The accurate characterization of material properties as thermal expansion, temporal length drift and relaxation is essential for semiconductor industry or for aerospace applications. PTB’s absolute length measuring Ultra Precision Interferometer enables investigation of these properties with high accuracy in the temperature range from 7 K to about 300 K. The Coefficient of Thermal Expansion (CTE) can be measured with uncertainties mainly below 3 × 10-9/K. In this paper we give an overview about the latest state of our experimental setup and evaluation methods. Recent measurement results on silicon carbide ceramics (SiC-100, HB-Cesic), silicon nitride ceramics (SN-PG and SN-Pu) and single crystal silicon (SCS), the latter being the reference material of choice in this regime, are presented.
In this work we demonstrate how absolute length measurements by interferometry, as used for regular gauge block
calibration, can be applied to measure the dimensional drift behavior of connections joined by gluing or screwing and
how these joining techniques are influenced by thermal treatment. While it is common to investigate the intrinsic
stability of material samples by repeated length measurements, there exist growing demands in precision engineering to
characterize the stability of assemblies, i.e. of joined material pieces. In order to enable investigation of joining
techniques representative joints were fabricated by a number of methods as wringing, screwing and gluing. By using
gauge block shaped samples as joining parts parallelism and flatness could be achieved which is needed for
interferometric length measurements. The stability of the joints has been investigated longitudinally and laterally to the
connection interface, and also mutual tilting of the parts was detected by analysis of the phase topographies. With the use
of sample joints, the behavior of connection elements used in ultrahigh-precision instruments can now be examined on
an accuracy level of about one nanometer. Results of approximately one year of observation show that screwed joints do
not exhibit a significant change of length or orientation. They also did not show response to temperature variations of
±10°C, which is different for adhesive joints where dimensional changes of up to 100 nm were observed.
Demands on dimensional stability of 'high tech' materials relevant for semiconductor industry are growing
considerably. Information about long term stability of materials could be extracted from high resolution length
measurements performed within a relatively short time, e.g. using high finesse Fabry-Perot-resonators. However, the
length changes observed during the short-term measurements can be overlapped by additional length relaxations induced
by even small temperature changes before such measurement is started. This effect is reduced when long-term stability is
studied from length measurements repeated in a larger period of time. This paper describes absolute length
measurements with PTB's Precision Interferometer performed at four gauge block shaped material samples in order to
extract reliable information about their long term stability. The long-term stability was found to be dependent not only on
the material and its age itself but also on the material's history. The latter effect regards a one hour heating to 220°C
applied to one of two identical sample bodies made of glass-ceramics which is still visible in the measurement results of
long-term stability even after a period of almost seven years.
Different measurement methods exist for the extraction of the coefficient of thermal expansion (CTE). Among them the observation of the sample length as a function of its temperature is the direct way. In the last decade, the use of phase shifting interferometry in combination with computer-based analysis of interference phase maps drastically improved interferometrical length measurements. In addition to the observation of the length itself, such measurements allow the extraction of a length topography L(x,y) of the sample as shown in this paper. From the behaviour of the length topography at different temperatures an upper limit of CTE-homogeneity can be obtained. It is shown in which way disturbing influences can be removed so that uncertainties of L(x,y) in the sub-nm range can be reached for different shaped samples
The evaluation of the coefficient of thermal expansion (CTE) from the observed temperature induced length changes becomes the more difficult the lower the final uncertainty of the CTE is desired. On a scale of nanometers the length as a function of the sample temperature clearly deviates from the linear approximation so that higher polynomials are used as fit functions to the measured data. From such polynomials of a certain degree the CTE can easily be evaluated according to its definition. In this paper it is demonstrated in which way the corresponding uncertainty of the CTE can
be calculated in accordance with the GUM what is done on the basis of symbolic computation by means of MATHEMATICA. On the other hand, the arbitrariness of the choice of the polynomial order causes an additional uncertainty contribution as discussed in this paper. Examples are given to illustrate the mentioned problems.
In interferometric length measurements the position of the sample with respect to the interference phase map is very important. Even the pixel resolution of the camera array may limit the measurement uncertainty, depending on the amount of the sample’s non-parallelism. In this case a correction can be applied taking into account a sub-pixel position at the sample’s front measuring face. In this paper three different methods are introduced which can be used for the definition of a sub-pixel central coordinate. Measurement examples illustrate that a value of 0.04 pixels for the standard uncertainty associated with the sub-pixel position seems realistic.
The detailed knowledge of thermal expansion and dimensional stability of low expansion materials is of growing interest and requires measurements of length changes with sub nm uncertainty. In addition to accurately defined environmental conditions the interferometer adjustment, namely the number of fringes covering the sample and also the method of autocollimation adjustment, become more important. Their influence, investigated with PTB's precision interferometer, will be discussed.
Modification of an interferometer instrument for highest accuracy calibration of long gauge blocks is presented. The interferometer design employs a Kosters prism, and a built-in 1 metre long vacuum cell for evaluation of refractive index of air in the direct neighborhood of the gauge block. The measurement set-up also includes platinum resistance thermometers and thermocouples for accurate measurements of gauge block temperature. Principles of the measurement method, including the application of phase stepping interferometry to both the length measurement and the correction for refractive index of air, are described in detail.
Interferometrically measured length changes of a silicon gauge block were performed under well defined environmental conditions. Special efforts - described in this paper - were made to reduce the uncertainties of the measurements. The used silicon crystal is of high purity and dislocation free. Expansion coefficients were obtained from thermal induced length changes in the range from 12 degrees C to 28 degrees C with uncertainties from about 0.01 percent to 0.03 percent. This corresponds to an uncertainty reduction by a factor of ten compared with earlier studies in this temperature range. The length change of the silicon gauge block induced by pressure variations from vacuum to atmospheric pressure provides a value for the compressibility of crystalline silicon with an uncertainty of about 1.5 percent. This directly measured compressibility slightly differs from literature data obtained from indirect measurements via ultrasonic wave velocities. The possible nature of this deviation is briefly discussed.
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