Optical and Chemical Origins of Lithography
3.2 Key Developments that Enabled the Invention and Development of Lithography
3.2.1 Developments in optical physics
A comprehensive treatment of the development of optical physics covering, among other topics, the theories of light has been given elsewhere.5 Here, only the key developments that directly or indirectly influenced the development of litho-graphy as practiced today are covered. In such a treatment, it is convenient to disregard the chronological order in which the developments occurred, but rather to present the materials from the historical point of view and to show how each of the developments has been incorporated into the development and practice of lithography. A summary of these developments are given in Fig. 3.1.
3.2.1.1 Tactile and emission theories of light
Historically, it has been known since antiquity that the earliest speculations on the nature of light were theories of vision. One school held that the eye sends out invisible antennae or sensitive probes or visual rays and is thus able to feel objects that are too distant to be touched by hands or feet. This theory was called the “tactile” theory. An alternative hypothesis held that light consists of small particles that are emitted by bright objects and that, on entering the eye, are able to affect some sensitive part of the eye and so give rise to the sensation of sight. This theory was called the “emission” theory. Both of these theories were current among Greek thinkers about 500 BC.6
In its inherent simplicity, the tactile theory is able to describe the unknown in terms of the known. The mystery of vision is directly related to the simpler and more obvious sense of touch. The theory does, however, experience some
5R.W. Ditchburn, Light, Dover Publications, New York (1991); P. Mason, The Light Fantastic, Penguin Books, New York (1981); M.I. Sobel, Light, University of Chicago Press, Chicago (1987).
6Many variations and combinations of these theories were also suggested. We need not consider them since they are more complicated than the two theories we have described and have no important compensating advantages.
difficulty in explaining why things can be felt, but not seen, in the dark, and why bodies can be made visible in the dark by heating them. The fact that certain bright bodies are able to make neighboring bodies visible is also not explained by the tactile theory.7
Some of these difficulties of the tactile theory can be explained away by post-ulating that the visual probes are able to feel only certain kinds of surfaces and then making a series of assumptions that surfaces can be modified under various conditions. But this approach only ends up making the theory intolerably complicated, since the simple sense of relation to the sense of touch—the very important attribute of the theory—is lost. These conflicts can be resolved in a simple and satisfactory way by the emission theory if it is assumed that some bodies are able to emit a radiation to which the eyes are sensitive, and that others are able to reflect or scatter this radiation so that it enters the eye.8 For these and similar reasons, the tactile theory was gradually superseded by and eventually replaced with the emission theory. The process for this transformation was, however, very slow, and it was not until about 1000 AD that, under the influ-ence of the Arabian astronomer Alhazen (discussed below), the tactile theory was finally abandoned.9
3.2.1.2 Early studies in optics and catoptrics
Another major notable development in the early studies of light phenomena is attributed to Euclid,10 the great Greek mathematician of the third century BC, who wrote two books on light, Optics and Catoptrica (meaning on reflection).
Little is known of the latter book, but a review of it, written perhaps many centuries later—and possibly spurious—discusses the properties of mirrors and provides an accurate law of reflection (see Fig. 3.2), which states that a ray is reflected from a plane surface at the same angle with which it strikes the surface. Euclid was certainly aware that light travels in straight lines, a fact that he employed in his discussions on the laws of perspective.11
7R.W. Ditchburn, Light, p. 4, Dover Publications, New York (1991).
8A modern interpretation of the emission theory will have light being defined as “visible radiation,”
which takes part in the following general account of the visual process. Light being emitted, reflected, or scattered enters the eye and is focused by the lens of the eye on the retina, located at a surface situated at the back of the eye. The retina contains a large number of nerve endings, which on receiving light transforms the latter into electrical impulses through some chemi cal and physical action. A series of electrical impulses is thus sent from the retina along an appro priate nerve fiber to the brain.
9R.W. Ditchburn, Light, p. 4, Dover Publications, New York (1991).
10Greek science reached its highest peak in Euclid’s century. Archimedes of Syracuse was the greatest scientist of the era, and he made advances in mechanics, hydrostatics, and mathematics. [Cited in M.I.
Sobel, Light, p. 2, University of Chicago Press, Chicago (1987)].
11M.I. Sobel, Light, p. 2, University of Chicago Press, Chicago (1987).
3.2.1.2.1 Refraction
Another significant contribution to the early studies of light phenomena was due to Claudius Ptolemy, who made the first systematic study of refraction. In the second century AD in Greek Alexandria, he developed his cosmology in which the Earth is at the center of the universe with the Sun and the planets orbiting around it. This cosmology reigned undisputed for 13 centuries. Although the Ptolemaic system was actually a compilation of works of earlier Greek astro-nomers, notably Hipparchus, Ptolemy recognized that to correctly determine the location of a planet he must take into account the bending of light as it enters the Earth’s atmosphere. He demonstrated that when light enters a dense medium from a less dense one, the ray is bent toward the normal and, conversely, it is bent away from the normal when entering a less dense medium.12
Ptolemy also studied air-water, air-glass, and water-glass interfaces, and made tables of the angle of incidence (the angle between the incoming light ray and the normal) and the corresponding angle of refraction (the angle between the refracted ray and the normal). He postulated, however incorrectly, that for a given interface the two angles were proportional. His Optics, only part of which has survived to the present day, is noteworthy, not so much for its data as for the very fact of its adherence to the experimental method.13
The next major figure in the story of light is found more than eight centuries later, during the height of Islamic civilization.14 Born in 965 AD,
i r I
R N
Figure 3.2 The law of reflection. An incident ray of light I upon hitting a mirror surface is reflected R such that the angle of incidence i angle of reflection r. The dashed line, N, is the normal to the surface. The angle of incidence is the angle between the incoming ray and the normal; the angle of reflection is the angle between the reflected ray and the normal. I, N, and R are in the same plane.
12ibid., pp. 2 3.
13ibid.
14By the year AD 750, Islamic soldiers fanning out from Arabia had overrun many lands around their region and built an empire along the entire Mediterranean Sea and as far east as India. Among the great thinkers of this era were al Khwarizmi the mathematician, Avicenna the physician, Averroe¨s
Alhazen15experimented and wrote extensively on optics. In his writings on optics, he used highly developed algebra and geometry, as well as an experimental approach in a very modern sense, involving the use of sighting tubes, strings, and plane and curved glasses and mirrors to study the laws of reflection and refraction. He refuted Ptolemy’s claim that the angle of incidence was proportional to the angle of refraction, although he himself did not obtain the correct mathe-matical relation. He showed that a convex lens (where each surface is a part of a sphere) can magnify an image. He carried out a rigorous mathematical treatment of reflection from spherical, cylindrical, and conical mirrors. He observed that if parallel rays of light strike a curved mirror that is a section of a sphere, the rays are not brought to a precise focus, a condition known as spherical aberration;
but a mirror in the shape of a paraboloid (a solid figure produced by rotating a parabola about its axis) can produce a sharp focus.16 Furthermore, he deduced that twilight, the persistence of daylight after the Sun has set, to be due to the refrac-tion of sunlight from the upper layers of the Earth’s atmosphere. By assuming that twilight ends when the Sun’s rays are refracted from the very top of the atmosphere, he deduced that the atmosphere was 20 to 30 miles high, a fairly good estimate by modern standards.17
Also in Alhazen’s writings we find reports of very detailed early dissection of the human eye. We also find speculations on the method of propagation of light that anticipates the seventeenth-century theory of Huygens. And we find the hints or rather the suggestion, demonstrated only in the nineteenth century, that light travels less easily (i.e., at lower velocity) when it enters a dense medium, and that this causes the ray to be bent toward the normal.18
It should be pointed out that the research and scholarship of the Muslim scholars were important not only in themselves, but also on account of the fact that they trans-mitted, in Latin translation, the spirit of learning to medieval philosophers such as Roger Bacon and Albertus Magnus, whose work foreshadowed the age of science in the West. Bacon was certainly familiar with Alhazen’s works in optics, under-stood how to trace rays of light through lenses and mirrors, and may very well have been the first to use a lens for spectacles. He also suggested combining two lenses to make a telescope, although it is not certain that he actually built one.19
3.2.1.2.2 The invention of the microscope and telescope
Next, our journey through the history of studies in light phenomena takes us to the age of Copernicus, specifically the invention of the microscope by Zacharias
the philosopher, and Alhazen the physicist [cited in M.I. Sobel, Light, p. 5, University of Chicago Press, Chicago (1987)].
15Alhazen is actually the Latinized version of the great Arabic scholar Abu Ali al Hasan ibn al Hasan al Haitham, born in 965 AD.
16M.I. Sobel, Light, pp. 4 5, University of Chicago Press, Chicago (1987).
17ibid.
18ibid.
19ibid.
Janssen about 1590, the invention of the telescope by Hans Lippershey in 1608, and its quick deployment by Galileo Galilei.20 The modern-day optical and electron microscopes that are widely used in the inspection of lithographically patterned wafers all trace their origins to Janssen’s invention.
3.2.1.2.3 Laws of refraction
Around 1621, the Dutch scientist Willibrod Snell discovered the correct law of refraction, which both Ptolemy and Alhazen were unable to deduce.21By applying heuristic momentum conservation arguments in terms of sines, Rene Descartes independently derived the law in his 1637 philosophical and mathematical treatise, Discourse on Method. Descartes was able to solve several optical problems with the aid of this law.
Snell’s law provides the relation between the angle of incidence and the angle of refraction (see Fig. 3.3) in terms of a quantity, called the index of refraction, which is characteristic of the medium into which light travels. Specifically, the ratio of the sine of the incident angle to the sine of the refracted angle is equal to the refractive index of the medium. According to modern wave theory, the refractive index is the ratio of the speed of light in vacuum to the speed of light in the medium.22 Expressed another way, Snell’s law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of velocities in the two media, or equivalent to the inverse ratio of the indices of refraction,
sin i sin t¼v1
v2¼n2
n1
(3:1) or
n1sin i ¼ n2sin t, (3:2)
where sin i is the sine of the angle of incidence, sin t is the sine of the angle of refraction, v1and v2are the velocities of the light ray in medium 1 and 2, respect-ively, and n1and n2are the refractive indices of the light ray in medium 1 and 2, respectively.
Not long after the formulation of Snell’s law, the French mathematician Pierre de Fermat unified the laws of reflection and refraction by showing that both could be deduced from the hypotheses that light travels a path of least time. In other words, given two points A and B in a region with mirrors or with different media, the path of a ray of light from point A to point B will be that for which the time of travel is least. The implication of Fermat’s principle is that light travels at a finite speed.23
20ibid., p. 5.
21ibid.
22ibid.
23ibid.
3.2.1.3 On the nature of light
From about the mid-seventeenth century, studies aimed at elucidating the nature of light consumed the attention of most scientists. Reasoning that light provides the primary information about the experience around them, these scientists thought that understanding what it is and how it works should provide the key to understanding the diversity of natural phenomena. Such studies (see below) were the purview of not only astronomers and physicists, but also of mathematicians, chemists, biologists, and even physicians. Other workers in related fields such as opticians, glass and lens makers, and instrument makers pursued theories of light derived from specific applications and improvements of their crafts.24 This desire to understand what light is and how it works was the impetus behind the work that eventually resulted in the invention of photography and photolithography.
Incident ray, I
Refracted ray, T Medium 1, n1, v1
Medium 2, n2, v2 i
t
Interface
Normal, N
Figure 3.3 Refraction of light at the interface between two media of different refractive indices, with n2greater than n1. An incident light ray I travels from medium 1 into medium 2, making an incident angle i with the normal, N. It traverses the interface and travels into medium 2, as the refracted ray T, making a refracted angle t with the normal N in medium 2. Given that the velocity of light is lower in medium 2, the angle of refraction t is smaller than the angle of incidence i.
24M.S. Barge and W.B. White, The Daguerreotype: Nineteenth Century Technology and Modern Science, p. 12, Johns Hopkins University Press, Baltimore (1991).
3.2.1.3.1 Light and color
In an attempt to elucidate why when sunlight is bent in a glass prism the colors of the rainbow are produced—a fact known since antiquity—Sir Isaac Newton (1641–1727) (see Fig. 3.4) in 1666 carried out a wide variety of experiments in which he allowed a narrow pencil of sunlight to pass through a small hole in a window shade of a darkened room, producing a small circle of light on the opposite wall. Next, he placed a prism in front of the hole and observed that the beams struck a different area of the wall. The displacement of the beams was not surprising because it resulted from the refraction of the entire beam by the prism. He observed that the spot of light was now elongated and was no longer a circle. He also observed that colors are spread out along its axis, red on one end, violet on the other. On measuring the angles subtended by the axes of the spot as seen from the hole, he found the long axis close to three degrees and the short axis about one-half a degree.25
Next, he proceeded to analyze the beam by keeping the prism in place and introducing beyond it a barrier with a small hole. Through this hole he allowed only the red portion of the beam to pass; later the orange, the yellow, and so on.
This allowed him to experiment separately with each color, which he did by placing a second prism beyond the barrier to refract light arriving through the small hole. He monitored the angle of refraction of red light alone, orange light alone, etc., and found that the angle is different for different colors; violet light is bent most, red least, the others falling in between, leading him to postulate two theorems: “Light which differ in color, differ also in their degrees of refrangibility [refraction],” and “The light of the sun consists of rays of differently refrangible.”26 In another set of experiments, he took the beam emerging from a prism—
separated into colors—and let it pass through a second prism, inverted with respect to the first. In this arrangement, the second prism performed the opposite function of the first. The result he obtained was a combination of the separated
Figure 3.4 Sir Isaac Newton (1641–1727), who among many things discovered the laws of universal gravitation and was a proponent of the particle theory of light.
(Published with permission from the Deutsches Museum, Munich.)
25M.I. Sobel, Light, pp. 6 8, University of Chicago Press, Chicago (1987).
26Sir Isaac Newton, Optics, pp. 20, 26, Dover Publications, New York (1979).
colors, which produced a white spot on the wall. He was thus convinced that sunlight is a combination of colors of the rainbow.27
In order to explain the basis of the colors of material objects, using a prism, he took light of a particular color (“uncompounded light,” as he called it) and let it shine on different objects. A red object in blue light, he observed, looks blue. In green light it looks green and in red it looks red, but in this case it appears brightest. This led him to conclude that a red object reflects all colors but reflects red more strongly, so that in the “compound” white light of the sun the object reflects red most strongly and appears red to the viewer.28
3.2.1.3.2 Light as a wave or particle
Toward the end of the seventeenth century, two opposing theories of light were being investigated. These fall into two broad categories, namely, (i) particle (also called the corpuscular or emission) theory and (ii) wave (or undulatory) theory.29Knowing that light is a form of energy that can be transferred from one place to another, many scientists of the seventeenth and eighteenth centuries sought to describe it by analogy with other methods of energy transport. They dis-tinguished between two methods of energy transport, that is, transport of matter or by wave. While energy transport by matter is associated with the movement of the material body or the medium in which the matter is contained, energy trans-port by waves is not accompanied by any bodily movement of the medium. When energy is transported, it is not easy to discern whether the mechanism of trans-port is matter or wave. But there is one fundamental difference—interference phenomenon—a difference that becomes the crucial factor in the history of the study of light phenomena.30
Interference is the phenomenon that distinguishes waves from matter. While waves can interfere with one another in a constructive (when the superposition of the waves add up) or destructive (when the superposition of the waves cancel each other) manner, matter cannot. It was thus reasonable for many scientists of the seventeenth and eighteenth centuries to describe light either in terms of
Interference is the phenomenon that distinguishes waves from matter. While waves can interfere with one another in a constructive (when the superposition of the waves add up) or destructive (when the superposition of the waves cancel each other) manner, matter cannot. It was thus reasonable for many scientists of the seventeenth and eighteenth centuries to describe light either in terms of