A Parameter Extraction Framework for DUV Lithography Simulation
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1 A Parameter Extraction Framework for DUV Lithography Simulation Nickhil Jakatdar 1, Junwei Bao, Costas J. Spanos Dept. of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA Xinhui Niu 2 Timbre Technology Inc., 2000 Walnut Ave, #H-103, Fremont, CA Joe Bendik National Semiconductor Corporation, 2900 Semiconductor Drive, Santa Clara, CA Stephen Hill Semiconductor Systems Division, Bio-Rad, 520 Clyde Avenue, Mountain View, CA ABSTRACT As the semiconductor industry moves into the deep submicron range, the costs associated with wafer processing are increasing rapidly. This calls for improved simulation capabilities that provide information for meaningful what-if analyses. This work proposes a common methodology for extracting information from Fourier Transform Infrared Spectroscopy (FTIR), Dissolution Rate Monitor (DRM) and ellipsometry measurements, to be ultimately used for the calibration of commercial lithography simulation tools. Using global optimization techniques, this approach uses cross-section CD data available in fabs to tune the simulation engine, thus giving it the predictive capabilities that could potentially improve yield ramp rates and hence reduce development costs. Results of this framework for a commercial Shipley resist are presented. Keywords: Fourier Transform Infrared Spectroscopy, Dissolution Rate Monitor, Ellipsometry, Prolith, Adaptive Simulated Annealing, Timbre VLB, Chemically Amplified Resists, Photolithography, Profile Matching, Process Simulation. 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 processing each wafer is increasing rapidly. Since time to market is crucial, we need a more efficient development process. Improvements in lithographic modeling are thus needed in order to extract the maximum amount of information from limited experimentation. The need for reliable modeling is especially true for chemically amplified resists (CARs). CARs are very sensitive to processing conditions and hence an ideal calibration procedure would entail determining the chemical, physical and kinetic quantities relevant to the resist system and the specific processing conditions. The objective is to use such a model with a lithography process simulator (such as Prolith) to accurately predict the lithographic performance. We begin by identifying the key parameters required for effective simulation. Using our newly proposed exposure and bake models, as well as existing develop models, many of the identified parameters were extracted using FTIR, DRM and ellipsometry experiments[1]. After this first round of parameter tuning, there still remained some parameters that did not lend themselves 1. Further author information - N.J. (correspondence): nickhil@eecs.berkeley.edu; WWW: Telephone: (510) ; Fax: (510) Formerly with U.C. Berkeley
2 to extraction from experimentation. These parameters were obtained using the Timbre Virtual Lithography Bench (Timbre VLB), a commercial software program that tunes the parameters of the lithography simulator in order to match simulation to experimentally obtained cross-section CD profiles (based on FEM data). Simulation tools are used routinely to predict first order effects, and lots of effort is spent calibrating those simulators. Still, there is a long way to go before a process engineer will depend entirely on simulations to design the next process. The work presented in this paper aims at improving the models and reducing the cost of calibration. 2. BACKGROUND 2.1 Critical Parameter Identification In this section, we identify the parameters in the lithography process simulators that we have typically found to be the most critical. The parameters listed in Table 2.1 can also be divided according to the specific step in the lithography sequence. Although this list would differ from one situation to the next, this is meant to serve only as a typical example. The methodology suggested in this paper is universal and can hence be applied across different parameters. Table 2.1. Critical Lithography Simulation Parameters Amp. Rate (Pre-exp.) 1/sec A amp Maximum Develop Rate A/sec R max Amp. Rate (Activation) Kcal/mole E amp Minimum Develop Rate A/sec R min Acid Loss Rate (Pre-exp.) 1/sec A α Developer Selectivity - n Acid Loss Rate (Activation) Kcal/mole E α Developer threshold PAC - m th Dill s A parameter µm -1 A Res. Refractive Index (Real) - n res Dill s B parameter µm -1 B Res. Refractive Index (Imag.) - k res Dill s C Parameter cm 2 /mj C ARC Refractive Index (Real) - n arc Relative Quencher Conc. - [Q] ARC Refractive Index (Imag.) - k arc PEB Diffusivity (Pre-exp.) nm 2 /sec A diff Relative Focus µm F PEB Diffusivity (Activation) Kcal/mole E diff Amp. Reaction Order - O 2.2 Models for Exposure, Bake and Develop The exposure process in chemically amplified resists has been modeled by Byers, et. al.[2]. The applied dose is first converted into the effective dose coupled into the resist as a function of depth into the resist. This depth dependence of the exposure dose uses a simplified form of the full wave equation result, and is given in Eq. 1. Dose() z = Dose( 0) e αz + r 2 e α( 2d z) 2 re αd cos 4πnd ( z) λ (1) where the Dose(0) is the applied dose in mj/cm 2, corrected by the reflectivity at the air-resist interface. α is the linear absorbance of the resist film in µm -1, d is the film thickness in nm, n is the real part of the refractive index, λ is the exposure wavelength in nm and r is the reflectivity coefficient of the resist/substrate interface. This exposure dose is then converted into acid as follows:
3 [ 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 Eq. 1. During the PEB process, the t-boc blocked polymer undergoes acidolysis to generate the soluble hydroxyl group in the presence of acid and heat [2]. The conventional modeling of the PEB process is given in Eq. 3. m = 1 e k loss t k amp Aciddose k loss e (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 depend on temperature with an Arrhenius relationship. k amp A exp E amp amp and RT E = k loss = A exp loss loss RT where R is the universal gas constant, 1.99 cal.mole -1 K -1 and T is the temperature in Kelvin. The assumption made here was that the concentration gradient of acid in the film as a result of changing exposure conditions caused by internal interference and absorbance during exposure, is close to zero. However, the combined exposure and PEB models (Eq. 3) do not account for the initial delay in the increase of the deprotection vs. dose at different temperatures. We assume that this is caused due to the quencher designed into most chemically amplified resists. We propose two models to account for the relative quencher concentration ([Q]). In the first model (Eq. 4), we assume that the quencher manifests itself as a reduced effective exposure dose, and that the quenching process occurs during the exposure step itself. This phenomenon is clearly seen when plotting deprotection vs. dose and temperature curves. The different temperatures yield different slopes for the curves, but all of them require a certain amount of exposure dose before any deprotection begins. This threshold dose can be used as a good first guess for the dose q value. This model is simplistic, in the sense that the mechanism is broken into two parts: the initial quenching reaction, followed by the actual deprotection reaction. The final normalized acid concentration can hence be written as follows: [ Acid] dose 1 e C ( dose dose q) = (4) while the relative quencher concentration can then be calculated as: Q 1 e C dose q = (5) In the second model, we assume that during the PEB process, acid is lost in neutralization reactions with bases that are either designed into the resist, or exist as unreacted portions of the polymer. This indicates that the bases will also correspondingly
4 reduce with time, and the difference between the acid and base concentrations will remain constant throughout the PEB process. We model the above mechanism through Eq. 6 and Eq. 7. [ Acid] = kα [ Acid] Q[ ] t (6) [ Acid] t Q[] t = Const = [ Acid] 0 Q[] 0 (7) where k α is the neutralization reaction coefficient modeled by an Arrhenius temperature relation, [Q] is the quencher concentration and [Acid] t is the acid concentration. The initial value for quencher [Q] 0 is a parameter that can be extracted from the procedure described in Section 4 while the initial acid concentration [Acid] 0 is obtained from Eq. 2. Solving the above equations yields the following analytical solution for the acid concentration as a function of the PEB time. ([ Acid] [ Acid] 0 Q[] 0 ) t = Q[ ] exp( [ Acid] k ([ Acid ] α 0 Q[] 0 )t ) 0 (8) Meanwhile, the deprotection reaction is typically modeled by Eq. 9, where k amp is the reaction amplification coefficient and is modeled by an Arrhenius relationship as a function of temperature. M[] = t kamp [ Acid] t M[] t (9) Substituting Eq. 8 in Eq.9 and solving for the normalized m, we get M[ ] t = m = M[ ] 0 ( [ Acid] 0 e k α( [ Acid] 0 Q[ ] 0 )t ) Q[ ] [ Acid] 0 Q[] 0 k amp k α (10) Eq. 10 differs from previous work in that it accounts for the fact that the bases (both parasitic and designed) are consumed in the neutralization reaction. Getting rid of the earlier simplifying assumption allows us to better model the initial delay in deprotection increase with exposure dose and hence provides an estimate of the relative quencher concentration [Q] 0. The development process is modeled by the standard Mack model [4] in our example, although more advanced models could also be used.
5 ( a + 1) ( 1 m) n R( m) = R max a + ( 1 m) n + R min ( n + 1) a = ( ( n 1) m ) n th (11) (12) 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. The develop parameters can be extracted through either a standard DRM or a poor man s DRM experiment [3]. 2.3 Lithography Profile Simulation Modern lithography simulation engines such as Prolith and Solid-C are widely used in the industry. The efficacy of a simulator is limited by both the accuracy of the models as well as the correctness of the parameters used. While the models used by the simulators have been widely studied and provide fairly accurate process models for the lithography sequence, they typically suffer from having a very large number of parameters that need to be tuned in order to match the simulation to real world data. While some of these parameters have a physical basis and hence can be extracted from unpatterned and patterned photoresist experiments, the others are empirical parameters that are difficult to obtain through experimentation. Today s calibration procedure involves a manual optimization sequence wherein the parameters of the simulator are changed one at a time to fit to some experimental CD data available from the fab. This process is both erroneous, since it neglects interaction effects between the different parameters, and is time consuming as well. Thus, the process simulation engineer requires a very large amount of time and data to calibrate his/her simulator. After that, the simulator can only be used to study first order behavior, due to the lack of faith in its results. To overcome the problems stated above, we used Timbre PXM, a commercial optimization package that wraps around commercial lithography simulators. Timbre PXM employs a global optimization toolkit that circumvents the problems associated with the one-parameter-at-a-time optimization approach. It also provides a means of using the complete CD profile information available from cross-section CD-SEMs and AFMs. It does this by digitizing cross-section images for direct comparisons with Prolith predicted cross-sections. The next step is to decide on the parameters that the lithography profile is most sensitive to. We noted the parameters considered the most crucial in our experience. The selected parameters are then assigned ranges within which the actual value lies. The range of the parameters extracted using the methodology provided above can be made relatively small, while the rest of the parameters are given larger ranges, due to the limited information available on their values. The selected parameters are then tuned by PXM until the simulated profiles match the digitized experimental profiles across the complete focus-exposure matrix (FEM). The larger the range of settings that the experimental data is available for, the more global the simulation calibration procedure is. Thus, we now have an automated method for feeding back experimental profile information to calibrate the parameters of the simulator. Figure 1 depicts the proposed framework that integrates the initial parameter extraction method with the parameter optimization method.
6 Unpatterned Photoresist Characterization Experiments (e.g. DRM, FTIR, Ellipsometry) Global Optimization of TCAD functions (using Simulated Annealing) Initial Values for TCAD parameters Parameter ID Front End TCAD Tool (e.g.prolith,solid-c) Simulated Profile TIMBRE VLB Global Optimizer Graphics Front End Experimental Profile Patterned Photoresist Experiments (e.g. FEM) FIGURE 1. Flowchart of the framework for automatic calibration of lithography simulators using a set of unpatterned and patterned photoresist characterization experiments 3. EXPERIMENTAL The experiments were divided into unpatterned experiments, using flood exposures, and patterned experiments. All the wafers were coated with a commercial chemically amplified resist at the standard processing conditions. Spectroscopic ellipsometry was used for all the thin film measurements. 3.1 Unpatterned Experiments We began with the Ellipsometry and FTIR experiments to extract parameters for the exposure and PEB modules. This involved three wafers that were each exposed with twenty-five different exposure doses ranging from 0 to 7.6 mj/cm 2, and each wafer was subjected to different PEB temperatures from 120 to 135 degrees Celsius. Before the exposure step, the anti-reflective coating and the resist was measured for thickness and optical constants (real and imaginary part of the refractive indices) using a spectroscopic ellipsometer. The thicknesses on all the 25 sites was measured again after the PEB step, thus yielding the deprotection Induced Thickness Loss (DITL) [4]. These wafers were then measured with a commercially available FTIR tool from Bio-Rad. The deprotection was measured by tracking the ester bond (1150 cm -1 peak). This experiment yielded deprotection vs. dose and temperature tables, as well as raw ellipsometry data containing thin film optical constant information.
7 We then conducted the Poor Man s DRM experiment using ten wafers with a range of exposure doses at different development times. This yielded develop-related thickness loss versus exposure doses, which was converted into develop rates versus concentration of unreacted sites. 3.2 Patterned Experiments We used two wafers for patterned experiments. A focus-exposure matrix (FEM) was done on each of the two wafers centered around dose-to-size (exposure dose required to produce the proper dimension of the resist feature) and optimum focus. The wafers were each patterned with three different line-space ratios for the FEMs, using quarter micron technology. These wafers were then cleaved and measured with cross-section CD-SEMs. 4. RESULTS AND DISCUSSION 4.1 FTIR The first model, the simplistic two-step acid quencher model, was used to extract Dill s C parameter, the relative quencher concentration [Q], the pre-exponent for acid amplification A amp, the exponent for acid amplification E amp, the pre-exponent for acid loss A loss and the exponent for acid loss E loss. The data, at three different temperatures, can be plotted in order to help estimate the inflection point. The data above the inflection point was then used to fit to Eq. 3 with the formula for [Acid] dose coming from Eq. 4. The fit is shown in Figure 2. Notice that we have used the existing formulation for m, which does not model the initial delay in the deprotection vs. dose curve well, and hence the only innovation introduced was the concept of the effective dose to estimate the relative quencher concentration. ln(a amp )= /s E amp = Kcal/mole Deprotection (1-m) ln(a loss )= /s E loss = Kcal/mole C = cm 2 /mj Q = (dose q = 2.674) Exposure Dose (mj/cm 2 ) FIGURE 2. Experimental and Fitted Values for Deprotection (1-m) vs. Exposure Dose as a function of 3 different temperatures (120C, 130C, 135C) with a 145C soft-bake, using Eq. 4. The second model attempts to extract the Dill s C parameter, the relative quencher concentration [Q], the pre-exponent for acid amplification A amp, the exponent for acid amplification E amp, the pre-exponent for the neutralization reaction A α and the exponent for the neutralization reaction E α. However, it models the data over the entire range of doses, and hence does not require any pre-processing. Using Eq. 10, the optimization procedure provides the fitted parameter values shown in Figure 3. Note that
8 the value of [Q] extracted from the second model is higher than that extracted from the first model, due to the latter accounting for parasitic bases in addition to the designed quencher. Also, the values of C, A amp and E amp extracted with both methods are similar. Deprotection (1-m) ln(a amp ) = /s E amp = Kcal/mole ln(a α ) = /s E α = Kcal/mole C = cm 2 /mj 0.1 Q = Exposure Dose (mj/cm 2 ) FIGURE 3. Experimental and Fitted Values for Deprotection (1-m) vs. Exposure Dose as a function of 3 different temperatures (120C, 130C, 135C) using Eq Modified Poor Man s DRM The development model was relatively straightforward to fit, and the results of the optimization are shown in Figure 4. The modified Poor Man s DRM algorithm was used for efficient parameter extraction R max = 2636 A/sec Develop Rate (A/sec) R min = A/sec n = m th = Normalized Concentration of unreacted sites (m) FIGURE 4. Develop rate versus the normalized concentration of unreacted sites. Figure shows the fitting of the Mack develop model [3] to the data
9 4.3 Patterned Profiles The objective of this section is to show how developed profiles can be used to further tune the models we discussed in Eq. 1 through Eq. 12. Cross-section SEM photographs of the patterned profiles were taken. These photographs were then digitized to yield ascii files that could directly be compared to the Prolith output files. The unpatterned experiments yielded most of the parameters mentioned in Table 1, and were given small ranges to account for experimental errors. However, some of the other parameters such as the pre-exponent and the exponent of the diffusivity, the relative focus of the simulator with respect to the actual stepper and the amplification order were given larger ranges to account for our limited knowledge about these numbers. We also assumed Dill s A and B parameters as specified by the resist vendor, with small ranges. The optimization process was carried out over 6 combinations of focus-pitch at optimum exposure dose and done with 14 parameters simultaneously. This took approximately 12 hours of CPU time on a 350 MHz P-II processor to converge to the error limit specified by us. Results of the fitted profiles are overlaid on the actual profiles in Figure PITCH 1 PITCH 2 FOCUS FIGURE 5. Fitted versus simulated profiles across different focus-pitch combinations. The optimization process was carried out over 14 parameters simultaneously and took approximately 12 hours on a 350 MHz P-II machine Table 4.1 summarizes the results of the parameter extraction and optimization procedure
10 Table 4.1. Final Values of Optimization of Critical Lithography Parameters ln(a amp ) /s R max 3914 A/sec E amp Kcal/mole R min 5.87 A/sec ln(a α ) /s n 13.6 E α Kcal/mole m th A 0.00 /µm n res B /µm k res C cm 2 /mj n arc 1.47 Q k arc ln(a diff ) nm 2 /s F µm E diff Kcal/mole O 1 5. CONCLUSIONS In the preceding sections, we have identified the lithography simulation parameters that we have found to be most critical to the lithography process and have proposed models for the combined exposure and PEB modules. The proposed model accounts for the gradual decrease in the quencher concentration rather than modeling it simply by assuming a constant base concentration throughout the PEB process, thus successfully modeling the latency in the experimentally observed deprotection vs. dose curves. In conjunction with a global optimization technique, we have outlined an experimental framework that allows for extraction of many of the above mentioned parameters using a minimum number of bake and develop experiments. The remaining parameters were then extracted using a commercial simulation-optimization package based on experimental patterned profiles. We believe this is the first successful attempt at methodically and automatically calibrating lithography simulation tools to complete experimental profile information based on a series of unpatterned and patterned characterization experiments. 6. ACKNOWLEDGEMENTS This work was supported by the MICRO under contract , and by the UC-SMART under contract MP REFERENCES [1] N. Jakatdar, et.al., Characterization of a Chemically Amplified Photoresist for Simulation using a Modified Poor Man s DRM Methodology, SPIE vol. 3332, pp , 1998 [2] J. Byers, et.al., Characterization and Modeling of a Positive Chemically Amplified Resist, SPIE vol. 2438, pp , 1995 [3] C.A. Mack, Development of Positive Photoresist, Jour. Electrochemical Society, Vol.134, No.1, Jan 1987, pp [4] N. Jakatdar, et.al. Characterization of a Positive Chemically Amplified Photoresist from the Viewpoint of Process Control for the Photolithography Sequence, SPIE vol. 3332, pp , 1998
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