Moore's Law and Dennard Scaling

For roughly fifty years, computers got dramatically faster every year while getting cheaper. That is not normal — cars, planes and buildings do nothing of the sort. Two distinct engines drove it, and they are constantly muddled together in casual conversation. Getting them straight is the key to understanding the biggest plot twist in modern computing: why, around 2005, the free lunch ended and every chip suddenly grew more cores instead of a faster clock.

The two engines are Moore's law (about how many transistors) and Dennard scaling (about how much power each one burns). They are not the same law. One is still limping along today; the other died.

Moore's law — the transistor count doubles

In 1965 Gordon Moore, co-founder of Intel, noticed that the number of transistors that fit economically on a chip was doubling at a steady cadence. The modern statement: transistor count per chip roughly doubles every two years. Write it as exponential growth with doubling time T_2 \approx 2 years:

N(t) \;=\; N_0 \cdot 2^{\,t/T_2}.

This is an economic and empirical observation, not a law of physics — Moore was describing the trend line of an industry, and the industry then treated it as a target to hit. Doubling every two years means a factor of 2^5 = 32\times per decade, and about 2^{25} \approx 34{,}000{,}000\times across fifty years. That is how we went from Intel's 1971 4004 (\approx 2{,}300 transistors) to modern chips with tens of billions.

Feel the exponential

Below is the growth multiplier 2^{t/T_2} over sixteen years. Drag the doubling-time slider and watch the "hockey stick": at a two-year doubling time the curve reaches 2^8 = 256\times in sixteen years; nudge the doubling time down to 1.5 years and it explodes far past the top of the chart. Exponentials are merciless — small changes in the rate produce astronomical changes in the total. (Plot the same curve on a logarithmic vertical axis and it becomes a straight line whose slope is 1/T_2 — which is exactly how these charts are always drawn in industry.)

Dennard scaling — shrinking is also free power

Moore alone only gives you more transistors. What made each generation also run faster at the same power was a separate gift, formalised by Robert Dennard in 1974. Shrink every linear dimension of a transistor by a factor k (so area drops by k^2), and if you also scale the voltage down by k, then capacitance, voltage and delay all fall together. The magic result:

shrink linear dimensions and voltage by k: you fit k^2 more transistors in the same area (that is Moore's gift);
each transistor switches \sim k faster (higher clock) and uses \sim 1/k^2 the power;
so power per unit area — power density — stays constant. More transistors, faster clock, same watts and heat. This is the "free lunch" of 1974–2005.

Dennard scaling is why clock speeds could climb from megahertz to gigahertz without the chip melting. Moore gave you the transistors; Dennard let you switch them faster for free. Two different laws, pulling together.

The death of Dennard, ~2005 — and the pivot to multicore

Dennard scaling assumed you could keep dropping the voltage. But voltage cannot fall forever: as the supply voltage V approaches the transistor's threshold voltage, leakage current (static power that flows even when the transistor is "off") climbs sharply. Around 90\,\text{nm} (~2005), voltage scaling essentially stalled. With V stuck, cranking the frequency f now raised power density — chips ran into a thermal power wall.

Moore's law kept delivering transistors, but you could no longer spend them on a faster single core — the clock froze at roughly 3\text{–}4\,\text{GHz}, where it still sits today. So the industry spent the extra transistors sideways, on more cores instead of a faster one. The dual-core era (Intel's 2005–2006 chips, AMD Athlon 64 X2) was born directly out of the death of Dennard scaling. Every "why do we have multicore?" answer traces back to this single graph flattening out.

// Moore's law: transistor count doubles every T2 years. function growthFactor(years: number, doublingYears: number): number { return Math.pow(2, years / doublingYears); } const T2 = 2; // doubling time in years for (const y of [2, 10, 20, 50]) { const f = growthFactor(y, T2); console.log(`after ${y} yr: ${f.toExponential(2)}x more transistors`); } // Dennard's gift (pre-2005): shrink dimensions & voltage by k -> power density constant. // Post-2005: voltage V is stuck, so raising frequency raises power with no relief. const k = 1.4; // one shrink generation (~sqrt 2) console.log(`\nDennard era: ${(k * k).toFixed(2)}x transistors, ~${k.toFixed(1)}x clock, SAME power density`); console.log("Post-2005: V floored by leakage -> clock stuck ~3-4 GHz -> spend transistors on CORES, not GHz");

Pull up a chart of top desktop clock speeds over time and you will see a near-vertical climb through the 1990s — 66 MHz, 200 MHz, 1 GHz, 3 GHz — and then, around 2004–2005, a cliff into flatness. Intel had publicly floated a 10\,\text{GHz} Pentium and then quietly cancelled the whole high-clock "Tejas" line. The culprit was the end of Dennard scaling: with voltage no longer scalable, every extra gigahertz now cost power the package could not dissipate. Twenty years later, flagship CPUs still boost to only about 5\text{–}6\,\text{GHz}. The frequency curve did not slow down — it hit a wall, and that wall reshaped the entire industry toward parallelism.

The most common muddle in this whole topic: people say "Moore's law is slowing down, that's why my PC isn't getting faster." Wrong on two counts. First, Moore's law only counts transistors — it says nothing about clock speed or performance. The thing that gave you free speed was Dennard scaling, and that is what died in ~2005. Second, Moore's law itself kept going long after: transistor counts kept doubling (just more slowly and expensively) well into the 2010s. So the correct sentence is: "Dennard scaling ended, which is why single-core speed stalled — even though Moore's law kept adding transistors, which we now spend on more cores." Keep the two laws in separate boxes.

Where this leaves us

Two exponentials, two fates. Moore's law (transistor count) is aged and expensive but not yet dead; Dennard scaling (constant power density) died around 2005 and took the free clock-speed lunch with it. Everything modern — multicore, big.LITTLE, accelerators, the obsession with performance per watt — is the industry adapting to a world where transistors are plentiful but the power budget is the true constraint. That power wall is the next lesson.