DEPTH OF FOCUS ENHANCEMENT IN OPTICAL LITHOGRAPHY

Apodization, or pupil plane filtering, can be used to enhance the depth of focus of lithographic projection systems. However, this improvement comes at the expense of decreasing radial concentration of energy in the point spread function. To examine this tradeoff quantitatively, we first define the average encircled energy as a criterion of the energy concentration over a nonzero axial distance. We then derive and numerically solve an integral equation for the apodization function that maximizes the average encircled energy. Finally, we use the eigenfunctions of this equation to construct pupil functions producing an on-axis intensity profile that is approximately constant over a nonzero axial distance, while maintaining a large value of the average encircled energy within that distance.