Characterization of a Chemically Amplified Photoresist for Simulation using a Modified Poor Man s DRM Methodology

Transcription

1 Characterization of a Chemically Amplified Photoresist for Simulation using a Modified Poor Man s DRM Methodology Nickhil Jakatdar 1, Xinhui Niu, Costas J. Spanos Dept. of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA ABSTRACT As we enter the DUV lithography generation, the developmental phase of the photolithography process is becoming crucial due to the high costs associated with the lithography equipment. Improvements in the modeling of chemically amplified resists are necessary to extract the maximum possible information from the minimum amount of experimentation. The poor man s dissolution rate monitor (drm) method has been used successfully to extract the post exposure bake (PEB) and develop rate parameters for conventional I-line photoresists and some DUV chemically amplified photoresists (CARs). However, the original method suffers from some drawbacks such as locally optimized results due to the highly non-linear nature of the Mack development model and the need for visual inspection to detect convergence of the rate data. This paper used a simulated annealing optimization engine for global optimization and uses the deprotection induced thickness loss phenomenon for the conversion of dose to m. Post-exposure bake and develop rate parameters have been extracted for Shipley s UV-5 DUV photoresist. Keywords: Poor Man s Dissolution Rate Monitor (DRM), Chemically Amplified Resists (CARs), Shipley UV-5 photoresist, Simulated Annealing (SA), Deprotection Induced Thickness Loss (DITL), Fourier Transform Infrared Spectroscopy (FTIR), Mack development model, Lithography Modeling. 1. INTRODUCTION As the semiconductor industry moves into the deep submicron regime (0.18 µm) and larger wafer diameters (300 mm), the cost associated with each wafer is increasing rapidly. This calls for a reduction in the number of characterization experiments usually devoted to developing a new process. Improvements in lithographic modeling are thus needed to extract the maximum possible information from the minimum amount of experimentation. The need for good modeling capabilities is especially true for chemically amplified resists. CARs are very sensitive to tool set (stepper, track, etc.) and hence an ideal calibration procedure would entail in-situ measurement techniques at each processing step [1]. This technique would analytically determine chemical, physical and kinetic quantities relevant to the resist system and processing conditions. Previous work with in-situ sensors for the lithography sequence by the authors have led to the development of a soft sensor that can be used in this context [2]. A soft or virtual sensor is one that monitors features that may correlate with that wafer parameter, but only indirectly. The basic assumption made in the Poor Man s DRM methodology is that the resist develop rate depends only on the final deprotection extent and not on the processing path. Hence, the resist exposure and Post-exposure Bake (PEB) model parameters can be extracted from measurements of the resist develop rate across a matrix of processing conditions [3]. The thickness as a func- 1. Further author information - N.J. (correspondence): nickhil@eecs.berkeley.edu; WWW: Telephone: (510) ; Fax: (510)

2 tion of dose and development time is first converted to develop rate as a function of dose and depth into the resist R(E,z). Hence, exposure, PEB and develop rate model parameter extraction should in principle be possible from resist contrast curves. In this paper, a modified R(E,z) to R(m,z) converter is discussed. Resist absorbance and standing waves are modeled using a 1-d simulation for the exposure module. The phenomenon of deprotection induced thickness loss is discussed briefly for the indirect measurement of deprotection. Simulated Annealing, a global optimization routine has been used for the parameter extraction process. Although only a single temperature was used in this experiment, the use of multiple temperatures would allow for determination of the Arrhenius coefficient and the activation energy of both the acid amplification and acid loss terms. 2. MODIFIED R(E,z) TO R(m,z) CONVERTER 2.1 Exposure The conversion of applied dose to the effective dose coupled into the resist was done by modeling the resist absorbance and standing waves along the z-direction (into the resist). The exposure model is the one used by Byers, et.al. The z dependence of the exposure dose, using a simplified form of the full wave equation result, is given in Equation 1. Dose( z) = Dose( 0) e αz + r 2 e α( 2d z) 2 re αd cos πn( d z) λ (1) where the Dose(0) is the applied dose corrected by the reflectivity at the air-resist interface. α is the linear absorbance of the resist film, d is the film thickness, n is the real part of the refractive index, λ is the exposure wavelength and r is the reflectivity coefficient of the resist/substrate interface. While the conventional DRM provides develop rate at every depth into the resist, the same is not the case with the Poor Man s DRM method. This method makes develop rate measurements at various thicknesses within the resist which are not completely controlled by the experimenter. Hence, the integrated dose through depth into the resist needs to be computed and this is correlated to the develop rate during that interval of time. Equation 1 is used to compute the dose at every depth into the resist by discretizing the thickness of the resist. The dose is then integrated over the thickness of the resist that was developed during any given time interval in the experiment. Mathematica, a commercial mathematical integration package, was used for numerical integration of the dose as a function of depth. The standard exposure model for acid generated as a function of dose is [ Acid] dose = [ PAG] 0 ( 1 e C dose ) (2) where Acid dose is the concentration of acid at any given dose, PAG 0 is the initial concentration of the photoacid generator, C is the rate of photoacid formation and dose is the effective dose given by Equation 1.

3 2.2 Post-Exposure Bake During the deprotection step, the acid produced during exposure attacks the side chains of the polymer and generates more acid ions, thus making the resist even more soluble. This takes place in the presence of heat. In the quenching stage, the acid ions are slowly quenched by anything more basic than the acid, such as the additives and the by-products of the reaction. In short, the t-boc blocked polymer undergoes acidolysis to generate the soluble hydroxyl group in the presence of acid and heat [4]. The conventional modeling of the PEB process is given in Equation 3. m = 1 k amp k loss e e k loss t Aciddose (3) where m is the normalized concentration of unreacted blocking sites, k amp is the acid amplification factor and k loss is the acid loss factor. Both these factors are modeled using a temperature dependent Arrhenius relationship. The assumption made here is that the concentration gradient of acid in the film as a result of changing exposure conditions caused by internal interference of light and absorbance of light by the resist film during exposure, is close to zero. This assumption is not needed in the modified Poor Man s DRM technique. The reason is that in the original model, there existed only one method of conversion of dose to m and there was no scientific way to check the validity of this conversion. However, in this technique, we use a soft sensor to determine the normalized concentration of unreacted sites by an indirect measurement of the deprotection. A brief introduction to this sensor is given next and the reader is referred to [2] for a more complete description. During the deprotection step, the side chains are very volatile in many chemically amplified photoresists and evaporate during the bake, causing film shrinkage in the exposed areas [5]. The extent of this exposed photoresist thinning is dependent on the molecular weight of the blocking groups. The deprotection is quantitatively followed by monitoring the absorption or the lack of absorption at specific wavelengths which can be correlated to specific stretching and bending motions and, in some cases, with the relationship of these groups to the remainder of the molecule. Fourier Transform InfraRed (FTIR) spectroscopy is a powerful analytical tool for characterizing and identifying organic molecules. It has been shown that the thickness loss in the exposed areas is correlated to the deprotection of the photoresist at different temperatures and this phenomenon is named Deprotection Induced Thickness Loss (DITL). This study accounted for the thickness loss due to solvent evaporation. The results of the study for Shipley s UV-5 DUV resist have been used here in the procedure for the conversion of dose to m [FIGURE 1] [Equation 5]. Deprotection x is the concentration of reacted blocking sites and hence the relation between m and x is simply m = 1 x (4) The modified Poor Man s DRM method thus requires the measurement of the exposed area resist thickness loss after the PEB step as an additional measurement. This can then be used to calculate the deprotection of the resist using Equation 5.

4 Thickness Loss in Angstroms x11[, 3] Deprotectionx11[, ester 4] Summary of Fit: Multiple R 2 = Average model prediction error = on 24 degrees of freedom F-statistic: 5460 on 1 and 24 degrees of freedom FIGURE 1. Thickness loss as a function of the deprotection measured by monitoring the normalized ester absorbance Model Value Std. Error t value Pr(> t ) Slope The final model for thickness loss as a function of deprotection is T loss = D ester (5) The final link in the conversion of dose to m is the correlation of effective dose and exposed area resist thickness loss. Piecewise linear models for the resist loss versus the applied dose are built for the different regions of operation of the resist.

5 All the above steps are combined in the modified methodology. The applied dose is first converted into an effective dose using Equation 1. The thickness loss corresponding to the effective dose is computed using the piecewise linear models. This thickness loss is then converted into an equivalent deprotection figure using Equation 5. The deprotection is transformed into m using Equation 4. Hence, there is a one to one correspondence between the applied dose and m. This provides us with a more direct method to determine m. 2.3 DEVELOP The standard Mack develop rate model has been chosen to model the develop step [6]. It models the develop step using a surface limited development, dependent upon the extent of deprotection. ( a + 1) ( 1 m) n Rm ( ) = R max a + ( 1 m) n + R min ( n + 1) a = ( ( n 1) 1 m ) n th (6) (7) where R max is the maximum development rate, R min is the minimum development rate, m th is the value of m at the inflection point of the data, called the threshold PAC concentration, and n is the dissolution selectivity parameter, which controls the contrast of the photoresist. These are the 4 parameters in this model that need to be optimized. Due to the highly non-linear nature of Equation 6, traditional optimization techniques might get trapped at local solutions. To overcome this problem, we use Simulated Annealing (SA) which is a probabilistic optimization technique well suited to multi-modal, discrete, non-linear and nondifferentiable functions [7]. SA s main strength is its statistical guarantee of global minimization, even in the presence of many local minima. We also used a commercial traditional optimization package to compare the results. We observed that different starting values gave widely varying results. This is one of the biggest drawbacks in the conventional data analysis of the Poor Man s data which is overcome by using SA. 3. EXPERIMENT inch wafers were coated with Shipley UV-5 resist to a thickness of 7600 Angstroms and then soft-baked at 135 degrees Celsius. The resist thickness was measured at 33 sites across the wafer on a spectroscopic ellipsometer. The wafers were then exposed using 16 different exposure doses ranging from 0 to 3.2 mj/cm 2 in steps of 0.2 mj/cm 2 on a 248 nm stepper. These exposures were replicated across the wafer to reduce noise in the data. After exposure, the wafers were baked using the standard PEB conditions of 130 degrees Celsius for 90 seconds. The wafers were once again taken to a spectroscopic ellipsometer where they were measured for thickness in the exposed areas. This measurement yielded the DITL. The wafers were then developed using different develop times ranging from 7 seconds to 100 seconds. The minimum development time used on the wafer track was 7 seconds because this was the minimum time required for the developer to uniformly spread across the wafer. The wafers were once again measured for remaining resist thickness in the 33 sites. R min was measured on the one unexposed site per wafer. For shorter develop times, the development process was very non-uniform and hence produced very noisy data. To get reliable estimates for R max, a different approach was used. 4 high dose exposures were made in the center of a single wafer instead of 32 exposures distributed uniformly around the wafer. Due to the small, localized nature of the blanket exposures, the developer

6 spread uniformly over the region in less than 2 seconds. The develop step was stopped after 2 seconds. The remaining thickness was measured after the develop step to compute the develop rate. The reader is warned however, that the development mechanism in this case is more spray rather than puddle and hence does not accurately represent the same mechanism of development used in the other 10 wafers. 4. RESULTS AND DISCUSSION The Poor Man s DRM involves the measurement of multiple contrast curves i.e. resist thickness remaining as a function of exposure dose for open frame exposures at different development times. Once this is done, the algorithm mentioned in the previous section is used to convert the applied dose to m. The conversion of applied dose to effective dose was done using Equation 1. The DITL was then plotted versus this average effective dose and piecewise linear models were built using linear regression [FIGURE 2]. These different regions correspond to the different regions of deprotection. In region A, the effective dose has not yet passed the threshold for deprotection and hence the small slope. In region B, the resist is in its linear region of operation. In region C, the resist is in its saturation region of operation due to almost complete deprotection of its side chains. The thickness loss was obtained using these linear models. Equation Exposed Area Resist Thickness Loss (Angstroms) A B C Y = *X Y = *X Y = *X Effective Dose (mj/cm 2 ) FIGURE 2. Exposed area resist thickness loss versus the effective dose 5 was used to convert the thickness loss to deprotection and Equation 4 was used to convert the deprotection to m. This yielded the modified R(E,z) to R(m,z) converter. We also used the conventional R(E,z) to R(m,z) converter. It was

7 noticed that this involved a lot of iterations based on subjective decisions and hence the final R vs. m plots differed from person to person. However, the values of m and dose, obtained from the modified technique were then plugged into Equation 3 to get the exposure and PEB parameters. Unfortunately, in this experiment, we did not vary the PEB conditions and hence could not estimate the individual activation energies and Arrhenius coefficients of the acid loss and acid amplification factors. We plan on repeating this experiment at different PEB conditions and extracting this vital information for simulation engines such as Prolith [8]. This optimization problem [Equation 3] had 2 unknowns viz. k amp and k loss. The value of C was chosen as that given by the resist manufacturer. The optimization was done using SA and it yielded a value of for K amp and for k loss R max = 3540 A/s R Develop Rate (A/sec) R min = 6 A/s n = 8.97 m th = K amp = /s K loss = /s m Normalized concentration of unreacted sites FIGURE 3. Develop rate versus the normalized concentration of unreacted sites. Figure shows the fitting of the Mack develop model to the data The optimization to extract develop rate parameters was done using both a traditional optimization technique, as well as the modified Levenberg Marquardt (LM) and SA. Initial guesses for R max and R min in the LM technique were obtained from the experiment, while guesses for n and m th were made by looking at the inflection point and the slope of the R vs. m plot. Different starting values yielded different final results. In the case of SA, the algorithm was independent of starting guesses and it converged to the same results in every attempt. [FIGURE 3].

8 5. CONCLUSION In this paper, we presented a modified version of the experimentation and data analysis for the Poor Man s DRM to obtain critical simulation for DUV lithography modeling. We showed that the current method suffers from an unreliable R(E,z) to R(m,z) conversion method. This problem was overcome by measuring exposed area resist thickness loss after the PEB and using this to estimate the resist deprotection and hence get a more reliable estimate of m. The second problem was that the optimization techniques currently being used, suffer from getting stuck at local minima in the solution and hence result in erroneous estimates for the exposure, PEB and develop rate parameters. We overcame this problem by using a global optimizer. The next step is to repeat this experiment at different PEB conditions and estimate the PEB model parameters more in detail and use these results in Prolith simulations. 6. ACKNOWLEDGEMENTS This work was supported by the SRC under contract and the MICRO under contract REFERENCES [1] J. S. Petersen, et.al., Characterization and Modeling of a Positive Chemically Amplified Resist, SPIE vol.2438, pp , 1995 [2] N. Jakatdar, et. al., Characterization of a Positive Chemically Amplified Photoresist from the Viewpoint of Process Control for the Photolithography Sequence, SPIE [3] J. Byers, J. S. Petersen, J. Sturtevant, Calibration of Chemically Amplified Resist Models, SPIE vol.2724, pp , 1996 [4] H. Ito, C.G. Willson, Applications of Photoinitiators to the Design of Resists for Semiconductor Manufacturing, in Polymers in Electronics, ACS Symposium Series 242 (1984) pp [5] C. Mack, Inside Prolith - A Comprehensive Guide to Optical Lithography Simulation, February [6] C. A. Mack, Development of Positive Photoresist, Jour. Electrochemical Society, Vol.134, No.1, Jan 1987, pp [7] L. Ingber, Adaptive Simulated Annealing (ASA), ftp://alumni.caltech.edu/pub/ingber/, 1995 [8] FINLE Technologies, P.O. Box , Austin, TX 78716