Projection Systems Contact vs. Projection Lithography Systems Contact Projection Single exposure Multiple devices per wafer Double-sided alignment Low cost More uniform light intensity Small feature sizes Grayscale masks Longer mask life d NA = 0 61 . λ DK3182_C001.fm Page 15 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 43. 16 Microengineering, MEMS, and Interfacing: A Practical Guide Where λ is the wavelength of the light, and NA the numerical aperture of the lens. This equation was derived from optical considerations alone and based on a consideration of point light sources. In photolithography, the achievable resolution (minimum feature size) is also related to other aspects, such as the chemistry of the photoresist. Additionally, one is generally more interested in lines than point sources. Considerations for contact, proximity, and projection systems are outlined in the following subsections. Also of interest is the depth of focus, the distance along the optical axis over which the optics produce an image of suitable quality. The Rayleigh criterion for depth of focus gives [1,2]: (1.2) As with considerations of resolution, this pure equation is not directly applicable to photolithography. 1.2.1.3.1 Contact and Proximity Printing In contact and proximity printing, the optical limits to minimum feature sizes are due primarily to diffraction effects. In this case, the mathematics analyzes the image of a slit in a grating. This gives rise to a resolution related to the wavelength of light and the separation, s, between the mask plate and the substrate [2,4]: (1.3) In practice, because of the dependence on process parameters, this is normally written as: (1.4) where k3 is empirically derived for the process and facility. Peckerar et al. give a practical value of k3 as 1.6, whereas Reche suggests that it can be as low as 1.5. TABLE 1.2 UV Sources and Wavelengths Wavelength (nm) Source Region of Spectrum 436 Mercury arc lamp g line 405 Mercury arc lamp h line 365 Mercury arc lamp i line 248 Mercury arc lamp or Excimer laser Deep ultraviolet 193 Excimer laser δ λ = 0 35 2 . NA d s = 1 4 . λ d k s = 3 λ DK3182_C001.fm Page 16 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 44. Photolithography 17 In the case of contact printing, the distance s will be half the thickness of the photoresist. Note that this can be quite substantial in micromachining applications (tens of micrometers) and that raised and indented micromachined features can mean that the surface of the resist may be considerably more rippled or featured than one normally finds. In the case of proximity printing, one may assume that the distance between mask and substrate is significantly greater than the thickness of the resist, so s will take this value, and the thickness of the resist may be neglected. Once again, beware of assumptions that may be invalidated by the unusual nature of MEMS processing. As mentioned previously, one of the advantages of contact or proximity printing is that the entire area of the substrate can be exposed in a single-process step. Unfortunately UV sources such as the mercury arc lamp appear somewhat point-like. These, therefore, require special optics to expand and homogenize (make the intensity uniform across the area of the substrate that is being exposed) the beam. Somewhat unintuitively, the best results are not provided by collimated light; a divergence of a few degrees will smooth out peaks that appear in the intensity towards the edge of the pattern [3]. The optics for a contact aligner are shown schematically in Figure 1.4. 1.2.1.3.2 Projection Printing The key parameters for projection printing are derived from the Rayleigh criteria for resolution and depth of focus (Equation 1.1 and Equation 1.2, respectively; [1,2,4]): (1.5) (1.6) Once again, k1 and k2 are empirically derived for the process in question. In practice, k1 will be between 0.5 and 1, typically, about 0.7 [1,4], and k2 will be somewhere about 0.5 ([4]; Peckerar et al. suggest that is closer to 1). Reche also FIGURE 1.4 Contact aligner exposure optics schematic. Alignment is usually performed through a binocular microscope system, not shown, which focuses at two points near the center of the wafer. The relative position of the mask and wafer are adjusted, and the optical components of the aligner are moved out of the way during exposure. d k NA = 1 λ δ λ = k NA 2 2 Source Homogenizer Optics Mask Substrate DK3182_C001.fm Page 17 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 45. 18 Microengineering, MEMS, and Interfacing: A Practical Guide gives the economically practical value of a numerical aperture as being no more than 0.5 for one-to-one projection printing. With reduction optics, it may be increased to 0.6 [1], although economically this would amount to using a production line stepper around the clock. The optics of a projection system are shown in outline in Figure 1.5. 1.2.1.3.3 Projection and Contact Printing Compared Working with Equation 1.4, Equation 1.5, and Equation 1.6 and taking values of 0.7, 1, and 1.6 for k1, k2, and k3, respectively, we find, with g-line (436 nm) exposure for a 1:1 projection system with a numerical aperture of 0.5, the achievable resolution will be approximately 0.61 µm with a depth of field of 1.7 µm. This would be adequate for many applications, but consider the situation in which a 10-µm thick resist is required. A trade-off between depth of field and resolution can be seen by examining Equation 1.5 and Equation 1.6. For a 10-µm depth of field (greater, preferably, to accommodate positioning and other errors), the resolution goes up to about 1.53 µm. Note that projection printing would typically be used for high-resolution printing on thin films of resist. Using the same numbers, contact printing would give a 3.34-µm resolution with the 10-µm resist. In this case, we have considered the entire thickness of the resist film as the separation distance, which will give a worst-case estimate of resolution. For thin resists, the separation distance can be set to half the thickness of the resist (implying that the resolution, in this case, is unlikely to be better than 2.36 µm). If we consider proximity printing with a 50-µm total separation, our achiev- able resolution increases to 7.47 µm, which will be adequate for many microengi- neering applications. Typically, thick resists are used as structural elements in MEMS. They may also be desirable in deep-etching applications, in which a thick resist is required to withstand long periods spent in the etching apparatus. In the latter situation, high resolutions can be achieved by the use of a hard mask. A thin layer of resist can be used to pattern an underlying layer of more resilient material for the etching of the next process stem: a metal film, for instance. This is the hard mask; the pattern in this would then be transferred to the underlying material during a long etch process before the hard mask (etch mask) is stripped. FIGURE 1.5 Schematic outline of a projection printing system. Source Homogenizer Condenser Mask Projection lens Substrate on movable stage DK3182_C001.fm Page 18 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 46. Photolithography 19 1.2.1.4 Optical Oddities Optical systems cannot be made completely free of aberrations or distortions, and further problems may be introduced by the nature of mask or substrate. A few of these are discussed in the following paragraphs, and some are covered in greater detail in Part III. 1.2.1.4.1 The Difference between Negative and Positive Resists Light will be scattered when it enters the resist layer. As illustrated in Figure 1.6, when the resist is overexposed, this leads to gaps in the developed resist that are larger than the mask features for positive resists and smaller than the mask features for negative resists. Because many etching procedures undercut the resist, particularly many wet etches, this has resulted in a preference to the use of negative resists in order to more closely reproduce the features in the mask. 1.2.1.4.2 Optical Aberrations and Distortions The results of any photolithographic process would be limited by the quality of the optical system. Typically, these will be more severe further from the optical axis. Astigmatism, arising from asymmetry in the optics for instance, will typically result in slightly poorer resolution in one horizontal direction than in others. It may also have knock-on consequences in terms of optical proximity effects, etc., mentioned later. Chromatic aberrations are particularly problematic with lens-based systems, as opposed to reflective focusing systems. Although lens-based optical systems normally achieve higher numerical apertures than reflective systems, the refractive index of the material employed is dependent on the wavelength of the light being transmitted. Some photoresists are sensitive to a specific wavelength of light, whereas other broadband resists are sensitive to a broad spectral range. In the latter case, projection printing results, in particular, will suffer because of chro- matic aberrations unless a filter is employed. Distortions can sometimes be introduced because the resist is capable of reproducing very-high-resolution features. In some forms of 1:1 projection and contact printing, for instance, the fly-eye homogenizer employed can introduce patterns in the resist. FIGURE 1.6 (a) Positive resists tend to develop with slightly wider than desired openings; (b) negative resists tend to develop with slightly smaller openings than mask features. Original mask pattern Developed photoresist pattern Substrate (a) (b) DK3182_C001.fm Page 19 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 47. 20 Microengineering, MEMS, and Interfacing: A Practical Guide 1.2.1.4.3 Optical Proximity Effects Optical proximity effects are another aspect of photolithography that are felt most acutely with modern high-resolution projection systems. They are exemplified by the situation illustrated in Figure 1.7. Diffraction effects in the gap have led to partial exposure of the resist there and poor reproduction of the mask pattern. Similar effects can also be seen in the rounding of corners and poor dimen- sional reproduction illustrated in Figure 1.7b. Note that corners in particular represent very-high-resolution objects, and thus it can be difficult to achieve good reproduction of sharp corners. These effects can be compensated for by mask design, but with the resolutions typically used in microengineering and MEMS, they do not normally represent significant problems. High-resolution nanolithography is dealt with in Part III of this book. 1.2.1.4.4 Reflection from the Substrate The classic example of an effect caused by reflection from the substrate is the striated or wavy patterns that appear in otherwise vertical resist sidewalls (Figure 1.8). These are a result of standing waves set up between incident light and that reflected from the substrate below the resist. FIGURE 1.7 Optical proximity effects (exaggerated): (a) the original mask pattern, (b) the pattern reproduced (shaded area), the lines are foreshortened, corners rounded, and the small gap partially filled. FIGURE 1.8 Schematic illustration of standing wave effects on resist (cross section). (a) (b) DK3182_C001.fm Page 20 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 48. Photolithography 21 Another problem that may be experienced is that of reflective proximity effects, in which a slope in the substrate reflects incident light horizontally into the resist. This can interfere with exposure of the resist in an adjacent area leading to overexposure. Antireflective coatings are available from suppliers of photolithographic chemicals, and these are the solution of first resort in cases in which reflected light causes a problem. 1.2.2 SHADOW MASKS An alternative to chrome on quartz masks is the use of stencils. Commonly, these would be laser-cut stainless steel stencils that are used in printed circuit board (PCB) manufacture. These are termed shadow masks and have two applications. The first is in certain thin-film deposition processes, notably sputtering and evaporation, in which the mask is clamped over the face of the substrate. The deposition process covers the entire surface so that when the mask is removed, unwanted material goes with it, leaving a stenciled pattern on the substrate. The second use, obviously, is in photolithography. Shadow masks cannot be used to achieve very high precision or small feature sizes. An additional problem with the use of stainless steel, particularly in de- position processes that develop heat, is that its dimensions change because of thermal expansion, giving rise to blurred edges. Cutting masks from alloys such as invar can reduce this problem. The main advantage of using shadow masks, however, is their low cost. 1.2.3 PHOTORESISTS AND RESIST PROCESSING The aim of the exercise is to produce controlled and repeatable profiles in the developed photoresist. The ideal profile has vertical sidewalls as shown in Figure 1.9a. For some applications, it may be desirable to employ different resist profiles; one of the most useful of these is the undercut profile for liftoff processing (see Tolerance Examples for Laser-Cut Stencils • Stainless steel, 0.1- to 0.2-mm thick • Design resolution, 0.5 µm • Precision, ±10 µm • Pitch (spacing between pads), 0.3 mm Although a very small design resolution is quoted, the ±10-µm precision limits the design minimum feature size. The pitch will be given for component pads on a PCB. Note that because this is a stencil, holes can be smaller than the spacing between them, and the designer has to consider mechanical support and stability across the design. Sub-100-µm holes may be achievable, but larger spaces (at least 100 µm) should be left between them. DK3182_C001.fm Page 21 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 49. 22 Microengineering, MEMS, and Interfacing: A Practical Guide section 2.6.4), as in Figure 1.9b. The optics, resist chemistry, and resist processing steps combine to produce the desired sidewall profile. 1.2.3.1 Photoresists A photoresist is normally supplied in liquid form. Most resists consist of two chemical components in an organic solvent. The first component is sensitive to light. The chemical products resulting from exposure of this component to light drive a polymerization in the other resist component. The developing process then removes the unpolymerized resist in the case of negative resists. In the case of positive resists, the result of exposure is usually that the second component in the exposed areas becomes more soluble in the developer. Generally, polymerization and development in negative resists are accompanied by dimensional changes that limit the resolution of the process more than for positive resists. However, there are now a variety of specialized chemistries available for both positive and negative resists, providing the engineer with a range of different options. Table 1.3 lists some photoresists that are popular for microengineering and MEMS. Table 1.4 lists some photoresist suppliers. FIGURE 1.9 Photoresist profiles: (a) the ideal with near-vertical walls, this profile would be slightly narrower at the top than the bottom; (b) undercut profile required for the lift- off process. Desirable Properties of Photoresists for Microengineering 1. Good resolution 2. Good adhesion to the substrate 3. Resistance to etching processes 4. Resistance to other micromachining processes (e.g., electroplating) 5. Ability to coat nonplanar topographies 6. Ability to apply and process thick coatings (5 µm to more than 100 µm) 7. Mechanically resilient Items 1 to 3 are general for any photoresist. Items 4 to 7 are more specific to micromachining, with items 5 and 6 being of particular interest when the resist is to be used as a structural component of the design. (a) (b) DK3182_C001.fm Page 22 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 50. Photolithography 23 TABLE 1.3 Popular Photoresists for Microengineering Resist Sourcea +/- Features SU-8 MCC − Epoxy-based resist, 2–200 µm thickness, very resilient, can be difficult to remove, excellent structural resist, adhesion promoters not normally required, image reversal possible, near-UV 350–400 nm SJR5740 S + High-aspect-ratio positive resist up to >20 µm thickness, broadband resist, good for electroplating S1800 S + Good general-purpose positive resists, 0.5–3 µm AZ4562 AZ + Thick positive resist AZ9260 AZ + Thick positive resist AZ5214 AZ + Image-reversible positive resist a +/− Signifies a positive or negative resist Source: MCC: MicroChem Corp., Newton, MA (www.microchem.com); S: Shipley (Rohm & Haas), Marlborough, MA (electronicmaterials.rohmhaas.com); AZ: Clariant Corp., Somerville, NJ (www.azresist.com). TABLE 1.4 Some Photoresist Suppliers MicroChem Corp., 1254 Chestnut Street, Newton, MA 02464, USA. Shipley: Rohm and Haas Electronic Materials, 455 Forest Street, Marlborough, MA 01752, USA. electronicmaterials.rohmhaas.com Clariant Corp. AZ Electronic Materials, 70 Meister Avenue, PO Box 3700, Somerville, NJ 08876, USA. www.azresist.com Wacker-Chemie GmbH, Hanns-Seidl-Platz 4, 81737 Munich, Germany. www.wacker.com GELEST, 11 East Steel Road, Morrisville, PA 19067, USA. www.gelest.com (for PDMS) Dow Corning, Midland, MI, USA. www.dowcorning.com SHE: Shin Etsu, 6-1, Ohtmachi 2-chome, Chiyoda-ku, Tokyo 100-0004, Japan. www.shinetsu.co.jp Futurrex Inc., 12 Cork Hill Road, Franklin, NJ 07416, USA. www.futurrex.com Eastman Kodak Company – PCB Products, 343 State Street, Rochester, NY 14650-0505, USA. www.kodak.com DK3182_C001.fm Page 23 Friday, January 13, 2006 10:57 AM Copyright © 2006 Taylor & Francis Group, LLC
- 51. Another Random Scribd Document with Unrelated Content
- 52. mercy, and compassion on whom he will have compassion.” Though the first scope of the apostle, in the beginning of the chapter, was to declare the reason of God’s rejecting the Jews, and calling in the Gentiles; had he only intended to demolish the pride of the Jews, and flat their opinion of merit, and aimed no higher than that providential act of God; he might, convincingly enough to the reason of men, have argued from the justice of God, provoked by the obstinacy of the Jews, and not have had recourse to his absolute will; but, since he asserts this latter, the strength of his argument seems to lie thus: if God by his absolute sovereignty may resolve, and fix his love upon Jacob and estrange it from Esau, or any other of his creatures, before they have done good or evil, and man have no ground to call his infinite majesty to account, may he not deal thus with the Jews, when their demerit would be a bar to any complaints of the creature against him?1007 If God were considered here in the quality of a judge, it had been fit to have considered the matter of fact in the criminal; but he is considered as a sovereign, rendering no other reason of his action but his own will; “whom he will he hardens” (ver. 18). And then the apostle concludes (ver. 20), “Who art thou, O man, that repliest against God?” If the reason drawn from God’s sovereignty doth not satisfy in this inquiry, no other reason can be found wherein to acquiesce: for the last condemnation there will be sufficient reason to clear the justice of his proceedings. But, in this case of election, no other reason but what is alleged, viz., the will of God, can be thought of, but what is liable to such knotty exceptions that cannot well be untied. (1.) It could not be any merit in the creature that might determine God to choose him. If the decree of election falls not under the merit of Christ’s passion, as the procuring cause, it cannot fall under the merit of any part of the corrupted mass. The decree of sending Christ did not precede, but followed, in order of nature, the determination of choosing some. When men were chosen as the subjects for glory, Christ was chosen as the means for the bringing them to glory (Eph. i. 4): “Chosen us in him, and predestinated us to the adoption of children by Jesus Christ.” The choice was not merely
- 53. in Christ as the moving cause; that the apostle asserts to be “the good pleasure of his will;” but in Christ, as the means of conveying to the chosen ones the fruits of their election. What could there be in any man that could invite God to this act, or be a cause of distinction of one branch of Adam from another? Were they not all hewed out of the same rock, and tainted with the same corruption in blood? Had it been possible to invest them with a power of merit at the first, had not that venom, contracted in their nature, degraded all of power for the future? What merit was there in any but of wrathful punishment, since they were all considered as criminals, and the cursed brood of an ungrateful rebel? What dignity can there be in the nature of the purest part of clay, to be made a vessel of honor, more than in another part of clay, as pure as that which was formed into a vessel for mean and sordid use? What had any one to move his mercy more than another, since they were all children of wrath, and equally daubed with original guilt and filth? Had not all an equal proportion of it to provoke his justice? What merit is there in one dry bone more than another, to be inspired with the breath of a spiritual life? Did not all lie wallowing in their own filthy blood? and what could the steam and noisomeness of that deserve at the hands of a pure Majesty, but to be cast into a sink furthest from his sight? Were they not all considered in this deplorable posture, with an equal proportion of poison in their nature, when God first took his pen, and singled out some names to write in the book of life? It could not be merit in any one piece of this abominable mass, that should stir up that resolution in God to set apart this person for a vessel of glory, while he permitted another to putrefy in his own gore. He loved Jacob, and hated Esau, though they were both parts of the common mass, the seed of the same loins, and lodged in the same womb. (2.) Nor could it be any foresight of works to be done in time by them, or of faith, that might determine God to choose them. What good could he foresee resulting from extreme corruption, and a nature alienated from him? What could he foresee of good to be done by them, but what he resolved in his own will, to bestow an
- 54. ability upon them to bring forth? His choice of them was to a holiness, not for a holiness preceding his determination (Eph. i. 4). He hath chosen us, “that we might be holy” before him; he ordained us “to good works,” not for them (Eph. ii. 10). What is a fruit cannot be a moving cause of that whereof it is a fruit: grace is a stream from the spring of electing love; the branch is not the cause of the root, but the root of the branch; nor the stream the cause of the spring, but the spring the cause of the stream. Good works suppose grace, and a good and right habit in the person, as rational acts suppose reason. Can any man say that the rational acts man performs after his creation were a cause why God created him? This would make creation, and everything else, not so much an act of his will, as an act of his understanding. God foresaw no rational act in man, before the act of his will to give him reason; nor foresees faith in any, before the act of his will determining to give him faith: “Faith is the gift of God” (Eph. ii. 8). In the salvation which grows up from this first purpose of God, he regards not the works we have done, as a principal motive to settle the top‑stone of our happiness, but his own purpose, and the grace given in Christ; “who hath saved us, and called us with a holy calling, not according to our own works, but according to his own purpose and grace, which was given to us in Christ, before the world began” (2 Tim. i. 9). The honor of our salvation cannot be challenged by our works, much less the honor of the foundation of it. It was a pure gift of grace, without any respect to any spiritual, much less natural, perfection. Why should the apostle mention that circumstance, when he speaks of God’s loving Jacob, and hating Esau, “when neither of them had done good or evil” (Rom. ix. 11), if there were any foresight of men’s works as the moving cause of his love or hatred? God regarded not the works of either as the first cause of his choice, but acted by his own liberty, without respect to any of their actions which were to be done by them in time. If faith be the fruit of election, the prescience of faith doth not influence the electing act of God. It is called “the faith of God’s elect” (Tit. i. 1): “Paul, an apostle of Jesus Christ, according to the faith of God’s elect;” i. e. settled in this office to bring the elect of God to faith. If men be chosen by God upon the foresight of faith,
- 55. or not chosen till they have faith, they are not so much God’s elect, as God their elect; they choose God by faith, before God chooseth them by love: it had not been the faith of God’s elect, i. e. of those already chosen, but the faith of those that were to be chosen by God afterwards. Election is the cause of faith, and not faith the cause of election; fire is the cause of heat, and not the heat of fire; the sun is the cause of the day, and not the day the cause of the rising of the sun. Men are not chosen because they believe, but they believe because they are chosen: the apostle did ill, else, to appropriate that to the elect which they had no more interest in, by virtue of their election, than the veriest reprobate in the world.1008 If the foresight of what works might be done by his creatures was the motive of his choosing them, why did he not choose the devils to redemption, who could have done him better service, by the strength of their nature, than the whole mass of Adam’s posterity? Well, then, there is no possible way to lay the original foundation of this act of election and preterition in anything but the absolute sovereignty of God. Justice or injustice comes not into consideration in this case. There is no debt which justice or injustice always respects in its acting: if he had pleased, he might have chosen all; if he had pleased, he might have chosen none. It was in his supreme power to have resolved to have left all Adam’s posterity under the rack of his justice; if he determined to snatch out any, it was a part of his dominion, but without any injury to the creatures he leaves under their own guilt. Did he not pass by the angels, and take man? and, by the same right of dominion, may he pick out some men from the common mass, and lay aside others to bear the punishment of their crimes. Are they not all his subjects? all are his criminals, and may be dealt with at the pleasure of their undoubted Lord and Sovereign. This is a work of arbitrary power; since he might have chosen none, or chosen all, as he saw good himself. It is at the liberty of the artificer to determine his wood or stone to such a figure, that of a prince, or that of a toad; and his materials have no right to complain of him, since it lies wholly upon his own liberty. They must have little sense of their own vileness, and God’s infinite excellency above them
- 56. by right of creation, that will contend that God hath a lesser right over his creatures than an artificer over his wood or stone. If it were at his liberty whether to redeem man, or send Christ upon such an undertaking, it is as much at his liberty, and the prerogative is to be allowed him, what person he will resolve to make capable of enjoying the fruits of that redemption. One man was as fit a subject for mercy as another, as they all lay in their original guilt: why would not Divine mercy cast its eye upon this man, as well as upon his neighbor? There was no cause in the creature, but all in God; it must be resolved into his own will: yet not into a will without wisdom. God did not choose hand over head, and act by mere will, without reason and understanding; an Infinite Wisdom is far from such a kind of procedure; but the reason of God is inscrutable to us, unless we could understand God as well as he understands himself; the whole ground lies in God himself, no part of it in the creature; “not in him that wills, nor in him that runs, but in God that shows mercy” (Rom. ix. 15, 16). Since God hath revealed no other cause than his will, we can resolve it into no other than his sovereign empire over all creatures. It is not without a stop to our curiosity, that in the same place where God asserts the absolute sovereignty of his mercy to Moses, he tells him he could not see his face: “I will be gracious to whom I will be gracious;” and he said, “Thou canst not see my face” (Exod. xxxiii. 19, 20): the rays of his infinite wisdom are too bright and dazzling for our weakness. The apostle acknowledged not only a wisdom in this proceeding, but a riches and treasure of wisdom; not only that, but a depth and vastness of those riches of wisdom; but was unable to give us an inventory and scheme of it (Rom. xi. 33). The secrets of his counsels are too deep for us to wade into; in attempting to know the reason of those acts, we should find ourselves swallowed up into a bottomless gulf: though the understanding be above our capacity, yet the admiration of his authority and submission to it are not. “We should cast ourselves down at his feet, with a full resignation of ourselves to his sovereign pleasure.”1009 This is a more comely carriage in a Christian than all the contentious endeavors to measure God by our line.
- 57. 2. In bestowing grace where he pleases. God in conversion and pardon works not as a natural agent, putting forth strength to the utmost, which God must do, if he did renew man naturally, as the sun shines, and the fire burns, which always act, ad extremum virium, unless a cloud interpose to eclipse the one, and water to extinguish the other. But God acts as a voluntary agent, which can freely exert his power when he please, and suspend it when he please. Though God be necessarily good, yet he is not necessitated to manifest all the treasures of his goodness to every subject; he hath power to distil his dews upon one part, and not upon another. If he were necessitated to express his goodness without a liberty, no thanks were due to him. Who thanks the sun for shining on him, or the fire for warming him? None; because they are necessary agents, and can do no other. What is the reason he did not reach out his hand to keep all the angels from sinking, as well as some, or recover them when they were sunk? What is the reason he engrafts one man into the true Vine, and lets the other remain a wild olive? Why is not the efficacy of the Spirit always linked with the motions of the Spirit? Why does he not mould the heart into a gospel frame when he fills the ear with a gospel sound? Why doth he strike off the chains from some, and tear the veil from the heart, while he leaves others under their natural slavery and Egyptian darkness? Why do some lie under the bands of death, while another is raised to a spiritual life? What reason is there for all this but his absolute will? The apostle resolves the question, if the question be asked, why he begets one and not another? Not from the will of the creature, but “his own will,” is the determination of one (James i. 18). Why doth he work in one “to will and to do,” and not in another? Because of “his good pleasure,” is the answer of another (Phil. ii. 13). He could as well new create every one, as he at first created them, and make grace as universal as nature and reason, but it is not his pleasure so to do. (1.) It is not from want of strength in himself. The power of God is unquestionably able to strike off the chains of unbelief from all; he could surmount the obstinacy of every child of wrath, and inspire
- 58. every son of Adam with faith as well as Adam himself. He wants not a virtue superior to the greatest resistance of his creature; a victorious beam of light might be shot into their understandings, and a flood of grace might overspread their wills with one word of his mouth, without putting forth the utmost of his power. What hindrance could there be in any created spirit, which cannot be easily pierced into and new moulded by the Father of spirits? Yet he only breathes this efficacious virtue into some, and leaves others under that insensibility and hardness which they love, and suffer them to continue in their benighting ignorance, and consume themselves in the embraces of their dear, though deceitful Delilahs. He could have conquered the resistance of the Jews, as well as chased away the darkness and ignorance of the Gentiles. No doubt but he could overpower the heart of the most malicious devil, as well as that of the simplest and weakest man. But the breath of the Almighty Spirit is in his own power, to breathe “where he lists” (John iii. 8). It is at his liberty whether he will give to any the feelings of the invincible efficacy of his grace; he did not want strength to have kept man as firm as a rock against the temptation of Satan, and poured in such fortifying grace, as to have made him impregnable against the powers of hell, as well as he did secure the standing of the angels against the sedition of their fellows: but it was his will to permit it to be otherwise. (2.) Nor is it from any prerogative in the creature. He converts not any for their natural perfection, because he seizeth upon the most ignorant; nor for their moral perfection, because he converts the most sinful; nor for their civil perfection, because he turns the most despicable. [1.] Not for their natural perfection of knowledge. He opened the minds and hearts of the more ignorant. Were the nature of the Gentiles better manured than that of the Jews, or did the tapers of their understandings burn clearer? No; the one were skilled in the prophecies of the Messiah, and might have compared the predictions they owned with the actions and sufferings of Christ, which they
- 59. were spectators of. He let alone those that had expectations of the Messiah, and expectations about the time of Christ’s appearance, both grounded upon the oracles wherewith he had entrusted them. The Gentiles were unacquainted with the prophets, and therefore destitute of the expectations of the Messiah (Eph. ii. 12): they were “without Christ;” without any revelation of Christ, because “aliens from the commonwealth of Israel, and strangers to the covenant of promise, having no hope, and without God in the world,” without any knowledge of God, or promises of Christ. The Jews might sooner, in a way of reason, have been wrought upon than the Gentiles, who were ignorant of the prophets, by whose writings they might have examined the truth of the apostles’ declarations. Thus are they refused that were the kindred of Christ, according to the flesh, and the Gentiles, that were at a greater distance from him, brought in by God; thus he catcheth not at the subtle and mighty devils, who had an original in spiritual nature more like to him, but at weak and simple man. [2.] Not for any moral perfection, because he converts the most sinful: the Gentiles, steeped in idolatry and superstition. He sowed more faith among the Romans than in Jerusalem; more faith in a city that was the common sewer of all the idolatry of the nations conquered by them, than in that city which had so signally been owned by him, and had not practised any idolatry since the Babylonish captivity. He planted saintship at Corinth, a place notorious for the infamous worship of Venus, a superstition attended with the grossest uncleanness; at Ephesus, that presented the whole world with a cup of fornication in their temple of Diana; among the Colossians, votaries to Cybele in a manner of worship attended with beastly and lascivious ceremonies. And what character had the Cretians from one of their own poets, mentioned by the apostle to Titus, whom he had placed among them to further the progress of the gospel, but the vilest and most abominable? (Titus i. 12): “liars,” not to be credited; “evil beasts,” not to be associated with; “slow bellies,” fit for no service. What prerogative was there in the nature of such putrefaction? as much as in that of a toad to be elevated to
- 60. the dignity of an angel. What steam from such dunghills could be welcome to him, and move him to cast his eye on them, and sweeten them from heaven? What treasures of worth were here to open the treasures of his grace! Were such filthy snuffs fit of themselves to be kindled by, and become a lodging for, a gospel beam? What invitements could he have from lying, beastliness, gluttony, but only from his own sovereignty? By this he plucked firebrands out of the fire, while he left straighter and more comely sticks to consume to ashes. [3.] Not for any civil perfection, because he turns the most despicable. He elevates not nature to grace upon the account of wealth, honor, or any civil station in the world: he dispenseth not ordinarily those treasures to those that the mistaken world foolishly admire and dote upon (1 Cor. i. 26); “Not many mighty, not many noble:” a purple robe is not usually decked with this jewel; he takes more of mouldy clay than refined dust to cast into his image, and lodges his treasures more in the earthly vessels than in the world’s golden ones; he gives out his richest doles to those that are the scorn and reproach of the world. Should he impart his grace most to those that abound in wealth or honor, it had been some foundation for a conception that he had been moved by those vulgarly esteemed excellencies to indulge them more than others. But such a conceit languisheth when we behold the subjects of his grace as void originally of any allurements, as they are full of provocations. Hereby he declares himself free from all created engagements, and that he is not led by any external motives in the object. [4.] It is not from any obligation which lies upon him. He is indebted to none: disobliged by all. No man deserves from him any act of grace, but every man deserves what the most deplorable are left to suffer. He is obliged by the children of wrath to nothing else but showers of wrath; owes no more a debt to fallen man, than to fallen devils, to restore them to their first station by a superlative grace. How was he more bound to restore them, than he was to preserve them; to catch them after they fell, than to put a bar in the
- 61. way of their falling? God, as a sovereign, gave laws to men, and a strength sufficient to keep those laws. What obligation is there upon God to repair that strength man wilfully lost, and extract him out of that condition into which he voluntarily plunged himself? What if man sinned by temptation, which is a reason alleged by some, might not many of the devils do so too? Though there was a first of them that sinned without a temptation, yet many of them might be seduced into rebellion by the ringleader. Upon that account he is no more bound to give grace to all men, than to devils. If he promised life upon obedience, he threatened death upon transgression. By man’s disobedience God is quit of his promise, and owes nothing but punishment upon the violation of his law. Indeed man may pretend to a claim of sufficient strength from him by creation, as God is the author of nature, and he had it; but since he hath extinguished it by his sin, he cannot in the least pretend any obligation on God for a new strength. If it be a “peradventure” whether he will “give repentance,” as it is 2 Tim. ii. 25, there is no tie in the case; a tie would put it beyond a peradventure with a God that never forfeited his obligation. No husbandman thinks himself obliged to bestow cost and pains, manure and tillage, upon one field more than another; though the nature of the ground may require more, yet he is at his liberty whether he will expend more upon one than another.1010 He may let it lie fallow as long as he please. God is less obliged to till and prune his creatures, than man is obliged to his field or trees. If a king proclaim a pardon to a company of rebels, upon the condition of each of them paying such a sum of money; their estates before were capable of satisfying the condition, but their rebellion hath reduced them to an indigent condition; the proclamation itself is an act of grace, the condition required is not impossible in itself: the prince, out of a tenderness to some, sends them that sum of money, he hath by his proclamation obliged them to pay, and thereby enabled them to answer the condition he requires; the first he doth by a sovereign authority, the second he doth by a sovereign bounty. He was obliged to neither of them; punishment was a debt due to all of them; if he would remit it upon condition, he did relax his
- 62. sovereign right; and if he would by his largess make any of them capable to fulfil the condition, by sending them presently a sufficient sum to pay the fine, he acted as proprietor of his own goods, to dispose of them in such a quantity to those to whom he was not obliged to bestow a mite. [5.] It must therefore be an act of his mere sovereignty. This can only sit arbitrator in every gracious act. Why did he give grace to Abel and not to Cain, since they both lay in the same womb, and equally derived from their parents a taint in their nature; but that he would show a standing example of his sovereignty to the future ages of the world in the first posterity of man? Why did he give grace to Abraham, and separate him from his idolatrous kindred, to dignify him to be the root of the Messiah? Why did he confine his promise to Isaac, and not extend it to Ishmael, the seed of the same Abraham by Hagar, or to the children he had by Keturah after Sarah’s death? What reason can be alleged for this but his sovereign will? Why did he not give the fallen angels a moment of repentance after their sin, but condemned them to irrevocable pains? Is it not as free for him to give grace to whom he please, as create what worlds he please; to form this corrupted clay into his own image, as to take such a parcel of dust from all the rest of the creation whereof to compact Adam’s body? Hath he not as much jurisdiction over the sinful mass of his creatures in a new creation, as he had over the chaos in the old? And what reason can be rendered, of his advancing this part of matter to the nobler dignity of a star, and leaving that other part to make up the dark body of the earth; to compact one part into a glorious sun, and another part into a hard rock, but his royal prerogative? What is the reason a prince subjects one malefactor to punishment, and lifts up another to a place of trust and profit? that Pharaoh honored the butler with an attendance on his person, and remitted the baker to the hands of the executioner? It was his pleasure. And is not as great right due to God, as is allowed to the worms of the earth? What is the reason he hardens a Pharaoh, by a denying him that grace which should mollify him, and allows it to another? It is because he will. “Whom he will he
- 63. hardens” (Rom. ix. 18). Hath not man the liberty to pull up the sluice, and let the water run into what part of the ground he pleases? What is the reason some have not a heart to understand the beauty of his ways? Because the Lord doth not give it them (Deut. xxix. 4). Why doth he not give all his converts an equal measure of his sanctifying grace? some have mites and some have treasures. Why doth he give his grace to some sooner, to some later? some are inspired in their infancy, others not till a full age, and after; some not till they have fallen into some gross sin, as Paul; some betimes, that they may do him service: others later, as the thief upon the cross, and presently snatcheth them out of the world? Some are weaker, some stronger in nature, some more beautiful and lovely, others more uncomely and sluggish. It is so in supernaturals. What reason is there for this, but his own will? This is instead of all that can be assigned on the part of God. He is the free disposer of his own goods, and as a Father may give a greater portion to one child than to another. And what reason of complaint is there against God? may not a toad complain that God did not make it a man, and give it a portion of reason? or a fly complain that God did not make it an angel, and give it a garment of light; had they but any spark of understanding; as well as man complain that God did not give him grace as well as another? Unless he sincerely desired it, and then was denied it, he might complain of God, though not as a sovereign, yet as a promiser of grace to them that ask it. God doth not render his sovereignty formidable; he shuts not up his throne of grace from any that seek him; he invites man; his arms are open, and the sceptre stretched out; and no man continues under the arrest of his lusts, but he that is unwilling to be otherwise, and such a one hath no reason to complain of God. 3. His sovereignty is manifest in disposing the means of grace to some, not to all. He hath caused the sun to shine bright in one place, while he hath left others benighted and deluded by the devil’s oracles. Why do the evangelical dews fall in this or that place, and not in another? Why was the gospel published in Rome so soon, and not in Tartary? Why hath it been extinguished in some places, as
- 64. soon almost as it had been kindled in them? Why hath one place been honored with the beams of it in one age, and been covered with darkness the next? One country hath been made a sphere for this star, that directs to Christ, to move in; and afterwards it hath been taken away, and placed in another; sometimes more clearly it hath shone, sometimes more darkly, in the same place; what is the reason of this? It is true something of it may be referred to the justice of God, but much more to the sovereignty of God. That the gospel is published later, and not sooner, the apostle tell us is “according to the commandment of the everlasting God” (Rom. xvi. 26). (1.) The means of grace, after the families from Adam became distinct, were never granted to all the world. After that fatal breach in Adam’s family by the death of Abel, and Cain’s separation, we read not of the means of grace continued among Cain’s posterity; it seems to be continued in Adam’s sole family, and not published in societies till the time of Seth. “Then began men to call upon the name of the Lord” (Gen. iv. 26). It was continued in that family till the deluge, which was 1523 years after the creation, according to some, or 1656 years, according to others. After that, when the world degenerated, it was communicated to Abraham, and settled in the posterity that descended from Jacob; though he left not the world without a witness of himself, and some sprinklings of revelations in other parts, as appears by the Book of Job, and the discourses of his friends. (2.) The Jews had this privilege granted them above other nations, to have a clearer revelation of God. God separated them from all the world to honor them with the depositum of his oracles (Rom. iii. 2): “To them were committed the oracles of God.” In which regard all other nations are said to be “without God” (Eph. ii. 12), as being destitute of so great a privilege. The Spirit blew in Canaan when the lands about it felt not the saving breath of it. “He hath not dealt so with any nation; and as for his judgments, they have not known them” (Ps. cxlvii. 20). The rest had no warnings from the
- 65. prophets, no dictates from heaven, but what they had by the light of nature, the view of the works of creation, and the administration of Providence, and what remained among them of some ancient traditions derived from Noah, which, in tract of time, were much defaced. We read but of one Jonah sent to Nineveh, but frequent alarms to the Israelites by a multitude of prophets commissioned by God. It is true, the door of the Jewish church was open to what proselytes would enter themselves, and embrace their religion and worship; but there was no public proclamation made in the world; only God, by his miracles in their deliverance from Egypt (which could not but be famous among all the neighbor nations), declared them to be a people favored by heaven: but the tradition from Adam and Noah was not publicly revived by God in other parts, and raised from that grave of forgetfulness wherein it had lain so long buried. Was there any reason in them for this indulgence? God might have been as liberal to any other nation, yea, to all the nations in the world, if it had been his sovereign pleasure: any other people were as fit to be entrusted with his oracles, and be subjects for his worship, as that people; yet all other nations, till the rejection of the Jews, because of their rejection of Christ, were strangers from the covenant of promise. These people were part of the common mass of the world: they had no prerogative in nature above Adam’s posterity. Were they the extract of an innocent part of his loins, and all the other nations drained out of his putrefaction? Had the blood of Abraham, from whom they were more immediately descended, any more precious tincture than the rest of mankind? They, as well as other nations, were made of “one blood” (Acts xvii. 26); and that corrupted both in the spring and in the rivulets. Were they better than other nations, when God first drew them out of their slavery? We have Joshua’s authority for it, that they had complied with the Egyptian idolatry, “and served other gods,” in that place of their servitude (Josh. xxiv. 14). Had they had an abhorrency of the superstition of Egypt, while they remained there, they could not so soon have erected a golden calf for worship, in imitation of the Egyptian idols. All the rest of mankind had as inviting reasons to present God with, as those people had. God might have granted the
- 66. same privilege to all the world, as well as to them, or denied it them, and endowed all the rest of the world with his statutes: but the enriching such a small company of people with his Divine showers, and leaving the rest of the world as a barren wilderness in spirituals, can be placed upon no other account originally than that of his unaccountable sovereignty, of his love to them: there was nothing in them to merit such high titles from God as his first‑born, his peculiar treasure, the apple of his eye. He disclaims any righteousness in them, and speaks a word sufficient to damp such thoughts in them, by charging them with their wickedness, while he “loaded them with his benefits” (Deut. ix. 4, 6). The Lord “gives thee not” this land for “thy righteousness;” for thou art a stiff‑necked people. It was an act of God’s free pleasure to “choose them to be a people to himself” (Deut. vii. 6). (3.) God afterwards rejected the Jews, gave them up to the hardness of their hearts, and spread the gospel among the Gentiles. He hath cast off the children of the kingdom, those that had been enrolled for his subjects for many ages, who seemed, by their descent from Abraham, to have a right to the privileges of Abraham; and called men from the east and from the west, from the darkest corners in the world, to “sit down with Abraham, Isaac, and Jacob, in the kingdom of heaven,” i. e. to partake with them of the promises of the gospel (Matt. viii. 11). The people that were accounted accursed by the Jews enjoy the means of grace, which have been hid from those that were once dignified this 1600 years; that they have neither ephod, nor teraphim, nor sacrifice, nor any true worship of God among them (Hos. iii. 4). Why he should not give them grace to acknowledge and own the person of the Messiah, to whom he had made the promises of him for so many successive ages, but let their “heart be fat,” and “their ears heavy” (Isa. vi. 10)? —why the gospel at length, after the resurrection of Christ, should be presented to the Gentiles, not by chance, but pursuant to the resolution and prediction of God, declared by the prophets that it should be so in time?—why he should let so many hundreds of years pass over, after the world was peopled, and let the nations all that
- 67. while soak in their idolatrous customs?—why he should not call the Gentiles without rejecting the Jews, and bind them both up together in the bundle of life?—why he should acquaint some people with it a little after the publishing it in Jerusalem, by the descent of the Spirit, and others not a long time after?—some in the first ages of Christianity enjoyed it; others have it not, as those in America, till the last age of the world;—can be referred to nothing but his sovereign pleasure. What merit can be discovered in the Gentiles? There is something of justice in the case of the Jews’ rejection, nothing but sovereignty in the Gentiles’ reception into the church. If the Jews were bad, the Gentiles were in some sort worse: the Jews owned the one true God, without mixture of idols, though they owned not the Messiah in his appearance, which they did in a promise; but the Gentiles owned neither the one nor the other. Some tell us, it was for the merit of some of their ancestors. How comes the means of grace, then, to be taken from the Jew, who had (if any people ever had) meritorious ancestors for a plea? If the merit of some of their former progenitors were the cause, what was the reason the debt due to their merit was not paid to their immediate progeny, or to themselves, but to a posterity so distant from them, and so abominably depraved as the Gentile world was at the day of the gospel‑sun striking into their horizon? What merit might be in their ancestors (if any could be supposed in the most refined rubbish), it was so little for themselves, that no oil could be spared out of their lamps for others. What merit their ancestors might have, might be forfeited by the succeeding generations. It is ordinarily seen, that what honor a father deserves in a state for public service, may be lost by the son, forfeited by treason, and himself attainted. Or was it out of a foresight that the Gentiles would embrace it, and the Jews reject it; that the Gentiles would embrace it in one place, and not in another? How did God foresee it, but in his own grace, which he was resolved to display in one, not in another? It must be then still resolved into his sovereign pleasure. Or did he foresee it in their wills and nature? What, were they not all one common dross? Was any part of Adam, by nature, better than another? How did God foresee that which was not, nor could be,
- 68. without his pleasure to give ability, and grace to receive? Well, then, what reason but the sovereign pleasure of God can be alleged, why Christ forbade the apostles, at their first commission, to preach to the Gentiles (Matt. x. 15), but, at the second and standing commission, orders them to preach to “every creature?” Why did he put a demur to the resolutions of Paul and Timothy, to impart light to Bithynia, or order them to go into Macedonia? Was that country more worthy upon whom lay a great part of the blood of the world shed in Alexander’s time (Acts xvi. 6, 7, 9, 10)? Why should Corazin and Bethsaida enjoy those means that were not granted to the Tyrians and Sidonians, who might probably have sooner reached out their arms to welcome it (Matt. xi. 21)? Why should God send the gospel into our island, and cause it to flourish so long here, and not send it, or continue it, in the furthest eastern parts of the world? Why should the very profession of Christianity possess so small a compass of ground in the world, but five parts in thirty, the Mahometans holding six parts, and the other nineteen overgrown with Paganism, where either the gospel was never planted, or else since rooted up? To whom will you refer this, but to the same cause our Saviour doth the revelation of the gospel to babes, and not to the wise—even to his Father? “For so it seemed good in thy sight” (Matt. xi. 25, 26); “For so was thy good pleasure before thee” (as in the original); it is at his pleasure whether he will give any a clear revelation of his gospel, or leave them only to the light of nature. He could have kept up the first beam of the gospel in the promise in all nations among the apostasies of Adam’s posterity, or renewed it in all nations when it began to be darkened, as well as he first published it to Adam after his fall; but it was his sovereign pleasure to permit it to be obscured in one place, and to keep it lighted in another. 4. His sovereignty is manifest in the various influences of the means of grace. He saith to these waters of the sanctuary, as to the floods of the sea, “Hitherto you shall go, and no further.” Sometimes they wash away the filth of the flesh and outward man, but not that of the spirit; the gospel spiritualizeth some, and only moralizeth
- 69. others; some are by the power of it struck down to conviction, but not raised up to conversion; some have only the gleams of it in their consciences, and others more powerful flashes; some remain in their thick darkness under the beaming of the gospel every day in their face, and after a long insensibleness are roused by its light and warmth; sometimes there is such a powerful breath in it, that it levels the haughty imaginations of men, and lays them at its feet that before strutted against it in the pride of their heart. The foundation of this is not in the gospel itself, which is always the same, nor in the ordinances, which are channels as sound at one time as at another, but Divine sovereignty that spirits them as he pleaseth, and “blows when and where it lists.” It has sometimes conquered its thousands (Acts ii. 41); at another time scarce its tens; sometimes the harvest hath been great, when the laborers have been but few; at another time it hath been small, when the laborers have been many; sometimes whole sheaves; at another time scarce gleanings. The evangelical net hath been sometimes full at a cast, and at every cast; at another time many have labored all night, and day too, and catched nothing (Acts, ii. 47): “The Lord added to the church daily.” The gospel chariot doth not always return with captives chained to the sides of it, but sometimes blurred and reproached, wearing the marks of hell’s spite, instead of imprinting the marks of its own beauty. In Corinth it triumphed over many people (Acts xviii. 10); in Athens it is mocked, and gathers but a few clusters (Acts xvii. 32, 34). God keeps the key of the heart, as well as of the womb. The apostles had a power of publishing the gospel, and working miracles, but under the Divine conduct; it was an instrumentality durante bene placito, and as God saw it convenient. Miracles were not upon every occasion allowed to them to be wrought, nor success upon every administration granted to them; God sometimes lent them the key, but to take out no more treasure than was allotted to them. There is a variety in the time of gospel operation; some rise out of their graves of sin, and beds of sluggishness, at the first appearance of this sun; others lie snorting longer. Why doth not God spirit it at one season as well as at another, but set his distinct periods of time, but because he will
- 70. show his absolute freedom? And do we not sometimes experiment that after the most solemn preparations of the heart, we are frustrated of those incomes we expected? Perhaps it was because we thought Divine returns were due to our preparations, and God stops up the channel, and we return drier than we came, that God may confute our false opinion, and preserve the honor of his own sovereignty. Sometimes we leap with John Baptist in the womb at the appearance of Christ; sometimes we lie upon a lazy bed when he knocks from heaven; sometimes the fleece is dry, and sometimes wet, and God withholds to drop down his dew of the morning upon it. The dews of his word, as well as the droppings of the clouds, belong to his royalty; light will not shine into the heart, though it shine round about us, without the sovereign order of that God “who commanded light to shine out of the darkness” of the chaos (2 Cor. iv. 6). And is it not seen also in regard of the refreshing influences of the word? sometimes the strongest arguments, and clearest promises, prevail nothing towards the quelling black and despairing imaginations; when, afterwards, we have found them frighted away by an unexpected word, that seemed to have less virtue in it itself than any that passed in vain before it. The reasonings of wisdom have dropped down like arrows against a brazen wall, when the speech of a weaker person hath found an efficacy. It is God by his sovereignty spirits one word and not another; sometimes a secret word comes in, which was not thought of before, as dropped from heaven, and gives a refreshing, when emptiness was found in all the rest. One word from the lips of a sovereign prince is a greater cordial than all the harangues of subjects without it; what is the reason of this variety, but that God would increase the proofs of his own sovereignty? that as it was a part of his dominion to create the beauty of a world, so it is no less to create the peace as well as the grace of the heart (Isa. lvii. 19): “I create the fruit of the lips, peace.” Let us learn from hence to have adoring thoughts of, not murmuring fancies against, the sovereignty of God; to acknowledge it with thankfulness in what we have; to implore it with a holy submission in what we want. To own God as a sovereign in a way of
- 71. dependence, is the way to be owned by him as subjects in a way of favor. 5. His sovereignty is manifested in giving a greater measure of knowledge to some than to others. What parts, gifts, excellency of nature, any have above others, are God’s donative; “He gives wisdom to the wise, and knowledge to them that know understanding” (Dan. ii. 21); wisdom, the habit, and knowledge, the right use of it, in discerning the right nature of objects, and the fitness of means conducing to the end; all is but a beam of Divine light; and the different degrees of knowledge in one man above another, are the effects of his sovereign pleasure. He enlightens not the minds of all men to know every part of his will; one “eats with a doubtful conscience,” another in “faith,” without any staggering (Rom. xiv. 2). Peter had a desire to keep up circumcision, not fully understanding the mind of God in the abolition of the Jewish ceremonies; while Paul was clear in the truth of that doctrine. A thought comes into our mind that, like a sunbeam, makes a Scripture truth visible in a moment, which before we were poring upon without any success; this is from his pleasure. One in the primitive times had the gift of knowledge, another of wisdom, one the gift of prophecy, another of tongues, one the gift of healing, another that of discerning spirits; why this gift to one man, and not to another? Why such a distribution in several subjects? Because it is his sovereign pleasure. “The Spirit divides to every man severally as he will” (1 Cor. xii. 11). Why doth he give Bezaleel and Aholiab the gift of engraving, and making curious works for the tabernacle (Exod. xxxi. 3), and not others? Why doth he bestow the treasures of evangelical knowledge upon the meanest of earthen vessels, the poor Galileans, and neglect the Pharisees, stored with the knowledge both of naturals and morals? Why did he give to some, and not to others, “to know the mysteries of the kingdom of heaven?” (Matt. xiii. 11.) The reason is implied in the words, “Because it was the mystery of his kingdom,” and therefore was the act of his sovereignty. How would it be a kingdom and monarchy if the governor of it were bound to do what he did? It is to be resolved
- 72. only into the sovereign right of propriety of his own goods, that he furnisheth babes with a stock of knowledge, and leaves the wise and prudent empty of it (Matt. xi. 26): “Even so, Father: for so it seemed good in thy sight.” Why did he not reveal his mind to Eli, a grown man, and in the highest office in the Jewish church, but open it to Samuel, a stripling? why did the Lord go from the one to the other? Because his motion depends upon his own will. Some are of so dull a constitution, that they are incapable of any impression, like rocks too hard for a stamp; others like water; you may stamp what you please, but it vanisheth as soon as the seal is removed. It is God forms men as he pleaseth: some have parts to govern a kingdom, others scarce brains to conduct their own affairs; one is fit to rule men, and another scarce fit to keep swine; some have capacious souls in crazy and deformed bodies, others contracted spirits and heavier minds in a richer and more beautiful case. Why are not all stones alike? some have a more sparkling light, as gems, more orient than pebbles;—some are stars of first, and others of a less magnitude; others as mean as glow‑worms, a slimy lustre:—it is because he is the sovereign Disposer of what belongs to him; and gives here, as well as at the resurrection, to one “a glory of the sun;” to another that of the “moon;” and to a third a less, resembling that of a “star” (1 Cor. xv. 40). And this God may do by the same right of dominion, as he exercised when he endowed some kinds of creatures with a greater perfection than others in their nature. Why may he not as well garnish one man with a greater proportion of gifts, as make a man differ in excellency from the nature of a beast? or frame angels to a more purely spiritual nature than a man? or make one angel a cherubim or seraphim, with a greater measure of light than another? Though the foundation of this is his dominion, yet his wisdom is not uninterested in his sovereign disposal; he garnisheth those with a greater ability whom he intends for greater service, than those that he intends for less, or none at all; as an artificer bestows more labor, and carves a more excellent figure upon those stones that he designs for a more honorable place in the building. But though the intending this or that man for service be the motive of laying in a greater provision in him
- 73. than in others, yet still it is to be referred to his sovereignty, since that first act of culling him out for such an end was the fruit solely of his sovereign pleasure: as when he resolved to make a creature actively to glorify him, in wisdom he must give him reason; yet the making such a creature was an act of his absolute dominion. 6. His sovereignty is manifest in the calling some to a more special service in their generation. God settles some in immediate offices of his service, and perpetuates them in those offices, with a neglect of others, who seem to have a greater pretence to them. Moses was a great sufferer for Israel, the solicitor for them in Egypt, and the conductor of them from Egypt to Canaan; yet he was not chosen to the high priesthood, but that was an office settled upon Aaron, and his posterity after him, in a lineal descent; Moses was only pitched upon for the present rescue of the captived Israelites, and to be the instrument of Divine miracles; but notwithstanding all the success he had in his conduct, his faithfulness in his employment, and the transcendent familiarity he had with the great Ruler of the world, his posterity were left in the common level of the tribe of Levi, without any special mark of dignity upon them above the rest for all the services of that great man. Why Moses for a temporary magistrate, Aaron for a perpetual priesthood, above all the rest of the Israelites? hath little reason but the absolute pleasure of God, who distributes his employments as he pleaseth; and as a master orders his servant to do the noblest work, and another to labor in baser offices, according to his pleasure. Why doth he call out David, a shepherd, to sway the Jewish sceptre, above the rest of the brothers, that had a fairer appearance, and had been bred in arms, and inured to the toils and watchings of a camp? Why should Mary be the mother of Christ, and not some other of the same family of David, of a more splendid birth, and a nobler education? Though some other reasons may be rendered, yet that which affords the greatest acquiescence, is the sovereign will of God. Why did Christ choose out of the meanest of the people the twelve apostles, to be heralds of his grace in Judea, and other parts of the world; and afterwards select Paul before Gamaliel, his instructor, and others
- 74. of the Jews, as learned as himself, and advance him to be the most eminent apostle, above the heads of those who had ministered to Christ in the days of his flesh? Why should he preserve eleven of those he first called to propagate and enlarge his kingdom, and leave the other to the employment of shedding his blood? Why, in the times of our reformation, he should choose a Luther out of a monastery, and leave others in their superstitious nastiness, to perish in the traditions of their fathers? Why set up Calvin, as a bulwark of the gospel, and let others as learned as himself wallow in the sink of popery? It is his pleasure to do so. The potter hath power to separate this part of the clay to form a vessel for a more public use, and another part of the clay to form a vessel for a more private one. God takes the meanest clay to form the most excellent and honorable vessels in his house. As he formed man, that was to govern the creatures of the same clay and earth whereof the beasts were formed, and not of that nobler element of water, which gave birth to the fish and birds: so he forms some, that are to do him the greatest service, of the meanest materials, to manifest the absolute right of his dominion. 7. His sovereignty is manifest in the bestowing much wealth and honor upon some, and not vouchsafing it to the more industrious labors and attempts of others. Some are abased, and others are elevated; some are enriched, and others impoverished; some scarce feel any cross, and others scarce feel any comfort in their whole lives; some sweat and toil, and what they labor for runs out of their reach; others sit still, and what they wish for falls into their lap. One of the same clay hath a diadem to beautify his head, and another wants a covering to protect him from the weather. One hath a stately palace to lodge in, and another is scarce master of a cottage where to lay his head. A sceptre is put into one man’s hand, and a spade into another’s; a rich purple garnisheth one man’s body, while another wraps himself in dunghill rags. The poverty of some, and the wealth of others, is an effect of the Divine sovereignty, whence God is said to be the Maker of the “poor as well as the rich” (Prov. xxii. 2), not only of their persons, but of their conditions. The earth,
- 75. and the fulness thereof, is his propriety; and he hath as much a right as Joseph had to bestow changes of raiment upon what Benjamins he please. There is an election to a greater degree of worldly felicity, as there is an election of some to a greater degree of supernatural grace and glory: as he makes it “rain upon one city, and not upon another” (Amos iv. 7), so he causeth prosperity to distil upon the head of one and not upon another; crowning some with earthly blessings, while he crosseth others with continual afflictions: for he speaks of himself as a great proprietor of the corn that nourisheth us, and the wine that cheers us, and the wood that warm us (Hos. ii. 8, 9): “I will take away,” not your corn and wine, but “my corn, my wine, my wool.” His right to dispose of the goods of every particular person is unquestionable. He can take away from one, and pass over the propriety to another. Thus he devolved the right of the Egyptian jewels to the Israelites, and bestowed upon the captives what before he had vouchsafed to the oppressors; as every sovereign state demands the goods of their subjects for the public advantage in a case of exigency, though none of that wealth was gained by any public office, but by their private industry, and gained in a country not subject to the dominion of those that require a portion of them. By this right he changes strangely the scene of the world; sometimes those that are high are reduced to a mean and ignominious condition, those that are mean are advanced to a state of plenty and glory. The counter, which in accounting signifies now but a penny, is presently raised up to signify a pound. The proud ladies of Israel, instead of a girdle of curious needlework, are brought to make use of a cord; as the vulgar translates rent, a rag, or list of cloth (Isa. iii. 24), and sackcloth for a stomacher instead of silk. This is the sovereign act of God, as he is Lord of the world (Ps. lxxv. 6, 7): “Promotion cometh neither from the east, nor from the west, nor from the south, but God is the Judge: he putteth down one, and setteth up another.” He doth no wrong to any man, if he lets him languish out his days in poverty and disgrace: if he gives or takes away, he meddles with nothing but what is his own more than ours: if he did dispense his benefits equally to all, men would soon think it their due. The inequality and changes preserve the notion of
- 76. God’s sovereignty, and correct our natural unmindfulness of it. If there were no changes, God would not be feared as the “King of all the earth” (Ps. lv. 19): to this might also be referred his investing some countries with greater riches in their bowels, and on the surface; the disposing some of the fruitful and pleasant regions of Canaan or Italy, while he settles others in the icy and barren parts of the northern climates. 8. His sovereignty is manifest in the times and seasons of dispensing his goods. He is Lord of the times when, as well as of the goods which, he doth dispose of to any person; these “the Father hath put in his own power” (Acts i. 7). As it was his sovereign pleasure to restore the kingdom to Israel, so he would pitch upon the time when to do it, and would not have his right invaded, so much as by a question out of curiosity. This disposing of opportunities, in many things, can be referred to nothing else but his sovereign pleasure. Why should Christ come at the twilight and evening of the world? at the fulness, and not at the beginning, of time? Why should he be from the infancy of the world so long wrapt up in a promise, and not appear in the flesh till the last times and gray hairs of the world, when so many persons, in all nations, had been hurried out of the world without any notice of such a Redeemer? What was this but his sovereign will? Why the Gentiles should be left so long in the devil’s chains, wallowing in the sink of their abominable superstitions, since God had declared his intention by the prophets to call multitudes of them, and reject the Jews;— why he should defer it so long, can be referred to nothing but the same cause. What is the reason the veil continues so long upon the heart of the Jews, that is promised, one time or other, to be taken off? Why doth God delay the accomplishment of those glorious predictions of the happiness and interest of that people? Is it because of the sin of their ancestors,—a reason that cannot bear much weight? If we cast it upon that account, their conversion can never be expected, can never be effected; if for the sins of their ancestors, is it not also for their own sins? Do their sins grow less in number, or less venomous, or provoking in quality, by this delay? Is
- 77. not their blasphemy of Christ as malicious, their hatred of him as strong and rooted, as ever? Do they not as much approve of the bloody act of their ancestors, since so many ages are past, as their ancestors did applaud it at the time of the execution? Have they not the same disposition and will, discovered sufficiently by the scorn of Christ, and of those that profess his name, to act the same thing over again, were Christ now in the same state in the world, and they invested with the same power of government? If their conversion were deferred one age after the death of Christ for the sins of their preceding ancestors, is it to be expected now; since the present generation of the Jews in all countries have the sins of those remote, the succeeding, and their more immediate ancestors, lying upon them? This, therefore, cannot be the reason; but as it was the sovereign pleasure of God to foretell his intention to overcome the stoutness of their hearts, so it is his sovereign pleasure that it shall not be performed till the “fulness of the Gentiles be come in” (Rom. xi. 25). As he is the Lord of his own grace, so he is the Lord of the time when to dispense it. Why did God create the world in six days, which he could have erected and beautified in a moment? Because it was his pleasure so to do. Why did he frame the world when he did, and not many ages before? Because he is Master of his own work. Why did he not resolve to bring Israel to the fruition of Canaan till after four hundred years? Why did he draw out their deliverance to so long time after he began to attempt it? Why such a multitude of plagues upon Pharaoh to work it, when he could have cut short the work by one mortal blow upon the tyrant and his accomplices? It was his sovereign pleasure to act so, though not without other reasons intelligible enough by looking into the story. Why doth he not bring man to a perfection of stature in a moment after his birth, but let him continue in a tedious infancy, in a semblance to beasts, for the want of an exercise of reason? Why doth he not bring this or that man, whom he intends for service, to a fitness in an instant, but by long tracts of study, and through many meanders and labyrinths? Why doth he transplant a hopeful person in his youth to the pleasures of another world, and let another, of an eminent holiness, continue in the misery of this, and wade through many floods of
- 78. afflictions? What can we chiefly refer all these things to but his sovereign pleasure? The “times are determined by God” (Acts xvii. 26). Thirdly. The dominion of God is manifested as a governor, as well as a lawgiver and proprietor. 1. In disposing of states and kingdoms. (Ps. lxxv. 7): “God is Judge; he puts down one, and sets up another.” “Judge” is to be taken not in the same sense that we commonly use the word, for a judicial minister in a way of trial, but for a governor; as you know the extraordinary governors raised up among the Jews were called judges, whence one entire book in the Old Testament is so denominated, the Book of Judges. God hath a prerogative to “change times and seasons” (Dan. ii. 21), i. e. the revolutions of government, whereby times are altered. How many empires, that have spread their wings over a great part of the world, have had their carcasses torn in pieces; and unheard‑of nations plucked off the wings of the Roman eagle, after it had preyed upon many nations of the world; and the Macedonian empire was as the dew that is dried up a short time after it falls.1011 He erected the Chaldean monarchy, used Nebuchadnezzar to overthrow and punish the ungrateful Jews, and, by a sovereign act, gave a great parcel of land into his hands; and what he thought was his right by conquest, was God’s donative to him. You may read the charter to Nebuchadnezzar, whom he terms his servant (Jer. xxvii. 6): “And now I have given all those lands” (the lands are mentioned ver. 3), “into the hands of Nebuchadnezzar, the king of Babylon, my servant:” which decree he pronounceth after his asserting his right of sovereignty over the whole earth (ver. 5). After that, he puts a period to the Chaldean empire, and by the same sovereign authority decrees Babylon to be a spoil to the nations of the north country, and delivers her up as a spoil to the Persian (Jer. l. 9, 10): and this for the manifestation of his sovereign dominion, that he was the Lord, that made peace, and created evil (Isa. xlv. 6, 7). God afterwards overthrows that by the Grecian Alexander, prophesied of
- 79. under the figure of a goat, with “one horn between his eyes” (Dan. viii.): the swift current of his victories, as swift as his motion, showed it to be from an extraordinary hand of heaven, and not either from the policy or strength of the Macedonian. His strength, in the prophet, is described to be less, being but one horn running against the Persian, described under the figure of a ram with two horns:1012 and himself acknowledged a Divine motion exciting him to that great attempt, when he saw Joddus, the high‑priest, coming out in his priestly robes, to meet him at his approach to Jerusalem, whom he was about to worship, acknowledging that the vision which put him upon the Persian war appeared to him in such a garb. What was the reason Israel was rent from Judah, and both split into two distinct kingdoms? Because Rehoboam would not hearken to sober and sound counsels, but follow the advice of upstarts. What was the reason he did not hearken to sound advice, since he had so advantageous an education under his father Solomon, the wisest prince of the world? “The cause was from the Lord” (1 Kings, xii. 15), that he might perform what he had before spoke. In this he acted according to his royal word; but, in the first resolve, he acted as a sovereign lord, that had the disposal of all nations in the world. And though Ahab had a numerous posterity, seventy sons to inherit the throne after him, yet God by his sovereign authority gives them up into the hands of Jehu, who strips them of their lives and hopes together: not a man of them succeeded in the throne, but the crown is transferred to Jehu by God’s disposal. In wars, whereby flourishing kingdoms are overthrown, God hath the chief hand; in reference to which it is observed that, in the two prophets, Isaiah and Jeremiah, God is called “the Lord of Hosts” one hundred and thirty times. It is not the sword of the captain, but the sword of the Lord, bears the first rank; “the sword of the Lord and of Gideon” (Judges vii. 18). The sword of a conqueror is the sword of the Lord, and receives its charge and commission from the great Sovereign (Jer. xlvii. 6, 7). We are apt to confine our thoughts to second causes, lay the fault upon the miscarriages of persons, the ambition of the one, and the covetousness of another, and regard them not as the effects of God’s
- 80. sovereign authority, linking second causes together to serve his own purpose. The skill of one man may lay open the folly of a counsellor; an earthly force may break in pieces the power of a mighty prince: but Job, in his consideration of those things, refers the matter higher: “He looseth the bond of kings, and girdeth their loins with a girdle” (Job xii. 18). “He looseth the bonds of kings,” i. e. takes off the yokes they lay upon their subjects, “and girds their loins with a girdle” (a cord, as the vulgar); he lays upon them those fetters they framed for others; such a girdle, or band, as is the mark of captivity, as the words, ver. 19, confirm it: “He leads princes away spoiled, and overthrows the mighty.” God lifts up some to a great height, and casts down others to a disgraceful ruin. All those changes in the face of the world, the revolutions of empires, the desolating and ravaging wars, which are often immediately the birth of the vice, ambition, and fury of princes, are the royal acts of God as Governor of the world. All government belongs to him; he is the Fountain of all the great and the petty dominions in the world; and, therefore, may place in them what substitutes and vicegerents he pleaseth, as a prince may remove his officers at pleasure, and take their commissions from them. The highest are settled by God durante bene placito, and not quamdiu bene se gesserint. Those princes that have been the glory of their country have swayed the sceptre but a short time, when the more wolvish ones have remained longer in commission, as God hath seen fit for the ends of his own sovereign government. Now, by the revolutions in the world, and changes in governors and government, God keeps up the acknowledgment of his sovereignty, when he doth arrest grand and public offenders that wear a crown by his providence, and employ it, by their pride, against him that placed it there. When he arraigns such by a signal hand from heaven, he makes them the public examples of the rights of his sovereignty, declaring thereby, that the cedars of Lebanon are as much at his foot, as the shrubs of the valley; that he hath as sovereign an authority over the throne in the palace, as over the stool in the cottage.
- 81. 2. The dominion of God is manifested in raising up and ordering the spirits of men according to his pleasure. He doth, as the Father of spirits, communicate an influence to the spirits of men, as well as an existence; he puts what inclinations he pleaseth into the will, stores it with what habits he please, whether natural or supernatural, whereby it may be rendered more ready to act according to the Divine purpose. The will of man is a finite principle, and therefore subject to Him who hath an infinite sovereignty over all things; and God, having a sovereignty over the will, in the manner of its acting, causeth it to will what he wills, as to the outward act, and the outward manner of performing it. There are many examples of this part of his sovereignty. God, by his sovereign conduct, ordered Moses a protectoress as soon as his parents had formed an “ark of bulrushes,” wherein to set him floating on the river (Exod. ii. 3‒6): they expose him to the waves, and the waves expose him to the view of Pharaoh’s daughter, whom God, by his secret ordering her motion, had posted in that place; and though she was the daughter of a prince that inveterately hated the whole nation, and had, by various arts, endeavored to extirpate them, yet God inspires the royal lady with sentiments of compassion to the forlorn infant, though she knew him to be one of the Hebrews’ children (ver. 6), i. e. one of that race whom her father had devoted to the hands of the executioner; yet God, that doth by his sovereignty rule over the spirits of all men, moves her to take that infant into her protection, and nourish him at her own charge, give him a liberal education, adopt him as her son, who, in time, was to be the ruin of her race, and the saviour of his nation. Thus he appointed Cyrus to be his shepherd, and gave him a pastoral spirit for the restoration of the city and temple of Jerusalem (Isa. xliv. 28): and Isaiah (chap. xlv. 5) tells them, in the prophecy, that he had girded him, though Cyrus had not known him, i. e. God had given him a military spirit and strength for so great an attempt, though he did not know that he was acted by God for those divine purposes. And when the time came for the house of the Lord to be rebuilt, the spirits of the people were raised up, not by themselves, but by God (Ezra i. 5), “Whose spirit God had raised to go up;” and not only the spirit of
- 82. Zerubbabel, the magistrate, and of Joshua, the priest, but the spirit of all the people, from the highest to the meanest that attended him, were acted by God to strengthen their hands, and promote the work (Hag. i. 14). The spirits of men, even in those works which are naturally desirable to them, as the restoration of the city and rebuilding of the Temple was to those Jews, are acted by God, as the Sovereign over them, much more when the wheels of men’s spirits are lifted up above their ordinary temper and motion. It was this empire of God good Nehemiah regarded, as that whence he was to hope for success; he did not assure himself so much of it, from the favor he had with the king, nor the reasonableness of his intended petition, but the absolute power God had over the heart of that great monarch; and, therefore, he supplicates the heavenly, before he petitioned the earthly, throne (Neh. ii. 4): “So I prayed to the God of heaven.” The heathens had some glance of this; it is an expression that Cicero hath somewhere, “That the Roman commonwealth was rather governed by the assistance of the Supreme Divinity over the hearts of men, than by their own counsels and management.” How often hath the feeble courage of men been heightened to such a pitch as to stare death in the face, which before were damped with the least thought or glance of it! This is a fruit of God’s sovereign dominion. 3. The dominion of God is manifest in restraining the furious passions of men, and putting a block in their way. Sometimes God doth it by a remarkable hand, as the Babel builders were diverted from their proud design by a sudden confusion of their language, and rendering it unintelligible to one another; sometimes by ordinary, though unexpected, means; as when Saul, like a hawk, was ready to prey upon David, whom he had hunted as a partridge upon the mountains, he had another object presented for his arms and fury by the Philistines’ sudden invasion of a part of his territory (1 Sam. xxiii. 26‒28). But it is chiefly seen by an inward curbing mutinous affections, when there is no visible cause. What reason but this can be rendered, why the nations bordering on Canaan, who bore no good will to the Jews, but rather wished the whole race of
- 83. them rooted out from the face of the earth, should not invade their country, pillage their houses, and plunder their cattle, while they were left naked of any human defence, the males being annually employed at one time at Jerusalem in worship; what reason can be rendered, but an invisible curb God put into their spirits? What was the reason not a man, of all the buyers and sellers in the Temple, should rise against our Saviour, when, with a high hand, he began to whip them out, but a Divine bridle upon them? though it appears, by the questioning his authority, that there were Jews enough to have chased out him and his company (John ii. 15, 18). What was the reason that, at the publishing the gospel by the apostles at the first descent of the Spirit, those that had used the Master so barbarously a few days before, were not all in a foam against the servants, that, by preaching that doctrine, upbraided them with the late murder? Had they better sentiments of the Lord, whom they had put to death? Were their natures grown tamer, and their malignity expelled? No; but that Sovereign who had loosed the reins of their malicious corruption, to execute the Master for the purchase of redemption, curbed it from breaking out against the servants, to further the propagation of the doctrine of redemption. He that restrains the roaring lion of hell, restrains also his whelps on earth; he and they must have a commission before they can put forth a finger to hurt, how malicious soever their nature and will be. His empire reaches over the malignity of devils, as well as the nature of beasts. The lions out of the den, as well as those in the den, are bridled by him in favor of his Daniels. His dominion is above that of principalities and powers; their decrees are at his mercy, whether they shall stand or fall; he hath a vote above their stiffest resolves: his single word, I will, or, I forbid, outweighs the most resolute purposes of all the mighty Nimrods of the earth in their rendezvouses and cabals, in their associations and counsels (Isa. viii. 9, 10): “Associate yourselves, O ye people, and ye shall be broken in pieces; take counsel together, and it shall come to nought.” “When the enemy shall come in like a flood,” with a violent and irresistible force, intending nothing but ravage and desolation, “the Spirit of the Lord shall lift up a standard against them” (Isa. lix. 19), shall give a
- 84. sudden check, and damp their spirits, and put them to a stand. When Laban furiously pursued Jacob, with an intent to do him an ill turn, God gave him a command to do otherwise (Gen. xxxi. 24). Would Laban have respected that command any more than he did the light of nature when he worshipped idols, had not God exercised his authority in inclining his will to observe it, or laying restraints upon his natural inclinations, or denying his concourse to the acting those ill intentions he had entertained? The stilling the principles of commotion in men, and the noise of the sea, are arguments of the Divine dominion; neither the one nor the other is in the power of the most sovereign prince without Divine assistance: as no prince can command a calm to a raging sea, so no prince can order stillness to a tumultuous people; they are both put together as equally parts of the Divine prerogative (Ps. lxv. 7), which “stills the noise of the sea, and tumult of the people:” and David owns God’s sovereignty more than his own, “in subduing the people under him” (Ps. xviii. 47). In this his empire is illustrious (Ps. xxix. 10): “The Lord sitteth upon the floods, yea, the Lord sitteth King for ever;” a King impossible to be deposed, not only on the natural floods of the sea, that would naturally overflow the world, but the metaphorical floods or tumults of the people, the sea in every wicked man’s heart, more apt to rage morally than the sea to foam naturally. If you will take the interpretation of an angel, waters and floods, in the prophetic style, signify the inconstant and mutable people (Rev. xvii. 1, 5): “The waters where the whore sits are people, and multitudes, and nations, and tongues:” so the angel expounds to John the vision which he saw (ver. 1). The heathens acknowledged this part of God’s sovereignty in the inward restraints of men: those apparitions of the gods and goddesses in Homer, to several of the great men when they were in a fury, were nothing else, in the judgment of the wisest philosophers, than an exercise of God’s sovereignty in quelling their passions, checking their uncomely intentions, and controlling them in that which their rage prompted them to. And, indeed, did not God set bounds to the storms in men’s hearts, we should soon see the funeral, not only of religion, but civility; the one would be blown out, and the other torn up by the roots.
- 85. 4. The dominion of God is manifest in defeating the purposes and devices of men. God often makes a mock of human projects, and doth as well accomplish that which they never dreamt of, as disappoint that which they confidently designed. He is present at all cabals, laughs at men’s formal and studied counsels, bears a hand over every egg they hatch, thwarts their best compacted designs, supplants their contrivances, breaks the engines they have been many years rearing, diverts the intentions of men, as a mighty wind blows an arrow from the mark which the archer intended. (Job v. 12): “He disappointeth the devices of the crafty, so that their hands cannot perform their enterprise; he taketh the wise in their own craftiness, and the counsel of the froward is carried headlong.” Enemies often draw an exact scheme of their intended proceedings, marshal their companies, appoint their rendezvous, think to make but one morsel of those they hate; God, by his sovereign dominion, turns the scale, changeth the gloominess of the oppressed into a sunshine, and the enemies’ sunshine into darkness. When the nations were gathered together against Sion, and said, “Let her be defiled, and let our eye look upon Sion” (Micah iv. 11), what doth God do in this case? (ver. 12), “He shall gather them,” i. e. those conspiring nations, as “sheaves into the floor.” Then he sounds a trumpet to Sion: “Arise, and thresh, O daughter of Sion, for I will make thy horn iron, and thy hoofs brass, and thou shalt beat in pieces many people; and I will consecrate their gain unto the Lord, and their substance unto the Lord of the whole earth.” I will make them and their counsels, them and their strength, the monuments and signal marks of my empire over the whole earth. When you see the cunningest designs baffled by some small thing intervening; when you see men of profound wisdom infatuated, mistake their way, and “grope in the noon‑day as in the night” (Job v. 14), bewildered in a plain way; when you see the hopes of mighty attempters dashed into despair, their triumphs turned into funerals, and their joyful expectations into sorrowful disappointments; when you see the weak, devoted to destruction, victorious, and the most presumptuous defeated in their purposes, then read the Divine dominion in the desolation of such devices. How often doth God take
- 86. away the heart and spirit of grand designs, and burst a mighty wheel, by snatching but one man out of the world! How often doth he “cut off the spirits of princes” (Ps. lxxvi. 12), either from the world by death, or from the execution of their projects by some unforeseen interruption, or from favoring those contrivances, which before they cherished by a change of their minds! How often hath confidence in God, and religious prayer, edged the weakest and smallest number of weapons to make a carnage of the carnally confident! How often hath presumption been disappointed, and the contemned enemy rejoiced in the spoils of the proud expectant of victory! Phidias made the image of Nemesis, or Revenge, at Marathon, of that marble which the haughty Persians, despising the weakness of the Athenian forces, brought with them, to erect a trophy for an expected, but an ungained, victory.1013 Haman’s neck, by a sudden turn, was in the halter, when the Jews’ necks were designed to the block; Julian designed the overthrow of all the Christians, just before his breast was pierced by an unexpected arrow; the Powder‑traitors were all ready to give fire to the mine, when the sovereign hand of Heaven snatched away the match. Thus the great Lord of the world cuts off men on the pinnacle of their designs, when they seem to threaten heaven and earth; puts out the candle of the wicked, which they thought to use to light them to the execution of their purposes; turns their own counsels into a curse to themselves, and a blessing to their adversaries, and makes his greatest enemies contribute to the effecting his purposes. How may we take notice of God’s absolute disposal of things in private affairs, when we see one man, with a small measure of prudence and little industry, have great success, and others, with a greater measure of wisdom, and a greater toil and labor, find their enterprises melt between their fingers! It was Solomon’s observation, “That the race was not to the swift, nor the battle to the strong, neither bread to the wise, nor riches to men of understanding, nor yet favor to men of skill” (Eccles. ix. 11). Many things might interpose to stop the swift in his race, and damp the courage of the most valiant: things do not happen according to men’s abilities, but according to the
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