Monday, February 27, 2012

Why Is The Symbol for Current "I"?

As I've mentioned once or twice before in this very blog, everybody who's ever done anything with circuits knows Ohm's law.  It's a simple little equation that states that the voltage across a linear circuit element is equal to the current passing through it times the element's resistance, or V=IR.  The symbol for voltage, for reasons that I really hope are obvious, is V.  The symbol for resistance is R.  The symbol for current is I.  One of these things is not like the others.

When you're a first- or second-year EE student you've got enough other crap to think about that it usually doesn't occur to you to wonder why all the symbols for things are what they are.  I was usually too busy frantically trying to solve for I to wonder why, in fact, they called it I and not C or something more logical.  The only time I remember it ever even coming up was when we did things with complex numbers.  Normally when you write out a complex number (if you've successfully put high school algebra out of your mind, a complex number is one with both real and imaginary components) you do it as the sum of the real and imaginary parts, with "i" being added to the imaginary so you can tell the difference (e.g. 5 + 3i).  For various reasons, complex numbers turn up a lot in circuit theory, so EEs use "j" in place of "i" to represent the imaginary component of a complex number.  You would think this would've sparked me to think "wait, isn't using I for current actually kind of confusing and stupid?" but I was probably thinking something more along the lines of "jesus christ math is hard and what's this crap with the letter j now?  Fine, I'll call imaginary numbers whatever you want if you pass me."

Much later, I've learned what every engineer eventually learns (all that hard math they made you do as an undergrad can be done pretty trivially with a computer) and have managed to avoid doing all but the most basic math for years now.  That and the general thrust of this blog is probably why I only got to wondering about the symbol for current over a decade after I learned it. 

As with most things in the world, this one is all France's fault.  One of the pioneering scientists who figured out the basics of electromagnetism back in the 19th century was a guy called André-Marie Ampère.  His contributions to the field were so important that he achieved the rare science twofer of getting both an equation (Ampère's Force Law, one of Maxwell's equations) and a unit of measurement (the Ampère, usually shortened to the Amp) named after him (eat that, Einstein!).  Said equation (Ampère's Law) basically states that an electric and/or magnetic field (this was pre-Maxwell, nobody knew they were pretty much the same thing yet) can cause charge in a conductor to move.  Since the charge is "flowing" through the conductor kind of like a liquid flowing through a pipe, Ampere decided to call the rate of charge flow the "current," with the designation for the amount of current being the "current intensity," or intensité de courant in the original French.  The canny reader will note that the first letter in that phrase is our culprit.

André-Marie Ampère (bottom) and his force law(s). 

Science is pretty much first-come-first-served with this stuff; Ampere figured it out first, so the naming conventions he used for the new units he derived became standard throughout the world pretty quickly (he didn't name the unit after himself, as that's widely considered to be a major Science Dick Move; someone else did that later).  There was a bit of pushback in England, with some people persisting in using C for current as late as 1896, but in general everybody stuck with I and was pretty okay with it, probably because C was starting to be widely used for capacitance around the same time.  Apparently older textbooks will still refer to current as "current intensity," although they apparently quit it with that before I went to college, hence the confusion. 

Now that the US is the greatest empire in the history of the world and English is pretty much the universal language of science, it's easy to forget that that wasn't always the case.  Lots of Western work in physics, chemistry, and biology was done in French, German, and even occasionally Italian well into the 20th century, once everybody gave up on Latin as a universal academic language.

Wednesday, February 22, 2012

How Does Capillary Action Work?

There's a good chance this is one of those "everyone knows but  me" questions, but since I write this blog purely for my own amusement you're just going to have to live with that.

Anyway, I got to wondering about capillary action via the usual route; I left the end of a towel or something hanging into the sink, which still had a bit of water in it, the other week.  About eight hours later, the towel was completely saturated with water in clear defiance of gravity.  This phenomena is called "capillary action" and is familiar to basically anyone who has encountered water and fabric in some combination in their lifetimes, but when I got to thinking about it I realized my poorly-thought-out mental justification for it ("it's just like a really slow siphon!") made no goddamn sense on a bunch of different levels.  To the internet!

You know what you never, ever run into in electrical engineering?  Fluid dynamics.  I'd argue that this is one of the best reasons to go into electrical engineering, but the fact that we make up for it with horrible things like electromagnetics and quantum mechanics kind of undercuts that.  Anyway, the point is that beyond the basic physics it shares with other things (e.g. diffusion) I know next to nothing about why liquids do whatever it is they do, including weird shit like climbing up fabric.

Apparently capillary action isn't exclusive to fabrics; it's something that will happen in lots of porous materials, including things like bricks and cinder blocks.  The key to the whole thing is narrow channels through the material.  Stick some water in a narrow, vertical-ish tube (the most idealized demonstration of this is a thin glass tube partly immersed in water; see below) and you've suddenly got two pretty big forces to think about.  Surface tension is the first one, which will cause the surface of our narrow water-channel to form something called a "concave meniscus", which is a fancy term for a liquid surface where the level at the edges is higher than the level at the center (the smaller the channel, the greater the meniscus curvature and the higher the surface tension). The formation of a concave meniscus is dependent on there being an attractive force between the liquid and the channel material; assuming our liquid is water, we'd need to make the channel out of something hydrophilic, like glass.

Idealized capillary force demonstration.  A narrow glass tube is placed in a bath of water; surface tension and liquid cohesion "pull" the water up the tube to some height where their force is exactly balanced by gravity.

Next you've got the interaction between the capillary medium and the water to consider.  A concave meniscus of water in a channel of hydrophilic material is going to have its edges drawn upward by adhesion forces between the water and the sides of the channel.  As the edges of the water meniscus move up the channel, surface tension and general cohesion of the water molecules ensures that the rest of the surface, as well as the water behind it, is also drawn upward to preserve the shape of the meniscus.

So you've got a combination of adhesion and surface tension creating an upward force that's stronger than the downward force of gravity on the mass of the water.  Obviously that can't last forever; the capillary force is constant with height (assuming a constant-width channel) while the force of gravity is going to increase as more mass (water) is drawn up into the channel.  At some point they'll balance and water will stop "flowing" upward.  This balance point depends largely on the channel diameter (smaller diameter = greater surface tension force, remember?), although the channel wall material (specifically, the hydrophilic-ness thereof) is obviously going to play a role. There's probably a really simple equation for the critical height of the water level in a capillary tube, so if that's of interest to you definitely look it up!

Now extrapolate that out to a porous medium like fabric or a paper towel.  The pores are basically thousands of very tiny channels, and we know from the fact that you can get them wet that paper towels and most cellulose-based fabrics are pretty hydrophilic.  Add in the fact that most of our pores/channels aren't even going to be perfectly vertical (reducing gravity's counter-force) and you've got a really good situation for capillary action to do its work.  In most cases, such as the towel in the sink that inspired this, capillary action can easily lift a decent volume of water up a distance of several inches if you give it enough time to work. 

Water climbs up a brick, which is basically an assload of microscopic glass channels from a fluid-dynamic standpoint

Besides making a mess of my counter that one time, capillary action has some legitimate applications.  It's basically the mechanism by which things like paper towels absorb water, which as most people know is just all kinds of handy.  It's also the mechanism by which certain fabrics "wick" sweat away from the body.  It actually encroaches on my field a little bit too; people building microfluidic and nanofluidic devices (small devices designed to move tiny amounts of liquid around strategically, in order to sort DNA and detect chemicals and things) rely heavily on capillary forces to do their work, since extremely narrow channels mean extremely strong capillary forces.

Per usual, thanks to Wikipedia for making me feel dumb.

Friday, February 17, 2012

Where Does Silicon Come From?

If I ever got it into my head to start believing that there had to be a god, the existence of silicon would probably be one of my main arguments in favor of.  It's just one of the several elements sitting on the edge of the metal/nonmetal divide on the periodic table, but as noted white supremacist/physicist William Shockley and friends figured out back in 1947, it's a semiconductor, meaning that whether or not it will conduct electricity is something we can exert control over pretty easily via some clever applications of quantum mechanics and materials science.

It wouldn't be an exaggeration to say that that single discovery probably transformed society more than anything has since the printing press; without it we've got no solid-state electronics, no computers, no internet, no solar cells, and basically none of the cool technology we all take for granted these days (I also wouldn't have a job).  On its own, being a semiconductor isn't that special; there are loads of materials that semiconduct, both elements and alloys.  Silicon has two other big things going for it though.  One is that it oxidizes spontaneously, meaning that if you want to make part of it into a nonconductive oxide it's almost stupidly easy to do so (most other semiconductors don't share this trait).  When you're making complex three-dimensional circuits out of silicon you're going to want to insulate lots of parts from other parts; the fact that it forms oxides so easily makes manufacturing Si-based devices vastly simpler (ergo cheaper) than other semiconductors.

The second, even more important advantage of silicon is that it's the second most common element in the earth's crust.  This miracle material that is the foundation of all modern technology is literally just sitting around all over the place in things like "sand" and "rocks"; unlike other useful things we dig out of the earth (oil, gold, helium, etc), we're never going to run out of silicon no matter how many cell phones each of us decides we need to own.  Even my shrivelled, agnostic engineer's soul is moved by the staggering serendipity of that one, although I'm sure there's a good reason for it that I just don't know (readers who know anything about planetary formation and earth science, feel free to chime in here).

Come on, it's pretty bananas right?

Unfortunately it's not as simple as just scooping up some sand and turning it into a bunch of Core i7 processors, which you'd probably already guessed from the fact that Core i7's cost significantly more than sand.  Remember when I said that silicon will oxidize spontaneously?  That's incredibly convenient in manufacturing, but it also means that basically none of the silicon found in nature is "pure;" it's all been oxidized into "silicate," or silicon dioxide (SiO2) if you like chemistry.  The flipside of the fact that silicon oxidizes so easily is that it's extremely goddamn hard to get it to un-oxidize back into elemental form; when you're making semiconductor devices, the only way to cut through a layer of SiO2 is with directed plasma or hydrofluoric acid (HF), a chemical whose lethality has become the stuff of legend among people in this line of work.

So that brings us to the question: how do you turn silicate from the ground into semiconductor-grade Si (which is 99.9999999% pure.  I might have missed a 9 in there) on the scale required to feed the insatiable monster that is the commercial semiconductor industry?  I assume they're not doing it with warehouse-sized plasma fields or gigantic vats of HF.  I hope not, anyway.

Did you know there's a whole field devoted to turning stuff into other stuff on industrial scales?  It's called metallurgy, and aside from that I know next to nothing about it.  Unsurprisingly, metallurgists solved this problem a long time ago (probably about when people were realizing that large quantities of very pure silicon would be a handy thing to have around) and I just never knew about it because it never occurred to me to question where the ultrapure, monocrystalline silicon wafers I work with actually come from. 

Any workable process to turn silicate into metallic Si is going to need:

  1. Input energy, because the oxygen isn't just going to un-bond from the Si if you ask it nicely

  2. Something else for the free oxygen to bond to and get it out of the way once you've separated it from the Si

  3. A way to get the now-free Si out and separated from any other byproduct you may have created while doing the first two things
It would also be nice if the process scaled, so you could make a ton of silicon as easily as a gram just by building a bigger reactor.

The most scalable, widely-used process by which SiO2 is turned into reasonably pure silicon is called carbothermic reduction, and for the most part it's pretty much what it sounds like.  The first thing you need is heat, a lot of heat (furnace temperatures run north of 2000C), in order to provide the necessary energy to split SiO2 into its component atoms.  This is achieved by running the whole mess inside something called an arc furnace, which produces heat via (yup) several sustained electrical arcs inside the furnace (it's not like you're going to get to 2000C by just lighting a fire under the thing or whatever).  Into this hellish environment you'll then dump both silicate and carbon feedstock.  It helps if both are reasonably pure, both for the purity of the final product and the minimization of nasty byproducts.  Coal is generally used for the carbon, while mined crystalline quartz is used for the silicate.

There are a few steps involved in the actual reaction, but basically what happens is that the extreme heat forces the silicon and oxygen atoms in SiO2 to separate.  Both atoms go through several intermediate reactions with the carbon we dumped in there, but eventually they'll settle into a combination of metallic silicon and carbon monoxide or carbon dioxide.  Metallic silicon is liquid at the furnace temperatures, so it'll drip down to the bottom where it can be collected.  CO/CO2, as we all know, are gases, so it'll leave via the furnace exhaust and do what it can to contribute to the global warming problem.

A Si-refining furnace, swiped from the survey paper I used as the main source for this thing.

The silicon you get out of this process is ~99% pure, or metallurgical-grade.  That's pretty good, but a far cry from the "nine 9's", or 99.9999999% purity, we need for semiconductor-grade material.  There are a variety of ways to increase the purity from here, both by adding things to the mix to precipitate out certain impurities and by good old-fashioned repeated distillation.  Even a few stray atoms of the wrong type can play absolute hell with semiconductor operation, so you really have to do a good job with this part.  That said, the details of it are extensive and boring, so I'm just going to stop here.  We've figured out the main question (how to get the Si out of SiO2 on a large scale) anyway; the rest is just gravy.

So we've learned how to make very pure metallic silicon out of most of the earth's crust and found a brand-new way to contribute to climate change, all in one shot!  If you're interested in all the gory details of this process, I yanked a lot of them from a survey paper that goes into much more detail on every step of getting silicon from the quartz mine to the inside of your iPhone.