Chapter 33: Chapter 31: The Gap Between Top Students
The next morning, the sky was just beginning to brighten at the crack of dawn.
KNOCK KNOCK KNOCK!
Li Dong was woken by the knocking. He groggily got out of bed and opened the door.
Then, a large face with dark circles under its eyes loomed toward him.
"Ah, Li Dong, how did you sleep last night?"
Zheng Hua asked, forcing himself to sound energetic.
It was actually his first time chaperoning for the physics competition’s semi-finals. He couldn’t help it; the students from Seventh Middle School had never given him such an opportunity before.
So, he was even more nervous than Li Dong.
"Um... you need to relax. I know this is your first time at an in-person competition, so don’t be nervous. With your skills, as long as you perform normally, making it to the finals will be no problem."
Li Dong rubbed his sleepy eyes. Seeing Zheng Hua’s expression, as if he were facing a formidable enemy, he found it amusing.
’Nervous?’
’What a joke.’
His mind was completely filled with the twenty-thousand-yuan scholarship. He had even planned out how to spend it in his dreams.
’First, I’ll get Mom a new phone. I heard the ones from Hua Wei are good, but it seems their Hongmeng OS isn’t fully compatible with the Qidian app yet.’
’Then I’ll buy a computer for myself to make it easier to read some cutting-edge international research papers. As for the rest... I’ll figure that out later.’
The thought of cashing in soon made Li Dong not only not nervous but even a little excited.
"Don’t worry, Teacher Zheng. I’m not nervous."
After quickly washing up, Li Dong followed Zheng Hua downstairs for breakfast.
In the elevator, Zheng Hua continued to chatter endlessly.
"When you get into the exam hall later, check the test paper first. If you run into something you don’t know, don’t get stuck on it. Start with the easy ones..."
Li Dong could only nod along, the words going in one ear and out the other.
When they reached the dining hall, many students and teachers were already there eating breakfast.
Li Dong immediately spotted the people from Jiangcheng Sixth Middle School. A boy with glasses among them glanced at him, then paid him no more mind and continued eating from his tray.
Zheng Hua naturally saw them too, but this time he didn’t go over to exchange pleasantries. He simply nodded at them in acknowledgment.
Then he led Li Dong to a corner table.
Just then, a commotion erupted at the entrance of the dining hall.
A middle-aged female teacher was leading a mighty contingent of over twenty students inside.
These students were all wearing identical blue and white school uniforms. Although they were holding meal trays, they all looked perfectly composed. Some were even memorizing words from an English vocabulary book.
Li Dong was dumbfounded. ’Memorizing English vocabulary during a physics competition? With that level of showing off, you might as well go sit with Jiang Yizhou.’
The other students and teachers in the dining hall couldn’t help but stop what they were doing.
"Rongcheng Seventh Middle School?"
someone whispered.
Li Dong took a bite of a steamed bun, a little curious.
"Teacher Zheng, is that Rongcheng Seventh Middle School?"
Zheng Hua nodded and lowered his voice.
"In total, only about a hundred people from the entire province made it to the semi-finals. Their school alone accounts for more than twenty of them."
Zheng Hua sighed, his tone a mixture of envy and resignation.
"And you should know, these twenty-plus students aren’t even their top tier."
"The real top students from Rongcheng Seventh Middle School aim for gold medals in the International Ossai. Their dream is to actually become scientists; they look down on commercial competitions like this."
After hearing this, Li Dong nodded, his internal alarm bells ringing.
’They’re here to steal my twenty thousand yuan!!’
After breakfast, the Huaxuan Cup semi-finals began as scheduled.
The exam halls this time were three of the hotel’s multi-purpose conference rooms. Nearly two hundred contestants lined up according to their admission ticket numbers and entered in order after strict identity verification and security checks.
Li Dong sat in a seat toward the back of the middle section.
The test paper for this competition was mainly divided into multiple-choice, fill-in-the-blank, calculation, and a final, high-value "experimental design problem."
Li Dong briefly skimmed through the entire test.
’This is the difficulty of the Huaxuan Cup?’
Overall, the difficulty was average.
And as expected, the problems were heavily skewed toward practical applications, with plenty of traps.
For example, the third multiple-choice question:
[A new energy vehicle uses an electromagnetic eddy current braking system. When the circular metal brake disc rotates at high speed in a magnetic field, find the relationship between the braking torque M and the angular velocity ω.]
At first glance, this problem seemed to require integration, but it was completely unnecessary. As long as you grasped the two key points—"induced electromotive force E∝v∝ω" and "Ampere force F∝I∝E"—you could easily deduce that the braking torque M∝F∝ω.
Therefore, the answer was B, a linear relationship.
There was also a calculation problem about liquid cooling for data centers.
[Given the specific heat capacity and flow rate of the coolant, determine the thermal resistance network model when the chip surface temperature stabilizes.]
This problem looked flashy, but in essence, it was just a thermoelectric analogy combining the first law of thermodynamics with Ohm’s law.
The temperature difference is equivalent to voltage, heat flow is equivalent to current, and thermal resistance is equivalent to electrical resistance.
Li Dong drew the equivalent circuit diagram and calculated the junction temperature in a flash.
The more he wrote, the smoother it went...
...until he flipped to the experimental problem on the last page.
A moment ago, Li Dong had only given it a cursory glance and didn’t think much of it. But now, reading it carefully...
’This question...’
’Did they just declassify and release a core problem from photolithography machines?’
The problem description was very long, taking up an entire page.
[An experimental group, in order to investigate the resolution capability of a projection lithography system, built a simplified experimental apparatus: a monochromatic parallel light with wavelength λ is used as the exposure source. Through a projection objective lens with a numerical aperture of NA, the fine patterns on a mask are projected onto the surface of a wafer coated with photoresist, thereby transferring the chip pattern.
The minimum resolvable feature size of the lithography system (the minimum distance between two adjacent lines that can be clearly distinguished) follows the Rayleigh criterion:
δ = 0.61λ/NA
where the numerical aperture NA = n・sinθ, n is the refractive index of the medium between the objective lens and the wafer, and θ is the half-angle of the maximum cone of light that can be accepted by the lens.
Complete the following questions:]
The problem had three parts. The first two could probably be solved by any student with slightly better-than-average grades; you didn’t even need to be a top student.
But the third part... if you said it was hard, it did have the difficulty of an Ossai problem, but not a top-tier one.
However, the key wasn’t just solving it, but how you solved it best.
Li Dong subconsciously looked up and around.
There were still forty minutes until the end of the exam, and most of the contestants were still scratching their heads, struggling with the earlier calculation problems.
The contestant next to him looked particularly young, a freshman at most. He was currently chewing on his pen, staring blankly at the final problem, his paper largely empty.
’Are kids these days all so competitive? A freshman participating in this kind of competition?’
Li Dong grumbled inwardly, then returned his gaze to the test paper.
Li Dong picked up his pen and started writing the answers to the first two parts.
[1. Find the minimum resolvable feature size δ₀ of this lithography system.]
Solution: From the Rayleigh criterion formula δ = 0.61λ/NA, substitute the values λ=436nm and NA=0.35.
δ₀ ≈ 0.76μm.
[2. Name two conventional technical solutions used in the industry and briefly explain their physical principles.]
This explanatory question was really a test of a student’s breadth of knowledge. If you just buried your nose in textbooks all day, you might not know the answer.
However, Li Dong had learned about this while tackling University Physics.
He had even specifically looked up news articles about it online.
One solution is to shorten the wavelength, for example, by using DUV (deep ultraviolet) light.
The principle is simple: δ is directly proportional to λ.
Another is to increase the numerical aperture, for example, by using immersion lithography.
The principle here is to use a medium like water to increase the refractive index n, thereby increasing NA.
After finishing the first two parts, Li Dong paused at the third.
[3. Based on the core knowledge of wave optics (interference and diffraction) from high school physics, design an innovative solution that can break the aforementioned Rayleigh resolution limit without replacing the light source with a shorter wavelength or using a projection objective lens.]
Li Dong stroked his chin.
’How do you form an image without a lens? How do you increase precision without a shorter wavelength?’
Several solutions from University Physics and even cutting-edge optics flashed through Li Dong’s mind: ’Near-field scanning optical microscopy? Surface plasmons?’
’No, those are too far beyond the curriculum. They’d be a pain to explain, and the question specifies it must be based on "high school physics wave optics."’
He quickly thought of a solution.
He could use multiple-patterning techniques to precisely shift the mask for multiple superimposed exposures to create finer lines, or use a high-contrast photoresist to improve the sharpness of the pattern edges, indirectly enhancing the effective resolution.
Either would work. Just as Li Dong was about to write the answer on his paper, he was suddenly influenced by his Physical Perception (Basic Edition) and a new question occurred to him.
’Wouldn’t that be too divorced from reality?’
Huaxuan Technology is a business; it needs to make a profit. You can’t think about problems with a laboratory mindset. You have to consider them from the perspective of profitable industrial implementation.
So, Li Dong put down his pen and started to think.
’The optimal solution must be low-cost, highly stable, and mass-producible within production constraints...’
Time ticked by. The freshman student next to him had already finished the experimental problem and was sighing to himself.
’As expected, the difficulty isn’t even on par with our school’s own practice questions. Only this experimental problem required a little bit of thought.’
His name was Qiao Fan, a student from Rongcheng Seventh Middle School. He had come to this competition to see how big the outside world really was.
’I’m not coming back next year. It’s boring.’
Then, out of the corner of his eye, he saw Li Dong and his still-blank experimental problem.
’Sigh, no wonder the teachers say there are gaps even between top students.’
After that, he paid Li Dong no more attention and started checking his own paper.
At that moment, Li Dong finally thought of an angle of attack.
He quickly wrote on his paper:
[Solution Name: Dual-Beam Laser Interference Maskless Lithography]
The core principle of this solution is based on wave interference. It doesn’t use traditional lens-based imaging; instead, it utilizes two beams of light interfering on the wafer’s surface to create fringes.
Having established the core idea, Li Dong quickly wrote out the derivation.
Let two coherent light beams of wavelength λ symmetrically illuminate the wafer at an incident angle θ.
According to the condition for constructive interference, bright fringes occur when the path difference Δx = kλ.
From the spatial geometry, the period (spacing) d of the interference fringes satisfies:
d = λ/(2sinθ)
Therefore, the minimum feature size (half-period) is:
δ_min = d/2 = λ/(4sinθ)
[Breakthrough Verification:]
As θ approaches 90°, sinθ approaches 1.
At this point, the theoretical limit can reach λ/4.
Compared to the traditional Rayleigh limit of 0.61λ/NA (where NA
After finishing the derivation, Li Dong briefly added the [Implementation Steps]: Beam splitting with a prism -> Alignment with mirrors -> Interference exposure.
[Note: Although this interference method is mainly applicable to the fabrication of periodic patterns, it can serve as a low-cost alternative for specific layers in advanced processes, achieving an optimal balance between yield and cost within production constraints.]
Li Dong put down his pen and glanced at the time.
Fifteen minutes left...
