Improving mask manufacturing is the simplest way to reduce wafer variation.
This is the second blog in a three-part series on pixel-level dose correction (PLDC). The first installment was “Improving Uniformity and Linearity for All Masks” from January 29, 2025.
Improving mask uniformity is the easiest, cheapest way to improve wafer uniformity. Uniformity is a measure of how similarly the exact same feature prints on various parts of the mask/wafer. A relatively new technology, pixel-level dose correction (PLDC), is about improving mask manufacturing by correcting for linearity and enhancing mask uniformity. It’s about making masks better. So how does that help wafer uniformity? We’ll discuss the three ways in this blog.
Global variation is when global effects, such as flare or loading effects, make the shapes that are intended to be identical print differently across the mask/wafer. Global uniformity is achieved through various correction mechanisms to counteract those global effects. Local variation is when near-term effects, such as resist blur or variable etch effect, make the shapes that are intended to be identical print differently even though the shapes are near enough to each other not to have large differences as a result of global effects.
Improving both global and local uniformity is important to wafer manufacturing. Wafer variation is the sum of mask variation and variation introduced in wafer lithography. Every variation present on the mask will be present on the wafer for each chip instance, and then wafer variation is added on top of that. So, improving mask uniformity is critical for improving wafer uniformity.
Traditional mask process correction (MPC) solutions include solutions for linearity, but not for uniformity. PLDC improves mask uniformity (and therefore wafer uniformity) by manipulating pixel doses of the multi-beam writer to provide edge enhancement, thereby improving the dose slope at the resist threshold, and improving dose margin everywhere for any shape, including Manhattan patterns as well as diagonal or curvilinear patterns on mask. Improving dose margin is known to be a good proxy for improving uniformity on the mask. PLDC therefore solves for both uniformity and linearity, including both dose-based and variable bias effects.
As the mask world moves toward curvilinear mask features, the fact that PLDC is performed in the pixel domain using multi-beam mask writers means that curvilinear features are naturally accommodated. The move to curvilinear masks is fueled by the need to improve wafer process window. Because light is naturally rounding, curvilinear mask shapes are better at producing more uniform wafer images with less wafer process variation than the traditional Manhattan mask shapes. [1]
Curvilinear inverse lithography technology (ILT) uses a mathematically rigorous inverse approach that determines the mask shapes that will produce the desired on-wafer results. Because of the rounding effects cited above, ILT naturally produces curvilinear shapes. Part of the process of curvy ILT is to use simulation to ensure that the mask shape hits the wafer target and that the wafer manufacturing variation is acceptable. So, curvy ILT together with PLDC improve wafer uniformity in three ways: 1) curvilinear mask features are best for wafer process window, which means they are more resilient to wafer manufacturing variation; 2) with the manufacturable curvy mask shapes output by a competent ILT tool and then corrected for linearity in mask manufacturing by PLDC, the ILT output exactly matches the physical mask produced. Only when this is the case can you know that the mask will reliably manufacture the desired wafers; and 3) PLDC uniformity enhancement on curvilinear ILT makes those curvilinear shapes more resilient to mask manufacturing variation and therefore improves wafer manufacturing variation even further.
PLDC composes numerous corrections together to avoid one correction rendering another correction inaccurate. As a result, local uniformity and global uniformity benefits are achieved through pixel-dose manipulation that are not practically possible with offline vector-based (or curvilinear format-based) processing.
Figure 1, below, shows three views of the same curvilinear mask shapes: on the left are the target mask shapes in pink; on the right is the SEM view of the manufactured mask using PLDC; the center shows the target and the SEM overlapped. As you can see, PLDC created mask shapes nearly identical to their targets, whether the shapes are large or small.
Fig. 1: Three views of the same curvilinear mask shapes.
PLDC can work with any angle, but what happens when you present PLDC with targets that are mask-rule incorrect? The kinds of shapes shown on the left of figure 2, below, with pointy ends, cannot be written as targeted, as they are subject to the pixel limits of the mask writer and resist blur. However, PLDC will do the best it can to produce these shapes, as seen in the SEM on the right. The question is, though, what is the behavior of the correction when PLDC is presented with a mask-rule incorrect target?
Fig. 2: Presenting PLDC with targets that are mask-rule incorrect.
The points of the target shape on the right form a circular inner ring, as shown by the blue tracing. If you draw that exact circle on the SEM image on the right, you can see that PLDC created a solution that also forms a circle, just a larger one (also shown in blue tracing) than that formed by the target shapes.
When looking at this type of test, the solution will never be exact because it is not possible for the mask writer to produce the target shape, but the question with any type of MPC applied to this kind of shape is, does the solution create a uniform deviance? Is the inner shape produced still a circle, just larger, or is it some other shape? This is a challenge and is a good test for any MPC handling curvilinear shapes.
Curvy ILT improves wafer process windows. Manufacturable curvy masks are more resilient to mask variation than Manhattan masks. And PLDC improves the uniformity of all masks of any shape. Wafer uniformity is the sum of resilience to mask and wafer variation. So PLDC being able to process curvy ILT shapes with the same accuracy and runtime as any other shapes including Manhattan shapes substantially improves wafer uniformity.
Our final blog in this series will cover advanced features and capabilities of PLDC.
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