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Generation of optical systems for lithography via saddle points

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What?

A new method to generate saddle points systematically: 1) start from a local minimum with N surfaces

2) at given positions in the system insert two new sur-faces (with parameters computed with our method) -> saddle point with N+2 surfaces

3) perturb it on both sides of the "saddle"

4) locally optimize the resulting two points -> two local minima with N+2 surfaces

DUVL

From the system in Fig. 1 six saddle points (SP) are created. They are linked to one relaxed solution (Hub) and six strained solutions (LMi) (Fig.2.). The significant deviations from the

hub are shown in blue. The hatches indicate the inserted lens. Similar results are obtained for the first bulge, too.

s

39

s

34

Hub

LM34 LM35 LM36 LM37 LM38 LM39 SP39 SP38 SP37 SP36 SP34 SP35

EUVL

Fig.2. Part around the hub of the network of local minima for a

monochromatic lithographic objective with N+2 = 45 surfaces. The indices show the surface in the original system where an extra lens has been inserted.

Fig.1. Starting local minimum with N = 43. The numerical aperture is 0.56

and the magnification is -0.25 at 248.3 nm.

Why?

Finding new local minima in the multidimensional merit function space of an optical system is a difficult task especially for lithographic objectives that have many varia-bles. Only methods, such as the present one, that use for this purpose a small number of local optimizations can be helpful. We use the fact that the local minima in the merit function space are connected via paths containing a certain type of saddle points.

Fig.4. Solutions resulting from a constructed SP at the second surface

(N+2 = 8) are reoptimized for a numerical aperture of 0.4. LM2 is poor,

but for LM1 the strehl ratio is larger that 0.996 and the distortion is

below 1 nm.

Fig.3. Starting local minimum (N = 6). At a numerical aperture of 0.16,

the object heights are in-between 114 and 118 mm and the magnification is 0.25.

A saddle point is constructed at the second surface of the system shown in Fig.3. and two new solutions are generated (Fig.4.). The tendency for a relaxed solution is maintained (LM1).

We thank ASML and TNO Science and Technology for the financial support of this Ph.D. research.

Generation of optical systems for lithography

via saddle points

Oana Marinescu, Florian Bociort, Joseph Braat

Optics Research Group, Delft University of Technology, The Netherlands

Phone: (+31) 15 278 8109 Fax: (+31) 15 278 8105 E-mail: O.Marinescu@tnw.tudelft.nl

Where?

SP

2

Cytaty

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