Method of designing a projection system, lithographic apparatus and device manufacturing method
First Claim
1. A method of designing a projection system for a lithographic projection apparatus, comprising:
- obtaining a projection system starting configuration comprising a plurality of surfaces and having a merit function value corresponding to a local minimum in a merit function space;
inserting two additional surfaces at a reference surface in the starting configuration, with a separation between the additional surfaces and between the additional surfaces and the reference surface, with the optical material between the additional surfaces being substantially the same as that at the reference surface and with the curvatures of the two additional surfaces being substantially the same as the curvature of the reference surface to generate a saddle point configuration of a projection system corresponding to a saddle point in merit function space;
perturbing the saddle point configuration and performing optimization on at least one side of the saddle point to obtain a new projection system configuration having a merit function value corresponding to a local minimum in the merit function space;
increasing the separation between the two inserted surfaces and between the inserted surfaces and the reference surface at which they were inserted; and
outputting the resulting projection system configuration.
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Abstract
Optimization of a projection system is performed to obtain a starting configuration that is at a local minimum of the merit function or simply a previously known minimum system is used as the starting configuration. A zero-thickness meniscus lens is inserted at a surface in the local minimum starting configuration with N surfaces to construct a saddle point with Morse Index=1 having N+2 surfaces. The saddle point is perturbed and optimization is performed on both sides of the saddle, and the distances at the two surfaces that have been introduced are increased, to generate two new configurations, m1 and m2, that are new minima in the merit function. Each resulting configuration is output, e.g., as a table of parameters specifying the projection system or as a computer file for use in making an actual projection system.
27 Citations
27 Claims
-
1. A method of designing a projection system for a lithographic projection apparatus, comprising:
-
obtaining a projection system starting configuration comprising a plurality of surfaces and having a merit function value corresponding to a local minimum in a merit function space;
inserting two additional surfaces at a reference surface in the starting configuration, with a separation between the additional surfaces and between the additional surfaces and the reference surface, with the optical material between the additional surfaces being substantially the same as that at the reference surface and with the curvatures of the two additional surfaces being substantially the same as the curvature of the reference surface to generate a saddle point configuration of a projection system corresponding to a saddle point in merit function space;
perturbing the saddle point configuration and performing optimization on at least one side of the saddle point to obtain a new projection system configuration having a merit function value corresponding to a local minimum in the merit function space;
increasing the separation between the two inserted surfaces and between the inserted surfaces and the reference surface at which they were inserted; and
outputting the resulting projection system configuration. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21)
-
-
22. A lithographic apparatus projection system comprising a plurality of lenses to be traversed by a beam in sequence, wherein the lenses constitute a sequence of surfaces Si, each surface indicated by a different value of i, each surface separated by a distance Pi from the following surface, wherein the refractive index of the medium following surface Si has the value Ni, wherein each surface has a curvature Qi, and wherein specific ones of the surfaces are further defined by aspheric coefficients Ai, Bi, Ci, Di, Ei, Fi, Gi,
wherein the distance Pi is in the range of from (1− - ε
1)pi to (1+ε
1)pi,wherein the refractive index Ni is in the range of from (1−
ε
2)ni to (1+ε
2)ni,wherein the aspheric coefficients Xi are in the range of from (1−
ε
3)xi to (1+ε
3)xi, where X and x indicate the letters A, B, C, D, E, F, G and a, b, c, d, e, f and g respectively,wherein the curvature Qi is in the range of from (1/ri)−
μ
to (1/ri)+μ
,where ε
1, ε
2 and ε
3 are each less than or equal to 0.01, where μ
is less than or equal to 3×
10−
2 mm−
1, and where the values pi, ni, ri, ai, bi, ci, di, ei, fi, gi are given in the following tables;
Surface Radius ri Distance pi ni i (mm) (mm) ref. index Object Infinity 32 1.000302 1 Infinity 4.9648180901e−
0161.000302 2 898.023859654604 11.4782608731 1.560786 3 134.463937760492 9.48178051201 1.000300 4 279.589510966665 12.1628486499 1.560786 5 429.713386743823 30.5763283345 1.000300 6 −
133.57582830491452.2609104477 1.560786 7 −
168.2294981088821 1.000300 8 −
322.65442443357852.1915639063 1.560786 9 −
332.1420845519941 1.000300 10 487.536690843154 53.4932785237 1.560786 11 −
336.5951246575928.83282118993 1.000300 12 208.196678465787 55.9584509243 1.560786 13 −
2623.497508431921 1.000300 14 193.30761811124 52 1.560786 15 155.968334943742 32.9455980804 1.000300 16 −
12881.357531010412.5915495035 1.560786 17 403.369936634196 38.7100608856 1.000300 18 −
105.748859109385.65846203479 1.560786 19 167.881505445566 26.2063087045 1.000300 20 −
163.08597183772443.3797347636 1.560786 21 −
217.1366872245117.75348256739 1.000300 22 −
797.72265687276721.7839396346 1.560786 23 207.582687341939 28.5496395352 1.000300 24 −
1088.1582922849836.4121314285 1.560786 25 −
181.2554829260782.87340786737 1.000300 26 298.782208978124 31.8456070276 1.560786 27 1037.54514485231 35.3190829377 1.000300 Stop Infinity 7.67288412877 1.000300 29 403.195003517407 54.0542249345 1.560786 30 −
3049.0001856326826.0031544427 1.000300 31 1664.90725274904 48.7708456771 1.560786 32 −
306.6600405659390.334832322002 1.000300 33 188.839828069829 46.8455217041 1.560786 34 208.117004701503 2.40815418959 1.000300 35 135.132628439669 46.3838349983 1.560786 36 396.103393693348 1 1.000300 37 116.187821079462 47.8154003025 1.560786 38 201.589370561389 9.00187082814 1.000300 39 536.431565230929 36.6317358331 1.560786 40 820.248661906301 3.20826206953 1.000300 41 Infinity 10 1.560786 42 Infinity 8 1.000302 Image Infinity
−
3.198e−
005ai bi ci i k ei fi gi di 2 0 1.827356401e−
007−
1.964723247e−
0112.826932271e−
015−
3.74016622e−
0193.076574013e−
023−
1.219964317e−
028−
2.296232868e−
0314 0 8.134674858e−
0081.104556698e−
011−
1.685618766e−
015
1.87988583e−
019−
1.023459956e−
023−
4.912925606e−
0281.749013548e−
03117 0 7.319068222e−
0082.110164496e−
012−
1.231572849e−
016
1.11183883e−
019−
4.827860977e−
0231.002154882e−
026−
1.010925070e−
03022 0 5.184566313e−
0082.219202716e−
0124.794557685e−
017−
2.37716357e−
0215.789862375e−
026−
5.785892172e−
0293.675508546e−
03327 0 1.322829666e−
008−
2.359107509e−
013−
7.418731240e−
018
6.10788293e−
023−
6.637329327e−
0275.771574474e−
031−
1.659844755e−
03530 0 5.200370613e−
0093.266751776e−
0133.648281997e−
018−
8.12903873e−
0237.955327013e−
027−
3.788219518e−
0317.724948872e−
03639 0 −
9.269356549e−
0082.721883131e−
0129.611406529e−
016−
3.52824389e−
020−
2.306888008e−
0233.782079247e−
027−
2.077933409e−
031 - View Dependent Claims (23, 24)
- ε
-
25. A lithographic apparatus projection system comprising a plurality of mirrors to be encountered by a beam in sequence, wherein the mirrors constitute a sequence of reflective surfaces Si, each surface indicated by a different value of i, each surface separated by a distance Pi from the following surface, wherein each surface has a curvature Qi, and wherein each surface is further defined by aspheric coefficients Ai, Bi, Ci, Di, Ei,
wherein the distance Pi is in the range of from (1− - ε
1)pi to (1+ε
1)pi,wherein the aspheric coefficients Xi are in the range of from (1−
ε
2)xi to (1+ε
2)xi, where X and x indicate the letters A, B, C, D, E and a, b, c, d, and e respectively,wherein the curvature Qi is in the range of from (1/ri)−
μ
to (1/ri)+μ
,where ε
1 and ε
2 are each less than or equal to 0.01, where μ
is less than or equal to 2×
10−
3 mm−
1, and where the values pi, ri, ai, bi, ci, di, ei are given in one of the following;
tables A1 and A2;
or tables B1 and B2;
or tables C1 and C2TABLE A1 Radius ri Distance pi Surface i (mm) (mm) Object Infinity 500.8243 1 −
412.8448−
145.5591Stop −
207.5412205.9176 3 −
600.5993−
318.94424 −
6.8944e+004610.0009 5 −
708.809−
228.20496 −
1785.61244.5 7 279.5399 −
229.5198 284.0269 250.0008 Image Infinity 5.6e−
007TABLE A2 i k ai bi ci di ei 1 −
1−
4.7933e−
0094.1498e−
014−
1.4112e−
019−
9.3179e−
0241.9103e−
028Stop −
1−
9.7923e−
0091.3794e−
0121.3993e−
0169.7324e−
0200 3 −
1−
3.0962e−
009−
8.41e−
016
−
3.9728e−
020−
8.281e−
0251.0759e−
0294 −
1−
4.1446e−
0092.2188e−
014−
4.1285e−
0181.162e−
022−
2.0614e−
0275 −
1−
1.6868e−
0099.5153e−
015−
1.2393e−
0195.0798e−
0250 6 −
1−
7.4658e−
009−
2.3282e−
0139.6627e−
018−
3.0365e−
0223.4264e−
0277 −
1
9.0763e−
008−
2.0467e−
0123.3919e−
0161.1278e−
020−
5.5313e−
0258 −
1
5.7961e−
0093.9097e−
0143.3856e−
0192.477e−
0245.5432e−
029TABLE B1 Reflective Radius ri Distance pi surface i (mm) (mm) Object Infinity 629.76 1 −
502.31−
192.98Stop −
443.57496.91 3 −
1194.91−
590.24 1174.92 638.2 5 252.84 −
304.936 379.33 353.24 Image Infinity 0 TABLE B2 i k ai bi ci di ei 1 −
1.0−
8.10492e−
10−
2.12812e−
152.00734e−
20−
2.91712e−
250 Stop −
1.02.52722e−
08
1.84295e−
127.68723e−
17
1.92816e−
200 3 −
1.03.89102e−
11−
1.20482e−
151.71841e−
20−
1.06109e−
250 TABLE C1 Reflective Radius ri Distance pi surface i (mm) (mm) Object Infinity 599 1 −
11649.62807−
420.38Stop 756.22 450.22 3 382.51 −
397.234 358.48 786.6 5 368.18 −
328.616 401.58 346.62 Image Infinity 0 TABLE C2 i K ai bi ci di ei 1 −
1.01.27808e−
09−
7.70834e−
151.08806e−
191.44611e−
24−
1.32003e−
28Stop −
1.01.28858e−
10−
3.04390e−
15−
1.03997e−
197.79798e−
250 3 −
1.04.99689e−
09−
7.16941e−
142.40645e−
17−
2.97337e−
21
1.48591e−
254 −
1.0−
2.83190e−
086.48095e−
13−
6.87654e−
182.16269e−
23
8.53426e−
295 −
1.01.56374e−
084.00468e−
13−
1.32774e−
183.49147e−
22−
2.61910e−
256 −
1.02.13882e−
097.73607e−
153.27542e−
203.54263e−
25−
1.24655e−
30 - View Dependent Claims (26, 27)
- ε
Specification