Method for measuring thickness and refractive index of film based on photon spin splitting weak measurement amplification displacement

Abstract

The invention discloses a method for measuring the thickness and refractive index of a film based on photon spin splitting weak measurement amplification displacement, which comprises the following steps of: firstly, establishing the thickness and refractive index of a film material under each refractive index and thickness according to a theoretical relation model between the photon spin splitting weak measurement amplification displacement and the thickness and refractive index of the measured film; a theoretical relation database of photon spin splitting weak measurement amplification displacement and a front selection angle and a rear selection angle of weak measurement; irradiating an incident light beam to the surface of the measured film at a certain incident angle, adjusting a front selection angle and a rear selection angle of weak measurement, and measuring a photon spin splitting weak measurement amplification displacement value at the moment; sequentially changing the front selection angle or the rear selection angle of the weak measurement to obtain a group of measurement data of photon spin splitting weak measurement amplification displacement under the front selection angle or the rear selection angle; and finally, analyzing and comparing theoretical data and measurement data, and determining the refractive index and the thickness of the measured film. According to the invention, non-contact, lossless, high-precision and high-stability measurement of the refractive index and the thickness of the nanoscale film is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of precision measurement, and in particular to a method for measuring film thickness and refractive index. Background Art

[0002] Nanofilms have unique optical, mechanical, electromagnetic and gas-sensitive properties, and are widely used in microelectronics, optoelectronics, aerospace, bioengineering, weapons and equipment, food science, medical instruments and polymer materials. Refractive index and thickness are the basic parameters of nanofilms. They are the basic parameters for optical analysis and optimization design of related devices in optical devices, optoelectronic devices, semiconductor devices and other devices, and affect the performance of various devices. However, the refractive index and thickness of nanofilms are different from those of bulk materials, and are affected by many factors, such as the deposition method, process parameters and material properties of nanofilms. This leads to different refractive indices or thicknesses of thin film materials with the same chemical composition under different deposition processes and preparation conditions. Therefore, accurate measurement of the thickness and refractive index of nanofilms is of great significance to the design, manufacture and application of micro-nano devices.

[0003] The main methods that can achieve simultaneous measurement of nano-scale film thickness and refractive index include ellipsometry and surface plasmon resonance. Ellipsometry is a strong light modulation measurement method, so it will be affected by the stability of the light source and background light. The surface plasmon resonance method has a phase modulation type, which is not affected by the stability of the light source and background light, but it can only detect film parameters in structures that can produce surface plasmon resonance.

[0004] The Photon Spin Hall Effect (PSHE) refers to the situation where a polarized light beam of finite size is reflected or refracted on an interface with a refractive index gradient, and the left-handed and right-handed components of the light beam will produce spin splitting displacement in the direction perpendicular to the refractive index gradient. This phenomenon occurs in both planes parallel to and perpendicular to the incident plane. The former is usually called in-plane spin splitting displacement, and the latter is called out-of-plane spin splitting displacement. The size of the spin splitting displacement is related to the properties of the reflection / refractive interface (such as thickness and refractive index) and the polarization state of the incident light beam. For example, the Chinese invention patent with patent number ZL201910681547.5 discloses a method for measuring the thickness of a thin film using the photon spin Hall effect. The size of the spin splitting displacement is jointly affected by the film thickness and the incident polarization. In the process of measuring the thickness, a group of out-of-plane photon spin splitting displacements corresponding to different polarization angles are measured to form an actual data group for measuring the thickness of the thin film, and the actual data group is compared with the theoretical value to determine the thickness of the measured film. However, this method can only measure the thickness of the film, and cannot measure the thickness and refractive index of the film at the same time; the Chinese invention patent with patent number CN202211669540.X discloses a method for measuring the refractive index of a nanoscale thin film using the photon spin Hall effect. This method is based on the in-plane photon spin Hall effect and measures the refractive index of the film by establishing a database of the relationship between the polarization state, the refractive index of the film and the in-plane photon spin splitting displacement. However, this method can only measure the refractive index of the film, and cannot measure the thickness and refractive index of the film at the same time.

[0005] The invention patent with application number 201810082442.3 discloses a device and a method for simultaneously measuring film thickness and refractive index, which can simultaneously measure film thickness and refractive index. However, the signal demodulation and sensing accuracy and resolution of the above invention rely on expensive signal demodulation equipment, and the detection system structure is complex and costly. Summary of the invention

[0006] In view of the technical problems that the existing methods for simultaneously measuring the thickness and refractive index of nano-scale films are complex, have low measurement accuracy and poor stability, the present invention proposes a method for measuring the thickness and refractive index of films based on photon spin splitting weak measurement amplified displacement. The simultaneous measurement of the thickness and refractive index of films is achieved by modulating the relationship between the front selection angle and the rear selection angle and the weak measurement amplified displacement. The method has high measurement accuracy and good stability, and the detection system has a simple structure and is easy to operate.

[0007] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0008] A method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplification displacement, comprising the following steps:

[0009] S1. According to the theoretical relationship model between the photon spin splitting weak measurement amplification displacement and the thickness and refractive index of the film to be measured, a theoretical relationship database between the photon spin splitting weak measurement amplification displacement and the front selection angle and the back selection angle of the weak measurement for the film material at various refractive indices and thicknesses is established;

[0010] S2, irradiating the incident light beam to the surface of the film to be measured at a certain incident angle, adjusting the front selection angle of weak measurement to a certain polarization angle, adjusting the rear selection angle of weak measurement to a certain polarization angle, and measuring the value of the photon spin splitting weak measurement amplification displacement at this time;

[0011] S3, sequentially changing the front selection angle or the back selection angle of the weak measurement to obtain a set of measurement data of the photon spin splitting weak measurement amplification displacement under the front selection angle or the back selection angle;

[0012] S4. Analyze and compare the pre-selection angle or post-selection angle and the photon spin splitting weak measurement amplification displacement data group obtained in step S3 with the photon spin splitting weak measurement amplification displacement theoretical data at different refractive indices and thicknesses in the database obtained in step S1 to determine the refractive index and thickness of the film being measured.

[0013] The photon spin splitting weak measurement amplification displacement in step S1 is an in-plane photon spin splitting weak measurement amplification displacement or an out-of-plane photon spin splitting weak measurement amplification displacement.

[0014] The theoretical relationship model between the photon spin splitting weak measurement amplification displacement and the film refractive index and thickness is:

[0015]

[0016] in:

[0017]

[0018]

[0019] ζ1, ζ2, ξ, χ1, χ2 are all intermediate parameters; xr represents the weak measurement amplification displacement of in-plane photon spin splitting, yr represents the weak measurement amplification displacement of out-of-plane photon spin splitting; θ represents the incident angle; γ represents the front selection angle; Δ represents the back selection angle; k r =2πn1 / λ represents the wave vector of the reflected light, n1 is the refractive index of the first medium, λ is the wavelength of the incident light when propagating in the first medium; z r represents the propagation distance; ω0 is the waist of the Gaussian beam; R p and R s They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s Modulus value; φ p and φs They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s The phase of and They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s The real part of the first derivative with respect to the angle of incidence is, and They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s Regarding the imaginary part of the first-order derivative of the incident angle, Re represents the real part of the complex number, and Im represents the imaginary part of the complex number; n represents the refractive index of the film to be measured, k represents the extinction coefficient of the film to be measured, and d represents the thickness of the film to be measured.

[0020] Furthermore, the reflection coefficient r of the horizontal polarization component of the incident light is p The reflection coefficient r of the polarization component perpendicular to the incident light s Through the Fresnel equation we get:

[0021]

[0022] in, is the reflection coefficient of the horizontal component of the interface between the first layer of medium and the film, is the reflection coefficient of the vertical component of the interface between the first layer of medium and the film, is the reflection coefficient of the horizontal component of the interface between the film and the third medium, is the reflection coefficient of the vertical component of the interface between the film and the third medium; i represents an imaginary number; m represents the number of medium layers in the reflection interface, n3 represents the refractive index of the third medium in the reflection interface; n2 represents the refractive index of the measured film in the reflection interface; k0 = 2π / λ represents the wave number of the incident light in vacuum; n t represents the refractive index of the tth layer of medium, k 1,z represents the wave vector in the z direction in the first layer of medium, k 2,z Represents the wave vector in the z direction in the second layer of medium.

[0023] Preferably, the method for determining the refractive index and thickness of the film to be measured is: calculating the residual sum of squares of theoretical data and measured data, and taking the film thickness and refractive index corresponding to the minimum residual sum of squares of theoretical data and measured data as the measured values ​​of the thickness and refractive index of the film to be measured.

[0024] Preferably, the certain incident angle is any angle between 0° and 90°.

[0025] Preferably, the pre-selection angle is any polarization angle between -90° and 90°.

[0026] Preferably, the post-selection angle is any polarization angle between -180° and 180°.

[0027] Preferably, the film is a film made of any material.

[0028] Preferably, the film is a single-layer or multi-layer structure.

[0029] Preferably, the method for measuring photon spin splitting displacement is a quantum weak measurement method, and a weak measurement system for measuring the refractive index and thickness of the film to be measured includes: a laser, a half-wave plate, a polarizer I, a focusing lens, a sample stage, a polarizer II, an imaging device, and a computer, wherein the centers of the laser, the half-wave plate, the polarizer I, and the focusing lens are in the same straight line and on the incident light of the sample stage, a film sample to be measured is placed on the sample stage, the polarizer II is arranged on the reflected light of the sample stage and is in the same straight line with the center of the imaging device, and the imaging device is connected to the computer.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] The present invention is based on photon spin splitting weak measurement amplification displacement. By modulating the front selection angle and the rear selection angle of the system and based on the dependence of photon spin splitting weak measurement amplification displacement on the refractive index and thickness of the nano-scale film, non-contact, non-destructive and high-stability measurement of the refractive index and thickness of the nano-scale film is achieved. The detection system has a simple structure, is easy to operate and is budget-friendly.

[0032] The present invention modulates the front selection angle or the rear selection angle of the weak measurement instead of the incident angle during measurement, and the eccentricity error caused by the change of the incident angle will not be introduced during the measurement process.

[0033] The present invention measures the deviation of the centroid of the light spot, and the deviation of the centroid of the light spot is not affected by ambient light. Therefore, the present invention has the advantages of high measurement accuracy and good stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 It is a graph showing the theoretical relationship between the out-of-plane photon spin splitting weak measurement amplification displacement and the gold film thickness in the present invention.

[0036] Figure 2 It is a graph showing the theoretical relationship between the out-of-plane photon spin splitting weak measurement amplification displacement and the real part of the gold film refractive index in the present invention.

[0037] Figure 3 It is a schematic diagram of a weak measurement system for measuring the thickness and refractive index of nano-scale films according to the present invention.

[0038] Figure 4 The present invention is a flow chart of a method for measuring film thickness and refractive index based on weak measurement amplification displacement of photon spin splitting.

[0039] In the figure, 1-laser, 2-half-wave plate, 3-polarizer I, 4-focusing lens, 5-tested film sample, 6-sample stage, 7-polarizer II, 8-imaging device, 9-computer. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] Example 1

[0042] In this embodiment, a method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplified displacement is used, the incident light beam used is a Gaussian light beam with a wavelength of 632.8nm, and the horizontally polarized light beam is incident on the surface of the nano film sample to be measured at an incident angle of 30°. The sample to be measured is a gold (Au) film, and the substrate material is BK7 glass with a refractive index of 1.515.

[0043] The theoretical relationship model between the out-of-plane photon spin splitting weak measurement amplified displacement yr and the film refractive index and thickness is:

[0044]

[0045] in:

[0046]

[0047] Among them, ξ, χ1, χ2 are all intermediate parameters; yr represents the weak measurement amplification displacement of out-of-plane photon spin splitting; θ represents the incident angle; γ represents the front selection angle; Δ represents the back selection angle; k r =2πn1 / λ represents the wave vector of the reflected light, n1 is the refractive index of the first medium, λ is the wavelength of the incident light when propagating in the first medium; z r represents the propagation distance; ω0 is the waist of the Gaussian beam; R p and Rs They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s Modulus value; φ p and φ s They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s The phase of and They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s The real part of the first derivative with respect to the angle of incidence is, and They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s Regarding the imaginary part of the first-order derivative of the incident angle, Re represents the real part of the complex number, and Im represents the imaginary part of the complex number; n represents the refractive index of the film to be measured, k represents the extinction coefficient of the film to be measured, and d represents the thickness of the film to be measured.

[0048] Furthermore, the reflection coefficient r of the horizontal polarization component of the incident light is p The reflection coefficient r of the polarization component perpendicular to the incident light s Through the Fresnel equation we get:

[0049]

[0050] in, is the reflection coefficient of the horizontal component of the interface between the first layer of medium and the film, is the reflection coefficient of the vertical component of the interface between the first layer of medium and the film, is the reflection coefficient of the horizontal component of the interface between the film and the third medium, is the reflection coefficient of the vertical component of the interface between the film and the third medium; i represents an imaginary number; m represents the number of medium layers in the reflection interface, n3 represents the refractive index of the third medium in the reflection interface; n2 represents the refractive index of the measured film in the reflection interface; k0 = 2π / λ represents the wave number of the incident light in vacuum; n t represents the refractive index of the tth layer of medium, k 1,z represents the wave vector in the z direction in the first layer of medium, k 2,z Represents the wave vector in the z direction in the second layer of medium.

[0051] In this embodiment, the first medium layer is air, the second medium layer is a gold film, and the third medium layer is BK7 glass.

[0052] From equation (1), we can see that the change of nano-scale film thickness and refractive index will cause the reflection coefficient r of the horizontal polarization component of the incident light to change to p The reflection coefficient r of the polarization component perpendicular to the incident light s , which in turn causes the change of the out-of-plane photon spin splitting weak measurement amplification displacement.

[0053] like Figure 1 and Figure 2 As shown in the figure, for different film thicknesses and refractive indices, the corresponding post-selection angle and the out-of-plane photon spin splitting weak measurement amplification displacement relationship curves are different. Figure 1 The graph is a theoretical relationship curve between the out-of-plane photon spin splitting weak measurement amplification displacement and different film thicknesses in the present invention. Figure 2 The figure is a graph of the theoretical relationship between the out-of-plane photon spin splitting weak measurement amplification displacement and the refractive index in the present invention. This in turn shows that the film thickness and refractive index corresponding to the relationship curves of different post-selection angles and out-of-plane photon spin splitting weak measurement amplification displacement are also different. It is also possible to determine the thickness and refractive index value of an unknown film by obtaining a set of out-of-plane photon spin splitting weak measurement amplification displacement data under different post-selection angles, based on the theoretical relationship model of the out-of-plane photon spin splitting weak measurement amplification displacement yr and the film refractive index and thickness, and the theoretical relationship database of the photon spin splitting weak measurement amplification displacement and the front selection angle and the back selection angle of the weak measurement.

[0054] In this embodiment, the schematic diagram of the weak measurement system for measuring the thickness and refractive index of nano-scale films is shown in FIG. Figure 3 As shown, it includes a laser 1, a half-wave plate 2, a polarizer I3, a focusing lens 4, a sample stage 6, a polarizer II7, an imaging device 8, and a computer 9. The centers of the laser 1, the half-wave plate 2, the polarizer I3, and the focusing lens 4 are in the same straight line and on the incident light of the sample stage 6, the polarizer II7 is arranged on the reflected light of the sample stage 6 and in the same straight line with the center of the imaging device 8, and the imaging device 8 is connected to the computer 9.

[0055] The laser 1 is used to generate a linearly polarized Gaussian beam; the half-wave plate 2 is used to adjust the light intensity brightness; the polarizer I 3 is used to adjust the front selection angle; the focusing lens 4 is used to focus the incident light on the thin film sample 5 to be measured; the sample stage 6 is used to place the thin film sample 5 to be measured; the polarizer II 7 is used to adjust the rear selection angle; the imaging device 8 is used to present the spot image; and the computer 9 is used to obtain the value of the photon spin splitting weak measurement amplification displacement.

[0056] The principle of the weak measurement system for measuring the thickness and refractive index of nano-scale films is as follows: the laser 1 generates a linearly polarized Gaussian beam, which passes through the half-wave plate 2, the polarizer I3 and the focusing lens 4 in sequence, and then is incident on the surface of the measured thin film sample 5, and is reflected on the surface of the measured thin film sample 5. Due to the refractive index gradient at the reflection interface, the light beam undergoes an out-of-plane photon spin Hall effect, and then the left-handed and right-handed components of the reflected light beam undergo out-of-plane spatial spin splitting. After the reflected light beam passes vertically through the polarizer II7, the spin splitting displacement will be amplified, and the light beam is finally vertically incident on the photosensitive imaging device 8, and the spot image information presented by the imaging device 8 is transmitted to the computer 9. The computer 9 is used to obtain the coordinates of the center of gravity position of the light spot in this spot image, and the coordinates of the zero point position are subtracted from the coordinates of the center of gravity position of the light spot to obtain the value of the weak measurement amplification displacement of the photon spin splitting. The front selection angle is adjusted to the desired polarization angle by rotating the polarizer I3; the rear selection angle is adjusted to the desired polarization angle by rotating the polarizer II7. The film sample 5 to be measured is placed on a sample stage 6. The angle at which the light beam is incident on the surface of the film sample 5 to be measured can be adjusted by rotating the sample stage 6. In this embodiment, the incident angle θ is 30°.

[0057] The following is combined with Figure 4 , and analyze in detail the specific measurement process of nanoscale film thickness.

[0058] ①, According to formula (1), a theoretical relationship database of the weak measurement amplification displacement of out-of-plane photon spin splitting and the front selection angle and back selection angle of weak measurement of thin film materials at various refractive indices and thicknesses is established. In the database, a 30° incident angle, a 0° front selection angle, and a back selection angle of 89° to 91° are selected, with an interval of Δ c When the refractive index is 0.1°, the corresponding post-selection angle under different refractive indices and thicknesses and the weak measurement amplified displacement theory of out-of-plane photon spin splitting [Δ c ,l c ].

[0059] ②. Irradiate the light beam that passes vertically through the focusing lens 4 onto the surface of the thin film sample 5 to be measured at an incident angle of 30°. Rotate the polarizer I3 to adjust the front selection angle of weak measurement to 0°. Rotate the polarizer II7 to adjust the back selection angle of weak measurement to 89°. Obtain the out-of-plane photon spin splitting weak measurement amplification displacement value at this time.

[0060] ③, through polarizer II7, at intervals of 0.1°, the polarization angle (post-selection angle) of the weak measurement post-selection angle is adjusted to 91° in sequence, and the out-of-plane photon spin splitting weak measurement amplification displacement values ​​under the corresponding post-selection angles are obtained in sequence, and then a set of out-of-plane photon spin splitting weak measurement amplification displacement measurement data under different post-selection angles is obtained [Δ c ,yr c ], c = {1, 2, ..., 21};

[0061] ④, the measurement data set [Δ c ,yr c ], and the theoretical data set of weak measurement amplification displacement of out-of-plane photon spin splitting at 30° incident angle, 0° front selection angle, and the corresponding back selection angle under different refractive index and thickness obtained in step ① [Δ c ,l c ] to analyze and compare, and take the film thickness and refractive index corresponding to the minimum residual sum of squares δ between theoretical data and measured data as the measured values ​​of the film thickness and refractive index. The specific calculation method of the residual sum of squares δ is as follows:

[0062]

[0063] In the formula, δ represents the residual sum of squares, l c Represents measurement data, yr c represents theoretical data, v c Represents the residual error.

[0064] Example 2

[0065] A method for measuring film thickness and refractive index based on weak measurement amplified displacement of photon spin splitting is disclosed. Next, based on the in-plane photon spin splitting weak measurement amplified displacement xr as an example, a specific implementation process of one of the present invention is introduced in detail.

[0066] The incident light beam used in the embodiment of the present invention is a Gaussian light beam with a wavelength of 632.8 nm. The horizontally polarized light beam is incident on the surface of the nanofilm sample to be measured at an incident angle of 30°. The sample to be measured is a gold (Au) film, and the substrate material is BK7 glass with a refractive index of 1.515. The theoretical relationship model of the weak measurement amplification displacement xr of the in-plane photon spin splitting and the refractive index and thickness of the film is:

[0067]

[0068] in:

[0069]

[0070] ζ1, ζ2, χ1, and χ2 are all intermediate parameters;

[0071] Furthermore, the reflection coefficient r of the horizontal polarization component of the incident light is p The reflection coefficient r of the polarization component perpendicular to the incident light s Through the Fresnel equation we get:

[0072]

[0073]

[0074] From equation (2), we can see that the change of nano-scale film thickness and refractive index will cause the reflection coefficient r of the horizontal polarization component of the incident light to change to p The reflection coefficient r of the polarization component perpendicular to the incident light s The change of causes the change of the in-plane photon spin splitting weak measurement amplification displacement xr. And the relationship curves of the post-selection angle and the in-plane photon spin splitting weak measurement amplification displacement corresponding to different film thicknesses and refractive indices are different. This in turn shows that the film thickness and refractive index corresponding to different post-selection angles and the in-plane photon spin splitting weak measurement amplification displacement curves are also different. Therefore, by obtaining a set of in-plane photon spin splitting weak measurement amplification displacement data under different post-selection angles, the thickness and refractive index values ​​of the unknown film can be determined based on the theoretical relationship model of the in-plane photon spin splitting weak measurement amplification displacement xr and the film refractive index and thickness, and the theoretical relationship database of the photon spin splitting weak measurement amplification displacement and the pre-selection angle and post-selection angle of the weak measurement.

[0075] In this embodiment, the weak measurement system for measuring the thickness and refractive index of nano-scale films is the same as that in Embodiment 1, such as Figure 3 As shown in the example 1, the measurement system has been introduced and will not be repeated here.

[0076] The specific measurement process of nanoscale film thickness is analyzed in detail below.

[0077] (I) According to equation (2), a theoretical database of the relationship between the weak measurement amplification displacement of in-plane photon spin splitting and the front selection angle and back selection angle of weak measurement of thin film materials at various refractive indices and thicknesses is established. When the incident angle is 30°, the front selection angle is 0°, and the back selection angle is 89° to 91°, with an interval of 0.1°, the corresponding back selection angle at different refractive indices and thicknesses and the theoretical relationship between the weak measurement amplification displacement of in-plane photon spin splitting [Δ c ,l c ].

[0078] (ii) The light beam passing vertically through the focusing lens 4 is irradiated onto the surface of the thin film sample 5 to be measured at an incident angle of 30°, the polarizer I3 is rotated to adjust the front selection angle of the weak measurement to 0°, the polarizer II7 is rotated to adjust the rear selection angle of the weak measurement to 89°, and the in-plane photon spin splitting weak measurement amplification displacement value is obtained at this time.

[0079] (III) By rotating the polarizer II7, the polarization angle of the weak measurement post-selection angle (post-selection angle) is adjusted to 91° at intervals of 0.1°, and the in-plane photon spin splitting weak measurement amplification displacement values ​​under the corresponding post-selection angles are obtained in turn, thereby obtaining a set of measurement data of the in-plane photon spin splitting weak measurement amplification displacement under different post-selection angles [Δ c ,xr c ], c = {1, 2, ..., 21};

[0080] (iv) The measurement data set [Δ c ,xr c ], and the theoretical data set of weak measurement amplification displacement of in-plane photon spin splitting at 30° incident angle, 0° front selection angle, corresponding back selection angle under different refractive index and thickness obtained in step (a) [Δ c, 1x c ] to analyze and compare, and take the film thickness and refractive index corresponding to the minimum residual sum of squares δ between theoretical data and measured data as the measured values ​​of the film thickness and refractive index. The specific calculation method of the residual sum of squares δ is as follows:

[0081]

[0082] In the formula, δ represents the residual sum of squares, lx c represents the measured data, xr c represents theoretical data, vx c Represents the residual error.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplification displacement, characterized in that: The following steps are involved: S1. According to the theoretical relationship model between the photon spin splitting weak measurement amplification displacement and the thickness and refractive index of the film to be measured, a theoretical relationship database between the photon spin splitting weak measurement amplification displacement and the front selection angle and the back selection angle of the weak measurement for the film material at various refractive indices and thicknesses is established; S2, irradiating the incident light beam to the surface of the film to be measured at a certain incident angle, adjusting the front selection angle of weak measurement to a certain polarization angle, adjusting the rear selection angle of weak measurement to a certain polarization angle, and measuring the value of the photon spin splitting weak measurement amplification displacement at this time; S3, sequentially changing the front selection angle or the back selection angle of the weak measurement to obtain a set of measurement data of the photon spin splitting weak measurement amplification displacement under the front selection angle or the back selection angle; S4. Analyze and compare the pre-selection angle or post-selection angle and the photon spin splitting weak measurement amplification displacement data group obtained in step S3 with the photon spin splitting weak measurement amplification displacement theoretical data at different refractive indices and thicknesses in the database obtained in step S1 to determine the refractive index and thickness of the film being measured.

2. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplified displacement according to claim 1, characterized in that: The photon spin splitting weak measurement amplification displacement in step S1 is an in-plane photon spin splitting weak measurement amplification displacement or an out-of-plane photon spin splitting weak measurement amplification displacement; The theoretical relationship model between the photon spin splitting weak measurement amplification displacement and the film refractive index and thickness is: in: ζ1, ζ2, ξ, χ1, χ2 are all intermediate parameters; xr represents the weak measurement amplification displacement of in-plane photon spin splitting, yr represents the weak measurement amplification displacement of out-of-plane photon spin splitting; θ represents the incident angle; γ represents the front selection angle; Δ represents the back selection angle; k r =2πn1 / λ represents the wave vector of the reflected light, n1 is the refractive index of the first medium, λ is the wavelength of the incident light when propagating in the first medium; z r represents the propagation distance; ω0 is the waist of the Gaussian beam; R p and R s They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s Modulus value; φ p and φ s They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s The phase of and They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s The real part of the first derivative with respect to the angle of incidence is, and They represent the reflection coefficient r of the horizontal polarization component of the incident light respectively. p The reflection coefficient r of the polarization component perpendicular to the incident light s Regarding the imaginary part of the first-order derivative of the incident angle, Re represents the real part of the complex number, and Im represents the imaginary part of the complex number; n represents the refractive index of the film to be measured, k represents the extinction coefficient of the film to be measured, and d represents the thickness of the film to be measured.

3. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplification displacement according to claim 2, characterized in that: The reflection coefficient r of the horizontal polarization component of the incident light p The reflection coefficient r of the polarization component perpendicular to the incident light s Through the Fresnel equation we get: in, is the reflection coefficient of the horizontal component of the interface between the first layer of medium and the film, is the reflection coefficient of the vertical component of the interface between the first layer of medium and the film, is the reflection coefficient of the horizontal component of the interface between the film and the third medium, is the reflection coefficient of the vertical component of the interface between the film and the third medium; i represents an imaginary number; m represents the number of medium layers in the reflection interface, n3 represents the refractive index of the third medium in the reflection interface; n2 represents the refractive index of the measured film in the reflection interface; k0 = 2π / λ represents the wave number of the incident light in vacuum; n t represents the refractive index of the tth layer of medium, k 1,z represents the wave vector in the z direction in the first layer of medium, k 2,z Represents the wave vector in the z direction in the second layer of medium.

4. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplified displacement according to claim 1 or 3, characterized in that: The method for determining the refractive index and thickness of the film to be measured is: calculating the residual sum of squares of theoretical data and measured data, and taking the film thickness and refractive index corresponding to the minimum residual sum of squares of theoretical data and measured data as the measured values ​​of the thickness and refractive index of the film to be measured.

5. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplified displacement according to claim 4, characterized in that: The certain incident angle is any angle between 0° and 90°.

6. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplification displacement according to claim 5, characterized in that: The front selection angle is any polarization angle between -90° and 90°.

7. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplification displacement according to claim 6, characterized in that: The post-selection angle is any polarization angle between -180° and 180°.

8. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplified displacement according to claim 7, characterized in that: The film is made of any material.

9. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplification displacement according to claim 8, characterized in that: The film is a single-layer or multi-layer structure.

10. The method for measuring film thickness and refractive index based on photon spin splitting weak measurement amplification displacement according to claim 9, characterized in that: A weak measurement system for measuring the refractive index and thickness of a measured film comprises: a laser (1), a half-wave plate (2), a polarizing plate I (3), a focusing lens (4), a sample stage (6), a polarizing plate II (7), an imaging device (8), and a computer (9), wherein the centers of the laser (1), the half-wave plate (2), the polarizing plate I (3), and the focusing lens (4) are located in the same straight line and on the incident light of the sample stage (6), the polarizing plate II (7) is arranged on the reflected light of the sample stage (6) and is located in the same straight line with the center of the imaging device (8), and the imaging device (8) is connected to the computer (9).

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