Gray scaling in high performance optical pattern generators

This paper is a comparison of different gray scaling techniques used in optical mask making. It shows that high address resolution and high throughput can be combined with the lithographic performance necessary for the most advanced applications. In the semiconductor industry, Moore's law continues to describe the ever-increasing demand for better performance in terms of clock-frequency and circuit density. One effect is shrinking design grids to cope with the tighter requirements on resolution, CD control, and aggressive OPC. For mask making this means that the address resolution of the mask writing equipment must be improved for every tool generation. The address resolution in the mask writer can be increased in two ways; either by decreasing the physical grid, or by introducing a virtual grid by using gray scaling. In the former case, the throughput, a performance parameter of utmost importance for reasonable mask costs and cycle times, will suffer a high penalty. In the latter case, however, a fine address grid is created, while keeping a large physical grid for high throughput. In earlier publications, a single pass raster scan gray scaling technique has been shown to reduce image quality in terms of image log-slope. This paper shows that the effects are kept to a minimum in the SLM-based DUV Sigma7300 mask writer, which uses partial coherent imaging and multiple writing passes. Analysis shows that the reduction in image log-slope due to gray scaling is less than 8%. In addition, the systematic averaging of four displaced writing passes makes the loss isotropic and independent of grid position. A detailed error analysis shows that a small address grid is more important for composite CD uniformity than the loss in image log-slope.