The Rayleigh's equations for resolution and depth of focus(DOF) have been the two pillars of optical lithography, defining the dependency of resolution and DOF to wavelength and to the numerical aperture (NA) of the imaging system. Scaling of resolution and DOF as well as determination of k 1 and k 2 have been depending on these two equations. However, the equation for DOF is a paraxial approximation. Rigorously solving the optical path difference as a function of wavelength and NA produces a DOF depending on the inverse of the square of the
numerical half aperture instead of the numerical full aperture. Using this new DOF scaling equation and a new coefficient of DOF k 3 , the previously
determined DOF have been shown to be overestimated by 10%-20% at NA of 0.6 and 0.8, respectively. The equation for resolution does not suffer from paraxial approximation but both new equations remove
an ambiguity when the refractive index in the imaging medium is larger than unity. Application to immersion lithography using these equations is included.
New degrees of freedom can be optimized in mask shapes
when the source is also adjustable, because required image symmetries can be provided by the source rather than the collected wave front. The optimized mask will often consist of novel sets of shapes that are quite different in layout from the target integrated circuit patterns. This implies that the optimization algorithm should have good global convergence
properties, since the target patterns may not be a suitable starting solution. We have developed an algorithm that can optimize mask and source without using a starting design. Examples are shown where the
process window obtained is between two and six times larger than that achieved with standard reticle enhancement techniques (RET). The optimized
masks require phase shift, but no trim mask is used. Thus far we can only optimize two-dimensional patterns over small fields (periodicities
of ;1 mm or less), though patterns in two separate fields can be jointly optimized for maximum common window under a single source. We also discuss mask optimization with fixed source, source optimization
with fixed mask, and the retargeting of designs in different mask regions to provide a common exposure level.
The International Technology Roadmap for Semiconductors lists F2 (157 nm exposure wavelength) optical lithography and extreme ultraviolet (EUV) next generation lithography as the two most feasible lithography solutions for the 70 nm technology node. It is very likely that both of these lithography solutions will be late, forcing ArF (193 nm exposure wavelength) lithography to operate at unprecedented resolution levels. Lithographically, alternating phase shifted masks (altPSM) can achieve the resolution required to manufacture 70 nm logic products with ArF lithography equipment [P. Schiavone, F. Lalanne, and A. Prola, "Clear field alternating PSM for 193 nm lithography," Proc. SPIE 3679, 582-589 (1999) and M. Fritz et al., "Application of chromeless phase-shift masks to sub-100 nm SOI CMOS transistor fabrication," Proc. SPIE 4000, 388-407 (2000)], but technical and logistical challenges associated with the broad implementation of altPSM require novel and invasive EDA solutions which have caused the industry to shy away from altPSM in the past. Since the resolution capabilities of altPSM are well understood in the lithography community, this paper will focus on the challenges facing altPSM implementation for the polysilicon gate level and will present the results of a detailed altPSM design feasibility study done at IBM for the 180 nm technology node. While the 70 nm technology node will push resolution harder then ever before, the design rules, EDA tools, and layout methodologies developed in the past lay the foundation for our attack on this challenging technology node.
Residual linear birefringence is an important property for quality control of optical components used in optical lithographic instruments. This paper shows that it is especially critical to control the residual linear birefringence in the substrate of photomasks at a very low level. A birefringence measurement system, known as Exicor®, was used for measuring both the magnitude and angular orientation of residual linear retardance in photomask substrates. Different patterns and levels of residual linear birefringence in these samples were identified. The effect of residual linear birefringence in photomask substrates, in determining wafer imaging quality, is discussed.
Influences of stress birefringence residual in lens elements of high-resolution projection optics are investigated based on a partially coherent imaging formula that has been modified to incorporate the change of the polarization state by birefringence. Birefringent properties are represented by two-dimensional distribution functions with respect to magnitude and fast-axis direction, and they are determined using random numbers to reproduce actual distributions observed in such materials as calcium fluoride. By repeating calculations using lens data created with different sets of random numbers, the degree of imaging performance degradation is analyzed statistically in terms of the magnitude of birefringence in each lens element, the number of lens element composing a projection lens, and the randomness of fast-axis distributions. It is found that the image contrast for a five-bar line/space pattern decreases squarely proportional to the magnitude, whereas the value decreases linearly proportional to the element number. The influence of randomness is understood in relation to image formations through random phase media.
A novel bilayer bottom antireflective coating (BARC) structure composed of a commercial KrF lithography resist and an organic BARC film is demonstrated for ArF lithography. The diluted deep ultraviolet (248 nm) resist is high absorption at the 193 nm regime, which is suitable as bottom layer of bilayer BARC structures. While the deep ultraviolet organic BARC material is low absorption at the 193 nm regime, which is suitable as top layer of bilayer BARC structures. Such a bilayer BARC can have large thickness control tolerances over various highly reflective substrates. The measured swing effect is found significantly reduced by adding such a bilayer BARC on both aluminum and silicon crystal substrates. Reflectance can be reduced to less than 2% on other highly reflectance substrates such as copper, poly-silicon, tungsten silicide, and aluminum silicon. Such a process has several advantages: high performance, relatively inexpensive, large thickness control tolerance, low contamination, and easy film removal.
Resonant mode micromechanical devices have great potential due to their high sensitivity and relatively easy signal processing. As they are also sensitive to environmental effects, vacuum packaging is often required, which largely increases the costs. The current study focuses on environment induced reliability problems and degradation processes. An adsorption-induced stiffening effect was observed on thin SiNx and SiCx cantilever beams in air. The resonance frequency gradually increases in time. When the cantilever is subjected to mechanical shock or large deflection, the resonance frequency suddenly drops, and then increases again. Air, increased humidity, argon rich, and nitrogen rich atmosphere influence the stiffening and the shock response behavior. The effects are explained with a surface oxidation model. The oxide layer introduces stress in the structure increasing the overall stiffness, while mechanical shocks crack the layer. Silicon resonators gather airborne particles from the atmosphere due to electrostatic charging. The mass loading decreases the resonant frequency. These mechanisms lead to unstable resonance frequency and eventually to failure of the resonant mode device. Tests in inert environment suggest, that cheap, inert atmospheric packaging will provide good performance and reliable operation.
The design and characterization of a two-axis rotational micromirror is explored. The mirrors were fabricated using a commercial microelectromechanical system (MEMS) foundry service, known as the multi-user MEMS processes (MUMPs) foundry service. The prototypes were then characterized using a phase-shifting Mirau interferometer. From these results, it was shown that the MUMPs process can be used to create satisfactory designs for rotational micromirrors with tilt angles in the range of 0-23 mrad and control voltages in the range of 0-30 V. In addition, the behavior of these mirrors was shown to fall within 5% of the values predicted by the theoretical models for the devices.