A method for detecting materials of a superlattice for enhancing CAP signals and its application

Abstract

The present invention relates to a method for detecting materials of a superlattice for enhancing CAP signals, which comprises the following steps: S1. Establishing a mathematical model, and the mathematical model is as shown in formula (1); #imgabs0#The present invention discloses a software simulation method. From the perspective of a mathematical model, it details the analysis of the properties of photoacoustic transducer materials that can affect CAP signals, namely that the linear thermal expansion coefficient, bulk modulus, specific heat, density, sound velocity, and refractive index can all affect the strain intensity in the materials. At the same time, it analyzes the correlation between different parameters and the magnitude of CAP signals, and points out the evaluation criteria of different parameters for CAP signal intensity. It is pointed out that even when the thermal expansion coefficient in the material is not very high, the CAP signal can be enhanced by improving other properties.

Description

Technical Field

[0001] The present invention belongs to the field of material detection, and particularly relates to a method for detecting materials of a superlattice for enhancing CAP signals and its application. Background Art

[0002] All along, detecting the physical properties of transparent materials (such as solid polymers, solutions, and biological tissues) through Coherent Acoustic Phonon (CAP) signals has been a research hotspot. In the field of biological tissue imaging, due to the poor optical contrast of cells, it is difficult to obtain high-quality optical images using traditional optical methods. A common solution is to stain biological samples with fluorescent substances, which will inevitably contaminate the samples. However, the method of imaging using CAP signals can effectively avoid various drawbacks in optical imaging technology. Moreover, the light absorption capacity of transparent media such as biological samples is very poor. A common method is to use a metal film as a photo-acoustic transducer to enhance the CAP signal intensity in the sample. It is not difficult to see that the intensity of the CAP signal is basically determined by the photo-acoustic transducer. Therefore, designing a transducer structure with a high conversion rate is of great significance for this method of detecting using CAP signals. In addition, measuring the CAP signal can also analyze parameters such as refractive index, sound velocity, and elastic modulus in several transparent media, which is a powerful tool for material analysis.

[0003] In the existing technologies for detecting signals in a matrix through CAP signals, most use a single-layer thin film as the photo-acoustic transducer to generate a strain wave through a metal with a high light absorption rate. However, the intensity of the thermal strain generated by the single-layer thin film is limited, and it is impossible to generate a signal with sufficient intensity to detect some subtle changes in the transparent material to be measured at the same laser energy flux density. The photo-acoustic transducer made of the material combination screened by this method can generate a stronger CAP signal intensity compared to the transducer made of a single-layer material.

[0004] Recently, a result has shown the use of a multi-layer superlattice material as a photo-acoustic conversion device to enhance the strain intensity in a transparent matrix (Applied Physics Letters, 2022, 120(21): 212201), but only proposed a theory for enhancing the CAP signal of the multi-layer structure from the perspective of the linear thermal expansion coefficient, and there are still many unsolved problems. Summary of the Invention

[0005] For the above reasons, the present invention discloses a method of software simulation. From the perspective of a mathematical model, it details the properties of the photoacoustic transducer material that can affect the CAP signal, namely that the linear thermal expansion coefficient, bulk modulus, specific heat, density, sound velocity, and refractive index all affect the strain intensity in the material. At the same time, it analyzes the correlation between different parameters and the magnitude of the CAP signal, and points out the criteria for judging the intensity of the CAP signal by different parameters. It is pointed out that even when the thermal expansion coefficient in the material is not very high, the CAP signal can be enhanced by improving other properties. Starting from the perspective of a mathematical model, the present invention not only analyzes the influence of the linear thermal expansion coefficient, but also analyzes the combined influence of multiple parameters such as the medium density, sound velocity, specific heat, bulk modulus, and refractive index, and conducts a more comprehensive analysis of the CAP signal intensity.

[0006] Specifically, the present invention discloses a method for material selection, which is used in the material selection of multi-layer superlattices. This method enables the superlattice structure composed of these two materials to generate a stronger CAP signal relative to one of the materials. Starting from a mathematical model, the present invention analyzes which parameters in the thin film structure material are related to the CAP signal intensity in the transparent medium, and analyzes the degree of correlation between different parameters and the CAP signal intensity; and screens the material parameters according to these criteria. Subsequently, through the mathematical model, the correctness of this material selection is verified. By using the multi-layer superlattice material designed in this way, stronger signals can be generated in the fields of defect detection, phonon imaging, etc., providing a better signal-to-noise ratio.

[0007] In the present invention,

[0008] The term "superlattice material" refers to a multi-layer film in which two different components grow alternately with a thickness of several nanometers to dozens of nanometers and maintain strict periodicity.

[0009] The term "homogenized material" refers to an equivalent approximation of the superlattice material. The superlattice material is regarded as a single medium material, and the parameters of the homogenized material are all linear superpositions of the properties of the two materials in the corresponding superlattice material.

[0010] An object of the present invention discloses a method for detecting the material of a superlattice for enhancing the CAP signal, which includes the following steps:

[0011] S1. Establish a mathematical model, and the mathematical model is shown in formula (1);

[0012]

[0013] Wherein, η is the strain intensity of the thermal strain generated by the pump source in the light-absorbing medium, T is the transmittance at the medium interface, k is the pump light wave number under vacuum conditions, z is any point on the multi-layer thin film structure, and is the vertical distance from the substrate interface;

[0014] F represents the pump light energy flux density, B represents the bulk modulus; β represents the linear thermal expansion coefficient; ρ represents the density; C represents the specific heat; v represents the sound speed; N and K respectively represent the real and imaginary parts of the refractive index;

[0015] The subscript 1 of the letter represents the equivalent parameter in the multilayer structure, and the subscript 2 of the letter represents the parameter in the sample to be measured;

[0016] a0 and a1 represent the coefficients related to the refractive index of the homogeneous material, as shown in formula (2);

[0017] a0 = (k + k1)(k1 + k2) + (k - k1)(k1 - k2)exp(2ik1d)

[0018] a1 = 2k(k1 + k2) (2)

[0019] Wherein, k1 represents the equivalent wave number of the excitation light in the multilayer structure; k2 represents the wave number of the excitation light in the transparent material to be measured; d represents the film thickness; i represents the imaginary number;

[0020] In the above formula, k1 is the equivalent wave number of the excitation light in the multilayer structure; k2 is the wave number of the excitation light in the transparent material to be measured; d is the film thickness. Generally, it is required that the parameters of the medium to be measured remain unchanged, and the strain intensity in the medium to be measured is changed by changing the physical parameters of the film structure. It can be seen that the intensity of the strain signal is proportional to the first power of the linear expansion coefficient β and the bulk modulus B of the film structure, and inversely proportional to the first power of the specific heat C. For the density ρ of the film, it can be considered that when the density of the film structure is greater than the density of the substrate, ρ1v1 in the component ρ1v1 + ρ2v2 plays a dominant role. At this time, it can be considered that the intensity of the strain is inversely proportional to the square of the density, and the change of the density contributes more to the strain than the linear expansion coefficient, the bulk modulus and the specific heat. Correspondingly, the relative contribution of the sound speed v in the film is less than the first power. At the same time, the influence caused by the change of the refractive index of the film can be obtained by the component N1K1|a1| 2 / |a0| 2 and its value will change with the wavelength of the pump light. In practice, it is necessary to select a suitable pump light wavelength to generate greater gain. It can be seen that if a strong transient reflectivity signal is to be generated in the transparent material, the equivalent density and sound speed of the homogeneous material need to be low, while the linear expansion coefficient, the bulk modulus and the specific heat need to be high. At the same time, for the pump light energy of different wavelengths, it is required that the value of N1K1|a1| 2 / |a0| 2 should be as high as possible. The relative contribution capabilities of different parameters also have a sequence. It can be seen from the formula that the relative contribution of the density ρ is the highest; the contributions of the three properties of β, B and C are the same, but weaker than ρ; and the relative contribution of v is the lowest.

[0021] S2. Under software simulation conditions, based on the mathematical model, select an absorbent medium, simulate the product of η(z) and T obtained according to formulas (1) and (2), and create a strain distribution map.

[0022] The mathematical model described in the present invention is essentially the numerical value of the function distribution formed by the product between the thermal strain generated in the absorbent medium and the transmittance at the medium interface.

[0023] Further, the absorbent medium is a superlattice material.

[0024] Further, the absorbent medium is selected from one or more of metal nitrides, metal carbides, metal sulfides, metal oxides, metallic elements, non-metallic elements for semiconductors, and compounds for semiconductors.

[0025] For example, the non-metallic element for semiconductors can be, but is not limited to, silicon; the compound for semiconductors can be, but is not limited to, silicon dioxide, etc.

[0026] Further, the absorbent medium is a homogenized material.

[0027] In this method, by utilizing the homogenization property of the double-layer superlattice material, stacking the two materials in multiple layers approximately produces a material with more ideal properties in all aspects. However, generally, the gain effect that cannot be achieved by conventional materials requires the design of multi-layer materials. And if we want to regard the multi-layer material as a homogenized material, generally the following several conditions need to be met:

[0028] (1) The single-layer thickness of the multi-layer material should be small, generally much smaller than the pump light wavelength and the CAP wavelength generated by the pump light.

[0029] (2) The total thickness of the multi-layer structure should be appropriate. If the total thickness is too small, the pump light cannot be fully absorbed, resulting in energy loss and reducing the strain intensity; if the total thickness is too thick, excessive strain attenuation will be introduced in the multi-layer structure, also reducing the strain intensity. Generally, the product of the total thickness h and the structural equivalent absorption coefficient α is more suitable between 3 and 5.

[0030] (3) The thermal strain generated in the multi-layer structure should be as uniform as possible. If one of the two selected materials in the double-layer material is a non-absorbing transparent material, the heat absorbed by the absorbing layer needs to be transferred to the adjacent transparent layer within the time of 1 / f B to achieve the effect of uniform thermal strain. Specific formulas will be discussed later.

[0031] Further, in the absorbent medium, the thickness of the single-layer material should be less than the pump light wavelength; and

[0032] The thickness of the single-layer material should be less than the CAP wavelength generated by the pump light.

[0033] Furthermore, the product of the thickness of the light-absorbing medium and the structural equivalent absorption coefficient α has a value of 3 - 5.

[0034] Furthermore, in the light-absorbing medium, at least one of the materials is a transparent material; the transparent material should satisfy that the extinction coefficient k approaches 0.

[0035] Furthermore, when there is an opaque material in the light-absorbing medium, the thickness of the single-layer material in the light-absorbing medium needs to be less than the L value, and the L value should satisfy the following formula (3):

[0036]

[0037] where L is the thickness of the single-layer material, κ is the thermal conductivity; n is the refractive index of the pump light; λ is the wavelength of the pump light.

[0038] Furthermore, the CAP signal is generated after the interference of the pump light and the probe light. The experiment of the present invention is carried out by the ultrafast pump-probe technique of femtosecond laser, mainly involving two beams of laser, namely the pump light responsible for exciting the sample to generate stress wave signals, and the probe light responsible for detecting the generated signals, as Figure 1 shown: The pump light (1030 nm) is incident from below into the photoacoustic transducer composed of a multi-layer structure to generate a CAP signal, and the probe light (515 nm) is incident from above into the transparent solution to detect the change in transient reflectivity.

[0039] Another object of the present invention is to disclose the application of the material detection method of the superlattice for enhancing the CAP signal in a photoacoustic transducer.

[0040] The beneficial effects of the present invention are as follows:

[0041] The present invention discloses a software simulation method. From the perspective of a mathematical model, it details the properties of the photoacoustic transducer materials that can affect the CAP signal, that is, the linear thermal expansion coefficient, bulk modulus, specific heat, density, sound velocity, and refractive index will all affect the strain intensity in the material. At the same time, it analyzes the correlation between different parameters and the magnitude of the CAP signal, and points out the evaluation criteria for different parameters regarding the CAP signal intensity. It is pointed out that even when the thermal expansion coefficient in the material is not very high, the CAP signal can be enhanced by improving other properties. Description of the Drawings

[0042] Figure 1 Shows the schematic diagram of the principle of action of the multi-layer structure formed by the light-absorbing medium of the present invention for enhancing the CAP signal;

[0043] Figure 2 In (a) of FIG. shows Example 1 and Comparative Example 1, the distribution function graph of η(z) obtained in the light-absorbing material at t = 0 ps;

[0044] Figure 2 In (b) of FIG. shows the distribution curve of η(z) at t = 50 ps.

[0045] Figure 3 Shows the transient reflectivity change signal of the photoacoustic transducer of the CAP signal obtained using a pump light of 1030 nm and a probe light of 515 nm. Detailed implementation mode

[0046] To more clearly illustrate the technical solutions of the present invention, the following examples are listed. The raw materials, reactions and post-treatment means that appear in the examples are all common raw materials on the market and technical means well-known to those skilled in the art, unless otherwise specified.

[0047] The materials screened by this method, but may be different from the two materials in the examples, may be composed of three or more materials, but the screening principle is still the principle described in this article.

[0048] The simulation software adopted by the present invention is a calculation program obtained by programming by conventional means using the C++ language, and the formula can be run in this calculation program.

[0049] Example 1

[0050] A method for detecting materials of a superlattice for enhancing CAP signals, comprising the following steps:

[0051] S1. Establish the following mathematical model as shown in formula (1):

[0052]

[0053] a0 and a1 represent coefficients related to the refractive index of the homogeneous material, as shown in formula (2);

[0054] a0 = (k + k1)(k1 + k2) + (k - k1)(k1 - k2)exp(2ik1d)

[0055] a1 = 2k(k1 + k2) (2)

[0056] In the above formula, all parameters are known data in the industry or are derived according to well-known formulas in the industry. z is an arbitrary point on the multi-layer thin film structure, the vertical distance from the substrate interface, and is a variable. Therefore, the value of formula (1) obtained is actually a function of z.

[0057] In this embodiment, two materials, titanium nitride (TiN) and aluminum nitride (AlN), are selected. The two materials are alternately stacked in a mass ratio of 1:1 to form a multi-layer material that can be regarded as a homogenized material. The number of layers of the multi-layer material is 8, including 4 layers of titanium nitride and 4 layers of aluminum nitride. Each layer is regarded as a single-layer material, forming a material for the superlattice, and software simulation is carried out. In the aluminum nitride-titanium nitride multi-layer material formed by the simulation, titanium nitride is the main light-absorbing substance, while aluminum nitride is a transparent material that basically does not absorb photons. In the ultra-short time when the pump light acts on the surface of the sample, the heat generated by titanium nitride absorbing photons needs to be transferred to aluminum nitride, so as to generate strain uniformly.

[0058] In addition, in order to meet the requirement that the light-absorbing medium of the above superlattice material is a homogenized material, the thickness of the single-layer material in the light-absorbing medium needs to:

[0059] (a) be less than the L value, and the L value needs to meet the requirements of the following formula (3):

[0060]

[0061] And,

[0062] (b) simultaneously, meet the requirement that the value of the product of the structural equivalent absorption coefficient α and the total thickness of the multi-layer structure thin film is in the range of 3 - 5.

[0063] After calculation, we take the thickness h of the single-layer structure of the light-absorbing medium to be about 20 nm.

[0064] S2. Multiply the obtained η(z) and T, and make a strain distribution diagram.

[0065] The relevant parameters in formulas (1)-(3) are all excerpted from the prior art (see References 1 - 7 at the back of the patent), and are authoritative.

[0066] Comparative Example 1

[0067] In this comparative example, all steps are the same as those in Example 1. The only difference is that the two materials, titanium nitride and aluminum nitride, with a multi-layer structure are replaced with a single-layer structure of titanium nitride with the same total thickness.

[0068] Comparative Example 2

[0069] In this comparative example, all steps are the same as those in Example 1. The only difference is that the two materials, titanium nitride and aluminum nitride, with a multi-layer structure are replaced with a single-layer structure of aluminum nitride with the same total thickness.

[0070] Test Example 1

[0071] A distribution curve was plotted for the distribution equation of the product of η(z) and T calculated by the software in Example 1. A single layer thickness of about 18 nm and a total thickness of about 150 nm were used.

[0072] The specific information is shown in Table 3.

[0073] Table 3 Information of light-absorbing media of Examples and Comparative Examples

[0074]

[0075] The obtained figure is as follows Figure 2 As shown in (a)-(b) in the figure. Figure 2 (a) shows the distribution function diagram of η(z) obtained in the light-absorbing material in Example 1 and Comparative Example 1. It can be seen from the figure that η(z) in Example 1 and Comparative Example 1 both decay with increasing distance from the sample surface, but η(z) in Example 1 is much higher than the value of η(z) in Comparative Example 1.

[0076] Figure 2 (a) in the figure shows the distribution curve of η(z) at the initial moment.

[0077] Figure 2 (b) shows the strain distribution in the medium after 50 ps of strain propagation, indicating that the thin film structure designed in this way can indeed enhance the strain strength in the medium.

[0078] The distribution functions of the aforementioned light-absorbing media were then substituted into the detection model (reference: Ultrasonics, 2004, 42(1-9): 653-656). The CAP signal detected in the H2O medium was calculated from the detection model. The calculations were then performed for all-titanium nitride, all-aluminum nitride, and a titanium nitride-aluminum nitride multilayer structure of equal proportions. The theoretical amplification factor that can be achieved with this multilayer structure was obtained. Calculation results Figure 3 shown. Figure 3 Figure 2 shows the oscillation curves of CAP detected in water using a titanium nitride thin film, an aluminum nitride thin film, and a multilayer structure composed of the two materials, where the probe light wavelength is 515 nm. Figure 3 The midpoint line represents the strain curve when the aluminum nitride film is used as a single layer. Since aluminum nitride is a transparent material, it cannot absorb the pump light and generate sufficient thermal strain when it is used as a single layer. At this time, the reflectivity of the detection light does not change. The dotted line represents the transient reflectivity signal when titanium nitride is used as a single layer. It has a strong light absorption coefficient and can generate a certain amount of thermal strain. Figure 3The dashed curve generates a certain oscillation signal. The solid line represents the transient reflectivity signal of the detection light generated by the titanium nitride and aluminum nitride multilayer structure. It can be clearly seen that the CAP signal generated in the multilayer structure is higher than that in the single-layer medium. When the proportion of the two materials is the same, the amplitude is enhanced by several times, verifying the correctness of our experimental theory.

[0079] In Figure 3 , the transient reflectivity change signal of the photoacoustic transducer of the CAP signal obtained using a pump light of 1030 nm and a detection light of 515 nm is shown. The solid line therein is the transient reflectivity signal generated by the multilayer structure. The dashed line TiN is the signal generated by the single-layer structure, and the dotted line is the signal generated in the single-layer AlN structure. Since AlN is a transparent material and basically does not absorb the pump light, no signal can be generated. It can be clearly seen that using a multilayer structure composed of two materials can generate a stronger transient reflectivity signal than that generated by the single-layer structures composed of the two materials respectively.

[0080] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, in any aspect, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention.

[0081] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0082] References

[0083] [1]BU G, CIPLYSD, SHUR M, et al. Surface Acoustic Wave Velocity in Single-Crystal Aln Substrates[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2006, 53(1): 251 - 254.

[0084] [2] J,ROSKOVCOVá L.Refraction Index Measurements on AlnSingle Crystals [J].physica status solidi(b),1966,14(1):K5-K8.

[0085] [3]SHUR M S.Handbook Series on Semiconductor Parameters[M].WorldScientific,1996.

[0086] [4]ZHAO Y,PENG X,FU T,et al.Investigation of Mechanical Behaviour ofAmorphous Aluminium Nitride[J].Materialia,2018,2:148-156.

[0087] [5]PFLüGER J,FINK J.Determination of Optical Constants by High-Energy,Electron-Energy-Loss Spectroscopy(Eels)[M].Handbook of OpticalConstants of Solids.Elsevier.1997:293-311.

[0088] [6]PATSALAS P,KALFAGIANNIS N,KASSAVETIS S.Optical Properties andPlasmonic Performance of Titanium Nitride[J].Materials,2015,8(6):3128-3154.

[0089] [7]MARLO M,MILMAN V.Density-Functional Study of Bulk and SurfaceProperties of Titanium Nitride Using Different Exchange-CorrelationFunctionals[J].Physical Review B,2000,62(4):2899.

Claims

1. A method for detecting materials of a superlattice for enhancing a Coherent Acoustic Phonon (CAP) signal, characterized in that It includes the following steps: S1. Establish a mathematical model, and the mathematical model is shown in formula (1); where η is the strain intensity of the thermal strain generated by the pump source in the light-absorbing medium, T is the transmittance at the medium interface, k is the pump light wave number under vacuum conditions, z is an arbitrary point on the multi-layer thin film structure, and is the vertical distance from the substrate interface; F represents the pump light energy flux density, B represents the bulk modulus; β represents the linear thermal expansion coefficient; ρ represents the density; C represents the specific heat; v represents the sound speed; N and K respectively represent the real part and the imaginary part of the refractive index; The subscript 1 of the letter represents the equivalent parameter in the multi-layer structure, and the subscript 2 of the letter represents the parameter in the sample to be measured; a0 and a1 represent the coefficients related to the refractive index of the homogeneous material, as shown in formula (2); a0 = (k + k1)(k1 + k2)+(k - k1)(k1 - k2)exp(2ik1d) a1 = 2k(k1 + k2) (2) where k1 represents the equivalent wave number of the excitation light in the multi-layer structure; k2 represents the excitation light wave number in the transparent material to be measured; d represents the film thickness; i represents the imaginary number; S2. Under the software simulation condition, based on the mathematical model, select the light-absorbing medium, simulate the product of η(z) and T obtained according to formula (1) and formula (2), and make a strain distribution diagram; The light-absorbing medium is a superlattice material; The CAP signal is generated after the interference of the pump light and the probe light.

2. The method for detecting materials of the superlattice for enhancing the coherent acoustic phonon CAP signal according to claim 1, characterized in that, The light-absorbing medium is selected from one or more of metal nitrides, metal carbides, metal sulfides, metal oxides, metal elements, non-metal elements for semiconductors, and compounds for semiconductors.

3. The method for detecting the material of the superlattice for enhancing the coherent acoustic phonon CAP signal according to claim 1, characterized in that, The light-absorbing medium is a homogenized material.

4. The method for detecting the material of the superlattice for enhancing the coherent acoustic phonon CAP signal according to claim 1, characterized in that, In the light-absorbing medium, the thickness of the single-layer material is less than the pump light wavelength; and The thickness of the single-layer material is less than the CAP wavelength generated by the pump light.

5. The method for detecting the material of the superlattice for enhancing the coherent acoustic phonon CAP signal according to claim 1, characterized in that The numerical value of the product of the thickness of the light-absorbing medium and the structural equivalent absorption coefficient α is 3 - 5.

6. The method for detecting materials of a superlattice for enhancing a coherent acoustic phonon CAP signal according to claim 1, wherein In the light-absorbing medium, at least one of the materials is a transparent material; the transparent material should satisfy that the extinction coefficient k tends to 0.

7. The method for detecting materials of the superlattice for enhancing the coherent acoustic phonon CAP signal according to claim 6, characterized in that, When there is an opaque material in the light-absorbing medium, in the light-absorbing medium, the thickness of the single-layer material needs to be less than the L value, and the L value should satisfy the following formula (3): where L is the thickness of the single-layer material, κ is the thermal conductivity; n is the refractive index of the pump light; λ is the pump light wavelength.

8. Application of the material detection method of the superlattice for enhancing the coherent acoustic phonon CAP signal according to any one of claims 1 - 7 in a photoacoustic transducer.

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