Moore's Law 1: 1. Electrons and Holes

No, NOT manic/depressive transistor; BIPOLAR transistor

Just as integrated circuits were introduced to world markets in the 1960's, the engineers who ran the semiconductor business then as they do now, converged on a brilliant idea. We put many transistors on a common carrier or a substratum of silicon crystal. These combined or integrated circuits are groups of transistors fabricated or combined on a single, flawless, substrate of silicon or gallium arsenide 'doped' or implanted with impurities.
The circuits comprise three elements:

1. A semiconductor crafted as a transistor or electrical switch with no moving parts (solid state)
2. A means of interconnecting the ensemble of circuits in a meaningful way
3. Compliance to normal and customary industry standards.

Important to note - the first available product which sets the industry standard is the least worse implementation from Natural Selection of technologies.

Here's how to build a bipolar transistor.

Notice that a light switch has two poles and is therefore a bipolar switch - the switch being a pole that is controlled by meat (any product of DNA which touches the switch) and not electricity. In a bipolar transistor there is another pole or contact which is controled by an electric current and voltage. Above pictured is a bipolar device with a material that has a quality called "P" on both ends with a material with a quality called "N". I will talk about what N and P really are some other time. Pretend that Jesus loves P and hates N for now.

Note that the N material is very narrow. That is because all the N-channel (river of available electrons in N) does is hold the two P-channels 'apart' (an open circuit or a circuit in which no current flows) so that the EMITTER (the left P-thingy) can have a different voltage or charge relative to the COLLECTOR (the right P-thingy). The BASE (the N-thingy in the middle) is like a dam in a bath tub.

If I completely wall off the water from one side of my bath tub from the other I can raise the water level on the right independently of the water level on the left. I am putting more H2O molecules on the side with the highest water level in my bath tub. All the H2O molecules have 8 electrons so there are more electrons on the half of the tub with more water. If I got rid of the protons and neutrons I would have only electrons left on both side. If the electrons were stopped by the sides of the tub and the dam, I would have a higher voltage on the side that used to be filled with the most water.

Now here the bath tub metaphor breaks down. Dump the electrons from each side of the tub AND the electrons in the dam into three containers. Call the containers EMITTER, BASE and COLLECTOR. There are more electrons in the EMITTER in this case because the bath tub with the most water and hence the most electrons raised the voltage of the EMITTER above that of the COLLECTOR which has the electrons from the almost empty side of the tub.

Now here is the magic. The reason this configuration is called a semiconductor can be explained thusly. Besides knowing how many electrons are in each container (E B C) I need to keep track of how fast the water or the electrons could mix together over time when the dam is removed. The electrons or the water will flow from the full side to the empty side. That flow of water or electrons is called current for obvious reasons - it is a current in a creek, river or semiconducting material.

Now I explain why I am a quantum cowboy for herding these currents and switching these voltages. In a perfect crystalline lattice of silicon - an absolutely flawless gem with no variation in three dimensions of volume - each electron can absorb energy and jump one unvarying unit - a quantum unit between valence bands -OR- release an equivalent quantum of energy as the electron falls back to a lower energy state. The average energy in a vast volume of electrons (in our bath tub or E and C) represents.

This is the lake you are looking for.

Picture a lake. All the electrons in the water of the lake can rise no higher than the surface of the lake (ignoring evaporation which I am sure you didn't even know you were ignoring). Now imagine that there was a magic wand (this is Lake Hogwarts) which could raise the whole level of the lake by a quantum amount. As the lake level rose your magic wand 'lifted' the water off the bottom of the lake - we created a gap at the bottom of the lake that was equal in volume to the rise of the surface. We have created a hole at the bottom of the lake that could, if we chose, accept water from another source of water.
Now we release the spell (expectorus mucuso!) and the water falls back into the hole. But we could also say that the hole in the bottom of the lake 'moved to the top' of the lake. I can call the flow of a hole or the flow of an electron (or water) a MINORITY CARRIER (the hole which I divide in my mind into vanishingly small volume "one quantum distance" on a side. Note that small moves in electron state are measured in the universes tiniest UNIT of MEASURE - Planck's Length or 0.0000..................................0001 meters
(43 zeros to the right of the decimal point). The entire volume of water or ensemble of electrons can be diced into cubes just several units (Planck Units) on a side. That is the elbow room a single electron needs to behave all electron-y at room temperature, at sea level, with 45 % relative humidity and all other things you cannot imagine being equal.

That's what happen in the BASE region (pink volume above). The lake of electrons do a quantum jump and the entire silicon lattice 'makes room at the bottom of the lake/tub/BASE' so that the lattice is filled with 'holes' that other electrons can fill.

Now for something completely different.

The moving around and rearranging of holes in the silicon lattice is a current (represents a current, can be though of as a current) or more precisely the idea of a current or the plausibility of a current of "Places electrons can fall into" or holes. BELSHAZZAR - the holes preform action at a distance which cause QUANTUM MECHANICS to happen. Strangeness take over. Every hole in each volume by FM (fucking magic) KNOWS where every electron might be - the entire contrivance becomes entangled in a vast and vanishing ONENESS where everything real becomes a superposition (stacking on top of) of all the probability waves.

Now you may bow before me - for I am the quantum wrangler. All the electrons that can PLAUSIBLY move from the electron packed EMITTER - jump the fuck over the BASE and are in every possible location that will hold them (the holes in the silicon crystal lattice) in the COLLECTOR until the voltage or number of electrons or the molecules of water completely level out.

Here is the recap

Electron - Hole recombination induces a minority carrier current in the BASE that induces (almost conducts or partially conducts or SEMI (sorta) CONDUCTS) majority carrier current (our beloved collections electrons or volume of water) from EMITTER to COLLECTOR.

Now comes the simple part.

It turns out that just about any carefully crafted configurations of multiple transistors can do SOMETHING. It is just a matter of cutting away all the configurations that do uninteresting things and wiring the rest of the good configurations. These collections of transistors can do digital things (exist in only one of two possible states) or do analog things (sense vanishingly small voltage and current changes) and amplify the crap out of very, very, very small differences. These are dissipative structures (they require energy to create and maintain) that are far from thermodynamic equilibrium (there are huge energy wells that hold vastly different or heterogeneous amounts of heat).

This will be on the final. Hell, this IS the final

So we build a very large, flat disk of silicon with a large number of transistors arranged across it. Then we stitch EMITTERS from one transistor to BASES of others and COLLECTORS connected to whatever (see diagram above for maximum confusion).

Industry Standards
The weird thing about electrical engineering is that we are always making it very easy for anyone to duplicate exactly what we just busted our hump designing. When the first integrated circuit was manufactured and sold at Texas Instruments the folks at Fairchild could copy that design and fold in some goodness from RCA or Motorola. We even go to conferences where we tell a room full of experts who can copy whatever we dream up exactly. how. we. did. it. With diagrams and photos and our email address written on everything so any of our competitors can just bloody ask us how do reproduce what we spent $50,000,000 in R/D $$$. This is because we know that every company we interview with later in our career will only hire us if we know enough from our last job to recreate in whole or in part exactly what we slaved over for a ruthless competitor.

The most reliable thing on this globe is a formal design specification from the Institute for Electrical and Electronic Engineers. You cannot spell g-ieee-k with out the I-triple-E (IEEE). The very first time anyone needed to add floating point numbers together (think scientific notation for computer scientists) the IEEE 754 specification for the behavior of ALL floating point operations (+-*/) had to be established. Before the first Ethernet packet was sent there needed to be IEEE 803. The first WiFi couldn't broadcast without IEEE 802.11. We are the brotherhood of the poorly kept secret.

Don't Try This Without IEEE 754

Just to scare you off a bit - IEEE 754 floating point is derived from axioms of number theory and the meets and bounds of universal computing machines. All approximations are "correct as if to infinite precision" and there are about 8 modes for rounding up, rounding down 1) toward infinity 2) toward negative infinity 3) toward zero 4) truncation (not rounding at all is a form of rounding). There are labs around the world that will break your floating point unit if you pay them enough and will break it for free so they can embarrass you in public. When Intel had the famous floating point bug I could only say 'There but for the grace of Zoroaster goes I." Run, run as fast as you can, you can't catch me I'm the FPU Gingerbread Man. I built four generations of FPU's and I never got caught. Yet.

How to Build a Microprocessor

So bipolar transistors are ok but I have just wasted your time because you cannot built a microprocessor (not a competitive one anyway) from bipolar devices. In fact most bipolar circuits are quite small and have few transistors. What rocks your world every day is another type of transistor called a Field Effect Transistor or FET. The particular kind of FET we all love uses a METAL OXIDE SEMICONDUCTOR and is built mostly in 2 dimensions across the face of a silicon wafer. There are four terminals instead of three. But explaining MOSFETs takes 10,000 hours of study so I will skip that part.

From the top view looking straight down on the waver, this is what a simple logic gate looks like. The single MOSFET transistor from the picture above is only a part of the bigger configuration of integrated (interconnected) circuit below - which is seen from the top instead of the side. I won't bother you with any detail except this one important fact. This is a leaf cell or a mosaic tile that is laid down many, many times across the surface of the die (singular of dice - as in "we dice them up into multiple die'). Imagine that the X and Y dimensions are critical and that the Z dimension is constant and uninteresting. The layout of this logic gate is the absolute minimalist rendering in 2-D space for this circuit. This is a beautiful circuit. There is no wasted space.


What the man/computer interface of the Technium has created here is constrained in two dimensions to be the most tightly packed 2-D space that gets the work done. What I mean is that there are spacing rules between every shape and that you could work for 3000 years on this layout and you could not make it smaller. The compaction is computer generated - I am not worthy. I started out by drawing these cells in colored pencil on gridded Mylar. Good times.

What does smaller mean?
The only way to compress this tile or leaf cell is to relax the spacing rule and allow me to shove some of the shapes closer together and make some of the widths of the lines narrower. Since this image is actually enlarged to hundreds of times the actual size on the die, the easiest way to shrink the finished image is to digitally resize the finished image to a smaller magnification.

But why not just do that in the first place to make it as small as we want it from the beginning. The reason can be extracted from the following blank verse from his holiness, Charles Darwin:

"If during the long course of ages and under varying conditions of [fabrication technology] life, organic beings [or useful products of technology]vary at all in the several parts of their organisation, and I think this cannot be disputed; if there be, owing to the high geometrical powers of increase of each species [or standard product from multiple factories], at some age, season, or year, a severe struggle for [market] life, and this certainly cannot be disputed; then, considering the infinite complexity of the relations of all organic beings [and the fruits of the technium] to each other and to their conditions of existence, causing an infinite diversity in structure, constitution, and habits, to be advantageous to them [and their customers in Cuppertino] and, I think it would be a most extraordinary fact if no variation ever had occurred useful to each [products ]being's own welfare, in the same way as so many variations have occurred useful to man ('s markets for high speed logic devices]. But if variations useful to any organic [or silicon] being do occur, assuredly individuals thus characterised will have the best chance of being preserved in the struggle for [product penetration in the market &] life; and from the strong principle of inheritance [of technical features from past products] they will tend to produce offspring [& derivatives] similarly characterised. This principle of preservation, I have called, for the sake of brevity, Natural Selection [by market forces]"

I must build each product in the technology of the factory that is up and running when the product launches. The size and shape of the die, the amount of power required (voltage * current is power), the speed of the clock, and all the rest completely depend on the capability of the fab to print via nano-photo-lithography. It's a goddamn silk screen. We print it in layers. Each layer is sandwiched between other layers in a vertical stack. We cannot put the shapes too close together and we cannot make the shapes to wide (or narrow). Every dimension on every polygon on every die on every wafer must be exactly the same or the die is rejected at final test.


Every 18 months a new piece of fab equipment is delivered from the tiny handful of companies that allow us to shrink the final dimensions on the die by 70% in the X and in the Y dimension. The reason is that the area of the logic gate above is 50% smaller in area because (0.7 * 0.7) = 0.5. Every 18 months like clockwork. And, as a commodity, you can go long or short on the minutes and seconds of the interval of 18 months between forklift upgrades to a fab. All competitive fabs in the world cost between $5B and $10B making this one of the planets largest capital assets. Capacity in mega-fabs must hover between 93% to 97% because.

1. output flow rate generates cash flow to cover fixed assets.
2. ability to tactically switch from a low margin die to a high margin die or to refuse risky product loads.
3. long fab cycle times (three to six months for a single die on a single wafer)
4. acts of God (the earth shakes and hurricanes blow)

This means that on the input side, fabs are run like commodity exchanges. The mega fabs of TSMC and UMC in Taiwan and Chartered Semi in Singapore service most of the worlds customers. A Mega-fab is beyond the reach of any single corporation to own and operate except for Intel. A fab with too much of "the car that floats and flys" work in progress (WIP) that never sells enough product has swallowed a turd. The worlds fabs buy and sell capacity of a very viscous quantity and they take a risk every time they pattern silicon.

The most precious real estate in the solar system is sold by the fempto-acre (exactly one Planck length on a side). That is Moore's law. Gordon Moore figured out exactly, precisely how to make the most silicon in the shortest time and with the fewest resources. Just shrink the bastard until half of it disappeared every 18 months.

But what about the megahertz and the gigahertz on my laptop?

Small, beautiful circuits run fast. Shrinking the area improves the speed and power as a second order effect. There is an intricate dance of reducing area while increasing speed. The only way to get there is through a team of EE's with plenty of diet coke and ping pong tables to play on in the break room.

There are really only two equations needed to figure this out.
Ohms Law V=IR (voltage = current * resistance)
Power/Frequency Law P=C*V^2*F (power = capacitance * voltage squared * frequency)

Ohms law is the measure of how much current that can be forced through a resistance. A fat garden hose (low resistance) can support a greater flow of water than a small garden hose (high resistance). The speed of the water through the hose depends on the water pressure (voltage).

How do I reduce power by 12% before lunch?

The goal of every chip designer is to reduce power, reduce power, reduce power in that order. Smaller circuits go faster since area is the most significant variable for capacitance (a capacitor is two conducting plates separated by a thin insulator). That is all an integrated circuit is - a collection of capacitors being charged and discharged by transistors turning on and turning off. Shrink the cap. reduce the voltage that needs to be moved around, reduce the current to move the voltage around, make the transistors stronger and smaller...

That delivers the capability to optimize for very low power for the ARM processor in your iPhone. It also delivers the capability to raise the power by increasing the frequency (the F in C * V^2 * F) for your laptop. The answer for the grieving man pictured is always the same "reduce voltage". We have our head in our hands because nothing runs fast enough at the voltage that keeps us inside the power envelope. So if you want to share in the persistent delusion that Moore's Law is about increasing speed go ahead and be slightly wronger than you are right now. And you thought quantum mechanics was unlearnable. Good thing I didn't think it was unteachable.