Big Changes Come in Small Packages.
The diode was the first important step into the semiconductor age, and the second major advance also came from Bell Labs, with the invention of the transistor. There are two different structures for a transistor-one that involves adding another n-type semiconductor to the pn junction (to make an npn device) and the simpler-to-understand (in my opinion) field-effect device. I discuss here the field-effect structure, as it will also help us understand how a flash memory stick (also known as a jump drive or a USB drive) works.
The arguments here do not depend on whether the material is n-type or p-type, but for simplicity we will pick a p-type semiconductor for definiteness. Imagine a semiconductor, such as silicon, as a rectangular slab, longer and wider than it is thick, as ill.u.s.trated in Figure 44a. On part of the top of the semiconductor we place an insulator that could be silicon dioxide, which in its crystalline form is called "quartz" and in an amorphous phase is termed "gla.s.s." On the top of the semiconductor surface there are two metal electrodes at each end, not touching the insulator. At one electrode a voltage is applied, and the resulting current pushed through the semiconductor is withdrawn at the other electrode. So far we have just described a way to measure the current pa.s.sing through the material for a given applied voltage, and the insulator plays no role in the conduction through the semiconductor. The metal electrodes on either side of the insulator have a surfeit of free electrons, and where they are in electrical contact with the p-type semiconductor they form an effective p-n junction. If we are trying to flow electrons through a p-type doped material these back-to-back p-n junctions will make it very difficult for the current to move through the semiconductor. Now, to make this device a transistor, let's put a sheet of metal atop the insulating slab. As shown in Figure 44a, there are two metal electrodes apart from each other on the top of the semiconductor, between which is an insulating slab, atop of which is another metal electrode. We have constructed a field-effect transistor.66 What happens if we apply a positive voltage to the metal electrode that is covering the insulating slab? As this top metal electrode is in contact with an insulator that does not conduct electricity, the charges will just stay on the metal, having no place to go. The electric field created by these charges will extend through the insulator into the semiconductor layer. Compared to the insulator, the semiconductor beneath the insulating slab is a pretty good conductor, though not as good as the metal. Electrons will be drawn toward the region near the insulator-semiconductor interface by the electric field. Without a voltage, the metal is electrically neutral, and there is no reason for any electrons in the semiconductor to be pulled toward this region. With a voltage applied to the insulator, piling up positive charges on the top of the insulating slab, a channel of electrons connecting the two other metal electrodes at either end of the semiconductor is created, shown in Figure 44b. This has the effect of reducing the electric field at each pn junction where the metal electrodes contact the semiconductor, and the ability of the material to carry a flow of electrons will be greatly improved. The positive voltage on the metal atop the insulator in a sense opens a gate through which the electrons can flow. Applying a negative voltage would push electrons away from the insulator-semiconductor interface, and the ability for electrons to flow would be reduced (the gate would swing shut in this case). This is what a transistor does-it provides a way, by applying a small voltage to the gate electrode, to dramatically alter and potentially amplify a current pa.s.sing through the semiconductor.
Figure 44: Sketch of a simple transistor device structure (a). Two metal electrodes on the top of the semiconductor are used to pa.s.s a current through the device. A thin insulator (such as gla.s.s), on which is a metal electrode, lies on top of the semiconductor between the two metal electrodes used to pa.s.s the current. When a positive voltage is applied to the "gate electrode," positive charges acc.u.mulate on the top of the insulator, which attract electrons in the semiconductor to the region underneath the insulator (b). These electrons improve the ability of the semiconductor to pa.s.s a current between the two metal electrodes, and the current is made much larger by the application of the "gate voltage."
Remember from the last chapter the discussion of the influence of a built-in electric field on a pn junction on the energy of the bands of states in a semiconductor. Changing the electric field alters the energy of the quantum states that are calculated using the Schrodinger equation (demonstrated through the influence of the electric field of the positively charged nucleus on the electrons' allowed energies). If no voltage is applied, then there is no extra field on the semiconductor, and the number of electrons available to flow in the p-type semiconductor is very low. If a positive voltage is applied to the insulator, it will change the energy of both the orchestra and balcony of states. The change is strongest near the positive charges on the insulator and decreases as one goes farther into the semiconductor. Near the region by the insulator, electrons can now be thermally promoted into the balcony of the material. Consequently, the region near the insulator, when there is a positive voltage applied to a p-type semiconductor, will see a large enhancement in its ability to carry a current of electrons. The sensitivity of the current pa.s.sing through this device to an externally applied gate voltage results from changes in the energy of the quantum states in the filled orchestra and empty balcony, which in turn are understood from the quantum theory of solids.
If the voltage applied to the insulator changes with time (such as in the case of a weak radio signal detected by an antenna), then the current pa.s.sing through the semiconductor will also vary in time but as an amplified version, capable of driving speakers so that the radio signal can be heard. Transistor radios and television sets, employing the amplification capability of these devices, were some of the first applications of these devices, replacing the vacuum tubes and making these consumer electronic products smaller and lighter.
Vacuum tubes accomplish the same task as a transistor, by heating a wire until electrons "boil off" the filament. A voltage applied to a screen then attracts these free electrons to a collector, and depending on the voltage, the electrons can be accelerated toward or reflected away from the collector. In order to minimize the electron beam's scattering from air molecules, all the air in the tube should be removed. Such devices are bulky and fragile, use considerable power, generate a great deal of heat (necessitating s.p.a.cing them a distance from each other), and are expensive to produce. A semiconductor transistor accomplishes the same task without requiring a gla.s.s-enclosed vacuum, in a compact, rugged design, and wastes very little energy as heat; and the only limitations on the size of the device are the ingenuity in constructing the insulating slab and applying the metal electrodes, and making contact with the rest of the circuit.
If we can make the transistors small, we can put several transistors on a single piece of silicon. By varying the concentration of chemical impurities that add either excess electrons or holes to the semiconductor, and through the placement of other metal electrodes and insulating slabs, one can incorporate diodes, resistors, and capacitors into the same semiconductor along with the transistor. In this way the various aspects of a complex circuit can be integrated onto a single semiconductor chip. In 1958, just a year after the Challengers of the Unknown faced off against ULTIVAC, whose electronic brain was as large as a room (Figure 39), Robert Noyce and Jack Kilby independently designed and constructed the first integrated circuits. The first of these devices incorporated roughly five to ten transistors on a single silicon wafer. In the introduction I discussed Moore's law, whereby the number of transistors on an integrated circuit doubles every two years. The continued accuracy of this prediction surprised even Moore, and in 2010 the number of transistors on a chip can be over a billion. Estimates of the number of transistors in a computer's microprocessor suggest that on a typical college campus there are many more transistors than there are stars in the Milky Way.
These transistors do more than simply amplify information, as in the case of a weak electromagnetic wave signal being boosted in a cell phone. They also can store and manipulate information. When a large positive voltage is applied to the gate electrode on the insulator, the current-carrying capability of the semiconductor is greatly enhanced. Removing this large voltage restores the silicon to its poorly conducting state. The first situation can be described as a "one," while the second is a "zero." Just as the DVDs and CDs in the previous chapter are able to encode complex information through a series of ones and zeros, the transistors on the integrated circuits can do the same. However, transistors offer the possibility of much greater sensitivity to small perturbations. Transistors have been fabricated in the research laboratory with dimensions of under a hundred nanometers, where, depending on the voltage applied to the gate electrode, the transport of a single electron can be detected. Computers use transistors as logic elements that can be in an "on" or "off" state-and transistors can be fabricated whereby the difference between the two conditions is the motion of one electron.
It may seem surprising that one could construct a complex literature using an alphabet consisting of only two letters. But if there is no constraint on the length of a given word, then there is indeed enough flexibility to perform even the most sophisticated mathematical operations, such as adding two numbers. A full discussion of how diodes and transistors are combined to perform a variety of logic functions, and the Boolean mathematics that underlies their calculations, warrants its own book, and would take us too far afield for a discussion of the applications of quantum mechanics. Nevertheless, I do want to conclude this chapter with a discussion of one modification of the transistor structure that is already changing our everyday life.
Long-term information storage in a computer is done via the magnetic hard drive. A disc contains a record of "ones" and "zeros" in the form of magnetic domains, with a magnetic field pointing in one direction counting as a "one" and a field pointing in the opposite direction as a "zero."67 An externally applied magnetic field can polarize regions ("bits") on the drive, and write the sequence of ones and zeros that encode information. A smaller magnetic sensor, essentially a layered metallic structure whose resistance is very sensitive to the external magnetic field, is brought near the disc. If the magnetic field of a bit points in one direction, the resistance of the sensor will have one value; it will have another if the bit's magnetic field is in the opposite direction. The disc itself spins like a DVD or CD at high speeds of more than five thousand revolutions per minute, and the sensor rides just above the hard drive, with a s.p.a.cing that is equivalent to one-hundredth the diameter of a human hair. To store more information, one makes the platter larger and the bits smaller. That this magnetic device is capable of storing information without an external power supply (once the bits are magnetized, they stay in the same orientation), and with a relatively low failure rate (despite fears of "hard-drive crashes," the medium is extremely reliable given the use it endures), is a testament to the skill of engineers.
Transistors are also able to store information. For the device configuration we have discussed, the conductance of the semiconductor is low if there is no voltage to the gate metal (representing a "zero"), and high (standing in for a "one") when a positive voltage is applied. However, once the external voltage is turned off, then all transistors in a circuit default back to their low conductance state.
How can I store and preserve the high-conductance channel of a transistor, that is, keep the "ones" from turning into "zeros" after the voltage is turned off? Flash memory devices add a very small wrinkle on the field-effect structure we have described. To the standard field-effect transistor configuration, the flash memory adds a second metal electrode in the insulating layer, a very small distance above the semiconductor. So the device has a metal gate, a thin layer of insulator, another thin metal electrode, and then a very thin layer of the insulator atop the semiconductor.
What's the point of the second metal layer? If the two electrodes that used to pa.s.s the current through the semiconductor are shorted, and a large voltage is applied to the gate metal, then electrical charges can quantum mechanically tunnel to this interior electrode. This electrode is not connected to any outside wires and is termed the "floating gate." The floating gate can be a thin metal film, or it could be a layer of silicon nanocrystals, separated from one another so that these charges remain on the silicon particles and do not leak away. The charged floating gate generates an electric field in the semiconductor, influencing the current-carrying channel and maintaining the device in either a high- or low-conductance state (that is, recorded as a "one" or a "zero") even after the voltage is removed from the gate metal. Until a voltage of opposite polarity is applied, the transistor will store this state of the transistor, even when the transistor is unplugged from any power supply (such a memory is termed "nonvolatile"). The story goes that a colleague of Fujio Masuoka, the inventor of this type of transistor memory, when describing how quickly the stored information could be erased, said that it reminded him of a camera's flash, whence the nickname for the device derives. At the time of this writing, flash memory devices capable of storing 256 gigabytes of information (large enough to store more than ten thousand copies of this book as Word doc.u.ments) are being manufactured.
Nonvolatile memories have also revolutionized photography. In conventional, nondigital cameras, a light photon induces a chemical change in a photographic film. The information as to where the photon was absorbed by the molecule in the film is stored, and then a series of wet chemistry steps transfers this information to a photographic print. The graininess of individual molecules in a conventional film is now replaced with a pixilated grid. When photons strike the photodetectors in a given pixel, they will, if absorbed, create mobile charges. Using different semiconductors, the energy separation between the filled and empty bands of states can be changed, enabling photodetectors that can image in the infrared, visible, or ultraviolet portion of the spectrum. The charges up in the balcony can be converted to voltages, and then stored on flash memories. The location of each pixel is known, so a digital record of the number of photons that struck the array of photodetectors is obtained.
Once an image is digitally captured, the ability to display it on a flat panel screen, as opposed to the bulky cathode ray tubes that were a feature of televisions up until fairly recently, also makes use of semiconductor transistor technology. The bits of information in this case are the pixels on the display screen. In each pixel is a small amount of a "liquid crystal," consisting of long chain organic molecules (that is, carbon atoms bonded in a line, with various other elements and chemical groups protruding from the carbon chain). Geometric constraints and electrostatic charges along the carbon line will lead certain long chain molecules to pack together in different arrangements, from a loose, random collection to a herringbone pattern not unlike a professor's tweed coat to a more ordered phase similar to matches tightly stacked in a box. Just as the matches can be easily poured out of the matchbox regardless of their packing, these long chain molecules retain the ability to fill a container and flow as a fluid.
Certain liquid crystal molecules will make a transition from one ordered configuration to another when the temperature is changed-or if an external electric field is applied to the molecules. The optical properties of water change dramatically when ice undergoes a phase transition and melts-similarly, when certain liquid crystals change from one packing state to another under an external voltage, there can be an a.s.sociated change in their optical properties, such as whether the material reflects light and is s.h.i.+ny or absorbs light and appears dark. Early "liquid crystal watches" had metal electrodes in "broken eight" pattern, and depending on which metal plate had an applied voltage, different regions of the liquid crystal would appear dark, and thus form different numerals depending on the time of day. These liquid crystal displays (LCDs) are still employed in certain clocks and timers. For more sophisticated image displays, a capacitor and a thin film transistor (sometimes referred to as a TFT) are placed behind each liquid crystal pixel. Color filters can convert a grayscale image to a color one, and by changing the timing of when each pixel is turned on and off, one can view a moving image, similar to the television screen shown on the cover of the December 1936 Amazing Stories science fiction pulp (seen in Figure 45).
The ability to instantly display the stored image (or video) and the convenience of data transfer and large storage capacity, coupled with the incorporation of these cameras into other devices (such as cell phones or computer screens), has exceeded the expectations of science fiction pulp magazines-well, with one exception. As ill.u.s.trated in Figure 46, the notion that a device capable of wireless video reception and broadcasting small enough that it would fit on a person's wrist was indeed antic.i.p.ated in 1964 by the comic strip creator Chester Gould. Wrist phones that are capable of video transmission are now becoming available, another example of fiction becoming reality through quantum mechanics. Now, if we could only figure out how to construct personal "garbage cans" (Chapter 4, Figure 8) that fly by means of magnetism!
Figure 45: While the s.p.a.ce Marines appear to be viewing a flat panel display on this cover, the story by Bob Olson indicates that they are in fact watching a 3-D picture tube image.
Figure 46: d.i.c.k Tracy using a two-way wrist phone with video capabilities, This gadget was introduced in 1964, a good forty years before real technology would catch up with the comic strips.
Everything-light and matter-has an
"intrinsic angular momentum," or "spin,"
that can have only discrete values.
One of the most surprising discoveries made by physicists probing the inner workings of the atom was that electrons-subatomic particles that are the basic carriers of negative charge-also are little bar magnets, like those shown in Figure 10 in chapter 4. This intrinsic magnetic field is a.s.sociated with a property called "spin," though this term is a misnomer-while it does relate to intrinsic angular momentum, the magnetic field a.s.sociated with the electron doesn't really come from its spinning like a top. Nevertheless, when physicists refer to the internal magnetic field possessed by electrons (or protons or neutrons), they inevitably speak of the particle's spin.
A transistor modulates the current flowing through a semiconductor by the application of an electric field to an insulating slab on top of the conducting material. In this way the current flowing through the semiconductor is regulated through the electron's negative charge. The magnetic field that the electron exhibits has been, in most electronics up till now, completely ignored. As one might imagine, this situation changes in devices characterized as "spintronic," a shorthand expression for "spin transport electronics." Here the electron's magnetic field is a crucial component of the signal being detected or manipulated. One form of spintronics has been employed in computer hard drives, while the next generation of such devices (discussed in Section 6) may make hard drives unnecessary.
As described in Chapter 15, a DVD encodes information in the form of ones and zeros as smooth or pitted regions on a s.h.i.+ny disc. A laser reflected from the surface of the disc does so either specularly, that is, smoothly onto a photodetector if the surface is smooth, or diffusely, away from the detector if it strikes a jagged pit. Similarly, the hard disc drive in a computer is a magnetic material with regions magnetized in particular patterns; the smallest elements of the pattern are termed "bits." The drive stores information in the form of ones and zeros as magnetized regions, with north poles pointing in one orientation representing a "one," and in the other direction standing for a "zero." Each bit (in current disc drives) is written by moving a magnet over the region, which orients the magnetic pattern. To create the opposite pattern, a magnetic field in the reverse direction is applied. To erase the bit, a depolarizing magnetic field is applied. To read the "one" or "zero" stored on the disc, hard drives employ sensors such as "giant magnetoresistance" devices or "magnetic tunnel junctions."
All solids have bands of allowed states in which the electrons may reside, separated by energy gaps where there are no allowed quantum states. The difference between an insulator and a metal is that for an insulator (or a semiconductor), the last filled band, the orchestra in our auditorium a.n.a.logy, is completely filled, with every possible energy state being occupied by an electron. In contrast, in metals, the lower orchestra level is only half filled, as shown in Figure 34b in Chapter 14. If a voltage is applied to a metal, the electrons feel a force. This force in turn accelerates the electrons, causing them to speed up and increase their kinetic energy. Recall the water-hose a.n.a.logy of metal wires-the voltage is like the water pressure, and the electrical current is the resulting flow of water through the hose. As there are always some unoccupied seats in the lower orchestra level of a metal, electrons in the upper, filled rows can always move to higher energy states, and the material is able to conduct an electrical current.
What determines the current observed in a metal for a given applied voltage? Normally the electrons can surf using the atoms in the metal wire-as long as the atoms are in a uniform crystalline arrangement, they do not impede the electrical current. One can run on a city sidewalk and never step on a crack (thereby preserving one's mother's back) as long as the placement of the concrete segments is uniform and matched to one's stride. If there is a hole in the sidewalk, or a protruding tree root, or a shortened segment, then it is likely that the runner will stumble. In any real metal wire there will be defects such as crystalline imperfections (atoms randomly located out of their preferred ordered positions) and impurities that inevitably sneak into the solid during the fabrication process. Electrons accelerated by a voltage will scatter from these defects and transfer some of their kinetic energy to these atoms.
Sometimes this scattering is a good thing, as in an incandescent lightbulb or a toaster. There a large current is forced through a narrow filament, and the accelerated electrons transfer so much of their energy to the atoms in the wire that they shake violently about their normal crystalline positions. This shaking heats the wire until it is glowing red-hot (as in the coils in your toaster), and for higher currents in thinner wires, the shaking can cause excitation of electrons to all higher energy states equally, with resultant emission of light of all frequencies, perceived as white light (as in the filament of a lightbulb). Sometimes the loss of energy through collisions with atoms in the metallic wire is a bad thing, as in electrical power transmission cables; in order to compensate for these energy losses, the voltages along the lines must be very high, requiring power substations and transformers along the line.
Computer hard-drive disc readers employ the scattering of an electrical current by magnetic atoms to sense the different fields of the magnetized bits. A thin, nonmagnetic metal is sandwiched between two magnetic metals. In the absence of an external magnetic field, one slice of magnetic "bread" is permanently polarized so that its magnetic field points in one direction within the layer, while the other slice of bread is polarized in another direction (the nature of the quantum mechanical coupling between the magnetic layers, separated by the nonmagnetic middle layer, leads to this configuration being the low-energy state).
Imagine a flow of electrons perpendicular through the top of this "sandwich," pa.s.sing through the face of one slice of magnetic bread, through the nonmagnetic metal meat of the sandwich, and finally through the face of the other magnetic metal bread slice, as shown in Figure 47. When first entering the first magnetized layer, the electrons are unpolarized-their internal magnetic fields are as likely to point in one direction (spin "up") as the other (spin "down"). The first ferromagnetic layer polarizes the electrons, and those that move into the nonmagnetic s.p.a.cer layer will have their internal magnetic fields pointing in the same direction as the field in the first metal layer. When they reach the second magnetized layer, which normally has a field pointing in the opposite direction, these polarized electrons are mostly reflected, so very little electrical current pa.s.ses through the second layer and leaves the sandwich. If very little current results for a given voltage, we say that the device has a high resistance for an electrical current pa.s.sing perpendicular through the three layers.
Now this structure is placed in an external magnetic field, such as that created by a magnetized bit on a computer hard drive. The external field forces both magnetic layers in this sandwich (Figure 47b) to point in the same direction. When an electrical current now pa.s.ses through this structure, the first layer polarizes the electron's magnetic fields as before, and the second layer, now pointing in the same direction, readily allows the electrons to pa.s.s through, and hence a large current flows through the three-layer device. This change in resistance with an external magnetic field can be very large, up to 80 percent or more (they are, seriously, technically known as giant magnetoresistance devices), which means that they are very sensitive to even small magnetic fields. One can thus make the magnetically polarized bits on the hard drive smaller and still be able to reliably read out the sequence of "ones" and "zeros." Smaller bits means more of them can be packed on a given disc area, and the storage capabilities of computer hard drives have increased dramatically since the introduction of this first spintronic device.
Figure 47: Sketch of the device structure used to measure magnetic fields with an electrical current in a computer hard drive. An electrical current has both a negative charge and a built-in magnetic field resulting from its quantum mechanical intrinsic angular momentum ("spin"). Electrons flowing into the device are magnetically polarized by the first layer. In (a), the second layer is aligned opposite to the first, so the electrons polarized by the first layer are repelled by the second, and a very small current results. In the second case (b), the second magnetic layer is aligned in the same direction as the first, and the polarized electrons easily pa.s.s through the second layer. This configuration would present a low resistance to the flow of current, while the first case (a) would represent a high resistance state.
The first generation of iPods was able to store large data files on a small magnetic disc because the sensors used to read the information made use of the giant magnetoresistance effect. The drive to pack smaller magnetic bits at higher densities has led to the development of magnetic sensors on hard drives that employ another quantum mechanical phenomenon-tunneling-to sense the magnetic fields of the bits. These sensors have essentially the same structure as the device in Figure 47. Instead of a nonmagnetic metal placed between the two magnetic slices of bread, a thin insulator is used. A current can pa.s.s through the device only via tunneling, and the probability of this process turns out to be very sensitive to the magnetic polarization on either side of the barrier. These devices provide an even more sensitive probe of very small magnetic fields and are found in computer hard drives currently available for purchase. Every time we access information on our computers, we are making use of the practical applications of quantum mechanical tunneling.
The basic principles underlying giant magnetoresistance are finding new applications in future spintronic devices. Giant magnetoresistance was discovered in 1988 by Albert Fert in France and independently by Peter Grunberg in Germany, for which they shared the n.o.bel Prize in Physics in 2007. By 1997, hard drives containing read heads using the giant magnetoresistance effect were available for sale. It is actually not unusual for quantum-mechanics-enabled devices to quickly find their way into consumer products. Bell Labs held a press conference announcing the invention of the transistor in 1948, and by 1954 one could purchase the first (expensive) transistor radio.
A Window on Inner s.p.a.ce.
In the 1963 Roger Corman science fiction film X: The Man with the X-ray Eyes, Dr. James Xavier, searching for improvements in patient care, develops a serum in the form of eye drops that enables a person to see through solid matter. Eschewing animal testing as not being suitably reliable, he experiments on himself and does indeed gain the ability to see through a person's clothing and epidermis. However, this success leads to one of the greatest catastrophes that can befall any scientist-he loses his research grant when his funding agency discounts his claims of "X-ray vision!" Nevertheless, his ability to see within the interior of a person enables him to save a small child's life, as he recognizes that she was about to receive an unnecessary and ineffective operation. Sadly for Dr. Xavier, his X-ray vision becomes stronger and stronger, until his eyelids and thick dark gla.s.ses provide no respite. It does not end well for the well-meaning doctor, as the biblical expression "If thine eye offend thee ..." plays a key role in the film's conclusion.
Fortunately we can safely peer inside a person, see his or her internal organs, and discriminate healthy tissue from cancerous growths, without the disastrous consequences suffered by Dr. Xavier. I now address a device that has become common in most hospitals and many medical clinics and would certainly have strained the credulity of the editors of any science fiction pulp magazine had it been featured in a submitted story-magnetic resonance imaging, or MRI. This process, enabling detailed high-resolution imaging of the interior of a person, is a striking ill.u.s.tration of how our understanding of the quantum nature of matter, driven by scientists' curiosity in the 1920s and 1930s about the rules governing the behavior of atoms and light, has led to the development of technologies that futurists could not suspect fifty years ago.
We have made use of the intrinsic angular momentum of fundamental subatomic particles when determining which form of quantum statistics-Fermi-Dirac or Bose-Einstein-they would obey. In this way the internal spin is crucial to understanding the nature of metallic or insulating solids but was not employed directly when describing the physics of diodes or transistors. a.s.sociated with the spin is a small intrinsic magnetic field that enabled Stern and Gerlach to measure the spin in the first place (Chapter 4), and remotely probing the magnetic field from the spin of nuclear protons enables magnetic imaging.
We are composed mostly of water-molecules consisting of an oxygen atom bound to two hydrogen atoms. Each hydrogen atom has a single proton in its nucleus. The intrinsic spin of the proton is /2, and there is a small magnetic field a.s.sociated with each proton. The magnetic field has a north and south pole (Chapter 4, Figure 10), and when we place the water molecule in an external magnetic field, the hydrogen atom's proton points either in the same direction as the applied field (that is, its north pole points up while the lab magnetic field does likewise) or in the opposite direction (its north pole points down while the external field's north pole points up). The proton in the nucleus has a series of available quantum levels, just as the electron has its own series of possible states. If the proton's magnetic field is in the same direction as the external magnetic field, it is in a lower energy state. If the proton's magnet is opposite to the external magnetic field, then it will have a higher energy, as it takes work to rotate it to the lower-energy, aligned configuration. As indicated in Figure 48, the energy level that is occupied by the single proton can thus be split into two energy values by placing the hydrogen atom between the poles of a strong magnet, with the proton's energy being lower than what we find with no outside field or the energy being higher, depending on whether the proton's magnetic field points with or against the external field, respectively.
Figure 48: Sketch of the energy level of a single proton in the nucleus of a hydrogen atom (a) when no outside magnetic field is applied and (b) when a field is present. In the second case the proton's energy is lowered if its own intrinsic magnetic field points in the same direction as the outside magnet, and the energy is higher if it points in an opposite direction. In this figure the proton is indicated with its spin aligned with the external magnetic field and thus in the lower energy state. If the spin were opposite to the external field, the proton would reside in the higher energy state.
Say a proton is aligned in the same direction as the external magnetic field, in the lower-energy split state (Figure 48b). If I provide energy, in the form of a photon, I can promote the proton to the higher-energy state, which corresponds to the proton's magnetic field being opposite to the outside magnet. This resonant absorption is entirely a.n.a.logous to the line spectra (Chapter 5, Figure 13) for electronic energy levels in an atom. In essence the photon provides energy to flip the proton's internal magnet, from pointing up to pointing down (for example). It is as if I had a top that was spinning clockwise, and with an appropriate pulse of energy I caused its direction to reverse, so that it was now rotating counterclockwise.
The bigger the external magnetic field, the larger the energy splitting. That is, it requires more energy to flip the orientation of the proton's magnetic field if it is in a large external field than in a weak field. If the hydrogen atom is placed in a magnetic field roughly twenty thousand to sixty thousand times stronger than the Earth's magnetic field,68 then the separation in energy between when the proton is aligned with and against the external field is less than a millionth of an electron Volt. In comparison, the binding energy holding the hydrogen atom to the oxygen atom in the water molecule is nearly five electron Volts. Recall from Chapter 2 Einstein's suggestion that the energy of a photon is proportional to its frequency (E = h f). A photon capable of promoting the proton from one magnetic orientation to the other (as in Figure 48b) is in the radio portion of the electromagnetic spectrum. As this form of electromagnetic radiation penetrates through a person (which is why you can hear your transistor radio even when you place your body between it and the broadcast antenna), this energy region is well suited to probing the proton's orientation within a person.
The idea begins to form. Place a person in a large magnetic field, strong enough to generate an appreciable energy splitting for the protons in the water molecules that are in every cell in his or her body. Direct a transmitter of radio waves at the person, and the more photons that are absorbed, promoting a proton from one magnetic orientation to the other, the more water molecules there must be. How do we determine whether a radio wave is absorbed or not? A high exposure will transfer many protons from the lower energy state to the higher energy level. When the radio-frequency light is turned off, the hydrogen atom's protons flip back down to the lower energy state, emitting photons as they do. In this way the person "glows in the dark," emitting radio-frequency light that is detected and is the hallmark of the resonant absorption. The number of aligned protons throughout the bulk of the person's body may thus be measured.69 How do we obtain spatial resolution throughout a cross section of the person? By varying the strength of the magnetic field. Make the magnetic field very small at the left-hand side of the person and very large on the right, increasing linearly from one side to the other. As the energy s.p.a.cing depends on the strength of the external magnet, the separation between levels will be small on the left and grow to a larger energy gap on the right. Consequently, the minimum photon energy that will induce a transition will be larger on the right than on the left. By varying the frequency of the radio signal, one can determine the amount of absorption on the left, middle, and right of the person. By using secondary magnets in the cylinder that encloses the person, information on the proton density with full spatial resolution can be obtained. As shown in Figure 49, this imaging of the magnetically induced resonant absorption enables us to probe the inner secrets of a three-pack of chocolate peanut b.u.t.ter cups, confirming, through application of advanced quantum mechanics, that there is indeed delicious peanut b.u.t.ter within the chocolate coating.
Figure 49: Magnetic Resonance Image of three packets of peanut b.u.t.ter cup candy. The difference in spin relaxation times provides a basis for contrast between the chocolate coating and the interior filling, confirming the presence of the peanut b.u.t.ter inside the candy without having to bite into the candy (not that we wouldn't be willing to make such sacrifices for science!). Courtesy of Professor Bruce Hammer at the University of Minnesota.
But all cells in the body contain water, so there will be strong proton absorption at all points in the body. Where does the contrast come from? There are other elements that exhibit a magnetically induced resonance absorption signal, such as sodium, phosphorus, carbon, oxygen, nitrogen, and calcium. These elements have radio resonances at different frequencies than hydrogen and can thus be distinguished from the single proton signal. However, a more powerful technique involves not the magnetically induced signal, but the manner in which it goes away and then returns.
When the magnetic field is applied, many of the hydrogen atom's protons in the water molecules will line up with the external field, so that nearly all of the lower energy states will be occupied, and the higher energy states, corresponding to the proton's magnetic field opposing the applied field, will be less occupied.70 Under a continuous exposure of radio-frequency light, more and more protons are promoted to the higher energy state, until the situation is reached when the average number in the upper state (with a magnetic field pointing down) is equal to the number in the lower state (with a magnetic field pointing up). At this stage, we have for the collection of protons an equal number with their north poles pointing up as we have with their north poles pointing down. The total net magnetization of the protons will therefore be zero. If we now stop the continuous illumination, the protons in the higher energy state will relax back to the lower energy configuration. The characteristic time that this will take is highly sensitive to the local environment in which the particular water molecule resides, as the interaction of the proton's magnetic field with thermal vibrations of other atoms and with the magnetic field from other elements in its vicinity determines how hard or easy it is to polarize. It was discovered through careful experimentation that the time dependence of the restoration of the net magnetization is different for the various tissues in the body, providing a basis for contrast in the resulting images. One can inspect for blood-vessel blockages, cysts, or growths, and determine whether or not tumors are benign, based on differences in magnetization times. By careful examination of the time dependence of how the protons resume their original magnetization, a thorough diagnosis, which previously would have required X-ray eyes, is possible.
There are of course a host of complex technical issues that go into generating a three-dimensional image using MRI. I never promised I would tell you how to construct your very own imaging device, only that I would explain the essential quantum mechanics that underlies such a process. Needless to say, all of the above would be useless without high-speed computers utilizing solid-state integrated circuits, to record, store, and a.n.a.lyze the radio-frequency absorption data. So in a sense, quantum mechanics enables MRI machines at two separate levels.
Dr. James Xavier could have saved himself a great deal of grief with his experimental eye drops by using an MRI to perform diagnoses on patients by peering at their inner organs. Similarly, Professor Charles Xavier (no relation), mutant leader of the X-Men and the world's most powerful telepath, can read people's thoughts. While this is not possible, by employing functional magnetic resonance imaging (fMRI), we can determine what regions of the brain a person is using, and from that make inferences as to what they are thinking.71 All cells in your body have a function and require energy when carrying out their designated tasks. Nerve cells-neurons-process information through the generation and transmission of voltages and ionic currents. When we eat, we ingest molecules originally generated by plants that contain stored chemical energy. The plants utilized the energy in photons from the sun to construct complex sugar molecules. The mitochondria in every cell synthesize adenosine triphosphate (ATP) from these sugars and thereby release some of that stored energy, which the cell can then use to perform various functions. The chemical trigger for the construction of ATP is the incorporation of oxygen molecules and the release of carbon dioxide. Consequently, whenever a cell is actively working, in particular for a prolonged period of time, there is an increase in blood flow to this cell, in order to maintain sufficient oxygen levels for ATP production. By looking where the blood is flowing, we can determine those cells that are most active.
Neurons do not store glucose, and consequently within a few seconds after you start some heavy thinking, there is an increase in blood flow to the region containing the active neurons. The brain has the same relations.h.i.+p to the body as the United States has to the rest of the world-the brain is roughly 3 percent of the total body ma.s.s, while it consumes 20 percent of the energy expended. You use different portions of your brain depending on the task you are performing-sitting while reading this book, walking while reading this book, or showering while reading this book. Thus, by monitoring which regions of the brain are receiving more oxygenated blood, one can ascertain what activity a person is engaged in, without having to look at the person directly. The true power of this technique for determining brain activity from the variations in blood flow involves distinguis.h.i.+ng between cerebral tasks-mentally doing arithmetic compared to recalling a pleasant summer memory. In this situation the beatific smile on the person's face would not betray which task was being performed.
When an MRI scan is taken of a person's brain, spatial resolution on the order of millimeters and time resolution of one to four seconds are possible. When red blood cells are carrying oxygen, they are diamagnetic-which means that their internal magnets orient opposite to the direction of an external magnetic field. Conversely, deoxygenated hemoglobin is paramagnetic; that is, it will align in the same direction as an external field but will have no net magnetization in the absence of an applied magnetic field. Using magnetic resonance imaging, one can examine a region deep within the cerebral cortex and determine its rate of blood flow. By measuring the time dependence of the variation in magnetization when the saturating radio-frequency radiation is removed, one can distinguish which regions of the brain are in high need of additional oxygen and energy.
Alfred Bester wrote of the difficulty that Ben Reich faced plotting and carrying out an undetected murder in a society where nearly everyone, particularly the police, is telepathic in his 1953 novel The Demolished Man. The ability to read minds, to know what another person is silently thinking, has long been a hallmark of science fiction stories, predating the pulps and continuing into the present. The cooperative behavior exhibited by the characters in Theodore Sturgeon's novels More Than Human and The Cosmic Rape, and the Hammer film Village of the d.a.m.ned, presumes the ability to remotely link neuronal activity for various individual agents. Certainly, the apparatus for a functional MRI device is considerably larger than the compact helmets for "mind reading" frequently depicted in science fiction magazines and comic books, and this technique provides information only about blood flow in the brain. While many remain unconvinced, some believe that this technique may someday serve as an accurate lie detector, enabling us to directly discern a person's thoughts and intentions. Quantum mechanics brought us a world unimagined by the science fiction stories of fifty years ago, and it may now actually start bringing aspects of the science fictional world into reality.
THE WORLD OF TOMORROW.
I have described the basic concepts underlying quantum mechanics and have discussed how these principles account for the properties of single atoms, nuclei, and many-body systems, such as metals and semiconductors. By elucidating the physics of the laser, the diode, the transistor, and disc drives, we now have an understanding of the basic building blocks of such modern technology as laptops, DVDs, and cell phones, which, for many, are part of everyday life in the twenty-first century. All of us routinely make use of devices and applications that would not be possible without the understanding of nature provided by quantum mechanics.
We have obviously not gone into any detailed descriptions as to how consumer products, such as a computer, operate. By combining the electrical-current inputs in a series of transistors and diodes in ingenious ways, one can arrange it so that two high currents cancel each other out and lead to either a low current (two "ones" combine to form a "zero") or a high current (two "ones" yield another "one"). Similarly, if one current level is high and the other is low, then a circuit can be constructed so that the output is either high or low, depending on the required logic operation. In this way the "ones" and "zeros" in the computer can be manipulated. A full discussion of Boolean mathematics, logic gates, and data storage and processing employed in a computer would be fascinating (in my nerdy opinion), but it would involve no new principles or applications of quantum mechanics.
Nevertheless, I would like to note in pa.s.sing that sometimes the physics from Section 3 (radioactivity) interferes with the physics of Section 5 (solid state devices). Few have not experienced the frustration of having a computer program freeze or crash for no particular reason, solved only by a rebooting of the operating system. Sometimes the source of the problem turns out to be thorium, a radioactive element that is a contaminant (thorium is as common as lead) in the circuitry packaging. When the thorium nucleus decays it emits an alpha particle and the high-energy helium nucleus can disrupt the current in an unlucky transistor. The loss of information in the middle of a calculation often requires that the entire program be restarted from scratch. What quantum mechanics giveth, quantum mechanics taketh away.
Similarly, the scheme by which mobile phones send and receive electromagnetic signals to radio towers that then connect to a land-based call router is rather clever. Present models use very sophisticated protocols to determine the optimal region, or "cell," with which to transmit the call, but the basic quantum mechanics in the cell phone itself essentially involves applications of transistors and diodes. The heart of the cordless phone is the a.n.a.log-to-digital converter, which takes a variable voltage generated when spoken sound waves are transformed into electrical signals (as occurs in a conventional landline phone) and, through what is effectively an operational amplifier (a series of transistors and resistors), converts this variable voltage to either a "one" or a "zero." Obviously, devices must also exist that operate in reverse, so that a digital-to-a.n.a.log conversion can transform the received signal into the variable sound we hear.
One really cool feature in the latest generations of cell phones is the touch screen. While many simple touch screens, as in kiosk information displays or automatic teller machines, detect the alteration in electric field caused by the electrical conductance and capacitance of your finger, the newest mult.i.touch versions send an LED-generated infrared light beam skimming along the inner surface of the screen. Touching the screen causes some of the infrared light to be scattered, and the location of your finger is ascertained by determining which photodetector behind the screen collects the scattered light. Here again, all the quantum physics in a touch screen is represented in the infrared light-emitting diodes and photodetectors.
Consequently, rather than delve into the inner workings of a variety of electronic products, which will not necessarily add much to our discussion of quantum mechanics, I use this final section to describe how quantum physics may continue to shape the future. That is, I would like to describe the concepts and devices that may become part of our world five or ten or twenty years from now. I will not try to make actual predictions, as that is a mug's game, but will rather explain the relevant quantum mechanics that underlies such phenomena as "quantum computers" and "nanotechnology." We already understand the basics; now I will discuss some novel advanced applications that may be coming to a consumer electronics store near you the day after tomorrow.
As described in Chapter 18, the greater sensitivity of read-head sensors using the giant magnetoresistance effect and magnetic tunnel junctions means that smaller magnetic bits can be detected, resulting in an increase in the storage capacity of hard drives. These magnetic sensors can also enable faster data retrieval. The polarization and depolarization of the magnetic layers in the sensor happens quickly, so the detector can read the bits even when the hard-drive platters are rotating at speeds of over ten thousand revolutions per minute. But the next generation of "semiconductor spintronic" devices may increase the speed of computers even more, by removing the need for a separate magnetic storage medium.
There has been considerable interest by researchers in developing semiconductor transistor structures that make use of the electron's internal magnetic field to process information. Using magnetic metals as the electrodes on a semiconductor device, it is possible to inject magnetically polarized electrons, that is, charge carriers whose internal magnetic fields all point in the same direction, into a semiconductor. By varying the magnetic field in the semiconductor device, the current could be controlled without the need to change the concentration of charge carriers, as in the field-effect transistor discussed in Chapter 17. The goal is to construct a device with a steeper on-off transition for the high-low current levels that are used to represent "ones" and "zeros," with faster switching between these two states that uses less energy to operate.
This last point is important. Each transistor in your computer creates a small amount of heat as it drives a current from low to high values and back again (pa.s.sing a current through a toaster wire or lightbulb filament generates heat, and the same physics applies inside a semiconductor transistor). When millions and millions of these transistors are packed into a confined s.p.a.ce, the resulting temperature rise can be significant, and in turn this consideration can limit the integrated circuit's performance. Hence the need for multiple cooling fans in most computer towers. "Spin transistors" use less power, thereby allowing a greater number of devices to be placed in close proximity, resulting in more computing power packed onto a microprocessor.
In addition, the ability to both store magnetic information and manipulate ones and zeros as in an integrated circuit suggests that it might be possible to combine both magnetic data storage and computer logic functions on a single chip. In the late 1950s, when the Challengers of the Unknown faced off against a "calculating machine" capable of independent thought, it was believed that such a device would have to be the size of a large room, while in the future, thanks to quantum mechanics, we may all be able to carry our own ULTIVACs in our back pockets.
The need for speed in computation is driving interest in an even more exotic use of quantum mechanical spin in calculators, often referred to as "quantum computers." Of course, in a sense all computers (aside from an abacus or a slide rule) are quantum computers, in that their fundamental data-processing elements, diodes and transistors, would not have been invented if not for the insights into the properties of matter provided by quantum theory.
A "quantum computer" is a different beast entirely. In short, rather than represent a "one" or a "zero" through a high or low current pa.s.sing through a transistor, or from a region of magnetic material with its north pole pointing in one direction or the other, the atoms themselves are the ones and zeros. Actually, quantum computers have been proposed that involve atoms, nuclei, ions, photons, or electrons as the basic computing element-I focus my discussion on electrons for simplicity. Electrons have an intrinsic angular momentum of either +/2 or -/2, and in a quantum computer these are the elements that will represent the ones and zeros.
While using electrons in this way would indeed shrink the size of the computer's elements nearly as far as physically possible, this alone is not what motivates research in quantum computers. Proposed quantum computers involve using pairs of identical particles, arranged so that their wave functions overlap. Recall the discussion from Chapter 12 of two electrons brought so close that their de Broglie waves interfered. In this case we represented the new two-electron wave function by a single ribbon, where one side of the ribbon was white and the other was black. In the example in Figure 30, both sides of the ribbon facing out were white. But we could also have held both black sides facing out, or the left side could have been black and the right side white, or the reverse. To represent these four possibilities-white, white; black, black; black, white; white, black-using conventional computer elements would require two transistors, and they could generate these states only one at a time, that is, in series.
With the quantum ribbon from Chapter 12, all four states are possible simultaneously-if the ribbon is in a dark room and we don't know which sides are facing out. In this case, all four states may be present, and until we turn on the lights and examine the ribbon, the ribbon can represent the four possible states in parallel. Where I need four separate conventional bits to represent these outcomes, I need only two "quantum bits," or "qubits," to accomplish the same task. While the ribbon a.n.a.logy breaks down when dealing with more than two entangled wave functions, the arguments hold, and one needs only three quantum bits to represent eight distinct conventional states, and ten qubits can do the work of 1,024 cla.s.sical bits.
This parallelism implies that a quantum computer could perform calculations must faster than a conventional computer. Encryption of information for national security, online commerce, or just using a credit card to pay for a purchase at a gas station involves knowledge of the prime-number factors72 of numbers that are so large that even the fastest conventional computers could not determine the factors in a reasonable time. Quantum computers, with the ability to perform multiple tasks at the same time, could change this situation. A small-scale prototype quantum computer has been able to successfully factor a two-digit number (15 = 5 3), but a fully operational quantum computer does not exist and is years and years away in the most optimistic scenario. Nevertheless, data security and cryptology will be dramatically changed if such devices are ever constructed. It will be up to all of us to ensure that this technology does not fall into the wrong hands, for who could forget when the evil Decepticons used quantum computers to hack into the Pentagon's secure computer system in the Transformers movie (2007), cracking a code in ten seconds that would take more than two decades for the most power supercomputer.
Now, to say that two overlapping electrons can represent all four spin combinations, provided we don't examine them, may seem a bit73 of a cheat-you can argue that any pair of transistors can represent all four states if I do not actually examine whether the currents pa.s.sing through them are high or low. But there is a fundamental difference in the quantum spin case that gets to the heart of some of the philosophical arguments over the role of measurement in quantum mechanics.
Throughout this entire book I have pulled a fast one on you, Fearless Reader, and its time to come clean. The difference between the quantum case of overlapping electronic wave functions and the conventional situation involving transistors, and the reason that the quantum ribbon can represent all four possible outcomes simultaneously, is that if the ribbon remains in the dark, that is, until I do a measurement and examine it, the very concept of the color of the ribbon is not well defined.
Let's return to the real world of electrons for a moment. I have specified that an electron can have only one of two possible values of its intrinsic angular momentum, rotating either clockwise (that is, spin "up") or counterclockwise (spin "down"). But we never asked the question: Up or down-relative to what? Clockwise or counterclockwise rotations-about what axis?
The intrinsic angular momentum has a small magnetic field a.s.sociated with it, with a north pole and south pole. If I don't measure this magnetic field, that is, in the absence of an external magnetic field, then I have no way of knowing where the pole is oriented. If I apply an external magnetic field and measure the electron's magnetic orientation, it will either line up with the field or be 180 degrees opposite to the external field (as in our discussion of MRI in Chapter 19). If the external magnet I apply has its north pole pointing toward the ceiling of the room you are in, then this defines the "up"/"down" direction. The electron's magnetic field will point either to the ceiling or to the floor. If the external magnetic field is instead applied pointing toward one of the walls in your room, then this defines the "up"/"down" direction, and the electron's magnetic field will point either toward the wall or toward the wall opposite it. Once I apply an external field and measure the electron's magnetic field, that very act defines the axis about which "clockwise" and "counterclockwise" make sense, and until I do, all I can say is that the electron is in some superposition of these possibilities. It is in this way that we can say that a quantum system can represent multiple states simultaneously.74 Einstein smelled a rat in this scenario and spent a considerable fraction of his later years trying to catch it, for the situation just described opens up the possibility for information to travel faster than the speed of light. Say I arrange two electrons so that their wave functions overlap, and they can be described by a two-particle wave function (as in Chapter 12) and with total intrinsic angular momentum together to be zero. One electron has spin = +/2 and the other has spin = -/2, but let's say I don't know which is which. When I measure the electron on the left and find that its spin is +/2, not only do I know logically that the other spin must be -/2 (since I already knew that the total spin was zero), but I also now know what axis the second electron will be anti-aligned with! The process of measuring the first electron's magnetic field picks a preferred direction not only for that electron, but for the other one as well, since they are both part of the same wave function, which contains all the information about the system.
Now, here's where it gets fun. Let's a.s.sume I have an infinitely stretchy ribbon representing the two electrons. I hold one end of the ribbon and pull the other end all the way across town, keeping the electrons still connected. Now I measure the spin of one electron, by placing it in an external magnetic field. This not only tells me if this electron is pointing with or against the applied field, but determines what direction the electron's magnetic field points. As soon as I do this, the properties of the other electron are also determined. After all, both electrons are described by a single wave function and thus behave as a single ent.i.ty. In this way the entangled quantum state is like the famous twins in fairy tales, joined by a special bond, so that what happens to one is instantly felt by the other. Einstein objected that this would enable information (about the direction of the magnetic field being used in my lab to measure the electron) to be transmitted from one point in s.p.a.ce to another, potentially faster than light could cover the same distance. In his famous phrase, this represented "spooky action at a distance," and he would have none of it.
Books have been written over the question of whether this scenario does indeed provide a mechanism for instantaneous transmission of information, and, if it does, how to reconcile this with the principles of the Special Theory of Relativity that states that nothing, not even information, can travel faster than light. It remains a topic of lively debate among physicists. As the man said when asked by the child about the nature of the afterlife-experts disagree. Now, questions of what "happens" to a quantum system in the moment of observation are fascinating, but a full discussion of these topics is not the focus of this text. I will therefore now exit, stage left, follo