A carrier diffusion prediction method and system based on high temporal and spatial resolution imaging

Abstract

The present invention discloses a method and system for predicting carrier diffusion based on high spatiotemporal resolution imaging, which belongs to the field of ultrafast detection of carrier diffusion. The system of the present invention includes a measured data acquisition unit, a diffusion model creation unit, and a carrier diffusion fitting result acquisition unit. The implementation method of the present invention is: obtaining measured data of carrier diffusion; constructing a Gaussian diffusion model based on the measured data, and establishing a carrier diffusion model based on the Gaussian diffusion model; predicting the diffusion coefficient, lifetime and diffusion distance of carrier diffusion based on the measured data and the carrier diffusion model, and based on the nonlinear least squares method and Gaussian fitting method. The present invention utilizes the ultrahigh spatial resolution and ultrafast time resolution of high spatiotemporal resolution imaging to ensure the accuracy of carrier diffusion measurement. The diffusion coefficient, lifetime and diffusion distance of carrier diffusion predicted by the present invention can optimize the high spatiotemporal resolution imaging system and improve the femtosecond laser processing effect.

Description

Technical Field

[0001] The present invention relates to a method and system for predicting carrier diffusion based on high-time-space resolution imaging, and belongs to the field of ultrafast detection of carrier diffusion. Background Art

[0002] Ultrafast laser micro-nanofabrication is a focal point and a cutting-edge area of ​​international competition. The shape and properties of femtosecond laser "light knives" are precisely controllable, enabling multi-scale, selective, non-contact, non-thermal processing of any solid material with high precision and quality. During femtosecond laser manufacturing, the dynamic distribution and changes of electrons determine both the manufacturing process and the outcome. Therefore, localized, instantaneous observation and control of the electrons are crucial.

[0003] During femtosecond laser processing, the primary carriers of photon energy absorption are the electrons in the material. All subsequent processing processes (including phase transitions and formability) are determined by the interaction between the femtosecond laser and the electrons. Therefore, studying the heat transfer characteristics of electrons after femtosecond laser excitation, as well as their interaction with other systems, is key to understanding the entire light-matter interaction process. In metal systems, three typical non-equilibrium heat transfer processes exist: 1. Thermal equilibrium heat transfer within the electron system; 2. Heat transfer caused by temperature differences between the electron system and the lattice system; and 3. Heat transfer between the electron system and the surrounding medium (e.g., substrate, environment). These three non-equilibrium heat transfer processes occur on femtosecond to picosecond timescales, with their spatial scales at submicrometer and nanometer levels, reaching their limits in both time and space. Therefore, to better control processing processes and outcomes and to understand the mechanisms of light-matter interaction, it is necessary to analyze electron diffusion and heat transfer behavior simultaneously at both the femtosecond and nanometer scales. This represents a bottleneck in studying the mechanisms of light-matter and metal-matter interactions.

[0004] Femtosecond laser transient absorption microscopy observation systems can simultaneously achieve femtosecond temporal resolution and nanometer-scale spatial measurement accuracy. They can directly image processes such as carrier transport, charge transfer, and energy transfer, revealing the mechanism of photon-material interaction. However, the laws governing carrier diffusion in space require fitting with scientific models to analyze important parameters such as carrier lifetime and diffusion distance. Due to the complexity of the diffusion model, it is difficult to fit it with ordinary software. Only ordinary linear diffusion models can be used for analysis, and an overall fit of the entire diffusion process cannot be achieved. As a result, information such as carrier lifetime can only be roughly assessed. The lack of an accurate fitting algorithm means that the laws of carrier diffusion cannot be fully revealed. Therefore, it is impossible to uncover the black box of the manufacturing process from a mechanistic perspective, and thus it is impossible to provide a processing optimization strategy. Summary of the Invention

[0005] To address the technical problem of low carrier diffusion fitting accuracy in the prior art, the present invention primarily aims to provide a carrier diffusion prediction method and system based on high-temporal-resolution imaging. These methods acquire measured carrier diffusion data, construct a Gaussian diffusion model based on the measured data, and establish a carrier diffusion model based on the Gaussian diffusion model. Furthermore, based on the measured data and the carrier diffusion model, the diffusion coefficient, lifetime, and diffusion distance of the carrier diffusion are predicted using a nonlinear least squares method and Gaussian fitting. The predicted diffusion coefficient, lifetime, and diffusion distance of the carrier diffusion can be used to optimize high-temporal-resolution imaging systems and improve femtosecond laser processing results.

[0006] In order to achieve the above objectives, the embodiments of the present invention provide the following technical solutions:

[0007] The present invention discloses a method for predicting carrier diffusion based on high temporal and spatial resolution imaging, comprising the following steps:

[0008] Acquiring measured data of carrier diffusion, wherein the measured data includes at least delay time information of the pump light and the probe light, scanning position information of the probe light, and intensity information of the differential signal;

[0009] Constructing a Gaussian diffusion model based on the measured data, and establishing a carrier diffusion model based on the Gaussian diffusion model;

[0010] According to the measured data and the carrier diffusion model, the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion are predicted based on a nonlinear least squares method and a Gaussian fitting method.

[0011] Furthermore, the carrier diffusion prediction method based on high spatiotemporal resolution imaging also includes obtaining the wavelength, frequency, laser pulse width, and initial spot size of the pump light and the probe light; and obtaining the scanning galvanometer step length and the number of scanning points.

[0012] Furthermore, a carrier diffusion model is established based on the Gaussian diffusion model, and the implementation method is as follows:

[0013] establishing a diffusion coordinate system based on the measured data of the carrier diffusion;

[0014] Based on the diffusion coordinate system, the following carrier diffusion model is established:

[0015]

[0016] Among them, u i (x, t) is the diffusion characteristic in time and space, t is the carrier diffusion time, x is the carrier spatial coordinate, n is the carrier diffusion space dimension, A i is the carrier diffusion coefficient, D i is the carrier diffusion rate, τ iis the carrier lifetime, σ 0i is the width of the initial Gaussian distribution of carriers.

[0017] Furthermore, according to the measured data and the carrier diffusion model, the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion are predicted based on a nonlinear least squares method and a Gaussian fitting method, and the implementation method includes:

[0018] Establishing a total data set from the collected carrier diffusion data, and extracting a preset proportion of data from the total data set as an input set;

[0019] The parameters to be solved in the carrier diffusion model are calculated based on the input set and the nonlinear least square method, and the parameter solution value and error of each parameter to be solved are obtained.

[0020] Furthermore, the carrier diffusion prediction method based on high temporal and spatial resolution imaging further includes:

[0021] The carrier spatial distribution data of the input set is fed into the carrier diffusion model.

[0022] Enter the values ​​of the constants and the initial values ​​of the variables to facilitate iterative fitting.

[0023] Enter ranges for each variable to speed up iteration.

[0024] The specific implementation method of the fitting process is as follows:

[0025] The overall carrier diffusion is obtained according to the following formula:

[0026] U=∑u i (x,t)

[0027] Normalize the total carrier diffusion at each moment separately;

[0028] A one-dimensional Gaussian fitting is performed on the normalized total carrier diffusion at each moment to obtain the Gaussian distribution at each moment.

[0029] The unknowns in the carrier diffusion model are solved based on the nonlinear least squares method, wherein the A obtained by the solution is i ,D i ,τ i ,σ 0i Set it as a constant value or the variable to be fitted as needed.

[0030] The parameter results and errors obtained by fitting are output through xlsx files for subsequent processing.

[0031] The present invention also discloses a carrier diffusion prediction system based on high temporal and spatial resolution imaging, which is used to implement the carrier diffusion prediction method based on high temporal and spatial resolution imaging. The system includes:

[0032] A measured data acquisition unit, configured to acquire measured data of carrier diffusion, wherein the measured data includes at least delay time information of the pump light and the probe light, scanning position information of the probe light, and intensity information of the differential signal;

[0033] a diffusion model creation unit, configured to construct a Gaussian diffusion model based on the measured data, and fit a carrier diffusion model based on the Gaussian diffusion model;

[0034] The carrier diffusion fitting result acquisition unit is used to predict the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion based on the measured data and the carrier diffusion model and based on the nonlinear least square method and Gaussian fitting method.

[0035] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the program.

[0036] Beneficial effects:

[0037] 1. The present invention discloses a method and system for predicting carrier diffusion based on high spatiotemporal resolution imaging, which obtains measured data of carrier diffusion; constructs a Gaussian diffusion model based on the measured data, and establishes a carrier diffusion model based on the Gaussian diffusion model; and based on the measured data and the carrier diffusion model, quickly and accurately predicts information such as the diffusion coefficient, lifetime, and diffusion distance of carrier diffusion based on a nonlinear least squares method and a Gaussian fitting method.

[0038] 2. The present invention discloses a carrier diffusion prediction method and system based on high-temporal-space resolution imaging. The ultra-high spatial resolution (20nm) and ultra-fast time resolution (150fs) of high-temporal-space resolution imaging can ensure the accuracy of carrier diffusion measurement, and combine the diffusion model to obtain the diffusion coefficient, lifetime and diffusion distance of carrier diffusion. It can not only quickly fit the carrier diffusion curve according to the collected values, improve the efficiency of carrier diffusion law analysis, but also improve the accuracy and efficiency of carrier diffusion coefficient, lifetime and diffusion distance prediction.

[0039] 3. The present invention discloses a carrier diffusion prediction method and system based on high-space-time resolution imaging. On the basis of achieving the above-mentioned beneficial effects 1 and 2, it can solve the problem in the prior art that information such as carrier lifetime can only be roughly evaluated and the lack of accurate fitting algorithms leads to the inability to thoroughly reveal the carrier diffusion law. The predicted diffusion coefficient, lifetime and diffusion distance of carrier diffusion can provide important support for femtosecond laser processing, and then optimize the high-space-time resolution imaging system, thereby greatly improving the quality, accuracy, consistency, controllability, etc. of femtosecond laser processing and expanding the ultimate manufacturing capabilities of femtosecond laser processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.

[0041] The structures, proportions, sizes, etc. illustrated in this specification are intended only to complement the contents disclosed herein and to facilitate understanding and reading by persons familiar with the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, without affecting the efficacy and objectives of the present invention, shall still fall within the scope of the technical contents disclosed herein.

[0042] Figure 1 This is a flow chart of a carrier diffusion prediction method based on high temporal and spatial resolution imaging of the present invention;

[0043] Figure 2 This is a carrier diffusion fitting diagram for a scenario;

[0044] Figure 3 This is a structural block diagram of a specific implementation of the diffusion model fitting system based on high spatiotemporal resolution imaging provided by the present invention. DETAILED DESCRIPTION

[0045] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0046] Ultrafast laser micro-nanofabrication is a focal point and a cutting-edge area of ​​international competition. The shape and properties of femtosecond "light knives" are precisely controllable, enabling multi-scale, selective, non-contact, non-thermal, high-precision, and high-quality processing of any solid material. During femtosecond laser fabrication, the dynamic distribution and changes of electrons determine both the fabrication process and the outcome. Therefore, local, instantaneous observation and control of the electrons are crucial. Femtosecond laser transient absorption microscopy observation systems achieve both femtosecond temporal resolution and nanometer-scale spatial measurement accuracy, enabling direct imaging of processes such as carrier transport, charge transfer, and energy transfer, revealing the mechanisms of photon-material interactions. However, understanding the spatial diffusion of carriers requires a scientific model to analyze key parameters such as carrier lifetime and diffusion distance. Due to the complexity of diffusion models, these models are difficult to fit using standard software. Consequently, conventional linear diffusion models can only be used for analysis, failing to fully capture the entire diffusion process. This results in only a rough estimate of information such as carrier lifetime. The lack of precise fitting algorithms hinders the complete understanding of carrier diffusion patterns.

[0047] like Figure 1 As shown, this embodiment discloses a method for predicting carrier diffusion based on high spatiotemporal resolution imaging, and the specific implementation steps are as follows:

[0048] S1: obtain the measured data of carrier diffusion, the measured data includes at least the delay time information of the pump light and the probe light, the scanning position information of the probe light, and the intensity information of the differential signal.

[0049] In a specific usage scenario, the necessary data required for high spatiotemporal resolution imaging measurement in step S1 include the wavelength, frequency, laser pulse width, initial spot size, scanning galvanometer step length, and number of scanning points of the pump light and probe light.

[0050] S2: The carrier diffusion measured by high spatiotemporal resolution imaging is a superposition of multiple component diffusions. A Gaussian diffusion model is constructed based on the measured data, and a carrier diffusion model is established based on the Gaussian diffusion model.

[0051] A diffusion coordinate system is established based on the measured data of the carrier diffusion. In a specific usage scenario, such as Figure 2 As shown, a diffusion coordinate system is established based on the data of the high temporal and spatial resolution imaging measurement, with the selected initial carrier distribution as the coordinate origin, the delay time as the X-axis, and the Gaussian distribution width σ at different times 2 After the coordinate system is established, the following carrier diffusion model is established based on the diffusion coordinate system:

[0052]

[0053] Among them, u i(x, t) is the diffusion characteristic in time and space, t is the carrier diffusion time, x is the carrier spatial coordinate, n is the carrier diffusion space dimension, A i is the carrier diffusion coefficient, D i is the carrier diffusion rate, τ i is the carrier lifetime, σ 0i is the width of the initial Gaussian distribution of carriers.

[0054] S3: Predicting the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion according to the measured data and the carrier diffusion model, and based on a nonlinear least squares method and a Gaussian fitting method.

[0055] Wherein, step S3 specifically includes:

[0056] S31: establishing a total data set from the collected carrier diffusion data, and extracting all data in the total data set as an input set;

[0057] S32: Calculating the parameters to be solved in the carrier diffusion model based on the input set and the nonlinear least squares method, and obtaining parameter solution values ​​and errors of each parameter to be solved.

[0058] Wherein, step S32 specifically includes:

[0059] The carrier spatial distribution data of the input set is fed into the carrier diffusion model.

[0060] Enter the values ​​of the constants and the initial values ​​of the variables to facilitate iterative fitting.

[0061] Enter ranges for each variable to speed up iteration.

[0062] The fitting process is as follows:

[0063] The overall carrier diffusion is obtained according to the following formula:

[0064] U=∑u i (x,t)

[0065] Normalize the total carrier diffusion at each moment separately;

[0066] A one-dimensional Gaussian fitting is performed on the normalized total carrier diffusion at each moment to obtain the Gaussian distribution at each moment.

[0067] The unknowns in the carrier diffusion model are solved based on the nonlinear least squares method, wherein the A obtained by the solution is i ,D i ,τ i ,σ 0iIt can be set as a fixed value or a variable to be fitted as needed.

[0068] The parameter results and errors obtained by fitting are output through xlsx files for subsequent processing.

[0069] In order to verify the accuracy of the calculation, in some embodiments, the method further includes:

[0070] Extracting a data set other than the input set from the total data set as a validation set;

[0071] The accuracy of the calculated carrier diffusion prediction results is evaluated based on the validation set.

[0072] Specifically, the observation data in S31 are repeated under the same conditions as a validation set to evaluate the accuracy of the parameters solved in step S3.

[0073] In addition to the above method, the present invention also provides a diffusion model fitting system based on high temporal and spatial resolution imaging, such as Figure 3 As shown, the system includes:

[0074] A measured data acquisition unit 100 is used to acquire measured data of carrier diffusion, wherein the measured data includes at least delay time information of the pump light and the probe light, scanning position information of the probe light, and intensity information of the differential signal;

[0075] A diffusion model creation unit 200 is used to fit a carrier diffusion model based on a Gaussian diffusion model;

[0076] The carrier diffusion fitting result acquisition unit 300 is used to calculate the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion according to the measured data and the carrier diffusion model based on a nonlinear least square method and a Gaussian fitting method.

[0077] The fitting result is: D1 = 1106.18 cm 2 / s,D2=13.34cm 2 / s, the diffusion lifetime of the electron subsystem τ1 = 0.28 ps, the diffusion lifetime of the lattice subsystem τ2 = 53653 ps, the standard deviation of the initial distribution of the electron subsystem σ0 = 653.79 nm, and the standard deviation of the initial distribution of the lattice subsystem σ1 = 1019.85 nm. The obtained lifetimes of the electron and lattice subsystems are close to those obtained using the pump-probe method in the literature (100–400 fs for the electron subsystem and >1 ns for the lattice subsystem), confirming the reliability of our experimental results.

[0078] In the above-mentioned specific embodiments, a carrier diffusion prediction method based on high spatiotemporal resolution imaging disclosed in this embodiment can quickly and accurately obtain information such as the diffusion coefficient, lifetime and diffusion distance of carrier diffusion. The ultra-high spatial resolution (20nm) and ultra-fast time resolution (150fs) of high spatiotemporal resolution imaging can ensure the accuracy of carrier diffusion measurement. Combined with the diffusion model, the diffusion coefficient, lifetime and diffusion distance of carrier diffusion are obtained. Not only can the carrier diffusion curve be quickly fitted according to the collected values, thereby improving the efficiency of analyzing the carrier diffusion law, but also more accurate carrier diffusion coefficient, lifetime and diffusion distance can be obtained, solving the problem in the prior art that information such as carrier lifetime can only be roughly evaluated and the lack of accurate fitting algorithm leads to the inability to thoroughly reveal the carrier diffusion law. Directly track and detect hot electrons in the material system after femtosecond laser action, study the energy transfer process within the photoexcited electronic system in the material and the heat transfer process between the electronic system and other systems, reveal the coupling mechanism and heat transfer characteristics of hot electrons and other systems, achieve nanoscale spatial resolution and femtosecond temporal resolution to observe and control electronic dynamics, open the "black box" of ultrafast laser manufacturing, and master new closed-loop intelligent manufacturing methods for electronic-level control. Reveal from the source the mechanism of ultrafast laser control of the physical and chemical properties of materials in the initial stage of manufacturing and the regulation of subsequent processing processes (phase change and forming properties), thereby significantly improving the quality, precision, consistency, controllability, etc. of femtosecond laser processing and expanding the ultimate manufacturing capabilities.

[0079] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for carrier diffusion prediction based on high temporal and spatial resolution imaging, characterized by: The steps include: Acquiring measured data of carrier diffusion, wherein the measured data includes at least delay time information of the pump light and the probe light, scanning position information of the probe light, and intensity information of the differential signal; Constructing a Gaussian diffusion model based on the measured data, and establishing a carrier diffusion model based on the Gaussian diffusion model; According to the measured data and the carrier diffusion model, the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion are predicted based on a nonlinear least squares method and a Gaussian fitting method; It also includes obtaining the wavelength, frequency, laser pulse width, and initial spot size of the pump light and probe light; obtaining the scanning galvanometer step length and number of scanning points; The carrier diffusion model is established based on the Gaussian diffusion model. The implementation method is: establishing a diffusion coordinate system based on the measured data of the carrier diffusion; Based on the diffusion coordinate system, the following carrier diffusion model is established: Among them, u i (x, t) is the diffusion characteristic in time and space, t is the carrier diffusion time, x is the carrier spatial coordinate, n is the carrier diffusion space dimension, A i is the carrier diffusion coefficient, D i is the carrier diffusion rate, τ i is the carrier lifetime, σ 0i is the width of the initial Gaussian distribution of carriers.

2. The method for carrier diffusion prediction based on high temporal and spatial resolution imaging according to claim 1, characterized in that: According to the measured data and the carrier diffusion model, and based on the nonlinear least squares method and Gaussian fitting method, the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion are predicted, and the implementation method includes: Establishing a total data set from the collected carrier diffusion data, and extracting a preset proportion of data from the total data set as an input set; The parameters to be solved in the carrier diffusion model are calculated based on the input set and the nonlinear least square method, and the parameter solution value and error of each parameter to be solved are obtained.

3. The method for carrier diffusion prediction based on high spatiotemporal resolution imaging according to claim 2, characterized in that: Also includes, Substituting the carrier spatial distribution data of the input set into the carrier diffusion model; Input A i ,D i ,τ i ,σ 0i The initial value of , which is convenient for iterative fitting; Input A i ,D i ,τ i ,σ 0i scope, speeding up iteration; The specific implementation method of the fitting process is as follows: The overall carrier diffusion is obtained according to the following formula: U=∑u i (x,t) Normalize the total carrier diffusion at each moment separately; Perform one-dimensional Gaussian fitting on the normalized total carrier diffusion at each moment to obtain the Gaussian distribution at each moment; Based on the nonlinear least squares method, the A i ,D i ,τ i ,σ 0i Solve, where the solved A i ,D i ,τ i ,σ 0i Set as a fixed value or variable to be fitted as needed; The parameter results and errors obtained by fitting are output through xlsx files for subsequent processing.

4. A carrier diffusion prediction system based on high temporal and spatial resolution imaging, for implementing a carrier diffusion prediction method based on high temporal and spatial resolution imaging as claimed in claim 1, 2 or 3, characterized in that: It includes a measured data acquisition unit, a diffusion model creation unit, and a carrier diffusion fitting result acquisition unit; A measured data acquisition unit, configured to acquire measured data of carrier diffusion, wherein the measured data includes at least delay time information of the pump light and the probe light, scanning position information of the probe light, and intensity information of the differential signal; a diffusion model creation unit, configured to construct a Gaussian diffusion model based on the measured data, and fit a carrier diffusion model based on the Gaussian diffusion model; The carrier diffusion fitting result acquisition unit is used to predict the diffusion coefficient, lifetime and diffusion distance of the carrier diffusion based on the measured data and the carrier diffusion model and based on the nonlinear least square method and Gaussian fitting method.

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: A program for executing a method for predicting carrier diffusion based on high temporal and spatial resolution imaging as claimed in claim 1, 2 or 3.

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