Metrological Atomic Force Microscope Research Articles

Traceability of measurement results in the nanometric range to the units of the international system of units of physical quantities

Questions involved in the assurance of the traceability of results of measurements in the nanometric range to standards included in the BIPM CMC base of measurements of geometric quantities are considered for which a set of calibrated (verified) gauges along with a chain of traceability to the standard, i.e., the metrological atomic-force microscope, are proposed. Two methods of calibration of scanning probe microscopes are also proposed, a direct method and a method that employs the Fourier transform of the measure topogram. A technique of calibration of scanning electron microscopes; the uncertainty budget and formulas for use in calculating its components in calibration relative to a relief measure in the TGQ1 nanometric range are also given.

Metrological atomic force microscope with self-sensing measuring head

A metrological atomic force microscope (AFM) adapting compact measuring head for the micro-nano dimensional measurement is introduced in this paper. Based on a novel self-sensing probe the head does not need any optical detector to measure the bending of the cantilever, significantly saving the working space to integrate with other measuring methods. This AFM operates in tapping mode and adapts frequency modulation (FM) mode to enhance measuring speed. A z-axis piezoelectric positioning stage (compact z-stage), with high resonant frequency, is responsible for the rapid motion of the sample in z-direction. A high-end digital signal processing (DSP) servo control system further guarantees high measurement speed. A nano-measuring machine (NMM) is equipped as the lateral moving stage to realize three-dimensional measurement. Three interferometers in the NMM enable the measurement to be traced to the meter definition. After calibration, the measurement of one-dimensional grating has been made. According to experimental results, the resolution of the AFM can reach nanometer level.

Methods for determining and processing 3D errors and uncertainties for AFM data analysis

This paper describes the processing of three-dimensional (3D) scanning probe microscopy (SPM) data. It is shown that 3D volumetric calibration error and uncertainty data can be acquired for both metrological atomic force microscope systems and commercial SPMs. These data can be used within nearly all the standard SPM data processing algorithms to determine local values of uncertainty of the scanning system. If the error function of the scanning system is determined for the whole measurement volume of an SPM, it can be converted to yield local dimensional uncertainty values that can in turn be used for evaluation of uncertainties related to the acquired data and for further data processing applications (e.g. area, ACF, roughness) within direct or statistical measurements. These have been implemented in the software package Gwyddion.

Multilaboratory comparison of traceable atomic force microscope measurements of a 70-nm grating pitch standard

The National Institute of Standards and Technology (NIST), Advanced Surface Microscopy (ASM), and the National Metrology Centre (NMC) of the Agency for Science, Technology, and Research (A*STAR) in Singapore have completed a three-way interlaboratory comparison of traceable pitch measurements using atomic force microscopy (AFM). The specimen being used for this comparison is provided by ASM and consists of SiO2 lines having a 70-nm pitch patterned on a silicon substrate. For this comparison, NIST used its calibrated atomic force microscope (C-AFM), an AFM with incorporated displacement interferometry, to participate in this comparison. ASM used a commercially available AFM with an open-loop scanner, calibrated with a 144-nm pitch transfer standard. NMC/A*STAR used a large scanning range metrological atomic force microscope with He-Ne laser displacement interferometry incorporated. The three participants have independently established traceability to the SI (International System of Units) meter. The results obtained by the three organizations are in agreement within their expanded uncertainties and at the level of a few parts in 104.

Design and characterization of MIKES metrological atomic force microscope

Abstract An interferometrically traceable metrological atomic force microscope (IT-MAFM) has been developed at MIKES. It can be used for traceable atomic force microscope (AFM) measurements and for calibration of transfer standards of scanning probe microscopes (SPMs). Sample position is measured online by 3 axes of laser interferometers. A novel and simple method for detection and online correction of the interferometer nonlinearity was developed. Effect of the nonlinearity in measurements is demonstrated. In the design, special attention has been paid to elimination of external disturbances like electric noise, acoustic noise, ambient temperature variations and vibrations. The instrument has been carefully characterized. The largest uncertainty components are caused by Abbe errors, orthogonality errors, drifts and noise. Noise level in Z direction was 0.25 nm, and in X and Y directions 0.36 nm and 0.31 nm, respectively. Standard uncertainties for X , Y and Z coordinates are u cx = q [0.48; 0.04 x ; 0.17 y ; 1.7 z ; 2 time] nm, u cy = q [0.45; 0.31 x ; 0.07 y ; 0.14 z ; 4 time] nm and u cz = q[0.42; 3 x ; 7.2 y ; 0.18 z ; 2 time] nm where x , y , z are in μm and time in h. Standard uncertainty for 300 nm pitch is 0.023 nm,and for 7 nm step height measurement is 0.35 nm. Uncertainty estimates are supported by an international comparison.

Directional Repetitive Control of a Metrological AFM

Atomic force microscopes (AFMs) are used for sample imaging and characterization at nanometer scale. In this work, we consider a metrological AFM, which is used for the calibration of transfer standards for commercial AFMs. The metrological AFM uses a three degree-of-freedom (DOF) stage to move the sample with respect to the probe of the AFM. The repetitive sample topography introduce repetitive disturbances in the system. To suppress these disturbances, repetitive control (RC) is applied to the imaging axis. A rotated sample orientation with respect to the actuation axes introduces a non-repetitiveness in the originally fully repetitive errors and yields a deteriorated performance of RC. Directional repetitive control is introduced to align the axes of the scanning movement with the sample orientation under the microscope. Experiments show that the proposed directional repetitive controller significantly reduces the tracking error as compared to standard repetitive control.

Metrological atomic force microscope using a large range scanning dual stage

We developed a metrological atomic force microscope (MAFM) using a large range scanning dual stage and evaluated the performance in the measurement of lateral dimension. AFMs are widely used in nanotechnology for very high spatial resolution, but the limitation in measurement range should be overcome to expand its application in nanometrology. Therefore, we constructed new MAFM having a large measurement of 200 mm × 200 mm by using a dual stage and an AFM head module. The dual stage is composed of a coarse and a fine stage to obtain large scanning range and high resolution simultaneously. Precision surfaces and PTFE sliding pads guide the motion of coarse stage, drove by a fine pitch screw and DC motors. Flexure hinges and PZT actuators are utilized for the fine stage. Multi-axis interferometers measure the five degrees of freedom motion of the dual stage for the position control and the compensation of parasitic angular motions. The vertical displacement of AFM tip is measured by a built-in capacitive sensor in the AFM head module within the range of 38 µm. The performance of the dual stage was evaluated and the expanded uncertainty (k = 2) in the measurements of 1-D displacement L was estimated as \( U(L) = \sqrt {(2.8nm)^2 + (3.0 \times 10^{ - 7} \times L)^2 } \). The relative uncertainty in pitch measurement was less than 0.02 % and the improvement of accuracy was verified by comparing with other MAFM, which are mostly due to the expansion of scan range and the compensation of angular motion. To enhance the performance, we will reduce the vibration and examine the motion of stage in the vertical direction during a long range scan.

Metrological atomic force microscopy integrated with a modified two-point diffraction interferometer

We propose a new concept for a metrological atomic force microscope integrated with a modified two-point diffraction interferometer that can determine the xyz-coordinates in an absolute manner. The interferometer consists of two single-mode optical fibers; one fiber is fixed to be stationary and the other is attached on an xyz-stage that moves with the measuring sample. The two fibers generate two separate spherical wavefronts that interfere with each other. Phase information can be obtained from this interference fringe pattern by applying well-known phase shifting techniques. This phase information is very sensitive to the relative coordinates between the two fiber ends, and thus the xyz-coordinates of the stage can be measured with respect to the fixed machine structure. A 100 µm × 100 µm × 20 µm working volume is available in the proposed system.

A concept for automated nanoscale atomic force microscope (AFM) measurements using a priori knowledge

The nanometer coordinate measuring machine (NCMM) is developed for comparatively fast large area scans with high resolution. The system combines a metrological atomic force microscope (AFM) with a precise positioning system. The sample is moved under the probe system via the positioning system achieving a scan range of 25 × 25 × 5 mm3 with a resolution of 0.1 nm. A concept for AFM measurements using a priori knowledge is implemented. The a priori knowledge is generated through measurements with a white light interferometer and the use of CAD data. Dimensional markup language is used as a transfer and target format for a priori knowledge and measurement data. Using the a priori knowledge and template matching algorithms combined with the optical microscope of the NCMM, the region of interest can automatically be identified. In the next step the automatic measurement of the part coordinate system and the measurement elements with the AFM sensor of the NCMM is done. The automatic measurement involves intelligent measurement strategies, which are adapted to specific geometries of the measurement feature to reduce measurement time and drift effects.

Design of a large measurement-volume metrological atomic force microscope (AFM)

The design of a large measurement-volume metrological atomic force microscope (AFM) is presented. The translation of the sample is accomplished with multiple stages which allow for separate ‘coarse’ and ‘fine’ motion. Interferometers and autocollimators are used to measure the position and orientation of the sample. The instrument does not attempt to control position via feedback from the interferometers, thereby allowing use of readily available commercial translation stages and controllers.

A metrological large range atomic force microscope with improved performance

A metrological large range atomic force microscope (Met. LR-AFM) has been set up and improved over the past years at Physikalisch-Technische Bundesanstalt (PTB). Being designed as a scanning sample type instrument, the sample is moved in three dimensions by a mechanical ball bearing stage in combination with a compact z-piezostage. Its topography is detected by a position-stationary AFM head. The sample displacement is measured by three embedded miniature homodyne interferometers in the x, y, and z directions. The AFM head is aligned in such a way that its cantilever tip is positioned on the sample surface at the intersection point of the three interferometer measurement beams for satisfying the Abbe measurement principle. In this paper, further improvements of the Met. LR-AFM are reported. A new AFM head using the beam deflection principle has been developed to reduce the influence of parasitic optical interference phenomena. Furthermore, an off-line Heydemann correction method has been applied to reduce the inherent interferometer nonlinearities to less than 0.3 nm (p-v). Versatile scanning functions, for example, radial scanning or local AFM measurement functions, have been implemented to optimize the measurement process. The measurement software is also improved and allows comfortable operations of the instrument via graphical user interface or script-based command sets. The improved Met. LR-AFM is capable of measuring, for instance, the step height, lateral pitch, line width, nanoroughness, and other geometrical parameters of nanostructures. Calibration results of a one-dimensional grating and a set of film thickness standards are demonstrated, showing the excellent metrological performance of the instrument.

Higher accuracy analysis of instrumented indentation data obtained with pointed indenters

We review current practice for describing force–displacement curves from pointed indenters, highlighting the consequences of the simplifications normally adopted. We derive two corrections, the ‘variable epsilon factor’ and the ‘radial displacement correction.’ These are especially important for highly elastic materials such as fused silica where the combined corrections can amount to 13% in the contact area, significantly increasing the accuracy of hardness and modulus results. In contrast, the so-called beta factor has minor importance. We compare our analytical results with finite element (FE) calculations and experimental results. Indenter area functions, obtained using the corrections, agree well with independent direct measurements by a traceably calibrated metrological atomic force microscope (AFM). Further formulae are derived to calculate the complete force–displacement curve of conical indenters and the indentation elastic and total energy. These formulae immediately identify a physical material limit above which a cone cannot generate plastic deformation; for a Berkovich indenter this is a hardness-to-modulus ratio of 0.18.

Detecting and addressing the surface following errors in the calibration of step heights by atomic force microscopy

Step height standards are widely used for the calibration of the z-axis scale of scanning probe microscopes. NPL, in common with a number of other national measurement institutes, has constructed a metrological atomic force microscope (MAFM) that delivers traceable calibration of step height standards. The measurement uncertainty of the calibrations is a combination of those uncertainties associated with the metrology frame, whose values can be estimated with good accuracy, and those associated with the AFM head, whose values are more difficult to quantify. Estimates of these values are usually based on the repeatability of measurements, either in isolation for a particular sample, or in combination with historical data on instrument performance. That the estimates are reasonable may be verified by comparing the AFM measurements with measurements made on other independent, traceable systems. This paper describes how the verification process led to the detection of a significant following error in one of the heads employed on the NPL MAFM, which could then be evaluated and addressed. The value of measurement uncertainty for the step height measurements is also dependent on the physical characteristics of the standard. Results are presented for measurements of a fine scale step height standard that has been designed for optimum compatibility with the measurement procedure in order to reduce the measurement uncertainty.

Final report on Supplementary Comparison APMP.L-S2: Bilateral comparison on pitch measurements of nanometric lateral scales (50 nm and 100 nm) between NMIJ/AIST (Japan) and PTB (Germany)

One-dimensional (1D) gratings are important standards in nanometrology. The pitch measurements of 1D gratings were included in a series of comparisons in the field of nanometrology by the CCL-WGDM7 in the year 1998. The comparison of 1D gratings (NANO4, CCL-S1) was completed in the year 2000; however, the pitches of 1D gratings used in the comparison were quite large (pitches of 700 nm and 290 nm). Since 1D gratings with smaller pitches are increasingly required especially in the semiconductor industries, NMIJ developed 'nanometric lateral scales', special 1D gratings with pitches of 100 nm and 50 nm, and started a bilateral comparison of the scales (APMP.L-S2) with PTB in March 2006. The pilot laboratory of the comparison was NMIJ and the APMP-TCL chair acted as an adjudicator of the comparison. Metrological atomic force microscopes were used for the pitch measurements. The reference values were calculated using all measurement results and normal En numbers were used for analysis.The comparison was performed very smoothly due to the good collaboration of the participants and the adjudicator. The rules of international comparison set up by the CIPM were strictly followed in the comparison. The calibration results from NMIJ and PTB show an excellent agreement. The deviation of the measurement results from NMIJ and PTB was less than 0.03 nm and 0.01 nm for the gratings with 100 nm and 50 nm pitch, respectively. All En numbers were much smaller than 1, indicating a very successful comparison. Uncertainty components of the calibration methods of both participants were almost the same; however, the values of combined standard uncertainty were quite different. This is mainly because the contributions of the uncertainty components in the expanded uncertainty budget were estimated in a different way, for instance, that of the interferometer nonlinearity. NMIJ and PTB have learned from this comparison that there is still room to reduce the measurement uncertainty and the comparison results are valuable for other NMIs.Main text.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the APMP, according to the provisions of the CIPM Mutual Recognition Arrangement (MRA).

Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope

Microscope calibration standards in nanometrology were calibrated using a metrological atomic force microscope (metrological AFM) and the validity of calibrated values was shown. The metrological AFM was developed through the modification of a commercial AFM, which replaced the PZT tube scanner with flexure hinge scanners and displacement sensors. These modifications improved the traceability of measured values to metrological primary standards. The grating pitch and step height specimens, which are typical standard artefacts for the calibration of lateral and vertical magnifications of microscopes, were measured using the metrological AFM. The expanded uncertainties (k = 2) of calibrated values were estimated considering the characteristics of the calibration process and were less than 1 nm. The measurement results were compared with those obtained by other metrological methods or the certified values and their consistency was verified by checking the En numbers. These experimental results show that the metrological AFM can be used effectively for the measurements of microscope calibration standards in nanometrology.

Design and Evaluation of Two Dimensional Metrological Atomic Force Microscope using a Planar Nanoscanner

An atomic force microscope (AFM) using a laser interferometer is regarded as one of the best solutions for the standardization of two dimensional length measurement systems. We propose a new two dimensional (2D) metrological AFM system, which uses an orthogonally decoupled XY scanner and a commercial AFM head. We designed a decoupled planar scanner having minimal parasitic errors, particularly crosstalk errors. The parasitic tilt error was measured and evaluated using an autocollimator. Furthermore, we evaluated the uncertainty of the combined system according to the Guide to the Expression of Uncertainty in Measurement.

Traceable calibration of transfer standards for scanning probe microscopy

A Metrological Atomic Force Microscope (MAFM) has been constructed for the traceable calibration of transfer standards for scanning probe microscopy. It uses optical interferometry to generate image scales with direct traceability to the national standard of length. Three interferometers monitor the relative displacements of the AFM tip and sample in the x, y and z directions and the interferometer data is used directly to construct 3D images of sample surfaces. Traceable dimensional measurement of surface features may then be derived from the image data. This paper describes the MAFM instrument and presents a measurement uncertainty budget. Examples are given of measurements of pitch and step height on calibration transfer standards for scanning probe microscopy.

Calibration of step heights and roughness measurements with atomic force microscopes

In this paper we present a method for the vertical calibration of a metrological atomic force microscope (AFM), which can be applied to most AFM systems with distance sensors. A thorough analysis describes the physical z-coordinate of an imaged surface as a function of the observed and uncorrected z-coordinate and the horizontal position. The three most important correction terms in a Taylor expansion of this function are identified and estimated based on series of measurements on a calibrated step height and a flat reference surface. Based on this calibration a number of step heights are calibrated by the AFM with measured values consistent with reference values, where available. Relative standard uncertainty of about 0.5% is achieved for step heights above 200 nm. For step heights below 50 nm, the standard uncertainty is about 0.5 nm. While a calibration of step heights done by AFM and interference microscopy can be compared directly as demonstrated here, this is not straightforward for roughness measurement. To asses this, the exact same area on an important applied surface (a hip joint prosthesis) was measured by both AFM and interference microscopy. Similarities in the images were seen; however, the calculated roughness was significantly different ( R q=3 and 1.5 nm). Applying a low-pass filter with a cut-off wavelength of λ c=1.5 μm, the appearance of the images and the calculated roughness become almost identical. This strongly suggests that the two methods are consistent, and that the observed differences in shape and roughness in the nanometer range can be explained by the limited lateral resolution of the interference microscope.

Long-range AFM profiler used for accurate pitch measurements

A long-range atomic force microscope (AFM) profiler system was built based on a commercial metrology AFM and a home-made linear sample displacement stage. The AFM head includes a parallelogram-type scanner with capacitive position sensors for all three axes. A reference cube located close to the tip acts as the counter electrode for the capacitive sensors. Below this metrology AFM head we placed a linear sample displacement stage, consisting of monolithic flexures forming a double parallelogram. This piezo actuated stage provides a highly linear motion over m. Its displacement is simultaneously measured by a capacitive position sensor and a differential double-pass plane mirror interferometer; both measuring systems have subnanometre resolution capability. For the measurement of periodical structures two operating modes are possible: a direct scanning mode, in which the position of the displacement stage is increased point by point while the AFM head measures the height, and a combined scanning mode where the displacement stage produces offsets which are multiples of the pitch to be measured while the AFM head is simultaneously scanning to locate an edge or a line centre position. Construction details, system characteristics and results from first pitch measurements are presented. The estimated relative combined uncertainties for pitch values on different standards are in the range to . Laser diffraction measurements of comparable uncertainty were performed on the same standards and show a very good agreement.