Exposure planning for scanning laser lithography

Lithography is the process of selectively exposing optically sensitive materials during semiconductor fabrication. One issue with standard projection lithography is the high cost of infrastructure and mask sets. These costs may be prohibitively expensive for prototyping and low-volume production. Scanning-beam lithography methods are attractive alternatives to projection lithography for low-volume applications. These methods include scanning electron-beam, ion-beam, and scanning optical lithography. This thesis aims to maximize the resolution of scanning lithography methods by model-based optimization of the exposure pattern. Scanning laser lithography is used as an example process; however, the proposed methods are applicable to a wide range of serial fabrication processes. The exposure pattern in a scanning lithography system describes the energy delivered versus the spatial coordinates. For a positive photoresist areas that receive an exposure dosage above a threshold are dissolved during development. The surface dosage is described as a two dimensional convolution of the exposure pattern with the beam profile. This thesis presents three methods for the optimization of exposure patterns. The first method casts the problem as a constrained non-linear optimization. This problem is then solved iteratively using an interior-point method. The second method involves a direct gradient-based search with an analytical gradient calculation and step-size approximation. Both methods converge to similar solutions; however, the interior point method requires less iterations, and the gradient-based method requires significantly less memory. The third proposed method interprets the process model as a constrained non-linear convolution. An exposure pattern is then derived by employing an iterative deconvolution method. This method requires the least computational resources. However, the deconvolution method does not explicitly minimize a cost function; therefore, it is difficult to explicitly penalize variables such as the total exposure energy. The performance of each proposed method is assessed through simulation and experimental results. The thesis is concluded by a comparison of the three methods using metrics including the minimum feature error, computational requirements, and the number of non-zero exposures.