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Production sequence of Si-spheres and interferometrical determination of the sphere volume

In-process measurement device for the manufacturing of high precision silicon spheres


As part of the redefinition of the International System of Units (SI), a process-chain for the manufacturing of high-precision silicon spheres was developed at PTB. Since such spheres can have mean roughness values of less than 0.3 nm and form deviations of less than 20 nm, very high-quality and reliable measurement technology is required for ongoing process monitoring. Sophisticated form measuring devices are available at PTB. These are extremely complex, unfortunately not always available every working day, and the entire measuring procedure requires time until results are available.

A new type of device was therefore developed for the daily and rapid measurement of the variation in the diameter of the superpolished silicon spheres. Due to the symmetry of the shape deviations of spheres made of monocrystalline silicon, knowledge of the changes in the diameter along three mutually perpendicular equators is sufficient to assess the shape deviation during machining. The interferometric structure specially developed for this purpose is very compact and thermally very stable. It enables a resolution in the sub-nanometer range with the lowest possible noise and a repeatability in the range of a few nanometers. A measurement along an equator only takes three minutes. The numerical processing of the results is also completed within a few minutes. The daily operation of the measuring system does not require any set-up routines.

Figure 1 shows the basic sketch of the measurement setup presented here in comparison to that of a typical commercial form measuring device. On the left, the commercially available device with rotating and translating devices for the sphere is shown. The components are typically stacked. The equator of the rotating sphere is captured either with a tactile or optical probe. The shape deviation is determined from the distance signal. It is necessary to know the systematic radial error motion of the axis of rotation, as it is part of the measurand. Numerous methods are known to eliminate this radial error motion. All of these methods are technologically demanding and mostly very time-consuming. In addition, the random error of the axis of rotation, the noise, should be significantly smaller than the expected shape deviation of the sphere. Given the form deviations of less than 20 nm present here, a corresponding rotary spindle is very expensive and technologically complex.

Fig. 1: Sketch of the setup for form measurement presented here (right) compared to a typical structure of commercial devices (left)

This is different with the principle shown in Figure 1 on the right. Here the measurement result is the sum of two interferometer signals. This sum signal is not affected by a displacement of the sphere in radial direction, the direction of the beam paths. The change in the distance between the silicon surfaces remains, which corresponds to the change in the diameter of the sphere. A shift of the sphere in the direction of the beam takes place e.g. by tumbling during rotation around the mechanically non-ideal axis of rotation. Compensation for these errors in the rotating spindle is therefore not necessary.

In addition, the measurement loop, shown in green in Figure 1, is much more compact and therefore less susceptible to temperature fluctuations in the system. All components of the measuring structure shown on the right are made of the same type of stainless steel, so that thermal stress is minimized. A thermal drift of the measurement signal due to the measurement objects, that may not yet be adequately tempered, on the other hand, can be modeled and compensated for a large temperature range using the evaluation software developed in-house.

The device is suitable for everyday use, easy to use and delivers results quickly. The spheres can be handled safely in the setup. Mechanical damage to the spheres is avoided by a special handling and transport device. All of this has been proven by hundreds of in-process measurements.


Rudolf Meeß, Dennis Dontsov and Enrico Langlotz, 2021, Interferometric device for the in-process measurement of diameter variation in the manufacture of ultraprecise spheres. Meas. Sci. Technol. 32 074004. https://iopscience.iop.org/article/10.1088/1361-6501/abe81c



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