Printing with Light — How Lithography Draws Smaller Than Its Own Wavelength

Circuits Are Printed

Semiconductor chip circuits are printed much like printing on paper. Light is shone through a mask, which is a plate holding the circuit pattern, and that pattern is transferred onto a wafer, which is the thin, round silicon plate used to make chips. The wafer is pre-coated with a photoresist, which is a thin film whose properties change when exposed to light. "Lithography — Painting Circuits with a Brush of Light" calls this work photolithography and defines it as the act of projecting a circuit pattern with light to transfer it onto silicon.

This article calls the same work lithography. Lithography is the entire process of coating a photoresist, shining light, and washing it away to leave a circuit pattern on a wafer. In the industry, the single step of shining light is sometimes narrowly called photolithography, and in this article, "photolithography" refers to that narrow meaning. The broad meaning of photolithography mentioned in the primer is what this article calls lithography.

The mask itself is also made by drawing on it. In the mid-1990s, the typical method for making semiconductor devices was to draw a circuit pattern with an electron beam on a glass plate coated with chromium (a photomask), and then repeatedly print that pattern onto a silicon wafer using an optical lithography tool (DOI: 10.1093/oso/9780198562832.003.0007). Once the master plate was made, the same pattern could be printed over and over again.

The reason the printing method survives is money. Back in 1994, lithography accounted for roughly one-third of integrated circuit manufacturing costs, and the capital investment required for a single fabrication plant was growing exponentially. A cost analysis from that same year projected that economic factors rather than technical ones would ultimately halt the progress of miniaturization, noting that any lithography process had to be cost-effective to be considered for mass production (DOI: 10.1364/eul.1994.elpm.13). The method of drawing lines directly onto a wafer with an electron beam remained stuck in the "next-generation" phase even in 2009 due to technical challenges and economic barriers (DOI: 10.1145/1862879.1862880).

The reason lithography is pointed to as the bottleneck in semiconductor manufacturing lies in resolution. Resolution is how clearly and distinctly objects down to what size can be printed using light. Because that size determines how many devices can fit into a given area, resolution equals integration density. This article traces how features smaller than the wavelength of the light used have been drawn, and what trade-offs each of those tricks required.

We apply, expose, wash, and carve

The skeleton of the process is just as "Lithography — Painting Circuits with a Brush of Light" followed in a single line: we coat the wafer with photoresist, project the mask's pattern onto it with light, wash away the photoresist, and carve away the areas the photoresist left uncovered. The property that changes in the photoresist upon receiving light is its solubility in the developer, which is the chemical used to wash the photoresist away (DOI: 10.2533/chimia.1993.387). Development is washing the exposed photoresist with a developer, leaving behind only one of two areas: the place that received light or the place that did not. Etching is using the remaining photoresist as a shield to carve away the underlying layer it does not cover.

The photoresist pattern becomes a solid structure by going through paths like this. Using a photoresist patterned with an electron beam as a shield, a hard mask—which is a shield made of a material harder than the photoresist—was first made with a width of 25 nanometers (nm) and a height of 57 nm. Using that hard mask as a shield to carve again left behind a silicon structure with a width of 18 nm and a height of 71 nm (DOI: 10.35848/1347-4065/adb4ff).

The Equation of Resolution, and the Price Called Depth of Focus

What blocks drawing smaller is the diffraction of light. Diffraction is the property where light traveling and spreading like water waves blurs toward the edges after passing through a sharp boundary. No matter how sharp the mask's boundary is, the image formed on the wafer blurs a little, and this blur determines the smallest size that can be drawn. Two values govern the size of the blur. As "Lithography — Painting Circuits with a Brush of Light" defines, the wavelength is the distance between one crest and the next in a wave of light, and numerical aperture (NA) is the value representing how wide an angle of light the lens gathers. The shorter the wavelength and the larger the numerical aperture, the smaller the blur.

This relationship is written as a single equation. The smallest size you can draw is $k_1$ multiplied by the wavelength and divided by the numerical aperture. $k_1$ is a proportionality coefficient attached to this equation, a value that captures how good tricks like the illumination method, mask, photoresist, and process are, besides the wavelength and numerical aperture. The smaller $k_1$, the smaller the features you can draw with the same wavelength and same numerical aperture. Thus, there are three paths to drawing smaller than the wavelength: shrinking the wavelength, increasing the numerical aperture, or lowering $k_1$.

The limit given by the equation is actually calculated. The yardstick used here is pitch. Pitch is the interval from the start of one line to the start of the next in densely lined-up lines—in other words, the combined length of one line and one space. If the numerical aperture of a KrF lithography tool using 248 nm light is 0.6, the diffraction limit for the narrowest printable pitch is calculated as $0.5\lambda/\text{NA}$, giving 207 nm (where $\lambda$ is the wavelength). Yet even this 207 nm line could be crossed. A 200 nm pitch grating was printed using a photoresist process called multiple development, where the phenomenon is split into multiple steps. The authors noted that this was a result unattainable with conventional tricks that lower $k_1$, such as off-axis illumination that shines light at an angle or phase-shifting masks that alter the phase of light (DOI: 10.1143/jjap.38.6999). This is an example of printing below the limit calculated by the tricks of the photoresist process.

The path the industry chose first was shrinking the wavelength. As tracked by "Lithography — Painting Circuits with a Brush of Light", the light used in lithography shortened from 436 nm to 365 nm, through 248 nm, and down to 193 nm. A 1934 [sic] report projected that 193 nm lithography would enable 0.25-micrometer ($\mu m$) patterning and become the mainstay mass-production technology at 0.18 $\mu m$ (DOI: 10.1364/eul.1994.elpm.10).

A price comes with gaining resolution. Depth of focus (DOF) is the range of depth over which an image remains in focus. Just as opening a camera's aperture makes the range in which things are in focus thinner, increasing the numerical aperture in lithography makes the depth of focus shallower. Depth of focus is written as a coefficient called $k_2$ multiplied by the wavelength and divided by the square of the numerical aperture. The drawable size is inversely proportional to the numerical aperture, while the depth of focus is inversely proportional to the square of the numerical aperture. Therefore, doubling the numerical aperture halves the drawable size and cuts the depth of focus to a quarter. A wafer is not a perfect flat plane, and the photoresist also has thickness. When the depth of focus becomes shallow, the focus easily drifts out within that height variation, making the process that much more sensitive.

This trade-off is confirmed by actual measurements. When resolution and depth of focus were measured while varying the numerical aperture in an ArF immersion lithography tool using 193 nm light, the theoretical trade-off between the two was revealed experimentally. The coefficients of the two equations, $k_1$ and $k_2$, came out to approximately 0.288 and 0.745, respectively. The same experiment also showed the problem of line width roughness increasing depending on the ratio of the area through which light passes on the mask. Line width roughness is the degree to which the thickness of a single line is slightly jagged from spot to spot. Room to ease the trade-off also emerged from the same experiment. Because depth of focus is governed not only by the numerical aperture but also by the photoresist thickness, the photoresist thickness can be optimized to match the target layer's line width and pattern density while keeping the numerical aperture fixed (DOI: 10.3390/mi13111971).

Increasing the numerical aperture is not always a gain. When a 0.3 $\mu m$ line/space pattern—where lines and spaces of the same thickness alternate—printed with 248 nm lithography was simulated using a vector model, the depth of focus was larger at 0.42 numerical aperture than at 0.6. This was because the contrast of the photoresist used in that experiment—in other words, the degree to which the melting behavior between areas that received light and areas that did not is sharply divided—was high (DOI: 10.1116/1.585149). Resolution is determined by wavelength, numerical aperture, and $k_1$, and the resolution gained through numerical aperture is paid back with depth of focus. This rule that getting one thing means giving up another attaches to every subsequent trick.

Four Ways to Draw Smaller Than the Wavelength and What They Cost

Printing structures much smaller than the wavelength using 193 nm light actually happened. First, numerical aperture was increased. Immersion lithography, as covered in "Lithography — Painting Circuits with a Brush of Light", fills the space between the lens and the wafer with liquid instead of air to increase numerical aperture (DOI: 10.1116/1.1520577). Immersion opened the path to making numerical apertures greater than 1, and an objective optical system with a numerical aperture of 1.35 was designed for immersion equipment (DOI: 10.1364/ao.457833). At that value, light entered the substrate more obliquely, increasing reflection, and the thickness of the film reducing reflection had to be re-determined for each polarization state of the light (DOI: 10.1143/jjap.45.9280).

Still, limits approached. As "What Is "3 Nanometers" the Length Of? — Measuring a Chip's Name with a Tape Measure" defines, a node is the name given to a generation of semiconductor processing, and that number does not point to any single length inside the chip. Even with all sorts of techniques mobilized, from immersion to computational lithography, the method of printing once with 193 nm was approaching its ultimate limit near the 22 nm node. Printing structures of the 45, 32, and 22 nm nodes with 193 nm was counted among the most fundamental tasks of nanometer-generation miniaturization. On the other hand, next-generation candidates like extreme ultraviolet still remained "next-generation" as of 2009 (DOI: 10.1145/1862879.1862880). Aside from immersion, there are four tricks for drawing smaller than the wavelength, and all four give up something to gain resolution.

The first method is to intentionally draw different shapes on the mask. An image blurred by diffraction blurs differently depending on how neighboring patterns are placed. When adjacent lines are close, line thickness changes, line ends shorten, and right-angle corners become rounded. Optical proximity effect is a phenomenon where light from adjacent patterns interferes, making the printed shape differ from the mask drawing. Optical proximity correction (OPC) is the task of pre-calculating that misalignment and twisting the mask drawing in the opposite direction. An example is appending a hammer-head shape to the ends of lines on the mask so that the line ends do not shorten. In a 0.25 μm pattern, line thickness within a single frame printed by this method fell evenly within a 20 nm (3σ) range. 3σ is three times the standard deviation representing the scatter of measured values, and most measured values fall within this width. The margin of tolerance for fluctuations in the exposure dose—the amount of light shone onto the photoresist—was 14%, and the depth of focus was 0.8 μm (DOI: 10.1143/jjap.37.6681).

What optical proximity correction gives up is computation and verification. Data used to fit the correction model can be kept small by choosing structures well. On the other hand, in the verification stage to check whether the correction was right, the amount of data becomes very large. It is necessary to check whether numerous structures on a test wafer are correctly printed across the entire range of fluctuating exposure doses and focuses, and finding "hotspots"—places with a high risk of being printed incorrectly—collides with getting results back quickly (DOI: 10.7567/jjap.55.06ga01).

The second method is messing with the phase of light. Phase-shift masks are masks that invert the wave of light passing through part of the mask so that peaks and troughs are swapped, sharpening boundaries by canceling it out with neighboring light. This mask comes with a cost too. In generations finer than 65 nm, printing a T-shape with a phase-shift mask causes collisions where phases crash into each other. In the same generation, it is difficult to correct the shortening of T-ends due to narrow gaps using optical proximity correction alone. When simulating a mask where phase-shifting pieces were mixed into optical proximity correction, the degree of line-end shortening dropped to 4.6 nm and a depth of focus exceeding 200 nm was secured (DOI: 10.1116/1.2823020).

The third method is dividing one layer to print it multiple times. Multiple patterning, as defined in "Lithography — Painting Circuits with a Brush of Light", is the method of dividing a single layer's drawing to print it in two or more passes. Among them, the method with the fewest exposure steps is self-aligned double patterning. Self-aligned double patterning (SADP) is a method where exposure is done just once, and films are coated on both sides of the printed line to expand a single line into two. First, a temporary pattern called a mandrel is made, another material is evenly covered over it, and dry etching leaves only the films attached to the sidewalls (spacers). When the mandrel is carved away at the end, two rows of spacers remain. This method has the advantage that there is only one exposure step and the final line thickness is determined by the thickness of the deposited film instead of exposure. Instead, it has the disadvantage of requiring deposition and etching to be repeated back-to-back, so the authors newly selected mandrel and spacer materials to demonstrate self-aligned double patterning with a reduced number of process steps as a proof of concept (DOI: 10.1116/1.4963194). Repeating the same principle extends it to three and four times.

Divided drawings can be printed evenly as well. This is the case, for example, where silicon pillars are densely erected so that the half-pitch—half of the pitch—becomes 25 nm, using a method where double patterning is stacked multiple times. The pillars were 23.6 nm in diameter and 114 nm in height. The 3σ of uniformity measured at 30 points on a 300 mm wafer was merely 1.7 nm, and no pillars collapsed in any inspected area (DOI: 10.1143/jjap.50.04da16).

What multiple patterning gives up is overlay and increased process steps. Overlay is how accurately two separately printed drawings overlap each other in their proper places. This is the same as what "Lithography — Painting Circuits with a Brush of Light" calls alignment. When applying 193 nm immersion double patterning to 20 nm technology, overlay control is one of the core indicators for making this technology succeed (DOI: 10.1149/06001.0173ecst). The increased process steps are the repetition of deposition and etching seen earlier (DOI: 10.1116/1.4963194).

The fourth method is reducing the wavelength itself. Extreme ultraviolet (EUV) lithography uses extremely short light with a wavelength of 13.5 nm, as defined in "Lithography — Painting Circuits with a Brush of Light". Dropping from 193 nm to 13.5 nm in one jump makes the wavelength fourteen times shorter. At the same numerical aperture, diffraction blur shrinks by that much as well. How the numerical aperture of actual equipment changes this math is touched upon in "Lithography — Painting Circuits with a Brush of Light". Numerically, it is the simplest solution, but it took decades for this path to reach factories.

Why Extreme Ultraviolet Took So Long — Mirrors, Masks, Light Sources, Vacuum

A report tracking the development of extreme ultraviolet lithography through bibliographic data calls it "the most important technology to emerge from the semiconductor industry in recent times," summarizing the research community and decades-long commercialization pathway from the 1980s up to when that report was written (DOI: 10.51593/20240003). Looking at what presentations at the 1994 and 1996 extreme ultraviolet lithography conferences were grappling with reveals why it took so long. Taking a long time does not mean the outlook was dim. A 2006 status report noted that the progress in those few years had been remarkable and that equipment vendors were shipping their first test tools (alpha tools). It also projected that once technical and business challenges were resolved, extreme ultraviolet would be the technology of choice at the 32, 22, 16, and 11 nm half-pitch nodes (DOI: 10.1016/j.crhy.2006.10.002). From that status report, it took another 13 years to reach actual mass production.

First, lenses cannot be used. Unlike conventional optical lithography, extreme ultraviolet exposure is a reflective optical system, gathering light with multilayer-coated mirrors instead of lenses (DOI: 10.1142/s0219607707000219). Therefore, the multilayer reflective coating applied to the mirror surface becomes the very condition for this technology to work. The materials did not cooperate easily. A study theoretically examining reflective coatings for light entering mirrors perpendicularly in the 40 to 70 nm wavelength region concluded that aluminum-based multilayer structures theoretically yielded the highest reflectivity but had almost no practical value because of the surface oxide film. Instead, it proposed silicon-based multilayer structures as an alternative, as oxidation seemed easier to manage there (DOI: 10.1364/eul.1996.rmc173). This is an example of bridging the gap between the optimal solution on paper and what can actually be built using a runner-up approach.

Second, the mask substrates had to be manufactured almost defect-free. Extreme ultraviolet masks are also made of multilayers that reflect light. A 1996 multilayer consisting of 81 alternating layers of molybdenum and silicon (Mo/Si) for mask blanks—the blank substrates before a pattern is etched—lowered the defect density to 2×10⁻² per square centimeter, a 100,000-fold reduction compared to existing levels (DOI: 10.1364/eul.1996.r44). Work to reduce defects in mask blanks continued afterward, and while the 2006 status report counted this as an important advance of those few years, it noted that requirements for masks remained very demanding (DOI: 10.1016/j.crhy.2006.10.002). Protecting the substrate from dust also remained. A pellicle is a thin, transparent film placed over a mask to prevent dust from settling on the pattern. Extreme ultraviolet pellicles are nanometers thick and mechanically fragile yet must withstand high temperatures and hydrogen radicals. A study that built a full-size pellicle out of metal silicide and secured a transmittance of 90% or higher verified its durability with a test equivalent to exposing 20,000 wafers under off-line conditions corresponding to 400 W of extreme ultraviolet light (20 W/cm²) (DOI: 10.1088/1361-6528/ad902d).

Third, what held things back the longest was the light source. Producing 13.5 nm light that was sufficiently bright, stable, and long-lasting was the problem. In 2004, a liquid xenon jet was struck by a 600 W class laser operating at 10 kHz (kilohertz), obtaining an output of 2.2 W at 13.5 nm (DOI: 10.1143/jjap.43.3707). A 2007 overview noted that the light source output required at the time exceeded 115 W, and equipment development was rushing toward operation by 2011 (DOI: 10.1142/s0219607707000219). Actual mass production deployment was in 2019 (DOI: 10.1364/euvxray.2022.ew6a.6). The 2.2 W of the research light source in 2004 (13.5 nm, 2% bandwidth and 2π sr) and the 115 W required by the equipment in 2007 had different measurement conditions and cannot be divided directly. Still, the order-of-magnitude difference and the gap between 2011 and 2019 show why this technology took so long. The 2006 status report also noted that while light source output had climbed to levels approaching specifications, reliable operation at that output had not yet been fully proven (DOI: 10.1016/j.crhy.2006.10.002). The light source does not just emit light. In the 2004 study mentioned earlier, sputtering—where fast ions popping out of the light-emitting plasma, which is a hot state where gas is split into ions and electrons, striking and carving away the Mo/Si multilayer mirror—was identified as the main mechanism of mirror damage (DOI: 10.1143/jjap.43.3707).

Fourth, the inside of the tool must be a vacuum, and even that vacuum is not cleanly empty. Inside extreme ultraviolet exposure tools, extreme ultraviolet light splits residual gas into ions, creating hydrogen plasma. This plasma is an essential element that prevents carbon from building up on the optics, but it can also affect the performance and lifespan of other components inside the equipment (DOI: 10.1116/6.0003701). One has to live with something that is both beneficial and harmful.

Overcoming these challenges, extreme ultraviolet entered factories. According to a 2022 report by a facility that has researched foundational technologies like masks, photoresists, and optical elements since 1996, extreme ultraviolet lithography began to be applied to mass production for 7 nm node logic devices starting in 2019, and for 5 nm node logic devices starting in 2020 (DOI: 10.1364/euvxray.2022.ew6a.6). Research on challenges such as pellicles and hydrogen plasma inside the equipment continued afterward (DOI: 10.1088/1361-6528/ad902d, DOI: 10.1116/6.0003701).

When You Shorten the Wavelength, You Have to Build Everything Anew

It is easy to think that just shortening the wavelength is enough. In reality, when a wavelength changes, you have to completely rebuild the lens materials, masks, photoresists, and light sources used at that wavelength. 157 nm lithography is an example of this. To realize this wavelength, $F_2$ lasers, optical systems, photomasks, and photoresists were all extensively researched. Researchers even had to separately evaluate the residual aberrations left when a 0.85 numerical aperture projection lens fails to focus an image perfectly, and how the inherent birefringence of the lens material, $CaF_2$, which splits light into two paths depending on its direction, affects the image. Based on experiments and simulations, the authors concluded that patterns below 70 nm were possible with 157 nm high-numerical-aperture optical systems and that the mass-production potential was also sufficient (DOI: 10.1116/1.1520577). Yet, a 2009 overview noted that the light used to shoot the 45, 32, and 22 nm nodes was 193 nm (DOI: 10.1145/1862879.1862880). "Technically possible" and "entering the factory" are two different things. On the 193 nm side, a 1994 report showed that highly transparent optical materials could be obtained, and projected that laser damage would be slow enough for projection optics to maintain their specifications during 10 years of continuous operation. It then concluded that the first step had been successfully taken and no major obstacles were anticipated (DOI: 10.1364/eul.1994.elpm.10). For a new wavelength to succeed, confirmations like these must pile up item by item.

In extreme ultraviolet, this requirement goes to the extreme. Mirrors must be used instead of refractive lenses (DOI: 10.1142/s0219607707000219), and a theoretical study reviewing the 40 to 70 nm region assessed that the material with the theoretically highest reflectance had almost no practical value because of its surface oxide layer (DOI: 10.1364/eul.1996.rmc173), and commercialization took decades (DOI: 10.51593/20240003). The requirements on the photoresist side were also high. Sensitivity is the degree to which a photoresist reacts even with a small amount of light. A 2006 status report noted that extreme ultraviolet photoresists needed considerable additional effort to simultaneously meet the requirements for resolution, line-width roughness, and sensitivity (DOI: 10.1016/j.crhy.2006.10.002).

Shortening the wavelength begins with rebuilding the lenses, masks, photoresists, and light sources suited to that wavelength from scratch.

As Things Get Smaller, Chance Takes Over — Stochastic Defects and Edge Roughness

The belief that matching exposure conditions will yield identical results breaks down at very small scales. Stochastic effects are a phenomenon where, as structures shrink and the number of photons and molecules involved in a given spot decreases, random jaggedness shakes the results. Photons are the smallest packets by which light exchanges energy. When the number of packets is small, they hit some spots heavily and other spots lightly by chance.

This realization is longstanding. When simulating the printing of 50 nm and 80 nm contact holes—small holes connecting upper and lower layers—using extreme ultraviolet light (in 2003), fluctuations in light intensity, fluctuations in the shape of the light spread within the hole, and the whims of local chemical reactions all changed the hole size. The authors concluded that achieving this level of precision requires extraordinary levels of control over photoresist chemistry and processing (DOI: 10.1116/1.1629294).

There is a 2022 stochastic simulation that weighed the proportions of these causes. Photon shot noise is the random jaggedness in the number of photons hitting a spot because light arrives in particle units. As a result of simulating defect formation in extreme ultraviolet photoresists, about 73% of the photon-side random number conditions produced failures in more than 60% of the trials. Material-side factors had many failures but small impacts, and in this simulation, failures coming from photon shot noise were dominant. The authors concluded that failures coming from photon shot noise cannot be mitigated by material improvements alone (DOI: 10.35848/1347-4065/ac5b22).

Stochastic defects are flaws where patterns are printed incorrectly wholesale because of that jaggedness. Lines become pinched (pinching), lines that should be separate stick together (bridging), or vias, the holes connecting upper and lower wiring, disappear entirely (DOI: 10.35848/1347-4065/ac54f5).

Stemming from the same root is edge roughness. Line edge roughness (LER) is the degree to which the edges of a line that should be straight ripple microscopically. When both edges ripple separately, line thickness also varies from spot to spot, which is the linewidth roughness we saw earlier. The problem lies in the fact that line edge roughness does not shrink together when structures become smaller. A 1 nm edge wobble when a structure is 10 nm is an entirely different story from when it is 100 nm. This wobble transfers to the device. FinFETs are a transistor structure where the channel stands up like a fin so that the gate wraps around three sides, as defined in A Transistor Is a Switch — A Tiny Faucet You Open and Close with Electricity. The same computational study quantified the process by which edge roughness shakes the FinFET's potential and drain current—the current passing through the transistor—manifesting as performance degradation (DOI: 10.3390/mi12121493).

The straightforward method to reduce roughness is to increase the number of photons. When the exposure dose is increased, edge roughness decreases in inverse proportion to the square root of the exposure dose. However, from a certain point, no matter how much the exposure dose is raised, it does not decrease further. When digging into the cause of this lower limit using Monte Carlo simulation—a method of calculating how results scatter by drawing random numbers countless times—the effect where acid generators, which are components that produce acid upon receiving light to change the solubility of the photoresist, are consumed during exposure emerged as the dominant factor (DOI: 10.1143/jjap.51.06fc01). Machines are also cited as unexpected contributors. A 2025 review that classified the causes of roughness using a fishbone diagram pointed to equipment vibration, thermal instability, and gas flow fluctuations as under-explored contributing factors (DOI: 10.1115/imece2025-167155).

Extreme ultraviolet lithography structurally carries this problem. Because the number of usable photons is limited at a given light source output, photon shot noise occurs, which simultaneously makes reducing edge roughness and eliminating defects difficult (DOI: 10.1117/1.jmm.25.3.031608). Attached to the back of the resolution gained by shortening the wavelength is the price of having to use fewer photons.

Beyond Resolution — Focus, Overlay, Metrology, and Cost

Resolution is one of the scoreboards for this work. Count only what we have seen, and there are already three. Raising resolution trades away depth of focus (DOI: 10.3390/mi13111971). Growing the numerical aperture increases substrate reflection, requiring the redesign of films that reduce reflection (DOI: 10.1143/jjap.45.9280). Patterning in multiple exposures makes overlay a new bottleneck (DOI: 10.1149/06001.0173ecst).

There is one more item that is rarely mentioned. It is the business of measurement. If you cannot accurately measure what you have made, you cannot control it either, and line edge roughness blurs the metrology itself. In optical critical dimension metrology, which measures line widths using the signal returned from illuminating light, if the grating has a high refractive index, the upper bound of uncertainty added by roughness reaches 3.7 nm or 1.2 nm depending on polarization. The authors pointed out that this is decisive in metrology measuring below the nanometer scale (DOI: 10.1051/epjconf/202430902011). Roughness not only makes devices worse, but even hinders the task of measuring just how bad they are.

The last is cost. As an analysis from 1994 notes, any lithography process must first be cost-effective to be considered for mass production (DOI: 10.1364/eul.1994.elpm.13). An extreme ultraviolet report from 2006 also noted that because wafer throughput is a decisive cost factor, light source power, photoresist sensitivity, and system design must be weighed together (DOI: 10.1016/j.crhy.2006.10.002). No matter how small it is drawn, if it is slow and expensive, it cannot enter the factory.

What Remains for the Next Generation — High Numerical Aperture, Self-Aligning Molecules, and Forking Paths

There are attempts to increase the numerical aperture even further in extreme ultraviolet. A 2016 study that printed sub-20 nm half-pitch patterns with a research-grade high-numerical-aperture extreme ultraviolet exposure tool and compared them with Monte Carlo simulations noted that suppressing the stochastic effects of the development process is crucial to realizing an 11 nm half-pitch (DOI: 10.7567/jjap.55.096501). The problem of chance we saw earlier waits for us just as it is in the next generation.

There are also approaches that look beyond the photoresist. Directed self-assembly (DSA) is a method where light draws only a rough guide frame, and molecules are made to line up on their own within it to form lines. In a Monte Carlo simulation where a block copolymer—a polymer made of two kinds of chains joined together—was self-assembled on a guide frame made with extreme ultraviolet, line-edge roughness was reduced and defects where lines incorrectly bridge together like bridges disappeared (DOI: 10.1117/1.jmm.25.3.031608).

A 2017 patterning roadmap foresaw forking paths. The roadmap views the fact that two "next-generation" technologies—extreme ultraviolet and nanoimprint, which presses a mold down like a stamp—could be introduced together as meaning that patterning technology is becoming increasingly specialized. The document's outlook is that this lowers overall costs, but the speed at which either technology is scaled up may conversely slow down (DOI: 10.1515/aot-2017-0039).

When numbers like 22 nm and 7 nm, which this article called generation names, first drifted away from actual lengths is traced by After Moore's Law — What a "Nanometer" Came to Mean. To look back at the main stream of lithography, Lithography — Painting Circuits with a Brush of Light is the starting point.

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Lithography is the job of printing circuits. The smallest size you can draw is determined by the wavelength, numerical aperture, and k1, and the resolution gained through the numerical aperture is paid back with depth of focus. 193 nm light drew things smaller than its wavelength by increasing the numerical aperture with immersion and adding four tricks on top of that. It deliberately distorted the drawn mask, inverted the phase of the light, split a single layer to print it multiple times, and ultimately reduced the wavelength itself. None of these were free. Immersion brought about reflection and polarization, mask correction brought about an explosion of calculation and verification, phase shifting brought about collisions between phases in shapes like a T, and multiple patterning brought about overlay and expanding processes. Extreme ultraviolet brought about reflective optics, light sources, vacuums, and pellicles, and above all, a new kind of problem called stochastic defects.

That final problem is still open. There is a simulation conclusion that failures caused by a low photon count cannot be reduced through material improvements alone, and ways to soothe that shaking, such as methods where molecules line up on their own, are being explored in simulations. When you think of the inside of the device in your hand, you may also think of a printing press that has narrowly won against light and chance every time instead of a precise carving knife.

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Source Papers

• "Nano-lithography or two-dimensional patterning systems" (1996) — DOI: 10.1093/oso/9780198562832.003.0007 — Basic structure of drawing on a photomask with an electron beam and replicating it onto a wafer using optical lithography.
• "EUV Lithography Cost of Ownership Analysis" (1994) — DOI: 10.1364/eul.1994.elpm.13 — Lithography accounts for roughly 1/3 of IC manufacturing costs, "must be cost-efficient to consider mass production."
• "Fabrication of Silicon Pillar with 25 nm Half Pitch…" (2011) — DOI: 10.1143/jjap.50.04da16 — 25 nm half-pitch Si pillars, 30 points on a 300 mm wafer 3σ 1.7 nm.
• "Photolithography at the Limits of Optical Resolution" (1993) — DOI: 10.2533/chimia.1993.387 — Definition of photoresist: a film whose solubility in developer changes upon exposure.
• "Gate patterning by EBL using a tone reversal process (EB-R)…" (2025) — DOI: 10.35848/1347-4065/adb4ff — Pattern transfer down to 18 nm wide Si structures via resist → hard mask → etch.
• "Sub-100 nm Lithography with KrF Exposure Using Multiple Development Method" (1999) — DOI: 10.1143/jjap.38.6999 — Diffraction limit of 0.6 NA KrF (248 nm) is 207 nm.
• "193 nm—Moderately EUV" (1994) — DOI: 10.1364/eul.1994.elpm.10 — Wavelength reduction from 436 to 365 to 248 to 193 nm, confirming transparency of 193 nm optical materials.
• "A Study on the Resolution and Depth of Focus of ArF Immersion Photolithography" (2022) — DOI: 10.3390/mi13111971 — Measured trade-off between resolution and depth of focus (coefficient 0.288/0.745).
• "An investigation of some depth of focus issues in high NA projection lithography…" (1990) — DOI: 10.1116/1.585149 — NA of 0.42 yields a larger depth of focus than 0.6.
• "Effect of high numerical aperture lens on lithographic performance in 157 nm lithography" (2002) — DOI: 10.1116/1.1520577 — Sub-70 nm line/space using immersion interference lithography aimed at increasing numerical aperture.
• "Single Anti-Reflection Coating Optimization… for Hyper NA Immersion Lithography" (2006) — DOI: 10.1143/jjap.45.9280 — Immersion equals hyper-NA; increased angle of incidence leads to increased reflectance; anti-reflection coatings per polarization.
• "Design of an objective for a hyper-NA immersion lithography tool…" (2022) — DOI: 10.1364/ao.457833 — Design of a 1.35 numerical aperture objective lens system for immersion lithography.
• "What is double patterning lithography and its impact on nanometer design?" (2009) — DOI: 10.1145/1862879.1862880 — Deep sub-wavelength lithography; single-exposure 193 nm hits its ultimate limit near the 22 nm node.
• "EBL patterned HSQ resist as a mandrel for self-aligned double patterning application" (2016) — DOI: 10.1116/1.4963194 — SADP principle, 1 exposure with line width determined by deposition thickness, at the cost of repeated deposition and etching.
• "Double Patterning Lithography Alignment and OVL-Control Strategy for 20nm Technology" (2014) — DOI: 10.1149/06001.0173ecst — Overlay control is a core metric in double patterning.
• "Optical Proximity Correction Methodology to Counteract Mask Error Effects…" (1998) — DOI: 10.1143/jjap.37.6681 — CD uniformity of 20 nm (3σ) and depth of focus of 0.8 μm using hammerhead OPC.
• "Potential of phase-shifted OPC for 65nm T-shaped pattern…" (2008) — DOI: 10.1116/1.2823020 — Tip reduction of 4.6 nm and depth of focus exceeding 200 nm via phase-shifted OPC.
• "Optical proximity correction: A cross road of data flows" (2016) — DOI: 10.7567/jjap.55.06ga01 — Explosion of data volume during verification, trade-off between hotspot detection and fast turnaround time.
• "Tracing the Emergence of Extreme Ultraviolet Lithography" (2024) — DOI: 10.51593/20240003 — Decades-long commercialization path of EUV from the 1980s to the present.
• "EUV LITHOGRAPHY FOR SEMICONDUCTOR MANUFACTURING AND NANOFABRICATION" (2007) — DOI: 10.1142/s0219607707000219 — Reflective optics + multilayer mirrors; challenges include source power exceeding 115 W and low-LER photoresists.
• "Reflectance coatings for the vacuum/extreme ultraviolet region" (1996) — DOI: 10.1364/eul.1996.rmc173 — Al-based multilayers have the highest theoretical reflectance but are impractical due to surface oxide films.
• "Reticle blanks for EUV lithography: … low defect density Mo/Si multilayers" (1996) — DOI: 10.1364/eul.1996.r44 — 81-layer Mo/Si, defect density reduced by a factor of 10⁵ to 2×10⁻²/cm².
• "Development and optimization of metal silicide EUV pellicle for 400W EUV lithography" (2024) — DOI: 10.1088/1361-6528/ad902d — Pellicle transmittance exceeding 90%, tested at 400 W across 20,000 wafers.
• "Laser-Produced Plasma Light Source Development for EUV Lithography" (2004) — DOI: 10.1143/jjap.43.3707 — 2.2 W at 13.5 nm using a 600 W 10 kHz laser, multilayer sputtering damage from fast ions.
• "EUV lithography," Comptes Rendus. Physique (2006) — DOI: 10.1016/j.crhy.2006.10.002 — Source power approaching specifications but reliable operation unverified; resist requirements for resolution, LWR, and sensitivity; cost of ownership and throughput.
• "Novel low-temperature and high-flux hydrogen plasma source for EUV lithography" (2024) — DOI: 10.1116/6.0003701 — Hydrogen plasma created by EUV photons, essential for preventing carbon deposition but impacts component lifespan.
• "R&D Activities of EUV Lithography at NewSUBARU…" (2022) — DOI: 10.1364/euvxray.2022.ew6a.6 — EUV entered mass production at the 7 nm node in 2019 and the 5 nm node in 2020.
• "Statistical limitations of printing 50 and 80 nm contact holes by EUV lithography" (2003) — DOI: 10.1116/1.1629294 — Light intensity, spatial fluctuations, and local chemical variations alter hole size.
• "Applying stochastic simulation to study defect formation in EUV photoresists" (2022) — DOI: 10.35848/1347-4065/ac5b22 — 73% of photon conditions fail in over 60% of trials, unmitigable by material improvements alone.
• "Calibration and application of Gaussian random field models… in EUV lithography" (2022) — DOI: 10.35848/1347-4065/ac54f5 — Forms of stochastic failure: pinching, bridging, and missing vias.
• "Line-Edge Roughness from EUV Lithography to Fin-Field-Effect-Transistor" (2021) — DOI: 10.3390/mi12121493 — LER does not scale down with feature size, transferring into degraded FinFET performance.
• "Lower Limit of Line Edge Roughness in High-Dose Exposure of Chemically Amplified EUV Resists" (2012) — DOI: 10.1143/jjap.51.06fc01 — Lower limit of LER, dominated by photoacid generator depletion.
• "Impact of Line Edge Roughness on Device Performance: A Review" (2025) — DOI: 10.1115/imece2025-167155 — Equipment vibration, thermal instability, and gas flow fluctuations as unexplored contributing factors to LER.
• "Directed self-assembly of linear and Janus-type bottlebrush block copolymers…" (2026) — DOI: 10.1117/1.jmm.25.3.031608 — Photon number limits set by source power lead to shot noise; LER mitigated via DSA.
• "Influence of line edge roughness in optical critical dimension metrology" (2024) — DOI: 10.1051/epjconf/202430902011 — LER contributes up to 3.7 nm / 1.2 nm per polarization to metrology uncertainty.
• "Analysis of line-and-space resist patterns with sub-20 nm half-pitch… high-NA EUV" (2016) — DOI: 10.7567/jjap.55.096501 — Suppressing stochastic effects during development is crucial for 11 nm half-pitch.
• "Patterning roadmap: 2017 prospects" (2017) — DOI: 10.1515/aot-2017-0039 — Coexistence of EUV and nanoimprint means specialization; lowers costs but may slow the expansion of a single technology.