Calibration of the electrical response of piezoelectric elements at low voltage usinglaser interferometryE. Riis, H. Simonsen, T. Worm, U. Nielsen, and F. Besenbacher Citation: Applied Physics Letters 54, 2530 (1989); doi: 10.1063/1.101064 View online: http://dx.doi.org/10.1063/1.101064 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/54/25?ver=pdfcov Published by the AIP Publishing Articles you may be interested in On the uncertainties of accelerometer calibration by laser interferometry J. Acoust. Soc. Am. 112, 2343 (2002); 10.1121/1.4779470 Full temperature calibration from 4 to 300 K of the voltage response of piezoelectric tube scanner PZT5A for usein scanning tunneling microscopes Rev. Sci. Instrum. 64, 896 (1993); 10.1063/1.1144139 Calibration and characterization of piezoelectric elements as used in scanning tunneling microscopy Rev. Sci. Instrum. 62, 989 (1991); 10.1063/1.1141989 Mechanical displacement induced in a piezoelectric structure: Experimental measurement by laser interferometryand simulation by a finite element method J. Acoust. Soc. Am. 84, 11 (1988); 10.1121/1.396978 Vibrational response of sonar transducers using piezoelectric finite elements J. Acoust. Soc. Am. 56, 1782 (1974); 10.1121/1.1903513

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Calibration of the electrical response of piezoelectric elements at low voltage using laser Interferometry

E. Riis,a) H. Simonsen, T. Worm, U. Nielsen, and F. Besenbacher Institute of Physics, University of Aarhus. DK~8000 Aarhus C, Denmark

(Received 2 February 1989; accepted for publication 12 April 1989)

A laser interferometric method is described by which the length-to-voltage sensitivity of piezoelectric elements, as used e.g" in scanning tunneling microscopes, can be calibrated. The method is based on measuring the optical frequency of a laser locked to a piezoelectrically tuned interferometer, relative to a stable reference. The high sensitivity of this technique allows the calibration to be carried out in the 10w~vo1tage regime.

In the scanning tunneling microscope (STM),1-3 a sharp tungsten tip is brought so close to the surface (5-10 A) that the electron wave functions of the ti.p and the sample overlap. Application of a small bias voltage (2 mV-2 V) between the tip and the sample then establishes a tunnel cur­rent (nA range). In the conceptually simplest version of the instrument, the tip is mounted on three orthogonal piezoe~ lectric transducers (a tripod). As the tip is scanned along the surface, the tunneling current tends to vary in the same way as the separation between the tip and the sample. The tunnel­ing current is kept at a constant value by a feedback loop that applies a correction voltage to the z transducer normal to the surface. This correction voltage is measured as the tip is ras­ter-scanned along the surface, thus tracking the height fl.uc~ tuations of the surface.

To convert this correction voltage into corrugation heights (absolute displacement), it is necessary to know the piezosensitivity for sman and fast-changing voltages. Cali­bration of the sensitivity for STM piezoelements has pre­viously been carried out by means of a Michelson laser inter­ferometer,4 a capacitance dilatometer,S an inductive linear gauge,6,7 or by scanning a region on a single crystal contain­ing a monatomic step.8.9 However, for some ofthe methods listed above, it is necessary to apply fairly high voltages to the piezoelectric element in order to obtain a measurable expansion and then extrapolate to the low-voltage regime applied for STM, Concerning the "monatomic step" calibra­tion scheme, it is difficult to be sure whether it really is a monatomic step, and furthermore, the surface may be re­laxed or expanded.

In this letter, we demonstrate a new scheme for accurate and absolute calibration of piezoelectric elements (pzt) in a low~voltage regime which is therefore directly applicable to work with the scanning tunneling microscope. Like the Mi­chelson technique:~ it is based on laser interferometry, but it takes advantage of an effective large multiplication of the length variation by a high-finesse optical cavity,

The piezoelectric element investigated in the present ex­periment was a piezotube fabricated from PZ~27, W a lead zirconate titanate material with a mechanical Q = 80, a Cu­rie temperature T c = 350 °C, and a piezoelectric constant d31 = 175 X 10- 12 m/V. The tubes are 6 mm long and have an inner and outer diameter of 3.05 and 4.4 mm, respective-

a) Present address: Department of Physics, Stanford University, Stanford, CA 94305.

ly. The voltage was applied between the silver-plated inner and outer surfaces (inset of Fig. 1). A high-reflecting spheri~ cal mirror (R-99%) was mounted on one end of the ele­ment Separated from a similar mirror by a 30-cm-Iong su­perinvar tube (linear expansion coefficient < 3 X 10- 7/,C),

it formed a near-confocal interferometer. A ReNe laser (HeNe 1 in Fig. I), tunable in single mode over 650 MHz, was mode matched into the fundamental mode of the inter­ferometer. This ensured narrow transmission maxima and eliminated alignment errors due to excitation of higher order modes in a not exactly confocal interferometer. Such an in­terferometer is characterized by its free-spectral range (FSR), 1I,12 and its finesse (F*), 1l,l2 which is related to the reflection coefficient R of the mirrors by

(0

The FSR of the interferometer used is cl2nL - 500 MHz, where c is the speed of light, n is the refractive index of air, and L is the spacing of the mirrors ( ~ 30 em). The laser was frequency modulated and locked to the center of an interfer­ometer transmission. A finesse of the order of 100 allows the HeNe laser to be locked to the cavity by a fraction of 1 MHz. However, the sensitivity of the interferometer to mechanical vibrations limited the absolute frequency stability to ± 1 MHz for the averaging period used in the experiment ( lOs). As L is changed by applying a small voltage to the pzt~ mounted mirror, the center lock will always ensure that the laser wavelength A. fulfins the relation

NJt = knL, (2)

where Nand k are fixed integers (k = 2 in the present con­figuration), which is the criterion for a transmission maxi­mum. Taking the logarithmi.c derivative of Eq. (2) and us-

PZT

FIG. 1. Experimental setup. The pzt are measured in millimeters.

2530 Appl. Phys. Lett. 54 (25), 19 .June 1989 0003-6951/a9/252530~02$01.00 @ 1989 American Institute of PhYSics 2530 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

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750

ii# I rr is ~ I I 0

500 Volta e

l .« >-z w

I ::E UJ u

I «

10 ct ({)

5 250r (0)-

o 20 VOLTAGE (V)

FIG. 2. Displacement and hysteresis of the piezoelectric transducer. The inset shows the flow of the measurement series. (a) the length difference between m;:" V and - ru;:" V divided by 2 as a function of m;:" V (m

= 1.2,3 .... , Li. V O~ 1.0 V); (b) the length difference between successive 0 voltage measurements as it fUllction of ! rnA V I on a fivc times expanded scale.

ing the fundamental relation A'll = nc, the frequency to length variation is found to be

! dv \ v I dL i = L' (3)

This frequency change was easily measured by beating the laser against a stable reference and counting the difference frequency. The reference was a HeNe laser (HeNe 2 in Fig. 1), stabilized to a constant intensity ratio oftwo longitudinal modes. 11 This locking scheme provides a reference with an excellent short-term stability (a fraction of 1 MHz over hours).

The length-to-frequency response of the apparatus was calibrated by measuring the frequencies of adjacent interfer­ometer modes yielding a FSR = 496.6 ± 0.4 MHz. In this way, a mirror spacing of 301.8 ± 0.3 mm wa<; found, corre­sponding to a length-to-frequency response dL I d1J = 6.371 ± 0.007 A/MHz. It should be emphasized that the major difference between the present scheme and cali­bration by means of a Michelson interferometer is a finesse of the latter in the orderofl, compared toF* in the order of 100 in this investigation. This means that the transmission linewidth of our interferometer is a factor of 100 narrower than that of a Michelson interferometer, which in turn yields the enhanced sensitivity for the center lock.

In order to map out the electrical response ofthe piezoe­lectric element, the frequency difference between the two lasers, from which the change of length can be derived, was recorded, as shown in the inset of Fig, 2. Starting off with zero voltage VappUed to the piezo, the voltage was increased tobY(AV = O,5-LO V), reduced toOVandlaterto - tlv,

2531 Appl. Phys. Lett., Vol. 54. No. 25,19 June 1989

and then increased again to 0 V and 2tl V. This loop was repeated for consecutively higher voltages up to 40 V, corre­sponding to laser frequency variations up to - 225 MHz.

To minimize effects of thermal drifts of the interferome­ter during the measurements, only differential quantities are used in the data analysis. Thus, curve (a) of Fig. 2 shows the length difference for a variation of voltage between mt:. Vand - mtlVas a function of mb.V (m = 1,2,3, ... ). This length-

to-voltage response of the pzt is nonlinear since the data (averaged over five series of measurements) best fit a qua­dratic polynomial:

D = aV + {3V 2, (4)

where D is the displacement {it} in Fig. 2, Vis the voltage in volts, (3 = 0.041 A./y2, and the linear length-to-voltage sensitivity a of the piezo element jn Eq. (4) is found to be a = 17.4 ± 0.1 A/v. The hysteresis, defined as the differ­ence between subsequent zero-voltage measurements, is shown by curve (b) of Fig, 2. The data points seem to indi­cate a pure quadratic voltage dependence, yielding a hystere­sis of 0.058 ± 0.007 A../y2. Systematic errors due to nonper­fect alignment of mirrors of the interferometer, as wen as deviation from perfect orthogonal mounting of one mirror on the pzt dement, are all easily made negligible as com­pared to the statistical uncertainties quoted.

In the typical STM application looking for atomic reso­lution on metal and semiconductor surfaces, voltage varia­tions will be ofthe order of 1 V or iess, and neither ofthe two nonlinearities will be ofimportance. Furthermore, one of the data sets was taken with an offset of 35 V applied to the pzt. However, no noticeable change in the measured response was observed. This implies that the calibration is not affected by an offset in the absolute piezovoltage needed to bring the STM tip close to the mechanically positioned sample.

In this letter we have presented a technique for an accu­rate calibration of piezoelectric elements used i.n, e.g., scan­ning tunneling microscopes. It offers a possibility of calib­rating the actual element that is being mounted in the microscope in the voltage range ofinterest, with an accu.racy of 0.6% in the linear region. Nonlinearities and hysteresis effects which depend quadratically on the applied voltage are of minor importance in the low voltage (atomic resolu­tion) regime, but might be crucial for higher voltage, i.e., when scanning over a large area.

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Chap. 7.6.

Riis etal. 2531

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