1、 PDF外文：http:/ 作者： Chad R. Snyder, Member Frederick I. Mopsik 国籍： America 出处： IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT A Precision Capacitance Cell for Measurement of Thin Film Out-of-Plane ExpansionPart III: Conducting and Semiconducting Materials AbstractThis paper describes the c
2、onstruction, calibration, and use of a precision capacitance-based 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 conduc
3、tors can be measured. The results of our measurements on p-type<100> -oriented single crystal silicon are compared to the recommended standard reference values from the literature and are shown to be in excellent agreement. Index TermsCapacitance cell, coefficient of thermal expansion (CTE), g
4、uarded 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
5、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
6、 CTE. However, standard test methods based on these techniques are limited to dimensions greater than 100 m m 1-2. 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 valu
7、es 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 capacitance-based measurements, in principle, can offer the necessary resolution for the
8、se films . For a pair of plane-parallel 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 well-known equationdACvac
9、0(1) where 0 is the permittivity of free space ( mpF854.80 ).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
10、 papers, the design and data reduction techniques were presented for our three-terminal capacitance-based metrology for thin polymer film measurements. The first paper (I) described the initial design based on gold-coated Zerodur. However, several problems were encountered. It was discovered that Ze
11、rodur displays ferroelectric behavior, with an apparent Curie temperature of 206 as determined by fitting with a CurieWeiss 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 n
12、egative 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 result in shorts when measurements were performed on thin samples. The second problem wi
13、th the gold was that it underwent mechanical creep under loading. To resolve these problems, a new electrode was designed from fused quartz coated with nichrome. A groove filled with conductive silver paint was added to the back side of the bottom electrode around the central contact to intercept an
14、y field lines between the central wire contact through the guard gap to the high electrode. The new design was described in the second paper (II) along with thermal expansion measurements on<0001>-oriented single crystal sapphire ( 32OAl ) and a 14- m thick inner layer dielectric m
15、aterial 10. It was recognized in II that the data reduction was simple as long as the air filling the gap between the capacitor plates was dry. However, to expand the utility of the capacitance cell to hygrothermal expansion (i.e., swelling in a humid environment), the third paper (III) described th
16、e data reduction techniques necessary for use of the capacitance cell under humid conditions . Fig. 1. Schematic of the electrodes. Note that the shaded areas correspond to the nichrome coating. The resolution of the instrument was determined in II and III. For dry, isothermal conditions, the
17、capacitance cell can measure relative changes in thickness on the order of 710 , for a 0.5-mm thick sample； this corresponds to a resolution on the order of m11105 . Under dry conditions in which the temperature is changed, the reproducibility of a relative thickness change (e.g., for CTE measurement) is on the order of 610 . Finally, under humid conditions, the ultimate resolution is primarily a function of temperaturethe actual values of which are given in III.
