Standards for nano- and picometer ranges on the basis of displacement gauges
Displacement gauges based on the inverse piezoelectric effect
The solution to the problems of manufacture and application of standards of nano- and picometer ranges is possible on the basis of application of displacement gauges. Displacement gauges, which change their size directly proportional to the magnitude of the control voltage, are made of a monocrystalline material with an inverse piezoelectric effect (lithium niobate). Vertical or horizontal displacement of the gauge’s surface depends on the direction of the control electric field and the orientation of the crystallographic axes of the single crystal used.
To increase the range of motion an assembly of series-connected single crystals are used. The displacement of the reference surface of the gauge is measured by the optical interferometer. For measurements the single crystals are influenced by pulses of positive and negative polarity.
Fig.2 shows photos of displacement gauges of vertical and lateral types, as well as the dependences of the movement of reference surfaces under the influence of the control voltage. The measurements confirmed that the linearity of the displacement of single crystals under the influence of the control voltage is ten times higher than the linearity of similar specimens of the traditional poly-domain piezoceramics.
Fig.3 shows the trapezoidal shape of the control voltage pulse and a corresponding pulse of displacement of the reference surface in a gauge of vertical type.
Fig.4 shows the multi-stage shape of controlled voltage rising and falling displacement of the reference surface of vertical gauge. Measure the initial and final position of the reference surface showed the virtual absence of hysteresis and creep.
For experimental measurements of the displacements of gauges the computer-controlled electronic systems were used (fig.5). The generated voltage was measured by a voltmeter Fluke884.
Vertical displacement gauges with a resonant frequency of over 10 kHz allow to measure the response time of servo systems of scanning probe microscopes.
Calibration of scanning probe and electron microscopes
The vertical displacement gauges may be used for calibration of scanning probe microscopes (atomic force, tunnel, near-field, etc.). During calibration it is placed on the microscope stage, and the probe comes to the reference surface to a distance, which is then held constant by servo system of the microscope. The control voltage is supplied to the gauge and the reference surface moves on a calibrated value. Servo system of the microscope, in turn, moves the probe on the same distance. The measured amount of movement is compared with the calibrated value of vertical displacement of the reference surface of the gauge.
The calibration with use of the vertical gauge, in contrast to the static calibration gauges, does not requires a set of sharp probes and samples with high-precision indentations. In addition, when applying different control voltages the same gauge may be used to calibrate in any of the fields of nano- and picometer range. The displacement of the reference surface does not depend on its shape that allows to operate outside the vacuum systems and "clean areas". Rapidity of measurement of vertical displacements (less than a second) greatly reduces the influence of temperature drift and mechanical relaxation.
The lateral displacement gauge with reference fragments (diffraction grating, nanoparticles, etc.) can be applied for calibration of scanning probe and electron microscopes. During calibration it is placed on the microscope stage, and the surface with the reference fragments is scanned by a probe or a focused electron beam of the microscope. As a result of the scan the position of the reference fragments is fixed. The electronic control system supply the control voltage and the reference surface with the reference fragments moves. Servo system of the microscope measures the amount of movement of the reference fragment relative to the initial position, and this value is set equal to the magnitude of the calibrated displacement of the reference surface of the gauge.
The use of a horizontal displacement gauge, in contrast to the static calibration gauges, does not requires the use of a symmetric probes or set of samples with reference fragments that are located at a distance of a few nanometers, and also provides the calibration by a single gauge in any field of nano- and picometer range .
High linearity and repeatability of the displacement gauges make it possible to use them as standards in transferring from the primary standard to the measuring units. Also the displacement gauges can be used as built-in high-precision linear handlers, providing the sharing of the results of forward and reverse scan, which twice reduces the time of frame measurement. Thus, the use in the scanning nanolithography of a vector scanning instead of raster one in dozens of times increases the speed of technological processes.
For measurements in the nano- and picometer ranges the different types of interferometers are developed:
•with the Bragg and cesium cells stabilization of laser radiation with a frequency instability of less than 10-5, which is produced as a block with integrated laser, an optical system for frequency stabilization and interferometer (fig.6a);
•with the Bragg cell stabilization of frequency of laser radiation (fig.6b). The relative instability of frequency of radiation of such a laser is not more than 10-3;
•compact interferometer with cesium cells stabilization of radiation that is transmitted over single-mode optical fiber from the remotely located laser unit.
The displacement of gauge under the influence of the control voltage pulses can be measured by the optical interferometer. The averaging of the obtained results allows to improve the signal-to-noise and to make measurements in the picometer range .
Fig.7 shows the results of the measurement by the method of accumulation and averaging of pulses of vertical displacement with amplitude of some picometers that experimentally confirms the possibility of use of displacement gauges in the nano- and picometer ranges. It should be noted that with the further decrease of the control voltage will decrease the magnitude of the displacement of the reference surface, therefore, the displacement gauges can also be used in femto- and attometer ranges.
Developed standards and interferometers can be used for the calibration of microscopes, can be integrated in nanotechnology facilities and high-sensitive sensors, and also can be used for research and educational activities in the fields of nanomaterials, nanomechanics and nano-metrology.