The Scaling Story  / Interlude I
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Mini-EE · Interlude I · after Chapter 8 · one 15 minute lesson

Three different curves have been sharing one name for sixty years.

You have just spent eight chapters on devices you could hold. Chapters 9 to 12 are about transistors nobody can touch, several billion at a time, on silicon that cost tens of billions of dollars to learn how to make. Before you open that box, it is worth knowing what actually happened to the transistor between 1971 and now — because the one sentence everybody uses to describe it, “Moore’s Law”, is doing the work of at least three separate claims that stopped being true at three different times, decades apart.

Assumes
Chapters 1 to 8
This lesson
15 min
Figures current as of
September 2026
Next
Chapter 9 · The Mirror Bench
01

Which curve do you mean?

15 minutes · density, speed and cost, and the years each one stopped
Recall From chapter 7: in the square-law model, what happens to a MOSFET’s drain current if you halve the channel length L and change nothing else? show answer

Chapter 7 gave you the reason the whole industry spent fifty years making transistors smaller. Drain current scales with W/L, so a shorter channel gives more current from the same gate voltage, and more current into the same capacitance means a faster switch. Smaller was not a tidiness exercise. Smaller was faster, and it was cheaper, and it was lower power, all at once, and that happy coincidence is what people are actually pointing at when they say “Moore’s Law”.

The misconception

“Moore’s Law is one law, and the only real question is whether it is alive or dead.” You will see this argued in both directions by people who know what they are talking about, which should already be a clue that something is wrong with the question. Jensen Huang says it is dead. TSMC keeps shipping denser nodes on schedule and says it is not. They are not disagreeing about the facts. They are answering different questions with the same three words.

At least three distinct curves get collapsed into that one name:

  1. Transistor count. How many switches fit on one chip. This is the curve people usually draw.
  2. Dennard scaling. Whether shrinking also buys you speed and power for free. Named for Robert Dennard, whose 1974 paper in the IEEE Journal of Solid-State Circuits showed that if you scale voltage and current down along with the dimensions, power per unit area stays constant — so you get more transistors and a higher clock, at the same power.
  3. Cost per transistor. Whether each new generation makes a switch cheaper to buy. This is the one Moore himself was actually writing about.

That last point is not a technicality. Moore’s 1965 article in Electronics carried the subtitle “With unit cost falling as the number of components per circuit rises, by 1975 economics may dictate squeezing as many as 65,000 components on a single silicon chip.” The body of the paper talks about “the complexity for minimum component costs”. It was an argument about economics that happened to be expressed in transistors. Sixty years of retelling turned it into a claim about physics.

Commit before you touch anything

Between 2004 and 2026 the largest chips you could buy kept roughly doubling their transistor count every two years. Over those same 22 years, what happened to the highest clock speed ever shipped?

Answer: C. The fastest part of 2004 ran at 3.65 GHz. Twenty years later the fastest desktop processor you could buy, Intel’s Core i9-14900KS, boosts to 6.2 GHz — and as of September 2026 nothing has beaten it. That is a factor of 1.7 in nineteen years, a doubling time near 23 years, against 2.67 years before 2004. Had the old rate held, 2024 would have shipped something around 550 GHz. Set the bench’s window to 2004–2026 and watch the clock curve crawl while the transistor curve carries on at its old slope.

Reading the bench

The bench plots each curve as doublings rather than raw numbers, because raw numbers are useless here: transistor counts span eight decades and clock speeds span four, so on any shared axis one of them is a flat line at the bottom. Doublings fix that. The slope of each line is doublings per year, and a slope you can compare across curves is exactly what the argument needs. A flat line means the curve has stopped improving.

Drag the two window sliders and the curves re-zero to the left edge of your window, so you are always looking at what happened inside the years you selected. The doubling times in the meters are least-squares fits through the real data points in that window, not smoothed or drawn by hand.

Curve one: count. Still going, and that is the honest answer

Fit the transistor curve over 1971–2004 and it doubles every 2.09 years. Fit it over 2004–2026 and it doubles every 2.13 years. Fifty-five years, one slope, straight through every announced death of Moore’s Law. Anyone who tells you transistor counts stopped growing is simply wrong, and the bench will show you why in about four seconds.

There is a catch, and it matters. Some of that recent growth is no longer coming from smaller transistors. Nvidia’s B200 reaches 208 billion by putting two separate pieces of silicon in one package and wiring them together; its Rubin successor reaches 336 billion with two compute dies plus two more for input and output. A reticle is the largest area a lithography machine can pattern in one exposure, and both parts are pressed against it. So “transistors per chip you can buy” and “transistors per square millimetre” have themselves begun to separate. Count is still doubling. Density is doing less of the work than it used to.

Curve two: Dennard. Died first, and died hardest

Dennard’s bargain broke somewhere around 2005. Two things refused to shrink: threshold voltage, and the subthreshold slope — a limit Dennard’s own 1974 paper names explicitly, writing that one must simply accept that subthreshold behaviour does not scale as desired. Because the threshold could not come down, the supply voltage could not come down either, and once supply voltage stops falling, power density starts climbing with every shrink. That is the power wall. Intel cancelled its Tejas and Jayhawk processors in 2004 rather than ship them, and the industry turned sideways into multiple cores instead of upward into higher clocks.

Put numbers on it. Clock speed doubled every 2.67 years from 1971 to 2004. From 2004 to 2026 it doubles every 23 years — and even that overstates the case, because the last three records are two-core boost clocks rather than the all-core speeds the older parts quoted. The engine did not slow down. It stopped, and everything since has been the last of the coasting.

Be careful with what died. Performance per watt did not stop improving. Jonathan Koomey’s work on computations per joule found a doubling every 1.57 years across the whole computer age, and on re-examining the data he found the doubling had slowed to about 2.6 years after 2000. Slower, by a lot — a hundredfold gain per decade became a sixteenfold one — but not stopped. What stopped dead was the free clock speed. Those are different claims and only one of them is a flat line.

Curve three: cost. Nobody agrees, and that is the finding

This is where you need a little vocabulary, because the cost curve is not a physics result. It is a price, and prices have interested parties attached.

Wafer
A disc of silicon, 300 mm across in a modern plant, on which many chips are made at once. About 70,700 mm² of usable surface.
Die
One chip’s worth of that wafer, before it is cut out and packaged. An Apple phone processor is roughly 100 mm², so several hundred fit on a wafer.
Yield
The fraction of dies that actually work. Dust, misalignment and random defects kill some of every wafer, and you pay for the whole wafer regardless.
Fab
The factory. A leading-edge one is a multi-billion-dollar building full of machines that cost more than aircraft.
Foundry
A company that owns fabs and manufactures other people’s designs to order. TSMC is the largest.
Fabless
A company that designs chips and owns no fab at all. Nvidia, AMD, Apple, Qualcomm. They buy wafers from a foundry.
Capex
Capital expenditure — money spent on buildings and equipment rather than on running costs. For a foundry it is the dominant number.

So the cost of a transistor is, roughly, the price of a wafer divided by the number of working transistors you get off it. Density pushes that number down. Wafer price pushes it up. For decades density won comfortably. The question is whether it still does, and here the sources genuinely contradict each other.

WhoWhenClaim about cost per transistor
Zvi Or-Bach, MonolithIC 3D, in EE Times2014Stopped falling at 28 nm; 28 nm is “the last node of Moore’s Law”
Handel Jones, IBS2015Flat from 28 nm through 7 nm
Milind Shah, Google, IEDM 2023 Short Course SC1.62023“Transistor cost scaling (0.7X) stalled at 28 nm and remains flat gen over gen”
Intel and TSMC slides of the period2013–15Cost per transistor still falling at 20, 16 and 14 nm
Samsung, on its own 14 nm2015Cost per transistor rose
Ben Bajarin, Creative Strategies, from supply-chain wafer pricesDec 2024Apple went 1 billion to 20 billion transistors while the wafer went $5,000 to $18,000

Take the last row seriously, because it is arithmetic you can do yourself. Twenty times the transistors for 3.6 times the wafer price, with die area staying inside the 80–125 mm² band Bajarin reports across the whole family, is about 5.6 times more transistors per dollar over eleven years — a doubling every 4.5 years or so. That is not flat. But it is not Moore’s Law either: at a two-year doubling those eleven years should have bought a factor of 45.

The rate was never the same as the density rate, even in the good years. Google’s own stated rule is 0.7× cost per node. Put TSMC’s own volume-production dates against that — 65 nm in 2006, 40 nm in 2008, 28 nm in 2011 — and cost per transistor was halving roughly every 4.9 years while density was doubling every two. The two curves were never one curve. They only ever pointed the same way, and pointing the same way is not the same as being the same thing.

A warning about the numbers on the boxes

“3 nm” is a marketing name. Nothing on a 3 nm chip measures three nanometres. The link between node name and any physical dimension broke in the late 1990s: Intel’s 0.13 µm process, shipping in 2001, had 70 nm gates, and its 22 nm process had 35 nm gates on 8 nm-wide fins. Chenming Hu, who co-invented the FinFET, told an IEEE Spectrum reporter in 2013 that nobody knows any more what 16 or 14 nm means. Intel’s Mark Bohr said in the same piece that he could not point to the one dimension that is 22 or 14 nm. The IRDS roadmap’s 2018 edition lists the physical gate length at the “3 nm” node as 16 nm.

Density figures are contested in the same way, and for the same reason: there is no agreed measurement. When Intel published 100 million transistors per mm² for its 10 nm process, a TSMC spokesperson asked EE Times whether Intel was playing paper games, pointing out that the same Broadwell part had been quoted at 18.4 million per mm² under the old metric and 37.5 under the new one. When you read a density number, find out whose ruler it was measured with.

In the wild

Your laptop stopped getting a faster clock, and got more cores instead. A 2007 desktop ran near 3 GHz and a 2026 one still does. Every generation since has spent its extra transistors on cores, cache and accelerators, because the clock is the thing Dennard was paying for and Dennard stopped paying. That is curve two showing up in a product you own.

The Raspberry Pi stayed on 28 nm for years, on purpose. Mature nodes are where the cheapest transistor lives, which is why 28 nm is still running at volume, why Texas Instruments is spending $30 billion on new fabs for 28 nm-to-130 nm analogue parts, and why the microcontroller in your project box is nowhere near the leading edge. Nobody is failing at anything. They are reading curve three.

Why chapter 8’s op-amp did not get 200 times cheaper while processors did. Op-amps are analogue, and analogue barely scales — the same Google short course puts logic cells shrinking about 1.7× per generation, SRAM 1.2×, and analogue only 1.1×. Matching, noise and headroom all want area. That is a large part of why a jellybean op-amp still costs what it costs, and it is exactly what Interlude II picks up after chapter 10.

Before you move on

Someone tells you “Moore’s Law is dead”. What is the single most useful thing to ask them?

The claim is unfalsifiable until you know which curve is meant, because all three answers are true of some curve: count is still doubling every two years, Dennard stopped around 2005, and cost is somewhere between flat and a 4.5-year doubling depending on whose figures you take. C is a reasonable follow-up but only after B, since “stopped or slowed” has a different answer for each curve. A and D are worth asking about node names, but they will not settle what was claimed.
Bench 01 · three curves, one time axis ALL THREE
● Locked until you commit a prediction above.
1971
197119922014
2026
198020032026
Transistors per chip—
Top clock speed—
Transistors per $ (Google)—
Transistors per $ (Creative Strat.)—
count clock cost, Google cost, Creative Strategies

Every word this interlude introduced

Dennard scaling L1
The 1974 result that scaling voltage and current down with a transistor’s dimensions holds power per unit area constant, so a shrink buys density and clock speed together. Broke down around 2005.
Power wall L1
The limit reached when threshold voltage stops scaling, so supply voltage cannot fall, so power density rises with every shrink. The reason clock speeds stalled and core counts rose instead.
Node name L1
A generation label such as “3 nm”. Since the late 1990s it has not corresponded to any measured dimension on the chip.
Wafer L1
The 300 mm silicon disc, about 70,700 mm², on which many dies are fabricated at once and which is priced as a unit.
Die L1
One chip’s area of a wafer, before dicing and packaging.
Yield L1
The working fraction of dies on a wafer. You pay for the wafer, not for the good dies.
Reticle limit L1
The largest area a lithography tool can pattern in one exposure, and therefore the largest single die. Bigger parts must use several dies in one package.
Foundry L1
A company that owns fabs and manufactures other companies’ designs. TSMC is the largest.
Fabless L1
A chip company that owns no fab and buys wafers from a foundry. Nvidia, AMD, Apple, Qualcomm.
Capex L1
Capital expenditure — spending on plant and equipment. TSMC’s was $40.9 billion in 2025 against $122.9 billion of revenue.

Where this goes next

CH 09

The Mirror Bench

Back to circuits. Current mirrors and active loads — the first structures that only make sense once transistors are free and matched, which is exactly what this interlude’s curves bought you.

INTERLUDE II

The Money

After chapter 10: the fabless and foundry split in full, what a fab actually costs, and why analogue and RF never scaled the way digital logic did — which you will feel directly once you have built a differential pair out of matched devices.

About the figures. Nothing here is simulated; every number is a sourced measurement or a sourced estimate, and the bench plots real data rather than solver output. Transistor counts and clock speeds are the running maxima of Karl Rupp’s 50 Years of Microprocessor Trend Data (CC-BY 4.0), the same dataset Google used at IEDM 2023, extended past its 2021 end with individually sourced parts. For count: Nvidia H100 (80 billion, 2022), B200 (208 billion across two dies, GTC March 2024) and Rubin VR200 (336 billion, GTC March 2026). For clock: Intel’s Core i9-13900K (5.8 GHz, October 2022), i9-13900KS (6.0 GHz, January 2023) and i9-14900KS (6.2 GHz, March 2024), which as of September 2026 still holds the highest stock desktop clock. Those three are max turbo on two cores, not all-core clocks, so if anything they make the clock curve look better than a like-for-like comparison with the older parts would; the flattening is real and slightly understated here. Taking the running maximum means each curve shows the best part shipped to date rather than the average of a mixed field, so a flat stretch means no faster part appeared, not that clocks fell. Dennard scaling is R. H. Dennard et al., IEEE J. Solid-State Circuits 9(5), 256–268, October 1974; the 2005–2007 breakdown date is the general industry reading, though Koomey puts it nearer 2000, and the efficiency figures (1.57-year doubling, slowing to 2.6 years after 2000) are Koomey et al., IEEE Annals of the History of Computing 33(3), 2011, and his later re-analysis. The Google cost line is reconstructed from the scaling rule stated on slide 7 of Milind Shah’s IEDM 2023 Short Course SC1.6 — 0.7× per node, flat from 28 nm — placed against TSMC’s own published volume-production years; it is the source’s stated rule, not bar heights read off the chart. The Creative Strategies cost line is derived from Ben Bajarin’s December 2024 figures as reported by Tom’s Hardware, and rests on his statement that die area stayed within 80–125 mm² across the family; at the extremes of that band the doubling time moves between 3.9 and 5.0 years. Those two cost lines disagree, which is the honest state of the evidence and the reason both are drawn. Node names, gate lengths and the density-metric dispute come from Rachel Courtland, The Status of Moore’s Law: It’s Complicated, IEEE Spectrum, October 2013, and IEEE Spectrum’s 2017 report on Intel’s density metric. What will date first: the wafer prices and the 2026 capex and revenue figures, which move every quarter; the Rubin transistor count, which comes from launch material rather than a die analysis; and the right-hand end of the count curve, which needs a new part added every year or two. The structural claims — that Dennard scaling ended, that the three curves are distinct, that node names are marketing — are stable and will not need revising.