Source: http://www.google.com/patents/US7973539?dq=7,339,580
Timestamp: 2016-08-30 15:18:23
Document Index: 128652657

Matched Legal Cases: ['Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'art 111', 'art 111', 'art 111', 'art 111', 'art 111', 'art 111', 'art 111']

Patent US7973539 - Methods for measuring dielectric properties of parts - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inPatentsA method is disclosed for calibrating a capacitance of an apparatus for measuring dielectric properties of a part. The apparatus includes an electrically grounded chamber, a lower electrode disposed within the chamber and connected to a radiofrequency (RF) transmission rod, an electrically grounded upper...http://www.google.com/patents/US7973539?utm_source=gb-gplus-sharePatent US7973539 - Methods for measuring dielectric properties of partsAdvanced Patent SearchPublication numberUS7973539 B1Publication typeGrantApplication numberUS 13/030,015Publication dateJul 5, 2011Priority dateOct 5, 2007Fee statusPaidAlso published asUS7911213, US20100079152, US20110140715Publication number030015, 13030015, US 7973539 B1, US 7973539B1, US-B1-7973539, US7973539 B1, US7973539B1InventorsJaehyun Kim, Arthur H. Sato, Keith Comendant, Qing Liu, Feiyang WuOriginal AssigneeLam Research CorporationExport CitationBiBTeX, EndNote, RefManPatent Citations (23), Non-Patent Citations (1), Classifications (8), Legal Events (1) External Links: USPTO, USPTO Assignment, EspacenetMethods for measuring dielectric properties of parts
This application is a divisional application of U.S. patent application Ser. No. 12/240,375, filed on Sep. 29, 2008, now U.S. Pat. No. 7,911,213 entitled “Methods for Measuring Dielectric Properties of Parts,” which claims priority under 35 U.S.C. 119(e) to each of the following U.S. Provisional Patent Applications: 1) U.S. Provisional Patent Application No. 60/978,082, filed Oct. 5, 2007; 2) U.S. Provisional Patent Application No. 60/978,085, filed Oct. 5, 2007; 3) U.S. Provisional Patent Application No. 60/978,087, filed Oct. 5, 2007; and 4) U.S. Provisional Patent Application No. 60/978,089, filed Oct. 5, 2007. Each of the above-identified patent applications is incorporated herein by reference.
This application is related to U.S. patent application Ser. No. 12/240,291, filed on Sep. 29, 2008, entitled “Apparatus for Measuring Dielectric Properties of Parts,” and U.S. patent application Ser. No. 12/240,329, filed on Sep. 29, 2008, entitled “Electrode for Use in Measuring Dielectric Properties of Parts,” and U.S. patent application Ser. No. 12/240,414, filed on Sep. 29, 2008, entitled “Methods for Characterizing Dielectric Properties of Parts,” now U.S. Pat. No. 7,777,500. The disclosure of each of the above-identified related applications is incorporated herein by reference.
Semiconductor wafer (“wafer”) fabrication often includes exposing a wafer to a plasma to allow the reactive constituents of the plasma to modify the surface of the wafer. Such plasma processing of a wafer can be performed in a plasma processing system in which a plasma is generated by transmitting radiofrequency (RF) power through a processing gas. The wafer characteristics resulting from the plasma processing operation are dependent on the process conditions, including the plasma conditions. Because the plasma conditions are closely tied to the RF power transmission through the system, it is beneficial to have an accurate knowledge of how the RF power is transmitted through the plasma processing system. Knowledge of how the RF power is transmitted through the plasma processing system is also necessary to match one plasma processing system to another, such that the plasma intensity in each plasma processing system is substantially the same for a given power input. To this end, it is necessary to have an accurate knowledge of the dielectric properties of the plasma processing system parts through which the RF power is transmitted.
FIG. 9 is an illustration showing a flowchart of a method for calibrating the relationship between the total capacitance (Ctotal — without — part) and the separation distance between the upper electrode and the hot electrode, in accordance with one embodiment of the present invention;
FIG. 6 is an illustration depicting capacitances between the hot electrode 109/RF rod 113 and the grounded upper electrode 105/chamber 101 when the exemplary part 111 is disposed between the upper electrode 105 and the hot electrode 109, in accordance with one embodiment of the present invention. As shown in FIG. 6, the capacitance between the upper electrode 105 and the hot electrode 109 is defined by the capacitance (Cpart) of the part 111 and the capacitance (Cst1) between the hot electrode 109 and the portions of the upper electrode 105 outside of the contact region between the part 111 and the upper electrode 105. Also, a capacitance (Cst2) exists between the RF rod 113 and the chamber 101 bottom. It should be understood that the capacitances (Cst1) and (Cst2) are functions of the separation distance (Y1) between the upper electrode 105 and the hot electrode 109. Also, the capacitance (Cpart) is a function of the dielectric constant of the part (kpart). Because the capacitances (Cpart), (Cst1), and (Cst2) represent parallel capacitances, the total capacitance (Ctotal — with — part) between the hot electrode 109/RF rod 113 and the grounded upper electrode 105/chamber 101 is defined as a sum of the capacitances (Cpart), (Cst1), and (Cst2), as shown in Equation 1.
(C total — with —part )=(C part {k part})+(C st1 {Y1})+(C st2 {Y1}) Equation 1
FIG. 7 is an illustration depicting capacitances between the hot electrode 109/RF rod 113 and the grounded upper electrode 105/chamber 101 when there is no part disposed between the upper electrode 105 and the hot electrode 109, in accordance with one embodiment of the present invention. As shown in FIG. 7, the capacitance between the upper electrode 105 and the hot electrode 109 is defined by the capacitance (Cst3) of the atmosphere within the chamber 101 interior cavity. Also, as in FIG. 6, the capacitance (Cst2) exists between the RF rod 113 and the chamber 101 bottom. It should be understood that the capacitances (Cst3) and (Cst2) in FIG. 7 are functions of the separation distance (Y2) between the upper electrode 105 and the hot electrode 109. Because the capacitances (Cst3) and (Cst2) represent parallel capacitances, the total capacitance (Ctotal — without — part) between the hot electrode 109/RF rod 113 and the grounded upper electrode 105/chamber 101 is defined as a sum of the capacitances (Cst3) and (Cst2), as shown in Equation 2.
(C total — without — part)=(C st3 {Y2})+(C st2 {Y2}) Equation 2
With reference to the configuration of FIG. 7 with the part absent, it should be understood that the resonance frequency of the RF power will change as the distance (Y2) between the upper electrode 105 and the hot electrode 109 is changed. In the configuration of FIG. 7, the variable capacitor 123 and RF signal generator 125 are maintained at their respective settings as applied in the configuration of FIG. 6 with the part 111 present in the chamber 101. Under these conditions, the upper electrode 105 in the configuration of FIG. 7 (without the part present) can be lowered toward the hot electrode 109 until the resonance frequency of the apparatus 100 according to the configuration of FIG. 7 substantially matches the resonance frequency of the apparatus 100 according to the configuration of FIG. 6 (with the part 111 present). When the upper electrode 105 is lowered to cause the substantial matching between the resonance frequencies of the configurations of FIGS. 6 and 7, the total capacitance (Ctotal — with — part) of configuration 6 will be substantially equivalent to the total capacitance (Ctotal — without — part) of configuration 7. In this situation, Equations 1 and 2 can be set equal to each other as shown in Equation 3.
(C part {k part})+(C st1 {Y1})+(C st2 {Y1})=(C total — without — part) Equation 3
The right side of Equation 3, (Ctotal — without — part) at the resonance frequency, can be measured directly by connecting a capacitance meter between the RF rod 113 and the upper electrode 105, with the RF rod 113 disconnected from the conductor plate 115 and the upper electrode 105 maintained at the vertical elevation corresponding to the resonance frequency when the part is absent. Also, the capacitance (Cst1{Y1}) between the hot electrode 109 and the portions of the upper electrode 105 outside of the contact region between the part 111 and the upper electrode 105 in the configuration of FIG. 6 can be simulated. Also, the capacitance (Cst2{Y1}) between the RF rod 113 and the chamber 101 bottom in the configuration of FIG. 6 can be simulated. In one embodiment, the capacitances (Cst1{Y1}) and (Cst2{Y1}) are simulated through a finite element model analysis of the configuration of FIG. 6. With the capacitances (Ctotal — without — part), (Cst1{Y1}), and (Cst2{Y1}) known, the capacitance of the part (Cpart{kpart}) can be calculated, as shown in Equation 4.
(C part {k part})=(C total — without — part)−(C st1 {Y1})−(C st2 {Y1}) Equation 4
As discussed above, to determine the total capacitance (Ctotal — without — part) at the resonance frequency, it is necessary to know the relationship between the total capacitance (Ctotal — without — part) and the separation distance between the upper electrode 105 and the hot electrode 109. FIG. 9 is an illustration showing a flowchart of a method for calibrating the relationship between the total capacitance (Ctotal — without — part) and the separation distance between the upper electrode 105 and the hot electrode 109, in accordance with one embodiment of the present invention. In an operation 901, the RF rod 113 is disconnected from the conductor plate 115 and from any other electrical connection within the electrical components housing 103. In an operation 903, a capacitance meter is connected between the RF rod 113 and the upper electrode 105. In an operation 905, using the capacitance meter, the capacitance between the RF rod 113 and grounded upper electrode 105 is measured and recorded for a number of vertical separation distances between the upper electrode 105 and the hot electrode 109. In one embodiment, operation 905 is performed by positioning the upper electrode 105 at a number of vertical separation distances from the hot electrode 109 extending from 0.05 inch to 1.2 inch, in increments of 0.05 inch. In the operation 905, at each vertical separation distance between the upper electrode 105 and the hot electrode 109, the upper electrode 105 is maintained in a substantially level horizontal orientation so as to be substantially parallel to the hot electrode 109. The method further includes an operation 907 for generating a capacitance calibration curve for the chamber 101 by plotting the capacitance versus vertical separation distance between the upper electrode 105 and the hot electrode 109 using the data measured in operation 905. The capacitance calibration curve for the chamber 101 can be repeatedly used to determine the total capacitance (Ctotal — without — part) at the resonance frequency once the vertical elevation of the upper electrode 105 at the resonance frequency (without the part present) is determined.
Once the resonant upper electrode 105 separation is determined, an operation 1013 is performed to determine the total capacitance (Ctotal — without — part) at the resonance frequency based on the resonant upper electrode 105 separation. In one embodiment, the capacitance calibration curve for the chamber 101, as generated in the method of FIG. 9, is used to determine the total capacitance (Ctotal — without — part) at the resonance frequency in operation 1013.
The method further includes an operation 1015 for simulating both the capacitance (Cst1{Y1}) between the hot electrode 109 and the portions of the upper electrode 105 outside of the contact region between the part 111 and the upper electrode 105, and the capacitance (Cst2{Y1}) between the RF rod 113 and the chamber 101 bottom. As previously mentioned, in one embodiment, the capacitances (Cst1{Y1}) and (Cst2{Y1}) can be simulated through a finite element model analysis. An operation 1017 is then performed to calculate the capacitance of the part (Cpart) as being equal to the total capacitance (Ctotal — without — part) determined in operation 1013 minus the capacitances (Cst1{Y1}) and (Cst2{Y1}) simulated in the operation 1015.
The method continues with an operation 1207 in which the RF signal generator 125 is controlled to sweep the frequency of the RF power over a range bounding the resonance frequency achieved in operation 1205, while using the RF voltmeter 127 to measure and record the gain of the apparatus 100 between the connections 129 and 131 at a number of frequencies within the frequency sweep range. In one embodiment, the frequency range covered by the frequency sweep of operation 1207 is defined to include a 3 dB variation in gain of the apparatus 100 on each side of the peak gain corresponding to the resonance frequency. The method further includes an operation 1209 for fitting a mathematical model of the gain of the apparatus 100 to the gain versus frequency data measured in operation 1207, wherein the fitting of operation 1209 provides a value for the total capacitance of the apparatus 100 with the part therein (Ctotal — without — part) and a value for the total resistance of the apparatus 100 with the part therein (Rtotal — with — part). The fitting of operation 1209 is further described below with regard to FIGS. 13-14 and Equation 5.
In the operation 1209, Equation 5 is fit to the gain versus frequency data measured in operation 1207 with the part present in the apparatus 100, thereby yielding a value for the total capacitance of the apparatus 100 with the part therein, i.e., (C)=(Ctotal — without — part) and a value for the total resistance of the apparatus 100 with the part therein, i.e., (Rx)=(Rtotal — without — part). FIG. 14 is an illustration showing an exemplary fitting of Equation 5 in accordance with operation 1209, based on gain versus frequency data measured and recorded in the frequency sweep of operation 1207. In one embodiment, a multivariate regression technique is used to fit Equation 5 to the measured gain versus frequency data in operation 1209. Also, in one embodiment, a confidence interval for each of the unknown parameters (C) and (Rx) is estimated by Monte Carlo simulation.
The method continues with an operation 1217 in which the RF signal generator 125 is controlled to sweep the frequency of the RF power over a range bounding the resonance frequency achieved in operation 1215, while using the RF voltmeter 127 to measure and record the gain of the apparatus 100 between the connections 129 and 131 at a number of frequencies within the frequency sweep range. In one embodiment, the frequency range covered by the frequency sweep of operation 1217 is defined to include a 3 dB variation in gain of the apparatus 100 on each side of the peak gain corresponding to the resonance frequency. The method further includes an operation 1219 for fitting a mathematical model of the gain of the apparatus 100, i.e., Equation 5, to the gain versus frequency data measured in operation 1217. The fitting of operation 1219 provides a value for the total capacitance of the apparatus 100 with the part absent, i.e., (C)=(Ctotal — without — part), and a value for the total resistance of the apparatus 100 with the part absent (Rx)=(Rtotal — without — part). As previously mentioned, a multivariate regression technique can be used to fit Equation 5 to the measured gain versus frequency data in operation 1219. Also, in one embodiment, a confidence interval for each of the unknown parameters (C) and (Rx) is estimated by Monte Carlo simulation.
The method continues with an operation 1221 for calculating the resistance of the part (Rpart) based on the total resistance of the apparatus 100 with the part therein (Rtotal — with — part), as determined in operation 1209, and the total resistance of the apparatus 100 with the part absent (Rtotal — without — part), as determined in operation 1219. More specifically, the resistance of the part (Rpart) is determined using Equation 6.
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