The ultra‑clean laboratory deep beneath XianGuang Research Institute resembled an isolated universe forgotten by time, where constant temperature, humidity, and near‑absolute cleanliness jointly guarded the precise dance within the microscopic world. Yet, at this moment, the control center of this universe—the core EUV R&D zone—was permeated with an atmosphere heavier than usual, different from the mood when conquering source power. That atmosphere did not stem from uncertainty in technical paths or lack of resources, but from a near‑philosophical, deep pressure facing ultimate barriers of the physical world.
Xiuxiu stood outside the prototype integration area of the new‑generation High NA EUV lithography machine, gazing through the thick observation window at the colossal entity composed of countless complex components. This prototype condensed the preliminary achievements of her and her team's charge toward higher resolution, supported by Mozi's unlimited funding. The enormous lens assembly for higher numerical aperture (NA) was preliminarily installed in place, like the eyes of a giant beast; the vacuum chamber and cooling system designed to meet higher power and harsher thermal‑management demands functioned like a robust circulatory system; the laser‑produced‑plasma (LPP) source module, optimized and upgraded based on previous successful experience, was also ready, theoretically capable of providing the energy foundation needed to push toward higher resolution.
However, all these hardware breakthroughs ultimately required an ultimate judge to verify their value—the actual circuit patterns etched onto silicon wafers, whether they achieved the design‑required, terrifyingly fine precision sufficient to define process nodes below 2nm. And the key to ensuring this precision, besides resolution and linewidth, was a parameter that in the High NA era became more critical and harder to control than ever—**overlay accuracy**.
Overlay accuracy, as the name implies, refers to the ability to superimpose dozens or even over a hundred different circuit pattern layers, one upon another, with absolute precision. Imagine building a hundred‑layer complex edifice with wildly different designs yet requiring perfectly aligned, seamless stacking on an area no larger than a fingernail; any layer exhibiting even a minuscule misalignment could cause complete chip‑function failure. At the process nodes targeted by High NA EUV, the requirement for overlay accuracy has advanced beyond nanometer scale toward **atomic scale**—demanding error control as small as **fractions of a nanometer**, merely a few silicon‑atom diameters!
This demand approaches the sensing limit of existing metrology technology. The **overlay‑accuracy metrology** technique Xiuxiu's team previously relied on, based on optical‑diffraction principles, now faced unprecedented challenges.
In the metrology analysis room next to the lab, Xiuxiu and her core metrology engineers frowned over a set of data freshly acquired from test wafers. The screen displayed the working principle and results of using **diffraction‑based overlay (DBO) marks** for measurement. This technique designs special, periodic grating structures as marks on each chip layer. When measurement light (typically visible or deep‑ultraviolet) illuminates these marks, the relative displacement between two mark layers produces specific **diffraction‑intensity** or **phase** changes. By precisely detecting and analyzing these changes, one can inversely deduce the overlay error between two pattern layers.
"Chief Xiuxiu, look," a senior metrology engineer pointed at the fluctuating error curve on screen, voice heavy. "Our DUV‑based diffraction‑metrology system has a theoretical precision limit constrained by light wavelength and optical‑system numerical aperture; it's now nearing its capability 'ceiling.' At sub‑nanometer scale, signal‑to‑noise ratio plummets; the system's own noise, tiny environmental vibrations, even the inherent atomic‑level lattice fluctuations of the silicon wafer itself become non‑negligible interference sources. Our obtained data… too volatile, poor repeatability, simply cannot serve as reliable basis for High NA process calibration and control."
Xiuxiu silently watched the curve fluctuating violently like an electrocardiogram—no longer a clear line pointing to a definite value, but a blurry, uncertainty‑filled band. It was like trying to measure a sheet of paper's thickness with a crudely‑graduated ruler, where the ruler's own error far exceeds the dimension to be measured. Optical‑diffraction metrology, that once‑sharp "ruler," appeared clumsy and powerless before the atomic‑scale precision demanded by High NA.
"We need new 'eyes,'" Xiuxiu's voice wasn't loud, yet carried undeniable resolve. "Eyes that see more accurately, more deeply."
Under the lab lighting, her gaze turned toward directions representing more advanced measurement technologies—**X‑ray** and **electron beam**.
"X‑ray metrology," another engineer responsible for frontier‑tech exploration brought up new materials. "Utilizing X‑rays with wavelengths much shorter than visible light (typically fractions to a few tenths of nanometers) can theoretically greatly enhance resolution. We could design X‑ray‑diffraction or scattering schemes extremely sensitive to overlay‑mark displacement. But…"
He paused, listing huge challenges: "High‑brightness, high‑stability X‑ray sources themselves are a major hurdle. More importantly, X‑ray‑matter interaction is strong, penetration limited, imposing extremely high demands on sample preparation and signal interpretation. Moreover, X‑ray equipment is exceedingly expensive and complex, difficult to integrate into online mass‑production environments; more likely used for offline, sampling‑style precision analysis."
Xiuxiu nodded, her eyes shifting to another option.
"**Electron‑beam metrology**, especially techniques like **critical‑dimension scanning electron microscopy**," that engineer continued. "Using an electron beam focused extremely finely scanning across the sample surface, imaging by detecting secondary‑electron or backscattered‑electron signals. Its resolution theoretically can reach sub‑nanometer levels, directly 'seeing' overlay‑mark positions. This currently seems the most promising path to achieve atomic‑scale‑precision measurement."
Behind hope lay deeper physical dilemmas. Electron‑beam metrology inevitably touches one of modern physics' cornerstones—the **Heisenberg uncertainty principle**. This principle profoundly states that you cannot simultaneously know both the position and momentum of a microscopic particle (e.g., an electron) with arbitrary precision. In electron‑beam‑metrology context, to obtain higher spatial resolution (i.e., determine more precisely where the electron strikes the sample), the electron beam must be focused finer, meaning smaller position uncertainty for the electrons. But according to the uncertainty principle, this necessarily increases momentum uncertainty, manifesting as worsened energy dispersion (chromatic aberration) of the beam, or inherent broadening effects of the electron wavelength when interacting with the sample becoming more significant.
It's a paradox: You want to "see" a point's location more clearly, so you must poke it with a sharper "needle" (fine electron beam). Yet this "needle" itself, due to physical law, becomes "blurry" or carries uncertain energy, potentially damaging the extremely fragile sample (e.g., deforming delicate photoresist) during interaction, or introducing measurement errors that cannot be eliminated. This isn't merely engineering noise; it's a **fundamental limitation rooted deep in nature's laws, impossible to completely overcome by any technological breakthrough**.
Xiuxiu felt unprecedented pressure. This was no longer a problem solvable entirely by optimizing parameters, improving materials, or designing cleverer algorithms. They were approaching a boundary, one drawn by quantum‑mechanical rules—the ultimate boundary concerning "measurement" and "knowability" itself. High NA EUV's overlay‑accuracy requirement had pushed them onto this boundary, forcing her to consider how to seek possible solutions while acknowledging and understanding this fundamental limitation.
Should they attempt to develop hybrid metrology combining X‑ray's high resolution with electron beam's direct imaging capability, mutually verifying and reducing uncertainty via data fusion? Or design more ingenious overlay‑mark structures insensitive to measurement error? Or leverage artificial intelligence and big‑data analytics to extract the true overlay‑error signal drowned in quantum fluctuations from noisy raw data?
Each line of thought implied huge investment and uncertain return; each could be a thorny exploration path.
She walked to the observation window, looking again at the massive High NA EUV prototype. It represented the pinnacle of human engineering, the crystallization of countless wisdom and effort. Yet, to truly master it, to carve atom‑level‑precise structures, they had to confront obstacles set by fundamental physical laws. This tension between macro‑fabrication and micro‑measurement—frustrating yet fascinating—made her profoundly realize that engineering's path is not an infinitely extrapolatable smooth curve; it will eventually encounter those boundary stones erected by nature's laws, impossible to surmount.
This **endless pursuit of precision**, and the deep limitations arising from the world's very essence encountered in the process, stirred a peculiar resonance within Xiuxiu. She thought of Yue'er, of that mathematical world constructed from pure logic and perfect symbols.
In Yue'er's mathematical universe, once a theorem is proved, its truth is absolute, eternal, unaffected by any physical conditions or measurement errors. The value of π, the beauty of Euler's identity e^(iπ) + 1 = 0, the zero‑distribution depicted by the Riemann hypothesis… These mathematical objects and laws exist in a realm of pure ideas transcending spacetime and matter; they themselves are perfect, unperturbed by the Heisenberg uncertainty principle. There, precision is infinite, logic self‑consistent, truth clear.
A complex smile involuntarily appeared at the corner of Xiuxiu's mouth. She, as an engineer, spent her lifetime wrestling with imperfect materials, noisy signals, physical processes full of uncertainty, attempting to carve out a controlled, precise zone of order within the chaotic real world. Yue'er, meanwhile, roamed that idealized mathematical kingdom full of certainty and perfection.
At this moment, she felt an unprecedented, deep **longing** for that world Yue'er inhabited. A longing for absolute precision, ultimate order, pure reason unfettered by physical constraints. Not an escapist desire from real challenges, but like gazing at a distant snow‑capped mountain symbolizing eternity and purity during a long, arduous desert trek—awe and yearning rising in the heart.
She knew she could never truly enter that pure‑mathematical world; her battlefield was here, in this physical reality full of constraints and imperfections. Yet perhaps this very longing for "perfection," this spirit of striving toward it despite knowing its unattainability, is the deepest inner drive propelling engineers like her to constantly challenge limits, turn the impossible into possible.
She picked up the internal communicator, her voice regaining usual calm and decisiveness: "Summon the X‑ray and electron‑beam metrology groups, plus computational‑lithography and data‑analysis teams, meeting in one hour. We need to draft a technology roadmap crossing current metrology limits. Also… help me schedule some time with Professor Yue'er. I have some… questions about 'perfection' I'd like to discuss with her."
Putting down the communicator, Xiuxiu again turned her gaze toward the deep observation window. The limits of measurement were a chasm lying across the High NA expedition. But she knew, whether by more powerful tools, smarter algorithms, or drawing inspiration from Yue'er's idealized mathematical world, she and her team must find a way to cross it. Because precision is an eternal pursuit etched into an engineer's soul; even if ahead lies the Heisenberg‑drawn invisible barrier, they must attempt to touch the world of atomic‑scale, ultimate accuracy beyond that barrier.