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

Scanning Probe Metrology

Working Group 5.25

Scanning Probe Microscope (SPM) metrology systems

 

In addition to other development activities in the field of SPM metrology, two commercial SFMs have been extended in the past two years by miniaturized homodyne laser interferometers. The positioning system of a third device developed into a large range SFM at PTB, has already been equipped with laser interferometers by the manufacturer. These laser interferometers were developed in cooperation with the Technical University IImenau and SIOS Messtechnik GmbH. In the case of all devices, special attention was already paid in the construction of the interferometer extension and the instrument design to the fact that principles as minimization of Abbe errors and tilting were complied with. At PTB, the SFMs described serve for the calibration of standards and the general characterization of microstructures. In the following, the SFMs equipped with laser interferometers will be referred to as metrological SFMs. 

Examples :

Scanning force microscopes of type Veritekt

 

Since 1995, two metrological SFMs with integrated laser interferometers have been constructed on the basis of the commercial SFM Veritekt-3 of Carl Zeiss, Jena. These devices allow measurement objects to be characterized in the "contact" SFM mode with a measuring range of 70 µm x 15 µm x 15 µm (x, y, z). Compared to other instruments, the advantage of these SFMs is that a precise flexure hinge stage is used as the basis for the positioning system and that position-controlled piezo actuators (with integrated capacitive sensors) are used for each axis of motion. A skilful geometry of the flexure hinges will allow factors such as cross-talk of the axes and non-orthogonality of the directions of motion to be minimized. Figure 1: Sketch of the metrological scanning force microscope Veritekt with integrated laser interferometers Veritekt B which has been completed in 1996 and optimized in the following years with respect to a minimization of the Abbe error, is used for calibrations at PTB. The results of international and internal comparisons have confirmed suitability of this SFM for calibration tasks. On the basis of the experience gained with Veritekt B, another metrological SFM, Veritekt C (see Figure 2), has been developed in the years until 2002. Essential sub-assemblies of the commercial basic instrument were adopted and supplemented by modern measuring and evaluation electronics. The arrangement of the laser interferometers was revised in such a way that it is now also possible to adapt measuring heads working in different SFM modes. Figure 2: Ansicht des SFM Veritekt C Contrary to the measuring strategy used for Veritekt B, in which the laser interferometers are used for calibration of the capacitive sensors at discrete measurement points (λ/2-zero points of the interferometer signals) and calculation of correction values, Veritekt C directly includes the interferometer values in the SFM's control loop. To allow the interferometers to be used as measuring and control systems, the data acquisition electronics were completely changed and signal processing realized on the basis of a fast signal processor. Integration of this data acquisition electronics into Veritekt C allows the resolution of the interferometer values to be increased to 0.04 nm and the interferometers to be operated at a data rate of 20 kHz. As nonlinearity of the interferometer signals (which amounts to approx. 3 nm in the uncorrected form) is a limiting factor when measurement uncertainties in the range of a few nanometers are concerned, diverse correction procedures for the nonlinearity were investigated when the measuring electronics was modified. Finally, a procedure which follows the principle developed by Heydemann was integrated into the control loop of the interferometers. This procedure corrects the deviations of the interferometers' electric signals u1d and u2d in amplitude, offset and phase by an ellipse fitting method:

In view of the calculation effort involved, this algorithm is usually not implemented as online method. The investigations performed on Veritekt C have, however, shown that the ellipse parameters p, q, r and α can be assumed to be constant over a sufficiently long period of time and need not, therefore, be permanently determined during correction. This allows the procedure to be integrated into the interferometer's measuring circle without restriction of the data rate. The correction described allowed remaining nonlinearities of the interferometer signals to be reduced to 0.3 nm.
After the interferometer data rate had been successfully increased, the measuring principle of the SFM was revised to accelerate data acquisition of all signals. On this basis, a new measuring mode was developed for scanning of the sample. Central triggering of all measuring and control elements installed in the SFM then allows the measurement object to be scanned with constant velocity and to simultaneously determine the measurement data of both, the positioning system and the SFM sensor acting as null indicator. This makes deceleration of the movement during acquisition of the measurement point data unnecessary; this "scan-on-the-fly" measuring principle allows the measurement velocity in the x-direction (fast scan axis) to be increased to up to 25 µm/s as a function of the topography to be investigated. Due to the fast data acquisition, the influence of thermal drifts and other environmental factors can be reduced.
Modernization of the data acquisition software, an automated sample positioning system and the measures taken to realize automatic measuring processes (batch processes) have further improved the handling of the devices. Due to the use of laser interferometers as displacement measuring sensors, calibration of the measuring system so far required can be dispensed. This leads to a reduction of the whole measuring time.

Metrological large range scanning force microscope

 

For an increasing number of practical applications of scanning probe microscopy - also in the field of SPM metrology - the measuring range of piezo scanning tables (x, y < 100 bis 200 µm) is too small.These applications comprise, for example, the determination of the roughness in accordance with written standards and investigations on lateral standards whose evaluation requires measurements in the millimetre range. For the reasons mentioned, different concepts have been developed to extend the measuring range of SFMs with the aim of increasing the displacement range of piezo actuators or using alternative positioning systems. The PTB decided to develop and manufacture a positioning systems on the basis of the so-called nanomeasuring machine which meets the specific metrological requirements of industrial metrology. This device was combined with a measuring head based on a focus sensor known from the Veritekt SFM. A measuring instrument is thus available which combines a positioning range of 25 mm x 25 mm x 5 mm with the detection principles of scanning force microscopy - the so-called metrological "Large Range Scanning Force Microscope (LR-SFM)". Its operating principle is shown in Figure 1. Figure 1: Diagrammatic sketch of the metrological large range SFM (LR-SFM) (components such as drives and rails are not shown for reasons of clarity.)

The object stage is moved via three linear driving systems which are position controlled by laser interferometers. Two angle measuring systems have been included in the control unit to correct for guidance erros of the motion stage. Similar to the Veritekt SFMs, the reference system is formed by plane mirrors; in the case of the LR-SPM, the mirrors have been combined to form a cube edge. The resolution of the measuring system amounts to 0.08 nm or 0.001", respectively. The construction of the device is aimed at achieving coincidence of measuring and reference plane to minimize Abbe errors.
To increase the dynamics of the positioning system, a compact vertically moving piezo stage was arranged on the sample table of the NMM. This one allows fast scanning with a range of up to 2 µm. Its compact and stiff design results in a high mechanical resonance frequency fr > 20 kHz. The movement of this table is measured and its position controlled via a capacitive sensor arranged in the middle of three symmetrically arranged piezo actuators. During scanning of the sample, the lateral movement is performed exclusively with the NMM, whereas the height adjustment results from a combined movement of the vertically adjustable z piezo table and the NMM. The whole device is controlled via two signal processor systems. One is responsible for the NMM, the other realizes height adjustment and data acquisition. The photo in Figure 2 shows the metrological LR-SPM.

Figure 2: View of the metrological large range SFM (LR-SFM)

After completion of the measuring software for the complete device, extensive investigations into the metrological properties of the LR-SPM were carried out. As an example, the first results of measurements performed on a flatness standard and on a sinusoidal lattice are shown. The topographic image of the flatness standard (Figure 3) can be used to estimate the quality of the motion (influenced by the guidance mechanism) and to evaluate the instrument's noise behaviour. 

Figure 3: Figure 3: Investigations into the guiding properties and noise behaviour of the LR-SPM: Topography image of a flatness standard

The image shows that the structure measured is very flat and that artefacts as they may, for example, be caused by the ball bearings, are not recognizable. The residual instrument noise (3 nm p-v) is mainly due to external influences such as building vibrations and acoustic excitations, and it should be reduced by optimizing the environmental conditions.
Suitability of the LR-SFM for measurements on lateral standards and determination of the structure period is illustrated by the example of a sinusoidal lattice.

Figure 4: Determination of the lattice constant on a sinusoidal lattice with approx. 3000 periods (measuring range in x-direction: 1.35 mm)

Figure 4 shows the scan image of a one-dimensional lattice which has been scanned in the x-direction with a measuring range of 1.35 nm (this corresponds to 20 times the scanning range of the Veritekt SFMs!). As calculation of the structure period is based on a statistical procedure, a larger number of structures allows to improve the measurement uncertainty of the measuring procedure, provided the sample structure is homogeneous. Repeated measurements on this sinusoidal lattice showed an identical periodic value of 416.67 nm. This result agrees with the reference value from diffractrometric optical measurements within two decimal places. Further measurements on nanostructures and step heights have confirmed the high spatial resolution of the measuring instrument and agreement of the measured values with reference values from international comparisons.The investigations initiated to optimize the LR-SPM and extend it by alternative detection principles are permanently continued and are to demonstrate that the measuring system is also suitable for the measurement of structures with a topography up to the millimetre range. Measurement tasks such as calibration of tip geometries on indenters for hardness measurement, investigation of structures on photo masks from semiconductor industry, determination of dimensional parameters on parts in the field of microsystem technology and the like are already demanded by industry and represent potential fields of application for the metrological LR-SPM.