Uncertainty in pitch measurements of one-dimensional grating standards using a nanometrological atomic force microscope
TL;DR: In this paper, the precision measurements of 240 nm-pitch one-dimensional grating standards were carried out using an atomic force microscope (AFM) with a high-resolution three-axis laser interferometer (nanometrological AFM).
Abstract: Precision measurements of 240 nm-pitch one-dimensional grating standards were carried out using an atomic force microscope (AFM) with a high-resolution three-axis laser interferometer (nanometrological AFM). Laser sources of the three-axis laser interferometer in the nanometrological AFM were calibrated with an I2-stabilized He–Ne laser at a wavelength of 633 nm. The results of the precision measurements using the nanometrological AFM have direct traceability to the length standard. The uncertainty in the pitch measurements was estimated in accordance with the Guide to the Expression of Uncertainty in Measurement. The primary source of uncertainty in the measurements was derived from interferometer nonlinearity, and its value was approximately 0.115 nm. Expanded uncertainty (k = 2) of less than 0.31 nm was obtained. It is suggested that the nanometrological AFM is a useful instrument for the nanometrological standard calibration.
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TL;DR: In this paper, the state of the art in scanning force microscopy for dimensional metrology is described and a detailed description is given of the important factors affecting the major components of a scanning force microscope from the metrological point of view.
143 citations
TL;DR: In this paper, the calibration of 1D and 2D gratings is performed using a metrological large range scanning probe microscope with optimized measurement strategies, and two different kinds of data evaluation methods, a gravity center method and a Fourier transform method, are developed and investigated.
Abstract: Accurate and traceable calibration of lateral standards (1D and 2D gratings) is a basic metrological task for nano- and microtechnology. Both the mean pitch and the uniformity of the gratings should be measured quantitatively. Although optical diffractometers are effective for measuring the mean pitch, they are not able to measure the uniformity of gratings. In this study, the calibration of gratings is performed using a metrological large range scanning probe microscope with optimized measurement strategies. Two different kinds of data evaluation methods, a gravity centre method and a Fourier transform method, have been developed and investigated. Cosine error, a significant error source of the measurement, is analysed and corrected. Calibrations on several 1D gratings have been carried out. The calibrated mean pitch values have an excellent agreement with those measured by optical diffractometry. Nevertheless, irregularities of the gratings were only deduced from the SPM results. Finally, the usage of the 1D/2D gratings for the calibration of a typical SPM is illustrated.
122 citations
TL;DR: The Molecular Measuring Machine (MME) as discussed by the authors is an SPM and Michelson interferometer-based metrology instrument for point-to-point measurements over a 50 mm by 50 mm working area.
Abstract: Nanometre accuracy and resolution metrology over technically relevant areas is becoming a necessity for the progress of nanomanufacturing. At the National Institute of Standards and Technology, we are developing the Molecular Measuring Machine, a scanned probe microscope (SPM) and Michelson interferometer based metrology instrument, designed to achieve nanometre measurement uncertainty for point-to-point measurements over a 50 mm by 50 mm working area. The salient design features are described, along with example measurements that demonstrate the measurement capabilities so far achieved. Both long-range measurements of sub-micrometre pitch gratings over 10 mm, and short-range, high-resolution measurements of a molecular crystal lattice have been accomplished. The estimated relative measurement uncertainty so far attained for pitch measurements is 6 × 10−5, coverage factor k = 2. We have also used this instrument and scanning probe oxidation lithography for creating some simple nanometre dimension patterns that could serve as prototype calibration standards, utilizing the SPM probe tip positioning accuracy.
100 citations
TL;DR: In this paper, the authors present a brief overview of how this has been achieved, highlights the future requirements for metrology to support developments in AFM technology and describes work in progress to meet this need.
Abstract: Scanning probe microscopes, in particular the atomic force microscope (AFM), have developed into sophisticated instruments that, throughout the world, are no longer used just for imaging, but for quantitative measurements. A role of the national measurement institutes has been to provide traceable metrology for these instruments. This paper presents a brief overview as to how this has been achieved, highlights the future requirements for metrology to support developments in AFM technology and describes work in progress to meet this need.
88 citations
TL;DR: In this paper, the authors developed a new atomic force microscope with differential laser interferometers (DLI-AFM), carried out test measurements of the prototype 1D-grating standards with pitches of 100, 80, 60 and 50 nm using the DLI-AAFM and evaluated the uncertainty in the pitch measurements.
Abstract: We have developed a new atomic force microscope with differential laser interferometers (DLI-AFM), carried out test measurements of the prototype 1D-grating standards with pitches of 100, 80, 60 and 50 nm using the DLI-AFM and evaluated the uncertainty in the pitch measurements. In the procedures of the pitch calculation, two types of definitions of the peak positions, 'the centre of gravity method', and 'the zero-crossing method', were compared. The zero-crossing method was adopted in this study since the standard deviation of pitches by the zero-crossing method was smaller than that by the centre of gravity method. The expanded uncertainty (k = 2) was approximately 0.20 nm and was only 0.4% for the nominal pitch of 50 nm. We propose a design of usable 1D-grating standards as certified reference materials.
69 citations
References
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TL;DR: In this article, the authors presented an improved dispersion formula for standard air, (n − 1)s × 108 = 8342, where σ is the vacuum wave-number in μm-1.
Abstract: Present knowledge of the refractive index of air is reviewed. Regarding the absolute values there are as yet no definite indications that the standard adopted in 1953 on the basis of Barrell and Sears' measurements should be changed, but new experiments aiming at reducing the present uncertainty of about ± 5 × 10-8 would be desirable. Several recent investigations have contributed important new information on the dispersion of air, which has made it possible to derive an improved dispersion formula for standard air, (n − 1)s × 108 = 8342.13 + 2406030 (130 − σ2)-1 + 15997 (38.9 − σ2)−1, where σ is the vacuum wave-number in μm-1. The deviations from the 1953 formula are small and practically negligible in most spectroscopic work. An equation for the dependence of refractivity on temperature and pressure based on theoretical considerations has been derived. For the range of atmospheric conditions normally found in a laboratory the equation can be approximated by the formula (n − 1)tp = (n − 1)s × 0.00138823 p/(1 + 0.003671 t), with p in torr, t in °C, and (n − 1)s given by the dispersion formula for standard air. The effect of carbon dioxide and water vapour is discussed. From Erickson's dispersion data for water vapour, combined with Barrell and Sears' absolute measurements, one obtains the equation ntpf – ntp = −f (5.722 − 0.0457 σ2) × 10-8 for the difference in refractive index of moist air, containing f torr of water vapour, and dry air at equal temperature and total pressure. The equation is valid for visible radiations and normal atmospheric conditions.
1,229 citations
IBM1
TL;DR: In this article, the state of the art in high-resolution displacement measuring interferometry is reviewed, and several approaches to improve this situation are described, including multi-wavelength inter-ferometry.
Abstract: The present state of high-resolution displacement measuring interferometry is reviewed. Factors which determine the accuracy, linearity and repeatability of nanometre-scale measurements are emphasized. Many aspects of interferometry are discussed, including general metrology and alignment errors, as well as path length errors. Optical mixing and the nonlinear relation between phase and displacement are considered, as well as the influence of diffraction on accuracy. Environmental stability is a major factor in the repeatability and accuracy of measurement. It is difficult to obtain a measurement accuracy of 10-7 when working in air. Several approaches to improving this situation are described, including multiwavelength interferometry. Recent measurements of the short- and long-term frequency stability of lasers are summarized. Optical feedback is a subtle, but important source of frequency destabilization, and methods of detection and isolation are reviewed. Calibration of phase measuring electronics used for subfringe interpolation is included. Progress in 'in situ' identification of error sources and methods of validating accuracy are emphasized.
496 citations
TL;DR: In this article, 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, consisting of monolithic flexures forming a double parallelogram.
Abstract: 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.
145 citations
TL;DR: An atomic force microscope with a high-resolution three-axis laser interferometer for real-time correction of distorted topographic images has been constructed and investigated in this paper, where standard samples for a scanning probe microscope can be directly calibrated on the basis of stabilized wavelength of He-Ne lasers.
Abstract: An atomic force microscope with a high-resolution three-axis laser interferometer for real-time correction of distorted topographic images has been constructed and investigated. With this apparatus, standard samples for a scanning probe microscope can be directly calibrated on the basis of stabilized wavelength of He–Ne lasers. The scanner includes a three-sided mirror block as a mobile target mirror for the interferometer, which realizes a rectangular coordinate system. The position coordinates of the sample is independently and simultaneously acquired with high-resolution (0.04 nm) X/Y/Z interferometer units and fed back for XY servo scanning and height image construction. The probe is placed on the sample surface at the intersection of the three optical axes of the interferometer with good reproducibility, so that the Abbe error caused by the rotation of the scanner is minimized. Image distortion in the XY plane and vertical overshoot/undershoot due to nonlinear motion of piezo devices, hysteresis, and creep are eliminated. The optical properties of the interferometers, mechanical characteristics of the scanner, and system performances in dimensional measurements for calibration standards are demonstrated.
115 citations
"Uncertainty in pitch measurements o..." refers methods in this paper
...Yawing, rolling and pitching for X-axis direction scanning were estimated before measurement of the pitch values [5]....
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...The National Metrology Institute of Japan, AIST (NMIJ/AIST), developed a ‘nanometrological AFM’ system with a ultra-high resolution three-axis laser interferometer in 1999 [5, 6]....
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...A detailed description of the nanometrological AFM system is described elsewhere [5, 6]....
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TL;DR: The calibrated AFM (C•AFM) as mentioned in this paper uses a flexure stage driven by piezoelectric transducers for scanning, a heterodyne interferometer to measure the X and Y displacements of the sample, and a capacitance sensor for measuring the Z displacement.
Abstract: Advances in the manufacture of integrated circuits, x‐ray optics, magnetic read–write heads, optical data storage media, and razor blades require advances in ultraprecision metrology. Each of these industries is currently investigating the use of atomic force microscopy (AFM) to improve the precision and accuracy of their manufacturing process control. To facilitate the use of AFMs for manufacturing we have developed an AFM capable of making accurate dimensional measurements. We call this system the calibrated AFM (C‐AFM). The C‐AFM has been constructed as much as possible out of commercially available components. We use a flexure stage driven by piezoelectric transducers for scanning, a heterodyne interferometer to measure the X and Y displacements of the sample, a capacitance sensor to measure the Z displacement of the sample, and a commercially available AFM control system. The control system has two feedback loops which read from the X and Y interferometers, respectively, and adjust the piezoelectric ...
70 citations
"Uncertainty in pitch measurements o..." refers methods in this paper
...A calibrated AFM (CAFM) was developed at the National Institute of Standards and Technology (USA) in 1994 [1]....
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