Ferroelectric characterization method for a piezoelectric sample

Abstract

The invention relates to a device for characterizing a piezoelectric sample having a lower electrode and an upper surface. The device comprises: a conductive tip placed at one end of a lever and intended to be in contact with a point on the upper surface; the assembly formed by the tip, the sample, and the electrode having a variable resonant frequency; a voltage generator configured to apply a characterization signal at a first frequency between the lower electrode and the conductive tip; a data acquisition chain configured to generate a measurement signal of the electromechanical response of the sample; and a control circuit configured to control the voltage generator by generating a control signal from the measurement signal received via a feedback loop. The first frequency is maintained at the resonant frequency by the control circuit.Figure for the summary: Fig. 1a.

Description

Title of the invention: Method for ferroelectric characterization of a piezoelectric sample

[0001] Scope of application

[0002] The present invention relates to the field of characterization of materials using the atomic force microscopy technique. More particularly, the invention relates to a method for ferroelectric characterization of a piezoelectric sample with operation in "piezoelectric force microscopy with polarization switching spectroscopy" SS-PFM mode (acronym for Switching Spectroscopy Piezoresponse Force Microscopy).

[0003] Problem raised

[0004] Thin layers of piezoelectric and / or ferroelectric materials are used in many microelectronics applications. Examples include, but are not limited to, applications in radiofrequency devices (4G, 5G, 6G filters), emerging memories for embedded applications (FeRAM, FeFET) or miniaturized sensor / actuator technologies (MEMS).

[0005] The quantitative measurement of the ferroelectric and piezoelectric properties of thin films presents a technical and experimental challenge. Indeed, this type of characterization is sensitive to several measurement artifacts such as the electrostatic effect induced by the measurement itself.

[0006] Piezoelectric force microscopy with SS-PFM polarization switching spectroscopy presents a promising candidate for characterizing ferroelectric and piezoelectric properties. For a sample comprising a layer of piezoelectric and ferroelectric material, this technique allows to determine locally on a surface of the sample: - The distribution and organization of local ferroelectric domains, - The influence of local ferroelectric domains on the macroscopic piezo / ferroelectric properties of the sample, and - The fundamental electromechanical mechanisms operating within the material.

[0007] “Piezoelectric force microscopy with polarization switching spectroscopy” SS-PFM is a particular mode of “piezoelectric force microscopy” PFM (acronym for Piezoresponse Force Microscopy). “Piezoelectric force microscopy” PFM is itself a particular operating mode of “atomic force microscopy” AFM (acronym for Atomic Force Microscopy). Thus, to fully understand the background of the invention, we will begin by explaining in general how atomic force microscopy AFM and piezoelectric force microscopy PFM work.

[0008] Atomic force microscopy (AFM) is a microscopy technique for measuring the topography of a material surface with atomic precision. An atomic force microscope has a fine tip attached to a lever. The lever and tip assembly have dimensions of the order of a micrometer. The tip is brought into contact with the surface of the sample. The tip is moved so as to scan the surface of the sample. A variation in the topography of the surface exerts a force on the tip, causing the lever to deform. By measuring this deformation using a laser, the surface profile can be deduced with atomic resolution and information on the elastic and mechanical properties of the surface can also be obtained.

[0009] Piezoelectric force microscopy PFM is a particular operating mode of atomic force microscopy AFM. This mode allows the simultaneous acquisition of the topography and the piezoelectric response of a piezoelectric sample. A conductive layer is deposited on one face of the piezoelectric sample to produce a lower electrode. When the PFM operating mode is chosen, an alternating electrical stimulation signal is injected between the lower electrode and the tip in contact with the upper surface of the sample. The tip behaves as an upper electrode of the tip - piezoelectric layer - lower electrode assembly. This induces a local electromechanical response of the piezoelectric sample. The response consists of lateral and / or vertical displacements proportional to the ferroelectric characteristics of the sample and to the injected signal.These displacements are measured by the reflection of a laser incident on the end of the lever towards a four-quadrant photodiode, by differential detection.

[0010] Piezoelectric force microscopy with SS-PFM polarization switching spectroscopy is a particular mode of "piezoelectric force microscopy" PFM. SS-PFM microscopy makes it possible to exploit the piezoelectric and ferroelectric characteristics of the sample with more precision. In addition to the first sinusoidal electrical signal usually used in PFM mode, a square wave signal modulating a second periodic signal is applied between the tip and the lower electrode. We will describe this signal in more detail in the rest of the description. This combination of signals makes it possible to cause local switching of the local electrical polarization of the sample while measuring the electromechanical response of the sample. The switching makes it possible to obtain a local hysteresis curve for each point scanned by the tip.

[0011] The assembly consisting of the lever, the tip, the piezoelectric sample and the electrode forms a local mechanical system. This mechanical system has a specific resonance frequency, denoted f0. The resonance frequency depends on the geometric characteristics and the materials which constitute each element of the assembly, as well as on the contact force between the tip and the sample. Thus, two operating modes are possible: resonance operation and non-resonance operation.

[0012] On the one hand, the resonance operation consists of using a first sinusoidal electrical signal having a frequency fi equal to the resonance frequency f0 . This makes it possible to maximize the measured amplitude of the electromechanical response of the sample. Indeed, the measured amplitude is multiplied by the quality factor of the resonance peak, having an order of magnitude of 100. Thus, the sensitivity of the measurement and the signal-to-noise ratio are improved. However, the resonance frequency f0 can fluctuate with measurement artifacts during characterization. These fluctuations result, for example, from the variation of the pressure applied by the tip to the surface of the sample. The latter can vary due to changes in the topography of the surface of the sample, changes in the elastic mechanical properties of the sample, or changes in Coulomb interactions between the tip and the sample.Tip wear can also cause the resonant frequency of the assembly to drift. The new value of the resonant frequency f0' is noted. The frequency of the first sinusoidal electrical signal fi is no longer aligned with the new resonant frequency f0'. The system no longer operates in resonance. The measured amplitude varies, without the actual amplitude of the resonant peak necessarily being modified. As a result, operation in resonance has a strong dependence on drifts in the resonant frequency.

[0013] On the other hand, off-resonance operation consists of using a first sinusoidal electrical signal having a frequency fi substantially lower than the resonance frequency f0. This mode has the advantage of simple implementation and makes it possible to have a signal that is weakly dependent on measurement artifacts (tip wear, variation in the tip-sample contact force, etc.). The disadvantage of this operating mode consists of limited sensitivity and signal-to-noise ratio. More particularly, this problem prevents measurements for samples with low piezoelectric coefficients.

[0014] Thus, there is a need to develop a characterization method by "piezoelectric force microscopy with polarization switching spectroscopy" SS-PFM combining improved sensitivity and signal-to-noise ratio. while being independent of fluctuations and drifts in the resonance frequency f0 of the system.

[0015] Prior art / State of the art restrictions

[0016] Existing techniques of "piezoelectric force microscopy with polarization switching spectroscopy" SS-PFM propose the "frequency sweep" solution to solve the problem of resonance frequency drifts. When operating in resonance mode, during each reading step, the frequency of the first sinusoidal electrical signal fl is varied according to a predefined frequency range. This involves a frequency sweep of the reading signal in order to detect the resonance peak of the system which may vary from one reading step to another. This solution has the disadvantage of a large quantity of measurements due to the frequency sweep. In addition, the processing of the measurements is complex. In addition, this lengthens the characterization time. This results in a considerable increase in the requirements for data storage resources and computing resources.Another disadvantage is that each reading step is limited to a single measurement corresponding to the maximum value of the detected peak. This increases the risk of measurement error and reduces its reliability.

[0017] Response to the problem and provision of solution

[0018] To overcome the limitations of existing solutions with regard to the elimination of the effect of fluctuations and drifts of the resonance frequency f0 of the measurement system, the invention proposes a SS-PFM type characterization method in which the frequency of the first sinusoidal electrical signal fl is kept equal to the resonance frequency of the system by a “dual frequency resonance tracking” DFRT system coupled to the atomic force microscope. The acronym DFRT corresponds to the English expression “Dual Frequency Resonance Tracking”.

[0019] This solution makes it possible to eliminate the impact of drifts in the resonance frequency f0 of the measurement system, unlike operation in conventional resonance mode.

[0020] Furthermore, the method according to the invention has the advantage of improved sensitivity and a high signal-to-noise ratio compared to operation in conventional off-resonance mode.

[0021] The method according to the invention also has the advantage of a considerable reduction in measurement times and in the size of the measurement data compared to the solution based on frequency scanning. This makes it possible to reduce the requirements for data storage and calculation resources.

[0022] The method according to the invention also has the advantage of simple and inexpensive experimental implementation.

[0023] The method according to the invention also has the advantage of being able to obtain a plurality of measurements for a single point on the surface in a short time. This makes it possible to use its multiple measurements with statistical processing of the mean and standard deviation type. It then becomes possible to evaluate the relevance of the measurements and increase the reliability of the characterization method.

[0024] Summary / Claims

[0025] The subject of the invention is a device for characterizing a piezoelectric sample having a lower electrode and an upper surface, the device comprising: - a conductive tip placed at one end of a lever and intended to be placed in contact with a point on the upper surface; the assembly formed by the tip, the sample and the electrode having a variable resonance frequency, - a voltage generator configured to apply, between the lower electrode and the conductive tip, a characterization signal at a first frequency, - an acquisition chain configured to generate a signal for measuring the electromechanical response of the sample, and - a control circuit configured to control the voltage generator by generating a control signal from the measurement signal received via a feedback loop. The first frequency being kept equal to the resonant frequency by the control circuit.

[0026] According to a particular aspect of the invention, the characterization device further comprises a calculator configured to plot an amplitude and / or phase hysteresis curve associated with the point from the measurement signal.

[0027] According to a particular aspect of the invention, the generator is configured to further generate: - a first rectification signal at a second frequency higher than the first frequency; - a second rectification signal at a third frequency lower than the first frequency; the two rectification signals respectively having an amplitude lower than that of the characterization signal and being superimposed with the characterization signal; and the second frequency and the third frequency being equidistant from the first frequency.

[0028] According to a particular aspect of the invention, the measurement signal comprises a first spectral component associated with the first frequency, a second spectral component associated with the second frequency and a third spectral component associated with the third frequency; and wherein the control circuit comprises a first filter for extracting the second spectral component and a second filter for extracting the third spectral component.

[0029] According to a particular aspect of the invention, the control circuit comprises a comparator circuit configured to estimate whether the amplitude of the second spectral component is equal to that of the third spectral component.

[0030] According to a particular aspect of the invention, the control circuit comprises a regulator for generating the control signal so as to maintain equality between the amplitude of the second spectral component and that of the third spectral component.

[0031] The invention also relates to a method for characterizing a piezoelectric sample having a lower electrode and an upper surface, said method being intended to determine the ferroelectric properties of at least one point on the surface of said sample, the method being carried out by a device comprising a conductive tip placed at the end of a lever, the method comprises the following steps for the at least one point: I. Bringing the conductive tip into contact with the upper surface at the point. The assembly formed by the lever, the tip, the sample and the electrode having a variable resonant frequency, and IL Apply between the lower electrode and the conductive tip, a characterization signal at a first frequency so as to locally modify the distribution of the local electrical polarization during a writing phase and measure the electromechanical response during a reading phase. The first frequency is kept equal to the resonant frequency.

[0032] According to a particular aspect of the invention, step II) comprises the following sub-steps: ii- applying for a writing duration between the lower electrode and the conductive tip, the characterization signal having a first continuous component and a first amplitude; iii- applying, during a reading time between the lower electrode and the conductive tip, the characterization signal having a second continuous component and the first amplitude; iv- measure, simultaneously with iii), the electromechanical response in phase and amplitude of the sample; and v- repeating steps ii) to iv) by varying the first continuous component according to a periodic envelope function having a second frequency lower than the first frequency, and having a second amplitude greater than the first amplitude; the number of iterations being sufficient to achieve at least one period of the periodic function.

[0033] According to a particular aspect of the invention, the method further comprises the following step: vi- plot an amplitude and / or phase hysteresis curve associated with the point from the measurements obtained in step iv) of each iteration.

[0034] According to a particular aspect of the invention, for the at least one point, steps ii) to vi) are repeated by varying the second continuous component for each cycle in order to obtain a plurality of hysteresis curves, each being associated with a value of the second continuous component.

[0035] According to a particular aspect of the invention, the method further comprises the following step for the at least one point: - selecting a hysteresis curve from among the plurality of hysteresis curves according to a predetermined selection criterion.

[0036] According to a particular aspect of the invention, the predetermined selection criterion corresponds to the hysteresis curve having a saturation portion having a minimum slope or a minimum offset from the origin.

[0037] According to a particular aspect of the invention, sub-step iii) comprises successively carrying out a plurality of measurements of the electromechanical response in phase and amplitude of the sample.

[0038] According to a particular aspect of the invention, the method further comprises the following step: - for each reading phase, carry out statistical processing of the plurality of average and / or standard deviation type measurements.

[0039] According to a particular aspect of the invention, the method is applied to a plurality of points on the surface and further comprises the following step after step v): - for each characterized point, generate a list comprising a quantification of several ferroelectric and / or piezoelectric and / or electrostatic characteristics extracted from the hysteresis curve associated with said point.

[0040] According to a particular aspect of the invention, the method further comprises the following step: - for each extracted ferroelectric characteristic, generate an associated surface map from the lists. Detailed description

[0041] Other characteristics and advantages of the present invention will appear better on reading the description which follows in relation to the following appended drawings:

[0042] [Fig. 1a] illustrates an embodiment of the experimental device according to the invention.

[0043] [Fig.lb] illustrates a diagram of a dual-frequency resonance tracking circuit of the experimental device according to the invention.

[0044] [Fig. 1c] illustrates a spectral analysis of the signal measured at the input of the dual-frequency resonance tracking circuit of the experimental device according to the invention.

[0045] [Fig.2] illustrates a flowchart of the steps of the characterization method according to a first embodiment of the invention for a point on the surface of the sample.

[0046] [Fig.3a] illustrates a first embodiment of the variation of the first continuous component of the characterization signal of the characterization method according to the invention.

[0047] [Fig.3b] illustrates a partial zoom on the characterization signal during an iteration of the characterization method according to the invention.

[0048] Figures 4a to 4g illustrate a succession of iterations of the characterization method according to the invention applied to a point on the surface.

[0049] [Fig.5a] illustrates the acquisition and stimulation curves during a state-of-the-art SS-PFM characterization process.

[0050] [Fig.5b] illustrates the acquisition and stimulation curves during the characterization method according to the invention.

[0051] [Fig.6] illustrates a second embodiment of the variation of the continuous component of the characterization signal of the characterization method according to the invention.

[0052] [Fig.7] illustrates a flowchart of the steps of the characterization method according to the invention applied to a plurality of points on the surface of the sample.

[0053] [Fig. 1a] illustrates an experimental device DI according to the invention. The experimental device DI is configured to implement a method for characterizing a test sample El according to an embodiment of the invention. The experimental device DI comprises a conductive tip PI secured to one end of a lever L1, an actuator Al for mechanically controlling the lever L1, a laser source SL1, a voltage generator Gl, a four-quadrant photodiode PDI, an amplifier stage AMP1, a control circuit 20 and a computer CALC.

[0054] The test sample El comprises a thin layer PZ1 made of a piezoelectric material and an electrically conductive layer acting as a lower electrode ELI. The lower electrode ELI is a layer deposited on one side of the PZ1 layer. The face opposite that of the lower electrode constitutes the surface to be characterized of the sample, it is noted SI.

[0055] For example, the PZ1 layer has a thickness of between 5 nm and 100 nm. For example, the PZ1 layer is made of lead zirconate titanoates PZT, barium titanate BaTiO3 or any other piezoelectric and ferroelectric material. For example, the lower electrode ELI is made of copper or aluminum or platinum.

[0056] The tip PI is intended to be brought into contact with the surface SL. The contact point denoted NI is the point to be characterized. The laser source SL1 is placed so as to emit a laser beam on the upper face of the tip PL. The laser beam is reflected by the tip PI towards the four-quadrant photodiode PDI. At rest, the laser beam is reflected on the center of the four-quadrant photodiode. This is a calibration to determine the measurement reference.

[0057] The voltage generator G1 generates an alternating electrical stimulation signal denoted VST(t) between the lower electrode ELI and the tip PI in contact with the upper surface SI of the sample EL. The signal Vst(0 is used to carry out reading and writing phases which will be detailed later. The generator G1 is controlled by the control circuit 20 via a control signal denoted Vcont. The control signal Vcont is a setpoint signal determining the frequency and amplitude characteristics of the stimulation signal Vsi(t).

[0058] As described previously, the application of the stimulation signal VST induces a local electromechanical response at the point NI of the piezoelectric layer PZ1. The response consists of lateral or vertical displacements proportional to the piezoelectric and ferroelectric characteristics of the sample and to the injected signal. These displacements are measured by the reflection of the incident laser on the end of the lever L1 towards the four-quadrant photodiode PDI, by differential detection. Indeed, the electromechanical response of the sample causes a deformation of the lever LL. The deformation of the lever L1 causes the change in the angle of incidence between the laser and the upper part of the tip, which deflects the laser. This causes a displacement of the point of incidence of the laser beam reflected on the four-quadrant photodiode PDI. This causes the generation of a differential measurement signal by the photodiode DPI, denoted VSPd.In order to quantify the amplitude of the differential measurement signal, the latter is amplified by the amplification stage AMP1 which generates an amplified measurement signal Vs. Thus, the amplitude of the signal Vs corresponds to the local displacement of the sample, and the phase of the signal Vs corresponds to the phase shift between the response of the piezoelectric material and the stimulation.

[0059] The CALC calculator is configured to process the measurement signal Vs in order to extract the piezoelectric and ferroelectric characteristics of the sample and plot a hysteresis curve for each characterized point of the surface SI.

[0060] We recall that the assembly consisting of the lever, the tip, the piezoelectric sample and the electrode has a specific resonance frequency, denoted f0. The control circuit 20 is configured to maintain operation in resonance throughout the characterization and independently of potential drifts in the resonance frequency. This function is carried out by means of a feedback loop propagating the amplified measurement signal Vs to the control circuit 20. This makes it possible to eliminate the impact of drifts in the resonance frequency f0 of the measurement system during operation in resonance mode.

[0061] In the following, we will explain the principle of “dual frequency resonance tracking” DFRT carried out by the circuit 20. [Fig. lb] illustrates a diagram of an example of a control circuit 20 of the experimental device according to the invention. [Fig. le] illustrates a spectral analysis of the amplified measurement signal Vs at the input of the control circuit 20

[0062] The control circuit 20 comprises a first frequency filtering circuit FIL1, a second frequency filtering circuit FIL2, a comparator circuit COMP and PID regulator (acronym for proportional, integral, derivative).

[0063] The control circuit 20 controls the generator G1 to generate a stimulation signal VSF(t) obtained by the superposition of a characterization signal VCar(1) and two rectification signals VDFRT+(t) and VDFRT_(t). Vsr( t) - VCAR(t, + VDFRT+ (t, fDFRT+ ) + VDFRT.(t, f DFRT )

[0064] The characterization signal VCar(1) has an amplitude greater than that of the two rectification signals VDFRT+(t) and VDFRT_(t). Thus, the characterization signal Vcar(I) is the useful signal for stimulating the sample during characterization. On the other hand, the rectification signals VDFRT+(t) and VDFRT_(t) are used to perform a function for maintaining the frequency of the characterization signal VcarCO equal to the resonance frequency f0 even in the event of drifts of the latter. + V AC (O = WO + + the continuous component of the signal y^), y^ ( (, = y^^ alternating component having a first amplitude Vq, a first frequency fp and an initial phase The continuous component plays the role of local polarization voltage at the level of the point NI. The first frequency f} is called “working frequency”.

[0065] The continuous component VDC ( t) varies between a first variable value Vdc\( O and a second constant value VDC2. The first value varies VDC1 ( t ) according to the periodic function g(t). The local characterization of the sample is composed of a plurality of iterations. Each iteration is broken down into a writing phase and a reading phase. The writing phase consists of stimulating the sample locally at point N1 so as to modify the distribution of the local electrical polarization by ferroelectric effect. The reading phase is used to quantify the local electromechanical response with the new distribution of electrical polarization obtained after the writing phase. During a writing phase, the DC component Vdc^ of the characterization signal is equal to the first variable value VDCl (t). During a reading phase, the DC component Vpc(C of the characterization signal is equal to the second constant value VDC2(t).

[0066] The first rectification signal VDFRT+(t) has a frequency fDFRT+=fi+ fBW with fBw of the order of magnitude of the frequency higher than fl corresponding to half the maximum amplitude of the resonance peak f0. The second rectification signal VDfrt(t) has a frequency fDFRT=fr Lwavcc fBW of the order of magnitude of the frequency lower than fl corresponding to half the maximum amplitude of the resonance peak f0.

[0067] The two rectification signals are superimposed on the characterization signal VCar (t). The amplified measurement signal Vs of the electromechanical response comprises three spectral components each having a measured amplitude: the measured amplitude ACar resulting from the characterization signal VcarO at the frequency f। the measured amplitude ADFRT+ resulting from the first rectification signal VDFRT+(t) at the frequency fDFRT+ and the measured amplitude ADFRT_ resulting from the second rectification signal VDFRT_ (t) at the frequency fDFRT

[0068] The first filter FIL1 is intended to filter the measurement signal Vs in order to extract the spectral component associated with the frequency fDFRT+ of amplitude ADFRT+. The second filter FIL2 is intended to filter the measurement signal Vs in order to extract the spectral component associated with the frequency fDFRT of amplitude ADFRT_. The comparator COMP is intended to compare the amplitude ADFRT.to the amplitude ADFRT+ If they are equal ADFRT_= ADFRT+ this means that the peak of the spectral component associated with the frequency fi is symmetrical and that the amplitude ACar is maximum. This indicates that the frequency fon has not drifted and that the first frequency fi is equal to the resonance frequency f0.

[0069] When the resonant frequency fo drifts, the equality fi=f0 is no longer respected. The peak of the spectral component associated with the frequency fi is no longer symmetrical with respect to the interval [fDFRT-,fDFRT+]- Thus, ADFRT_is different from ADFRT+ and the comparator circuit COMP generates a signal which activates the PID regulator. The PID regulator then modifies the frequency setpoint fi carried by the control signal Vcont. The PID regulator is configured to act on the frequency fide so as to keep the amplitudes ADFRT+ and ADFRT_ equal to each other. This allows the frequency fi to be adjusted in real time with the variations in the resonance frequency f0.

[0070] For example, the PID regulator implements a setpoint signal proportional to the difference in the amplitudes ADFRT+ and ADFRT_ to correct the frequency fi in the direction of this difference.

[0071] [Fig.2] illustrates a flowchart of the steps of the characterization method according to a first embodiment of the invention applied to a point NI of the surface SI of the sample.

[0072] The first step i) of the CARAC characterization method consists of placing the conductive tip PI in contact with the upper surface SI at the point NI to be characterized.

[0073] The second step ii) consists of applying, for a writing duration Atl, between the lower electrode ELI and the conductive tip PI, the characterization signal VCar (t)) having a first continuous component VDci, the first frequency fi and a first amplitude Vo. Vc^'^V^ V ( / )= VDC| + V*sin(2^7 component continuous signal y^) and ( (} = component alternating current having a first amplitude Fo, the first frequency fv and an initial phase V. The continuous component FDC1 is constant during the writing time Atl. The writing phase consists of stimulating the sample locally at point NI so as to modify the distribution of the local electrical polarization by ferroelectric effect.

[0074] The third step iii) consists of applying, during a reading time At2 between the lower electrode ELI and the conductive tip PI, the characterization signal V cAR(t) having a second continuous component VDc2 and varying according to the first frequency fi and the first amplitude Vo. v Xt) = .rlV The alternative component of the characterization signal Fcar^ is identical to that applied during writing. Thus, the frequency fi and the amplitude Vo are the same. The DC component FDC2 is constant during the reading time At2. The DC component VDC2 is different from that of the applied during writing. The characterization signal FCAR( t ) during a reading serves to locally electromechanically stimulate the sample without changing the polarization of the material affected by the previous writing step. This allows to quantify the local electromechanical response with the new electrical polarization distribution obtained after the writing phase.

[0075] Simultaneously with step iii), the fourth step iv) is carried out during the reading time At2. It consists of measuring the electromechanical response in phase and amplitude of the sample El. This step is carried out by the acquisition means constituted by the laser source SL1, the tip L1, the photodiode PDI and the amplification stage AMP1.

[0076] The working frequency fi is maintained equal to the resonance frequency f0 during the execution of the CARAC method. The maintenance of the equality fi=f0 is achieved by the mechanism described previously.

[0077] The set of steps ii) to iv) constitutes a first iteration II in the CARAC characterization method of a point NI of the surface. The fifth step v) consists of repeating steps ii) to iv) by varying the first continuous component VDCi according to a periodic envelope function g(t). The tip PI is always kept in contact with the point NI of the surface SL

[0078] The periodic envelope function g(t) has a second frequency f2 lower than the first frequency fb. In addition, it has a second amplitude V2 greater than the first amplitude Vo. The number of iterations Ij of steps ii) to iv) (j a non-zero natural integer) is chosen so as to cover at least one period of the periodic function g(t). For each iteration Ij, a pair of values ​​(output amplitude, output phase) is obtained in response to the characterization signal VCar(1)- The envelope function g(t) modulates the amplitude of the continuous component in writing VDCi. Thus, from one iteration to another, a variation in the value of VDci is obtained while keeping the value of the continuous component in reading VDC2 constant.

[0079] The sixth step vi) consists of plotting a hysteresis curve using the CALC computer which receives the measurement signal Vs(t) in real time. The hysteresis curve corresponds to the local hysteresis of the amplitude and / or phase associated with the point NI from the measurements obtained for each iteration Ij at the end of step iv).

[0080] Optionally, the CARAC characterization method comprises a seventh step consisting of generating a list comprising a quantification of several ferroelectric characteristics extracted from the hysteresis curve associated with the NI point. As a non-limiting example, the list L1 covers the following characteristics of the NI point: - The local electromechanical response of the sample to saturation, - The local electromechanical response of the residual sample, - Coercive tensions for which the response is cancelled, - The nucleation tension, for which we are beginning to grow a new domain, - The area of ​​the hysteresis curve, - Remanent amplitude, - Amplitude at saturation, - The affine component of the hysteresis curve, and - The offset of the hysteresis curve (offset in English).

[0081] Each step of the method of [Fig.2] is now described in detail.

[0082] Figure 3a illustrates a first embodiment of the variation over time of the continuous component VDC(t) characterization signal VCAR in order to carry out a plurality of iterations of steps ii) to iv).

[0083] Diagram 301 illustrates a period T2 of the periodic function g(t). The DC component varies in this case according to a periodic triangular signal modulated by a square wave signal. The period T2 is the inverse of the second frequency f2 lower than the first frequency fL

[0084] Diagram 302 illustrates a partial zoom on the variation curve of the continuous component VDC(t) - ^tat ^aut corresponds to a writing step ii). A low state corresponds to a reading step iii). The succession of two steps ii) and iii) corresponds to an iteration Ij. Thus, the average value of During a period corresponds to the continuous component Vdcï- For each iteration Ij the plateau of a pulse corresponds to the continuous component VDC! of the characterization signal car^) during writing. Here, as an example, iterations II to 17 are represented, each comprising a reading step and a writing step.

[0085] The variation of the continuous component VDCl of the signal of VCar^) (in writing), from one iteration to another, makes it possible to plot a hysteresis curve. Indeed, the continuous component Vdc\ describes during a period T2, the range of values ​​between -V2 and +V2; V2 being the amplitude of the envelope function g(t).

[0086] Figure 3b illustrates a partial zoom on the characterization signal V car^) during an iteration Ij. This figure illustrates the variable continuous component depending on the step carried out (reading or writing) and the alternating component common to the two reading and writing steps.

[0087] We will describe in the following the physical mechanism of reading and writing in order to determine the ferroelectric characteristics at a point NI of the surface SL. Figures 4a-4g illustrate a succession of iterations of the characterization method according to the invention applied to said point of the surface.

[0088] Figure 4a illustrates an initial reading step. The tip PI is in contact with the surface at the point NI. The generator G1 is configured to apply between the tip PI and the lower electrode ELI a characterization signal having a frequency fi=f0. The characterization signal has a DC component ^dcz = 0V. The output amplitude of the measured signal Vs(t) at the origin is determined and it corresponds to the point “0” of the curve 401. The sectional view 401' illustrates the initial local electrical polarization of the ferroelectric sample. As a non-limiting illustrative example, it is assumed that the polarization is oriented upwards. The initial electrical polarization domain is noted PolO.

[0089] Figure 4b illustrates the progress of the first iteration Ib. The generator G1 is configured to apply between the tip PI and the lower electrode ELI a characterization signal having a frequency fi=f0. During a write operation, the characterization signal has a strictly positive DC component Kdci > 0V. This causes the local formation of a ferroelectric domain Poil with polarization oriented downwards as illustrated in the sectional view 402'. Then, a falling edge at Vdcz ~ 0 triggers a reading step associated with the first iteration Ii. During the reading step, the electromechanical response (phase and amplitude) of the created ferroelectric domain Poil (downwards), opposes that of the peripheral domain PolO, oriented in the opposite direction. The output amplitude associated with the iteration h corresponds to point “1” of the curve 402.

[0090] Figure 4c illustrates the progress of the second iteration I2. During the writing step, the amplitude of the DC component is increased compared to the previous iteration. The ferroelectric domain created (downwards) increases. The change in the electromechanical response continues until reaching a zero point noted "2". There is mutual compensation between: on the one hand, the effect of the ferroelectric domain created locally downwards; and on the other hand the effect of the peripheral ferroelectric domain oriented upwards.

[0091] Figure 4d illustrates the progress of the fourth iteration I4. During the writing step, the amplitude of the DC component VDC! is increased compared to the previous iteration. The created ferroelectric domain (downward) continues to grow. The change in the electromechanical response continues until reaching a saturation point noted “3”. The electromechanical response is induced essentially by the predominant effect of the created ferroelectric domain.

[0092] During iterations 15 and 16, the amplitude of the continuous component VDCj is decreased until it reaches 0. The response always remains equal to the saturation value obtained at the end of the fourth iteration I4-

[0093] Figure 4e illustrates the progress of the seventh iteration I7. During the writing step, the characterization signal has a strictly negative DC component Vdc\ < 0V. This causes the local formation of a second ferroelectric domain with upward polarization in the first ferroelectric domain with downward polarization. The polarization of the second local domain opposes that of the first locally created domain. The electromechanical response (amplitude in this case) begins to decrease compared to the saturation threshold previously reached. The output amplitude associated with iteration L corresponds to point “4” of curve 405’.

[0094] Figure 4f illustrates the progress of the eighth iteration I8. During the writing step, the value of the continuous component LDC1 is decreased compared to the previous iteration. The ferroelectric domain created (downwards) continues to increase. The change in the electromechanical response continues until reaching a zero point noted "5". There is mutual compensation between: on the one hand, the effect of the ferroelectric domain created locally upwards; and on the other hand the effect of the ferroelectric domain created locally downwards.

[0095] Figure 4g illustrates the progress of the ninth iteration 19. During the writing step, the value of the continuous component Vdci is reduced compared to the previous iteration. The created ferroelectric domain (downward) continues to grow until the upward-oriented local domain disappears. The original ferroelectric state of the local environment of the NI point is found. The change in the electromechanical response continues until a saturation point noted “6” is reached. The electromechanical response is essentially induced by the predominant effect of the created ferroelectric domain.

[0096] We thus obtain, following a period of the envelope function g(t), the measurement points necessary to plot an amplitude and / or phase hysteresis curve associated with point NI from the measurements obtained in step iv).

[0097] In order to demonstrate the advantages of the method according to the invention, we will compare the measurement signals of a method according to the state of the art with those of the method according to the invention.

[0098] [Fig.5a] illustrates the measured signal C0 (at the output of the amplifier stage AMP1) and the characterization signal C0' with a state-of-the-art SS-PFM characterization method, more particularly a method with "frequency sweep". For each iteration of the method, and during each reading and writing step, the "working frequency" fi is varied. The variation covers a frequency range which must include the value of the resonance frequency f0. During reading, a single value corresponds to the value of the resonance peak. This point is determined by seeking the maximum of the measured amplitude of the CO signal during a reading phase. We recall that the resonance peak is not known beforehand because it can drift from its initial value during characterization. We observe that during a 2.5 second window, 13 iterations are carried out. At the end of each iteration, only one measurement point can be used to plot the resonance hysteresis curve.

[0099] [Fig.5b] illustrates the measured signal Cl and the characterization signal Cl' with the characterization method according to the invention. The "working frequency" fi is always kept equal to the resonance frequency fo following its fluctuations. During each iteration it is possible to successively carry out a plurality of measurements of the electromechanical response in phase and amplitude of the sample. Indeed, each measured point of the amplitude of the signal Cl during the reading phase corresponds to an operation in resonance. It is observed that during a window of 1.7 seconds, 17 iterations are carried out. At the end of each iteration, a plurality of measurement points (of the order of a few hundred points) can be used to plot the hysteresis curve because they all correspond to an operation in resonance.

[0100] Thus, the characterization method according to the invention presents a considerable gain in execution time and in quantity of useful measurements. This makes it possible to reduce the requirements for computing resources and storage of measurement data during characterization.

[0101] Advantageously, it is possible to improve the reliability of the measurements by carrying out statistical processing of the plurality of measurement points associated with a single iteration. This is not possible with “frequency sweep” methods which have a single useful point per iteration. In this case, step v) comprises the following sub-steps: - successively carry out a plurality of measurements of the electromechanical response in phase and amplitude of the sample, and - carry out statistical processing of the plurality of average and / or standard deviation type measurements. It then becomes possible to evaluate the relevance of the measurements and increase the reliability of the characterization process.

[0102] [Fig.6] illustrates a second embodiment of the variation of the continuous component of the characterization signal of the CARAC characterization method applied to a single point NI of the surface SL. In this embodiment, several periods T2 of envelope signal g(t) are applied. The continuous reading component VDC2 is varied for each period of the envelope function g(t). For example, the continuous reading component VDc2 is greater than that of the previous period T2. At the end of each period T2, a hysteresis curve is obtained via the mechanism described above. A hysteresis curve is thus associated with each value of VDC2. This serves to minimize the electrostatic effect which can reduce the reliability of the measurement results. Indeed, the electrostatic effect on a hysteresis curve manifests itself in two ways: 1- the first effect consists in increasing the slope of the upper saturation part (segment from 3 to 4 on [Fig.4g]) on [Fig.4g] and / or lower (segment from 6 to 1 on [Fig.4g]) of the hysteresis curve. The upper (or lower) saturation part of a hysteresis curve is called "the saturation portion", and 2- the second effect consists in shifting the hysteresis curve upwards or downwards (offset in English).

[0103] Advantageously, the characterization method further comprises a step of selecting a hysteresis curve from among the plurality of hysteresis curves according to a predetermined selection criterion. The selection criterion may be the minimization of the slope of a chosen saturation portion. Alternatively, the selection criterion may be the minimization of the offset by centering the hysteresis curve relative to the origin (0,0). This helps to minimize the disturbance of the electrostatic effect and improve the accuracy of the characterization.

[0104] [Fig.7] illustrates a flowchart of the steps of the characterization method according to the invention applied to a plurality of points on the surface of the sample.

[0105] All of steps i) to vii) are carried out for a plurality of points NI to Nk (k a strictly positive integer) so as to totally or partially scan the surface SL. We thus obtain a plurality of lists L1 to Lk each associated with a point of the surface SL. Each list L1 to Lk includes a quantification of the ferroelectric characteristics such as the local electromechanical response in saturation, the remanent local electromechanical response, the coercive voltages, the nucleation voltage, the area of ​​the hysteresis curve, the remanent amplitude, the amplitude at saturation, the affine component of the hysteresis curve and the offset of the hysteresis curve (offset in English). In addition, it is possible to extract from the measurements of the electrostatic properties of the sample, information on the variations of the local mechanical properties of the material thanks to the acquisition of the resonance frequency for example.It is also possible to extract the piezoelectric coefficient d33 which corresponds to the linear part of the PFM amplitude hysteresis curve. Advantageously, the characterization method according to the invention further comprises a mapping step. For each ferroelectric characteristic extracted from lists L1 to Lk, an associated mapping of the surface is generated from the lists previously obtained. This produces an imaging of the . surface of the sample allowing to exploit the piezoelectric and ferroelectric characteristics of the SI surface of the sample.

Claims

1.

2. Claims Device (Dl) for characterizing a piezoelectric sample (El) having a lower electrode (ELI) and an upper surface (SI), the device comprising: - a conductive tip (PI) placed at one end of a lever (Ll) and intended to be placed in contact with a point (NI) of the upper surface (SI); the assembly formed by the tip, the sample and the lower electrode having a variable resonance frequency (f0); - a voltage generator (Gl) configured to apply, between the lower electrode (ELI) and the conductive tip (PI), a characterization signal (VCar) ​​at a first frequency (fi); - an acquisition chain (21) configured to generate a measurement signal (Vs) of the electromechanical response of the sample; - a control circuit (20) configured to control the voltage generator (Gl) by generating a control signal (Vcont) from the measurement signal (Vs) received via a feedback loop; and the first frequency (fi) being kept equal to the resonance frequency (f0) by the control circuit (20); the generator (Gl) being configured to further generate: - a first rectification signal (VDfrt+) at a second frequency (fDpRT+) higher than the first frequency (fi); - a second rectification signal (Vdfrt) at a third frequency (fDFRT-) lower than the first frequency (fj; the two rectification signals (Vdfrt-, VDfrt+) respectively having an amplitude lower than that of the characterization signal (VCar) ​​and being superimposed with the characterization signal (VCar); and the second frequency (fDFRT+) and the third frequency (fDFRT ) being equidistant from the first frequency (f0). Characterization device (Dl) according to claim 1 further comprising a calculator (CALC) configured to plot an amplitude and / or phase hysteresis curve associated with the point (NI) from the measurement signal (Vs).

3. Characterization device (Dl) according to any one of claims 1 or 2 wherein the measurement signal (Vs) comprises a first spectral component associated with the first frequency (fi), a second spectral component associated with the second frequency (fDFRT+) and a third spectral component associated with the third frequency (fDFRT); and wherein the control circuit (20) comprises a first filter (FIL1) intended to extract the second spectral component (Vs(fDFRT+)) and a second filter (FIL2) intended to extract the third spectral component (Vs(fDFRT))•

4. Characterization device (Dl) according to claim 3 wherein the control circuit (20) comprises a comparator circuit (COMP) configured to estimate whether the amplitude of the second spectral component (Vs(fDFRT+)) is equal to that of the third spectral component (Vs(fDFRT ))•

5. Characterization device (Dl) according to any one of claims 3 or 4 in which the control circuit (20) comprises a regulator (PID) for generating the control signal (Vcont) so as to maintain equality between the amplitude of the second spectral component (Vs(fDFRT+)) and that of the third spectral component (Vs(fDFRT ))•

6. Method for characterizing (CARAC) a piezoelectric sample (El) having a lower electrode (ELI) and an upper surface (SI), said method being intended to determine the ferroelectric properties of at least one point (NI) of the surface (SI) of said sample (El), the method being carried out by a device (1) according to any one of claims 1 to 6, the method comprising the following steps for the at least one point (NI): I. Bringing the conductive tip (PI) into contact with the upper surface (SI) at the point (NI); the assembly formed by the lever, the tip, the sample and the lower electrode having a variable resonance frequency (f0); and II. Applying between the lower electrode (ELI) and the conductive tip (PI), a characterization signal (VCar) ​​at a first frequency (fi) so as to locally modify the distribution of the local electrical polarization during a writing phase and measuring the electromechanical response during a reading phase and applying a first rectification signal (VDFRT+) at a second frequency (fDFRF+) higher than the first frequency (fi) and a second rectification signal (VDFRT_) at a third frequency (fDFRF) lower than the first frequency (fi); the two rectification signals (VDFRT_, VDFRT+) respectively having an amplitude lower than that of the characterization signal (VCar) ​​and being superimposed with the characterization signal (VCar); the second frequency (fDFRT+) and the third frequency (fDFRT_) being equidistant from the first frequency (f0); the first frequency (fi) being kept equal to the resonance frequency (f0);

7. Characterization method (CARAC) according to claim 6 wherein step II) comprises the following sub-steps: ii- Applying during a writing time (Atl) between the lower electrode (ELI) and the conductive tip (PI), the characterization signal (VcarO) having a first continuous component (VDCi) and a first amplitude (Vo); iii- Applying during a reading time (At2) between the lower electrode (ELl) and the conductive tip (PI), the characterization signal (VcarO) having a second continuous component (VDC2) and the first amplitude (Vo); iv- Measuring, simultaneously with iii), the electromechanical response in phase and amplitude of the sample (El);and v- Repeat steps ii) to iv) by varying the first continuous component (VDCi) according to a periodic envelope function (g(t)) having a second frequency (f2) lower than the first frequency (fj, and having a second amplitude (V2) greater than the first amplitude (Vi); the number of iterations (II, 12,13,14) being sufficient to achieve at least one period of the periodic function (g(t)).;

8. Characterization method (CARAC) according to claim 7 further comprising the following step: vi- Plot an amplitude and / or phase hysteresis curve associated with point (NI) from the measurements obtained in step iv) of each iteration (II, 12,13,14).

9. Characterization method (CARAC) according to claim 8, in which for the at least one point (NI) steps ii) to vi) are repeated by varying for each cycle (Cyl, Cy2, Cy3, Cy4) the second continuous component (VDC2) in order to obtain a plurality of hysteresis curves, each being associated with a value of the second continuous component (VDc2)-

10. Characterization method (CARAC) according to claim 9 further comprising the following step for the at least one point (NI): selecting a hysteresis curve from among the plurality of hysteresis curves according to a predetermined selection criterion.

11. Characterization method (CARAC) according to claim 10 wherein the predetermined selection criterion corresponds to the hysteresis curve having a saturation portion having a minimum slope or a minimum offset from the origin.

12. Characterization method (CARAC) according to any one of claims 7 to 11, in which sub-step iii) comprises successively carrying out a plurality of measurements of the electromechanical response in phase and amplitude of the sample (El).

13. Characterization method (CARAC) according to claim 12, further comprising the following step: - for each reading phase, carrying out statistical processing of the plurality of measurements of the average and / or standard deviation type.

14. Characterization method (CARAC) according to any one of claims 7 to 13, the method being applied to a plurality of points (NI, N2 N3, N4) of the surface (SI) and further comprising the following step after step v): for each characterized point (NI, N2 N3, N4), generating a list comprising a quantification of several ferroelectric and piezoelectric and / or electrostatic characteristics extracted from the hysteresis curve associated with said point.

15. The characterization method (CARAC) of claim 14, further comprising the following step: for each extracted ferroelectric feature, generate an associated surface mapping (SI) from the lists.

Images