A review of nanometer resolution position sensors: Operation and performance
Introduction
The sensor requirements of a nanopositioning system are among the most demanding of any control system. The sensors must be compact, high-speed, immune to environmental variation, and able to resolve position down to the atomic scale. In many applications, such as atomic force microscopy [1], [2] or nanofabrication [3], [4], the performance of the machine or process is primarily dependent on the performance of the position sensor, thus, sensor optimization is a foremost consideration.
In order to define the performance of a position sensor, it is necessary to have strict definitions for the characteristics of interest. At present, terms such as accuracy, precision, nonlinearity and resolution are defined loosely and often vary between manufacturers and researchers. The lack of a universal standard makes it difficult to predict the performance of a particular sensor from a set of specifications. Furthermore, specifications may not be in a form that permits the prediction of closed-loop performance.
This article provides concise definitions for the linearity, drift, bandwidth and resolution of position sensors. The measurement errors resulting from each source are then quantified and bounded to permit a straightforward comparison between sensors. An emphasis is placed on specifications that allow the prediction of closed-loop performance as a function of the controller bandwidth.
Although there are presently no international standards for the measurement or reporting of position sensor performance, this article is aligned with the definitions and methods reported in the ISO/IEC 98:1993 Guide to the Expression of Uncertainty in Measurement [5], and the ISO 5723 Standard on Accuracy (Trueness and Precision) of Measurement Methods and Results [6].
The noise and resolution of a position sensor is potentially one of the most misreported sensor characteristics. The resolution is commonly reported without mention of the bandwidth or statistical definition and thus has little practical value. To improve the understanding of this issue, the relevant theory of stochastic processes is reviewed in Section 2. The variance is then utilized to define a concise statistical description of the resolution, which is a straight-forward function of the noise density, bandwidth, and 1/f corner frequency.
The second goal of this article is to provide a tutorial introduction and comparison of sensor technologies suitable for nanopositioning applications. To be eligible for inclusion, a sensor must be capable of a 6σ-resolution better than 10 nm with a bandwidth greater than 10 Hz. The sensor cannot introduce friction or contact forces between the reference and moving target, or exhibit hysteresis or other characteristics that limit repeatability.
The simplest sensor considered is the metal foil strain gauge discussed in Section 3.1. These devices are often used for closed-loop control of piezoelectric actuators but are limited by temperature dependence and low sensitivity [7]. Piezoresistive and piezoelectric strain sensors provide improved sensitivity but at the cost of stability and DC performance.
The most commonly used sensors in nanopositioning systems [8] are the capacitive and eddy-current sensors discussed in 3.4 Capacitive sensors, 3.6 Eddy-current sensors. Capacitive and eddy-current sensors are more complex than strain sensors but can be designed with sub-nanometer resolution, albeit with comparably small range and low bandwidth. They are used extensively in applications such as atomic force microscopy [2], [9], [10], [11] and nanofabrication [12], [4]. The linear variable displacement transformer (LVDT) described in Section 3.7 is a similar technology that is intrinsically linear. However, this type of sensor is larger than a capacitive sensor and due to the larger range, is not as sensitive.
To achieve high absolute accuracy over a large range, the reference standard is the laser heterodyne interferometer discussed in Section 3.8. Although bulky and costly, the interferometer has been the sensor of choice for applications such as IC wafer steppers [13], [14] and metrological systems [15]. New fibre interferometers are also discussed that are extremely compact and ideal for extreme environments.
Aside from the cost and size, the foremost difficulties associated with an interferometer are the susceptibility to beam interference, variation in the optical medium, and alignment error. Since an interferometer is an incremental position sensor, if the beam is broken or the maximum traversing speed is exceeded, the system must be returned to a known reference before continuing. These difficulties are somewhat alleviated by the absolute position encoders described in Section 3.9. A position encoder has a read-head that is sensitive to a geometric pattern encoded on a reference scale. Reference scales operating on the principle of optical interference can have periods of 128 nm and a resolution of a few nanometers.
Other sensor technologies that were considered but did not fully satisfy the eligibility criteria include optical triangulation sensors [16], hall effect sensors, and magnetoresistive sensors. In general, optical triangulation sensors are available in ranges from 0.5 mm to 1 m with a maximum resolution of approximately 100 nm. Hall effect sensors are sensitive to magnetic field strength and hence the distance from a known magnetic source. These sensors have a high resolution, large range and wide bandwidth but are sensitive to external magnetic fields and exhibit hysteresis of up to 0.5% which degrades the repeatability. The magnetoresistive sensor is similar except that the resistance, rather than the induced voltage, is sensitive to magnetic field. Although typical anisotropic magnetoresistive (AMR) sensors offer similar characteristics to the Hall effect sensor, recent advances stimulated by the hard disk industry have provided major improvements [17]. In particular, the giant magnetoresistive effect (GMR) can exhibit two orders of magnitude greater sensitivity than the AMR effect which equates to a resistance change of up to 70% at saturation. Such devices can also be miniaturized and are compatible with lithographic processes. Packaged GMR sensors in a full-bridge configuration are now available from NVE Corporation, NXP Semiconductor, Siemens, and Sony. Aside from the inherent non-linearities associated with the magnetic field, the major remaining drawback is the hysteresis of up to 4% which can severely impact the performance in nanopositioning applications. Despite this, miniature GMR sensors have shown promise in nanopositioning applications by keeping the changes in magnetic field small [18], [19]. However, to date, the linearity and hysteresis of this approach has not been reported.
Section snippets
Calibration and nonlinearity
Position sensors are designed to produce an output that is directly proportional to the measured position. However, in reality, all position sensors have an unknown offset, sensitivity and nonlinearity. These effects must be measured and accounted for in order to minimize the uncertainty in position.
The typical output voltage curve for a capacitive position sensor is illustrated in Fig. 1. A nonlinear function maps the output voltage to the actual position x. The calibration process
Resistive strain sensors
Due to their simplicity and low-cost, resistive strain gauges are widely used for position control of piezoelectric actuators. Resistive strain gauges can be integrated into the actuator or bonded to the actuator surface. An example of a piezoelectric actuator and resistive strain gauge is pictured in Fig. 14(a). Other application examples can be found in references [28], [29], [30], [31].
Resistive strain gauges are constructed from a thin layer of conducting foil laminated between two
Comparison and summary
Due to the extreme breadth of position sensor technologies and the wide range of applications, it is extremely difficult to make direct performance comparisons. In many applications, characteristics such as the physical size and cost play a greater role than performance. Nevertheless, it is informative to compare some aspects of performance.
In Table 3 the specifications under consideration are the range, the dynamic range, the 6σ-resolution, the maximum bandwidth, and the typical accuracy.
Outlook and future requirements
One of the foremost challenges of position sensing is to achieve high resolution and accuracy over a large range. For example, semiconductor wafer stages require a repeatability and resolution in the nanometers while operating over a range in the tens of centimeters [13], [14]. Such applications typically use interferometers or high resolution optical encoders which can provide the required performance but can impose a significant cost. Long range sensors are also becoming necessary in standard
Acknowledgements
This work was supported financially by the Australian Research Council (DP0986319) and the Center for Complex Dynamic Systems and Control.
Andrew J. Fleming graduated from The University of Newcastle, Australia (Callaghan campus) with a Bachelor of Electrical Engineering in 2000 and Ph.D. in 2004. He is presently an Australian Research Fellow and Senior Lecturer at the School of Electrical Engineering and Computer Science, The University of Newcastle, Australia. His research includes nanopositioning, high-speed scanning probe microscopy, micro-cantilever sensors, metrological position sensors, and optical nanofabrication. Academic
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Andrew J. Fleming graduated from The University of Newcastle, Australia (Callaghan campus) with a Bachelor of Electrical Engineering in 2000 and Ph.D. in 2004. He is presently an Australian Research Fellow and Senior Lecturer at the School of Electrical Engineering and Computer Science, The University of Newcastle, Australia. His research includes nanopositioning, high-speed scanning probe microscopy, micro-cantilever sensors, metrological position sensors, and optical nanofabrication. Academic awards include the University of Newcastle Vice-Chancellors Award for Researcher of the Year and the IEEE Control Systems Society Outstanding Paper Award for research published in the IEEE Transactions on Control Systems Technology. Dr. Fleming is the co-author of three books, several patent applications and more than 100 Journal and Conference papers.