EUV Lithography — The Madness of Making 13.5nm Light

Light at 13.5nm is absorbed by air and by every lens material there is. So why did the semiconductor industry build an entire industry around it? Tin plasma sources, optics with no lenses at all, and the cost arithmetic against multi-patterning — explained from zero.

The Limits of a Stencil and a Spray Can

Chip circuits are printed. A pattern drawn on a master (the mask) is projected through optics, shrunk down, onto a light-sensitive film (resist) on the wafer. Think of it as photographic enlargement run in reverse.

Something counterintuitive happens here. No matter how finely you draw the pattern on the mask, past a certain width the image on the wafer smears out and collapses. The cause is not lens quality — it is that light is a wave. Spray paint through a stencil and the paint creeps around the edge of each hole, softening the outline. Light does the same: passing through a narrow gap it bends around the edges (diffraction), and the closer the gap gets to the wavelength, the worse the bending.

That limit fits in one line.

$\mathrm{CD}$ is the finest feature you can print, $\lambda$ is the wavelength of light you use, and $\mathrm{NA}$ is the numerical aperture — how wide a cone of angles the optics can collect. $k_1$ bundles together how you shape the illumination and how good the resist is, and for a single exposure it cannot go below 0.25. So the equation is really saying: to print finer lines, either shorten the wavelength or open the optics wider. There is no third option.

The industry spent two decades on the second one. The endpoint was ArF immersion: 193nm light, with the gap between the final lens and the wafer filled with water so rays bend more steeply, pushing $\mathrm{NA}$ to 1.35. Put $k_1=0.25$ into equation (1) and you get $0.25 \times 193 / 1.35 \approx 36$nm — lines and spaces 36nm wide, the floor for one exposure.

And there it stalled. $\mathrm{NA}$ is capped by the refractive index of the fluid you can put in the gap; $k_1$ is capped by physics. As for the numerator, the 157nm source that was supposed to follow 193nm died because no practical lens material transmits that wavelength. The path of shortening the wavelength a little had closed.

Why the Odd Number 13.5nm?

So the industry jumped — not to the wavelength next door but to one-fourteenth of it: 13.5nm, extreme ultraviolet (EUV). The size of the jump is the strange part. Why not 50nm, or 5nm?

The answer is not "shorter is better." 13.5nm is where two completely unrelated constraints happen to overlap — very nearly the only window that exists.

The first is the mirror. In this band every material has a refractive index near 1 and absorbs strongly. Bending light by refraction — that is, a lens — is impossible in principle. What does work is a multilayer mirror: dozens of thin film pairs whose individual weak reflections add up in phase. That constructive interference (Bragg reflection) requires the layer period to be about half the wavelength, roughly 6.9nm. Alternating molybdenum and silicon at that spacing is what gives a usable reflectivity — and the wavelength where that combination works out is near 13.5nm.

The second is the source. Heat tin (Sn) into a plasma and the transitions of its highly stripped ions crowd together into a strong emission band, also near 13.5nm.

A material that shines brightly and a mirror that reflects well, at the same wavelength. 13.5nm is that intersection — not a number anyone chose, but the one gap nature left open. And only a narrow slice of it counts: roughly ±1% around the center. Everything emitted outside that band turns into heat and nothing else.

The Source: Shooting 50,000 Tin Droplets a Second

So how do you make this light? Here is where it turns genuinely absurd.

An EUV source runs on laser-produced plasma (LPP). Tin droplets tens of micrometers across are fired into a vacuum chamber at 50,000 per second. Each droplet in flight is hit first by a weak pre-pulse that flattens it into a pancake, then by a high-power CO₂ laser at 10.6 micrometers that blows it into a plasma of tens of electron volts. A bowl-shaped collector mirror gathers the EUV that comes off and feeds it into the scanner.

The brutality shows up in the conversion efficiency. Only a few percent of the drive laser energy ends up as in-band EUV; the rest becomes heat, out-of-band light, and scattered tin. You pour in tens of kilowatts of laser power continuously, and what reaches the scanner is a few hundred watts.