The lights in the cleanroom were perpetually that constant, impersonal pallid white, reflecting off the immaculate epoxy resin floor and the metallic cold gleam of equipment outlines. The air carried a unique scent, a mixture of faint ozone, specialized solvents, and the near-absolutely pure air blown by high-efficiency filtration systems. Time here seemed to flow differently, stretched and solidified by an almost obsessive pursuit of nanometer-scale precision.
Xiuxiu stood in the core laboratory of a top domestic lithography machine R&D base, wrapped in an airtight anti-static cleanroom suit that revealed only her eyes—bloodshot yet sharp as a hawk's at this moment. Before her was the engineering prototype of the EUV lithography machine, into which the team had poured countless efforts and which had just achieved a breakthrough in extreme ultraviolet light source power. Yet now it stood silently, like a colossal beast trapped in an invisible cage. What bound it was no longer the previously entangled barrier of light source power, but a component that appeared thin and lightweight yet harbored countless technical nightmares—the EUV mask.
The breakthrough in the light source had once electrified the entire team, as if they could already see the dawn of victory piercing through layers of mist. The stable 250-watt power output was a milestone on the path to EUV practicality, a hard-fought victory that Xiuxiu and her team had wrestled from countless sleepless nights and failed attempts. It meant there was sufficient photon energy to "carve" silicon wafers, defining the hundreds of billions of transistors on future chips. But having a sufficiently bright light source was not enough; an extremely precise, nearly perfect "negative" was also needed to faithfully transfer the designed circuit patterns onto the silicon without the slightest deviation. This "negative" was the mask.
In traditional DUV lithography, the mask was "transmissive." It resembled a complex glass slide, with circuit patterns drawn in opaque metals like chromium. Deep ultraviolet light passed through the transparent glass portions, blocked by the metal patterns, thereby casting shadow patterns onto the photoresist-coated silicon wafer to complete pattern transfer. This technology, having evolved over decades, was already highly mature. But in the EUV era, with wavelengths drastically reduced to 13.5 nanometers, almost all materials strongly absorbed this extreme ultraviolet light, making it impossible to find a suitable "transparent" material for the substrate.
Thus, EUV masks embarked on an entirely different technical path—reflective. Instead of letting light "pass through," they made light "reflect." Xiuxiu's gaze turned to the specially designed, inert gas-filled precision cassette beside her, inside which lay an EUV mask designed by their team and trial-produced by the most skilled domestic mask manufacturer. It looked like an exquisitely tiny mirror, but its structure was dauntingly complex.
Its substrate was typically ultra-low thermal expansion glass or a silicon wafer, polished to atomic-level flatness—fluctuations over fifty square centimeters could not exceed several tens of picometers, equivalent to limiting the elevation variations across the entire map of China to within a few millimeters. Upon this near-perfect substrate, a special multilayer film structure needed to be deposited—usually alternating layers of silicon and molybdenum, each layer's thickness precisely controlled at the nanometer scale, with each pair of Si/Mo layers summing to around 6.7 nanometers, corresponding to half the 13.5-nanometer wavelength. Forty, fifty, or even more pairs of such silicon/molybdenum layers were precisely stacked to form a "Bragg reflector" for 13.5-nanometer extreme ultraviolet light. When EUV light struck this multilayer film at a very shallow angle (typically a few degrees), reflections from each interface interfered constructively, like soldiers marching in perfect unison, ultimately forming a powerful reflected beam. The designed circuit patterns were then "drawn" atop this perfect reflective multilayer film using absorber materials like tantalum nitride. Where absorber patterns existed, reflected light was absorbed; where they did not, light was efficiently reflected. Thus, through the "presence or absence" of reflected light, circuit pattern transfer was achieved.
The principle sounded clear, but the difficulty of manufacturing and inspection increased exponentially. The challenge Xiuxiu's team now faced was precisely this "reflective structure," which was thousands of times more complex than in the DUV era. She walked over to the mask defect inspection instrument; the screen displayed the results of a full-area scan of the newly arrived mask. Dense red dots, representing defects, spread like a despairing crimson sandstorm across what should have been pristine pattern regions.
"Engineer Wang, is the data analysis ready?" Xiuxiu's voice, muffled by the mask, sounded somewhat stifled, yet the fatigue and anxiety within were unmistakable.
The engineer in charge of inspection, Lao Wang—a capable middle-aged man similarly wrapped in a cleanroom suit—pointed to another data analysis screen beside the main display, his brow furrowed. "Director Xiuxiu, the situation isn't optimistic. Preliminary judgment indicates the main issues lie with defects in the multilayer film. Look here," he zoomed in on an area. "Based on scattering signals and phase-contrast imaging analysis, there's a tiny protrusion beneath the multilayer film here, causing distortion in the uppermost absorber pattern. And here, what appears to be a minute particle that fell onto the substrate and got 'buried' beneath during multilayer deposition, forming a 'phase-shift defect'…"
Xiuxiu's heart sank. Multilayer film defects were among the mostthorny, mostdeadly enemies of EUV masks. Unlike surface scratches or deviations in absorber patterns, which were relatively easier to locate and repair, these defects lay buried beneath dozens of nanometer-thin film layers. They could originate from an undetectedtiny bump during substrate polishing, ananometer-scale dust particle falling during deposition, or tiny grain abnormalities caused by stress and lattice mismatch during film growth… These almost inevitable, random, minuscule flaws during manufacturing were covered and amplified layer by layer, ultimately altering the phase or amplitude of reflected EUV light locally, leading to unwanted "ghosting," blurred line edges, or even completely erroneous patterns on the silicon wafer.
Even more terrifying was the extreme difficulty in detecting these defects. Visible light inspection tools were utterly powerless, as the wavelengths didn't match. Dedicated inspection equipment based on EUV light or electron beams was necessary. Their existing domestic EUV mask defect inspection instrument, though already top-tier domestically, still lagged behind the world's most advanced levels in detection sensitivity, speed, and precise characterization capability for deeply buried defects. The alarming red dots on the screen might only be the tip of the iceberg; more subtle, hidden defects could be lurking within the noise, undetected. Any undetected and unrepaired defect larger than a few nanometers, when transferred onto the chip, could cause an entire valuable chip to be scrapped outright.
"Deep-seated phase-shift defects like these are almost impossible to effectively repair with our current processes and inspection capabilities," Lao Wang's voice carried a note of helplessness. "Even if located, existing repair techniques tend to cause secondary damage to the surrounding intact multilayer structure. This mask… its yield likely won't meet mass production requirements."
Mass production requirements. These four words hammered Xiuxiu's heart. Breakthroughs achieved in the laboratory, if they couldn't be transformed into stable, reliable, and scalable mass-production technology, were as meaningless as the moon's reflection in water or flowers in a mirror. The joy of victory from the light source hadn't fully dissipated, yet the even steeper, more slippery cliff of the mask now loomed before them. This wasn't just a technical problem; it was the ultimate test of a nation's entire foundational industrial capabilities in high-precision nanofabrication, ultra-precision inspection, specialty materials, and more. She felt an unprecedented pressure squeezing from all sides, making it hard to breathe. This pressure came not only from the technical bottleneck itself but also from time, from the watchfulblockade and competition abroad, from the unyielding nationalmission within her heart that couldn't tolerate failure.
She signaled Lao Wang to continue with deeper data analysis, then slowly walked to the laboratory's observation window, gazing out at the equally white corridor beyond. Her fingers unconsciously clenched, nails digging deep into her palms, the sharp pain barely suppressing the sourness rising in her nose. She couldn't collapse, couldn't show weakness. She was the backbone of this team, the guide on this technological Long March. She had to find a solution.
Just then, the private encrypted communicator in her cleanroom suit pocket vibrated softly yet persistently. She took it out to see a message from Mozi—no extra words, just a brief greeting and a night scene photo: the view from the top of Shanghai Tower, outside the window a glittering sea of city lights. He asked nothing, said nothing, but this seemingly casual gesture quietly infused her nearly exhausted heart with silent strength. She knew he must have sensed something from her unusually silent state lately. He didn't pry, just told her this way: he was here.
That silent support reminded her suddenly of Yue'er. The woman navigating the mathematical world faced an equally abstract, equally precision-pursuing realm. Mathematical proofs demanded absolute logical rigor, every step of deduction flawless, leaving no room for "close enough." This pursuit of "precision," on a spiritual level, bore striking resemblance to her own engineering obsession with nanometer-scale accuracy. One was constructing perfect edifices in an abstract symbolic world; the other carving microstructures in the physical world.
An idea, like a flash of lightning in the dark night, streaked across Xiuxiu's mind. She needed to think from a different angle. Perhaps Yue'er's purely mathematical way of thinking could offer some unexpected inspiration for understanding, even solving, mask defect problems. For instance, how to more precisely describe the distribution patterns of these random defects? How to establish more accurate mathematical models between defects and final imaging distortions? These were areas Yue'er might excel in or have encountered.
This thought invigorated her spirit. Almost without hesitation, she returned to the rest area, carefully removed her cleanroom suit, disinfected, and took out her laptop. She opened the encrypted video communication software she almost never used for direct contact with Yue'er. Taking a deep breath, she sent a connection request.
The few seconds waiting for the connection felt exceptionally long. She even felt somewhat apprehensive, worried her abruptness might disturb the other. But the screen soon lit up, Yue'er's figure appearing in the frame. She seemed to be in her study, with floor-to-ceiling bookshelves behind her, filled with books and manuscripts. She wore a comfortable beige sweater, her hair casually tied up, a trace of interrupted thought clouding her face, but seeing it was Xiuxiu, those clear eyes immediately warmed with a gentle smile.
"Xiuxiu?" Yue'er's voice came through the speaker, soft and slightly surprised. "I really didn't expect you to contact me."
"Sister Yue'er, sorry to disturb you," Xiuxiu somewhat awkwardly smoothed the stray hairs at her forehead. "I… I've encountered some technical difficulties and feel quite confused. I suddenly thought of you, thinking perhaps… perhaps you could give me some inspiration from a different perspective." She rarely confided her struggles so directly to someone not very familiar, but now, facing Yue'er's pure and serene gaze, she felt a strange urge to open up.
"It's fine, go ahead," Yue'er adjusted her posture, appearing very attentive. "Though I know nothing about engineering, perhaps hearing about different 'problems' might bring me some inspiration too."
Xiuxiu collected her thoughts and began describing the EUV mask challenge to Yue'er in as plain language as possible. Starting from the reflective structure, she explained how the multilayer film was like a meticulously designed "stack of mirrors," reflecting EUV light through interference effects. Then she focused on describing those ghost-like defects buried deep within the multilayer film—how difficult to detect, how randomly distributed, how they caused complex phase and amplitude changes optically, ultimately leading to chip pattern "distortion."
"…Our current inspection methods are like searching for tiny particles hidden under a blanket in a foggy room," Xiuxiu used what she thought was an apt metaphor. "We can roughly see where something's wrong, but it's hard to know precisely the size, shape of the particles, and what specific effect they have on the 'light' (here meaning EUV light). And this information is crucial for us to assess defect hazards and even think about repair solutions." She paused, her tone deeply helpless. "Sometimes I feel like we're using a roughly calibrated ruler to measure a world requiring nanometer precision. This 'ruler' itself is part of the problem."
On the video, Yue'er had been quietly listening, her fingers unconsciously tracing lightly on the desktop, her gaze focused, clearly striving to understand the unfamiliar, complex physical world Xiuxiu described. When Xiuxiu finished, she remained silent a moment, as if digesting the information.
"Precision…" Yue'er softly repeated the word, as if savoring its meaning. "In my world, 'precision' means absolute logical rigor, a binary opposition of 'true' and 'false.' A proposition is either proven or disproven; there's no 'almost' correct. A theorem's validity allows no counterexamples, like Euclid's geometric world—under axioms, all deductions must perfectly align."
She leaned slightly forward, looking at Xiuxiu on the screen, her eyes sparkling with thoughtful light. "But it sounds like in your world, 'precision' is more a probability problem, a process of finding statistically 'optimal solutions' or 'acceptable boundaries' amidst countless random disturbances and inherent errors. What you pursue isn't mathematical absolute 'perfection,' but 'feasible perfection' under physical laws and engineering constraints. That's quite interesting—these are two completely different philosophies of 'precision.'"
Xiuxiu was stunned. She'd never considered the problem from this angle. All along, her and her team's goal had been to infinitely approach the physically possible "perfection," eliminate all defects, achieve theoretical resolution limits. But Yue'er's words were like a new light illuminating a blind spot in her thinking. Indeed, in reality, absolute, zero-defect perfection might itself be a nonexistent "mathematical ideal." Engineering wisdom might lie in how to define "good enough," how to understand, quantify, and control these errors and defects so they don't affect the overall system functionality and yield.
"Statistical significance… probability…" Xiuxiu murmured to herself, as if grasping some key point. "You mean perhaps we shouldn't obsess over capturing every isolated, random defect, but should instead, from a more macro level, understand the 'distribution patterns' and 'statistical characteristics' of these defects? Build correlation models between defect density, type, spatial distribution, and final chip imaging quality (like critical dimension uniformity, line edge roughness)?"
"I'm just an outsider," Yue'er smiled modestly, but her eyes were bright. "But it sounds like this is a typical 'stochastic process' and 'system response' modeling problem. In my research field, like the Langlands program, we often deal with very complex mathematical structures, also full of 'randomness' and 'symmetry breaking.' We introduce special functions and group theory tools to characterize these structures' essential features, ignoring non-essential, random details. Perhaps in your mask defect analysis, you could also try finding some 'invariant,' or establish a 'filtering' model to filter out defect 'noise' with negligible impact on final imaging, focusing on those 'critical defects' that cause systematic distortion?"
Xiuxiu felt her heart pounding fiercely in her chest. Though Yue'er spoke in mathematical language, the ideas contained within held powerful transferability. Filter noise, focus on the critical! Their existing inspection data contained massive information—both truly fatal defect signals and large amounts of irrelevant instrument noise, background scattering, etc. If they could introduce more advanced mathematical tools, like the stochastic process analysis Yue'er mentioned, filtering theory from signal processing, or even certain pattern recognition algorithms, to reprocess this inspection data, might they more effectively distinguish defect "danger levels," prioritize handling defects most likely to cause chip failure? This could not only improve inspection efficiency but also provide precise guidance for subsequent limited repair resources!
"I see! Sister Yue'er, thank you!" Xiuxiu's voice trembled slightly with excitement. "You've given me a completely new perspective! We've been stuck in technical details of how to 'see clearer,' 'catch more accurately,' overlooking the possibility of using smarter methods at the data level to 'understand' and 'screen' these defects! This might greatly alleviate the pressure from our current insufficient inspection capability!"
Seeing the light rekindled in Xiuxiu's eyes, Yue'er genuinely felt happy. "I'm glad I could help. The value of mathematics shouldn't remain only on paper. Seeing it can inspire in a completely different field… feels wonderful."
Two women, across the screen—one on the physical frontline of nanofabrication, the other at the abstract pinnacle of the mathematical universe—engaged in a deep cross-disciplinary dialogue sparked by different understandings of "precision." They discovered their worlds weren't without intersection; on the path pursuing truth and the ultimate, they shared the same dedication, the same resilience, and the same solitude and contemplation when facing unknown difficulties.
"Xiuxiu," Yue'er's voice grew softer. "I learned about Mozi's anonymous donation of computing equipment." She didn't spell it out, but her meaning was clear. "That's just how he is, supporting what he believes important in his own way, quietly. We… we're both fortunate."
Xiuxiu's heart quivered slightly. Yue'er voluntarily mentioning Mozi, using "we," was agoodwill, alliance-signaling gesture. She was indicating she understood and respected thespecial bond between Xiuxiu and Mozi, and that she herself was part of it. This candor dissolved the faint awkwardness and sense of competition in Xiuxiu's heart.
"Yes," Xiuxiu responded softly, a complex yet relieved smile touching her lips. "He truly is… special. We're both fortunate." This "we" included Yue'er as well. In this moment, a friendship based on mutual appreciation, understanding, and shared secrets—amutual appreciation connection—quietly formed between twoexceptional women. They were independent individuals shining in their respective fields, yet entwined by fate's threads through the same man and their shared pursuit of career and ideals, forming a stable, peculiar triangular support.
The video call lasted nearly two hours, far exceeding Xiuxiu's initial expectation. They discussed mathematical models for mask defects, anecdotes and setbacks from their research, and occasionally, somewhat shyly, mentioned some trivial matters about Mozi. When Xiuxiu finally ended the call and closed her laptop, darkness had deepened outside the window. But she felt the lamp in her heart, nearly extinguished by technical difficulties, had been relit, burning even brighter.
She immediately returned to the lab, gathering core members in charge of inspection and data analysis. She didn't provide specific mathematical formulas—that wasn't her expertise—but conveyed the core idea Yue'er had inspired: re-examining defect data from statistical and modeling perspectives, seeking intelligent methods to distinguish "critical defects" from "background noise." She directed the team to promptly research relevant cutting-edge technologies like stochastic process analysis, machine learning applications in image defect classification, and attempt establishing collaborations with domestic universities or research institutes excelling in applied mathematics and data processing.
Deployments made, the lab once again filled with intense research atmosphere. Though the mask challenge remained enormous, the path ahead still thorny, Xiuxiu no longer feltisolated and unsupported orlost. She had a new direction, team support, that distant man's silent yet steadfast guardianship, and… an unexpected ally from the mathematical world.
She walked over to the silent EUV lithography machine prototype, gazing through the observation window at the mask inside—still appearing flawless to the naked eye yethidden dangers. Her eyes regained firmness and sharpness.
"Precision…" she murmured, as if declaring war on herself and the mask. "Whether mathematical absoluteness or engineering feasibility, we must conquer you. This path, we must walk it, and we certainly can walk it."
Night was deep, the lab lights still bright, illuminating these explorers trekking through the microscopic world, and thenever extinguished light pursuing the extreme in their leader's eyes.