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【正文】 d expansion data on silicon obtained from [14]. It should be noted that the standard reference data was defined relative to 20 ℃ whereas we have measured, for convenience, relative to 25 ℃ . Therefore, the standard reference, relative expansion data was shifted in Fig. 4 by an amount S equal to ? ?? ?KS T 5?? ? (5) where T? is the CTE at temperature T taken from It is apparent that the two sets of data agree within the experimental uncertainty. (The error bar is smaller on the 25 ℃ data point than on the higher temperatures due to the fact that more repeat runs were performed, which reduced the uncertainty for that data point.) This demonstrates several key conclusions regarding the capacitance cell. First, the limitations of the previous design have been eliminated。 作者： Chad R. Snyder, Member Frederick I. Mopsik 國籍： America 出 處 ： IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT A Precision Capacitance Cell for Measurement of Thin Film OutofPlane Expansion–Part III: Conducting and Semiconducting Materials Abstract—This paper describes the construction, calibration, and use of a precision capacitancebased metrology for the measurement of the thermal and hygrothermal (swelling) expansion of thin films. It is demonstrated that with this version of our capacitance cell, materials ranging in electrical properties from insulators to conductors can be measured. The results of our measurements on ptype100 oriented single crystal silicon are pared to the remended standard reference values from the literature and are shown to be in excellent agreement. Index Terms—Capacitance cell, coefficient of thermal expansion (CTE), guarded electrode, high sensitivity displacement, inner layer dielectrics, polymers, thin films. I. INTRODUCTION THE coefficient of thermal expansion (CTE) is a key design parameter in many applications. It is used for estimating dimensional tolerances and thermal stress mismatches. The latter is of great importance to the electronics industry, where thermal stresses can lead to device failure. For accurate modeling of these systems, reliable values are needed for the CTE. Traditionally, displacement gauge techniques such as thermomechanical analysis (TMA) have been utilized for determining the CTE. However, standard test methods based on these techniques are limited to dimensions greater than 100 m? m [12]. This is problematic for materials which can be formed only as thin layers (such as coatings and certain inner layer dielectrics). Additionally, there is some question as to whether values obtained on larger samples (bulk material) are the same as those obtained for thin films, even when the effects of lateral constraints are included in the calculations . It has long been recognized that capacitancebased measurements, in principle, can offer the necessary resolution for these films . For a pair of planeparallel plate capacitors, if the sample is used to set the spacing of the plates d while being outside of the measurement path, then for a constant effective area of the plates A , the capacitance in a vacuum vacC is given by the wellknown equation dACvac 0??(1) where 0? is the permittivity of free space ( ?? ).With the sample outside of the measurement path and only air etween the electrodes, the vacuum capacitance is obtained rom the measured capacitance C byairvacCC ?? (2) where air? is the dielectric constant of air. In three previous papers, the design and data reduction techniques were presented for our threeterminal capacitancebased metrology for thin polymer film measurements. The first paper (I) described the initial design based on goldcoated Zerodur. However, several problems were encountered. It was discovered that Zerodur displays ferroelectric behavior, with an apparent Curie temperature of 206 ℃ as determined by fitting with a Curie–Weiss law. The rapid change in the dielectric constant of the Zerodur along with a coupling from the central contact through the guard gap to the high electrode created an apparent negative thermal expansion . The second problem with the initial design was with the gold coating. This coating had the tendency to ―snow plow‖ when scratches formed in the surface creating raised areas which would res
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