Diodes, Solitons, and Taoism
Philosophy. It’s a framework for technical understanding; it is what guides me through difficult technical problems when analysis and intuition doesn’t cut it.
It might sound a little bit hokey, but I get a rise out of discovering those little “just-so” revelations about nature that help refine my philosophies. One such revelation that I’ve had is that some of the most interesting and useful things arise out of the tenuous cancellation of fundamental opposing phenomena. That being said, let’s discuss the link between Taoism, Diodes, and Solitons.
The Ying-Yang symbol, a popular Taoist icon. I’ve always admired it because of its symmetry and when I look at it, I see a vigorous balance of two forces. To quote, “It represents the balance of opposites in the universe. When they are equally present, all is calm. When one is outweighed by the other, there is confusion and disarray.” I think there is a lot of wisdom behind this philosophy of gestalt.
The diode, one of the most fundamental semiconductor components. The diode is a testament to the power of fundamental opposing forces. In this case, diode behavior is a result of a delicate balance between “drift” and “diffusion”.
“drift” is jargon for the force imparted on a particle (or pseudo-particle) through electrostatic fields. You can experience this force directly by holding the back of your hand near an old CRT TV or a balloon rubbed on wool. The presence of electrical charge on these objects will impart a force on the tiny hairs on the back of your hand. This is the drift force. Remember, the drift force is attractive between opposite (+ and -) charges, and repulsive between like (+ and + or – and -) charges.
“diffusion” is jargon for the natural tendency of things to spread out and mix over time. In a macroscopic sense, you can imagine a yard with a pile of leaves in it. As the wind blows, it spreads the leaves out across the yard–the leaves are “diffusing” across the yard. Another example is what happens when you put a drop of food coloring in a glass of water. If you watch it long enough, the food coloring will eventually spread itself throughout the water through a diffusive process. At the atomic level, diffusion is driven by heat, which manifests itself as vibrations of atoms. Electrons and holes within a diode tend to diffuse outward at a rate governed by various material properties and the temperature of the material.
The key thing to remember is that at the atomic level, these vibrations are quite large. The macroscopic analogy for these atomic vibrations might be like taking a bucket full of light and dark pebbles and shaking them about to mix them. Intuitively, one can see that shaking the bucket harder will cause the pebbles to mingle more rapidly. This shaking is like the thermal vibrations in an atomic lattice. How fast do electrons “mix” Silicon? It’s a statistical process, so the answer is given stastically. As a rough estimate, 50% of a population of electrons will have spread out to a radius of about 1 foot (30 cm) in a second–assuming no recombination process. Imagine shaking a bucket of pebbles so that within one second, any given pebble has a 50% chance of being on the other side of the bucket! Diffusion is quite vigorous in deed at the atomic scale.
Now, how do these two phenomena fight each other? Well, first imagine a silicon atom, happily sitting there at neutral charge. Now, imagine that atom being randomly bumped by another atom due to thermal vibration. What happens? Under the right conditions, the atom will lose an electron, or a – charge (also referred to as an “electron carrier”). This leaves the atom with a net + charge (also referred to as a “hole carrier”). The electron will diffuse through the silicon crystal until it encounters another + charge, at which point it will recombine.
Device engineers diabolically contaminate these pure silicon lattices with foreign atoms called “dopants”. These dopant atoms are either deprived of an electron, so they tends to steal electrons, or they are endowed with an extra electron that is very loose and tends to fall off and diffuse about easily. Remember, however, that an equilibrium is alwasy maintained: when an electron is stolen, the victim is left positively charged.
Now imagine a strip of deprived (p-type) silicon deposited on a strip of endowed (n-type) silicon. What happens?
Nature takes its course, and diffusion plays the role of Robin Hood: the endowed diffuses its wealth of electrons unto the deprived. However, this comes with a price. Remember that the electrons stolen from the n-type region will leave fixed + charges in its wake. Remember that drift effect that was mentioned earlier? As more electrons are stolen, a voltage bias builds up across the junction, and the stolen electrons feel compelled to return home. At some point a tenuous balance is reached, where drift forces create a potential barrier that equally cancels the rate of electron and hole diffusion, and a neutral “depletion region” is formed between the n-type and the p-type silicon. This neutral “depletion region” acts like an insulator. This is the “resting state” of a diode.
So, we have a stand-off, a cold-war of natural forces. Diffusion is attempting to equalize the distribution of + and – charges in the diode, and drift is attempting to keep all of the + and – charges at their home positions. What happens when we tilt the balance of power by applying an external voltage to the diode?
Simply put, if you apply a bias in favor of the drift force–make the positively charged n-region more positive–the diffusion force is supressed and only a drift current flows. This drift current is very tiny, as the source of its flow relies on the spontaneous thermal generation of – charges in the p-type (+ rich) region (and vice versa). This condition is called a “reverse bias” and the diode acts like an open circuit.
However, if you apply a bias in favor of the diffusion force–make the positively charged n-region more negative–the diffusion force is allowed to run amok, and a deluge of charges diffuse across the junction into the opposite region. These charges sweep through bulk regions of the diode and are happily collected by the wire contacts at either end of the diode, allowing a large net current to flow; thus the diode acts as a short circuit.
The fascinating thing about this situation is that the actual flow of current in a forward-biased diode is due primarily to diffusion, not drift! In other words, the applied bias simply liberates carriers to diffuse freely through the diode, but the bias itself has little to do with actually coercing the electrons to move through the diode. I think that’s really neat.
To be technically correct, this analysis applies as well to the mobile “holes”, but it is easier just to consider one carrier element on its own at an intuitive level.
The soliton. It’s quite possible that the bits your browser retrieved to display this text you are reading spent some of its short life as it journeys across the internet backbones in the form of a soliton. The simple description of a soliton is an optical pulse that can travel through thousands of kilometers of optical fiber with no degradation (non-soliton pulses can only go a few kilometers or so). The soliton is a remarkable optical phenomenon that is again the “just-so” cancellation of two powerful opposing forces: self-phase modulation, and chromatic dispersion.
Chromatic dispersion–it’s what happens when light of different colors travel at different speeds. Imagine a “packet” of red and blue light travelling together. If you could somehow sieze this packet in mid-flight and examine it, you would see the color purple. In a dispersive medium, these two colors will travel at different speeds. In the fiber example, the blue light will travel slower. Thus, if you were to inject this purple packet in at one end of a long fiber with only chromatic dispersion, you would get out two packets on the other end, first red, and then blue. This spreading of light out in time and space degrades information because it causes bits to smear into one another. In many fiber communication systems, visible light is not used for communication, but rather infra-red light around the 1550nm wavelength is used. In this range, chromatic dispersion works backwards, speeding up “bluer” wavelengths and slowing down “redder” wavelengths.
Fear not, self-phase modulation comes to the rescue! This effect happens when very intense light, such as that from a communications laser, is present in a material. Very intense light can actually modulate its own speed of propagation due to self-phase modulation. In this case, self-phase modulation will tend to slow down “bluer” wavelengths and speed up “redder” wavelengths. Again, self-phase modulation will cause information to smear and bits will be lost.
Wait…just like peanutbutter and chocolate, don’t you see a grand union coming together here? Anomalous dispersion speeds up “bluer” light; self-phase modulation slows down “bluer” light, and vice-versa for the “redder” light. These two effects will cancel out, and voila! Your optical information pulse will travel forever–so long as no impurities are encountered in the fiber. Fortunately, optical fibers are very pure, and solitons can travel through thousands of kilometers of fiber and preserve the information they were meant to convey. Neat!
How does this impact my philosophy? Well, when faced with a difficult situation where I must be creative, I can now expand my mental solution space to include looking for fundamental/powerful effects, and looking for things that may oppose them in some way. By finding ways to match them together, sometimes a new and interesting, non-intuitive solution is derived. And that is part of the Tao of bunnie.