Proximity lithography simulation: from shadow printing to holographic lithography

Proximity lithography, based on the principle of near-field diffraction, offers advantages such as technical maturity, structural simplicity, and high throughput. It is widely regarded as a preferred technique for applications such as MEMS fabrication, 3D integrated circuits, through-silicon via interconnections, advanced packaging, and wafer-level packaging. However, due to diffraction limitations, conventional proximity lithography suffers from low resolution, making it unsuitable for advanced semiconductor manufacturing processes. With the development and application of resolution enhancement techniques (RETs), such as off-axis illumination (OAI), optical proximity correction (OPC), and phase- shifting masks (PSMs), the resolution and pattern transfer capabilities of proximity lithography have been significantly improved. Holographic lithography enhances control over the optical field by introducing phase modulation into binary masks and is therefore considered a resolution enhancement method for proximity lithography. Holographic mask design typically relies on projection iterative algorithms that define the relationship between the transmission function at the mask plane and the aerial image at the wafer plane. The amplitude and phase distributions of the mask are then computed based on the target intensity profile. Due to the complexity and sensitivity of the computational process, which directly influences imaging performance, holographic lithography is often referred to as computational proximity lithography. Accurate proximity lithography simulation is fundamental to holographic mask design, as it enables precise prediction of aerial images and resist profiles on the wafer. This paper discusses a comprehensive simulation workflow for proximity lithography, encompassing aerial image and bulk image formation in the resist, post-exposure bake (PEB), and development to predict the final resist profile. The process includes modeling the aerial image, material concentration dynamics, and 3D resist profile evolution, followed by simulation-based analysis of the impact of lithographic parameters on the process window. On this basis, a holographic mask design framework is applied, extending conventional proximity lithography simulation to the modeling and simulation of holographic lithography. This paper provides the theoretical foundation, simulation guidelines, and reference data necessary for the design and simulation of synthetic holographic masks.