Projection Optics and High NA Imaging

Abstract

The projection system must transport a mask's diffracted field to a moving wafer with useful contrast, placement, focus, and uniformity. High NA raises numerical aperture from 0.33 to 0.55, enabling smaller features at 13.5 nanometers while sharply reducing depth of focus and enlarging the required angular range. The resulting mirrors are larger and more strongly curved, mask three-dimensional effects intensify, polarization matters more, and a conventional four-times reduction geometry becomes impractical. High NA therefore uses anamorphic imaging with different magnification in scan and non-scan directions and a reduced exposure field. I develop the optical architecture from source shape through illuminator, reflective mask, projection pupil, aberration control, flare, focus, and scanning. I then connect the half-field consequence to die layout and stitching. High NA is not a drop-in resolution upgrade. It is a coordinated change to scanner, mask, resist, metrology, stage, fab, and design.

Numerical aperture collects angular information

For refractive index $n$ and acceptance half-angle $\theta$,

$$NA=n\sin\theta.$$

In vacuum $n\approx1$. Increasing NA lets the projection system accept higher spatial-frequency diffraction orders and improves resolution. The same increase expands the ray-angle range at mask and mirrors, tightens pupil behavior, and reduces depth of focus.

At 13.5 nanometers, the first-order resolution comparison is

$$\frac{CD_{0.55}}{CD_{0.33}}=\frac{0.33}{0.55}=0.60$$

at constant process factor. Depth of focus scales with $1/NA^2$, giving about 36 percent of the 0.33 NA value. That loss becomes a wafer and process problem: topography, film thickness, stage vertical control, focus mapping, and resist process must all improve.

Illumination chooses which patterns receive margin

The illuminator does not simply make the mask bright. It shapes angular intensity and pupil fill to control diffraction-order overlap. Different source shapes favor different pitches and orientations.

I represent source distribution as $S(\sigma_x,\sigma_y)$. The aerial image depends on source, mask spectrum $M$, pupil $P$, polarization, and aberration phase $W$:

$$I(x,y)=\int S(\boldsymbol{\sigma}) \left|\mathcal{F}^{-1}\left[M P e^{i2\pi W/\lambda}\right]\right|^2d\boldsymbol{\sigma}.$$

The expression is schematic, but it shows why source and mask are co-optimized. A freeform source can increase image contrast for selected clips while consuming illumination efficiency or margin elsewhere.

Illumination uniformity and stability matter across the slit and scan. Angular distribution must remain calibrated. Mirror coating variation, contamination, actuator state, and source far-field changes can alter the effective pupil.

Optical control	Primary purpose	Coupled burden
Source shape	Select useful diffraction orders	Pattern specificity and efficiency
Pupil correction	Control amplitude and phase	Calibration and actuator stability
Mirror position	Align image and wavefront	Thermal and mechanical sensitivity
Focus control	Place aerial image on resist	Wafer height and thin-film stack
Dose control	Set resist energy	Throughput and stochastic defects

Anamorphic imaging makes the mirror train feasible

High NA rays and reflective-mask geometry create severe packaging and mask-angle constraints. A symmetric four-times reduction would require impractically large optical elements and mask interaction. High NA systems use different reduction magnifications by axis, commonly maintaining four-times in one direction and using eight-times in the other.

This anamorphic projection reduces the wafer field in one dimension. A full-size die may require two exposures with a stitch. Mask data, mask writing, reticle stage travel, wafer stage motion, scanner correction, and design all change.

IlluminateShape angular source

Distributes photons across pupil positions that support target features.

DiffractReflect from three-dimensional mask

Creates orientation- and material-dependent complex orders.

ProjectAccept 0.55 NA wavefront

Uses large precision mirrors and active aberration control.

ScanMap anamorphic half field

Synchronizes reticle and wafer motion with asymmetric magnification.

The stitch should be designed as a process region, not left as an accidental boundary. Features can be split or placed to reduce sensitivity. Dose and overlap can be shaped. Electrical test structures must reveal resistance, capacitance, leakage, timing, and reliability consequences.

Large dies also affect exposure strategy and throughput. Two half fields need additional stage transitions and correction. Design rules may encourage chiplet partitioning or floorplans aligned with field geometry, linking lithography to system architecture.

Aberration becomes feature displacement

Wavefront error can be expanded in orthogonal modes such as Zernike polynomials, but the scanner ultimately cares about pattern response. The same aberration coefficient can shift one feature, blur another, and leave a third relatively unchanged depending on source, pitch, orientation, and mask stack.

I want feature-aware sensitivity

$$\Delta E_j\approx\sum_k\frac{\partial E_j}{\partial a_k}\Delta a_k,$$

where $E_j$ is edge position and $a_k$ is aberration coefficient. This Jacobian connects optical metrology to edge budget and helps allocate actuator correction.

High NA optics incorporate many precision components and substantial mass. ZEISS reports projection optics with more than 40,000 parts and a weight near twelve tonnes. Mechanical stability, thermal gradients, vacuum forces, cable and cooling disturbances, and actuator noise can all alter wavefront.

Correction requires sensors, models, and actuators whose own calibration drifts. Not every mode is correctable at every time scale. Fast disturbance may average or print. Slow drift may be recalibrated. Spatially fixed error can enter computational correction. The control architecture needs a hierarchy.

Polarization and mask effects grow with angle

At larger angles, s- and p-polarized components interact differently with multilayers. Polarization state affects diffraction efficiency and imaging. The illuminator and projection system must control or model it across the pupil.

Reflective-mask absorber height creates shadowing and phase effects. High NA broadens the angular spectrum and increases orientation dependence. Low-n absorber research aims to improve image behavior, but changes etch, durability, inspection, and repair.

Mask roughness and multilayer variation can transfer differently under High NA. Specifications should derive from wafer failure probability rather than scaling old mask limits mechanically.

Focus becomes a film-stack problem

Reduced depth of focus pushes resist thinner. Thin resist may not survive etch, so engineered underlayers and hard masks become necessary. Wafer topography and film stress influence surface height. Focus sensors measure a physical surface whose relation to the chemical imaging plane depends on stack.

The focus budget includes wafer flatness, chucking, stage vertical position, leveling measurement, reticle heating, optical drift, film thickness, and local topography. Correlations matter. A wafer bow signature can combine with field focus to produce systematic edge change.

MeasureMask, wafer, and optical state PredictFeature-level sensitivities AllocateSource, pupil, stage, and dose corrections ExposeScan anamorphic field VerifyMetrology and electrical response

Qualification must include the ecosystem

ASML and imec’s High NA lab brings scanner, track, metrology, mask, and process partners together because isolated scanner resolution is insufficient. The production path needs qualified masks, resists, underlayers, etches, cleans, inspection, computational models, and designs.

I would qualify High NA through increasing hierarchy: optical calibration patterns, resist process windows, stochastic failure structures, mask-3D-sensitive clips, stitched interconnect, full cells, and electrical devices. Each result should retain scanner state and process trace.

The High NA frontier is not reached when a record pitch prints once. It is reached when the ecosystem can manufacture that pitch across wafers, fields, patterns, tools, and time at acceptable yield and throughput. Numerical aperture creates the possibility. Industrial coordination creates the product.