A device for measuring electro-optic coefficient of ferroelectric thin film

Abstract

The application provides a device for measuring an electro-optic coefficient of a ferroelectric thin film, comprising a sample placing module, an incident module, an electric field module and a double optical path interference module, the double optical path interference module is used for outputting an electro-optic coefficient component corresponding to the ferroelectric thin film to be measured according to a phase difference between two polarized lights generated after linearly polarized light penetrates the ferroelectric thin film to be measured, wherein the double optical path interference module comprises a birefringence interference unit and a Mach-Zenhder interference unit, the birefringence interference unit is used for measuring an electro-optic coefficient component that can be separated by using a birefringence interference method in the ferroelectric thin film to be measured, and the Mach-Zenhder interference unit is used for measuring an electro-optic coefficient component that cannot be separated by using the birefringence interference method in the ferroelectric thin film to be measured; and different electro-optic coefficient components can be measured by comprehensively utilizing two kinds of interference results.

Description

Technical Field

[0001] This invention relates to the field of photoelectric measurement technology, and in particular to a device for testing ferroelectric thin film materials. Background Technology

[0002] Ferroelectric materials include lithium niobate, barium titanate, lead zirconate titanate, and lanthanum zirconate titanate, among others. Ferroelectric thin films are widely used in high-speed electro-optic modulators, tunable filters, and other fields. These thin film materials possess multiple non-zero electro-optic coefficient components. The effective electro-optic coefficient varies depending on the crystal orientation, the direction of the modulation electric field, the polarization state of the light, and the direction of propagation. Measuring the electro-optic coefficient is necessary during the development of thin film materials and the fabrication of devices to guide the development of materials and devices.

[0003] Currently, the electro-optic coefficient of ferroelectric thin film materials is usually measured using the birefringence of crystals. This method mainly involves placing a quarter-wave plate behind the ferroelectric thin film sample, adjusting the birefringence phase difference by rotating the quarter-wave plate, and adjusting the birefringence output light to linearly polarized light. When a sinusoidal modulation voltage is applied to the ferroelectric thin film material, the phase difference is modulated, and the azimuth angle of the output linearly polarized light changes according to a sinusoidal law. The azimuth angle is detected by an analyzer, and the signal is detected by a lock-in amplifier. By analyzing the relationship between the azimuth angle and the amplitude of the modulation voltage, the electro-optic coefficient can be obtained.

[0004] However, in existing methods, a quarter-wave plate adjusts the birefringed light into linearly polarized light. Under the influence of the modulation voltage, the azimuth angle of the linearly polarized light changes, and the electro-optic coefficient is measured by detecting the change in azimuth angle with the modulation voltage. This method has three problems: First, under the influence of the modulation voltage, the polarization state of the light becomes elliptically polarized, which can only be approximated as linearly polarized light, thus introducing a certain measurement error. Second, after the quarter-wave plate adjusts the birefringed light into linearly polarized light, the operating point is not at the orthogonal bias point, resulting in low linearity and sensitivity of the electro-optic modulation response. These two problems lead to large measurement errors and low sensitivity in existing methods. Third, it is impossible to separate the electro-optic coefficient components that simultaneously affect the phase change in birefringence, such as the electro-optic coefficient component r of barium strontium titanate thin films. 13 and r 33 . Summary of the Invention

[0005] The purpose of this invention is to provide an apparatus for testing ferroelectric thin film materials, which improves the technical problem of low detection sensitivity in existing apparatuses for testing ferroelectric thin film materials. Compared with the prior art, this invention can measure more electro-optic coefficient components.

[0006] To address the aforementioned technical problems, this invention provides an apparatus for measuring the electro-optic coefficient of a ferroelectric thin film, comprising a sample placement module, an incident module, an electric field module, and a dual-optical-path interference module. The sample placement module is used to place the ferroelectric thin film to be tested, the incident module is used to provide linearly polarized light to irradiate the ferroelectric thin film to be tested, the electric field module is used to provide an electric field to the ferroelectric thin film to be tested, and the dual-optical-path interference module is used to output the electro-optic coefficient component corresponding to the ferroelectric thin film to be tested based on the phase difference between the two polarized lights generated after the linearly polarized light penetrates the ferroelectric thin film to be tested.

[0007] The dual-optical-path interference module includes a birefringence interference unit and a Mach-Zenhder interference unit. The birefringence interference unit is used to measure the electro-optic coefficient components that can be separated by birefringence interference in the ferroelectric thin film under test, while the Mach-Zenhder interference unit is used to measure the electro-optic coefficient components that cannot be separated by birefringence interference in the ferroelectric thin film under test.

[0008] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in this embodiment of the invention, the sample placement module is a rotatable sample stage, which is used to place the ferroelectric thin film to be tested.

[0009] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in this embodiment of the invention, the incident module includes a laser, a half-wave plate, and a polarizer arranged coaxially. The laser is used to provide a light source in the visible or infrared band, the polarizer is used to convert the light emitted by the light source into linearly polarized light, and the half-wave plate is used to adjust the polarization direction of the light emitted by the light source so as to maximize the light intensity of the light emitted by the polarizer.

[0010] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in this embodiment of the invention, the electric field module includes a signal generator, a voltage amplifier, a first electrode, and a second electrode. The signal generator is used to provide a first voltage signal, and the voltage amplifier is used to amplify the first voltage signal into a second voltage signal. The first electrode and the second electrode are respectively attached to both ends of the ferroelectric thin film to be tested, so as to transmit the second voltage signal to the ferroelectric thin film to be tested.

[0011] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in this embodiment of the invention, the first electrode and the second electrode are made of gold, and the distance between the first electrode and the second electrode is in the range of 5 μm to 10 μm.

[0012] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in the embodiments of the present invention, the birefringent interference unit includes a phase compensator, a polarizer and a first detector arranged coaxially in sequence. The phase compensator is arranged coaxially with the incident unit, and the first detector is used to detect the intensity of the received interference signal.

[0013] The phase compensator is used to adjust the operating point of the interference between the two polarized lights generated in the dual-path interference module to the orthogonal bias point.

[0014] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in the embodiments of the present invention, the Mach-Zenhder interferometer unit includes a first optical path unit and a second optical path unit. The first optical path unit includes a first beam splitter, a phase compensator, a polarizer, a second beam splitter, and a first detector arranged coaxially in sequence. The second optical path unit includes a first beam splitter, a first mirror, a second mirror, a second beam splitter, and a first detector.

[0015] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in the embodiments of the present invention, the first reflector and the second reflector are further provided with a reference sample stage. The reference sample stage is used to place a reference thin film sample, which is made of quartz glass, and is used to compensate for the optical path difference between the first optical path unit and the second optical path unit.

[0016] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in the embodiments of the present invention, the apparatus further includes a second detector, a lock-in amplifier, and a computer control system. The lock-in amplifier is electrically connected to the first detector, and the computer control system is electrically connected to the lock-in amplifier.

[0017] The second detector is used to detect the light intensity of the portion of the beam that does not undergo birefringence interference when the birefringence interference unit is working normally. The lock-in amplifier is used to detect the interference signal received by the first detector. The computer control system is used to output the electro-optic coefficient component corresponding to the ferroelectric thin film under test according to the interference signal.

[0018] In the apparatus for measuring the electro-optic coefficient of ferroelectric thin films provided in this embodiment of the invention, when the ferroelectric thin film to be measured is a barium strontium titanate thin film, a birefringent interferometer is used to measure the electro-optic coefficient component r of the barium strontium titanate thin film. 42 The electro-optic coefficient component r of barium strontium titanate thin films was measured using Mach-Zenhder interferometers. 13 and the electro-optic coefficient component r 33 .

[0019] The beneficial effects of this invention are as follows: Unlike existing technologies, this invention provides a device for measuring the electro-optic coefficient of ferroelectric thin films, including a sample placement module, an incident module, an electric field module, and a dual-path interference module. The sample placement module is used to place the ferroelectric thin film to be tested. The incident module is used to provide linearly polarized light to irradiate the ferroelectric thin film. The electric field module is used to provide an electric field to the ferroelectric thin film. The dual-path interference module is used to output the electro-optic coefficient component corresponding to the ferroelectric thin film based on the phase difference between the two polarized lights generated after the linearly polarized light penetrates the ferroelectric thin film. The dual-path interference module includes a birefringence interference unit and a Mach-Zenhder interference unit. The birefringence interference unit is used to measure the electro-optic coefficient components of the ferroelectric thin film that can be separated using birefringence interference. The Mach-Zenhder interferometer is used to measure the electro-optic coefficient components of the ferroelectric thin film that cannot be separated using birefringence interferometry. The device for measuring the electro-optic coefficient of ferroelectric thin films provided by this invention introduces a Mach-Zenhder interferometer structure based on a birefringence interferometer structure. The birefringence interferometer is used to measure the electro-optic coefficient components of the ferroelectric thin film that can be separated using birefringence interferometry, while the Mach-Zenhder interferometer is used to measure the electro-optic coefficient components that cannot be separated using birefringence interferometry. By comprehensively utilizing the two interference results, different electro-optic coefficient components can be measured, thereby greatly improving the detection sensitivity and accuracy of the device for measuring the electro-optic coefficient of ferroelectric thin films, and thus saving detection costs. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the device for measuring the electro-optic coefficient of ferroelectric thin films provided in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] Please see Figure 1 , Figure 1This is a schematic diagram of the structure of the apparatus 100 for measuring the electro-optic coefficient of a ferroelectric thin film provided in an embodiment of the present invention. Specifically, the apparatus 100 for measuring the electro-optic coefficient of a ferroelectric thin film includes a sample placement module, an incident module, an electric field module, and a dual-optical-path interference module. The sample placement module is used to place the ferroelectric thin film 105 to be tested. The incident module is used to provide linearly polarized light to illuminate the ferroelectric thin film 105 to be tested. The electric field module is used to provide an electric field to the ferroelectric thin film 105 to be tested. The dual-optical-path interference module is used to output the electro-optic coefficient component corresponding to the ferroelectric thin film 105 to be tested based on the phase difference between the two polarized lights generated after the linearly polarized light penetrates the ferroelectric thin film 105 to be tested.

[0023] The dual-path interference module includes a birefringence interference unit and a Mach-Zenhder interference unit. The birefringence interference unit is used to measure the electro-optic coefficient components that can be separated by birefringence interference in the ferroelectric thin film 105 under test. The Mach-Zenhder interference unit is used to measure the electro-optic coefficient components that cannot be separated by birefringence interference in the ferroelectric thin film 105 under test.

[0024] In this embodiment of the invention, the sample placement module is a rotatable sample stage 104, which is used to place the ferroelectric thin film 105 to be tested.

[0025] In this embodiment of the invention, the Mach-Zenhder interferometer unit has a Mach-Zenhder switch structure. The principle of the Mach-Zenhder switch structure is based on the coherence of light. That is, by using the same light source to pass through two different paths, two equivalent beams are obtained, and then they are put together, so that the mode change caused by the phase difference can be observed.

[0026] In this embodiment of the invention, the incident module includes a laser 101, a half-wave plate 102, and a polarizer 103 arranged coaxially. The laser 101 is used to provide a light source in the visible or infrared band. The polarizer 103 is used to convert the light emitted by the light source into linearly polarized light, and it can adjust the azimuth angle of the linearly polarized light. The half-wave plate 102 is used to adjust the polarization direction of the light emitted by the light source so that the light intensity of the light emitted by the polarizer 103 is maximized.

[0027] In this embodiment of the invention, the electric field module includes a signal generator 118, a voltage amplifier 117, a first electrode 106, and a second electrode 107. The signal generator 118 is used to provide a first voltage signal, and the voltage amplifier 117 is used to amplify the first voltage signal into a second voltage signal. The first electrode 106 and the second electrode 107 are respectively attached to both ends of the ferroelectric thin film 105 to be tested, so as to transmit the second voltage signal to the ferroelectric thin film 105 to be tested.

[0028] Specifically, the first electrode 106 and the second electrode 107 are made of gold, and the distance between the first electrode 106 and the second electrode 107 is in the range of 5μm to 10μm; wherein, the larger the distance between the first electrode 106 and the second electrode 107, the higher the electric field strength input to the ferroelectric thin film 105 under test.

[0029] In this embodiment of the invention, the birefringent interference unit includes a phase compensator 108, a polarizer 109 and a first detector 116 arranged coaxially in sequence. The phase compensator 108 is arranged coaxially with the incident unit, and the first detector 116 is used to detect the intensity of the received interference signal.

[0030] The phase compensator 108 is used to adjust the operating point of the interference between the two polarized lights generated in the dual-optical-path interference module to the orthogonal bias point.

[0031] In this embodiment of the invention, the Mach-Zenhder interferometer unit includes a first optical path unit and a second optical path unit. The first optical path unit includes a first beam splitter 110, a phase compensator 108, a polarizer 109, a second beam splitter 114, and a first detector 116 arranged coaxially in sequence. The second optical path unit includes a first beam splitter 110, a first reflector 111, a second reflector 113, a second beam splitter 114, and a first detector 116.

[0032] Specifically, the first reflector 111 and the second reflector 113 are also provided with a reference sample stage, which is used to place a reference thin film sample 112. The material of the reference thin film sample 112 is quartz glass, and the thickness of the reference thin film sample 112 is equivalent to the thickness of the ferroelectric thin film 105 to be tested. The reference thin film sample 112 is used to compensate for the optical path difference between the first optical path unit and the second optical path unit.

[0033] Furthermore, the ferroelectric thin film 105 to be tested is provided by the user, and the thickness of different samples may vary slightly; the reference thin film sample 112 is used to adjust the interference optical path difference of the optical instrument, and the thickness is generally fixed or several can be provided.

[0034] In this embodiment of the invention, the device 100 for measuring the electro-optic coefficient of ferroelectric thin films includes a second detector 115, a lock-in amplifier 119, and a computer control system 120. The lock-in amplifier 119 is electrically connected to the first detector 116, and the computer control system 120 is electrically connected to the lock-in amplifier 119.

[0035] The second detector 115 is used to detect the light intensity of the part of the beam that does not undergo birefringence interference when the birefringence interference unit is working normally. The lock-in amplifier 119 is used to detect the interference signal received by the first detector 116. The computer control system 120 is used to output the electro-optic coefficient component corresponding to the ferroelectric thin film 105 under test according to the interference signal.

[0036] Specifically, when the ferroelectric thin film 105 to be tested is a barium strontium titanate thin film, the electro-optic coefficient component r of the barium strontium titanate thin film is measured using a birefringence interferometer. 42 The electro-optic coefficient component r of barium strontium titanate thin films was measured using Mach-Zenhder interferometers. 13 and the electro-optic coefficient component r 33 .

[0037] Specifically, the procedure for measuring the electro-optic coefficient components of a ferroelectric thin film using the aforementioned apparatus 100 is as follows:

[0038] Before measurement, determine the crystal orientation of the ferroelectric thin film material and the electro-optic coefficient component of the ferroelectric thin film 105 to be measured, and determine whether the second reflector 113 needs to be removed.

[0039] During measurement, the azimuth angle of the polarizer 103 is first set according to the measurement requirements, the interference signal detected by the first detector 116 is read, and the half-wave plate 102 is rotated to maximize the signal value.

[0040] Then place the sample to be tested, and select normal or oblique incidence according to the measurement requirements, and connect the drive signal line to the modulation electrode.

[0041] Afterwards, the interference phase difference is adjusted, the signal value of the first detector 116 is read, the maximum and minimum values ​​are recorded, and then the phase difference is set at the middle value, which is the orthogonal bias point. When the birefringent interferometer unit is working normally (the second reflector 113 is removed), the interference phase difference is adjusted only by the phase compensator 108. When the Mach-Zenhder interferometer unit is working normally (dual-beam measurement, without removing the second reflector 113), the interference phase difference is adjusted by the phase compensator 108 and the reference thin film sample 112.

[0042] Finally, a sinusoidal modulation voltage is applied, and the interference output signal is detected by the lock-in amplifier 119. The amplitude of the sinusoidal modulation voltage is changed, multiple data are recorded, and the data are analyzed to obtain the electro-optic coefficient measurement value.

[0043] Specifically, the working principle of the device 100 for measuring the electro-optic coefficient of ferroelectric thin films is as follows:

[0044] The laser 101, half-wave plate 102, and polarizer 103 form the incident module, which can adjust the azimuth angle of the incident linearly polarized light. After the light passes through the first beam splitter 110, a beam of light is incident on the sample to be tested. The sample is placed on the rotatable sample stage 104. The phase compensator 108 and the analyzer 109 form a birefringence interference optical path for measuring the separable electro-optic coefficient components. At this time, the second reflector 113 is moved away under the control of the computer control system 120, and the optical loop formed by the reflector is broken. This optical path does not participate in the interference. The birefringence interference method is used to measure the electro-optic coefficient components. The optical power reaching the second detector 115 is used for internal optical power detection and system fault diagnosis.

[0045] When the second beam of light, after passing through the first beam splitter 110, enters the loop composed of the first reflecting mirror 111 and the second reflecting mirror 113, the two beams undergo two-beam interference at the second beam splitter 114, forming a Mach-Zenhder interferometer structure. By properly arranging the polarization state, the crystal orientation of the ferroelectric thin film 105 under test, and the modulation voltage between the first electrode 106 and the second electrode 107, a single ordinary or extraordinary beam of light can be split into two beams to participate in the interference, which is used to measure the electro-optic coefficient that cannot be separated by birefringence interferometry. Since the detectable signal is usually very weak, a lock-in amplifier 119 is required for detection.

[0046] Specifically, the linearly polarized light after passing through polarizer 103 is incident on the sample under test. The half-wave plate 102 is rotated to maximize the intensity of the light emitted from polarizer 103. When using birefringence interferometry, due to birefringence, the polarized light becomes elliptically polarized after passing through the sample. The phase compensator 108 is adjusted to compensate for the phase of the two birefringed beams, bringing them to an orthogonal bias state to achieve high sensitivity and linearity. Generally, the azimuth angle of polarizer 103 is set to 45°. At this angle, the light after phase compensator 108 is circularly polarized, and the amplitudes of the two polarized beams participating in the interference are equal, providing excellent interference contrast. At this time, the analyzer 109 is perpendicular to the transmission axis of polarizer 103, and the two polarized beams passing through analyzer 109 interfere. Furthermore, the sample stage in the sample placement module can be rotated, allowing for precise adjustment of the incident angle. When the crystal orientation of the ferroelectric thin film 105 to be tested is

[001] , the sample stage of the ferroelectric thin film 105 to be tested is rotated and placed, and the light is obliquely incident on the ferroelectric thin film 105 to be tested, forming an angle with the optical axis, thereby generating birefringence.

[0047] Furthermore, when using two-beam interferometry, the azimuth angle of the polarizer 103 is adjusted according to the electro-optic coefficient component to be measured, so that only ordinary or extraordinary light is transmitted in the ferroelectric thin film 105 under test, without birefringence, and the transmission axes of the analyzer 109 and the polarizer 103 are parallel to each other. The phase compensator 108 and the reference ferroelectric thin film 105 under test are adjusted to compensate the phase of the two beams, and the phase is compensated to an orthogonal bias state. The two beams interfere at the second beam splitter 114. Among them, the propagation paths of the two beams in the Mach-Zenhder interferometer unit are significantly different. It is difficult to complete the phase compensation by the phase compensator 108 in the first optical path unit alone. It is necessary to place the reference thin film sample 112 in the second optical path unit at the same time to compensate for the optical path difference between the first and second optical path units. Specifically, when a voltage is applied between the first electrode 106 and the second electrode 107, the refractive index of ordinary or extraordinary light will change, and the phase difference of the interference will also change, thereby changing the intensity of the interference light. By applying voltage between the first electrode 106 and the second electrode 107 in different directions, and by adjusting the polarization state and the direction of incident light, different electro-optic coefficient components can be measured.

[0048] Furthermore, in order to detect weak signals, a sinusoidal modulation voltage is typically applied between the first electrode 106 and the second electrode 107, and then the intensity of the interference signal received by the first detector 116 is detected by the lock-in amplifier 119.

[0049] The technical solution of this application will now be described in conjunction with specific embodiments.

[0050] 1. Electro-optic effect analysis:

[0051] Taking BTO (barium strontium titanate thin film) as an example, its electro-optic coefficient component was measured. According to the literature, BTO is a negative uniaxial crystal when no voltage is applied. When natural light enters the BTO crystal from one direction, it will form two polarized rays. The light that vibrates perpendicular to the optical axis is called the ordinary ray (o-ray), and the light that vibrates in the plane parallel to the incident direction and the optical axis is called the extraordinary ray (e-ray).

[0052] Among them, the refractive index (n) of BTO material for ordinary light. o The refractive index of BTO material for unusual light is greater than that of BTO material (n). e ), n o =2.437, n e =2.365.

[0053] Specifically, by consulting a linear electro-optic coefficient matrix handbook, it can be seen that the electro-optic coefficient of BTO material has three non-zero independent variables (r). 13 r 33 and r 42 ).

[0054] According to the refractive index ellipsoid theory, the z-axis is usually taken as the optical axis direction; in this case, the refractive index ellipsoid of the BTO material is a positive ellipsoid, and the equation of the ellipsoid is:

[0055]

[0056] Since the electro-optic coefficient of BTO material has three non-zero independent variables, the coefficient of variation of the refractive index ellipsoid (second-order symmetric tensor) will change under the influence of an external power source, as shown below:

[0057]

[0058] Where Δβ1 to Δβ6 are the coefficients of change of the refractive index ellipsoid of the BTO material under the action of an external power source, E X Let E be the voltage along the x-axis of the refractive index ellipsoid. y Let E be the voltage along the y-axis of the refractive index ellipsoid. z Let be the voltage along the z-axis of the refractive index ellipsoid.

[0059] Substituting equation (2) into equation (1), the inductive refractive index ellipsoid equation of the BTO material after applying voltage can be expressed as:

[0060]

[0061] As can be seen from formula (3), applying a voltage along the x-axis of the refractive index ellipsoid has the same effect as applying a voltage along the y-axis of the refractive index ellipsoid, and they can be interchanged. The effects of Ex and Ey are exactly the same, so it is only necessary to analyze the effect of applying E. x With E z Two scenarios.

[0062] In one embodiment, when E x ≠0 and E y =E z When =0, formula (3) can be expressed as:

[0063]

[0064] Comparing formula (4) with formula (1), the zx cross term appears, indicating that one principal axis of the induced refractive index ellipsoid coincides with the y-axis of the original refractive index ellipsoid, and the other two principal axis directions can be obtained by rotating around the y-axis (the induced refractive index ellipsoid can be obtained by rotating the original refractive index ellipsoid by θ in the xoz plane):

[0065] Among them, when E x When E > 0, it rotates counterclockwise; when E x When < 0, it is a clockwise rotation; the angle of rotation θ satisfies the following formula:

[0066]

[0067] Let y = 0, substitute it into formula (4), and we get the equation of the refractive index ellipse in the xoz plane as follows:

[0068]

[0069] In general, when the rotation angle θ is very small, the lengths of the three principal axes of the induced refractive index ellipsoid also change, and the refractive index changes in the three directions are as follows:

[0070]

[0071] Substituting formula (5) into formula (7), we get the following:

[0072]

[0073] As can be seen from formula (8), after applying an external voltage, the change in refractive index is proportional to the square of the voltage.

[0074] In another embodiment, when E z ≠0 and E x =E y When =0, formula (3) can be expressed as:

[0075]

[0076] At this point, it can be seen from formula (9) that, compared with the case without voltage, the induced refractive index ellipsoid does not rotate relative to the original refractive index ellipsoid and remains a positive ellipsoid. However, the length of the principal axis of the induced refractive index ellipsoid changes (when an electric field is applied in the z-axis direction of the original refractive index ellipsoid, both the ordinary and extraordinary refractive indices change), as follows:

[0077] n′ x =n′ y =n′ o ,n′ z =n′ e (10);

[0078] At this point, the film surface is the xoz plane, and light passes through the BTO film perpendicular to the optical axis. The birefringence occurs in the x and z directions, and the inductive refractive index change is as follows:

[0079]

[0080] As can be seen from formula (11), after applying a voltage in the z-axis direction of the original refractive index ellipsoid, the change in refractive index is proportional to the voltage.

[0081] 2. Measurement Scheme Analysis:

[0082] In the first embodiment of the present invention, when the z-axis (optical axis) of the original refractive index ellipsoid is perpendicular to the surface of the BTO film to be tested, a voltage can only be applied in the x-axis direction of the original refractive index ellipsoid. The film surface is the xoy plane, and light passes through the BTO film along the optical axis. At this time, let z = 0, and after substituting into formula (4), the equation of the inductive refractive index ellipsoid is as follows:

[0083]

[0084] As can be seen from formula (12), there is no birefringence (n does not exist). e This is equivalent to the optical axis z on the original refractive index ellipsoid rotating by an angle to reach z′. z′ is the new crystal axis, but not the optical axis. The BTO crystal becomes a biaxial crystal. The z direction is one of the optical axes C1 of the biaxial crystal. That is to say, the angle between the optical axis and z′ is θ. The direction of the optical axis C1 is independent of the electric field and is always in the z direction. The other optical axis is on the other side of z′.

[0085] To achieve birefringence, light can be transmitted at a 45° angle between xoz (achieved by rotating the sample stage of the BTO material to be tested), with the polarization direction at a 45° angle to the xoz plane (achieved by adjusting the polarizer 103).

[0086] Accordingly, when the birefringent interferometer unit is working, the phase difference δ generated when light from two polarization directions passes through the BTO sample of length L will be... E (λ is the wavelength, E) x (Voltage applied along the x-axis to the original refractive index ellipsoid):

[0087]

[0088] At this point, the phase change is proportional to the voltage applied to the original refractive index ellipsoid in the x-axis direction. Therefore, the electro-optic coefficient component r of the BTO material can be obtained by using the birefringence interference unit and formula (13). 42 .

[0089] In a second embodiment of the present invention, when the z-axis (optical axis) of the original refractive index ellipsoid is on the surface of the BTO film to be tested, a voltage can be applied in the x-axis direction or the z-axis direction of the original refractive index ellipsoid.

[0090] (a) When a voltage E is applied along the x-axis of the original refractive index ellipsoid x hour:

[0091] Its film surface is an xoz plane, and light passes through the BTO film perpendicular to the optical axis, which is consistent with r 42 Relatedly, the birefringence occurs in the x and z directions, and the inductive refractive index change is shown in formula (8):

[0092]

[0093] Accordingly, the distance between the two polarization directions of light transmitted through the BTO film can be obtained from E according to formula (8). x The resulting phase difference is (ignoring static phase difference and rotation in the xoz plane):

[0094]

[0095] At this point, the phase change is proportional to the square of the voltage applied to the original refractive index ellipsoid in the x-axis direction. Therefore, the electro-optic coefficient component r of the BTO material can be obtained by using the birefringence interference unit and formula (14). 42 .

[0096] (b) When a voltage E is applied along the z-axis of the original refractive index ellipsoid z hour:

[0097] Its film surface is an xoz plane. Light passes through the BTO film perpendicular to the optical axis. The birefringence occurs in the x and z directions. The inductive refractive index change is shown in formula (11):

[0098]

[0099] Accordingly, the distance between the two polarization directions of light transmitted through the BTO film can be obtained from E according to formula (11). z The resulting phase difference is (ignoring static phase difference and rotation in the xoz plane):

[0100]

[0101] At this point, the phase change is proportional to the voltage applied to the original refractive index ellipsoid along the z-axis, and the induced refractive index change is related to r. 13 and r 33 Relatedly, the birefringence interferometry method cannot be used to determine r. 13 and r 33 Separating the two unknowns (according to formula (15), it is impossible to solve an equation for two unknowns), therefore, the electro-optic coefficient component r of the BTO material cannot be measured through the birefringence interference unit. 13 and r 33 .

[0102] 3. Analysis of a specific measurement scheme using the apparatus 100 for measuring the electro-optic coefficient of ferroelectric thin films according to the present invention.

[0103] The Mach-Zenhder interferometer is used to measure two electro-optic coefficients that cannot be separated by birefringence interferometry, such as the electro-optic coefficient component r of BTO material. 13 and r 33This forms a Mach-Zenhder interferometer structure. The second mirror 113 can be moved away under the control of the computer control system 120. When measuring other electro-optic coefficients, such as the r-value of the electro-optic coefficient component of the BTO material... 42 The optical path formed by the second reflector 113 is then broken and does not participate in interference. At this time, the light can reach the second detector 115 for internal optical power detection and system fault diagnosis. The following analysis of the research scheme takes BTO crystal thin film as an example.

[0104] (a) Measuring the electro-optic coefficient component r using a birefringent interferometer. 42 :

[0105] Let the azimuth angle of polarizer 103 be θi (the angle with the horizontal plane), and the analyzer 109 be perpendicular to the transmission axis of polarizer 103. Then the intensity of the received light is:

[0106]

[0107] Where I is the light intensity received by the first detector 116 after applying a voltage, I0 is the light intensity received by the first detector 116 without applying a voltage, and δ is the phase difference between the two polarized lights participating in the interference. After applying a voltage to the BTO thin film, the refractive index ellipsoid changes, thereby causing a change in the phase difference δ. The change in δ can be used to calculate the electro-optic coefficient.

[0108] By applying voltages in different directions and using different polarized light, different electro-optic coefficient components can be measured. To improve detection accuracy, a modulation voltage with a frequency of ω can be applied to the first electrode 106 and the second electrode 107. Assume the voltage is:

[0109] E = E0cosωt (17);

[0110] Based on the previous analysis, the applied voltage E x Time-optic coefficient component r 42 When used alone, when a voltage E is applied along the x-axis of the original refractive index ellipsoid... x hour:

[0111] According to formulas (13) and (14), the phase difference is proportional to the first power or square of the voltage. Here, we take formula (14) as an example for analysis, which requires measuring the harmonic component. At this time, the phase difference generated by the voltage can be expressed as:

[0112] δ E =δ e0 cos 2 ωt (18);

[0113] Where, δ E0The amplitude of the cosine phase can be obtained from the phase difference expression in formula (14). When calculating, |δ| can be taken as the value. E0 Substitute the values ​​into the equation. According to formula (14), we get:

[0114]

[0115] At this point, the total phase difference can be written as:

[0116] δ=δ0+δ E0 cos 2 ωt (20);

[0117] Where δ0 is the static phase difference, including the phase difference generated by the devices in the optical path and the phase difference generated by the DC bias voltage. Therefore, according to formula (16):

[0118]

[0119] Let δ0 = π / 2, θ i =π / 4, approximately assuming cosδ E ≈1, sinδ E =δ E We can obtain:

[0120]

[0121] By using double-angle functions for transformation, we can obtain:

[0122]

[0123] In formula (23), the first two terms are DC components, and the third term is a frequency harmonic component. The frequency harmonic component is measured by lock-in amplifier 119, and the electro-optic coefficient component r is calculated by combining formula (19). 42 .

[0124] (b) Measuring the electro-optic coefficient component r using a Mach-Zenhder interferometer. 13 and electro-optic coefficient component r 33 Independent measurements:

[0125] In this scheme, the phase difference is proportional to the modulation voltage, and the detected light intensity is:

[0126] I = I0 + I0cosδ (24);

[0127] The resulting phase difference can be expressed as:

[0128] δ E =δ E0 cosωt (25);

[0129] At this point, the total phase difference can be written as:

[0130] δ=δ0+δ E0 cosωt (26);

[0131] Assuming the light intensity is equal in both arms, according to formulas (25) and (26):

[0132] δ=δ0+δ E =δ0+δ E0 cosωt (27);

[0133] When measuring the electro-optic coefficient component r 13 When using ordinary light (o-ray) with its polarization direction perpendicular to the optical axis, we obtain:

[0134]

[0135] When measuring the electro-optic coefficient component r 33 When using extraordinary light (e-ray) with its polarization direction parallel to the optical axis, we obtain:

[0136]

[0137] Let δ0 = π / 2, and approximate cosδ E ≈1, sinδ E =δ E From formulas (24) and (27), we can obtain:

[0138] I = I0 - I0δ E0 cosωt (30);

[0139] Formula (30) is similar to formula (23), where the first term is the DC component and the second term is the fundamental frequency component. The fundamental frequency component is measured by lock-in amplifier 119 to obtain δ. E0 Thus, the electro-optic coefficient component r can be calculated by combining formula (28) or formula (29). 13 or r 33 .

[0140] Therefore, the birefringence interference method cannot be used to obtain the electro-optic coefficient component r of the BTO crystal. 13 and electro-optic coefficient component r 33 Separating them only yields an equivalent electro-optic coefficient. To further separate them, the aforementioned Mach-Zenhder interferometer unit can be used, selecting o-ray and e-ray transmission separately, and then analyzing the electro-optic coefficient components r... 13 and electro-optic coefficient component r 33 Perform individual measurements.

[0141] Typically, the modulated output signal is a weak signal, requiring a sinusoidal modulation voltage with frequency ω to be applied between the first electrode 106 and the second electrode 107. The intensity of the interference output light is then detected by the lock-in amplifier 119. (Measurement of r) 42 Time-displacement detection of harmonic components and measurement of electro-optic coefficient component r 13 and electro-optic coefficient component r 33 The fundamental frequency component is detected in real time, and the corresponding electro-optic coefficient is calculated based on the detection results.

[0142] Correspondingly, the methods for measuring other ferroelectric thin film materials are similar. PLZT (lead lanthanum zirconate titanate thin film) and BTO both belong to the 4mm point group in crystals, have the same independent electro-optic coefficients, and require the same processing scheme during measurement. LN (lithium niobate) thin film belongs to the 3m point group asymmetric crystal, with 8 non-zero electro-optic coefficient components, 4 of which are independent, namely r 13 r 33 r 22 and r 42 . Measurement r 13 and r 33 The processing method is similar to that for BTO thin films, applying an electric field E. z Detect the fundamental frequency component; measure r 22 and r 42 When an electric field E is applied y , measuring r 22 Time-based detection of fundamental frequency component, measurement of r 42 Time-based detection of harmonic components.

[0143] Currently, there are generally two mainstream methods for measuring the electro-optic coefficient of ferroelectric thin films:

[0144] Option 1: Place a quarter-wave plate behind the ferroelectric thin film sample. Adjust the birefringence phase difference by rotating the quarter-wave plate to convert the birefringence output light into linearly polarized light. Apply a sinusoidal modulation voltage to the ferroelectric thin film material. The phase difference is modulated, and the azimuth angle of the output linearly polarized light will change according to a sinusoidal law. Detect the azimuth angle using an analyzer 109 and use a lock-in amplifier 119 to detect the signal. Analyze the relationship between the azimuth angle and the amplitude of the modulation voltage to obtain the electro-optic coefficient.

[0145] Option 2: Building upon Option 1, a magneto-optical modulator is placed behind the quarter-wave plate. Based on the Faraday rotation effect, the magneto-optical modulator can rotate the polarization state of light. In this option, a DC voltage is applied to the ferroelectric thin film material, and a sinusoidal modulation voltage is applied to the magneto-optical modulator. The DC voltage determines the azimuth angle and its variation of the linearly polarized light output from the quarter-wave plate. This azimuth angle is further transferred to the modulation frequency of the magneto-optical modulator and can be detected by a lock-in amplifier 119. By changing the magnitude of the DC voltage and analyzing the change in azimuth angle with the DC voltage, the electro-optic coefficient can be obtained.

[0146] However, the above two solutions have the following drawbacks:

[0147] (1) Existing methods can only measure ferroelectric thin films with

[100] and

[010] crystal orientations. Since the existing methods use perpendicular incidence, for thin films with

[001] crystal orientation, the light propagates along the optical axis, there is no birefringence, and there is no interference output, so it is impossible to measure them.

[0148] (2) Existing methods can only measure a limited number of electro-optic coefficients. Because existing methods utilize the birefringence of the crystal, some electro-optic coefficients (two or more) simultaneously determine the birefringence interference effect, making it impossible to separate them. Specifically:

[0149] When a voltage is applied to a ferroelectric thin film sample, the ordinary and extraordinary refractive indices of the material change due to the electro-optic effect. These changes in refractive index can be detected using birefringence. However, due to the complexity of the electro-optic coefficient matrix of ferroelectric materials, in some cases, the changes in the ordinary and extraordinary refractive indices are associated with multiple different electro-optic coefficient components. In these cases, they cannot be separated using birefringence interference (for example, the electro-optic coefficient component r of barium titanate thin films cannot be separated). 13 and electro-optic coefficient component r 33 ).

[0150] (3) Existing solutions suffer from significant measurement errors and low sensitivity. Existing solutions use a quarter-wave plate to adjust the birefringent light into linearly polarized light. Under the influence of a modulation voltage, the azimuth angle of the linearly polarized light changes, and the electro-optic coefficient is measured by detecting this change in azimuth angle. This method has two problems. First, under the influence of the modulation voltage, the light's polarization state becomes elliptically polarized, which can only be approximated as linearly polarized light, thus introducing measurement errors. Second, after adjusting the birefringent light into linearly polarized light using a quarter-wave plate, the operating point is not at the orthogonal bias point, resulting in low linearity and sensitivity of the electro-optic modulation response. These two problems lead to significant measurement errors and low sensitivity in existing solutions.

[0151] (4) Existing solutions have structural complexity issues. Solution 2 uses a magneto-optical modulator, which increases the complexity of the system structure, making system debugging, calibration, measurement operations, and data processing more complicated, and also increases the sources of system errors.

[0152] To address the aforementioned problems in existing technologies, this invention employs two-beam interferometry. Specifically, it introduces a Mach-Zenhder two-beam interferometer structure based on birefringence interferometry, and comprehensively utilizes the two interference results to measure different electro-optic coefficients.

[0153] Compared with existing technical solutions, the technical solution of the present invention has the following advantages:

[0154] (1) The electro-optic coefficient measurement method for ferroelectric thin films of the present invention can measure thin film materials with different lattice orientations, including

[100] ,

[010] and

[001] crystal orientations. In the present invention, a rotatable sample stage is used. For thin films with

[001] orientation, light is incident obliquely to produce a birefringence effect, and the birefringence interference result is determined according to the incident angle.

[0155] (2) The electro-optic coefficient measurement method of the ferroelectric thin film of the present invention can measure more electro-optic coefficients. Due to the complexity of the crystal electro-optic coefficient matrix, some electro-optic coefficients (two or more) simultaneously determine the birefringence interference effect, and they cannot be separated by adjusting the polarization state, incident light, and modulation voltage direction. The present invention introduces a Mach-Zenhder interferometer structure on the basis of birefringence interference, and by combining the two interference results, different electro-optic coefficients can be measured.

[0156] (3) The electro-optic coefficient measurement method of the ferroelectric thin film of the present invention has higher sensitivity and accuracy. The present invention uses a phase compensator 108 in the optical path to set the interference working point at the orthogonal bias point. The system output and the modulation voltage have a linear relationship and the most sensitive response.

[0157] Unlike existing technologies, this invention provides a device 100 for measuring the electro-optic coefficient of a ferroelectric thin film, comprising a sample placement module, an incident module, an electric field module, and a dual-path interference module. The sample placement module is used to place the ferroelectric thin film 105 to be tested. The incident module provides linearly polarized light to illuminate the ferroelectric thin film 105. The electric field module provides an electric field to the ferroelectric thin film 105. The dual-path interference module outputs the electro-optic coefficient component corresponding to the ferroelectric thin film 105 based on the phase difference between the two polarized lights generated after the linearly polarized light penetrates the ferroelectric thin film 105. The dual-path interference module includes a birefringence interference unit and a Mach-Zenhder interference unit. The birefringence interference unit measures the electro-optic coefficient components of the ferroelectric thin film 105 that can be separated using birefringence interference. The Mach-Zenhder interferometer is used to measure the electro-optic coefficient components of the ferroelectric thin film 105 that cannot be separated using birefringence interferometry. The device 100 for measuring the electro-optic coefficient of ferroelectric thin films provided by the present invention introduces a Mach-Zenhder interferometer structure on the basis of a birefringence interferometer structure. The birefringence interferometer is used to measure the electro-optic coefficient components of the ferroelectric thin film 105 that can be separated using birefringence interferometry, while the Mach-Zenhder interferometer is used to measure the electro-optic coefficient components of the ferroelectric thin film 105 that cannot be separated using birefringence interferometry. By combining the two interference results, different electro-optic coefficient components can be measured, which greatly improves the detection sensitivity and accuracy of the device 100 for measuring the electro-optic coefficient of ferroelectric thin films, and thus saves detection costs.

[0158] It should be noted that all the above embodiments belong to the same inventive concept, and the descriptions of each embodiment have different focuses. Where the description in a particular embodiment is not detailed, please refer to the description in other embodiments.

[0159] The above embodiments merely illustrate implementation methods of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. An apparatus for measuring the electro-optic coefficient of ferroelectric thin films, characterized in that, The device includes a sample placement module, an incident module, an electric field module, and a dual-optical-path interference module. The sample placement module is used to place the ferroelectric thin film to be tested. The incident module is used to provide linearly polarized light to illuminate the ferroelectric thin film to be tested. The electric field module is used to provide an electric field to the ferroelectric thin film to be tested. The dual-optical-path interference module is used to output the electro-optic coefficient component corresponding to the ferroelectric thin film to be tested based on the phase difference between the two polarized lights generated after the linearly polarized light penetrates the ferroelectric thin film to be tested. The dual-optical-path interference module includes a birefringence interference unit and a Mach-Zenhder interference unit. The birefringence interference unit is used to measure the electro-optic coefficient components that can be separated by birefringence interference on the ferroelectric thin film under test, while the Mach-Zenhder interference unit is used to measure the electro-optic coefficient components that cannot be separated by birefringence interference on the ferroelectric thin film under test.

2. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 1, characterized in that, The sample placement module is a rotatable sample stage, which is used to place the ferroelectric thin film to be tested.

3. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 2, characterized in that, The incident module includes a laser, a half-wave plate, and a polarizer arranged coaxially. The laser is used to provide a light source in the visible or infrared band. The polarizer is used to convert the light emitted by the light source into linearly polarized light. The half-wave plate is used to adjust the polarization direction of the light emitted by the light source so as to maximize the light intensity of the light emitted by the polarizer.

4. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 3, characterized in that, The electric field module includes a signal generator, a voltage amplifier, a first electrode, and a second electrode. The signal generator is used to provide a first voltage signal, and the voltage amplifier is used to amplify the first voltage signal into a second voltage signal. The first electrode and the second electrode are respectively attached to both ends of the ferroelectric thin film under test to transmit the second voltage signal to the ferroelectric thin film under test.

5. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 4, characterized in that, The first electrode and the second electrode are made of gold, and the distance between the first electrode and the second electrode is in the range of 5μm to 10μm.

6. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 4, characterized in that, The birefringence interferometer unit includes a phase compensator, a polarizer, and a first detector arranged coaxially in sequence. The phase compensator is coaxially arranged with the incident module, and the first detector is used to detect the intensity of the received interference signal. The phase compensator is used to adjust the operating point of the interference between the two polarized lights generated in the dual-optical-path interference module to an orthogonal bias point.

7. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 6, characterized in that, The Mach-Zenhder interferometer unit includes a first optical path unit and a second optical path unit. The first optical path unit includes a first beam splitter, the phase compensator, the analyzer, the second beam splitter, and the first detector arranged coaxially in sequence. The second optical path unit includes the first beam splitter, the first mirror, the second mirror, the second beam splitter, and the first detector.

8. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 7, characterized in that, The first and second reflectors are also provided with a reference sample stage, which is used to place a reference thin film sample, which is quartz glass, to compensate for the optical path difference between the first optical path unit and the second optical path unit.

9. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 8, characterized in that, The device further includes a second detector, a lock-in amplifier, and a computer control system. The lock-in amplifier is electrically connected to the first detector, and the computer control system is electrically connected to the lock-in amplifier. The second detector is used to detect the light intensity of the portion of the beam that does not undergo birefringence interference when the birefringence interference unit is working normally. The lock-in amplifier is used to detect the interference signal received by the first detector. The computer control system is used to output the electro-optic coefficient component corresponding to the ferroelectric thin film under test according to the interference signal.

10. The apparatus for measuring the electro-optic coefficient of ferroelectric thin films according to claim 9, characterized in that, When the ferroelectric thin film under test is a barium strontium titanate thin film, the electro-optic coefficient component r of the barium strontium titanate thin film is measured using the birefringent interferometer unit. 42 The electro-optic coefficient component r of the barium strontium titanate thin film was measured using the Mach-Zenhder interferometer. 13 and the electro-optic coefficient component r 33 .

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