Beneath the MEEF
08/01/2000
Byung-Gook Kim, Seong Woon Choi, Woo Sung Han, Jung Min Sohn, Semiconductor R&D Center, Samsung Electronics, Yongin-City, Korea
overview
The effects responsible for enhancing small photomask CD errors are the same as those which narrow the exposure latitude. Innovations that increase the process window also reduce the mask error enhancement factor, thus doubly improving yield.
The reduction in feature size required by Moore's Law has recently outpaced the rate of exposure wavelength (Λ) decrease and numerical aperture (NA) increase. The k1 factor, which characterizes the quality of diffraction-limited optical images (k1 = NA x CD/Λ), has fallen to unimagined low levels in manufacturing. In the low-k1 region, small variations in critical dimensions (CDs) on the mask cause disproportionately large changes in wafer CDs. This amplification of mask errors is called the mask error enhancement factor (MEEF). In mathematical terms,
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where the mask CDmask is corrected for the magnification and expressed in wafer dimensions. If MEEF >1, the errors in mask CDs are nonlinearly transferred to the wafer even if the mask CD itself gets geometrically reduced by the proper ratio (ex. 1/4). Therefore, it is difficult for lithographers to control wafer CDs in the presence of inevitable mask errors, not to mention the decreased exposure latitude and depth of focus also characteristic of the low-k1 regime.
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This now well-known error enhancement phenomenon has also been called MEF, but we prefer the term MEEF, which emphasizes that the defectivity is produced by the lithography system and not solely by the maskmakers. Figure 1 illustrates the increase in MEEF due to reduced aerial image quality for three common IC structures. The points represent experimental resist exposures, whereas the lines result from aerial image simulation [1]. For the dense line/space pattern, both theory and experiment indicate that mask errors are amplified by 2.5x at k1 = 0.35. In the current low-k1 environment (k1 <0.5), MEEF has become the third key consideration when evaluating lithographic processes; the other two are exposure latitude and depth of focus. Some regard the MEEF as a new phenomenon, but we will show that is not entirely so.
Process window
A production environment must have sufficient latitude to maintain yield. MEEF must be considered when searching for the conditions that produce the widest process window, since MEEF depends on the process. Otherwise, the condition that produces the greatest margin for a particular mask feature may yield unacceptably small common windows for nominally identical features, because of mask CD errors. To avoid these problems, many lithographers specify tight photomask CD uniformity, but that may not be sufficient to ensure good wafer yields unless MEEF and its related nonlinear imaging effects are also reduced.
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As the feature size is decreased, diffraction spreads light from the mask to larger and larger angles, not all of which can be collected by the projection lens. Fundamentally, nonunity MEEF originates from the decrease of aerial image contrast arising from the loss of those higher diffraction orders. The k1 factor is roughly proportional to the number of diffraction orders captured, a low k1 implies a high MEEF value. The same mechanism may be applied to explain the decrease in exposure latitude (even for a perfect resist) as the feature size decreases. Thus two problems, decrease of exposure latitude and MEEF, both originate from the same underlying phenomenon.
The familiar Bossung plot and process window can be used to understand MEEF as well as exposure latitude and depth of focus. In Fig. 2, we compared process volumes for k1 values of 0.55 and 0.35. Qualitatively, the MEEF behaves inversely to the exposure latitude. One may thus regard the mask error as a kind of nonuniform exposure error. This means that exposure latitude is more fundamental than MEEF and steps to increase exposure latitude should also reduce MEEF and improve CD control.
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The MEEF discussed so far is the ideal case (properly termed "image MEEF"), occurring for perfect optics and resist. Unfortunately, our lithographic world is far from this ideal. Any effect that shifts the focus-exposure matrix can induce larger MEEF than calculated for the perfect aerial image. All the possible exposure error sources — including lens aberrations, swing curve effects, illumination nonuniformity, flare, etc. — make small MEEF less likely. The strategies that minimize MEEF are those that broaden the process window in a given lithographic environment.
A previously published paper [1] described various MEEF reduction strategies such as optimized pattern design, processing, and the choice of mask type. One easy, but unobvious, method to reduce MEEF is to choose proper mask and process bias. When the mask is biased, the best exposure latitude condition is not always coincident with minimum image MEEF.
Biasing
Figure 3 shows the image MEEF for line/space patterns of constant pitch as a function of the ratio of the linewidth to the spacewidth (L/S). The minimum MEEF occurs for a 1.0 ratio because the log-slope of the aerial image is maximum at that point. In general, the more gentle the log-slope at the resist threshold, the larger the MEEF [2]. When the illumination is incoherent and the pitch p obeys Λ/2NA<p<Λ/NA, the image MEEF depends only on the line/space ratio L/S [2].
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where MTF is the optical modulation transfer function.
MEEF also depends only on L/S when the illumination is perfectly coherent. However, when partially coherent or off-axis illumination is used and when the local exposure dose is varied intentionally by decreasing the mask line-to-space ratio and readjusting the exposure dose to place the resist threshold value at the desired position (i.e., biasing), MEEF can still be decreased. In this regime, increasing the log-slope of the aerial image produces a lower MEEF with negative mask bias (i.e., larger openings between the chrome lines), even though the image contrast is reduced as shown in Fig. 4a.
 Figure 3. The MEEF as ratio of the line/space ratio (L/S) when pitch is constant. Annular illumination reduces MEEF for negative bias. |
Figure 4 shows the difference in aerial image and MEEF between positive mask bias (L>S on mask for L/S = 1 on an overexposed wafer) and negative bias (L<S on mask with underexposed wafers). While positive bias increases image contrast as in Fig 4a, it also increases aerial-image MEEF for all values of k1 (Fig. 4b). The dotted traces in Fig. 4a correspond to 0.6mm defocus and illustrate that, in general, the focus latitude is not favorable in the negative bias case, even though the log-slope is steep at best focus.
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Figure 4. a) Aerial image for the different mask bias conditions and b) MEEF as a function of k1 value. The negative bias image has the steepest slope but least contrast. Defocus values (in mm) appear in parentheses in a).
The exposure latitude depends on the resist contrast as well as the aerial image. The table compares process windows for low- and extremely high-contrast resists with different mask biases. With a low-contrast resist, negative bias gives the largest process window, whereas the opposite is true for very high-contrast resist. The relationship between the focus-exposure process window and MEEF depends in subtle ways on the resist, illumination condition, and mask biasing. However, in optimizing processes, the focus-exposure matrix has top priority.
Attenuated-phase-shift mask
The performance of two masks with the nearly same CD uniformity (3o ~ 12nm), one chrome and the other an attenuated-phase-shift (halftone) mask, illustrates the primary importance of the focus-exposure matrix. Even though the CD uniformity was slightly poorer for the 5% transmission attenuated-phase-shift mask (att-PSM), the wafer CD uniformity was better (3o = 9nm) in the attenuated case (vs. 3o = 19nm for the Cr mask) and the apparent MEEF smaller (1.6 vs. 1.9).
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In the previous work [1], the att-PSM was not shown superior to the chrome mask in terms of MEEF. Then how can we reduce the CD uniformity? The answer is that the att-PSM has a larger exposure latitude as shown in Fig. 5. The phase-shifted background transmittance reduces the relative intensity of the zeroth order diffraction, increasing contrast and improving the modulation transfer. Small changes in dose due to local mask irregularities then change the developed resist pattern less.
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In conclusion, decreased exposure latitude accompanies the decrease in feature size in all types of lithography. The physics of MEEF is the same as that of reduced exposure latitude; mask CD errors simply cause local dose changes that enhance the changes in wafer CDs beyond the geometrically expected factor. Steps taken to enlarge the process window will decrease MEEF and improve chip yield.
Conclusion
MEEF is an important consideration and the mask industry will play a critical role in lithography from now on. Large MEEF has now introduced a new paradigm, altering the photolithography strategy. Nonlinear imaging, however, is fundamentally caused by the decrease of dose latitude. Clearly a MEEF>1 also enhances the printability of defects and necessarily forces a tightening of all reticle specifications. Tight reticle CD uniformity and defect specifications, however, will not solve all the mask-related problems in optical lithography. The resist vendors, stepper companies, maskmakers and wafer fabs must endeavor to widen the exposure latitude using all the means available, including improving the aerial image contrast with strong phase-shift masks.
References
- B-G. Kim et al., "Photomask and X-ray Mask Technology," SPIE.3748, pp. 572-578, 1999.
- C.A. Mack, "The Lithography Expert: More on the Mask Error Enhancement Factor," Microlithography World, Vol. 8, No. 4, pp. 18-20, Autumn, 1999.
Byung Gook Kim received his MS and BS in chemistry from Yonsei University. He is a member of the photomask team at Samsung Electronics, where he has worked since 1995. His current research includes CD error analysis in variably shaped e-beam systems; applications of e-beam chemically amplified resist in maskmaking; and masks for next-generation lithography. Samsung Electronics, Semiconductor R&D Center, San 24, Nongseo-ri, Kiheung-up, Yongin-city, Kyunggi-do, 449-711, Korea; ph 82/331-209-6459, fax 82/331-209-6455, e-mail [email protected].
Seong Woon Choi received his BS and MS in physics from Korea University. He has worked on the photomask team at Samsung since 1991, and is currently a senior engineer in advanced photomask development. He has extensive experience in photomask processing and photolithography, and his research includes advanced photomask technologies; mask CD uniformity enhancement technologies; OPC maskmaking; and process development for phase-shift masks.
Woo Sung Han received his MS in electronic engineering from Kyung Hee University, and his PhD in physics from Swiss Federal Institute of Technology, where he studied lithography based on deep ultraviolet holography. During his 16 years of photolithography experience, Han has developed numerous advanced photolithography technologies for DRAM device application, for which he has been awarded a number of patents. He joined the photomask team in 1999 and is manager of photomask development.
Jung Min Sohn received his BS and MS in physics from Hanyang University. With more than 15 years of experience in photomask technology, he has played a major role in the development of the Korean photomask industry since 1984. Sohn has published a number of photomask-related papers and has numerous photomask patents. He is currently a senior manager on the photomask team at Samsung.