CN112986704A

CN112986704A - Longitudinal piezoelectric coefficient measuring method based on atomic force microscope

Info

Publication number: CN112986704A
Application number: CN202110207388.2A
Authority: CN
Inventors: 曾慧中; 黄芬; 孟奔阳; 张文旭; 张万里
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2021-02-24
Filing date: 2021-02-24
Publication date: 2021-06-18
Anticipated expiration: 2041-02-24
Also published as: CN112986704B

Abstract

The invention belongs to the field of piezoelectric coefficient testing, and specifically provides a longitudinal piezoelectric coefficient measurement method based on an atomic force microscope; ‑Analysis of the variation relationship of the sample gap z ₀ , set the initial value of the probe‑sample gap z ₀ z ₀₀ ≥1μm, and the end value 0<z ₀₁ ≤10nm, so that the same piezoelectric material sample is in the probe‑sample gap z ₀₀ and At z ₀₁ , there are two states: non-piezoelectric and piezoelectric, respectively, and the enclosed area S of the lg(|F _es |)‑lg(V _tip ) curve in the two states is used as the value of the longitudinal piezoelectric coefficient d ₃₃ . Characterize the parameters, and finally obtain the d ₃₃ ‑S curve through the calibration of the standard piezoelectric film sample, and then realize the measurement of the longitudinal piezoelectric coefficient of the piezoelectric film to be measured. The invention can obtain the longitudinal piezoelectric coefficient d ₃₃ of the piezoelectric material sample to be measured by using the non-contact mode measurement of the atomic force microscope probe on the premise that the surface of the piezoelectric material sample to be measured does not need a precipitation electrode, and the measurement operation is simple and the measurement is accurate high degree.

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 quantitative measurement d by PFM₃₃It is very difficult. To overcome this difficulty, it is common to deposit a dimension on the sample surfaceThe electrode is a few square microns, so that an 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 a probe bias voltage V_tip＝V₁Setting the initial distance z between the probe and the sample₀₀：z₀₀Not less than 1 μm, 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 V_tip＝V₁Is of_es|-z₀Curve, | F_esI 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 turn_tip＝V₂,...,V_nSeparately measuring probe bias voltage V_tip＝V₂,V₃,...,V_nIs of_es|-z₀A curve;

step 1.3, according to the probe bias voltage V_tip＝V₁,V₂,...,V_nN pieces of | F_es|-z₀Curves, taking z on each curve₀＝z₀₁And taking logarithm of the obtained data to obtain lg (| F)_es|)-lg(V_tip) Curve, for lg (| F)_esI) and lg (V)_tip) A third order fit was performed, labeled lg (| F)_es,z01|)-lg(V_tip) Curve, | F_es,z01I represents taking z₀＝z₀₁The probe bias voltage is V_tipElectrostatic force on the probe; taking z in the same way₀＝z₀₀To obtain lg (| F)_es|)-lg(V_tip) Curve, for lg (| F)_esI) and lg (V)_tip) A linear fit was performed, labeled lg (| F)_es,z00|)-lg(V_tip) A straight line;

step 1.4, in the same coordinate system, the

The curve is translated so that

Curve and

the start points of the curves coincide, in lg (V)₁) As starting point, lg (V)_n) As an end point, calculatingTo obtain

Curve and

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,

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 right graph in FIG. 1 shows the ratio η of the probe to the total electrostatic force as a function of the tip-sample gap, and it can be seen that the electrostatic force contribution of the sphere is greater than 50% within 200nm, while in general, it is trueTip-sample gap z during measurement₀<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:

wherein, V_tipFor probe bias, e ═ e₀ε_r、ε_rIs 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)，

R is the radius of the sphere;

when z is₀R, the formula (1) can be simplified to

As can be seen, | F_esI is proportional to V_tip 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, | F_esL with z₀Taking several points in each curve: z is a radical of₀1nm, 3nm, 9nm, 1 μm, obtained at each z₀< F > of_esI with V_tipVariation curve, labeled | F_es|-V_tipThe 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 μm_esI with V_tipThe 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 materials_esI with V_tipThe variation curves have large difference and the difference value is delta | F_esI with V_tipIncreased by an increase; when z is₀1 μm, | F of piezoelectric and non-piezoelectric materials_esI with V_tipThe 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) below_esI) 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(V_tip) Curve when z is₀₁1nm, lg (| F)_esI) with lg (V)_tip) The curve of the change is a curve B, which is a straight line C, and the curve B and the straight line C overlap each other at lg (1V) (starting point) by translating the straight line A upwardThe area of a shadow part enclosed between 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 a 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 states_es|)-lg(V_tip) Curve, obtaining lg (| F) under two states through data processing_es|)-lg(V_tip) 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 measured₃₃And the measurement operation is simple, the measurement accuracy is higher, and the measurement in a non-contact mode can effectively avoid the influence of pressure on the measurement 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, | F_es|-V_tipThe graph is schematic.

FIG. 5 shows the equation when z₀1nm, | F for piezoelectric and non-piezoelectric material samples_es|-V_tipThe 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 solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.

The embodiment provides a method for measuring the longitudinal piezoelectric coefficient of a piezoelectric thin film AlN based on an atomic force microscope, wherein V_tip＝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 is carried out in the S curve to obtain the longitudinal piezoelectric coefficient d of 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. a longitudinal piezoelectric coefficient measuring method based on atomic force microscope, is characterized in that, comprises the following steps:

Step 1. Use several standard piezoelectric film samples, and perform the following measurements on each standard piezoelectric film sample:

Step 1.1. Place the standard piezoelectric thin film sample under the probe, set the probe bias voltage V _tip =V ₁ , set the initial distance between the probe and the sample as z ₀₀ : z ₀₀ ≥ 1 μm, and the termination distance as z ₀₁ : 0 < z ₀₁ ≤ 10 nm, control the movement of the probe to the standard piezoelectric film sample according to the probe movement step, and measure the electrostatic force on the probe in real time, and then measure the probe bias V _tip = V ₁ |F _es |-z ₀ curve, |F _es | represents the electrostatic force on the probe measured by atomic force microscope, z ₀ represents the distance between the probe and the sample surface;

Step 1.2, adjust the probe bias voltage V _tip =V ₂ ,...,V _n in turn, and measure the probe bias voltage V _tip =V ₂ , V ₃ ,...,V _n |F _es |- z ₀ curve;

Step 1.3. According to n |F _es |-z ₀ curves of probe bias voltage V _tip =V ₁ , V ₂ ,...,V _n , take z ₀ =z ₀₁ on each curve, and compare the obtained Take the logarithm of the data of , obtain the lg(|F _es |)-lg(V _tip ) curve, and perform third-order fitting on lg(|F _es |) and lg(V _tip ), marked as

curve,

represents the electrostatic force on the probe when z ₀ = z ₀₁ and the probe bias is V _tip ; taking z ₀ =z ₀₀ in the same way, the lg(|F _es |)-lg(V _tip ) curve is obtained, A linear fit is performed on lg(|F _es |) and lg(V _tip ), labeled as

curve;

Step 1.4, in the same coordinate system, for

The curve is translated so that

curve with

The starting points of the curves coincide, with lg(V ₁ ) as the starting point and lg(V _n ) as the end point, the calculation

curve with

The enclosed area S of the curve;

Step 2. According to step 1, the enclosed area S of each standard piezoelectric film sample and the a priori longitudinal piezoelectric coefficient d ₃₃ of each standard piezoelectric film sample are obtained, and the fitting curve between the longitudinal piezoelectric coefficient and the area S is obtained , marked as d ₃₃ -S curve;

Step 3. Use steps 1.1 to 1.4 to measure and obtain the enclosed area S' of the piezoelectric film to be measured, and bring the enclosed area S' into the d ₃₃ -S curve to perform interpolation fitting to obtain the longitudinal direction of the piezoelectric film to be measured. Piezoelectric coefficient.