Fast convolution method and its application in mask optimization for intensity calculation using basis expansion.

Area of Science:

• Computational lithography
• Semiconductor manufacturing technology
• Image processing algorithms

Background:

• Accurate mask pattern representation in inverse lithography requires finer grids, leading to large data sizes and high computational demands.
• Intensive convolutions during mask optimization pose significant computational challenges.

Purpose of the Study:

• To introduce a novel method, convolution using basis expansion (CBE), to mitigate computational costs in mask optimization for inverse lithography.
• To enable efficient mask pattern analysis and simulation without sacrificing accuracy.

Main Methods:

• Projection of fine grid matrices onto a coarse grid using a base matrix set.
• Performing convolutions on the coarse grid using expansion coefficients.
• Approximating fine grid convolution via interpolation and a sum of coarse grid convolutions.

Main Results:

• The CBE method was validated through random matrix convolutions and lithography simulation intensity calculations.
• Demonstrated similar image quality compared to traditional convolution methods.
• Achieved significant running speed enhancements.

Conclusions:

• Convolution using basis expansion (CBE) effectively reduces computational load in inverse lithography.
• The method offers a practical solution for accelerating mask optimization and lithography simulations.
• CBE presents a viable approach for enhancing efficiency in semiconductor mask design.