The Amazing Story of Quantum Mechanics Part 5

CHAPTER FOURTEEN.

Quantum Invisible "Ink"

Light is an electromagnetic wave that is actually

comprised of discrete packets of energy.

New York City in 1933 boasted many skysc.r.a.pers, but only one had an eighty-sixth floor. In our world the eighty-sixth floor of the Empire State Building is dedicated to the Observatory deck, but in the world of the pulps, this entire floor was rented to one man, who made it his residential home, complete with an extensive library and advanced chemical, medical, and electronic laboratories. This man, who excelled in all pursuits intellectual and physical, was frequently joined by his five close a.s.sociates, each an expert in a different field of the practical and mechanical arts, such as chemistry, law, electronics, engineering, and archeology, on adventures that spanned the globe. The leader of this team, not content to rely solely on his amazing mental capabilities and his imposing physical prowess, would also employ a host of seemingly miraculous inventions and gadgets. Many of these exotic devices would not be realized in our world until years later, when nonfictional scientists and engineers had mastered the principles of quantum mechanics I've described, and managed to catch up to the achievements of one of pulp fiction's greatest heroes, Clark Savage, Jr. Though he had the equivalent of several Ph.D.s, owing to his M.D. from Johns Hopkins and several years studying brain surgery and neurology in Vienna, his friends and the public knew him as "Doc."

Doc Savage's adventures were described in the pulp magazine t.i.tle that bore his name, and his first story, The Man of Bronze, was published in March 1933, written by Lester Dent. Before the year was out, Doc Savage would be one of the top-selling pulps on the newsstand. Dent would go on to write 160 more full-length Doc Savage novels over the next sixteen years, at a pace of nearly one a month.56 Even at the pay rate of a penny a word, his writing income enabled Dent and his wife to live a life of personal adventure and travel that would inform his fictional tales. Doc Savage and his team would often travel the high seas in one of Doc's yachts or his personal submarine, battling modern-day pirates or exploring an island where dinosaurs still walked the Earth. Meanwhile, Dent and his wife lived for several years on a forty-foot schooner, traveling along the eastern seaboard, fishing and diving for buried treasure in the Caribbean by day and writing pulp adventures by night. Dent was a licensed pilot and radio operator, climbed mountains, prospected for gold in Death Valley, was a vast storehouse of obscure information, and was elected a member of the Explorers Club.

Dent's most famous literary creation would serve as the inspiration for Superman and Batman (Doc would retreat to an arctic sanctuary to develop new inventions that he called his Fortress of Solitude, and he carried many of his crime-fighting gadgets in a utility vest), James Bond and the Man from U.N.C.L.E. (Doc's tie and jacket b.u.t.tons hid the chemical ingredients of thermite and his car could produce a smokescreen to blind pursuers), and Marvel Comics' Fantastic Four (the comic-book superhero foursome also lived in a skysc.r.a.per headquarters, and the friendly bickering between two of Doc's teammates presaged the relationship between the Thing and the Human Torch), and even Star Trek's Mr. Spock (Doc could incapacitate foes by pinching certain nerves in their neck).

Doc's gadgets were similarly ahead of his time. In 1934 Doc employs a version of radar, long before its debut in World War II. (According to Dent, a reference to radar in a 1943 Savage novel was censored by the military immediately prior to publication, requiring him to scramble to come up with an alternative plot device).57 Doc Savage employed shark repellant and colored dyes to mark a pilot's location when forced to eject over the ocean a good ten years before the navy would adopt these innovations. He invented a small tracking device that, when affixed to an automobile, would transmit a radio signal, enabling the car's position to be monitored from a remote location. And one of Doc's inventions-ultraviolet writing-employed in his first pulp adventure makes use of the same quantum mechanical principles that underlie the laser.

In 1933's The Man of Bronze, Doc and his team of adventurers search their quarters on the eighty-sixth floor for a message from Doc's recently deceased father. Knowing that his father would often leave him missives using a form of invisible writing, Doc brings out a small metal box that resembles a magic lantern. Showing the interior of the mechanism to Long Tom, the group's electrical expert, Doc tests his companion, asking him whether he recognizes the device. "Of course. [. . .] That is a lamp for making ultraviolet rays, or what is commonly called black light. The rays are invisible to the human eye, since . . . [their wavelengths] are shorter than ordinary light." Long Tom then points out that while we may not see in the ultraviolet, many common substances, such as quinine and Vaseline, fluoresce when so illuminated. When they shine this ultraviolet light on a window in Doc's office, sure enough, a message from his father is revealed in glowing blue letters, directing them to the hiding place where they would find important papers that would in turn send them on a perilous journey to the fictional Central American nation of Hidalgo. The mechanism by which Doc and his father, and in later pulp adventures Doc and his teammates, communicate through ultraviolet writing relies on the variation in transition rates for quantized levels.

We have seen that electrons bound in atoms are constrained to particular energy levels. A consequence of this discreteness is that the atoms can absorb or lose energy only when it enables transitions between these allowed energy states (we will neglect transitions of protons or neutrons within the nucleus, as these energy scales are in the gamma-ray range, and we are interested now in transitions in the visible portion of the electromagnetic spectrum). Any energy interacting with the atom, in the form of a light photon or a collision with another electron or atom, will not induce an electronic transition if the change in energy does not correspond to the difference between two energy levels.

In our a.n.a.logy of students in a cla.s.sroom, where the rows of seats represent allowed energy levels, students may be promoted from their original seats at the front of the room to empty seats near the rear of the lecture hall. However, students are not allowed to stand between rows and may change their seats only if the energy they absorb takes them exactly from one row to another (and if the seat they are moving to is unoccupied). When an atom relaxes from some high-energy state back to the ground state, it similarly may do so only by emitting a photon whose energy is equal to the difference between the starting and final energy levels. That is, only electronic transitions that satisfy the principle of conservation of energy are allowed. This accounts for the discrete-line spectrum, with only a very select number of wavelengths observed (see Figure 13 in Chapter 5) when an atom is placed in a high-temperature environment. Different elements will have their allowed quantum levels at different energies, so that the s.p.a.cing between levels, and hence the frequency of the light emitted when the electron moves between states, will differ.

Just because an electron can make a jump between two quantized energy levels does not determine how fast or slow such a transition may be. For a collection of atoms, the light will be brighter for those transitions for which the probability of a jump is higher. Some lines will be present, but very faint, as the probability of a transition occurring at any given moment might be very low. One of the great successes of the quantum theory is that it actually makes predictions of the transition rates, that is, the probability per second that an atom with an electron in an excited state would drop down to a lower energy state, emitting a photon in the process. Thus, the quantum theory correctly predicts not only what wavelengths will be observed for a given atom, but even how bright the lines will be.

What determines these transition rates is fairly complicated and depends on details of the wave functions for the initial and final states. The important point is that quantum mechanics is able to account for the following: (1) the fact that electrons in atoms may have only certain energies, (2) the fact that only certain transitions between allowed states are possible, and (3) the probability per second of a given transition occurring. That is, the theory can explain why only discrete lines rather than continuous spectra will be observed for the light emitted by an atom, as well as predicting the wavelengths of the line spectrum and the intensity of the lines, all in excellent agreement with experimental observations. We now know enough about how atoms interact with light to explain two of the most important inventions of the twentieth century: lasers and glow-in-the-dark action figures!58 Let's first consider glow-in-the-dark materials. Each atom in the solid has a highest occupied energy level (as in Figure 31), and when a trillion trillion of these atoms are collected, all of these "seats" broaden into an auditorium of quantum states, as ill.u.s.trated in Figure 34. In Chapter 12 we saw that, thanks to the Pauli exclusion principle, each seat is actually a "love seat" in which two electrons can sit, if they have opposite spins (one with + /2 and the other with -/2). The trillion trillion "seats" in this "ground-state auditorium" can therefore accommodate two trillion trillion electrons.

If the atoms in the solid form bonds by keeping their electrons in "boxes," as in the case of the carbon-carbon bonds in diamond (Figure 32), then every love seat in the auditorium has two electrons, and the auditorium is completely filled (Figure 34a). The electron thus has to move to a higher energy (the next available empty quantum state) in order to find a vacant level. All of these higher energy states will also broaden into an "auditorium" of seats. Atoms that form solids similar to diamond can be considered to have an orchestra of seats, all of which are completely filled, and a higher-energy balcony with an equal number of seats, which are all empty.59 When a current flows in a solid in response to an applied voltage, the electrons gain kinetic energy, but this cannot happen if there are no unoccupied higher energy states accessible to the electrons. Consequently, only those electrons promoted to the balcony, by either heat or light, will be able to partic.i.p.ate in an electrical current, moving along the newly available empty seats. Diamond is an electrical insulator because normally there are too few electrons in the balcony to provide an appreciable current.

Figure 34: Sketch of the band of quantum states from the highest energy occupied levels in a solid and the band formed from the next highest energy available quantum states. In an insulator (a) the lower band is a.n.a.logous to a completely filled orchestra in an auditorium, where there is an energy gap separating the electrons in the lower band from the band of empty states (the balcony). The second figure (b) shows a situation where the lower orchestra is only half-filled and the electrons have ready access to empty seats-which describes a metal.

In contrast, in metals the ground-state electrons are localized in "momentum s.p.a.ce," and the orchestra that can seat two trillion trillion electrons is occupied by only one trillion trillion electrons. There are therefore many empty seats in the half-filled orchestra, as sketched in Figure 34b, and it is easy for the electrons to move from seat to seat when carrying an electrical current.

To construct a "glow-in-the-dark" nonmetallic solid, we need a filled orchestra, an empty balcony, and a "mezzanine" of seats, also unoccupied, just below the balcony (sketched in Figure 35). Let's a.s.sume, for the sake of argument, that blue light is required to promote an electron from the orchestra to the balcony, but the mezzanine can be filled using lower-energy green light. The energy separation between the balcony and the mezzanine is in the infrared portion of the electromagnetic spectrum. These mezzanine seats may arise from a different element that is incorporated into the solid.

Figure 35: Sketch of the band structure of a fluorescing solid, represented by a filled orchestra, an empty balcony at a high energy, and an unoccupied mezzanine level at a slightly lower energy than the bottom of the balcony. When the solid is illuminated with white light, electrons are easily promoted from the orchestra to the balcony, and photons are emitted when the electrons fall back into the lower level. Occasionally an electron will wind up in the mezzanine level, from which the transition rate to the orchestra is low. When the light exposure is stopped, these charges trapped in the mezzanine will eventually drop back into empty spots in the orchestra, emitting slightly lower energy photons in the process. In this way the material will give off light after being illuminated-that is, it will glow in the dark.

Now a.s.sume that the transition rate from the orchestra to the balcony is high. This means that it is easy to promote the electron up from the filled lower auditorium to the balcony, and once up in these states, the electron quickly falls back to the orchestra. The mezzanine is different-it has a very low transition probability, so that it is very hard to promote an electron from the orchestra into these levels. Once in the mezzanine, the electron has a very low probability of dropping back to the lowest energy state-it will thus sit in this state for a long time before dropping down.

Now, what will happen if we shine white light on this solid? White light is comprised of all visible colors in equal intensities. Due to the discrete nature of the quantized energy levels, the atom will ignore all colors except for the blue and the green (let's not worry about the finite energy width of the orchestra and balcony for now). The blue light will be readily absorbed, as the transition rate for the orchestra to the balcony is high. Of course-easy come, easy go-and the electron in the balcony also has a high probability of dropping back down to the orchestra (in either its original seat or an empty seat created when another electron was promoted into the balcony), emitting a blue light photon as it does so (Figure 35a). For the most part this cycle continues-orchestra absorbs blue light, promoting electron to balcony; electron then releases another blue photon when falling back to the lower energy state. Occasionally, if we do this enough times, a seat in the mezzanine level becomes occupied, either by an electron being directly promoted from the orchestra to this level (just because the probability is low doesn't mean it won't happen if we try enough times) or possibly from the electron in the balcony dropping down into the lower-energy mezzanine instead of falling back to the orchestra (Figure 35b). We would not notice the infrared light emitted when the electron went from the balcony to the mezzanine unless we had specific detectors sensitive to this portion of the spectrum (alternatively, the electron can emit thermal energy as it moves from the balcony to the mezzanine). Once in the mezzanine, the electron will stay there until (1) an infrared photon excites it back into the balcony (not likely, as there is very little infrared light of the necessary energy in the white light source I am using); or (2) the electron drops back to an empty seat in the orchestra, emitting a green-light photon in the process (which can happen but has a low transition probability).

So, as we expose this solid to white light, blue light is absorbed and we get blue light back, but eventually the solid ends up with electrons sitting in the mezzanine, leaving unoccupied seats in the orchestra. Now the light is turned off. All the electrons that are still up in the balcony rapidly drop down into the empty orchestra seats, and then as time goes on, the electrons in the mezzanine seats also fall back to the orchestra (Figure 35c), emitting photons as they do, even if the solid is now in a completely darkened room, glowing in the dark! Eventually, as the number of electrons in the mezzanine decreases, the light emitted by the solid becomes dimmer and dimmer, until it is recharged with another prolonged exposure to white light. From such simple quantum mechanical phenomena are totally awesome toys made.

Doc Savage's invisible writing must employ an "ink" for which the separation between the orchestra and the balcony is in the far ultraviolet portion of the spectrum, while the s.p.a.cing between the mezzanine level and the filled orchestra corresponds to blue light. Doc used the "black-light" lamp that emits ultraviolet light to promote electrons to the balcony, which then subsequently charge up the mezzanine. From the fact, as described in the pulp adventure, that the blue writing rapidly fades, we can a.s.sume that the electrons do not stay in the mezzanine level for more than a few seconds. The intensity of ultraviolet light in the Planck spectrum for sunlight is apparently too weak to charge up these states, which is why Doc needed to use the "black-light" lamp.

The energy separation between the balcony level and what we have termed mezzanine states, and how long electrons will remain in these states in the dark, depends on the particular elements that one introduces into the solid to produce these long-lived states. One does not need to use ultraviolet or visible light to promote electrons into these levels-any source of energy that can excite electrons from the orchestra to the balcony states can work.

Back in the 1950s, the hands of some alarm clocks were painted with radium, and the continuous emission of alpha particles would provide the energy necessary to keep the balcony in the phosphor material occupied, thereby enabling the hands to glow in the dark. When the radium emits an alpha particle, the nucleus converts into radon, which is also radioactive. Eventually the materials for glow-in-the-dark alarm clocks were replaced with less toxic substances. Nevertheless, radioactive materials, and their ability to emit sources of energy at a uniform rate, are hard to give up. Smoke alarms use a radioactive isotope to create a beam of particles, and an alarm is triggered when this beam is obscured from its detector by smoke or haze. Certain wrist.w.a.tches with glow-in-the-dark faces have replaced radium as the radioactive element that excites the phosph.o.r.escent material with high-energy electrons from the decay of tritium as the source of external energy. Most diners are likely relieved that Fiestaware dishes no longer employ uranium oxide in their bright orange-red glaze, as they did back in the 1930s. The shine on modern Fiestaware dinner plates may be not quite as bright, but it is much safer.

CHAPTER FIFTEEN.

Death Rays and DVDs.

The popularity of the Buck Rogers newspaper strip led to a similarly successful radio serial program, and in 1934 a competing strip featuring the adventures of Flash Gordon was introduced. By the mid-1930s the demand for Buck Rogers- and Flash Gordon-inspired toy ray guns was so high that the Daisy Manufacturing Company, which had the license to create stamped-metal versions of Buck's XZ-31 Rocket Pistol, ran out of both steel and cardboard boxes. Given the a.s.sociation of ray guns with the future conquest of s.p.a.ce, perhaps it is not surprising that in 1960, when the development of the laser was announced, the first thing the public wanted to know was whether science had at last delivered the long-antic.i.p.ated "death ray."

A patent for a laser, capable of projecting a high-intensity beam of visible light, designed by Charles H. Townes and Arthur L. Schawlow at Bell Labs, was filed in 1958, and in 1960 Theodore H. Maiman at Hughes Research Laboratory in California successfully constructed the first working device. At his press conference in 1960, Maiman was peppered with journalists' questions about whether he had in fact invented a death ray. When speaking to the public, scientists from Bell Labs were instructed by management to deflect any questions concerning using the laser as a lethal weapon and took pains to avoid saying anything that might be misconstrued or misquoted. Yeah, good luck with that. In 1961, the report in the Detroit News of a lecture by a Bell Labs scientist involved in their laser program prominently featured "Death Ray" as the invention's first potential application. Four years after Maiman's announcement, in 1964's MGM film Goldfinger James Bond is threatened with a slow, painful death while strapped to a table. The circular buzz saw of the 1959 novel was replaced in the movie with a high-power industrial laser, its beam slowly moving along the length of the table on a trajectory intended to bisect Agent 007.

The physics of the laser is essentially that of a glow-in-the-dark solid. Depending on their chemical composition and material properties, lasers can emit not just green light, but red, green, blue, ultraviolet, or infrared photons. The two big differences between lasers and glow-in-the-dark solids is that in lasers, the mezzanine levels are nearly completely occupied with electrons, and, more important, when the electrons in the mezzanine level drop down to the ground state, they all do so at the same time.

How can one ensure that all the electrons residing in the laser levels will choose to drop down to the ground state, emitting photons, simultaneously? Consider the auditorium a.n.a.logy for a solid, shown in Figure 35.60 I use essentially the same argument as for the glow-in-the-dark situation from the last chapter. Electrons from the filled orchestra level are promoted up to the balcony by, for example, the absorption of light, or an electrical current. The electrons excited up into the balcony leave behind empty seats in the orchestra. The transition rate is high for electrons to go from the orchestra to the balcony, and it is similarly easy for these electrons to drop back down into the orchestra, emitting light as they do so. Occasionally, an electron will not fall from the balcony to the orchestra, but into a mezzanine seat instead. The transition rate into or out of these mezzanine levels is very low, so once the electron is in one of these quantum states it will stay there for quite some time. If electrons can be excited up to the balcony, and from there to the mezzanine, faster than they spontaneously drop down from the mezzanine level back to the orchestra, then we can obtain a situation where we have nearly as many electrons in the mezzanine level as in the orchestra.

We are now ready for some laser action, as shown in Figure 36. There are two ways that an electron in the mezzanine band can return to an empty seat in the orchestra-it can fall or it can be pushed. The transition rate for an electron to spontaneously fall from the mezzanine to the orchestra can be, for some materials, up to a hundred million times slower than for the electron to move from the balcony to the orchestra. This was why we needed to go through the balcony levels in order to populate this intermediate energy band. What could push an electron down to the orchestra? Light.

During the transition from the mezzanine to the orchestra, the electron's wave function can be expressed as the overlap of the orchestra and mezzanine quantum states. During this process the electron's average location may be considered to oscillate between its value for each state. An oscillating electric charge emits electromagnetic waves at the frequency of vibration. A formal quantum mechanical a.n.a.lysis of this process finds that the energy emitted is in a discrete packet of energy (that is, a photon) whose energy corresponds to the energy difference between the mezzanine and orchestra levels.61 Once a photon is emitted, this quantum of the electromagnetic wave can induce oscillations in another electron up in the mezzanine level, making it easier for this second electron to jump down into the orchestra, emitting its own light quantum in the process. This second photon can stimulate another electron to make the transition, generating yet another photon with an energy given by the separation of the mezzanine and orchestra bands. In this way a cascade of falling electrons, each induced (pushed) by the oscillating electric field of a light quantum, results. One photon in therefore leads to potentially trillions of photons out, all with exactly the same energy, emitted all at the same time. As the photons are fast, as in speed-of-light fast, there is no noticeable time lag between the first electron falling from the mezzanine and the trillions of electrons stimulated by other photons. The device produces light amplification by stimulated emission of radiation and is called a "laser" for short.

Figure 36: The auditorium model from the last chapter, only now the occupation of the mezzanine level is quite high. A single photon can stimulate an electron in the mezzanine to drop down to an empty seat in the orchestra, emitting a photon in the process. This photon can in turn induce another electron to make this transition, with the net effect that a very large number of electrons may be stimulated into dropping down to the lower energy band, all emitting identical energy photons. This procedure is the basic physical mechanism underlying the laser.

Of course, if I want this stimulated emission of light to occur more than once, I have to continue to excite electrons up to the balcony level, so that I can maintain the population inversion of electrons in the mezzanine. Thus, it will take a great deal of energy to run the laser. The more photons that I want to be emitted per second, the more energy I have to expend maintaining the occupancy of the mezzanine level. A laser pointer used in a lecture presentation is relatively low intensity and can be run from two AA or AAA batteries, while the high-power versions used in industrial-laser cutting procedures require a thousand Watts of power, enough energy to run a standard household.

Lasers make use of the fact that the emitted light is coherent (that is, all the light waves are in phase with one another, as in the constructive interference example from Chapter 2, Figure 4). The material that is being stimulated to emit photons is typically housed in a long cylinder, both ends of which are mirrored, with one end having a small hole for light to escape. Consequently all the walls of the auditorium reflect photons, and only those light quanta moving in exactly the right direction toward the single exit will depart the hall.62 Those photons that do not leave the chamber will bounce back and forth, inducing more transitions from the mezzanine to the lower level. The laser light thus forms a tightly focused beam, and as the photons are in phase, they will exhibit minimal spreading upon leaving the laser cavity. Laser light is therefore invisible unless you look directly at the aperture of the laser cylinder, unlike incandescent lightbulbs, from which the illumination spreads out uniformly in all directions. We can see light from an incandescent bulb regardless of where we are looking, but in a sense these photons' energies are wasted, as light is. .h.i.tting objects I don't care about seeing. The laser beam can be seen only if it reflects off a surface. If there is no dust or particulates in the air to scatter the laser beam, the only way to see it is when it gets to where it is going. A tight, narrow laser beam, sent out from a lab on Earth, was measured to have broadened out to a width of only about two miles after traveling 240,000 miles to the moon.

Thanks to the quantization of energy levels, when the electrons drop from the mezzanine to the lower-energy orchestra in response to the photon stimulation, they will all emit light of exactly the same energy. The light from a laser will thus be of a single frequency, that is, one color, with remarkably small variations. An efficient mechanism to generate red laser light is to use a mixture of two gases, helium and neon. Both of these elements have completely filled outer quantum levels (as shown in Figure 31b) and are thus chemically inert-they do not lower their energy by forming any type of chemical bond. When an electron beam is pa.s.sed through this gas mixture, the kinetic energy of the electron current can be transferred when it collides with a helium atom. An electron in the helium atom is excited from the ground state to an "excited state"-which we have been terming the balcony level. The s.p.a.cing of their quantum levels is such that when the helium atom with its electron in the higher-energy state collides with a neon atom, it promotes an electron into a very long-lived excited state in the neon atom that acts as the mezzanine level. When light of the necessary frequency stimulates the neon atoms, they drop back to their ground state, emitting red photons.

By using electrically charged (that is, ionized) argon gas instead of a helium-neon mixture, green light can be produced. Using semiconducting diodes (much more on this in the next chapter), one can dispense with the gases and construct a completely solid-state laser, capable of producing red, green, or even blue light. Red light has a lower energy, of 1.9 electron Volts, and longer wavelength (about 650 nanometers) compared to blue light's photon energy of 2.6 electron Volts and a wavelength of 475 nanometers. The difference in wavelength may not seem like much, but it makes a big difference in your DVD player.

Anyone who has closely examined an old-style newspaper photograph, composed of a series of black and white dots, understands that the information contained in an image may be relayed via a series of pixels. Digital versatile discs (DVDs) and compact discs (CDs) encode images and sound or just sound, respectively, through a set of instructions for either a video display or audio system. Pixels are binary, in that they have just two states: on or off, bright or dark. All digital data representation basically involves strings of "ons" and "offs," often referred to as "ones" or "zeros."

The development of inexpensive, compact solid-state lasers enables one to "read" the storage of these ones and zeros on a disc. A laser is bounced off the shiny side of the disc, and the reflected light is detected by an optical sensor. If the surface of the disc is smooth, then the laser light, which travels in a straight line, will be reflected directly onto the optical detector, and that location on the disc will be recorded as being a bright spot. If the laser light falls on a region of the disc that is distorted (for example, at the edge of a little pit gouged into the disc or a b.u.mp protruding from the surface), then the light will scatter in some random direction and not be reflected onto the optical detector. The detector will thus indicate a dark spot at this location of the disc. Calling the bright spot a "zero" and the dark spot a "one," we can store and transmit digital information.

Moving the laser along the disc, one can record the sequence of smooth and rough regions and translate that into ones and zeros, which in turn can be decoded to make beautiful music. Actually, it's easier to keep the laser fixed and move the disc underneath it (rotating the disc at high speed-typically at several hundred revolutions per minute) as the laser spot is moved from the center of the disc to its outer edge. The higher the density of ones and zeros (that is, the more bits of information in a given length), the higher the resolution of the video or audio signal. Here is where innovations in laser technology, thanks to quantum mechanics, have had a real impact on consumer entertainment technology.

If you wish to paint a two-inch-high statuette of an Orc (to take a random geeky example), you do not use the same large brush you would use for painting your house (a.s.suming you are interested in doing more than just glopping a single color of paint on the figure). In order to apply different colors over the small details on the tiny character, you will need a very fine brush that would make house painting tedious but is well suited for the detailed work on the statuette. When light is used as a probe, the wavelength plays the same role as the fineness of the brush's bristles. One cannot use a wave to detect features smaller than the s.p.a.cing between the peaks or troughs of the wave.

This is why optical microscopes, using visible light whose wavelengths are on the order of several hundred nanometers, are not able to let us see viruses or other nanometer-scale objects, regardless of the focusing. To "see" such small-scale structures, either you need light with a wavelength on the order of nanometers or smaller (such as high-energy X-rays, which lead to the necessity to develop X-ray lenses and focusing procedures) or you can employ electrons. The de Broglie wavelength of electrons can be adjusted by varying the momentum, which is easy to control by changing the magnitude of the accelerating voltage acting on the electron beam, and a series of charged plates can focus the electron beam. Detection of the current either reflected from a surface or transmitted through a thin sample can thereby provide "images" with atomic-scale resolution, and these electron microscopes are another example of quantum mechanics in action.

In the early days of compact disc storage media, only infrared solid-state diode lasers were available. The wavelength of infrared light is fairly long, so the density of bits (bits per area) was low. As the size of the disc was fixed, this meant that the s.p.a.cing between pits on the disc had to be relatively large, and a typical disc could hold roughly 600-800 million bits. With fewer ones and zeros available, these pioneering compact discs could store enough information for music but not enough for high-quality video.63 With the fabrication of visible-light red solid-state lasers, the wavelength of the light decreased and the number of bits that could be squeezed on a disc similarly increased, up to approximately five billion bits. These digital discs were highly versatile (hence the name DVD), as they could encode both images and music. With the recent innovation of relatively inexpensive blue-light solid-state lasers, the density of bits can be increased even further. Now the same movie can be stored using a much greater number of pixels per inch, and these high-definition Blu-ray DVD players (where "Blu" stands for blue) can bring theater-quality video to the home.

How do the pits get on the DVD disc in the first place? With another laser. Readers of Dr. Solar-Man of the Atom # 16 in 1966 were treated to a feature page after the regular story, divulging "Secrets of Atom Valley." One such page discussed the "Birth of the Death Ray," which in comics at the time consisted of a laser mounted on a rifle. The concentrated beam of photons emanating from a laser can indeed do great damage, depending on the surface it illuminates. The light carries energy, and when the material absorbs this light, it must have a way to dissipate the excess energy per atom provided by the laser. "Temperature" is a bookkeeping device used in physics to keep track of the average energy per atom in a system. If the material cannot reemit the energy absorbed as light, then it must do so as atomic vibrations. That is, the material will heat up due to the application of the laser light, and if the power density (that is, the number of absorbed photons per area per second) is large enough, the material can be heated by the laser faster than the excess heat can be transferred to the rest of the solid. In that case the atoms may be shaken so violently that they break the bonds holding them in the material, and either melt or vaporize. The power of early lasers in the 1960s was characterized by the number of Gillette razor blades they could melt through. Laser ablation, where a laser beam evaporates a material, creating a vapor of a substance that is ordinarily a solid, is used in research laboratories to synthesize novel semiconducting materials, when the resulting vapor condenses onto a substrate or reacts with another chemical.

When writing information on DVDs and CDs, say, in the CD/ DVD burner in some home computers, the laser need not vaporize the disc. Rather, either it induces a chemical change in a dye that coats the disc, darkening it so that it is no longer reflective, or it can melt the material under the laser spot. When rapidly cooled, instead of being a smooth, uniform surface, the newly melted region will be rough and will ably serve as a "pit" that will scatter a second laser beam in the CD or DVD player. For commercially manufactured CDs and DVDs, a laser is used to cut a master disc, which is then used to stamp out multiple copies that contain the encoded information.

Figure 37: An "educational" page from Dr. Solar-Man of the Atom # 16 in 1966, showing how lasers can be used for good or evil.

The trouble with using lasers as "death rays" is that it is difficult to achieve the necessary power density needed to wreak any significant mayhem. To locally melt a small region on a DVD disc, one must supply a significant amount of energy in a short amount of time-faster than the energy can be transferred to the rest of the material. The issue is thus the rate at which the energy can be delivered, which in physics is termed the "power." One could construct a laser capable of melting large holes in the steel plating of tanks, but the laser would be as large as a desktop-not counting the required power supply.

The last panel of the Dr. Solar informational page in Figure 37 alludes to the laser's potential for healing, as well as harm. This was antic.i.p.ated in comic books as well. In "A Matter of Light and Death" in 1979's Action # 491, Superman removes the thick cataracts that have blinded a companion by using his focused heat vision. First Superman takes two lumps of coal and squeezes them until they form large, perfect diamonds. This is harder than you think-as Superman muses while compressing the coal, "Transforming carbon from its crude coal form to its purest state is no easy trick . . . even for me! After all, it takes Mother Nature millions of years and just as many tons of underground pressure to produce even one raw diamond . . . let alone two!" As coal is fossilized peat moss, what happens to the impurities in the lumps Superman squeezes, such as sulfur, nitrogen, and other chemicals, which are present in coal but not in an optically pure diamond, is not revealed. Holding these two large diamonds in front of his friend's eyes, he then uses his heat vision. As he performs the operation, the Man of Tomorrow thinks to himself, "These diamonds are filtering and concentrating my beams of heat vision into two super-laser beams-enabling me to do what man-made lasers couldn't-burn away those cataracts and restore his eyesight." (Good thing for readers that superheroes always narrate their actions in their heads!) Eight years later, Dr. Stephen Trokel would patent and perform the first non-superhero-enabled laser eye surgery, using an excimer laser that emits ultraviolet light (as opposed to Superman's heat vision, which presumably consists of infrared light) and was previously used to pattern semiconductor surfaces. While not a common method for treating cataracts, laser surgery for re-forming the cornea to correct myopia and other refractive vision processes is now quite common.

Did Doc Savage understand all of this when he communicated via invisible writing that could be read only under ultraviolet illumination, employing the same physics as glow-in-the-dark solids? Perhaps he didn't know all the details of how high-resolution DVD players work, but we need not wonder whether Doc was familiar with basic quantum mechanics. In 1936's Doc Savage adventure The South Pole Terror, Doc and his band of adventurers foil the elaborate scheme of a group of thieves and murderers who attempt to mine platinum from an Antarctic valley. The crooks are able to melt vast quant.i.ties of ice, and also kill interfering witnesses, using a strange heat ray, whose operation mystifies all but Doc. As he explains at the tale's conclusion: "It has long been known that the atmosphere layer around the earth stops a great many rays from the sun. Some of these rays are harmless, and others are believed capable of producing death or serious injury to the human body. [. . .] The particles of air, for instance, are made up, according to the Schroedinger theory, of atoms which in turn consist of pulsating spheres of electricity."

Doc had correctly surmised that his opponents had "an apparatus for changing the characteristics of a limited section of atmosphere above the earth to permit the entrance, through this atmospheric blanket, of the cosmic rays." Nine years before the Manhattan Project, Doc Savage was citing Schrodinger and fighting fiends who possessed a device that could open, at will, a hole in the ozone layer above Antarctica, demonstrating his mastery over both quantum physics and evildoers.

CHAPTER SIXTEEN.

The One-Way Door.

Matter is comprised of discrete particles that

exhibit a wavelike nature.

Science fiction pulps and comic books from fifty years ago told of how, by the year 2000, robots would break free of their shackles of servitude and rebel against their human overlords. In order to be capable of such insubordination, these automatons must have electronic brains capable of independent thought and initiative. They must therefore possess very sophisticated computers that are able to go far beyond the mathematical calculations of the "difference engines" of the 1950s. Such powerful computers are closer to reality than the writers back then may have thought, thanks to scientists at Bell Labs who, in 1947, making use of the advances in our understanding of the solid state afforded by quantum mechanics, developed a novel device that would dramatically shrink the size and simultaneously expand the computing power of electronic brains-the transistor.

In the 1957 issue of DC comics Showcase # 7, the Challengers of the Unknown crossed swords with a sophisticated computer atop a giant robot body. The Challengers are four adventurers-a test pilot, a champion wrestler and explorer, a professor and deep-sea-diving expert, and a mountain climber and circus daredevil-who are the sole pa.s.sengers on a doomed cross-country flight. Crashing in a freak storm, the plane is completely destroyed, yet the four pa.s.sengers walk away from the carnage unharmed. Realizing that they are "living on borrowed time," they devote their lives to adventure, repeatedly throwing themselves in harm's way as they 4 thwart alien invaders, mad scientists, and undersea monsters. Frankly, my response to the premise of this team's origin would be quite different-if I were to survive a horrific car crash, for example, I doubt I would then jump out of airplanes without a parachute or juggle nitroglycerin reasoning that as I could have died in the traffic incident, I am now able to take additional insane risks. But luckily for comic book readers, the Challengers' att.i.tude toward danger differed from my own, as not only were their tales exciting in their own right, but the foursome served as one of the models for Marvel Comics' 1961 superteam, the Fantastic Four.

Figure 38: Panels from Showcase # 7, where the Challengers of the Unknown discover that "ULTIVAC Is Loose!" Hesse, a German scientist captured by the Allies, gives physics lessons to his cellmate, bank robber Floyd Barker. Upon their release, the pair design and construct a "new type of calculating machine"-ULTIVAC!

The Challengers' challenge in Showcase # 7 is ULTIVAC, a fifty-foot-tall robot capable of independent thought. ULTIVAC is constructed by Felix Hesse, a German scientist who was captured by the Allies at the end of World War II and sent to prison as a war criminal. Hesse is a.s.sisted by Floyd Barker, a bank robber he meets in prison. They pa.s.s the time with physics lessons-the scientist teaching Barker ("All it takes is some study!" says the bank robber). Not too long after being released, they design and construct a giant calculating machine, as shown in Figure 38. The scientist remarks that ULTIVAC must be enormous "to do all the things we want it to do! This is going to be the greatest calculator of all time!" Apparently, as later revealed in the story, their get-rich scheme involves exhibiting their creation in Yankee Stadium, charging admission to see "two tons of steel . . . that thinks and talks like a man!" ULTIVAC rebels against this public display and flees, joined by Dr. June Robbins, a scientist who convinces ULTIVAC that humans and computers can be friends. Addressing an a.s.sembly of politicians, scientists, and national leaders, ULTIVAC promises, "I am willing to apply my power to the cause of helping mankind-if humanity meets me halfway!" However, rather than hand over to the government what he imagines to be a source of great wealth, the German scientist who built ULTIVAC damages him mortally. Emergency repairs are effected, and in the final panel we see that ULTIVAC is now a stationary calculating machine. As shown in Figure 39, Dr. Robbins has the last word, telling the Challengers, "The spark that made ULTIVAC think like a man is gone! But as a pure machine, he is still contributing much to man's knowledge!"

Figure 39: Final panel from Showcase # 7, where Dr. June Robbins describes to the Challengers of the Unknown the final disposition of ULTIVAC-while "just a stationary calculating machine," it is "still contributing much to man's knowledge."

By 1957, computers had indeed begun contributing much to humanity's knowledge, helping us with complex tasks. In 1946, scientists at the University of Pennsylvania constructed the first electronic computer, called ENIAC, for Electronic Numerical Integrator and Computer. It was more than eighty feet long and weighed nearly fifty-four thousand pounds. As the semiconductor industry did not yet exist, ENIAC employed vacuum tubes-nearly 17,500 of them-and more than seven thousand crystal diodes. It was owned by the U.S. military, and its first calculations were for the hydrogen bomb project. In 1951, the same scientists who built ENIAC, now working for Remington Rand (which would become Sperry Rand), constructed UNIVAC, a UNIVersal Automatic Computer that consisted of more than five thousand vacuum tubes and was capable of performing nearly two thousand calculations per second. This computer sold for more than $125,000 in the early 1950s to the military or large corporations and was used by CBS-TV to predict Dwight D. Eisenhower's victory in his run for the presidency in 1952. UNIVAC was unable to walk or fight jet planes, but it was about the size of ULTIVAC's electronic brain, as shown in Figure 39. Absent the semiconductor revolution, increasing the computing power of such devices entailed using more and more vacuum tubes and complex wiring, and as mentioned in the introduction, only a few large companies or the government would have the resources to purchase such machines.

The groundwork for the dramatic change that would reverse this trend, leading to smaller, yet more powerful computers, began in 1939, when a Bell Labs scientist, Russell Ohl, invented the semiconductor diode. We now know enough quantum mechanics to understand how this device and its big brother-the semiconductor transistor-work, and why many believe them to be the most important inventions of the twentieth century.

The first thing we need to address is the definition of a "semiconductor." We discussed two types of materials in Section 4-metals and insulators. Metals satisfy the Pauli exclusion principle by allowing each atom's "valence" electrons (those last few electrons not paired up in lower energy levels) to occupy distinct momentum states. The uncertainty in their momentum is small, and the corresponding uncertainty in their position is large-as these electrons can wander over the entire solid. At low temperatures there are many electrons available to carry an electrical current. Insulators satisfy the requirements of the Pauli principle by spatially restricting each atom's valence electrons, keeping them localized in bonds between the atoms, like the carbon-carbon bonds in diamond, sketched in Figure 32 in Chapter 12. At high temperatures, some of these electrons can be thermally excited to higher energy states (that is, from the orchestra to the balcony), where they can conduct electricity, but at low temperatures all the electrons stay locked within each atomic bond and the material is electrically insulating.

But what is a "low" temperature? Low compared to what? A convenient and natural temperature scale to compare "low" and "high" to would be room temperature. In this case, there is a third cla.s.s of materials that are much better conductors of electricity at room temperature than insulators such as gla.s.s or wood, but much poorer conductors than metals such as silver or copper. These partway-conducting solids are termed "semiconductors."

Recall from our discussion in the previous chapter that a laser is a material with an orchestra of seats, all filled with electrons, separated from a balcony where all the seats are empty. Let us ignore for the time being the "mezzanine" we posited residing between the filled orchestra and the empty balcony (we'll get back to those states soon). In an insulator the energy separation between the orchestra and the balcony is typically five to ten electron Volts, well into the ultraviolet portion of the electromagnetic spectrum. Consequently, only light of this energy could promote an electron up into the balcony (like Doc Savage's "invisible writing" from Chapter 14). The intensity of this light is normally low, and at room temperature there isn't enough thermal energy from the atoms to promote a significant number of electrons to the empty balcony. Consequently, if a voltage is applied to an insulator, there is a negligible current at room temperature. In a semiconductor, the energy gap between the orchestra and the balcony is much smaller, usually one to three electron Volts. Visible light photons, of energy between 1.9 and 3.0 electron Volts, have sufficient energy to excite electrons up to the conducting balcony. Similarly, at room temperature, the thermal energy of the atoms is large enough to excite some electrons into the upper band. Of course, the larger the energy separation between the filled states and the empty band, the fewer electrons will be thermally excited up to the conducting balcony at room temperature.

Semiconductors make convenient light detectors, as the separation between the bands of filled and empty states corresponds to energies in the visible portion of the spectrum. A particular material will have an energy gap of, let's say, one electron Volt (which is in the infrared portion of the spectrum that our eyes cannot detect). Normally, in the dark some electrons will be thermally promoted to the empty conduction band, leaving behind empty seats in the orchestra. These missing seats are also able to conduct electricity, as when an electron moves from a filled seat to occupy the empty one, the unoccupied state migrates to where the electron had been, as sketched in Figure 40. These missing electrons, or "holes," in a filled band of seats act as "positive electrons" and are a unique aspect of the quantum mechanical nature of electrical conduction in solids. This process occurs in insulators as well, only then there are so few empty spots in the lower-energy orchestra, and so few electrons in the balcony, that the effect can be ignored. The electrons up in the balcony in the semiconductor will fall back into the empty seats in the orchestra, but then other electrons will also be thermally promoted up to the empty conducting band. So at any given moment there are a number of electrons and holes in this semiconductor that can carry current. The current will be very small compared to what an equivalent metal wire could accommodate, and a circuit with the semiconductor will look like it has an open switch in the dark. When I now shine light of energy one electron Volt or higher on this semiconductor, depending on the intensity of the light, I can excite many, many more electrons into the empty band, and leave many, many more holes in the filled band. The ability of the material to conduct electricity thereby increases dramatically. In the circuit it will look as if a switch has been closed, and the electronic device can now perform its intended operation.

And that's how quantum mechanics makes television remote controls possible!64 The remote control sends a beam of infrared light (invisible to our eyes) to your set. If you point the front edge of the device away from the set, the signal does not reach the photodetector and the setting remains unchanged (with certain models one is able to bounce the infrared beam off a wall and still have a sufficient intensity of photons reach the set to be detected). Once the light beam reaches the semiconductor and is absorbed, the conductance of the material increases and the circuit is closed. The infrared beam sent when you press a b.u.t.ton on the remote control encodes information through a prearranged series of pulses (not unlike Morse code), and thus, different instructions can be transmitted to the set.

Figure 40: Sketch of nearly filled lower energy and nearly empty higher energy bands in a semiconductor. There will be some electrons promoted up to the "balcony" that can carry current (as they have easy access to higher energy quantum states, so they are able to gain kinetic energy and carry an electrical current). At the same time the vacant seats in the orchestra are also able to act as positive charge carriers, as other electrons slide over to fill the vacancy.

This is the same physics by which your smoke detector works. Some models use a beam of infrared light directed toward a photodetector. When the particulates in the smoke scatter the beam away from the detector, the circuit is broken and a secondary circuit sends current to the loud, high-pitched alarm. Other models employ a small amount of the radioactive isotope americium, which emits alpha particles when it decays. These alphas electrically charge the air in the immediate vicinity of the source, and the electrical conductivity of the charged air molecules is measured. Smoke particles trap these charges, and again, once the primary circuit is broken, a secondary circuit sets off the alarm. From automatic doors that open when you approach, to street lights that turn on when darkness falls, we do not notice how often we employ semiconductors' ability to change their electrical properties dramatically when illuminated by light.

These photodetectors played a key role in a broadcast of The Shadow radio show back in 1938. The Shadow, who in reality is Lamont Cranston, wealthy man-about-town whose true ident.i.ty is known only to his constant aide and companion, Margo Lane, has learned while in the Orient various mental powers that enable him to cloud men's minds. In Death Stalks the Shadow, a crooked lawyer, Peter Murdoch, sets a death trap for the Shadow using solid-state light sensors. When Lamont and Margo are out at a nightclub, they note a gimmicked door that opens whenever a waiter approaches. Lamont explains to his companion that the door is controlled by a photoelectric ray emitted by and detected by chromium fixtures on either side of the door, so that whenever the beam is broken, the door is opened. Lamont muses that such innovations pose a risk for him, as "the Shadow can hide himself from the human eye, Margo, but he has a physical being, and the photoelectric beam could detect his presence."

This is just the plan of Peter Murdoch, who hires an electrician to wire a sealed room with a steel door that will slam shut when a similar invisible beam ("You can't see it. The beam is infrared," explains the electrician) is broken when the Shadow enters the room. The death-room trap set, the electrician is murdered so that he cannot reveal Murdoch's plans. The Shadow does indeed enter the room, the steel door slams tight and is electrified, and poison gas is pumped into the room. Through this all the Shadow chuckles his low, sinister laugh. For he knows not only what evil lurks in the hearts of men, but also that in 1930s radio serials, even master criminals with law degrees are not very smart. To taunt his adversary, Murdoch has left the body of the electrician in the room with the Shadow. Removing a pair of pliers from the dead worker's overalls, our hero proceeds to disable the electricity in the room. The door no longer a threat, the Shadow escapes, captures Murdoch and his gang, and hands them off to Commissioner Weston and a promised cell on death row (the weed of crime bears bitter fruit, after all). Even infrared photodetectors are no match for . . . the Shadow!

But if this were the only advantage of semiconductors, the world we live in would not look that dramatically different from that of the 1930s. The real power of semiconductors is realized when different chemical impurities are added to the material, a process that goes by the technical term "doping." Consider Figure 41, featuring filled states, and the empty band of states at higher energy, likened to the filled orchestra and empty balcony in a concert hall. When discussing the physics of lasers, we introduced a "mezzanine" level, at a slightly lower energy than the balcony, which resulted from the addition of another chemical (typically phosphorus) to the material. In semiconductors there are two kinds of "mezzanines" that can be incorporated, depending on the specific chemical atoms added-those that are very close to the empty balcony and those that are just above the filled orchestra. If I manage my chemistry correctly, I can ensure that the benches right below the empty balcony have an electron in their normal configuration (Figure 41a). Then, even at room temperature, since there is only a very small gap in energy between the occupied bench and the empty balcony, nearly all the electrons will hop up to the balcony, and the holes they leave behind will be not in the orchestra, but in the seats in the upper mezzanine (Figure 41b).

Similarly, with a careful reading of the periodic table of the elements, a narrow band of seats (a "lounge," let's call it) can be placed just above the filled orchestra (Figure 41c). These lounge seats normally would be empty of electrons, depending on the chemistry of the added atom and the surrounding semiconductor material. An electron can then jump up from the filled orchestra, leaving a hole in the lower band without having to promote an electron up in the balcony (Figure 41d). The seats in the lower-energy lounge band, as well as the higher-energy mezzanine, are far enough apart from each other that it is hard for an electron or hole to move from seat to seat in these states. The mezzanine and lounge states are ineffective at carrying electrical current, but they can dramatically change the resistance of the surrounding semiconductor by easily adding either electrons to the balcony or holes in the orchestra. The first situation, with the mezzanine adding electrons to the balcony, is called an n-type semiconductor, since I have the net effect of adding mobile negatively charged electrons, while the second situation, with a low-energy lounge accepting electrons from the orchestra, leaving behind holes in the lower band, is termed a p-type semiconductor, as the current-carrying holes added are positively charged. As the atoms added to the material were previously electrically neutral, promoting an electron to the balcony from the mezzanine leaves behind a positively charged seat in these upper states, and accepting an electron into the lounge, leaving a mobile positively charged hole in the orchestra, makes the lounge seat negatively charged.

Figure 41: Sketch of a semiconductor where impurity atoms are added, resulting in a mezzanine level beneath the balcony, which at low temperatures is normally filled with electrons (a) that are easily promoted at room temperature into the previously empty balcony (b). Alternatively, different chemicals can produce states right above the filled orchestra (c) that at low temperatures are normally empty of electrons. At room temperature electrons can be easily promoted from the orchestra to these lower "lounge" seats, leaving empty seats (holes) in the orchestra that are able to carry electrical current (d).

If we added either n-type impurities or p-type impurities to a semiconductor, then the number of electrons or holes would increase, with the effect that the semiconductor would be a better conductor of electricity. Of course, if all we wanted was a better conductor of electricity, then we could have used a metal. No, the real value of doping comes when we take two semiconductors, one that has only n-type impurities so that it has a lot of mobile electrons in the balcony and holes stuck on the benches, and another semiconductor with mobile holes in the nearly filled orchestra and electrons sitting on the benches near the filled band, and bring them together. If these two pieces were each a mile long, then we would expect that very far from the interface each material would look like a normal n-type or p-type semiconductor. But the junction between the two would be a different matter.

The n-type material has electrons in the balcony but no holes in the orchestra, while the p-type semiconductor has mobile holes in the orchestra but none in the balcony. As shown in Figure 42, when they are brought together, the electrons can move over from the n-type side to the p-type (and the holes can do the reverse), where they combine, disappearing from the material. That is, the electrons in the balcony can drop down into an empty seat in the orchestra (remember that the Pauli exclusion principle tells us that no two electrons can be in the same quantum state, so the electron can drop down in energy only if there is an empty s.p.a.ce available to it), and it will be as if both an electron and a hole were removed from the material. But the positive charges in the seats in the mezzanine in the n-type solid and the negative charges in the seats in the lounge in the p-type material do not go away. As more and more mobile electrons fall into the mobile holes, more positive charges in the mezzanine in the n-type material and negative charges in the lounge in the p-type material acc.u.mulate, neither of which can move from one side to the other.

The net effect is to build up an electric field, from the positive charges in the n-type side to the negatively charged seats in the p-type material. Eventually this electric field is large enough to prevent further electrons and holes from moving across the junction, and a built-in voltage is created. Remember that the energy of these quantum states was found by the Schrodinger equation and is determined by the electrical attractions between the positively charged nucleus of each atom in the semiconductor and the negatively charged electrons. The effect of having an electric field across the interface between the n-type and p-type semiconductors is to raise the energy of the seats on the p-type side, relative to the energy of the seats on the n-type side, as shown in Figure 42b. Electrons on the left will now find it harder to move over to the right, and holes on the right will find a barrier inhibiting them from moving to the left. I have now made one of the most revolutionary devices in solid-state physics-the diode.

Figure 42: Sketch of an n-type doped semiconductor and a p-type semiconductor (a) brought into electrical contact, enabling electrons from the n-type side to fall into holes from the p-type side, leaving behind positively charged mezzanine seats and negatively charged lounge seats in the n-type and p-type semiconductors, respectively. These char