Phororesisr Exposure Kinetics 8 5 B}? measuring the incident exposing light intensity. the output of the experiment becomes overall transmittance as a function of incident exposure dose, RTE}. Figure 55 shows a typical result. Assuming careful measurement of this function, and a knowledge of the thickness of the photoresist. all that remains is the analysis of the data to extract the ABC parameters. Dill proposed two methods for extracting the parameters [5.4]. Those methods will be reviewed here and a third more accurate approach will be shown. Note that the effectiveness of this measurement technique rests with the non-zero value of A. If the photoresist does not change its optical properties with exposure (is. if A = 0). then measuring transmittance will provide no insight on the exposure reaction, making C'unohtainable by this method. Trans mittanuc D 200 400 EDD EDD 1000 - '3' Exposin'c Dose [in] our) Figure 5-5. Typical transmittance curve of a positive g- or iIine bleaching photoresist measured using an apparatus similar to that pictured in Figure 54. 86 Inside PROLITH 1. Graphical Data Analysis (Method 1) Analysis of the experimental data is greatly simplified if the experimental conditions are adjusted so that the simple exposure and absorption equations (5.23) and (5.24) apply exactly. This means that light passing through the resist must not reflect at the resist/substrate interface. Further, light passing through the substrate must not reflect at the substrate/air interface. The first requirement is met by producing a transparent substrate with the same index of refraction as the photoresist. The second requirement is met by coating the backside of the substrate with an interference-type antireflection coating (ARC). Given such ideal measurement conditions, Dill showed that the ABC parameters can be obtained from the transmittance curve by measuring the initial transmittance 7(0), the final (completely exposed) transmittance T(co), and the initial slope of the curve. The relationships are: A = I(00) D T(0 ) (5.43a) B = - 1In( I(00) ) (5.43b) D C = A + B dT (5.43c) AT(0)(1-T(0)}712 dE E=0 where D is the resist thickness and 712 is the transmittance of the air-resist interface and is given, for a resist index of refraction nresist, by I12 = 1- nresist (5.44) nresist + 1Photoresist Exposure Kinetics 87 2. Differential Equation Solution (Method 2) Although graphical analysis of the data is quite simple, it suffers from the common problem of errors when measuring the slope of experimental data. As a result, the value of C (and to a lesser extent, A) obtained often contains significant error. Dill also proposed a second method for extracting the ABC parameters from the data. Again assuming that the ideal experimental conditions had been met, the ABC parameters could be obtained by directly solving the two coupled partial differential equations (5.23) and (5.24) and finding the values of 4, B, and C for which the solution best fits the experimental data. Obviously, fitting the entire experimental curve is much less sensitive to noise in the data than taking the slope at one point. Several techniques are available to provide a simple numerical solution [5.8-5.10]. 3. Full Simulation (Method 3) Methods 1 and 2 give accurate results only to the extent that the actual experimental conditions match the ideal (no reflection) conditions. In reality, there will always be some deviation from this ideal. Substrates will invariably have an index somewhat different that of the photoresist. And since the index of refraction of the photoresist changes with exposure, even a perfect substrate will be optically matched at only one instant in time during the experiment. Backside ARCs may also be less than perfect. In fact, most experimenters would prefer to use off-the-shelf glass or quartz wafers with no backside ARC. Under these conditions, how accurate are the extracted ABC parameters? The dilemma can be solved by eliminating the restrictions of the ideal experiment. Rather than solving for the transmitted intensity via equations (5.23) and (5.24), one could use a lithography simulator to solve for the transmittance in a non-ideal case including changes in the resist index of refraction during exposure and reflections from both the top and bottom of the substrate. Then, by adjusting the ABC parameters, a best fit of the model to the data could be obtained. This method provides the ultimate accuracy in obtaining extracted ABC parameters [5.20]. All three methods described above have been incorporated into ProABC.(2) From the graph below, determine A, B, and C the dill parameters. 0.9 0.8 0.7 0.6 0.5 Transmittance 0.4 0 200 400 600 800 1000 Exposure Dose (mJ/cm ) Figure 5-5. Typical transmittance curve of a positive g- or i-line bleaching photoresist measured using an apparatus similar to that pictured in Figure 5-4. Hint: Read Inside_prolith.pdf from the ref section: text pages 85-87