The Amazing Story of Quantum Mechanics

by Kakalios, James

  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 class of materials that are much better conductors of electricity at room temperature than insulators such as glass 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 button 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 identity 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 en
ergy, 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 space 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 accumulate, 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 Schrödinger 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 charged mezzanine and lounge seats create a built-in electric field that affects the flow of electrical current through the semiconductor. The influence of this electric field is to tilt the two auditoriums, relative to each other (b). For simplicity only the first rows of the balcony and orchestra are shown in the figure to the right (b). If an external voltage is applied across this junction, it can cancel out this built-in field, making it easy for a current to pass from one side to the other.

  The built-in voltage across the junction between the p-type and n-type semiconductors serves as a one-way door, like a turnstile that rotates in only one direction, for electrons.65 Unidirectional valves are of course quite common, from the valves in your heart to the “cat’s-whisker” rectifiers employed in early radio sets (used to convert an alternating current into a direct current). Solid-state semiconductor diodes are durable and small and can easily be tailored for specific electronic needs. If an external voltage is applied across the junction with a polarity that is opposite to that of the built-in electric field, it will cancel out the internal energy barrier at the interface. The seats on the left- and right-hand sides will line up as if there is no built-in electric field. It will then be easy for electrons to move from the n-type side to the p-type side, and we will see a large current. If the direction of the voltage is reversed, the applied voltage adds to the built-in voltage, there will be a larger electric field opposing current flow, and the seats on the right-hand side are pushed up to an even higher energy. The diode then acts as a very high-resistance device. This directionality is important in radio detection or for power supplies, where an alternating-current input must be converted into a direct current.

  One way to moderate the current passing through a diode is to vary the barrier that inhibits charges from moving from one region to another. In addition to barriers created by internal electric fields at the p-n interface, one can construct a diode where the two regions of an i
dentical semiconductor are separated by a very thin insulator. The electrons cannot jump over this insulating partition, and the only way they can move across the interface is to quantum mechanically tunnel! Changing the voltage applied to the insulator has the effect of changing the height of the barrier seen by the electrons, and the tunneling current is a very sensitive function of the barrier height. In this way a small applied voltage can have a large influence on the flow of electrical current, and these tunneling diodes are an integral part of many consumer electronic devices, such as cell phones. Though I cannot predict whether any particular electron will pass through the barrier or not, when dealing with a large number of electrons I can accurately determine the fraction that will make it across. In this way electronic devices that rely on one of the most fantastic of quantum mechanical phenomena can be designed and counted on to operate in a routine, dependable manner.

  A one-way door for electrical current is sometimes referred to as a “rectifier” and is useful for converting a current that alternates direction into one that moves in only a single direction, as in a radio receiver. In 1939 Russell Ohl, a scientist at Bell Labs, was studying the electrical properties of semiconductors for use as rectifiers when he examined a sample that accidentally contained a p-n junction. As he investigated the unusual current-carrying properties of this sample, he was surprised to find that a large voltage spontaneously appeared across the material when he illuminated it with a forty-Watt desk lamp. Ohl was looking for a rectifier, and he found a solar cell.

  If I shine light on the semiconductor pn junction, as shown in Figure 43a, then as the energy separation between the orchestra and the balcony is the same on either side (the built-in electric field has just shifted the energy of the seats on one side relative to the other) photons will be absorbed on both sides, creating electrons in the balcony and holes in the orchestra. As everything we say about electrons in a diode will hold for the holes, but in reverse, we will focus on just the electrons. From the point of view of the electrons, if they are on the p-type side the internal, built-in electric field, it is as if they start at the top of an energy hill. These electrons will easily move down the hill in the balcony over to the left-hand side, and through the device. The electrons and holes are generated throughout the material, but those in the vicinity of the interface between the p-type and n-type semiconductors will see an internal voltage that will push the electrons down the hill and through the device. We will be able to draw a current, and obtain usable electrical energy, simply by shining light on the diode. So a solar cell is an illuminated p-n junction that generates a current.