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# NVIDIA Unveils cuLitho: A “Breakthrough in Computational Lithography”

March 22, 2023 by Jake Hertz

## At NVIDIA’s GTC this week, the company lifted the curtain on a software suite that may drastically improve the resolution of existing lithographic systems.

As the semiconductor industry scales its chips smaller, manufacturers face larger production challenges.

To overcome these obstacles, many of which are infrastructural in nature, production facilities now rely heavily on computational lithography, the mathematical and algorithmic methods used to improve resolution through photolithography. However, as node sizes shrink far beyond the 22 nm CMOS fabrication process, current computational lithography must improve to keep up with resurfacing throughput and capability concerns.

##### Rendering of an ASML EUV lithography machine. Image used courtesy of NVIDIA

Yesterday, at NVIDIA's GPU Technology Conference (GTC), the company announced a new software library to accelerate computational lithography and solve these challenges.

### The Rayleigh Criterion: A Fundamental of Photolithography

Before we can understand the implications of NVIDIA’s new software, we must first discuss some fundamentals of photolithography.

In the semiconductor industry, photolithography is the process of patterning a chip on a semiconductor wafer by covering areas of the substrate with a photomask and shining an ultraviolet light of specific wavelengths onto the exposed area. When it comes to photolithography, arguably the most important specification is the critical dimension, which defines the smallest possible feature size that can be achieved through the lithography process. A smaller critical dimension is required for manufacturing smaller semiconductor nodes.

The achievable critical dimension is defined by the Rayleigh Criterion:

$$C_D=k_1 \frac{\lambda}{NA}$$

Where:

• k1 = A constant that depends on many factors related to the chip manufacturing process
• $$\lambda$$ = The wavelength of the light used
• NA = The numerical aperture of the optics, defining how much light they can collect

This criterion describes how the critical dimension is proportional to the exposure wavelength of light but is also inversely proportionally to the numerical aperture of the projection optics. The constant, k1 is a lumped parameter representing the complexity of manufacturing in the lithography process, the physical limit of which is 0.25.

### Computational Lithography, a Much-needed Improvement

Historically, as semiconductor nodes have scaled down, photolithography has reduced the critical dimension by decreasing the wavelength of used light. However, as the industry stands today, further decreasing wavelength requires entirely new lithographic technologies like extreme ultraviolet (EUV).

##### Computational lithography. Image courtesy of ASML

While researchers and manufacturers have been hard at work to bring about shorter wavelengths, they’ve also looked into ways to reduce the k1 factor. To do this, one of the most powerful and important techniques has been computational lithography.

Computational lithography uses algorithmic models of the manufacturing process to compensate for manufacturing defects. With computational lithography, it is possible to optimize the photomask by intentionally deforming the patterns to account for physical and chemical effects that naturally occur in the standard process. By doing this, computational lithography results in more accurate photolithography. In the context of Rayleigh’s Criterion, this equates to lowering the k1 value and hence increasing the critical dimension.

### NVIDIA Accelerates Computational Lithography With cuLitho

As nodes shrink and designs become more complex, the computational requirements for algorithmic modeling become extremely demanding. To address this limitation, NVIDIA this week announced its new software library for computational lithography.

The new library, called cuLitho, is an extension of NVIDIA's CUDA library optimized for the workloads associated with computational lithography. Consisting of tools and algorithms for GPU acceleration, cuLitho claims to speed up the manufacturing process for semiconductors by orders of magnitude over CPU-based methods. Specifically, NVIDIA is claiming a 40x speed up of inverse lithography with cuLitho, resulting in 3x to 5x more masks being generated per day than possible with CPU systems.

##### cuLITHO is a library that accelerates computational lithography and is meant to be embedded into OPC software. cuDOP is for diffractive optics and cuCompGeo is for computational geometry, cuOASIS for optimization, and cuHierarchy for AI. Image used courtesy of NVIDIA

The implications of cuLitho are seemingly significant, resulting in semiconductor manufacturing that is faster, cheaper, and more accurate while aiming to keep Moore’s law alive. So far, NVIDIA says that ASML, TSMC, and Synopsys have already adopted cuLitho, and they anticipate more major fabs will follow suit soon.

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