UNIT 15 • LIGHT, LENSES, AND RESOLUTION

What limits the smallest feature

CD = k₁ · λ / NA

CD is the smallest printable half-pitch, λ is the wavelength of the light, and NA is the lens's numerical aperture. Shorter wavelength and larger NA both shrink the feature. The k₁ factor bundles everything else: the resist, the mask, the illumination, and the process.

Print smaller by using shorter light, a bigger lens, or a smarter process.

THE WAVELENGTH LADDER

Light got shorter to make chips smaller

g-line, 436 nm Mercury lamp light, the workhorse of early chips

i-line, 365 nm Another mercury-lamp line, still used for less demanding layers

KrF, 248 nm Deep ultraviolet from a krypton-fluoride laser

ArF, 193 nm The argon-fluoride laser, the main tool for two decades

EUV, 13.5 nm Extreme ultraviolet, in volume production since around 2019

Each step down in wavelength opened a new generation of smaller chips.

NUMERICAL APERTURE

A wider cone of light prints smaller

The lens gathers light from a wide cone and focuses it onto the wafer. The wider the cone, the sharper the spot. Numerical aperture measures that width: NA is the refractive index n of the medium times sin θ, where θ is the half-angle of the cone.

A bigger NA means a tighter focus and smaller features.

IMMERSION

Put water under the lens

With air between lens and wafer, NA cannot reach 1. Filling the gap with ultra-pure water, whose refractive index at 193 nm is about 1.44, lets the lens use a wider cone. Immersion scanners reach an NA of about 1.35 and were the main production tool for years.

Water under the lens is a cheap trick that added a whole generation.

DEPTH OF FOCUS

Sharper images have less room for error

DOF = k₂ · λ / NA²

Depth of focus is how far the wafer surface can be out of focus before the image blurs. Shorter wavelengths and larger NA both shrink it, and NA enters squared. At advanced nodes the depth of focus is only tens to a couple hundred nanometers, which is why wafers must be polished flat.

The better the resolution, the flatter the wafer has to be.

THE k₁ FACTOR

Squeezing more out of the same light

The limit For a single exposure, k₁ cannot go below 0.25

Example: ArF immersion 0.3 × 193 nm / 1.35 is about 43 nm half-pitch

Example: EUV at NA 0.33 0.4 × 13.5 nm / 0.33 is about 16 nm half-pitch

Ways to lower k₁ Better resists, off-axis illumination, phase-shift masks, and optical proximity correction

Resolution enhancement techniques are how fabs push k₁ down toward its limit.

UNIT 15 STUDY COMPLETE

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Ready for the Fab Challenge?

You can use wavelength, NA, and k₁ to reason about resolution.