T h e L i t h o g r a h y E x e r t (November 4) Deth of Focus and the Alternating Phase Shift Mask Chris A. Mack, KLA-Tencor, FINLE Division, Austin, Texas One of the biggest advantages of the use of a strong hase shifting mask, such as the alternating PSM, is the increased deth of focus of fine itch atterns (see the May, 3 edition of this column). Here we will numerically evaluate the deth of focus for an alternating PSM, and show its deendence on artial coherence. A conventional, binary chrome on glass mask of lines and saces will roduce a diffraction attern of discrete diffraction orders at satial frequencies that are multiles of the inverse itch, /. For a high resolution (fine itch) attern, only the zero and the lus and minus first diffraction orders ass through the lens, as seen in Figure a. An alternating hase shift mask, as deicted in Figure b, adds shifters over every other sace to shift the hase of the light by 8. This mask then uses the destructive interference of light assing through adjacent saces to comletely eliminate the zero order. The image is obtained from the interference of the two first diffraction orders, now located at the satial frequencies f = ±/(). Often, the binary mask imaging shown in Figure a is referred to as three beam imaging (due to the interference of the three diffraction orders) while the hase shift case, with two diffraction orders assing through the lens, is called two beam imaging. The lane of best focus is determined by the hase of the interfering beams that combine to form the image. At best focus all of the interfering beams have the same hase. For the case of three beam imaging, roagation of the beams ast this lane of best focus creates a hase difference between the beams. Since a ath difference results in a hase difference (light changes hase 36 for every wavelength of distance traveled), the beams have an increasing hase error as a function of defocus, resulting in degraded image formation. For the two beam imaging case, if the two beams arrive at the wafer from the same angle (on oosite sides of the otical axis) a dislacement of the wafer from the focal lane gives the same hase change to each beam. Thus, the hase difference between the beams remains zero and a erfect, in-focus image results. Translating this discussion to the diffraction lane, imroved deth of focus (DOF) results from image formation with two beams when those two beams are equally saced about the center of the lens. For line sace atterns made with alternating hase shift masks, this arrangement of two equally saced diffraction orders occurs naturally for all reasonably small itches. Thus, an ideal alternating hase shifting mask, when illuminated with coherent, normally incident illumination, will exhibit infinite deth of focus for fine itch atterns! As one might exect, achieving the ideal conditions that create an infinite deth of focus is not easy. In fact, real lithograhic rojection tools cannot rovide ure, coherent illumination. Partially coherent illumination, with artial coherence σ that can be varied down to about.3, is the closest that ractical lithograhy tools can come (σ = is coherent illumination). How does
artial coherence affect deth of focus for an alternating PSM? How close to infinite DOF can a real exosure tool get? The effect of artial coherence is to sread the diffraction order oints into larger sots, the shae of each order s sot being determined by the shae of the source. Each oint on the source is indeendent, i.e., incoherent, with no fixed hase relationshi to any other source oint. Each source oint roduces a coherent aerial image, the total image being the (incoherent) sum of all the intensity images from each source oint. Since only the exact center source oint roduces an image with infinite deth of focus, all of the other source oints contribute to a loss of DOF. To evaluate how much the DOF is affected by the artial coherence, we can analytically calculate the aerial image given some simle assumtions. First, consider the case where only the first diffraction orders make it through the lens and that these orders are comletely inside the lens (not clied by the aerture), as shown in Figure. This occurs, for a given wavelength λ and numerical aerture NA, when λ 3λ < < NA( σ ) NA( + σ ) () A quick look at this constraint shows that it can ossibly be true only when σ <.5. Since, as we shall see, good DOF is obtained when σ is small, this constraint will be reasonable. Second, we shall use the araxial aroximation for the effects of focus, so that the otical ath difference (OPD) due to a defocus error δ will be a quadratic function of the sine of the incidence angle θ, or the satial frequency, f. OPD 4 6 sin θ sin θ = δ ( cosθ ) = δ sin θ + + + K δsin θ = δλ f () 4 8 Now the aerial image in the resence of defocus can be calculated analytically by integrating over the source. Considering only equal lines and saces for the sake of simlicity, 4 I( x) = ( + Dcos(πx / ) ) (3) π where D = J ( π δ σ NA/ ) π δ σ NA/ and J is the Bessel function of the first kind, order one. This defocus function D is lotted in Figure 3 and has the familiar Airy disk form. Given the aerial image of equation (3), what is the deth of focus? A convenient way of estimating DOF is through the use of the normalized image log sloe (NILS). For a nominal feature size of /, the NILS will be:
NILS = π D. (4) Feature sizes that have duty factors other than : will give different coefficients. When the NILS goes to zero, obviously the aerial image will have degraded beyond any usability. At this extreme,. DOF = δ <. (5) σ NA Perhas a more reasonable estimate would be the range of focus that kees the NILS within one half of its in-focus value (conservative) to one third of its in-focus value (aggressive). For these criterion,.7.85 < DOF < (6) σ NA σ NA As equation (6) shows, the deth of focus for an alternating PSM mask imroves as the artial coherence factor is reduced, aroaching the theoretically ossible infinite DOF as σ goes to zero. Note that the wavelength does not aear exlicitly in equation (6), but only in the assumtions leading to it. Although the derivation of equation (6) has some constraints on itch, uses an aroximate defocus exression, assumes an ideal resist (only the aerial image was taken into account) and ignores flare, the trends are still accurate. This equation can be useful in understanding the basic effects of artial coherence on alternating PSM deth of focus. An analogous exression can be derived for other two-beam imaging cases. Figure Cations: Figure. A mask attern of lines and saces of itch has an idealized amlitude transmittance function m(x) that roduces a diffraction attern M(f x ) where f x is the satial frequency. A binary chrome on glass mask is shown in (a), and an alternating hase shift mask is shown in (b). Figure. The diffraction attern, sread out by a artially coherent source, for an alternating hase shift mask. Figure 3. The Airy disk function D (which is linearly roortional to NILS) as it falls off with defocus. 3
illumination mask m(x) - M(f x ) f x f x lens (a) (b) Figure. A mask attern of lines and saces of itch has an idealized amlitude transmittance function m(x) that roduces a diffraction attern M(f x ) where f x is the satial frequency. A binary chrome on glass mask is shown in (a), and an alternating hase shift mask is shown in (b). 4
σ NA λ NA λ f Figure. The diffraction attern, sread out by a artially coherent source, for an alternating hase shift mask. 5
...8 D.6.4......3.4.5.6 δσna/ Figure 3. The Airy disk function D (which is linearly roortional to NILS) as it falls off with defocus. 6