Introduction

Resolution

W = k(/NA),         (1)

where and NA are respectively the wavelength and numerical aperture of the exposure tool, and k is an empirical constant. The numerical aperture (NA) is the sine of half the angle of the image-forming cone of light at the image. It is well known that under idealized conditions such as two incoherent point sources, the Rayleigh criterion implies that k = 0.61 [3]. In practice, k depends on lens aberrations, illumination conditions (degree of coherence and intensity distribution in the aperture plane), mask (e.g., whether phase-shift masks are used), geometrical shapes (or spatial frequencies), exposure tool conditions, resists, process, and operator. Resolution can be improved in three ways: by shortening the exposure wavelength, by increasing the numerical aperture, and by decreasing the value of k. Lithographers have been developing technologies at progressively shorter wavelengths. In the past, wavelengths used were 436 nm (G-line) and 405 nm (H-line). Currently, most of the systems use 365 nm (I-line) and 248 nm. In the future, wavelengths will be shortened to 193 nm or less. At the same time, optical designers are vigorously developing systems having higher numerical apertures (up to 0.8). Finally, smaller k values have also been pursued. Historically, k 1 for high-volume manufacturing processes when W 0.5 µm. The 0.5-µm process was practiced at k 0.8. Tool vendors and process developers are pushing k 0.5 or less [4]. The smaller the k, the narrower the process windows are. This has been demonstrated in terms of k versus geometric shapes [5], or in terms of exposure-defocus diagrams [6].

Depth of focus

DOF = k(/NA²),         (2)

where k is also an empirically determined constant. We use k = 1, which is usually achievable with good-quality lenses. (Note that this constant must be determined for each tool in practice.) Table 2 lists the DOF as a function of NA at 365 nm, 248 nm, and 193 nm. Because of the inverse square dependency on NA, the depth of focus is extremely shallow. For this reason, high-NA lenses are always associated with stringent requirements on planarization techniques for resists (top-surface imaging or multilayer resists) and processes.

Table 2 Depth of focus (µm) for k = 1.

	(nm) = 365	(nm) = 248	(nm) = 193
NA = 0.35	2.98	2.02	1.58
0.40	2.28	1.55	1.21
0.45	1.80	1.22	0.95
0.50	1.46	0.99	0.77
0.55	1.21	0.82	0.64
0.60	1.01	0.69	0.54
0.65	0.86	0.59	0.46
0.70	0.74	0.51	0.39
0.75	0.65	0.44	0.34
0.80	0.57	0.39	0.30

Minimum   -0.5  µm
linewidth   -0.35 µm
                      -0.25 µm

DOF = (k/k²)(W²/).         (3)

This equation shows explicitly that at the same NA and same lens resolution, a shorter wavelength gives a larger depth of focus. From the viewpoint of lens resolution, this is the motivation for exploring shorter wavelengths (EUV, X-ray), even when a longer wavelength seems adequate. Another observation is that a smaller k increases the depth of focus quadratically. Since a phase-shift mask can achieve a smaller k, it is used to extend the depth of focus.

Historical perspective of IBM high-NA lenses

Figure 1

There are numerous configurations used to explore the lens design space. At high NA, different design challenges are encountered. The design possibilities are widened by a combination of reflective mirror surfaces and refractive lens elements. The pros and cons of these catadioptric systems are reviewed in [9].

A simple and compact catadioptric configuration is the 1× Dyson-Wynne design [10,11]. Figure 2 shows a 1× Dyson lens using a beam splitter to achieve a large field of 20 × 20 mm²; Table 4 gives the related design data. This lens was designed in 1985 at a NA = 0.55 at a wavelength of either 308 nm or 248 nm for the generation of chips with a minimum linewidth of 0.35 µm. The extendibility of this lens with the beam splitter beyond NA = 0.55 was considered difficult. (This difficulty does not apply to the split-field Dyson lens, where half of the field is the object and the other half is its image. In that case, Ultratech has extended the design to NA = 0.7 [12].)

Figure 2

Figure 3 shows a 4× catadioptric lens with a beam splitter at NA up to 0.6; Table 5 gives related design data. Both 4× and 5× lenses have been designed. They have a field size of 11 × 22 mm². These lenses were designed at 248 nm for the 0.35-µm generation in 1990. They were later extended to 193 nm for the 0.25-µm generation. IBM designs [13,14] differ from the Micrascan series [15] in that IBM uses laser illumination (either a KrF excimer laser at 248 nm or an ArF excimer laser at 193 nm) instead of the Hg lamp that Micrascan uses. In this configuration, stringent requirements on the uniformity and coatings of the beam splitter are necessary. The issues in the design of beam-splitter coatings required by these lens configurations are described in the next section.

Figure 3

Figure 4 and Table 6 provide a cross section and design data for a different 4× catadioptric lens at NA up to 0.7 which does not include a beam splitter. It has a field size of 15 × 30 mm². This lens was designed at 248 nm for the 0.25-µm generation in 1991. This configuration [16] relaxed the three-dimensional uniformity requirements of the beam splitter. This design is extendible to a NA of 0.8 at a 193-nm wavelength.

Figure 4

Design of beam-splitter coating

A simple Gaussian-optics description of the ray bundles incident on the beam-splitter hypotenuse is sufficient to incorporate such requirements into the coating design. Linear relations then define the angles at which a ray traverses the coating in each pass. The effect of the coating on the ray involves a product of the (complex) reflectance and transmittance at the two different angles. For example, intensity exposure at a given field position will be proportional to a weighted integral of the squared magnitude of such reflection-transmission products, with the range of the integral essentially determined by the range of ray angles incident on the coating from the particular field position. In a Gaussian-optics description of the beams, the integration limits can be defined as linear functions of one of the field coordinates (the coordinate parallel to the beam-splitter P-polarization plane, where S and P are the two orthogonal linearly polarized components of the electromagnetic vector). The weighting function represents an integration of the circular beam aperture along the other field coordinate.

A typical functional requirement associated with the geometrical intensity might be that the coating impose an exposure nonuniformity over the field no larger than ±2%. This requirement can be written into the merit function used to design the coatings as a penalty term, written as the standard deviation of certain sums (approximations to the above integrals) divided by the 2% target. The total merit function for the coating includes several other terms relating to image performance, in addition to the usual terms prescribing reflectance and transmittance. These image-based criteria must be borne in mind when choosing a starting design for numerical optimization via the merit function.

The following list summarizes typical functional requirements incorporated into the design procedure:

• Coating must leave image-forming bundles unperturbed after two passes.
  • Total power in different bundles must be uniform to ±2%.
  • Image shift must be <0.025 µm.
  • Wavefront apodization must be less than ±10%.
  • Wavefront aberration must be less than ±/20.
• Coating should support alignment at a second nonactinic wavelength, where many of the above image uniformity requirements also apply.
• Absorption in each pass should be <1%, in order to avoid thermally induced index gradients in the prism substrates.

Taking as an example a 5× version of the lens in Figure 3, a summarized description of the ray paths through the cube is as follows:

• Total angular range is 45° ± 18°.
  • Principal ray from center of field is incident at 45°.
  • Principal rays from different field points are incident over ±2°.
  • Each spherical wave subtends ±16° in reflection pass.
  • Each spherical wave subtends ±5° in transmission pass.

The 36° angular range in the above example illustrates a key trade-off between the lens and coating designs. Such a large angular range makes it quite difficult to design the beam-splitter coating as a polarizer that reflects an S-polarized beam in one pass and then transmits the beam as P-polarization in the second pass after conversion by a waveplate. A simpler alternative is to pursue designs in which a single polarization (most conveniently S) is propagated through the lens in both passes. One consequence of such a choice is that the beam splitter limits the transmission of the system to 25%. (The 25% upper limit is attained with a 50/50 beam splitter, but splitting ratios between, e.g., 60/40 and 40/60 are almost as efficient.) Even with a laser source this intensity loss can matter, depending on the wavelength and bandwidth required. (Efficiency is not as important at the laser alignment wavelength, since the photoresist is transparent at that wavelength, and only a small area is illuminated by the beam.) Furthermore, with a nonpolarizing beam splitter, the wafer is not screened from potential ghost images of the laser source beam that can be formed from the unused portion of the light. To prevent these ghost images, the beam homogenizer (i.e., the illuminator subsystem that folds the source beam over on itself several times to improve uniformity) must be designed in such a way that the multiple folded copies of the beam are projected into the pupil with a carefully prescribed set of directions that do not reach the wafer except along the nominal propagation path through the system [17].

Within these limitations, suitable coatings can be designed. Table 7 shows a six-layer design for the system specified in the above bulleted list. With only six layers, the dominant terms of the variation in phase and amplitude with respect to angle tend to be linear, and these terms must be balanced between the two passes for the different field coordinates. Higher-order terms are small even in the starting design, and can be optimized independently in each pass. The calculated performance and amplitude reflectance and transmittance of the Table 7 design are shown respectively in Tables 8 and 9.

Table 7 Beam-splitter coating for the lens shown in Figure 3 (design wavelength = 248 nm).

Layer number	Material	Thickness (Å)	Tolerance (Å)	Design index
	(Bulk SiO)			1.508
1	AlO	211	±15	1.720 + 0.0005i
2	MgF	409	±25	1.412 + 0.0005i
3	HfO	207	±11	2.190 + 0.002i
4	MgF	383	±30	1.412 + 0.0005i
5	AlO	203	±30	1.720 + 0.0005i
6	HfO	257	±20	2.190 + 0.002i
	(Bulk SiO)			1.508

Table 8 Performance of Table 7 design.

	S-polarization			P-polarization
	T	R	R	T	R
27°	0.4969	0.4966	0.495	0.707	0.2856
29°	0.4919	0.5015	0.4998	0.7331	0.2591
31°	0.4876	0.5056	0.5038	0.761	0.231
33°	0.4843	0.5088	0.5068	0.7899	0.2018
35°	0.482	0.511	0.5087	0.8191	0.1724
37°	0.4808	0.512	0.5096	0.8476	0.1436
39°	0.4807	0.5119	0.5092	0.8745	0.1164
41°	0.4817	0.5106	0.5077	0.8991	0.0915
43°	0.4838	0.5084	0.5051	0.9208	0.0696
45°	0.4866	0.5053	0.5017	0.9392	0.05095
47°	0.49	0.5017	0.4977	0.9543	0.0356
49°	0.4935	0.498	0.4935	0.9663	0.02338
51°	0.4966	0.4947	0.4897	0.9752	0.01414
53°	0.4986	0.4925	0.4869	0.9812	0.00788
55°	0.499	0.4919	0.4857	0.984	0.004859
57°	0.497	0.4938	0.4869	0.9829	0.005634
59°	0.492	0.4986	0.4911	0.9774	0.01092
61°	0.4838	0.5068	0.4986	0.9667	0.02133
63°	0.4719	0.5186	0.5097	0.9507	0.03709

Table 9 Amplitude reflectance and transmittance of Table 7 design.

	S-polarization			P-polarization
27°	0.6336	-0.7038	0.4016	0.7843	0.5321
	+0.309i	+0.03534i	+0.5777i	+0.3031i	-0.04947i
29°	0.651	-0.705	0.4599	0.8243	0.5034
	+0.2609i	+0.06672i	+0.537i	+0.2315i	-0.07556i
31°	0.6662	-0.7042	0.5174	0.8596	0.4703
	+0.2093i	+0.0986i	+0.4859i	+0.1485i	-0.09902i
33°	0.6786	-0.7013	0.5721	0.8871	0.4333
	+0.1542i	+0.1305i	+0.4237i	+0.05372i	-0.1188i
35°	0.6876	-0.6962	0.6216	0.9035	0.393
	+0.09594i	+0.1619i	+0.3498i	-0.05209i	-0.134i
37°	0.6925	-0.6892	0.6632	0.9053	0.3505
	+0.03454i	+0.1924i	+0.2642i	-0.1674i	-0.144i
39°	0.6927	-0.6803	0.6937	0.8892	0.3071
	-0.0297i	+0.2214i	+0.1672i	-0.2895i	-0.1486i
41°	0.6873	-0.67	0.71	0.8528	0.2638
	-0.09644i	+0.2485i	+0.06i	-0.4146i	-0.1479i
43°	0.6756	-0.6586	0.7086	0.7944	0.2218
	-0.1652i	+0.2732i	-0.05527i	-0.5383i	-0.1429i
45°	0.6568	-0.6466	0.6862	0.7138	0.1813
	-0.2351i	+0.2953i	-0.1755i	-0.6555i	-0.1344i
47°	0.6299	-0.6347	0.6402	0.6118	0.1425
	-0.3054i	+0.3145i	-0.2963i	-0.7615i	-0.1237i
49°	0.5943	-0.6234	0.5687	0.4907	0.1045
	-0.3745i	+0.3307i	-0.4123i	-0.8517i	-0.1116i
51°	0.5497	-0.6136	0.4715	0.3535	0.0666
	-0.441i	+0.3438i	-0.5171i	-0.9221i	-0.09852i
53°	0.4959	-0.6058	0.3502	0.204	0.02759
	-0.5027i	+0.3542i	-0.6036i	-0.9693i	-0.08437i
55°	0.4335	-0.6007	0.2086	0.04689	-0.0133
	-0.5577i	+0.3621i	-0.665i	-0.9908i	-0.06843i
57°	0.364	-0.5987	0.05322	-0.1126	-0.05631
	-0.6037i	+0.3679i	-0.6958i	-0.985i	-0.04963i
59°	0.2891	-0.6	-0.1078	-0.2684	-0.1009
	-0.6391i	+0.3723i	-0.6924i	-0.9515i	-0.02696i
61°	0.2118	-0.6048	-0.2651	-0.4144	-0.146
	-0.6625i	+0.3755i	-0.6544i	-0.8916i	+0.0001564i
63°	0.1348	-0.613	-0.4097	-0.5446	-0.19
	-0.6736i	+0.3779i	-0.5846i	-0.8088i	+0.03144i

Concluding remarks

The difficulty of using high-NA optical lithography tools lies in their shallow depth of focus. Thus, top-surface imaging, multilayer resists, and planarization of device layers are of the utmost importance for widespread adoption of these tools.

We have described a design of beam-splitter coating for use with catadioptric systems with beam cubes to widen the design space of high-NA lenses. It must be emphasized that beam cubes impose stringent requirements on the 3D uniformity of index of refraction.

Figure 5 illustrates the NA as a function of time at IBM Research. Table 10 summarizes a representative (but not exhaustive) list of commercial lithography tools from the open literature. It is clear that tool vendors are also pursuing the development of systems having higher NA and shorter wavelength. Incidentally, field size is also currently increasing to accommodate larger chips. This is accomplished either by the lens design or by scanning the object and the image through the highly corrected lens field. This research in high-NA designs has served to guide IBM optical lithography strategy.

Figure 5

Table 10 Commercial lithography tools.

Manufacturer	Model number	Reduction	NA	Wafer (in.)	Resolution* (µm)	Field size (mm)	DOF (µm)
		I-line (365 nm)
NIKON	NSR2205i11D	--	0.5-0.63	8	0.4	31 **	0.92
CANON	FPA3000i4	5×	0.6	8	0.43	31	1.01
ASM	PAS5500/100D	5×	0.48-0.62	8	0.41	29.7	0.95
		248 nm
NIKON	NSRS201A	4×	0.6	8	0.29	25 × 33	0.69
CANON	FPA3000EX3	5×	0.6	10	0.35	31	0.69
CANON	FPA3000EXLS	4×	0.6	--	--	25 × 32.5	0.69
ASM	PAS5500/step	4×	0.63	8	0.25	31	0.62
ASM	PAS5500/scan	4×	0.63	8	0.25	26 × 34	0.62
SVGL	MS III	4×	0.6	8	0.35	26 × 32.5	0.69
ULTRATECH	Half Dyson	1×	0.7	12	0.25	20 × 40	0.5
		193 nm
SVGL	Prototype to LL^	4×	0.5	8	0.6/0.23	22 × 32.5	0.77

References

Received February 9, 1996; accepted for publication August 27, 1996