Virpi Korpelainen

Calibration of a commercial AFM: traceability for a coordinate system

Traceability of measurements and calibration of devices are needed also at the nanometre scale. Calibration of a commercial atomic force microscope (AFM) was studied as part of a dimensional nanometrology project at MIKES. The calibration procedure and results are presented here. The metrological properties of the AFM were characterized by several measurements. A method developed to calibrate the z scale by a laser interferometer during a normal measurement mode of an AFM is presented. x and y movements were studied with a laser interferometer and the scales were also calibrated using a calibration grid, which was calibrated at MIKES using a laser diffraction method. The advantages and disadvantages of the two methods are discussed. Orthogonalities of the axes were determined by calibration grids and an error separation method. Out-of-plane deviation was measured with a flatness standard. Uncertainty estimates for the coordinate system of the AFM scanner are presented.

A method for linearization of a laser interferometer down to the picometre level with a capacitive sensor

This paper describes methods for dynamic measurement and correction of laser interferometer periodic nonlinearity down to the picometre level. A capacitive sensor is used as an external reference for measuring and calculating the periodic interferometer nonlinearity correction function. The experimental interferometer setup is a heterodyne interferometer with symmetrical paths to detectors and time-interval-based phase detection. The periodic nonlinearity is represented as harmonic Fourier components. The time evolution of the nonlinearity function is tracked during measurement. The method is verified by spatial and temporal repeatability of the measured nonlinearity. Linearization repeatability in the 10 pm range is observed.

Acoustic method for determination of the effective temperature and refractive index of air in accurate length interferometry

An acoustic method for the measurement of the effective tem- perature and refractive index of air for precision length interferometry is described. The method can be used to improve the accuracy of interfero- metric length measurements outside the best laboratory conditions and also in industrial conditions. The method is based on the measurement of speed of 50-kHz ultrasound over the same distance measured with a laser interferometer. The measured speed of ultrasound is used to define the effective temperature or the refractive index of air along the laser beam path using the equations presented. The measured speed of sound, Cramer equation, dispersion correction, and Edlen equations are used in the fitting of new equations for the effective air temperature and refractive index of air as a function of speed of 50-kHz ultrasound. The standard uncertainties of the effective temperature and the refractive index of air equations are 15 mK and 1.7310 28 , respectively. The un- certainties of the effective temperature and refractive index of air mea- sured with the test setup for distances of about 5 m are 25 mK and 2.6 310 28 , respectively.

Measurement strategies and uncertainty estimations for pitch and step height calibrations by metrological atomic force microscope

Gratings and step height standards are useful transfer standards for lateral and vertical length scale calibration of atomic force microscopes (AFMs). In order to have traceability to the SI-meter, the standards must have been calibrated prior to use. Metrological AFMs (MAFMs) with online laser interferometric position measurements are versatile instruments for the calibrations. The developed task-specific measurement strategies for step height and pitch calibrations with the Centre for Metrology and Accreditations (MIKESs) metrological AFM are described. The strategies were developed to give high accuracy and to reduce measurement time. Detailed uncertainty estimations for step height and grating pitch calibrations are also given. Standard uncertainties are 0.016 and 0.018 nm for 300 and 700 nm pitch standards, respectively, and 0.21 and 0.44 nm for 7 and 1000 nm step height standards.

High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating

Laser diffractometer constructed at MIKES for calibration of pitches of 1D and 2D gratings is based on the Littrow configuration. The grating is rotated by a rotary table. In order to obtain optimal beam quality a fibre-coupled frequency-doubled stabilized Nd:YAG laser is used as a light source and a CCD without internal reflections is used to detect the diffracted beam position. The angle corresponding to the Littrow null position is calculated using a linear fit to equidistantly spaced angles around the null position, which reduces the effect of nonlinearity of the angle encoder scale. Pitch is calculated as a weighted average of the diffraction orders. Novel use of an uncalibrated 1D grating applied to classical error separation methods for angle calibration by full-circle subdivision is described. Diffraction angle measurements are repeated in many sample holder alignments rotated relative to the absolute angle scale. The sequences overlap so that the full circle of the angle scale is covered with multiple evenly distributed sequences, needed for circle-subdivision metrology. The average grating pitch over all sequences is used to separate angle scale errors and a correction table for the rotary table is calculated. The method was verified using a calibrated polygon and an autocollimator. Uncertainty estimates for the grating pitch calibration are given, e.g. the standard uncertainty of 9 pm for 2 µm grating.

Acoustic method for the determination of the effective temperature and refractive index of air

An acoustic method for measurement of the effective temperature and refractive index of air along a laser beam path is described. The method can be used to improve the accuracy of interferometric length measurements outside the best laboratories, and even in severe environmental conditions. The method is based on the measurement of the speed of ultrasound over the same distance measured with a laser interferometer. The effectiveness of the method derives from the fact that the relative effect of a change in air temperature is about two thousand times greater on the speed of sound than on the refractive index of air. Experimental equations for the effective temperature or refractive index of air as a function of the speed of sound, pressure, humidity and CO2 concentration are fitted using the measured speed of sound, the Cramer equation, the dispersion correction and Edlén equations. The standard uncertainties of the effective temperature and the refractive index of air equations are estimated to be 15 mK and 1.7×10-8, respectively. The uncertainties of the effective temperature and refractive index of air measured with the test setup were 25 mK and 2.6×10-8 (for L = ~5 m), respectively.

Intercomparison of lateral scales of scanning electron microscopes and atomic force microscopes in research institutes in Northern Europe

An intercomparison of lateral scales of scanning electron microscopes (SEM) and atomic force microscopes (AFM) in various research laboratories in Northern Europe was organized by the local national metrology institutes. In this paper are presented the results of the comparison, with also an example uncertainty budget for AFM grating pitch measurement. Grating samples (1D) were circulated among the participating laboratories. The participating laboratories were also asked about the calibration of their instruments. The accuracy of the uncertainty estimates seemed to vary largely between the laboratories, and for some laboratories the appropriateness of the calibration procedures could be considered. Several institutes (60% of all results in terms of En value) also had good comprehension of their measurement capability. The average difference from reference value was 6.7 and 10.0 nm for calibrated instruments and 20.6 and 39.9 nm for uncalibrated instruments for 300 nm and 700 nm gratings, respectively. The correlation of the results for both nominally 300 and 700 nm gratings shows that a simple scale factor calibration would have corrected a large part of the deviations from the reference values.

Joint Research on Scatterometry and AFM Wafer Metrology

Supported by the European Commission and EURAMET, a consortium of 10 participants from national metrology institutes, universities and companies has started a joint research project with the aim of overcoming current challenges in optical scatterometry for traceable linewidth metrology. Both experimental and modelling methods will be enhanced and different methods will be compared with each other and with specially adapted atomic force microscopy (AFM) and scanning electron microscopy (SEM) measurement systems in measurement comparisons. Additionally novel methods for sophisticated data analysis will be developed and investigated to reach significant reductions of the measurement uncertainties in critical dimension (CD) metrology. One final goal will be the realisation of a wafer based reference standard material for calibration of scatterometers.

Dynamical Nonlinearities in Piezoelectric Materials

Dynamical nonlinearities in piezoelectric materials have been investigated over different time and frequency scales using four different methods; measurements of displacement and electric polarization of bulk material, measurements of nanometer scale surface structure of the material by an atomic force microscope (AFM), and numerical modelling of ferroelectric materials with quenched randomness. Laser vibrometer measurements of the deformations of piezoelectric materials, d31 type PZT and PMN-PT sheets, have been done under sinusoidal voltage loading with different frequencies. This yields information about the dynamical hysteresis behavior, such as the area of the hysteresis loops as a function of the applied frequency f and voltage amplitude. Similarly the hysteresis loops have been measured for the electric polarization of the same samples. Relaxation behaviors of the same materials have been measured by an AFM. Topography of the piezo sheets was measured after applied DC voltage, indicating slow collective changes in the polarization close and at the sample surface. To investigate the time-dependent hysteresis, we have studied numerically a Ginzburg-Landau-Devonshire (GLD) model for ferroelectric materials including dilution type quenched randomness. Quantities studied include the area of the hysteresis loop, of the polarization in the material, and the coercive electric field E c as a function of the frequency f , both as a function of the disorder strength.