DIFFUSION OF ACID AND ACTIVATION ENERGY OF POSITIVE CHEMICAL AMPLIFICATION RESIST

Journal of Photopolymer Science and Technology Volume 6, Number 4(1993) 505-514 1993TAPJ DIFFUSION OF ACID AND ACTIVATION ENERGY OF POSITIVE CHEMICAL AMPLIFICATION RESIST Koi 7ASAKAWA Toshiba Research and Development Center 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki 210, JAPAN A new simple method of measuring diffusion range of acid in chemical amplification resist has been designed. With this method, PEB temperature and PEB time dependence of diffusion range were investigated, and apparent activation energy of diffusion was estimated. Comparing this and activation energy of decomposition of inhibitor, decomposition was revealed to be ratedetermining reaction during PEB. This is thought to be the reason for PEB dependence on the pattern profile of the resist. 1, Introduction The diffusion range of acid is most important parameter for the performance of chemical amplification resist systems. Resists of this type have been regarded as most promising in view of their sensitivity to deep-uv, X-ray, and electron beam. Several studies have reported the measurement of the diffusion range of acid in resists of various systems and in various waysl11~21131. In most of these studies, the resist pattern was observed with scanning electron microscope (SEM) after development, and undercut path was measured from a surface or an edge. In these studies, this undercut was defined as the diffusion range, since it is considered that the acid diffuses and decomposes inhibitors which protect resist from dissolving in the developer. These methods are, however, very time consuming and incapable of clarifying the dependence of dissolution rates on the depth from the surface. We have designed a new simple method to measure the acid diffusion range using development rate monitor (DRM). Using the new method, we observed the diffusion range of the acid from one polymer layer which contains excess acid, to another layer which is protected with inhibitor. The diffusion range under various conditions of post-exposure-bake (PEB) time and temperature was estimated. From these results, diffusion of acid is considered to obey diffusion equation, and the apparent activation energy of diffusion was derived. Comparing this and the activation energy of inhibitor decomposition, real activation energy of diffusion was proved to be much smaller than the activation energy of inhibitor decomposition. Furthermore, PEB temperature dependence of diffusion profile is discussed in this paper. Received Accepted April 12, 1993 May 10, 1993 505

J. Photopolvm. Sci. Technol., Vol. 6, No. 1, 1993 2. Materials Random copolymer of poly(p-t-butoxycarbonylmethoxystyrene) and poly(4-hydroxyst}gene) (BCM-PVP) was used in this study. BCM-PVP was synthesized by a reaction of t-butoxycarbonyla-bromoacetate with poly(4-hydroxystyrene) (PVP) (M=5 W100, Maruzen Petroleum Chemical Co.) in the presence of potassium carbonate and potassium iodide according to the literature'. Triphenylsulphonium trifluoromethanesulphonate (TPS-OTf) as photo acid generator (PAG) was obtained from Midori Chemical Co. An alkali developer of the concentration of 0.28N of tetramethylammonium supplied by Tama Chemical Co. hydroxide was 3. Activation Energy of Inhibitor Decomposition The activation energy of inhibitor decomposition in the presence of the acid as a catalyst can be estimated from a relation between sensitivity and PEB temperature~51. This relation can be expressed as: Eoexp(-Ea/RT)H(t)=Const., (1) where Eais the exposure dose, Ea is activation energy of inhibitor decomposition, R is gas constant, T is absolute temperature, and H(t) is PEB time dependence factor. In this experiment H(t) is set constant since PEB time was constant. The resist with 1% ~% PAG was prepared from the solution in 2-ethyl- l -ethoxyethane. It was spincoated onto a silicon wafer to make a film approximately lp.m thick and prebaked on a hot plate at 95 C for 90s. It was exposed to a filtered (7,=252nm,=2%) t6mercury lamp light at various exposure doses. This exposure condition was thought to be equal to exposure with KrF excimer laser. The exposure dose where remained resist was just Onm was plotted as a function of inverse PEB temperature (Arrehenius plot) in fig. 1. The activation energy on two assumptions. was estimated based One is that the number of acid molecules generated by photo-induced reaction is proportional to the exposure dose. This assumption was confirmed by the fact that only 10% or less of the PAG reacted under this exposure condition. The other is that the number of the acid is much less than the number of the inhibitor, so that ability of acid as a catalyst at the same temperature is independent of the exposure condition. Activation energy of Ea of 117kJ/mol was derived from the slope of the plot. Fig.l. Exposure dose vs inverse PEB temperature 506

J. Photopolym. Sci. Technol., Vol. 6, No. I, 1993 4. Diffusion of Acid a. Methods The resist without PAG was prepared from solution in 2-ethyl-1-ethoxyethane. It was spincoated onto a silicon wafer to a film thickness of approximately 1µm and prebaked on a hot plate at 95 C for 90s. Next, it was kept under the vacuum condition to vaporize the remained solvent. Then water-soluble polymer with PAG was spincoated on it and baked again at 90 C for 60s. This baking temperature was set to be lower and shorter than baking temperature of the resist to avoid unexpected reaction or decomposition in the resist. We consider that the resist layer, which is soluble to organic solvent, and the water-soluble polymer layer form a sharp interface by the request of thermodymics, that is, the balance of the ordering force of enthalpy and the disordering force of entropy. The interaction parameters of the two, which are related to the solubility parameter, are supposed to be large. This means the thickness of interface must be smaller than the radius of gyration of the polymer coils, which is approximately several nmt6~1'~. When the sample was exposed to a mercury lamp at various exposure times, acid was generated from PAG by photo-induced reaction. Therefore we could compare the differences of the dissolution rates between non exposed part, where no acid exists, and exposed parts, where acid was generated. Next, the sample was baked at various elevated temperatures and times. In this paper, this baking process is referred as post-exposure-bake (PEB), since though differing somewhat from conventional PEB, since its function is the same as that of PEB in conventional methods. During this process the acid diffused from acid-containing water-soluble polymer layer into the resist layer, decomposing the inhibitor by acid-catalyst thermal reaction, making the resist soluble to the developer. The water-soluble polymer was removed from the surface of the wafer by washing with pure water. Then it was set on a development rate monitor (DRM) to measure the changes in dissolution rate of the resist for an alkali developer at 23.0 C. Fig.2. Experimental method 507

J. Photopolym. Sci. Technol., Vol. 6, No.4, 1993 b. Determination of diffusion range of acid Figure 3 shows typical data of the experimental result of the change in the resist thickness as a function of developing time when PEB was at 100 C for 800s. The exposure times here were 0, 10, 30, 60, or 120 seconds. We have estimated from another experiment that 1 second exposure to this mercury lamp light corresponds to 0.6mJ/cm2 to KrF excimer laser. These values indicate the relative quantity of generated acid. In the exposed area, we observed the dissolution rate was large at first and later became smaller. This suggests the dissolution rate near the surface was fast because the diffused acid decomposed the inhibitors. On the contrary, the dissolution rate in the deeper part was slower because less acid had diffused and at last it became a constant value because of the absence of acid influence. In the unexposed area, however, the dissolution rate was always constant, indicating that no acid was generated, and therefore, this was the intrinsic rate of this resist with inhibitor. There are three techniques to determine the diffusion range of acid from these data. The first is to determine the differences of.the thickness of the remained resists between the exposed part and unexposed part at a certain developing time. For example, at the developing time of 100 seconds, the remained resist thickness of the unexposed area was 910nm and at the exposed time of 60 seconds was 790nm. So we could estimate the diffusion range as 120nm in this way. With this technique, the same result would be obtained by measuring the undercut depth from the surface or the edge observed with SEM~'1~2~. However, this technique does not always indicate correct diffusion range because a decomposed part may still remained according to the condition. The second technique is to derive the deviation point from the straight line. This would appear to be the most suitable point from which to determine the diffusion range, but there is a drawback; it requires extremely precise measurement which may not always available. Fig.3. Development time vs remained resist thickness 508

J. Photopolym. Sci. Technol., Vol. 6, No.4 1993 The third technique is to measure the difference between the initial resist thickness and the thickness extrapolated from the linear data to the initial point. This diffusion range Df is the integration of elevated dissolution rate. Df = j'(dr(eo,t)-dr(o,t) )dt, (2) where DR(Eo,t) is dissolution rate of resist at exposure dose (exposure time here) Ea and development time t. This definition is the easiest way to determine the diffusion range though it is difficult to understand it intuitively. In this paper we use this as the definition of the diffusion range of the acid. From these data we could obtain dissolution rates as a function of remained resist thickness. These results of exposure time of 60 seconds are shown in fig.5. At the exposed area, the dissolution rate was large near the surface and became smaller and constant in the deeper part. The deviation point is equal to the deviation point of the plot of the resist thickness versus time. On the contrary, the dissolution rate was always constant at the unexposed area. We also tried to determine the remained inhibitor ratio. The dissolution rate of the blends of the pure PVP and BCM-PVP is shown in fig.4. From inhibitor concentration of 10 % to 30W1%, it seems to obey the following experimental equation, although this exponential been clarified theoretically. logdr= -0.12C+2.58, (3) relation has not where DR is disolution rate, C is inhibitor concentration. We estimated the inhibitor concentration from dissolution rate with equation (3). To obtain this rate, we made an assumption that the dissolution rate of blend of PVP and BCM-PVP was the Fig.4. Inhibitor concentration vs dissolution rate same as the rate of resist inhibitor which was not decomposed by acid-catalyst. This assumption has two difficulties. The first one is that the reference was the blend of two polymers but decomposed resist consist of one polymer. This difference seems not to be a problem when the BCM and PVP are mixed at the molecular level. The dissolution rates were the same for both of the blend and block copolymer of the same inhibitor content. The other problem is decomposed BCM has the ability to accelerate dissolution rate. This makes it difficult to obtain the accurate value because the inhibitor concentration tends to be underestimated. We have not conceived theory yet, and could not evaluate the influence of the decomposed BCM. However, since the tendency is considered not to change, the decomposed inhibitor concentration as a function of the resist depth was evaluated. The results are shown in fig.5. 509

z J. Photopolvm. Sci. Technol., Vol.6, No.4, 1993 The acid, generated in the watersoluble polymer, diffuses into resist layer during PEB. The diffusion can be considered to be one dimensional diffusion, so it is only necessary to consider the direction perpendicular to. the resist surface. The density of acid p(z,t) obeys the following diffusion equation. a a2 p( -D-.---., a z,t) = p, t az2 (4) where D is diffusion constant, z is distance from surface, t is PEB time. If it is assumed that the concentration of the acid does not decrease drastically during the PEB at the interface of the two layers, we could obtain the following relationship. Fig.5. Remained resist thickness vs dissolution rate Remained resist thickness vs inhibitor concentration erfc(z) =1-erf(z) =1 2 2 Dt exp(-uz)du where erfc(z) is error-function compliment which describes the distribution of the acid (fig.6). If another assumption is made that the decomposed inhibitor ratio is proportional to the acid concentration, it is possible to calculate the relationship between remained inhibitor ratio and distance from the surface. This assumption can be proper under the condition of low acid concentration and decomposed inhibitor ratio is not high. The result is indicated in fig.7 by a dotted line. Furthermore, dissolution rate can be derived from the equation (3). Comparing with the experimental result (fig.5), this calculated curve seems to be fit very well. Therefore distribution of the acid profile obeys the equation (5). This result suggests that the diffusion of the acid in this system obeys the diffusion equation. Fig.6. Error-function compliment Fig.7. Dissolution rate and inhibitor concentration calculated from fig.6 510

J. Photopolym. Sci. Technol., Vol. 6, No. 4, 1993 C. PEB temperature dependence The diffusion range is also considered to be a function of PEB temperature. According to the diffusion equation, the diffusion range Df is expressed as follows. Df= 2Dt, (6) where D is diffusion constant, t is diffusion time. This diffusion constant D depends on temperature. The Einstein relation is well known for diffusion of electrons and holes in semiconductors. This equation, however, cannot be used for the diffusion in liquid or bulk, because activation energy is required for an acid to move its position to that occupied by another molecule. According to Eyring, the relationship between diffusion constant D and this activation energy Ep is written as follows. D=(a2/'t)exp(-Ep/RT). (7) This equation shows that diffusion constant D strongly depends on temperature. By substituting equation (7) for equation (6), the following relation is obtained. Dfaexp(-Ep/2RT). (8) Therefore, diffusion range is proportional to exponent of half of the activation energy Ep. Since we obtain the diffusion range from the results of the acidic decomposed reaction of inhibitors, we must consider the influence of the decomposing reaction. The reaction rate of decomposing reaction of inhibitor Ri is written as follow. Riocexp(-Ea/kT). (9) The activation energy of decomposed reaction of inhibitor under the existence of acid is Ea. This Ea was already estimated in this paper, and it was 117kJ/mol. The apparent diffusion range as a function of inverse temperature T(K) is shown in fig.8. The baking time was 800 seconds and correspondent temperature in Celsius degrees is shown on the upper axis. The exposure time is proportional to the concentration of generated acid in watersoluble polymer layer since we confirmed that less than 10% of PACs generated acid. So the longer exposure time is, the more acid exists, and the apparent diffusion range seems to be larger. The apparent diffusion range involves the Ea and Ep. To compare the two activation energies, Ea and Ep, Ea is almost the same value as Ep. Ep is too small to estimate from this experiment because it seems less than error value. Therefore diffusion is not rate-determining but decomposing reaction of inhibitor is rate-determining reaction in this series of reactions. Fig.8. PEB temperature dependence Of d if f u Sion range 511

J. Photopolym. Sci. Technol., Vol.6, No.4, 1993 d. PEB time dependence The acids diffuse in the resists and decompose the inhibitors during PEB. In this process the diffusion range obeys the diffusion function and is considered to be proportional to the square root of PEB time. Each diffusion range is plotted as the function of the square root of PEB time at PEB temperature of 85 C and 95 C in fig.9. This PEB time shown here is much longer then the routine process, Because it is difficult to measure the diffusion range less than loonm because of error, we tried to increase accuracy by measuring longer PEB time. We consider it to be possible to estimate the diffusion range in the routine process from these results. Figure 9 shows diffusion range versus square root of PEB time. The measurement values are on a straight line. We confirmed that diffusion range is proportional to the square root of PEB time and obeys diffusion equation. This fact indicates that the sensitivity of diffusion to PEB time is slight. The diffusion range in the routine process can be determined from this result: for example, at 95 C for IOOsec the diffusion range is approximately 25nm, at 85 C for 24Osec it is 3Onm. It should be noted that this value is measured under the condition that the remained solvent was considerably evaporated by vacuum drying. The diffusion range significantly depends on remained solvent after prebake, and it is already known that increasing remained solvent causes extension of diffusion range. We shall report on this topic in the near future. Since diffusion is proportional to square root of PEB time, these phenomena can be explained by random walk model. An acid generated by optical reaction diffuses in resist resin without any proper direction and attacks the nearest inhibitor to decompose it. This attack is usually ineffective because the activation energy of decomposing reaction of inhibitor is considerably higher than activation energy of diffusion. Therefore, probability is that a decomposing reaction rarely occurs as the Fig.9. square root of PEB time vs diffusion range 512

J. Photopolym. Sci. Technol., Vol. 6, No.4, 1993 result of an attack. This probability is predicted by the Boltzmann equation. But the acid repeatedly attacks inhibitors, and sometimes decomposition occurs. After this PEB process, the position of acid from original point x is related to after time t. x=1't, (10) where 1 is moving distance of acids per unit time. e. Influence of PEB time, temperature on diffusion profile Comparing inhibitor decomposition, rate under the PEB condition at lower temperature and longer time is higher than that at higher temperature and shorter time. This is why the apparent diffusion range increases more than the real diffusion range of acid as PEB temperature elevates. This means that a smaller number of acids decompose more inhibitors at higher temperature. Therefore, diffusion profile must be closer to the initial state profile at higher PEB temperature, because fewer acids need to diffuse and effectiveness of acid as catalyst is amplified by heat. Therefore, the less acid is amplified by heat, the apparent diffusion distribution widens, and hence, contrast appears to be inferior. Figure 10 shows two diffusion profiles of longer PEB time at lower temperature and shorter time at higher temperature under the condition to obtain the same apparent diffusion range. For this condition, integration of both decomposed inhibitors is the same. This apparent diffusion range is the most effective parameter in the routine process. Therefore, increasing PEB temperature is predicted to cause inferior contrast in resist pattern profiles. Regarding line & space patter, for example, the pattern profiles become unclear at the interface of exposed and unexposed parts because of mutual diffusion of acids. We have confirmed that this system obeys the diffusion equation, and therefore, distribution of acids at the interface is expressed by the Green function. From the same consideration as fig.10, better contrast resist profiles can be developed at lower temperature and longer time. Fig.10. Comparison of diffusion profiles between high PEB temperature and low temperature 513

I Photopolym. Sci. Technol., Vol. 6, No. 4, 1993 5. Summary In this paper, we reported a new simple method of measuring the diffusion range of acid in chemical amplification resists. From this method, more information can be obtained, for example, dissolution rate distribution as a function of the depth from the surface. Diffusion of acid in this positive chemical amplification resist also obeys the diffusion equation. Random walk model can explain these phenomena at the molecular scale. Diffusion range measured in this experiment was, for example, approximately 25nm at 95 C for 100sec PEB, and 30nm at 85 C for 240sec PEB. Since diffusion range is proportional to the square root of PEB time, diffusion range would double when PEB time quadrupled. This fact indicates that sensitivity of diffusion to PEB time is slight. On the contrary, diffusion range is very sensitive to temperature. Diffusion range increases rapidly as PEB temperature is elevated. We clarified from comparison between activation energy of diffusion and decomposition reaction that this strong temperature dependence is temperature dependence of apparent diffusion range. Therefore, the decomposition reaction of inhibitor has much more influence than acid diffusion. From this result, the resist pattern profile is considered to be better under the PEB condition of lower temperature and longer time than higher temperature and shorter time. 6. Acknowledgements The author would like to thank Y. Hongu, T. Naito, and T. Ushirogouchi for many discussions and N. Oyasato, and R. Hayase for cooperation in synthesizing polymer. The author is also grateful to M. Nakase for his encouragement. 7. References 1. L. Schlegel, T. Ueno, N. Hayashi, T. Iwayanagi; J.Vac.Sci.Technol.,B9(2)(1991)278 2. K. Deguchi, T. Ishiyama, T. Horiuchi, A. Yoshikawa; Jpn.J.Appl.Phys.,29(1990)2207 3. D. R. McKean, R. D. Allen, P. H. Kasai, U. Schaedeli, S. A. MacDonald; SP1E,1672(1992)94 4. F. Houlihan, F. Bouchard, J. M. J. Frechet, C. G. Willson; Can.J.Chem., 63(1985)153 7. J. W. Thackeray, T. H. Fedynyshyn, A. A. Lamola, R. D. Small; J.Photopolym.Sci.Technol.,5( 1992)207 6. J. W. Cahn, J. E. Hilliard; J.Chem.Phys.,28(1958)258 7. E. Helfand; J.Chem.Phys.,62(1975)999,2192 514