Oana Marinescu

Network search method in the design of extreme ultraviolet lithographic objectives

The merit function space of mirror system for extreme ultraviolet (EUV) lithography is studied. Local minima situated in the multidimensional optical merit function space are connected via links that contain saddle points and form a network. We present networks for EUV lithographic objective designs and discuss how these networks change when control parameters, such as aperture and field, are varied, and constraints are used to limit the variation domain of the variables. A good solution in a network, obtained with a limited number of variables, has been locally optimized with all variables to meet practical requirements.

Saddle-point construction in the design of lithographic objectives, part 1: method

The multidimensional merit function space of complex optical systems contains a large number of local minima. We illustrate a method to find new local minima by constructing saddle points, with examples of deep and extreme UV objectives. The central idea of the method is that, at certain positions in a system with N surfaces that is a local minimum, a thin meniscus lens or two mirror surfaces can be introduced to con- struct a system with N+2 surfaces that is a saddle point. When optimi- zation rolls down on the two sides of the saddle point, two minima are obtained. Often one of these two minima can also be reached from sev- eral other saddle points constructed in the same way. With saddle-point construction we can obtain new design shapes from existing ones in a simple, efficient, and systematic manner that is suitable for complex de- signs such as those for lithographic objectives.

Saddle-point construction in the design of lithographic objectives, part 2: application

Optical designers often insert or split lenses in existing de- signs. Here, we apply in the design of objectives for deep and extreme UV lithography an alternative method for adding new components that consists of constructing saddle points in the optical merit function land- scape and obtaining new local minima from them. The design examples show that this remarkably simple method can be easily integrated with traditional design techniques. The new method has significantly im- proved our design productivity in all cases in which we have applied it so far. High-quality designs of lithographic objectives are obtained with this method.

The network structure of the merit function space of EUV mirror systems

The merit function space of mirror systems for EUV lithography is studied. Local minima situated in a multidimensional merit function space are connected via links that contain saddle points and form a network. In this work we present the first networks for EUV lithographic objectives and discuss how these networks change when control parameters, such as aperture and field are varied and constraints are used to limit the variation domain of the variables. A good solution in a network obtained with a limited number of variables has been locally optimized with all variables to meet practical requirements.

Optimization of extreme ultraviolet mirror systems comprising high-order aspheric surfaces

When extreme ultraviolet EUV mirror systems having sev- eral high-order aspheric surfaces are optimized, the configurations sometimes enter into highly unstable regions of the parameter space. Small changes of system parameters lead then to large changes in ray paths and optimization algorithms fail. A technique applicable for any rotationally symmetric optical system that keeps the configuration away from unstable regions during optimization is described. Afinite-aberration quantity is computed for several rays, and its average change per sur- face is determined for all surfaces. For not too large values of these average changes, optimization remains stable. A design for EUV litho- graphy is discussed.

Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces

When Extreme Ultraviolet mirror systems having several high-order aspheric surfaces are optimized, the configurations often enter into highly unstable regions of the parameter space. Small changes of system parameters lead then to large changes in ray paths, and therefore optimization algorithms crash because certain assumptions upon which they are based become invalid. We describe a technique that keeps the configuration away from the unstable regions. The central component of our technique is a finite-aberration quantity, the so-called quasi-invariant, which has been originally introduced by H. A. Buchdahl. The quasi-invariant is computed for several rays in the system, and its average change per surface is determined for all surfaces. Small values of these average changes indicate stability. The stabilization technique consists of two steps: First, we obtain a stable initial configuration for subsequent optimization by choosing the system parameters such that the quasi-invariant change per surface is minimal. Then, if the average changes per surfaces of the quasi-invariant remain small during optimization, the configuration is kept in the safe region of the parameter space. This technique is applicable for arbitrary rotationally symmetric optical systems. Examples from the design of aspheric mirror systems for EUV lithography will be given.