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

The scientific problems treated in this thesis are expressed within the framework ofstatistical optics and are generated out of the optical lithography industry. Opticallithography uses partially coherent light, i.e. light with a random wavefront, toincrease the performance of the lithographic process.One of the goals of this work has been to explore ways to numerically simulatethe behavior of partially coherent radiation. In this work a method is introducedthat decomposes the simulation of a partially coherent field into a simulation ofseveral coherent field, thus enabling the use of existing efficient numerical methodsfor coherent fields.Although the degree of partial coherence is an important property of light, it iscumbersome to measure and characterize. In this work an inverse method is presented,where the degree of partial coherence can be retrieved, using a numericalalgorithm, from a number of simple intensity measurements. An inverse methodfor the design of microlenses with short focal lengths under coherent illuminationis 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 coherentlight source. Recently, an often applied solution has been to use diffractiveoptical elements. In this thesis an analysis of the efficiency of this approach is madefor different types of diffractive optical elements.Furthermore, a previously little-recognized, yet fundamental phenomenon referredto as “dynamic speckle”, is introduced. It is found that dynamic specklemay have a detrimental effect on the accuracy of optical lithography since it limitsthe uniformity of the deposited energy for pulsed partially coherent sources

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

The scientific problems treated in this thesis are expressed within the framework ofstatistical optics and are generated out of the optical lithography industry. Opticallithography uses partially coherent light, i.e. light with a random wavefront, toincrease the performance of the lithographic process.One of the goals of this work has been to explore ways to numerically simulatethe behavior of partially coherent radiation. In this work a method is introducedthat decomposes the simulation of a partially coherent field into a simulation ofseveral coherent field, thus enabling the use of existing efficient numerical methodsfor coherent fields.Although the degree of partial coherence is an important property of light, it iscumbersome to measure and characterize. In this work an inverse method is presented,where the degree of partial coherence can be retrieved, using a numericalalgorithm, from a number of simple intensity measurements. An inverse methodfor the design of microlenses with short focal lengths under coherent illuminationis 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 coherentlight source. Recently, an often applied solution has been to use diffractiveoptical elements. In this thesis an analysis of the efficiency of this approach is madefor different types of diffractive optical elements.Furthermore, a previously little-recognized, yet fundamental phenomenon referredto as “dynamic speckle”, is introduced. It is found that dynamic specklemay have a detrimental effect on the accuracy of optical lithography since it limitsthe uniformity of the deposited energy for pulsed partially coherent sources

Partially Coherent Laser Radiation - Modeling and Application to Optical Microlithography

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 worlds 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 havea 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

Partially Coherent Laser Radiation - Modeling and Application to Optical Microlithography

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 worlds 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 havea 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