I in semiconductor manufacturing. As a result, considerable

IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 9, NO. 3, AUGUST 1996 335 Development of a TiW Plasma Etch Process Using a Mixture Experiment and Response Surface Optimization David A. Shumate and Douglas C. Montgomery Abstract-The characteristics of SF6/He plasmas used to etch TiW have been studied with statistically designed experiments using a Tegal 804 single wafer system. Two processes were developed using both positive and negative photoresist as the mask material for etching TiW. The goal was to consolidate both processes into one. A two-phase experimental approach was taken to generate the processes. In phase 1 a fractional factorial screening experiment was used to identify key factors, and in phase 2 a mixture experiment was used for process optimization. The fractional factorial experiment was initially used to study the effects of reactor pressure, RF power, SF6/He gas ratio, overetch time, and hard bake. The results of this initial experiment were used to identify the appropriate levels for the main process parameters. Then, at these parameter levels, a mixture experiment was conducted using the partial pressures of SFe, He, and the nitrogen ballast as the design variables. Since the total pressure in the system is fixed, these three variables are the components of a mixture, and thus form a constrained design space for the experiment. Quadratic and special cubic response surface models were generated for the following responses: TiW etch rate, photoresist etch rate, selectivity between the TiW and photoresist, uniformity of all etch rates and selectivities, and critical dimension control for the photoresist and TiW. Contour plots for all responses as a function of the partial pressure of SFs, He, and nitrogen ballast were generated. The contours from these empirical models were analyzed jointly to optimize the processes. I. INTRODUCTION N recent years, plasma etching has become widely used I in semiconductor manufacturing. As a result, considerable effort has been devoted to characterizing and optimizing this complex process. Characterization usually focuses on developing models that describe the behavior of critical output responses to changes in the important input process parameters. Models for plasma etching have been developed using a variety of approaches, such as first engineering principles [ 11-[5], statistical experimental design including standard response surface methodology [7]-[ 131, a combination of these two approaches [14], and neural networks [15]. Because the complexity of modern plasma etch technology is currently ahead of the theoretical modeling efforts, empirical models based on statistically designed experiments Manuscript received June 1, 1995; revised February 7, 1996. D. A. Shumate is with the Semiconductor Product Sector, Motorola Inc., Phoenix, AZ 85064 USA. D. C. Montgomery is with the Department of Industrial Engineering, Arizona State University, Tempe, AZ 85287-5906 USA. Publisher Item Identifier S 0894-6507(96)05672-2. and response surface methodology have been widely used. Motorola Semiconductor Product Sector conducts extensive training on experimental design for engineering personnel, and both standard response surface methodology and mixture experiments are used within the organization for process optimization. Implementation of these tools has resulted in substantial yield improvements and cycle time reduction. This paper presents the development and optimization of a SF6/He plasma etch for TiW using a Tegal 804 single wafer etch system. The process is used to pattern TiW over a layer of Au using both positive and negative photoresist (PR) as the masking agent. A pattern is etched into the TiW stopping on the Au. Essentially, there are two processes, one for positive PR, and another for negative PR. The goals of the experiment were to model and consolidate both positive and negative PR etch processes and establish a manufacturing process with the following specifications: 1) Delta critical dimension (CD) positive PR < 0.25 pm; 2) Delta CD negative PR < 0.25 pm; 3) Positive PR etch uniformity < 2.5%; 4) Negative PR etch uniformity < 2.5%; 5) Selectivity (TiW: positive PR) > 0.85; 6) Selectivity (TiW: negative PR) > 0.85; where uniformity = (standard deviatiodmean) x 100. The approach used in this study is to initially characterize the system in terms of five primary process parameters using a fractional factorial experiment. The results of this experiment were then used to determine the desired target levels for these process parameters. Then, at this set of factor levels, a three-component mixture experiment was performed using the three gases SF6, He, and N2 ballast as the variables in the mixture design. The choice of this design will be discussed in the next section. The partial pressure of all three gases were forced to add to a constant value of total pressure to form the mixture constraint. The logic behind this experimental strategy is discussed more fully in the next section. During the mixture experiment, seven response variables were measured. The responses, test vehicles, and methods are as follows, respectively: 1) TiW etch rate, used TiW over a silicon wafer, delta thickness was measured before and after etching; 2) Delta CD positive PR, patterned 3 pm lines using positive PR on top of a layer of Au, CD were measured before and after etching; 0894-6507/96$05.00 0 1996 IEEE

336 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 9, NO. 3, AUGUST 1996 3) Delta CD negative PR, patterned 3 pm lines using positive PR on top of a layer of Au, CD were measured before and after etching; 4) Positive PR etch rate and etch uniformity, positive PR on top of silicon wafer, measured PR thickness before and after etching; 5) Negative PR etch rate and etch uniformity, negative PR on top of silicon wafer, measured PR thickness before and after etching; 6) Selectivity TiW: positive PR, calculated ratio of two etch rates; 7) Selectivity TiW: negative PR, calculated ratio of two etch rates. Note that the TiW etch rate was only used in the two selectivity calculations. Thus, the main responses from the experiment were items 2-7 listed above, thereby giving a total of six responses. The gauges used to measure the changes in test vehicles are as follows: 1) Prometrix 600; measured PR thickness before and after etching, 49 sites per wafer. The average, standard deviation and uniformity (standard deviatiodmean) were determined with this system; 2) ITP 850; measured line widths before and after etching, 5 sites per wafer. The average CD was determined with this system; 3) Metler; measured TiW thickness before and after etching. The average thickness was determined with this system. The six responses were modeled using quadratic and special cubic mixture polynomials. These models will be presented in Section 111 of this paper. Response surface contours plots were generated for all response variables considered, and the process was subsequently optimized by combing these individual response surfaces graphically. The results of this graphical optimization revealed an operating region that would satisfy all of the process specifications. To validate the results, confirmation runs were conducted at the optimum conditions predicted by the model. These confirmations runs were successful and the process was subsequently introduced into manufacturing. 11. EXPERIMENTAL STRATEGY AND DESIGNS The Performance of the etch system can be described in terms of seven factors. Four of these factors are process variables: reactor pressure, RF power, overetch, and hard bake. The other three factors are the partial pressures of the gases SFG, He, and N2 that are introduced into the etching chamber. We refer to the first four factors as process variables because they can be independently adjusted. The partial pressures of the gases are mixture variables; that is, these factors are measured on a partial pressure basis and the sum of the partial pressures must add to the total pressure that has been selected for etch system operation. In general, a mixture experiment is a special class of experiment where the design variables are the components of a mixture. These components are measured by their proportion- ate amounts (usually on a weight, volume, mole ratio, or, as in this case, partial pressure basis), and the response variables depend only on the component proportions that are present, not their absolute amounts. See Myers and Montgomery [16], Come11 [17], and Montgomery [18] for more discussion of mixture experiments. Because of this feature, in any trial of a mixture experiment, the sum of the component proportions must be constant. In this problem, the mixture constraint is where 2 1 = partial pressure of SFG, 22 = partial pressure of He, 23 = partial pressure of N2 (ballast), and P is the total pressure selected for the system. The problem of optimizing etch performance involves a combination of process variables and mixture variables. Furthermore, one of the process variables, total pressure, is involved in the mixture constraint. Thus, the type of experimental design required is called a mixture experiment with process variables and a mixture-amount variable (see [16] and [17] for more details). Investigating all of these factors simultaneously would require a large number of runs. To illustrate, suppose that each of the four process variables were run at two levels. As we will subsequently discuss, it will require a minimum of seven runs to adequately model the mixture variables. An experimental design that simultaneously investigates all of the factors would require that the mixture runs be performed at each of the 16 combinations of the process variables. Therefore, the number of runs in the combined design is at least 16 x 7 = 112. If a fractional factorial is used in the two-level process variables, then the number of runs could be reduced to 56. This is still a prohibitively large number of runs for a single experiment. In situations such as this, a sequential strategy of experimentation is suggested (see Myers and Montgomery [16], Montgomery [18], and Box, Hunter, and Hunter [19] for in-depth discussion of sequential experimentation). Such an approach usually allows fewer overall tests to be conducted, and takes advantage of growing process knowledge at earlier stages to design more efficient experiments in subsequent stages. A sequential strategy of experimentation was adopted in this study. In the first phase we used a 25-1 resolution V fractional factorial design. The details of constructing this design are presented in Montgomery [ 181 and Box, Hunter, and Hunter [19]. This design gives estimates of the main effects that are aliased with four-factor interactions and estimates of two-factor interactions that are aliased with three-factor interactions. Therefore, based on our belief that the higherorder interactions were negligible, this design provided good estimates of all main effects and two-factor interactions. The five variables used in this characterization experiment were reactor pressure (550-750 micro torr), RF power (100-200 W), overetch (0.1-0.2 min), SF& e gas ratio (40/50-60/50 sccdsccm), and hard bake (no-yes). The design included four center points so that an estimate of experimental error could be obtained, and a check on second-order curvature in the response variables could be performed.

SHUMATE AND MONTGOMERY: DEVELOPMENT OF A TiW PLASMA ETCH PROCESS 331 TABLE I RESULTS FROM THE FRACTIONAL FACTORIAL EXPERIMENT Over all results I I I I I I I I I I a,.- N L- c.- a, c 0, - z c. z E - C 3 T 8 3 1 Notice that this 20-run design includes the four process DESIGN POINTS variables and that it also includes the mixture variables through Xi ( 22().,micron) the ratio SF6/He. The purpose here is to incorporate the effects....., :'.. I. of gas mixture into the experiment, so that if there is a large,..... interaction between the process variables and the gas mixture, the correct levels of the process variables will be selected for the final stage of the optimization experiment. The effects of these design factors on the six responses defined previously were determined, and an analysis of variance was performed for each response. Normal probability x3 330 plots of the residuals were generated for each response and all model diagnostics analyzed were satisfactory. Furthermore, the residuals gave no indication of problems with nonconstant variance or time trends in the data. Table I is a display 11 indicating the nature of the effect that each of the design variables has on the six responses. Based on careful study of the results from the characterization experiment, we concluded the following: X2 ( 220 micron) X1 ( 100 micron) X3 ( 450 micron) b Power: use the high level as this yielded the best selectivity ; Fig, 1, The design. 0 Pressure: results were mixed for some responses but the of the SF6, He, and the N2 ballast was used in the next phase of middle level (the design center point) yielded the best the study. This design included the N2 ballast partial pressure overall results; as a variable (even through it is not involved in the etch 0 Overetch: the low level gave the best results but some reaction) because it is required to maintain the total system wafers had excess metal, so the center point was chosen; pressure at 650 p torr. (micrometers). Therefore, the mixture 0 Hard bake: the low level (no bake) yielded the best delta constraint given earlier as (1) can be rewritten as CD and selectivities; 0 SF6/He ratio: this variable is very important, and will be 21 + 2 2 + 23 = 650 micrometers (2) optimized in the next phase of the study. The fractional factorial design indicated that the composition of the SF6-He gas mixture was critical to etch performance. Furthermore, total reactor pressure of 650 pm is an excellent target operating pressure for the system. A threecomponent mixture experiment involving the partial pressure where 21 = partial pressure of SFs, 22 = partial pressure of H~, and 23 = partial pressure of N~. addition, the partial pressures of SF^ and H~ were constrained as follows: 100 micrometers < 21 < 160 micrometers 100 micrometers < 2 2 < 160 micrometers.

338 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 9, NO. 3, AUGUST 1996 TABLE I1 THE MIXTURE EXPERIMENT AND THE OBSERVED RESPONSES It is customary to represent a three-component mixture design space graphically as a simplex on which trilinear coordinates are superimposed. Fig. 1 presents the design space for this problem with the partial pressure constraints for SFG and He applied. When the constraints are imposed, the feasible design space is the polytope shown in the lower right-hand corner of the figure. When the mixture space is an irregular polytope, the standard mixture design techniques discussed in references [ 161-[ 181 cannot be used, and some computer-based design construction algorithm must be employed to generate an appropriate experimental design. There are several types of computer-based design generation algorithms that are appropriate for mixture experiments. One of these is the D-optimal point selection criterion, which chooses the design points to minimize the variance of the regression coefficients in the fitted response surface model. While D-optimal is only one choice among several alphabetic-optimality design criteria, it is widely implemented on computer software, and usually gives satisfactory results. Another procedure is the distance-based point selection criterion. This criterion attempts to spread the design points out relatively uniformly over the region of interest to obtain information about the response from all parts of this region. Both of these are good criteria fm designing mixture experiments in constrained regions. The D-optimal criteria has a tendency to concentrate points at the vertices of the region. Because some of the responses used in this study were expected to exhibit strong nonlinear behavior over the constrained region shown in Fig. 1, we elected to use the distance-based criterion. The distance-based point selection algorithm in the Design- Expert software system [20] was used to choose the eleven points shown in Fig. 1. The distance-based procedure will typically select vertices of the constrained region, and then, as noted above, it will spread the remaining design points out as uniformly as possible over the region. This design would be adequate to support the Scheffk quadratic mixture model Notice that this model has six unknown parameters (the p s) and no intercept term. The intercept term is not included because of the constraint (2) on the mixture component proportions. Only six runs would be required to estimate the model parameters in (3); therefore, the design employed will have five degrees of freedom to examine the quadratic model for lack of fit. If necessary, the model could be expanded by adding cubic terms. The four vertices of the design were also replicated to reduce the leverage, or potential influence, that these points would have on the fitted response surface polynomial, and to provide an estimate of experimental error. For more details concerning computer-aided construction of experimental designs, see Myers and Montgomery [16], Cornel1 [17] and Montgomery and Voth [21]. A total of 15 experimental runs were required for this experiment. This design provides four degrees of freedom for pure experimental error. Table I1 presents the 15 runs used in this design and the observed responses. 111. RESPONSE SURFACE MODELS We used standard least-squared model-building techniques for all six responses. The approach was to initially fit the

SHUMATE AND MONTGOMERY: DEVELOPMENT OF A TiW PLASMA ETCH PROCESS 339 R2 Adj R2 Residual D. F. 0.88 0.90 0.61 0.92 0.93 0.83 0.81 0.84 0.31 0.87 0.89 0.72 9 9 8 9 9 9 DELTA CD POSITIVE PR SF6 ( 220 micron) POSITIVE PR UNIFORMITY SF6 ( 220 microns) N2 ( 330 micron) N2 ( 330 microns) K -, He ( 100 microns) b=.................................................... He ( 220 micron) SF6 ( 100 micron) N2 ( 450 micron) Fig. 2. Delta CD positive photoresist. He ( 220 microns) SF6 ( 100 microns) NZ ( 450 microns) Fig. 3. Positive photoresist uniformity simplest model possible, the Scheffk linear mixture model, consisting of only the linear terms in (3). For all responses, the linear model displayed statistically significant (a = 0.05) lack of fit. Then we added the quadratic terms (the pijx~x, terms) to complete the model in (3). The quadratic terms were statistically significant for all six responses. However, the model for the Delta CD negative PR response variable still had statistically significant lack of fit; consequently, we

340 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 9, NO. 3, AUGUST 1996 DELTA CD NEGATIVE PR SF6 (220 micron) SELECTIVITY, POSITIVE PR:TiW SF6 ( 220 micron) N2 ( 330 micron) Fig. 4. Delta CD negative photoresist. Fig. 6. Selectivity, positive photoresist: TiW. NEGATIVE PR UNIFORMITY SF6 (220 micron) SELECTIVITY, NEGATIVE PR:TiW SF6 ( 220 micron) N2 ( 330 micron) He ( 220 micron) SF6 (100 micron) Fig. 5. Negative photoresist uniformity \ N2 ( 450 micron) He ( 220 micron) SF6 ( 100 micron) N2 (450 micron) Fig. I. Selectivity, negative photoresist: TiW. fit the special cubic model Y = PIX1 + Pzxz + P323 + P12x1x2 + P13xlx3 f P23x2x3 + P123xlxZx3 + (4) for this response. Lack-of-fit was no longer significant for this response. Some of the response variables used in this study are typically difficult to model with response surface regression techniques, because of the strong nonlinear behavior they often exhibit and occasional departures from regression assumptions, such as equality of variance over the design region. It is always essential to check these assumptions though residual analysis, as described in [16], [18], and [19]. We examined plots of the residuals versus predicted response, residuals versus run order and normal probability plots of the residuals. No substantial departures from the underlying assumptions were noted. If these problems are present, the use of data transformations or other model-fitting techniques as described in [16], [17], and [19] will be required. The Design-Expert software package was used to perform the statistica1 modeling and analysis. Table 111 presents the least squares estimates of the regression coefficients along with the standard summary statistics for each model. The values of the model summary statistics are within reasonable levels for models built to data from a designed experiment. Note that adding the special cubic term to the model for the Delta CD negative PR response did not drastically affect the number of residual or error degrees of freedom available for statistical testing. Even if other full cubic terms were added, there would always be at least four degrees of freedom available for statistical testing because of the replicated runs at the design vertices. In situations were one is building up the order of a

SHUMATE AND MONTGOMERY, DEVELOPMENT OF A TiW PLASMA ETCH PROCESS 341 PROCESS ~ ~ ~ POSITIVE ~ PR I ~ PROCESS T I OPTIMI2XTlON ~ ~ NEGATIVE PR PROCESS OPTIMIZATION BOTH PROCESSES Fig. 8. Region of optimum operating conditions. (a) Positive photoresist. (b) Negative photoresist. (c) Combined process for both positive and negative photoresist. model sequentially using data from a designed experiment, this number of residual degrees of freedom would usually allow acceptable statistical sensitivity. A final point to note is that the regression coefficients in Table I11 are displayed in terms of pseudocomponents variables, defined as where 2; is the actual level of the ith mixture variable and Li is the lower bound on the constraint for the ith mixture variable. As noted in [16], [17] and [21], it is best to fit (4) mixture models over constrained design regions in terms of pseudocomponents because it minimizes the ill-conditioning in the least-squares normal equations that is an inherent aspect of the mixture problem. One of the principal reasons we selected the Design-Expert software package was that it incorporated this model-fitting feature. Figs. 2-7 are the contour plots for the six responses over the feasible portion of the constrained mixture space, in terms of the actual ranges of the mixture components. These plots were generated with the Design-Expert software. Notice that all six contour plots display relatively strong curvature, an indication of the nonlinear blending effects of the SFG and He plasma mixture.

342 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 9, NO. 3, AUGUST 1996 The most significant reason for using mixture experiments for modeling plasma etching in contrast to other more traditional experimental design methods is that the mixture approach provides better models of the uniformity responses. Controlling etch uniformity is one of the most important factors in generating a repeatable production process, particularly when the line widths are in the sub-micrometer range. The only successful way in which we have fully modeled the plasma etch system has been to use the mixture experiment approach. The uniformity response in this experiment is defined as the standard deviation divided by the mean. Modeling the nonlinear behavior of a standard deviation is a significant challenge. Traditional experimental design and response surface methods are usually successful in producing a model for the mean, but often fail when they are used to model the standard deviation. We have found that the mixture experiment approach is very helpful in solving this problem. IV. SYSTEM OPTIMIZATION The objective of this study was to achieve the defined process specifications listed in the introduction to the paper. Specifically, it is necessary to identify a set of operating conditions for the process variables that produce desired or target values for all six responses. Optimal operating conditions for pressure, power, overetch, and hard bake were established via the fractional factorial characterization experiment, and the response surface generated from the mixture experiment can be used to optimize the gas mixture formulation. The original goal of this project was to develop a process to etch TiW with high CD control and to stop on Au. While there are several numerical optimization techniques that could be applied to this problem, we chose to overlay the responses surface contours corresponding to the above objectives for each response on the same set of trilinear coordinates. This graphical optimization procedure is particularly effective with three-component mixtures, because it allows the process engineer to visually determine how large the operating window is for the process. If more than three components are present on the mixture, then numerical optimization must be used. A standard nonlinear optimization procedure such as the GRG2 method usually works well. Fig. 8(a) and (b) shows the overlay plots of the responses, variables for positive PR, and negative PR, respectively. The unshaded area shown in each parts of the figure is the region or operating window where all response objectives will be satisfied. From examining these displays, we note there are many different blends of the three gases that will produce satisfactory results. Furthermore, there is a region for which both the positive PR and negative PR responses can be simultaneously optimized, as shown in Fig. 8(c). Therefore, it is possible to combine both the negative and positive PR processes into a single manufacturing process, one of the original process development objectives. We computed the predicted mean value of each response and the associated standard error of prediction at several points in the operating window. To assess the magnitude of prediction error, we also computed 95% confidence limits on the mean response. Table IV contains the results of this study for one TABLE IV PREDICTED RESPONSES, STANDARD ERROR, AND 95% CONFIDENCE LIMITS AT OPERATING CONDlTIONS of these candidate operating points. The confidence intervals are not unreasonably wide. To further check the validity of our results, confirmation runs were made by conducting actual tests at different points both inside and outside the operating window shown in Fig. 8(c). The data from the confirmation runs closely matched the predicted results from the mixture response surface models. Furthermore, when the process was introduced into full-scale production, and actual product was manufactured at locations inside the window, these actual production units also closely matched the predicted results. V. CONCLUSION This paper has presented the characterization and optimization of a TiW plasma etch process using a two-stage approach, based on statistically designed experiments. The first stage consisted of a fractional factorial experiment, and this was followed by a mixture experiment in the second stage. The mixture experiment and the resulting response surface models proved to be an excellent procedure for modeling and optimizing the gas mixture in a plasma etch system. Previous characterization studies of this system based on classical fractional factorial and response surface designs that did not treat the problem as a mixture experiment had not provided satisfactory results. We have found that mixture experiments and their associated response surface modeling and optimization techniques are particularly useful for developing new plasma etching processes or improving existing process performance. REFERENCES M. S. Barnes, T. J. Cotter, and M. E. Elta, Large-signal, time-domain modeling of low-pressure RF glow discharges, J. Appl. Phys., vol. 61, no. 1, Jan. 1987. A. Paranjpe, J. McVittie, and S. A. Self, Numerical simulation of 13.56 MHz symmetric parallel plate RF glow discharges in argon, in Proc. 41st Gas. Elec. Con$, Oct. 1988. S. K. Park and D. J. Economou, Parametric study of radio-frequency glow discharge using continuum model, J. Appl. Phys., vol. 68, no. 9, Nov. 1990. T. J. Cotler, M. S. Barnes, and M. E. 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SHUMATE AND MONTGOMERY DEVELOPMENT OF A TiW PLASMA ETCH PROCESS 343 [8] P. E. Riley and D. A. Hanson, Study of etch rate characteristics of SF6/He plasmas by response surface methodology: Effects of interelectrode spacing, IEEE Trans. Semiconduct. Manufact., vol. 2, no. 4, Nov. 1989. [9] E. Gogoledes and H. H. Sawin, nf-polysilicon etching in CC14/He discharges: Characterization and modeling, J. Electrochem. Soc., vol. 136, no. 4, Apr. 1989. [lo] P. E. Riley, A. P. Turley, and W. J. Malkowski, Development of a multistep Si02 plasma etching process in a minibatch reactor using response surface methodology, J. Electrochem. Soc., vol. 136, no. 4, Apr. 1989. [l 11 P. C. Kmlkar and M. A. Wirzbicki, Characterization of etching of silicon dioxide and photoresist in a fluorocarbon plasma, J. Vac. Sci. Tech. B., vol. 6, no. 5, Sept.-Oct. 1988. [12] B. E. Thompson and H. H. Sawin, Polysilicon etching in SF6 RF discharges, J. Electrochem. Soc., vol. 133, no. 9, Sept. 1989. [13] M. Jenluns, M. Mocella, K. Allen, and H. Sawin, The modeling of plasma etching processes using response surface methodology, Sol. St. Tech., Apr. 1986. 1141 K. Lin and C. Spanos, Statisucal equipment modeling for VLSI manufacturing: An application for LPCVD, IEEE Trans. Semiconduct. Manufact.. vol. 3. no. 4. Nov. 1990. C. D: Himmell and G. S. May, Advantages of plasma etch modeling using neural networks over statistical techniques, IEEE Trans. Semiconduct. Manufact., vol. 6, no. 2, May 1993. R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments. New York Wiley, 1995. J. A. Comell, Experiments with Mixtures, 2nd ed. New York Wiley, 1990. D. C. Montgomery, Design and Analysis of Experiments, 3rd ed. New York Wiley, 1991. G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters. New York Wiley, 1978. Design-Expert Users Manual, version 4.0, Stat-Ease, Inc. Minneapolis, 1994. D. C. Montgomery and S. R, Voth, Multicollinearity and leverage in mixture experiments, J. Qual. Tech., vol. 26, no. 2, Apr. 1994. David A. Shumate received the M.S. degree in electrical engineering from Georgia Institute of Technology, Atlanta, and the B.S. degree in ceramic engineering from The University of Illinois, Urbana. He is a Characterization Engineer in the Semiconductor Sector, Power Products Division, Motorola Inc., Phoenix, AZ. He has worked in the semiconductor manufacturing area for eight years, and as a characterization engineer for two years. Douglas C. Montgomery received the Ph.D. degree in engineering from Virginia Polytechnic Institute, Blacksburg. He is Professor of Engineering at Arizona State University, Tempe. His professional interests are in the development and application of statistical methodology for problems in engineering and the sciences. He is the author of ten books and numerous technical papers. Dr. Montgomery was the recipient of the Ellis R. Ott Award, and both the Shewell Award and the Brumbaugh Award from the American Society for Quality Control. He is a Fellow of the American Statistical Association, the American Society for Quality Control, and the Institute of Industrial Engineers. He is currently the Editor of the Journal of Quality Technology.