Partially Coherent Laser Radiation - Modeling and Application to Optical Microlithography
Licentiatavhandling, 2006

This work deals with a type of light that has properties somewhere between blackbody radiation and conventional laser light; such light is referred to as partially coherent. One example is the radiation from the pulsed excimer laser, which is used in the manufacturing of most of the world’s integrated circuits. The fabrication step is known as optical microlithography, and the central process is the imaging of a circuit pattern on a photomask onto a silicon wafer. The emphasis of this work is on how to simulate the partially coherent radiation numerically, in an efficient way. There is no point in exactly describing the optical field, since it is stochastic, i.e. random. Rather, the simulation aims at obtaining a numerical representation of the optical field whose statistical properties are similar to those of the physical field. We show that there is such a representation that can be obtained with relatively little computational effort. The representation consists of a number of conventional, coherent, fields whose oscillation frequencies are carefully selected. Since each field is coherent, it can be propagated with conventional algorithms. Further, a previously little-recognized fundamental phenomenon, which we refer to as dynamic speckle, is introduced. It is found that dynamic speckle may have a detrimental effect on the accuracy of microlithography tools and fundamentally limit the dose uniformity for pulsed excimer laser sources. Moreover, the spatial statistical properties of the dynamic speckle are found to be a function of the illumination conditions.



temporal speckle

partial coherence

optical propagation

number of degrees of freedom

dynamic speckle


Christer Rydberg

Chalmers, Mikroteknologi och nanovetenskap (MC2), Fasta tillståndets elektronik


Elektroteknik och elektronik

Technical report MC2 - Department of Microtechnology and Nanoscience, Chalmers University of Technology: 58

Mer information