Statistical optics and optical elements for microtechnologies: Partial coherence, lithography and microlenses

Doctoral thesis, 2007

The scientific problems treated in this thesis are expressed within the framework of statistical optics and are generated out of the optical lithography industry. Optical lithography uses partially coherent light, i.e. light with a random wavefront, to increase the performance of the lithographic process. One of the goals of this work has been to explore ways to numerically simulate the behavior of partially coherent radiation. In this work a method is introduced that decomposes the simulation of a partially coherent field into a simulation of several coherent field, thus enabling the use of existing efficient numerical methods for coherent fields. Although the degree of partial coherence is an important property of light, it is cumbersome to measure and characterize. In this work an inverse method is presented, where the degree of partial coherence can be retrieved, using a numerical algorithm, from a number of simple intensity measurements. An inverse method for the design of microlenses with short focal lengths under coherent illumination is also introduced. One particular problem in optical lithography, and other industrial processes, is to produce a uniform illumination over a surface using an unstable partially coherent light source. Recently, an often applied solution has been to use diffractive optical elements. In this thesis an analysis of the efficiency of this approach is made for different types of diffractive optical elements. Furthermore, a previously little-recognized, yet fundamental phenomenon referred to as “dynamic speckle”, is introduced. It is found that dynamic speckle may have a detrimental effect on the accuracy of optical lithography since it limits the uniformity of the deposited energy for pulsed partially coherent sources.