Copyright 2001 by the Society of Photo-Optical Instrumentation Engineers.

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1 Copyright 001 by e Society of Photo-Optical Instrumentation Engineers. This paper was published in e proceedings of Photomask and X-Ray Mask Technology VIII SPIE Vol. 4409, pp It is made available as an electronic reprint wi permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or oer means, duplication of any material in is paper for a fee or for commercial purposes, or modification of e content of e paper are prohibited.

2 Electron Beam Liography Simulation for Mask Making, Part VI: Comparison of 10 and 50 kv GHOST Proximity Effect Correction Chris A. Mack KLA-Tencor, 8834 N. Capital of Texas Hwy, Suite 301, Austin Texas Abstract GHOST uses two exposures, e primary dose and its complement, in an attempt to equalize e effects of backscattering and reduce proximity effects. Unfortunately, image contrast is reduced compared to exposures done wiout GHOST. A simplified raster scan eory is developed in order to examine e effects of backscattering and GHOST proximity correction on e quality of e images produced. Electron beam liography simulation is used to examine e effect of spot size and voltage on e spot image generated in 400 nm of ZEP 7000 resist, and e effects of GHOST on proximity effects and process latitude. Keywords: ProBEAM/3D, e-beam liography modeling, GHOST, proximity effect correction. 1. Introduction The necessity for performing proximity correction on electron beam mask liography will increase as e device generation migrates from 180 to 130 nm. GHOST proximity effect correction is one proposed meod to improve CD linearity and to reduce backscatter-induced proximity effects. Along wi migration to smaller feature sizes, increasing e accelerating voltage has major benefits in reducing e forward scatter of e incident beam. GHOST uses two exposures, e primary dose and its complement, in an attempt to equalize e effects of backscattering and reduce proximity effects. Because of e way e aerial image for GHOST correction is built, image contrast will be less favorable an exposures done wiout GHOST. At 50 kev, however, improved forward scatter (and e smaller spot sizes at is enables) means at GHOST has much less of an impact on process latitude an at 10 kev. In is paper, simulation of e electron beam imaging process using ProBEAM/3D examines e effect of spot size and voltage on e spot image generated in 400 nm of ZEP 7000 resist. Results show e benefits of using e higher voltage. This paper also uses simulation to examine e effects of GHOST proximity correction for bo 10 and 50 kev imaging, and e impact of proximity correction on process latitude.. Theory of Raster Scan Imaging Raster scan imaging can be ought of as e formation of an image by e summation of many spatially distinct basis images of (possibl differing energies [1,]. In practice, is summation is always incoherent, meaning e energy deposited into e resist material for each basis image is added togeer to form e total energy of e total image. A basis image, for example, could be simply e intensity of e spot of a laser beam as it is projected onto e surface of a substrate (or more correctly, deposited into a photoresist film). For e simplest raster scan imaging scheme, only one basis image is used, a so-called spot or pixel image, and each basis image has equal energy. Ignoring, for e purposes of is discussion, e distribution of energy rough e ickness of e resist film, e raster scan image I(x, can be described as e summation of many spatiallyshifted basis images.

3 N I ( x, P( x x, y y ) (1) i 1 where P(x, is e image of a single pixel or spot, and e set of points (x i,y i ) represent e centers of each pixel at are being summed to form e final image (i.e., e address grid). For bo laser beam and electron beam raster scan writing tools, e pixel image can be fairly approximated as a Gaussian beam. As a simple starting place, let us assume at e only basis image being used is a symmetric Gaussian pixel. Normalizing e pixel to have a peak intensity of 1, i i P( x, x + y exp σ x y exp exp σ σ () where e wid of e Gaussian is defined by σ. Assume at e raster scan strategy being employed uses a fixed address grid wi grid spacings x and y. The image being produced is en given by equation (1) wi address grid points turned eier on or off..1. Image of a Single Spot Two very simple examples will illustrate e formation of a raster scan image. First, consider e simplest image a single spot. In is case, only one address grid point is on so at e total image is just x + y I spot ( x, exp (3) σ Note at is is also e general result of e image in e vicinity of x y 0 whenever x and y are much greater an σ. Using is simple result, we can derive some of e basic liographic properties of e image. First, where is e of e image? In oer words, when is image is printed in resist, where will e s of e resist lie? Alough is is a raer complicated question, it can be simplified by assuming e response of e resist to a Gaussian-shaped image is such at e resist will occur at an normalized energy reshold of I. For example, picking I 0.5 would produces s corresponding to e full wid half maximum (FWHM) point of e image. In optical liography, it has been shown empirically at most resists have near optimum performance when I 0.3. For an arbitrary reshold intensity, e position of e left (at y 0) is given by x σ ln(1/ I ) (4) where e center of e spot is at x 0. As an example, e FWHM (I 0.5) wid ( x ) is equal to.355σ. For e image of a spot, what is e quality of e image? One of e most useful metrics of image quality is e image log-slope: e slope of e logarim of e image at e nominal photoresist. For e Gaussian spot image, e image log-slope is just

4 d ln I ln(1/ I ) log slope (5) dx x σ It is quite apparent at equation (5) predicts improved image quality (improved log-slope) for a smaller spot beam (i.e., smaller σ). The image log-slope can be normalized by multiplying by e desired feature wid to give e dimensionless normalized image log-slope (NILS). For is case, e NILS becomes NILS 4ln(1/ I ) (6) If I 0.5 e NILS will have a value of about.8. For I 0.3 e NILS will become about 4.8. This increasing NILS wi lower reshold intensity means at resist images printed at ese lower reshold intensities will have much greater linewid control... Image of an Edge A second, somewhat less trivial, example is e image of an where all pixels such at x i 0 are turned on. I ( x, ( x n x) A( exp n 0 σ (7) where A( is e result of summing all pixels in e y-direction. An interesting special case occurs when e address grid becomes infinitely small. For such a case, e summation in equation (7) becomes an integral, A( becomes a constant ( πσ ), and an ideal image can be formed: I ideal ( x, 1 erfc x σ (8) where e image has been normalized to have a peak value of 1 and erfc(z) is e complimentary error function. Note at is image is ideal only in e sense at it is a limiting behavior and, in fact, may not be e best image for a particular application. Where is e for is image of an? For two cases, x» σ and x «σ, e result can be determined analytically. When e address grid is much bigger an e Gaussian spot size, e position is just given by equation (4) since e is influenced almost exclusively by e nearest spot. When e address grid is much smaller an e spot size, a simple result is also possible. Consider first e limiting case of an infinitely small address grid. Picking a specific reshold intensity, equation (8) can be solved for e position of e. For I 0.3, x 0.53σ For I 0.5, x 0 (9) When e address grid size x is bigger an zero, but still much smaller an e spot size, e position becomes

5 For I 0.3, x 0.53σ x / For I 0.5, x x / (10) For I 0.3, log slope 1.16 σ / π For I 0.5, log slope (11) σ σ As in e case of a single spot, bo a smaller spot size and a lower I results in a better quality image of e. Note at a desire to improve image quality by using a lower I will necessitate e use of a bias, a difference between e actual resist position and e nominal position half way between e rows of on and off pixels..3. Effects of E-Beam Backscattering The above discussion of e nature of raster scan imaging assumed a simple Gaussian basis function. For electron beam writing, scattering wiin e resist and e substrate can lead to an energy distribution in e resist at is more complicated an a simple Gaussian. Many auors have noted at is backscattering of electrons leads to a distribution at can be reasonably approximated by a double Gaussian. In one dimension, is could take e form P( x, x + y x + y (1 β )exp + β exp (1) σ σ B where σ B defines e wid of e backscatter component of e distribution (σ B > σ) and β describes its streng (roughly equivalent to e fraction of electrons at are backscattered per unit area). Consider an made of e summation of ese double Gaussian spots. For e ideal case (infinitely small address grid), e becomes e sum of two complimentary error functions: I ideal The image quality of e raster scan printed can again be described by e image log-slope. Defining e log-slope at e position given by equation (10), e two cases are again x» σ and x «σ. If e address grid is much larger an e spot size, e image log-slope is given by equation (5), e log-slope of a single spot. When e address grid is much smaller an e spot size, equation (8) can be used to derive e logslope. 1 x x ( x) (1- β )erfc + β erfc (13) σ σ B βσ B where β 1 β ) σ + βσ ( B The impact of is scattering on e log-slope of e image at e is given by

6 For I 1 β β 0.5, log slope + (14) π σ σ B It is clear from is equation at bo larger β and larger σ B result in a lower log-slope. As an example, 10 kev exposure of 400nm ick resist on a mask blank wi a 50nm size spot (FWHM) would typically produce σ 115nm, σ B 510nm, and β This would give a β The log-slope in is case is about 40% lower an if ere had been no scattering. For a 50 kev exposure using a 100nm spot size (FWHM), σ 43nm, σ B 6.5µm, and β This would result in a value of β 0.50 (curiously similar to e value obtained for 10 kev). The log-slope of e image of an isolated at 50 kev is reduced by 50% due to backscattering. While e percent reduction in log-slope due to backscattering is larger at 50 kev an at 10 kev, e smaller spot sized used at 50 kev more an makes up for is difference..4. The Effects of Ghost Exposure Ghost exposure is a means to correct for e varying affects of backscattering as a function of pattern density. This is accomplished by subjecting e resist to a second exposure (after e normal writing of e pattern) comprised of a negative of e original pattern, exposed using a large spot and wi a dose smaller an e original. In oer words, e goal of e ghost exposure is to mimic e backscattered portion of e exposure in e nominally unexposed areas, us equaling out e impact of is unwanted effect. For example, e ghost correction pattern for e isolated of equation (13) would be an opposite-facing wi lower energy: where σ g is e wid of e ghost exposure spot and α is e ghost dose relative to e normal exposure dose. If e ghost spot wid is adjusted to equal e backscatter Gaussian wid (i.e., σ g σ B ), e ghost simplifies to Adding e ghost pattern to e original exposure of equation (13), I total α x I ( x) erfc + (16) ghost σ B α x x I ( x) (1- β )erfc β erfc (15) ghost g g σ g σ B 1 x x α + x ( x) (1- β )erfc + + β erfc erfc (17) σ σ B σ B By letting α β, an interesting result occurs: e backscattered pattern becomes a simple, uniform background dose. I ( x) total 1 x (1- β )erfc + β σ (18) The impact of is optimized ghost pattern on e log-slope of e can now be determined.

7 1 β 1 For x 0, log slope (19) π 1 + β σ Thus, ghosting reduces e log-slope even furer. For e cases described previously (where β 0.5 for bo 10 kev and 50 kev), e log-slope is decreased by 35-45% compared to e no-ghost case. Figure 1 shows how e ghost proximity correction scheme affects is image of an for e 10 kev case. Interestingly, since β is about e same for bo 10 kev and 50 kev, e use of an optimum GHOST exposure condition has e same relative impact on e log-slope of an isolated compared to e ideal case of no backscattering. The only advantage at e 50 kev exposure gives is e smaller spot size (e smaller value of σ in equation (19)) at in turn produces a higher image log-slope. Since, in general, one can expect e minimum forward scattered spot size in resist (σ) to be at least twice as large at 10 kev an at 50 kev, e image log-slope of an isolated wi an optimum GHOST exposure should be at least twice as high at 50 kev an at 10 kev Relative Energy Wi Ghost 0. Wiout Ghost Horizontal Position (nm) Figure 1. The impact of an optimized ghost exposure on an ideal (wi σ 100m, σ B 400nm, and β 0.1). 3. Simulation Results ProBEAM/3D v6. was used to simulate typical raster scan imaging situations at 10and 50 kev, wi and wiout GHOST. Parameters for ZEP 7000 (wi ZED 750 developer), measured previously for 10 kev exposure [1], were assumed to be remain e same at 50 kev. Obviously is assumption should be confirmed experimentally, but it suits e purposes here to compare voltages using an identical resist. 400nm of resist on 100nm of chrome on glass was used. Figure shows e results of e Monte Carlo scattering calculations, providing e average energy deposited in resist per electron. The difference between forward and back scattering energies for e two voltages is apparent. In Figure 3, ese scattering results are convolved wi a Gaussian beam shape to predict e deposited energy for a single spot exposure. Again it is obvious at e 50 kev exposure produces less forward scattering (and us more vertical energy contours near e of e spot) compared to e 10 kev case. It is also obvious at e 50 kev exhibits a much longer backscatter range.

8 Figure. Monte Carlo simulations of electron energy distributions (contours of log-energy per electron). Top graph show results for 10 kev electrons, bottom for 50 kev. (a) (b) Figure 3. (c) (d) Energy distributions in resist for a single spot exposure for (a) 10 kev, 60 nm FWHM spot size, (b) 50 kev, 60 nm spot size, (c) 10 kev, 10 nm spot size, and (d) 50 kev, 10 nm spot size.

9 The above simulations show clearly e impact of forward scattering on e liographic results. It is not as clear what e impact of e different backscattering behaviors between ese two voltages will be. To see is effect, one must look for proximity effects. One simple proximity effect measure is to examine how e printed resist linewid of a line/space pair varies wi changing spacewid. Figure 4 shows e proximity effect for 10 kev exposure of an 800 nm line. The dose was adjusted to give e correct linewid for e equal line/space case. As can be seen, when no proximity correction is used, e isolated line (represented by e large pitches of e figure) shows a 60 nm bias due to e increased backscatter of e larger spaces. By applying a GHOST correction wi a 1000 nm spot size at a dose of 40% of e primary dose, nearly perfect printing rough pitch is obtained. Obviously, GHOST is quite effect at reducing is type of proximity effect to wiin acceptable levels. As mentioned earlier, however, e price to be paid is e loss of linewid control due to e reduced log-slope of e exposure gradient at e resist. Figure 5 shows how develop latitude is reduced rough e use of GHOST as 10 kev Wi GHOST Linewid (nm) No GHOST Pitch (nm) Figure 4. Simulation of 10 kev proximity effects shown by printing an 800 nm line wi varying pitch wi and wiout GHOST. The primary exposure used a 50 nm spot on a 50 nm grid. For e GHOST case, e GHOST exposure used a 1000 nm spot at a dose of 40% of e primary dose.

10 1100 Linewid (nm) No GHOST Wi GHOST Development Time (sec) Figure 5. Impact of GHOST on process latitude is shown at 10 kev as linewid as a function of development time using e same conditions as Figure 5. As Figure 6 shows, proximity effects at 50 kev are much worse an at 10 kev. GHOST is also effective at reducing proximity effects at 50 kev. It is apparent at e GHOST parameters chosen for is simulation are not optimum, and no attempt was made to find e optimum parameters for is system. It appears at higher GHOST doses are required, however Linewid (nm) Wi GHOST (40%) 100 No GHOST Wi GHOST (5%) Pitch (nm) Figure 6. Simulation of 50 kev proximity effects shown by printing an 500 nm line wi varying pitch wi and wiout GHOST. The primary exposure used a 100 nm spot on a 5 nm grid. For e GHOST case, e GHOST exposures used a 6000 nm spot at doses of 5% and 40% of e primary dose.

11 4. Conclusions Through e use of a simple aerial image eory of raster scan imaging and rough full electron beam liography simulations, e use of GHOST proximity effect correction for 10 kev and 50 kev exposure was presented. Simulation showed what is commonly know in e industry: higher accelerating voltages will reduce forward scattering, but at e cost of a longer range of backscattering. As e aerial image eory predicts, reduced forward scattering resulting in a higher energy gradient near e line, which in turn will provide increased linewid control in e presence of processing and exposure errors. GHOST, while reducing proximity effects, has e detrimental side effect of reducing is energy gradient. For 10 kev, GHOST is very effective at eliminating e rough pitch type of proximity effect. However, e already shallow energy gradient produced by e forward scattering at is voltage means at e final ghosted image will have an exceedingly low energy gradient. At 50 kev, e improved forward scattering results in a significantly better energy gradient at e feature. It was not clear at e beginning of is study, however, how much GHOST would impact is fundamentally better behavior. Simple eory predicted e need for a GHOST dose at about 50% of e primary exposure, e same as for 10 kev. However, while a smaller an expected GHOST dose proved adequate at 10keV, e same 40% GHOST dose seemed too small at 50 kev. While no attempt was made to find e optimum dose, it seems apparent at a higher dose is required. These higher doses will in turn furer reduce e image log-slope of e total dose. Fortunately, e smaller spot size possible at 50 kev still provides more benefit an is taken away by e GHOST proximity correction. Alough is work shows e effectiveness of GHOST at reducing proximity effects, oer proximity correction schemes at don t reduce e image quality in e same way would certainly be desirable. Furer, any imaging scheme at can produce a spot (basis function) wi a fundamentally higher log-slope an a Gaussian spot will always lead to improved image quality in a raster scan imaging tool. 5. Acknowledgments The auor wishes to ank Chuck Sauer for many useful discussions. 6. References 1. C. Sauer and C. A. Mack, Electron Beam Liography Simulation for Mask Making, Part IV: Effect of Resist Contrast on Isofocal Dose, Photomask and X-Ray Mask Technology VI, Proc., SPIE Vol (1999) pp C. A. Mack and C. Sauer, Electron Beam Liography Simulation for Mask Making, Part V: Impact of GHOST proximity effect correction on process window, 19 Annual BACUS Symposium on Photomask Technology and Management, Proc., SPIE Vol (1999) pp. -0.