반도체디스플레이기술학회지 제20권 제2호(2021년 6월) Journal of the Semiconductor & Display Technology, Vol. 20, No. 2. June 2021.
CFD Study for the Design of Coolant Path in Cryogenic Etch Chuck
Soo Hyun Jo * , Ji Hee Han ** , Jong Oh Kim * , Hwi Han * and Sang Jeen Hong ***†
* Department of Mechanical Engineering, Myongji University,
** Department of Industrial Management Engineering, Myongji University,
***† Department of Electronics Engineering, Myongji University, LINC+ Semiconductor Equipment Engineering Program, Myongji University
ABSTRACT
The importance of processes in cryogenic environments is increasing in a way to address problems such as critical dimension (CD) narrow and bottlenecks in micro-processing. Accordingly, in this paper, we proceed with the design and analysis of Electrostatic Chuck(ESC) and Coolant in cryogenic environments, and present optimal model conditions to provide the temperature distribution analysis of ESC in these environments and the appropriate optimal design. The wafer temperature uniformity was selected as the reference model that the operating conditions of the refrigerant of the liquid nitrogen in the doubled aluminum path were excellent. Design of simulation (DOS) was carried out based on the wheel settings within the selected reference model and the classification of three mass flow and diameter case, respectively. The comparison between factors with p-value less than 0.05 indicates that the optimal design point is when five turns of coolant have a flow rate of 0.3 kg/s and a diameter of 12 mm. ANOVA determines the interactions between the above factor, indicating that mass flow is the most significant among the parameters of interests. In variable selection procedure, Case 2 was also determined to be superior through the two- Sample T-Test of the mean and variance values by dividing five coolant wheels into two (Case 1 : 2+3, Case 2: 3+2).
Finally, heat transfer analysis processes such as final difference method (FDM) and heat transfer were also performed to demonstrate the feasibility and adequacy of the analysis process.
Key Words : Cryogenic etch, Wafer temperature uniformity, CFD, DOS, ANOVA, Heat transfer
1. Introduction
1Semiconductor industry has seen the need for research and development of ultra-fine processes as demands for improved integration and increased productivity have increased [1]. Research is under way to overcome this development of technology, as it simultaneously raises several issues during the manufacturing process. Critical dimension (CD), defined as the minimum line width distance between patterns, has a significant impact on-line
† E-mail: [email protected]
width refinement and aggregation and generates multiple Issues at the same time, which is currently considered one of the critical parameters of ultrafine processes.
Etching process, which is one of the core processes of
semiconductor process, is a process that creates circuit
patterns on semiconductors by selectively removing desired
parts. Polymer can be accumulated on the side of the etched
sidewall of the pattern, causing passivity, which prevents the
electrically unaffected polarity radical from touching the
sidewall, preventing chemical reactions [2]. However, with
the development of ultra-fine processes, CDs become
narrower, resulting in the accumulation of polymers on the
CFD Study for the Design of Coolant Path in Cryogenic Etch Chuck 93
side wall, resulting in bottlenecks. This interferes with CD Uniformity and gradually narrows the entrance of the pattern, which makes it a major issue in the etching process.
To solve bottlenecks caused by CD refinement, cryogenic etching process has been emerged [3]
Cryogenic etching refers to a process in which the temperature of the chamber is created at cryogenic temperature to minimize the activity of polymers and other gases. Due to the degradation of gas activity in these environments, bottlenecks and wafer contamination and loading effects are minimized. Accordingly, a design and analysis study of the coolant shape inside the ESC which can control the temperature distribution of the Wafer during the above process, is required [4].
First, in this Study, we design the Coolant Model through computational fluid dynamic (CFD) and interpret the thermal distribution. In the process, the controllable factors of the flow rate, number of turns, and coolant diagram are set. Second, we determine the level of the Factor with Design of simulation (DOS) and derive a regression expression for the model through ANOVA to determine which Factor has a large effect on the temperature distribution. Finally, we present the final model of ESC and coolant in cryogenic etching processes through a comparison of two-Sample T-Test and heat transfer calculation of the two selected models.
2. Simulation Detail 2.1 Initial Design
The cooling water pipe is designed to have a wide contact area while avoiding interference with lift pin, helium (He) gas line, electrodes, etc. The flow of the fluid used in the analysis is set to k-ε model assuming no turbulence occurs.
Type of coolant and refrigerants are set to aluminum and liquid nitrogen, which are currently used in most industrial sites. After the refrigerant in the tube was set at a flow rate of 0.2 kg/s and a temperature of 70 K, the analysis was carried out. At the beginning of the interpretation, the desired objective was a uniform heat distribution on the surface of the coolant, so we replaced the heat transfer coefficient (20 w/m 2 K), radiation (1000 K), convection (10,000 K) and radiation (1) on the top of the coolant to give uniform heat across the wafer. The experiment was conducted through simulation. The results of the analysis
were visually identified to derive first-order results, and the maximum temperature, mean, minimum temperature, thermal distribution, and temperature values at specific locations of the wafer were extracted.
2.2 Design Option
To select the reference model, the primary interpretation results were derived by substituting the Default ANSYS Tool above. Basically, the pipe shape is designed from a conventional single path to a double path to minimize the time the refrigerant travels by making the pipe large while simultaneously shortening the length of the pipe.
Among them, the best temperature distribution was determined by separating the path inside and outside the cooler and making it easier to control the temperature of the edge part. Based on this, the final reference model was selected.
Fig. 1. Reference model.
3. Analysis 3.1 Design of Simulation
3.1.1 3 Factors, 2 Levels Box-Benhnken
Based on the preceding elements, we extract controllable factors among the design factors and proceed with the 3- factors 2-levels Box-Benhken response surface analysis.
Table 1. below shows the experimental factors and their
levels. Each factor A, B, and C represents the number of
winds in the path, the diameter of the path, and the flow rate
of the refrigerant. Through this, we designed a total of 27
models, ranging from the minimum Level model to the
Maximum Level model, and conducted a total of 30
simulations by repeating three simulations at center point.
Soo Hyun Jo, Ji Hee Han, Jong Oh Kim, Hwi Han and Sang Jeen Hong 94
Table 1. 3 factors, 2 levels experimental design
A B C
Level 1 3 8 0.1
Level 2 5 12 0.3
The response variable for the analysis was specified as the maximum temperature minus the minimum temperature, and the confidence level was set at 95%. In response surface regression, the interaction of diameter*flow rate and wheel count*diameter*flow rate was pooled, and R-sq was 97.2%
R 2 -adj was 96.2% with relatively high reliability. In other words, we found that the effect of selected factors on the ESC temperature distribution was statistically significant.
Primary terms, secondary terms, and interaction terms have been shown to be significant, and it is primary terms that drive the overall response.
Y = 24.8774 -37.7449 A +24.4812 B -214.649 C
+7.72439 A*A-0.69098 B*B +657.814 C*C -2.49450 A*B -39.3349 A*C (1) Table 2. Estimated regression coefficients for Max-Min
Term Coef. SE Coef. T p
Constant 26.405 0.9922 26.611 0.000 A -8.762 0.6076 -14.42 0.000
B 1.842 0.6076 3.032 0.006
C -11.006 0.6076 -18.114 0.000 A*A 7.724 0.8944 8.636 0.000 B*B -2.716 0.8944 -3.037 0.006 C*C 6.548 0.8944 7.321 0.000 A*B -4.989 0.8593 -5.806 0.000 A*C -3.933 0.8593 -4.577 0.000
Table 3. Analysis of variance for Max-Min
Source DF Seq SS Adj SS Adj MS F p Regression 8 4351.85 4351.85 543.98 92.09 0.00
Linear 3 3220.79 3220.79 1073.60 181.74 0.00 Square 3 808.16 808.16 269.39 45.60 0.00 Interaction 2 322.90 322.90 161.45 24.33 0.00 Res. Error 21 124.05 124.05 5.91
* *
Lack-of-Fit 4 124.05 124.05 31.01 Pure Error 17 0.00 0.00 0.00
Total 29 4475.90
Table 4. Estimated regression
Term Coefficient
Constant 24.8774
A -37.7449
B 24.4812
C -214.6490
A*A 7.7244
B*B -0.6791
C*C 654.8140
A*B -2.4945
A*C -39.3349
We derive a regression expression using uncoded data to understand the influence and interaction of each factor on the model and use it as a single model that can be substituted for a real model. The coefficients of each term show that the flow rate has the greatest effect on minimizing the Max-Min value of the temperature.
3.1.2 Selecting the optimal design point
’The optimal design points for minimizing Max-Min values of the preceding model's temperature are A=5, B=12, and C=0.3 as shown in Fig. 1. Furthermore, since there is no star point, it is safe to assume that all design points are within the safe operating area.
Figures 2, 3 and 4 are contour plot for identifying optimal design intervals based on simulation results. At this time, the diameter was not shown to have a significant impact on the outcome, and it seems that each contour plot is led by flow rate. Given that it has been shown to be more sensitive to the number of wheels and flow rate compared to the diameter, it
Fig. 2. Contour Plot of Max-Min VS B, A.
CFD Study for the Design of Coolant Path in Cryogenic Etch Chuck 95
Fig. 3. Contour Plot of Max-Min VS C, A.
Fig. 4. Contour Plot of Max-Min VS C, B.
can be interpreted as a result that in later modeling, it is desirable to keep the diameter at 10 mm or higher and set to 5 turns and 0.3 kg/s, respectively.
After the optimal design point setting, we design two models with different numbers of inner and outer paths.
Model 1 has two inner paths and three outer path, Model 2 has three inner paths and three outer paths. Each model measured 65 point temperatures on a total of eight circles, including the origin, at intervals of 20 mm.
In the two-sample T-test for two models, the null hypothesis H 0 is ଵ ଶ the adversarial hypothesis H 1 is
ଵ ଶ and μ 1 implies the mean temperature of Model 1 and μ 1 means the average temperature of Model 2. The p- value of the analysis results is 0.043, which cannot be rejected by the null hypothesis that model1 will have a higher average temperature. Comparisons of mean temperatures are shown in Fig. 5 and Table 5. Furthermore, as shown in Fig. 6 and Table 6, our analysis of the variance
shows that the null hypothesis H 0 stands for ⁄ ଶ 1 and the adversarial hypothesis H 1 stands for ଵ ⁄ ଶ 1 .
The difference between the two model variances is statistically significant and Model 2 is judged to have a large variance.
Fig. 5. Boxplot of Model 1, Model 2.
Fig. 6. Test for equal variance for Model 1, Model 2.
Table 5. Two-sample t-test
N Mean St Dev SE Mean
Model 1 65 111.94 6.31 0.78
Model 2 65 110.19 5.23 0.65
Table 6. Test for equal variance
N Lower St Dev Upper
Model 1 65 5.25929 6.30535 7.84354
Model 2 65 4.35897 5.22597 6.50084
Soo Hyun Jo, Ji Hee Han, Jong Oh Kim, Hwi Han and Sang Jeen Hong 96
3.2 Heat transfer
We compared the error of the experimental value and the resulting value through finite differential method. In two- dimensional conduction, the finite differential method can be defined as shown in Fig. 1 below the temperature relationship between the cut points (m, n) defined as the center and the four adjacent cut points. First, we set up four sections of each edge section and five sections of the center section at 90 degree intervals in the ESC we designed. In each section, the points that become centers were specified and then four points were specified at equal intervals, and the mean value of the points was viewed as theoretical values through finite differential calculations, and the center value at that point was compared to the actual experimental value. As a result, we were able to obtain the same results as in Table 1, and the error values were calculated by com- paring the two, resulting in a theoretical and experimental error of at least 0.009% to up to 0.17%. Although the measurement was made in an environment with a large temperature difference between external and internal fluids, it was confirmed that the error value was not significant, and thus the reliability of the ANSYS program was obtained based on the selected model and setting value.
Comparison of the two models obtained above was carried out by calculating heat transfer volume through algebraic mean temperature differences. The heat transfer equation is defined as the product of the flow rate, the heat wave, and the temperature difference between the inlet and outlet, as shown in Fig. 3 below [5]. By setting the properties of aluminum 6061 the calculation showed that the heat transfer volume of 0.934 KW for Model 1 and 0.938 K for Model 2. Although no significant differences were found, this led to the conclusion that Model 2 was superior, as was the case with the above deviation-variance process.
ଶ = ଶ ́ ∙ ,ଶ ∙ ଶ,୧୬ − ଶ,୭୳୲
= ∙ ∙ (2) We derive a regression expression using uncoded data to understand the influence and interaction of each factor on the model and use it as a single model alternative to the real model. The coefficients of each term show that the flow rate has the greatest effect on minimizing the Max-Min value of the temperature.
4. Discussion
To design ESC and Coolant, which obtain excellent temperature distributions under cryogenic conditions, the initial reference model design process was first conducted to construct the initial model and to set the internal design and conditions to general defaults, widen the contact area under this design condition, while selecting models with as few internal and external temperature differences as possible. As a result, we separated the two Paths and concluded that the Coolant design, which consists of five turns, was suitable for the reference model.
We proceed with Box-Benhken response surface analysis for the full-fledged optimal condition design of the reference model set above. To this end, we set three factors: the number of persimmons in path, the diameter, and the flow rate of refrigerants, and conducted a total of 30 simulations including center point through 27 model designs from Minimum Level to maximum level model. As a result, R-sq is 97.2% and R 2 - adj is 96.2%, confirming that the above factors have relatively high reliability. Furthermore, the regression formula also shows that flow rate is a significant factor in minimizing Max-Min values.
Through the Contour Plot, we can see that diameter does not have a significant impact on the outcome, and that flow rate is leading the outcome as above. This allowed us to conclude that setting the number of wheels and flow rate at 5 turns and 0.3 kg/s while maintaining a diameter of at least 10 mm at modeling time would result in excellent results.
Furthermore, based on the above data, two models were selected as the final candidate models and, with statistically significant conclusions, the variance of Model 2 was shown to be excellent through the null hypothesis H 0 and the adversarial hypothesis H 1 .
Since it is a study conducted with ANSYS, a commercial
analysis program, the reliability of this study through the
calculation of error values is weighed. As a result, an error
of at least 0.009% to up to 0.17% was achieved, thereby
securing reliability in this study. Furthermore, we compute
the heat transfer volume to reaffirm the conclusion that
Model 2 from the above experimental results has better heat
dissipation and distribution than Model1. As a result, we
could narrowly confirm that Model 2 had excellent results.
CFD Study for the Design of Coolant Path in Cryogenic Etch Chuck 97
