Do you really know how good your UHP pressure transducers are based on the manufacturer-provided datasheet as end users?
BY YANLI CHEN and MATTHEW MILBURN, UCT, Hayward, CA
As a widely-used components in the semiconductor industry, the performance of UHP pressure trans- ducers are very important for process control and process monitoring. Selecting a proper UHP pressure transducer with good performance for specific application is challenging, because different UHP pressure transducers manufacturers have different parameters listed in their datasheet/specification. For example, FIGURE 1, 2 and 3 are displaying the published speci- fication of UHP pressure transducers from three major manufacturers. Manufacturer A states “BFSL” (Best-fit straight line) method in its accuracy. However, manufacturer C uses “BFSL” in its non-linearity. Except accuracy, manufacturer B and C list non-linearity and hysteresis in their datasheet as well, but those parameters are not shown in manufacturer A’s datasheet. Behinds the datasheet/ specification, it was found that they have different test procedure and data processing methods to determine performance characteristics, such as non-linearity, hysteresis, non-repeatability, and accuracy. So, for neither the specifier nor the end users is it possible to compare the performance of different brands of pressure transducers without standardized test methods. To date, the industry has not recognized the full scope of the specification problem nor developed a standardized testing and reporting program.
Technical data and their definition
Before conducting any test, it is necessary to understand the definition of technical data. The common used parameters in the datasheet, such as non-repeatability, non-linearity, hysteresis, and accuracyRSS are explained in the following sections.
Non-repeatability error is defined as the largest deviation between the highest and lowest measurements of the same pressure taken under identical conditions. Non-repeatability characterizes the extent to which the output signals for successive measurements of the same pressure vary, and it is an important parameter to judge the design and manufacturing quality of the instrument. High repeatability (i.e., a small non-repeatability error) is a basic requirement of every dependable sensor system. Sometimes, it is expressed as repeatability in percent of full scale.
Non-linearity is defined as the largest deviation (positive or negative) between the actual-characteristic curve and a reference straight line. There are several ways to determine the reference straight line. The two most common are the terminal straight line (TSL) and the best-fit straight line (BFSL) as shown in FIGURE 4. In the TSL method, the zero error and span error are ignored and an ideal line connecting the zero and full-scale test is drawn and used as the reference straight line (red line in Figure 4). In the BFSL method, the reference straight line is positioned in relation to the measured characteristic curve in such a way that the sum of squares of the deviations is minimal (green line in Fig. 4). There is no requirement for this line to be parallel or in any other way related to the ideal line of the TSL method. The BFSL method is the standard data fitting method used by the major pressure trans- ducer manufacturers in the United States. Sometimes, non-linearity is expressed by linearity in percent of full scale.
Hysteresis is defined as the maximum deviation between the increasing and decreasing characteristic curves as shown in FIGURE 5, which is caused by the applied pressure. Due to the nature of hysteresis, the output readings during rising pressure typically lower than the readings on the return path to zero.
AccuracyRSS, UncertaintyRSS and Inaccuracy Historically, most major manufacturers are using a traditional root sum squares (RSS), defined as the square root of the sum of the squares of non-linearity/linearity, non-repeatability/repeatability and hysteresis, as a method to quantify the accuracy of a pressure transducer. In reality, the RSS method cannot truly reflect the accuracy/inaccuracy behavior of a pressure transducer which can be proved by the test results in the following sections.
A new term, inaccuracy, is introduced. It is defined as the worst case performance or absolute value of the maximum deviation at any measured value from the ideal value across the full pressure range of a transducer. Inaccuracy is much more representative of a device’s performance.
In order to be able to compare the test results with the manufacturers’ published specification, a new term, “uncertaintyRSS”, is introduced based on the “uncertainty” definition from SEMI International Standards: Compilation of Terms. Actually, it is the same as the historical accuracyRSS listed in most manufacturers’ published specification.
Experimental
Three UHP pressure transducer manufacturers (MFG A, MFG B and MFG C) participated in this comprehensive performance evaluation project by providing their products as test samples. FIGURE 6 shows the detailed information of devices under tests (DUTs). Twelve DUTs were installed in a test fixture designed by UCT for running simultaneous tests. The schematic of the test fixture is shown in FIGURE 7. The benefit of this design is to save significant amounts of time for assembly, disassembly, and testing, and eliminate potential setup errors occurring in the sequential tests.
The tests were conducted in a temperature controlled environment (20 ± 20C). FIGURE 8 shows the DUTs in the environmental chamber. The tests were completed by running total ten ascending (from 0%FS to 100%FS in 10%FS steps with a rate of change setpoint every 200 seconds) and descending (from 100%FS to 0%FS in 10%FS steps with a rate of change setpoint every 200 seconds) cycles.
Test results and discussion
The test results are summarized in FIGURE 9. In each sample group, the highest test value is highlighted in red and the lowest test value is highlighted in green. For each testing parameter, the best case is not always the same DUT in each sample group; the worst case is not always the same DUT in each sample group, either. For better comparison, the test results are graphically shown in FIGURE 10. As shown in Fig. 10, repeatability and hysteresis of the twelve DUTs do not have obvious fluctuations and all of the twelve DUTs have similar values for hysteresis and repeatability.
However, linearity, uncertaintyRSS and inaccuracy of the twelve DUTs have dramatic fluctuations, especially inaccuracy. Four DUTs from manufacturer C shows higher inaccuracy than the rest of other DUTs. Specifically, DUT 10 is showing extremely high inaccuracy (2.420%FS), which is about thirty-three times worse than the best case (0.074%FS). Four DUTs from manufacturer C also shows poorer linearity than the rest of other DUTs. For the uncertaintyRSS values, three DUTs from manufacturer C have much higher values than the rest of DUTs. Devices from manufacturer B have the best repeatability (0.039%FS), linearity (0.069%FS), inaccuracy (0.238%FS), and uncertaintyRSS (0.090%FS). A device from manufacturer C has the best hysteresis (0.038%FS). Devices from manufacturer A have the worst repeatability (0.050%FS) and hysteresis (0.057%FS) values. Devices from manufacture C have the worst linearity (0.372%FS), uncertaintyRSS (0.376%FS), and inaccuracy (2.420%FS) values. It can be concluded that the devices from manufacturer B have the best overall performance compared to devices from manufacturer A and C.
In order to conduct the side by side comparison of each manufacturer’s product, the worst case of each manufacturer’s sample for repeatability, linearity, hysteresis, uncertaintyRSS, and inaccuracy is summarized in FIGURE 11 and graphically shown in FIGURE 12.
The worst case value is reported as the representative values of that brand’s pressure trans- ducer. For each testing parameter, the highest value is highlighted in red and the lowest value is highlighted in green. As shown in Fig. 11, MFG A has the highest repeatability (0.050%FS) and MFG B has the lowest repeat- ability (0.039%FS); MFG C has the highest linearity (0.372%FS) and MFG B has the lowest linearity (0.069%FS); MFG A has the highest hysteresis (0.057%FS) and MFG C has the lowest hysteresis (0.038%FS); MFG C has the highest uncertaintyRSS (0.376%FS) and MFG B has the lowest uncertaintyRSS (0.090%FS); MFG C has the highest inaccuracy (2.420%FS) and MFG B has the lowest inaccuracy (0.238%FS).
When compared with the manufacturers’ published specification, the DUTs of MFG B meet the published specification of repeatability, linearity, hysteresis and uncertaintyRSS; the DUTs of MFG C meet their hysteresis specification, but do not meet their published linearity and uncertaintyRSS specification except that DUT 10 meet the uncertaintyRSS specification. However, DUT 10 has the highest inaccuracy value among the twelve DUTs, which totally supports our findings that uncertaintyRSS or accuracyRSS cannot reflect the true accuracy/inaccuracy behavior.
Conclusions
The results of this study prove that the performance indicator “accuracyRSS” used by most the pressure transducer manufacturers cannot truly reflect the performance. Based on this study, transducers marketed as comparable to each other display dramatically difference performance levels which could lead to process reproducibility challenges. It also demonstrates that the manufacturers’ published specification needs to be improved in order to truly reflect the performance of a UHP pressure transducer. Also, and of critical value, a proper test procedure and data processing method needs to be adopted in the industry. The pressure measurement task force of SEMI North America Gases and Facilities Committee is developing a new pressure transducer measurement standard based on this study.
References
1. Gassmann, Eugen. “Pressure-sensor fundamentals: inter- preting accuracy and error.” Chemical Engineering Progress, June (2014). http://www.aiche.org/sites/default/files/ cep/20140328.pdf
2. Gassmann, Eugen. “Introduction to pressure measurement.” Chemical Engineering Progress, March (2014). http://www. aiche.org/sites/default/files/cep/20140328.pdf
3. SEMI E56-0314, Test method for determining accuracy, linearity, repeatability, short-term reproducibility, hysteresis, and dead band of thermal mass flow controllers
4. SEMI International Standards: Compilation of Terms (Updated 0915) http://www.semi.org/en/sites/semi.org/files/data15/ docs/CompilationTerms0915.pdf
5. IEC 61298-2, Process measurement and control devices- General methods and procedures for evaluating performance- Part 2: Tests under reference conditions
MATTHEW MILBURN is a principal engineer at UCT, Hayward, CA. UCT provides OEMs manufacturers with an array of services including design, engineering, system assembly, testing, and global supply chain management. The company does not manufacture pressure transducers.