CN112986704B - Longitudinal piezoelectric coefficient measuring method based on atomic force microscope - Google Patents

Longitudinal piezoelectric coefficient measuring method based on atomic force microscope Download PDF

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CN112986704B
CN112986704B CN202110207388.2A CN202110207388A CN112986704B CN 112986704 B CN112986704 B CN 112986704B CN 202110207388 A CN202110207388 A CN 202110207388A CN 112986704 B CN112986704 B CN 112986704B
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曾慧中
黄芬
孟奔阳
张文旭
张万里
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/22—Measuring piezoelectric properties
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
    • G01Q60/00—Particular types of SPM [Scanning Probe Microscopy] or microscopes; Essential components thereof
    • G01Q60/24—AFM [Atomic Force Microscopy] or apparatus therefor, e.g. AFM probes

Abstract

The invention belongs to the field of piezoelectric coefficient testing, and particularly provides a longitudinal piezoelectric coefficient measuring method based on an atomic force microscope; by analyzing the contribution ratio of electrostatic force of each part of the probe of the atomic force microscope, and the electrostatic force applied to the probe and the probe-sample gap z0Analysis of the variation relationship of (a) by setting a probe-sample gap z0Initial value z of00More than or equal to 1 mu m, a termination value of 0 < z01Less than or equal to 10nm, so that the same piezoelectric material sample is in the probe-sample gap z00And z01The time is respectively expressed as a non-piezoelectric state and a piezoelectric state, and lg (| F) in the two states is adoptedes|)‑lg(Vtip) The enclosed area S of the curve is used as the longitudinal piezoelectric coefficient d33Finally obtaining d by calibrating a standard piezoelectric film sample33And an S curve, so that the longitudinal piezoelectric coefficient of the piezoelectric film to be measured is measured. The method can obtain the longitudinal piezoelectric coefficient d of the piezoelectric material sample to be measured by utilizing the non-contact mode measurement of the atomic force microscope probe on the premise of not needing a precipitation electrode on the surface of the piezoelectric material sample to be measured33And is andthe measurement operation is simple and the measurement accuracy is high.

Description

Longitudinal piezoelectric coefficient measuring method based on atomic force microscope
Technical Field
The invention belongs to the field of piezoelectric coefficient test, and relates to a longitudinal piezoelectric coefficient (d) of a piezoelectric material33) The measuring technology specifically provides a longitudinal piezoelectric coefficient measuring method based on an atomic force microscope.
Background
The piezoelectric coefficient is a crucial parameter for measuring the electromechanical conversion efficiency of the piezoelectric element, is used for representing the conversion coefficient of converting mechanical energy into electric energy or converting electric energy into mechanical energy, and is a key parameter for realizing an MEMS device, so that the accurate measurement of the piezoelectric coefficient of the piezoelectric film is an important link for developing a micro-force sensor. The traditional measurement technology of the piezoelectric coefficient is mainly divided into direct measurement and indirect measurement, and the piezoelectric coefficient of the material is measured in a macroscopic scale. Early methods for measuring the piezoelectric coefficient of a piezoelectric material include a static method, a dynamic method and a quasi-static method, wherein the static method has low measurement precision, the dynamic method has complex operation and only can test a cylindrical sample; although the quasi-static method has high test accuracy, the vibration force is applied to the sample through the point contact electrode, so the measured piezoelectric coefficient only reflects the local performance of the contact part of the electrode, and the measured piezoelectric coefficients may be different when the contact points are different.
In recent years, the Atomic Force Microscope (AFM) technology has been rapidly developed in the field of piezoelectric coefficient measurement, and an AFM operating in a piezoelectric response mode is called a Piezoresponse Force Microscope (PFM). The PFM technology is taken as a nano-scale testing means, and the tested piezoelectric coefficient is the nano-scale piezoelectric coefficient. For the PFM testing technology, on one hand, a probe is taken as a movable electrode during PFM testing, the radius of a needle point is very small, and a sample has very high dielectric constant, so that an electric field in the sample caused by the needle point has highly non-uniform characteristics; on the other hand, the piezoelectric displacement of the PFM test is also related to intrinsic parameters of other materials than the piezoelectric coefficient; thus, accurate determination by PFMQuantity test d33It is very difficult. To overcome this difficulty, an electrode with a size of several square microns is usually deposited on the sample surface, so that the electric field is uniformly distributed in the electrode; however, this test method greatly reduces the PFM resolution and may cause various errors due to improper operation during the deposition process, which may cause the test results to deviate from the actual results; therefore, how to avoid depositing electrodes to reduce process errors has been the research direction of the present invention.
Furthermore, the piezoelectric coefficient d of the piezoelectric material is influenced33The test accuracy of the test method has a plurality of factors, wherein the factors which have great influence on the stress state of the test sample, such as whether pressure is completely applied to the test sample, whether the direction of the pressure is parallel to the polarization axis of the test sample, whether the test working surfaces are flat and parallel to each other, whether the areas stressed and generating the induction electric effect are equal, whether the test sample shakes at the moment of pressure release, and the like; therefore, how to avoid the pressure to the longitudinal piezoelectric coefficient d of the test33The adverse effects of accuracy are also a consideration of the present invention.
Disclosure of Invention
The invention aims to solve the problems of the conventional piezoelectric material longitudinal piezoelectric coefficient measuring method and provides a novel atomic force microscope-based longitudinal piezoelectric coefficient measuring method33(ii) a In addition, the method is simple to operate, small in measurement error and high in measurement accuracy.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a longitudinal piezoelectric coefficient measuring method based on an atomic force microscope is characterized by comprising the following steps:
step 1, adopting a plurality of standard piezoelectric film samples, and carrying out the following measurement on each standard piezoelectric film sample:
step 1.1, placing a standard piezoelectric film sample below a probe, and setting probe bias voltageVtip＝V1Setting the initial distance z between the probe and the sample00：z00More than or equal to 1 mu m and a termination spacing of z01：0＜z01Less than or equal to 10nm, controlling the probe to move to the standard piezoelectric film sample according to the moving step length of the probe, and measuring the electrostatic force borne by the probe in real time so as to measure the probe bias voltage Vtip＝V1Is ofes|-z0Curve, | FesI represents electrostatic force, z borne by the probe measured by the atomic force microscope0Representing the distance between the probe and the sample;
step 1.2, adjust probe bias voltage V in turntip＝V2,...,VnSeparately measuring probe bias voltage Vtip＝V2,V3,...,VnIs ofes|-z0A curve;
step 1.3, according to the probe bias voltage Vtip＝V1,V2,...,VnN pieces of | Fes|-z0Curves, taking z on each curve0＝z01And taking logarithm of the obtained data to obtain lg (| F)es|)-lg(Vtip) Curve, for lg (| F)esI) and lg (V)tip) A third order fit was performed, labeled lg (| F)es,z01|)-lg(Vtip) Curve, | Fes,z01I represents taking z0＝z01The probe bias voltage is VtipElectrostatic force on the probe; taking z in the same way0＝z00To obtain lg (| F)es|)-lg(Vtip) Curve, for lg (| F)esI) and lg (V)tip) A linear fit was performed, labeled lg (| F)es,z00|)-lg(Vtip) A straight line;
step 1.4, in the same coordinate system, for
Figure BDA0002949813520000021
The curve is translated so that
Figure BDA0002949813520000022
Curve and
Figure BDA0002949813520000023
the start points of the curves coincide, in lg (V)1) As starting point, lg (V)n) As an end point, the calculation results in
Figure BDA0002949813520000024
Curve and
Figure BDA0002949813520000025
the enclosed area S of the curve;
step 2, obtaining the enclosed area S of each standard piezoelectric film sample and the prior longitudinal piezoelectric coefficient d of each standard piezoelectric film sample according to the measurement in the step 133Obtaining a fitting curve of the longitudinal piezoelectric coefficient and the area S, marked as d33-an S-curve;
step 3, obtaining the enclosed area S 'of the piezoelectric film to be measured by adopting the steps 1.1 to 1.4 to carry the enclosed area S' into the step d33And carrying out interpolation fitting in the S curve to obtain the longitudinal piezoelectric coefficient of the piezoelectric film to be measured.
In terms of working principle:
the invention provides a method for measuring the longitudinal piezoelectric coefficient d of a piezoelectric material33The basic principle of the method is as follows:
the measuring instrument used in the invention is an atomic force microscope, and the probe of the atomic force microscope comprises: cantilever (cantilever), cone (cone) and sphere (sphere), as shown in the left diagram of FIG. 1, the electrostatic force applied to each part of the probe is dependent on the tip-sample gap z0The change curve of (a), wherein,
Figure BDA0002949813520000031
as can be seen, the electrostatic force on the sphere is along with the tip-sample gap z0Becomes larger and sharply attenuated, and the electrostatic force borne by the cone is also along with the space z between the needle tip and the sample0Becomes smaller but at a slower speed, while the cantilever is at a smaller electrostatic force and hardly changes with distance, due to its being farther from the sample surface (cantilever-sample spacing-tip-sample gap + tip height, typically greater than 10 μm); the ratio of the electrostatic force of each part of the probe to the total eta in the right diagram of FIG. 1 is shown as a function of the tip-sample gapIn variation, it can be seen that the electrostatic force contribution of the sphere is greater than 50% within 200nm, whereas in general the tip-sample gap z is the actual measurement process0<100nm, therefore, the electrostatic force applied to the sphere is approximate to the electrostatic force applied to the probe in the invention, namely the probe of the atomic force microscope is simplified into the sphere; whereas according to the reference the sphere-sample electrostatic force is expressed as:
Figure BDA0002949813520000032
wherein, VtipFor probe bias, e ═ e0εr、εrIs the relative dielectric constant of the medium between the sphere and the sample (i.e., the relative dielectric constant of air is 1), epsilon0The dielectric constant is vacuum (8.854 × 10)-12F/m)，
Figure BDA0002949813520000033
R is the radius of the sphere;
when z is0R, the formula (1) can be simplified to
Figure BDA0002949813520000034
As can be seen, | FesI is proportional to Vtip 2Namely: lg (| F)esI (ordinate) with lg (V)tip) The change curve (abscissa) is a straight line and has a slope of 2.
Further, the sample to be measured of the present invention is a piezoelectric sample, as shown in fig. 3, when the distance between the needle tip and the piezoelectric sample is relatively long, the electrostatic force applied to the needle tip is relatively small, the surface of the piezoelectric material is almost not deformed, and the electrostatic force is mainly related to the probe bias voltage; when the needle tip is gradually close to the surface of the piezoelectric sample, the electrostatic force borne by the needle tip comprises a pure electrostatic action influenced by the bias voltage and a piezoelectric part influenced by the piezoelectric material, and the surface of the piezoelectric sample is deformed due to the electrostatic force. The invention sets a plurality of probe bias values: v tip10V, obtained under each probe bias, | FesL with z0Taking in each curveSeveral points: z is a radical of01nm, 3nm, 9nm, 1 μm, obtained at each z0< F > ofesI with VtipVariation curve, labeled | Fes|-VtipThe curves are shown in fig. 4. Further, the same test as above was carried out using piezoelectric and non-piezoelectric materials as samples, respectively, to obtain a signal at z01nm, | F at 1 μmesI with VtipThe variation curve of (A) is shown in FIG. 5, and it can be seen from the figure that when z is01nm, | F of piezoelectric and non-piezoelectric materialsesI with VtipThe variation curves have large difference and the difference value is delta | FesI with VtipIncreased by an increase; when z is01 μm, | F of piezoelectric and non-piezoelectric materialsesI with VtipThe curves are nearly coincident and lg (| F)esI) with lg (V)tip) The slope of the change curve is 2, which is consistent with the formula (1); it can be seen that when z is0When the diameter is more than or equal to 1 mu m, the electrostatic force borne by the spherical cap is basically pure electrostatic, the influence of a piezoelectric material is very small and can be ignored, and the situation is equivalent to the non-piezoelectric situation; z is a radical of0When the diameter is less than or equal to 10nm, the electrostatic force borne by the spherical cap comprises a pure electrostatic part influenced by bias voltage and a piezoelectric part influenced by a piezoelectric material; according to the characteristics, the invention can utilize the same piezoelectric material sample in different tip-sample gaps z0Lg (| F) belowesI) with lg (V)tip) The variation curve is used for extracting piezoelectric contributions under different piezoelectric coefficients, and the specific process is as follows:
when z is0≤10nm(z01) When, for lg (| F)esI) and lg (V)tip) Performing third-order fitting to obtain lg (| F)esI) with lg (V)tip) A change curve; when z is0≥1μm(z00) When, for lg (| F)esI) and lg (V)tip) Linear fitting is carried out to obtain lg (| F)esI) with lg (V)tip) A change curve; as shown in FIG. 6, in z01＝1nm、z 001 μm as an example, when z 001 μm, lg (| F)esI) with lg (V)tip) The curve is a straight line A marked as lg (| F)es|)-lg(Vtip) Curve when z is011nm, lg (| F)esI) with lg (V)tip) The curve of variation is curve B byThe straight line A is translated upwards to enable the straight line A to coincide with the straight line C when lg (1V) is taken as a starting point, the area of a shadow part enclosed by the curve B and the straight line C between lg (1V) and lg (10V) is S, and the area S can be used for effectively representing the piezoelectric contribution of the piezoelectric material, namely representing the longitudinal piezoelectric coefficient d of the piezoelectric material sample33(ii) a Then, the longitudinal piezoelectric coefficient d is obtained by calibrating a plurality of standard piezoelectric material samples33Fitting a curve to the area S, denoted d33S curve, when the area S parameter of the piezoelectric material to be measured is obtained through measurement, the area S parameter can pass through d33The longitudinal piezoelectric coefficient d of the piezoelectric material to be measured is obtained by S curve fitting33。
The invention has the beneficial effects that by combining the working principle:
the invention provides a method for measuring the longitudinal piezoelectric coefficient d of a piezoelectric material based on an atomic force microscope33By analyzing the contribution ratio of electrostatic force to each part of the probe of the atomic force microscope, and the electrostatic force applied to the probe and the probe-sample gap z0Analysis of the variation relationship of (a) by setting a probe-sample gap z0Initial value z of00More than or equal to 1 mu m, a termination value of 0 < z01Less than or equal to 10nm, so that the same piezoelectric material sample is in the probe-sample gap z00And z01The time is respectively expressed as a non-piezoelectric state and a piezoelectric state according to lg (| F) in the two stateses|)-lg(Vtip) Curve, obtaining lg (| F) under two states through data processinges|)-lg(Vtip) Curve at starting point V1The enclosed area S under superposition is used as the longitudinal piezoelectric coefficient d33Finally obtaining d by calibrating a standard piezoelectric film sample33-an S-curve; the enclosed area S' of the piezoelectric film to be measured is brought into d33And carrying out interpolation fitting in the S curve to obtain the longitudinal piezoelectric coefficient of the piezoelectric film to be measured.
In conclusion, the method can obtain the longitudinal piezoelectric coefficient d of the piezoelectric material sample to be measured by utilizing the non-contact mode measurement of the atomic force microscope on the premise of not needing a precipitation electrode on the surface of the piezoelectric material sample to be measured33Simple measurement operation and higher measurement accuracyHigh, the measurement under the non-contact mode can effectively avoid pressure to cause the influence to the measuring result.
Drawings
FIG. 1 shows electrostatic forces acting on various parts of an AFM probe and electrostatic contribution η of the various parts with respect to a tip-sample gap z0The change curve of (2).
FIG. 2 is a graph of electrostatic force applied to a spherical cap of an AFM probe with a sphere-sample gap z0The change curve of (2).
FIG. 3 is a schematic diagram of the deformation of the surface of a sample when an atomic force microscope probe is close to a piezoelectric film sample.
FIG. 4 shows the equation when z01nm, 3nm, 9nm, 1 μm, | Fes|-VtipThe graph is schematic.
FIG. 5 shows the equation when z01nm, | F for piezoelectric and non-piezoelectric material sampleses|-VtipThe curves are compared with the graph.
FIG. 6 shows the longitudinal piezoelectric coefficient d33The characterization parameters of (1): schematic diagram of enclosed area S.
FIG. 7 shows z in an embodiment of the present invention01D at 1nm, 3nm, 9nm33-S fitting a curve.
Detailed Description
The technical scheme of the invention is explained in detail by combining the drawings and the embodiment.
The embodiment provides a method for measuring the longitudinal piezoelectric coefficient of a piezoelectric thin film AlN based on an atomic force microscope, wherein Vtip＝1V、1.5V、2V...10V，z01＝1nm、3nm、9nm，z00D is 1 μm, normalized33The S-curve is shown in FIG. 7;
when z is01When the thickness is 1nm, the enclosed area S' of the piezoelectric thin film AlN is 71/60000, and d is substituted for the enclosed area S33Interpolation fitting is carried out in the S curve to obtain the longitudinal piezoelectric coefficient d of the piezoelectric film to be measured33≈4.89pm/V；
When z is01When the thickness is 3nm, the enclosed area S 'of the piezoelectric thin film AlN is 13/30000, and the enclosed area S' is substituted by d33Interpolation fitting in S curve to obtainLongitudinal piezoelectric coefficient d to the piezoelectric film to be measured33≈5.00pm/V；
When z is01When the thickness is 9nm, the enclosed area S 'of the piezoelectric thin film AlN is 11/120000, and the enclosed area S' is substituted by d33Interpolation fitting is carried out in the S curve to obtain the longitudinal piezoelectric coefficient d of the piezoelectric film to be measured33≈5.14pm/V；
And the longitudinal piezoelectric coefficient d of the piezoelectric thin film AlN334.96pm/V, therefore, the invention can measure and obtain the longitudinal piezoelectric coefficient d of the piezoelectric material sample to be measured by utilizing the non-contact mode of the probe of the atomic force microscope on the premise of not needing a precipitation electrode on the surface of the piezoelectric material sample to be measured33And the measurement operation is simple and the measurement accuracy is high.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.

Claims (1)

1. A longitudinal piezoelectric coefficient measuring method based on an atomic force microscope is characterized by comprising the following steps:
step 1, adopting a plurality of standard piezoelectric film samples, and carrying out the following measurement on each standard piezoelectric film sample:
step 1.1, placing a piezoelectric film below a probe, and setting a probe bias voltage Vtip＝V1Setting the initial spacing between the probe and the piezoelectric film to z00：z00Not less than 1 μm, and a termination spacing of z01：0＜z01Less than or equal to 10nm, controlling the probe to move towards the piezoelectric film according to the moving step length of the probe, and measuring the electrostatic force borne by the probe in real time so as to measure the probe bias voltage Vtip＝V1Is ofes|-z0Curve, | FesI represents electrostatic force, z, applied to the probe measured by the atomic force microscope0Representing the distance between the probe and the surface of the piezoelectric film;
step 1.2, adjust probe bias voltage V in turntip＝V2,...,VnSeparately measuring probe bias voltage Vtip＝V2,V3,...,VnIs ofes|-z0A curve;
step 1.3, according to the probe bias voltage Vtip＝V1,V2,...,VnN pieces of | Fes|-z0Curves, taking z on each curve0＝z01And taking logarithm of the obtained data to obtain lg (| F)es|)-lg(Vtip) Curve, for lg (| F)esI) and lg (V)tip) Performing a third order fit, labeling
Figure FDA0003499586190000011
The curves are shown in the figure, and,
Figure FDA0003499586190000012
is expressed by taking z0＝z01The probe bias voltage is VtipElectrostatic force on the probe; taking z in the same way0＝z00To obtain lg (| F)es|)-lg(Vtip) Curve, for lg (| F)esI) and lg (V)tip) Performing a linear fit, labeling
Figure FDA0003499586190000013
A curve;
step 1.4, in the same coordinate system, for
Figure FDA0003499586190000014
The curve is translated so that
Figure FDA0003499586190000015
Curve and
Figure FDA0003499586190000016
the start points of the curves coincide, in lg (V)1) As starting point, lg (V)n) As an end point, the calculation results in
Figure FDA0003499586190000017
Curve and
Figure FDA0003499586190000018
the enclosed area S of the curve;
step 2, obtaining the enclosed area S of each standard piezoelectric film sample and the prior longitudinal piezoelectric coefficient d of each standard piezoelectric film sample according to the measurement in the step 133Obtaining a fitting curve of the longitudinal piezoelectric coefficient and the area S, marked as d33-an S-curve;
step 3, obtaining the enclosed area S 'of the piezoelectric film to be measured by adopting the steps 1.1 to 1.4 to carry the enclosed area S' into the step d33And carrying out interpolation fitting in the S curve to obtain the longitudinal piezoelectric coefficient of the piezoelectric film to be measured.
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