Hard disk drives, optics, and semiconductors are just a few of the devices that depend more and more on reliable metrology in the nanometer domain. Thus, there has been great effort to extend our understanding of the macro regime to the nanometer world of molecules, atoms, and crystal structures. Metrology tools such as optical interferometers, contact profilometers, and atomic force microscopes (AFMs) constitute the essential infrastructure needed to address the needs of these applications and the atomic scale that developments are driving them toward.
Part of the challenge of nanometer metrology is that each metrology tool has its own strengths and weaknesses. Optical interferometers require skilled installation, calibration, and operation to achieve accurate measurements in the nanometer domain. Contact profilometers lack sensitivity at the nanometer scale, while AFMs suffer stability issues with their piezoelectric probes. Profilometer and AFM transducers with good stability do not have the sensitivity to observe a nanometer, and transducers with good sensitivity are not stable enough for reliable and usable measurements.
All of these challenges have been aggravated by the dearth of calibration artifacts at the nanometer scale. nanocalibration conundrum
Most nanometer measurements are to assess a surface. The calibration problem is particularly acute in the z-axis (normal to the surface). In the x-y plane (parallel to the surface), the surface usually has features whose size we may estimate with some accuracy; for example, the crystal lattice of the base material or larger fabricated grooves and ridges. The z-axis direction has no such features to guide the assessment of heights since the depth or height of manufactured grooves and steps is much harder to control dimensionally. This uncertainty becomes increasingly large for heights under about 20 nm. Commercially available step height standards under around 10 nm can have uncertainties in their height of 10%.
Figure 1. NIST created a single-atom-silicon step-height calibration unit with step heights of 0.31 nm and uncertainty of 6%; this uncertainty can preclude the use of this calibration guide for some industrial applications.
The National Institute of Standards and Technology (NIST; Gaithersburg, MD) has developed a single-silicon-atom step as a height standard by ion etching a silicon crystal at a shallow angle to the lattice (see figure 1). This has resulted in steps about 0.31 nm high but with an uncertainty of about 6%, which makes it only marginally useful in industry.
NASA recently came to the rescue by developing space-rated transducers that have great stability and sensitivity suitable for nanometer and picometer positioning in space instruments.1 This same technology has been adapted to the z-axis calibration problem by incorporation into a calibrated displacement actuator (CDA) that can be used to create nanometer-sized and even picometer-sized artifacts suitable for calibrating metrology instruments. The CDA is actually a transfer standard that can itself be calibrated by interferometer and is therefore directly traceable to the wavelength of light, the international standard of length. The uncertainty of CDA artifacts has been demonstrated to be as low as 0.04% for ±180 nm in height/depth.
The CDA is a compound transducer created by cascading a Lorenz-force transducer and an elastic transducer. The Lorenz-force transducer consists of a wire coil placed between a pair of permanent magnets. An electrical current in the coil produces a force between the coil and the magnets that is directly proportional to the current. These forces are then applied to the elastic transducer. The elastic transducer converts the Lorenz forces into elastic stresses and strains, and these, in turn, create a displacement proportional to the Lorenz forces.
If everything is assembled properly, the elastic displacement output of the CDA is linearly proportional to the current input to the coil. Tests have shown that the compound transducer comprising the CDA is linear and repeatable to less than one part in ten thousandfar better than the accuracy of commercially available step-height standards.
The current may be measured by digital ammeter to four or five decimal places so the accuracy of the calibration coefficient depends only on the accuracy of the calibrating interferometer. Accuracies for common interferometers of λ/100 are common and can reach λ/1000; higher-resolution interferometry techniques can produce higher accuracies.
In tests at the Naval Air Warfare Center (China Lake, CA) and NIST, the CDA has shown itself to be linear and repeatable to better than one part in 10,000 and stable to better than six parts in 10,000 per year.2 This stability combined with its sensitivity in the trans-nanometer dimensional domain make the CDA very useful for calibrating metrology instruments that are attempting to make nanometer-sized measurements. applications and standards
One typical laboratory application for a CDA is end-to-end checkout of interferometers to ensure that the entire system, including software, is performing as expected. Interferometers may be intrinsically self-calibrating if they are appropriately installed, aligned, and operated and if the software has been suitably written for the fringe-interpretation task; these criteria are not always met, however.
Figure 2. A CDA in a vacuum bottle checks the end-to-end performance of an interferometer. Initial tests at a national laboratory showed that an operational interferometer was off by as much as 30 to 40%. ALSON E. HATHEWAY INC.
In a typical case, a major research laboratory wanted to measure magnetostrictive actuator performance at the nanometer scale in a cryogenic environment. A NIST-calibrated CDA inserted in the active leg of the interferometer acted as a surrogate for the actuator to be later tested (see figure 2 on p. 14). The technicians programmed a known displacement into the CDA. The resultant interferometer readings showed errors of 30 to 40%, which was four to five times the resolution specified by the instrument manufacturer.
The software was not suspect in this case so the engineers and scientists adjusted the installation, alignment, and operation of the interferometer. Repeated trials with the CDA led to changes in a combination of environmental controls, installation guidelines, and operating procedures that permitted the interferometer to operate repeatably and reliably at the limits of its resolution in the nanometer regime. If the checkout with a CDA had not been performed, it is likely that all of the interferometer's installation, alignment, and operational errors would have been attributed to the magnetostrictive actuators under test, giving a very false impression of their behavior.
Another typical application for a CDA in industry involves the need to measure the thickness of a deposited film or the depth of an etched groove on a silicon wafer. Such measurements are often made with AFMs because of the fine sensitivity of the piezoelectric transducers they use for measurement. The piezoelectric transducers are not stable, however, and their coefficients may drift 15 to 20% over the course of minutes or days.
Piezoelectric transducers need to be calibrated frequently to minimize the influence of their drift over time (see oemagazine, November 2003, p. 40). One root cause is that the piezoelectric coefficient is sensitive to the history of the voltage applied to the transducer. To address this issue, the transducer needs to be calibrated at the size of the intended measurement so the voltage applied during measurement is the same as that applied during calibration.
Figure 3. A CDA can be placed directly on the stage of an AFM, allowing "at-size" calibration prior to measurement or periodically within batch measurements.
The CDA can perform both frequent and "at-size" calibrations of an instrument (see figure 3 on p. 14). It can actually help to stabilize the piezoelectric coefficient by repeating the at-size calibration a number of times, establishing a stable voltage history for the transducer prior to measurement. The device can thus minimize the influences of both drift over time and voltage history in AFM measurements.
Because of its stability, sensitivity, and reliability, several groups have adopted the CDA as a calibration standard for metrology instruments, including the American National Standards Institute committee B46. The committee, under the guidance of the American Society of Mechanical Engineers, has just published the first national standard that addresses the issues of nanometer metrology.3
As described above, the CDA promises a continuous dimensional scale through the trans-nanometer domain from the wavelength of light to the diameter of the atomic nucleusover eight orders of magnitude, and perhaps beyond. In the future, this metrology capability and the research it inspires may make it finally possible to reconcile quantum and Newtonian mechanics. Surely, this is not too much to expect from our new generation of researchers. oe
1. A. Hatheway, Type 2 Actuator, Final Report, NASA Langley Research Center, Hampton, VA (Contract No. NAS1-98035).
2. A. Hatheway, Proc. SPIE 4608, p. 132 (2001).
3. ASME/B46.1-2002, Surface Texture (Roughness, Waviness and Lay), an American National Standard (New York: American Society of Mechanical Engineers, 2003); www.asme.org.
Hatheway rides his own wave
Ask Alson Hatheway about waves and the response is as likely to be about optical interference as it to be about slipping some radical curls just south of Los Angeles. After all, diehard surfers die hard. Hatheway was born in Laguna Beach, CA, with a love for surfing and a strongly held scientific tenet: "If something always happens, there's a damned good reason why," Hatheway explains with a wry smile. "Engineering school followed because science was too philosophical and I was always in the thrall of the design arts."
Apparent contradictions are no stranger to Hatheway, who has spent his professional career investigating a variety of topics from crack transient-propagation software to seat-sensors for automobiles. These days, he focuses on calibration standards for nanometer metrology instruments.
Initially, Hatheway studied to be a set designer, eventually becoming his community college's stage manager for theatrical productions before going on to earn his BS in mechanical engineering at the University of California, Berkeley. The theater remained a focal point after college as Hatheway's days were spent at Boeing Aerospace (Seattle, WA) while his nights were the property of a community playhouse in Seattle.
Hatheway would continue his professional development in optical engineering at Ford Aerospace (Palo Alto, CA), Xerox (Stamford, CT), Hughes Aircraft (El Segundo, CA), and Gould Inc. (El Monte, CA) before opening his own engineering company in 1979. In addition to his renewed focus on optomechanical and precision engineering, Hatheway continues to be an important part of the optical community as a Fellow of SPIE and a Fellow and past president of the Optical Society of Southern California.
Do the twist
In torsion-mode AFM, the cantilever twists about its long axis to execute small torsion resonant oscillations.
By Michael Serry, Veeco Instruments
Atomic force microscopes track the motion of a sharp-tipped, low-force microcantilever drawing across the surface under test to extract dimensional and surface-property data. Each primary atomic force microscopy (AFM) imaging mode uses a different way to sense and control the tip-sample interaction, and enables numerous derivative modes. Torsion resonance (TR) mode is the latest primary imaging mode in AFM.
In TR mode, the atomic force microscope cantilever is mechanically driven at or near its fundamental torsion resonance frequency. As the cantilever executes small torsion resonant oscillations by twisting about its long axis, the cantilever's free end and the AFM tip rotate a very small angle about that axis. The tip apex, then, executes pendulum-like oscillations, which, at these small angles, are exceedingly small (typically, 0.2 to 2.0 nm rms) and substantially parallel to the x-y plane (see figure).
TR mode is a unique primary imaging mode, first because it combines perpetual tip-sample proximity with a small lateral tip dither in a way that makes it possible for the tip to scan near the sample surface nearly all the time and yet not be in contact. This results in much better control of tip-sample interaction strength than is possible in contact-mode AFM. TR mode and TR-mode derivatives such as TR-mode tunneling AFM can thus image softer samples much more effectively than contact-mode AFM or derivatives. Chances of damaging a soft sample are much reduced or eliminated.
Dynamic tip-sample interaction of TR-mode AFM is mainly in-plane (or lateral), which sets the method apart from the other primary imaging modes whose dynamic tip-sample interactions are mainly vertical, or out-of-plane. TR-mode AFM is sensitive to differences that arise in lateral tip-sample interaction strength at the same sample location when the in-plane orientation of the sample is changed. In other words, TR-mode can detect differences in tip-sample interaction that indicate azimuthal anisotropy on or near the sample surface.
The information revealed in TR-mode images is often complimentary to that in tapping-mode AFM images; in fact, the two are often collected together in the same area, using interleaving. TR-mode phase images have revealed new information complimentary to interleaved tapping-mode phase images about the domains in heterogeneous polymer samples. Even on highly-oriented pyrolytic graphite (HOPG), extensively imaged and studied with various AFM modes for more than a decade, TR-mode AFM has revealed new features and information, the origin and interpretation of which is now the subject of fresh debate.
Groups at major research institutions are using TR mode to study nanotribology of self-assembled monolayers and perform fast scans of polymers. A growing body of evidence suggests that TR-mode AFM will become a significant new mode of operation for visualizing and otherwise characterizing matter on the nanometer scale.
Michael Serry is senior applications scientist at Veeco Instruments, Santa Barbara, CA.
Alson Hatheway is a president of the engineering consulting firm Alson E. Hatheway Inc., Pasadena, CA.