The Amazing Story of Quantum Mechanics (31 page)

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.

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.
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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 identical 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.

And a light-emitting diode (LED) is a pn junction with a current that generates light. How do we get light from a diode? Remember that very far from the interface, the device looks like either a normal n-type semiconductor or a normal p-type semiconductor. In an n-type material there are a lot of electrons but very few holes (because the electrons were not excited from the filled band but were introduced by the chemical impurities). Thus, there is very little light generated when electrons in the nearly empty balcony fall to the orchestra, simply because there are very few vacant seats for them to fall into. If I force the electrons, by way of an external voltage, to move from the n-type side to the p-type side, there will be a lot of electrons in the middle junction region, where there will also be a lot of holes heading in the opposite direction (Figure 43b). As the electrons fall into the holes, they emit photons. It takes electrical energy to move the electrons up the hill into the p-type region, and we get some of that energy back in the form of photons. With a cylindrical transparent plastic lens covering the LED, we now have a light source without a filament (so nothing to burn out) and that is highly efficient (as very little electrical energy is converted to waste heat).