DLCP data analysis method and system based on mathematical modeling and human-computer interaction visualization

Abstract

The present application relates to the technical field of defect state characterization of optoelectronic devices, and in particular to a DLCP data analysis method and system based on mathematical modeling and human-computer interactive visualization. The method comprises generating a sample data set sorted by depth; generating a depth-concentration sample curve, constructing corresponding mathematical model libraries for the left half, right half, and middle transition portion of the sample curve, respectively, and completing the parameter determination and fitting of the segmented models based on a random consistency sampling method and an adaptive fitting strategy; weightedly splicing the segmented models fitted to the left half, right half, and middle transition portion of the curve through weighted fusion to generate a complete fitting model; and constructing a multi-frequency DLCP data analysis and interactive three-dimensional visualization platform based on the complete fitting model. The present application effectively overcomes the uncertainty caused by depth mismatch and curve perturbation in traditional differential analysis, and improves the accuracy of defect state density extraction and data processing efficiency.

Description

Technical Field

[0001] The present application relates to the technical field of defect state characterization of optoelectronic devices, and in particular to a DLCP data analysis method and system based on mathematical modeling and human-computer interaction visualization. Background Art

[0002] With the rapid development of optoelectronic technology, various optoelectronic materials and devices (such as perovskite solar cells, silicon-based optoelectronic devices, organic photovoltaic devices, etc.) have made significant progress in energy conversion efficiency and device stability. However, in the development and performance optimization of these devices, accurate characterization of defect state distribution has always been one of the key factors affecting device efficiency and lifespan. As an effective means of achieving depth-resolved defect state profile detection within semiconductor materials and devices, DLCP has been widely used in photovoltaic cells, thin-film transistors and other fields in recent years. This technology measures the capacitance change of the device under different frequencies, different AC voltage excitations and DC bias conditions, and then inverts the carrier concentration and trap state distribution in the depth direction, providing important support for in-depth research on the defect properties within optoelectronic materials and devices.

[0003] Currently, DLCP testing typically generates large amounts of data, covering multiple voltages, voltage sweep directions, frequencies, and AC excitation voltage conditions. Data processing often suffers from high noise, low fitting accuracy, and strong subjectivity, making it difficult to efficiently and accurately extract effective defect state information. Traditional methods typically calculate the depth-carrier concentration relationship based on CV curves at different frequencies, then obtain the defect state density by directly interpolating the data points. However, this method has two major drawbacks: First, the depth points extracted at different frequencies are not completely consistent, making it difficult to achieve accurate comparison at the same spatial location, resulting in depth mismatch errors in defect state extraction; second, the nonlinearity and noise interference of the CV curve easily introduce localized anomalous fluctuations, affecting the stability and physical interpretation of the defect state density curve. Therefore, when processing large-scale data at multiple frequencies, existing DLCP methods struggle to stably reconstruct concentration curves and accurately extract defect state density in a unified depth coordinate system, limiting both the accuracy and efficiency of data analysis. Summary of the Invention

[0004] This application provides a DLCP data analysis method and system based on mathematical modeling and human-computer interaction visualization, which effectively overcomes the uncertainty caused by depth mismatch and curve perturbation in traditional differential analysis, and significantly improves the accuracy of defect state density extraction and data processing efficiency. This application provides the following technical solutions:

[0005] In a first aspect, the present application provides a DLCP data analysis method based on mathematical modeling and human-computer interaction visualization, the method comprising:

[0006] Obtain the output data of the DLCP experiment, invert the data pairs of depth and corresponding carrier concentration, and generate a sample data set sorted by depth;

[0007] A depth-concentration sample curve is generated based on the sample data set. Corresponding mathematical model libraries are constructed for the left half, right half, and middle transition part of the depth-concentration sample curve. The parameters of the segmented model are determined and fitted based on the random consistency sampling method and adaptive fitting strategy.

[0008] The segmented models fitted on the left half, right half and middle transition part of the depth-concentration sample curve are weightedly spliced ​​by weighted fusion to generate a complete fitting model;

[0009] A multi-frequency DLCP data analysis and interactive three-dimensional visualization platform was constructed based on a complete fitting model of the depth-concentration sample curve.

[0010] In a specific possible implementation scheme, generating a depth-concentration sample curve based on a sample data set, constructing corresponding mathematical model libraries for the left half, right half, and middle transition portion of the depth-concentration sample curve, and completing parameter determination and fitting of the segmented model based on a random consistency sampling method and an adaptive fitting strategy include:

[0011] Generate depth-concentration sample curves based on a sample data set sorted by depth; each sample data is represented as a set of binary value pairs (x, y), where x represents the normalized depth and y represents the logarithmic transformed carrier concentration;

[0012] The first segment model library, the second segment model library and the third segment model library are constructed corresponding to the left half, the right half and the middle transition part of the depth-concentration sample curve respectively;

[0013] For the left and right halves of the depth-concentration sample curve, the first and second model libraries are called respectively, and the optimal model parameters are determined based on the random consistency sampling method to generate a fitting model;

[0014] For the middle transition part of the depth-concentration sample curve, the third segment model library is called, and the optimal model parameters are determined based on the adaptive fitting method to generate a fitting model.

[0015] In a specific embodiment, the first segment model library includes a logarithmic function model 1, a skewed normal distribution model 2, and a logarithmic normal distribution model 3; the second segment model library includes a logarithmic function model 4, a skewed normal distribution model 5, and a logarithmic normal distribution model 6;

[0016] Logarithmic function model 1 is: ;

[0017] in, 、 、 are all parameters of the logarithmic function model 1 to be solved;

[0018] The skewed normal distribution model 2 is: ;

[0019] in, 、 、 are the parameters of the skewed normal distribution model 2 to be solved;

[0020] Lognormal distribution model 3 is: ;

[0021] in, 、 are the parameters of the lognormal distribution model 3 to be solved;

[0022] Logarithmic function model 4 is: ;

[0023] in, 、 、 are all parameters of the logarithmic function model 4 to be solved;

[0024] The skewed normal distribution model 5 is: ;

[0025] in, 、 、 are the parameters of the skewed normal distribution model 5 to be solved;

[0026] The lognormal distribution model 6 is: ;

[0027] in, 、 are the parameters of the lognormal distribution model 6 to be solved.

[0028] In a specific embodiment, for the left half and the right half of the depth-concentration sample curve, respectively calling the first segment model library and the second segment model library, determining the optimal model parameters based on the random consistency sampling method and generating the fitting model includes:

[0029] Call the pre-built first and second segment model libraries. For the left half of the depth-concentration curve, select the fitting sample subset according to the sample set index range [1:i]. For the right half of the depth-concentration curve, select the fitting sample subset in the index range [ni:n], where n represents the total number of samples in the entire depth-concentration sample curve.

[0030] For each mathematical model in the model library, the following parameter fitting process is performed: the maximum number of iterations K and the initial optimal mean square error RMSE_best are set. In each iteration j, a fixed number of sample points are randomly selected from the fitting sample subset to obtain the current parameter combination param(j). The corresponding mean square error RMSE(j) is calculated based on the current parameter combination param(j). If the mean square error RMSE(j) is less than the initial optimal mean square error RMSE_best, the current parameter combination param(j) is updated to the optimal model parameter, and the iteration is repeated until the maximum number of iterations K is reached.

[0031] After completing all iterations, the optimal parameter combination and its fitting error under the current mathematical model are obtained, and the next mathematical model in the model library is traversed, and the parameter fitting process is repeated. Among all the combinations of mathematical models and optimal parameter combinations, the group with the smallest mean square error is selected as the optimal mathematical model and its optimal model parameters for this part of the curve.

[0032] In a specific embodiment, the third segment model library includes an exponential model 7 and a polynomial function model 8, and the exponential model 7 is: ;

[0033] in, 、 、 are the parameters of the exponential model 7 to be solved;

[0034] The polynomial function model 8 is: ;

[0035] in, 、 are all parameters of the polynomial function model 8 to be solved.

[0036] In a specific embodiment, for the intermediate transition portion of the depth-concentration sample curve, calling the third segment model library, determining the optimal model parameters based on the adaptive fitting method and generating the fitting model includes:

[0037] Based on the boundary information of the left and right halves that have been fitted, let the right boundary sample index of the left half be p and the left boundary sample index of the right half be q. The theoretical boundary interval of the middle transition segment is determined to be the index interval [p,q]. The sample set for the middle segment fitting is constructed by extending the index p to the left by r sample points and the index q to the right by r sample points. The index range is extended to [pr,q+r].

[0038] Traverse the mathematical models in the third section of the model library and perform the following adaptive fitting process in sequence: set the maximum number of iterations K and the initial optimal mean square error RMSE_best. In each iteration j, randomly select m groups of sample points from the expanded fitting sample set as the current training subset, use the selected model to perform parameter fitting, and obtain the current parameter combination param(j). Based on the current parameter combination param(j), calculate the corresponding mean square error RMSE(j). If the mean square error RMSE(j) is less than the initial optimal mean square error RMSE_best, update the current parameter combination param(j) to the optimal model parameters, and repeat the iteration until the maximum number of iterations K is reached;

[0039] After completing all iterations, the optimal parameter combination and fitting error under the current mathematical model are obtained; continue to traverse the next mathematical model in the third segment model library and repeat the parameter fitting process. Among all the combinations of mathematical models and optimal parameter combinations, the one with the smallest mean square error is selected as the candidate optimal model and optimal model parameters for the middle segment;

[0040] The mean square error of the candidate optimal model is compared with the preset threshold. If it is less than the preset threshold, the candidate optimal model is determined as the optimal mathematical model of the intermediate transition section; if it is greater than or equal to the preset threshold, the fitting process is repeated until the mean square error is less than the preset threshold.

[0041] In a specific embodiment, the weighted fusion method is used to perform weighted splicing on the segmented models fitted on the left half, the right half, and the middle transition part of the depth-concentration sample curve to generate a complete fitting model, including:

[0042] A transition region is defined between the left half and the middle part, and between the middle part and the right half. For each transition region, the Bayesian information criterion is used. The fitting quality of the two models in the transition region is measured. The specific calculation formula is as follows:

[0043] ;

[0044] in, is the number of parameters of the fitting model, n represents the number of samples in the current transition region, Indicates the maximum likelihood value corresponding to the model; the calculation formula of the maximum likelihood value is as follows:

[0045] ;

[0046] in, Indicates the The observed value of the sample, Indicates the The predicted value of the sample, Represents the standard deviation between the observed values ​​of all sample points and the model predicted values, For all The average value of the BIC value of different models is used to perform normalization operations to calculate the weight coefficient of each model. The solution formula for the weight coefficient is:

[0047] ;

[0048] in, Indicates the The weight of each model in the spliced ​​region, is the number of models involved in the splicing; within the splicing area, based on the output values ​​of the two fitting models and their weight coefficients, the fitting results of each sample point are weighted summed to generate a splicing fitting segment;

[0049] Repeat the processing of the two splicing areas on the left and right, and splice the three segmented models by splicing the fitting segments to generate a complete fitting model.

[0050] In a second aspect, the present application provides a DLCP data analysis system based on mathematical modeling and human-computer interaction visualization, which adopts the following technical solutions:

[0051] A DLCP data analysis system based on mathematical modeling and human-computer interaction visualization, including:

[0052] The data acquisition module is used to obtain the output data of the DLCP experiment, invert the data pairs of depth and corresponding carrier concentration, and generate a sample data set sorted by depth;

[0053] The segmented fitting module is used to generate a depth-concentration sample curve based on the sample data set. The corresponding mathematical model library is constructed for the left half, right half, and middle transition part of the depth-concentration sample curve, and the parameters of the segmented model are determined and fitted based on the random consistency sampling method and adaptive fitting strategy.

[0054] The weighted splicing module is used to perform weighted splicing on the segmented models fitted on the left half, right half and middle transition part of the depth-concentration sample curve by weighted fusion to generate a complete fitting model;

[0055] The visualization interaction module is used to build a multi-frequency DLCP data analysis and interactive 3D visualization platform based on the complete fitting model of the depth-concentration sample curve.

[0056] In a third aspect, the present application provides an electronic device comprising a processor and a memory; the memory stores a program, which is loaded and executed by the processor to implement a DLCP data analysis method based on mathematical modeling and human-computer interaction visualization as described in the first aspect.

[0057] In a fourth aspect, the present application provides a computer-readable storage medium storing a program, which, when executed by a processor, is used to implement a DLCP data analysis method based on mathematical modeling and human-computer interaction visualization as described in the first aspect.

[0058] In summary, the beneficial effects of this application include at least:

[0059] (1) This application proposes a segmented fitting method based on a model library to address the differences in morphological characteristics of depth-concentration sample curves in different regions. Specifically, corresponding mathematical model libraries are preset for the left, middle, and right segments. Each model library covers a variety of typical function forms. Random consistency sampling and error assessment mechanisms are used to select the optimal model from the corresponding library to match the local trend of the current sample interval, thereby achieving high-precision regional fitting and significantly improving the global adaptability and physical interpretation ability of the model.

[0060] (2) To achieve continuous splicing between segmented models, this application introduces a symmetrically constructed transition region between each two adjacent model segments, and evaluates the fitting quality of the two models to be spliced ​​within this region. Specifically, the Bayesian information criterion is used to measure the performance of each model in the transition region, and then its normalized weight is calculated. The output of the two models is weightedly fused based on the weight to generate a smooth transition curve. This method avoids the problems of mutation or fault in traditional splicing methods, ensuring that the final fitting results have good continuity and consistency at both the function value and derivative levels.

[0061] A complete fitting model is constructed by combining segmented fitting with weighted splicing for depth-carrier concentration sample data. This fitting model generates local optimal fitting models in the left half, right half and middle transition region of the sample curve respectively, and achieves a natural and seamless connection between the segmented models based on weighted fusion based on the Bayesian information criterion. Based on the complete fitting model, it is possible to perform unified interpolation and reconstruction on DLCP data of different frequencies in a unified depth coordinate system, and accurately obtain the carrier concentration value corresponding to any depth point, thereby effectively avoiding the spatial mismatch error caused by inconsistent depth points extracted at different frequencies in traditional methods. At the same time, the smoothness and robustness of the complete fitting model greatly suppress the local abnormal fluctuations introduced by the nonlinearity and noise of the CV curve, and significantly improve the stability of the carrier concentration curve and the rationality of the physical interpretation.

[0062] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application and to implement it in accordance with the contents of the specification, the following is a detailed description of the preferred embodiments of the present application in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 4 is a flow chart of a DLCP data analysis method based on mathematical modeling and human-computer interaction visualization in an embodiment of the present application.

[0064] Figure 2 FIG. 4 is a schematic diagram of the distribution of DLCP output data in an embodiment of the present application.

[0065] Figure 3 It is a flowchart of step S1023 in the embodiment of the present application.

[0066] Figure 4 It is a flowchart of step S1024 in the embodiment of the present application.

[0067] Figure 5 It is a schematic diagram of the use case of the carrier concentration fitting curve in the embodiment of the present application.

[0068] Figure 6 3 is a space-energy mapping diagram of the trap state density achieved by DLCP measurement in an embodiment of the present application.

[0069] Figure 7 This is a comparison chart of the DLCP defect state density extraction method based on frequency difference and mathematical modeling in the embodiments of the present application.

[0070] Figure 8 It is a structural block diagram of the DLCP data analysis system based on mathematical modeling and human-computer interaction visualization in an embodiment of the present application.

[0071] Figure 9It is a block diagram of an electronic device for DLCP data analysis based on mathematical modeling and human-computer interaction visualization in an embodiment of the present application. DETAILED DESCRIPTION

[0072] The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0073] Optionally, the present application uses the DLCP data analysis method based on mathematical modeling and human-computer interaction visualization provided in each embodiment as an example for explanation in an electronic device, where the electronic device is a terminal or a server. The terminal can be a computer, a tablet computer, etc. This embodiment does not limit the type of electronic device.

[0074] Reference Figure 1 , is a flow chart of a DLCP data analysis method based on mathematical modeling and human-computer interaction visualization provided by an embodiment of the present application, which method includes at least the following steps:

[0075] Step S101: Obtain output data of a DLCP experiment, invert to obtain data pairs of depth and corresponding carrier concentration, and generate a sample data set sorted by depth.

[0076] In step S101, the output data of the DLCP experiment is first obtained. The output data of the DLCP experiment in this application is a plurality of sets of capacitance-bias curve data collected in the test frequency range of 1kHz to 500kHz, the AC excitation voltage amplitude of 20mV to 200mV, and the bias interval of 0 to 1.2V. Based on the capacitance-bias curve data output by the DLCP experiment, the nonlinear relationship curve between capacitance and bias is used. The polynomial model form of is the measured capacitance of the device under specific bias and excitation conditions, is the zero-order coefficient of capacitance to bias voltage in the fitting expression, is the first-order nonlinear response of the capacitor to the bias voltage, is the second-order nonlinear response, It represents the differential change of the charge accumulated in the device under the action of the electric field. Represents a small voltage change applied across the device. Fit each set of data and use fitting methods such as least squares or maximum likelihood estimation under ideal conditions to extract the corresponding bias points. and parameter.

[0077] Furthermore, based on the extracted and Parameters, use the following formula to calculate the equivalent depth corresponding to each set of measurement data and carrier concentration :

[0078] ; ;

[0079] in, is the unit charge, is the dielectric constant of the material, is the effective junction area; the above calculation methods are all existing technologies and will not be described in detail here.

[0080] The data calculated at each frequency point and each bias condition are compared After unified collection, the depth data is normalized, and the calculation formula for normalized depth is as follows:

[0081] ;

[0082] in, represents the original depth, and Denote the minimum and maximum values ​​in the sample, respectively. All carrier concentration data are then logarithmically transformed to reduce the order of magnitude span. Finally, the normalized depths are mapped one-to-one to the transformed concentration values, and the data pairs are sorted in ascending order of normalized depth to construct the final depth-concentration sample dataset.

[0083] Step S102: Generate a depth-concentration sample curve based on the sample data set, construct corresponding mathematical model libraries for the left half, right half, and middle transition part of the depth-concentration sample curve, and complete the parameter determination and fitting of the segmented model based on the random consistency sampling method and adaptive fitting strategy.

[0084] Step 102 includes at least the following sub-steps:

[0085] Step S1021 : generating a depth-concentration sample curve based on the sample data set sorted by depth.

[0086] In step S1021, a depth-concentration sample dataset is obtained, sorted from smallest to largest by normalized depth. Each sample data point is represented as a set of binary value pairs (x, y), where the variable x represents the normalized depth and the variable y represents the logarithmically transformed carrier concentration. To achieve continuous modeling of the sample numerical structure, this dataset must be further converted into a depth-concentration sample curve suitable for fitting.

[0087] Specifically, the sorted data set can be viewed as a set of discrete sampling points, and based on their monotonicity on the horizontal axis (normalized depth), a curve expression with local continuous characteristics is formed. In this process, the curve is not directly defined by a function expression, but is formed as a fitting input basis in the form of a discrete point sequence. For example, refer to Figure 2 Figure 2 shows the distribution of measured carrier concentration data at different frequencies. The blue curve represents the depth-to-carrier concentration data for a conductive material at a frequency of 10 kHz, while the red curve represents the corresponding measurement data at a frequency of 500 kHz. It can be observed that the concentration curves corresponding to different frequencies exhibit significant misalignment and fluctuation in the depth dimension.

[0088] Step S1022 : constructing a first segment model library, a second segment model library, and a third segment model library corresponding to the left half, the right half, and the middle transition part of the depth-concentration sample curve, respectively.

[0089] In step S1022, to characterize the depth-dependent carrier concentration in the DLCP experiment, three model libraries are constructed, corresponding to the left half, right half, and middle transition portion of the concentration curve. Each model library consists of several basic mathematical models, each used to fit the local numerical characteristics within different depth ranges.

[0090] First, the first segment model library is constructed for the left half of the depth-concentration sample curve. The first segment model library includes logarithmic function model 1, skewed normal distribution model 2, and logarithmic normal distribution model 3. Logarithmic function model 1 is: ;

[0091] in, 、 、 are all parameters of the logarithmic function model 1 to be solved;

[0092] The skewed normal distribution model 2 is: ;

[0093] in, 、 、 are the parameters of the skewed normal distribution model 2 to be solved;

[0094] Lognormal distribution model 3 is: ;

[0095] in, 、 are the parameters of the lognormal distribution model 3 to be solved.

[0096] Secondly, the second segment model library is constructed for the right half of the depth-concentration sample curve. The second segment model library includes logarithmic function model 4, skewed normal distribution model 5, and logarithmic normal distribution model 6. Logarithmic function model 4 is: ;

[0097] in, 、 、 are all parameters of the logarithmic function model 4 to be solved;

[0098] The skewed normal distribution model 5 is: ;

[0099] in, 、 、 are the parameters of the skewed normal distribution model 5 to be solved;

[0100] The lognormal distribution model 6 is: ;

[0101] in, 、 are the parameters of the lognormal distribution model 6 to be solved.

[0102] In implementation, the logarithmic function model, skewed normal distribution model and lognormal distribution model are selected to form the first and second segment model libraries for the two end regions of the depth-concentration curve. The logarithmic function has the characteristics of rapid initial growth and then gradually flattening, which is suitable for fitting sections with sharp concentration changes near the electrode or in defect-rich areas. The skewed normal distribution model introduces a skew parameter, which can accurately fit local asymmetric peaks by controlling the tilt direction and symmetry of the curve, and capture local distortions caused by material heterogeneity. The lognormal distribution model is suitable for describing the phenomenon that certain defect densities or carrier mobilities are positively skewed on a logarithmic scale, and can effectively capture nonlinear slow-changing morphologies caused by microscopic mechanisms. The above three models synergistically cover a variety of change modes such as steep mutations, fluctuating drifts and asymmetric convergence that are common at both ends of the DLCP concentration curve, improving the adaptability and robustness of modeling in boundary areas.

[0103] Finally, the third segment model library is constructed for the intermediate transition portion of the depth-concentration sample curve. The third segment model library includes exponential model 7 and polynomial function model 8. The exponential model 7 is:

[0104] ;

[0105] in, 、 、 are the parameters of the exponential model 7 to be solved;

[0106] The polynomial function model 8 is: ;

[0107] in, 、 are all parameters of the polynomial function model 8 to be solved;

[0108] In implementation, for the middle transition region of the depth-concentration curve, the exponential model and the polynomial function model were selected to construct the third segment model library. The exponential function model is suitable for characterizing the section where the concentration slowly transitions from the boundary state to the bulk material. Its exponential decay or growth characteristics can reflect the physical process of the capacitance response gradually transitioning from the surface drive to the deep layer. The polynomial function model has flexible local fitting capabilities and can accurately capture numerical fluctuations under non-explicit physical laws by setting different orders. It performs particularly well when fitting the area in the middle of the concentration curve with slight fluctuations but no obvious trend. In addition, the polynomial model is often used as a benchmark model to verify the fitting effect and anomaly detection capabilities of other models.

[0109] It should be noted that the reason why this application divides the entire depth-concentration variation curve into the left half, the right half and the middle transition part, and constructs an independent model library for each of them, is that, on the one hand, the carrier concentration extracted by the DLCP experiment shows asymmetry and regional characteristic differences in different depth intervals. For example, near the contact area or impurity-enriched area, the concentration changes are often drastic and show an exponential or logarithmic trend; while in the middle area, it presents a relatively smooth transition band morphology with a certain slope change. Therefore, it is difficult to simultaneously take into account the local feature expression ability and global fitting accuracy of multiple regions by using a single model to uniformly fit the entire curve. On the other hand, segmenting the depth-concentration curve according to regional characteristics and selecting the most adaptable mathematical structure for modeling can improve the expression ability of the fitting model, and also help to optimize the robustness of each segment model through subsequent algorithms, thereby enhancing the ability to eliminate outliers and the reliability of defect feature extraction.

[0110] Step S1023: for the left half and the right half of the depth-concentration sample curve, respectively call the first segment model library and the second segment model library, determine the optimal model parameters based on the random consistency sampling method and generate a fitting model.

[0111] In step S1023, for the left and right halves of the depth-concentration sample curve, the pre-built first-segment model library and second-segment model library are respectively called, and the improved random consensus sampling (RANSAC) method is used to determine the optimal model parameters and generate the corresponding fitting model.

[0112] Specific, combined Figure 3For the left and right parts of the constructed depth-concentration sample curve, the pre-built first and second model libraries are respectively called. For the left half of the depth-concentration curve, the fitting sample subset is selected according to the sample set index range [1:i]. For the right half of the depth-concentration curve, the fitting sample subset is selected according to the index range [ni:n], where n represents the total number of samples in the entire depth-concentration sample curve.

[0113] For each mathematical model in the model library, the following parameter fitting process is performed: the maximum number of iterations K and the initial optimal mean square error RMSE_best are set. In each iteration j (j=0,1,…,K-1), a fixed number of sample points are randomly selected from the fitting sample subset to fit the parameters of the model, and the current parameter combination param(j) is obtained. The corresponding mean square error RMSE(j) is calculated based on the current parameter combination param(j). If the mean square error RMSE(j) is less than the initial optimal mean square error RMSE_best, the current parameter combination param(j) is updated to the optimal model parameters, and the iteration is repeated until the maximum number of iterations K is reached.

[0114] After all iterations are complete, the optimal parameter combination and fitting error for the current mathematical model are obtained. The process continues with the next mathematical model in the model library and repeats the above process. Finally, among all combinations of mathematical models and optimal parameter combinations, the one with the smallest mean square error is selected as the optimal mathematical model and its optimal model parameters for that portion of the curve. The optimal mathematical model and its optimal model parameters are then used to generate the corresponding fitting curve, and the fitting results are displayed using a visualization script.

[0115] It should be noted that although the algorithm adopted in this step is based on the basic idea of ​​the random consistency sampling method, its implementation and application purpose are significantly different from the classic random sampling consistency algorithm in the field of traditional computer vision. The traditional random sampling consistency algorithm is mainly used for the processing of images and video frames. The core purpose is to reduce the amount of calculation through random sampling, while reducing the impact of noise in the signal on model fitting, thereby improving the efficiency and robustness of the algorithm. The method proposed in this step, although it draws on the random sampling idea of ​​random consistency sampling, its focus is not on reducing the computational burden, but on solving the measurement noise problem that is prevalent in material characterization test data. Material test data usually has inevitable noise interference due to factors such as inconsistent measuring point positions, calibration errors of measuring equipment, and different measurement settings. Traditional mathematical modeling methods and optimization algorithms may lead to no solution or serious parameter estimation deviations in the fitting of such noisy data, thereby affecting the accuracy and effectiveness of the model. This application adopts an algorithm framework based on random consistency sampling, repeatedly randomly samples the segmented depth-concentration sample data, and combines multiple fitting calculations. For each fit, the corresponding mean squared error is calculated as an evaluation metric, and the model parameters with the smallest fitting error are dynamically selected and retained. It is worth emphasizing that during the fitting process, the parameters are estimated based on a limited set of data for each segment, rather than using the entire data set. This greatly improves the ability to resist noisy data and the stability of parameter estimation.

[0116] Step S1024: for the middle transition portion of the depth-concentration sample curve, call the third segment model library, determine the optimal model parameters based on the adaptive fitting method, and generate a fitting model.

[0117] In step S1024, for the transition area between the left half and the right half of the depth-concentration sample curve, the pre-built third-segment model library is called, and an optimization fitting method based on sample adaptive selection is used to jointly determine the optimal mathematical model and its parameter combination, and generate an intermediate transition segment fitting curve for connecting the models on both sides.

[0118] Specific, combined Figure 4 First, based on the boundary information of the left and right halves that have been fitted in step S1023, the right boundary sample index of the left half is set to p, and the left boundary sample index of the right half is set to q. The theoretical boundary interval of the middle transition segment is thus determined to be the index interval [p,q]. To further enhance the transition smoothness and closedness of the fitting model at the boundary, a sample extension mechanism is introduced on this basis. The index p is extended to the left by r sample points, and the index q is extended to the right by r sample points to construct a sample set for fitting the middle segment. The index range is expanded to [pr,q+r].

[0119] After preparing the sample set, the mathematical models in the third-stage model library are traversed and the following adaptive fitting process is performed sequentially: a maximum number of iterations K and an initial optimal mean square error (RMSE_best) are set. In each iteration j (j = 0, 1, …, K-1), m groups of sample points are randomly selected from the expanded fitting sample set as the current training subset. Parameters are fitted using the selected model to obtain the current parameter combination param(j). The corresponding mean square error (RMSE(j)) is calculated based on the current parameter combination param(j). If the RMSE(j) is less than the initial optimal mean square error (RMSE_best), the current parameter combination param(j) is updated to the optimal model parameters. The iteration is repeated until the maximum number of iterations K is reached. After all iterations are completed, the optimal parameter combination and fitting error for the current mathematical model are obtained. The next mathematical model in the third-stage model library is traversed and the above process is repeated. Ultimately, among all combinations of mathematical models and optimal parameter combinations, the one with the smallest mean square error is selected as the candidate optimal mathematical model and optimal model parameters for the intermediate segment. The mean square error of this model is then compared with a preset threshold. If it is less than the preset threshold, the model fitting result is considered to meet the accuracy requirements and is officially determined as the optimal mathematical model for the intermediate transition segment. If it is greater than or equal to the preset threshold, it indicates that there are outliers in the current sample subset or the model structure is not suitable. The fitting process needs to be repeated by reducing the sample set or replacing the model function until the mean square error is less than the preset threshold. Finally, the optimal mathematical model and its optimal model parameters are used to generate the corresponding fitting curve, and the fitting effect is displayed through a visual script.

[0120] Compared with the left and right sections, which can directly select the model structure and parameters with the smallest fitting error from the model library, the middle transition section structurally inherits the front and back sections, is more susceptible to boundary disturbances in sample distribution, and may show non-monotonicity or turning trends in the physical sense. If the minimum error selection mechanism is directly adopted, it may cause the fitting curve to jump or overfit at the boundary. This application significantly enhances the fitting smoothness, structural continuity and noise resistance of the middle section model by introducing a fitting error threshold control mechanism and combining the model function type selection and sample subset reconstruction strategy. This mechanism ensures the overall connection continuity of the three-segment fitting model, effectively avoids the mutation phenomenon of the fitting curve at the boundary, and improves the engineering applicability and precision controllability of the fitting curve.

[0121] Step S103 : weightedly splicing the segmented models fitted from the left half, the right half and the middle transition part of the depth-concentration sample curve in a weighted fusion manner to generate a complete fitting model.

[0122] In step S103, the corresponding model libraries were called for the left half, right half, and intermediate transition portion of the depth-concentration sample curve. Using a randomized consensus sampling method and an adaptive fitting strategy, three mathematical fitting models with locally optimal parameters were generated. To further improve the overall continuity and smoothness of the model, the three segmented models were fused into a complete depth-concentration fitting model using a segmented model concatenation strategy based on the Bayesian Information Criterion (BIC) and residual normalization weighted fusion.

[0123] Specifically, a transition region is first defined between the left half and the middle section, and between the middle section and the right half. The sample sets in these transition regions are derived from the sample extension mechanism introduced in step S102. This involves extending the right-hand sample of the left half by r points, and the left-hand sample of the middle section by r points, to the left, forming the overlapping region required for splicing. The right-hand splicing region is generated in the same manner, by extending the samples at the right end of the middle section and the left end of the right half.

[0124] For each transition region, there are two models to be fused: for example, the left splicing region contains the left segment model and the middle segment model, and the right splicing region contains the right segment model and the middle segment model. In order to determine the influence weight of the two models on the final fitting result in this region, this step adopts the Bayesian Information Criterion The fitting quality of the two models in the transition region is measured. The specific calculation formula is as follows:

[0125] ;

[0126] in, is the model complexity of the currently evaluated model, that is, the number of parameters of the fitting model, n represents the number of samples in the current transition region, Represents the maximum likelihood value corresponding to the model. The calculation formula of the maximum likelihood value is as follows:

[0127] ;

[0128] in, Indicates the The observation value of samples, that is, the depth The actual carrier concentration value at Indicates the The predicted value of samples, that is, the fitting model at depth Enter the estimated concentration value to be predicted. Represents the standard deviation between the observed values ​​of all sample points and the model predicted values, For all Then, based on the BIC value results of different models, a normalization operation is further performed to calculate the weight coefficient of each model. The solution formula for the weight coefficient is:

[0129] ;

[0130] in, Indicates the The weight of each model in the spliced ​​region, is the number of models involved in the splicing. In this scheme, each transition section usually involves the splicing of two different mathematical models, so the default In other embodiments, if the number of models involved in the splicing is greater than 2, the formula is also applicable and can be dynamically expanded according to the specific model configuration.

[0131] Finally, within the splicing area, based on the output values ​​of the two fitting models and their weight coefficients, a weighted summation is performed on the fitting results of each sample point, thereby generating a splicing fitting segment with continuous transition characteristics. This strategy is repeated to process the two splicing areas on the left and right. After completing the weighted fusion of the left and right splicing areas, the front segment of the left segment fitting model, the middle segment of the middle segment model, and the back segment of the right segment fitting model are directly spliced ​​in sequence, and the weighted fusion results are used as transition values ​​at each splicing point to construct an overall continuous depth-concentration fitting model. Through the above-mentioned weighted fusion strategy, the overall fitting model of the depth-concentration sample curve finally generated has good continuity and smoothness at the function value and first-order derivative levels, which can effectively reflect the distribution characteristics of the actual sample data and its regularity under depth changes, while taking into account both model fitting performance and physical rationality.

[0132] Step S104: construct a multi-frequency DLCP data analysis and interactive three-dimensional visualization platform based on the complete fitting model of the depth-concentration sample curve.

[0133] In step S104, based on the complete fitting model of the depth-concentration sample curve, an interactive analysis and 3D visualization platform for multi-frequency DLCP data is constructed. This platform centrally reconstructs DLCP data at different frequency, bias, and AC amplitude combinations within a unified depth coordinate system and extracts the defect state density corresponding to each depth point. The defect state density is calculated based on the frequency difference principle, obtaining the carrier concentration difference at a unified depth.

[0134] For example, see Figure 5 Taking the depth-carrier concentration curves of a conductive material at 10 kHz and 500 kHz as an example, the green and red curves represent the curves corresponding to the experimentally measured concentration data at 10 kHz and 500 kHz, respectively. The blue dots and red stars indicate the concentration value distribution calculated by the corresponding fitting model, clearly demonstrating the fitting model's complete coverage of all depth points. Therefore, the fitting model can support effective comparison and analysis of multi-frequency concentration differences.

[0135] Specifically, the platform first calls the complete fitting model to generate carrier concentration values ​​under various frequency conditions on the preset depth coordinate axis, so that test data of different frequencies can be accurately aligned under a unified depth system. In response to the large amount of different bias voltage, AC amplitude and frequency combination data involved in the DLCP test, the platform automatically selects response depth points with consistent physical meanings, and calculates and extracts the defect state density at the depth position based on the fitting concentration results under various frequency conditions. The calculation of the defect state density is based on the frequency difference principle, which is specifically calculated from the carrier concentration difference under different frequencies, thereby forming a standardized data structure. In order to improve the flexibility and adaptability of the analysis, the platform supports users to manually fine-tune the frequency range, fitting model parameters and depth mapping strategy through a graphical interface. At the same time, it can refresh the fitting results and defect state density profiles in real time based on user settings, automatically generate and update analysis data, and enhance the interactive experience and research convenience.

[0136] In addition, in terms of visual expression, the platform usually uses test frequency, response depth and defect state density as three-dimensional coordinate axes to construct a three-dimensional distribution diagram of defect state density, thereby intuitively displaying the spatial evolution process of defects under various test conditions. In addition, as a preferred method, by establishing a mapping relationship between depth position and energy level with the support of a specific physical model, the three-dimensional defect state diagram can also be converted into a projection of the defect energy level distribution in the frequency or response energy range, referring to Figure 6 As shown, it can assist researchers in deeply exploring the defect state energy level structure, dynamic capture behavior and its impact mechanism on device performance, and realize multi-dimensional analysis from the space-frequency domain to the energy level domain.

[0137] In summary, a complete fitting model is constructed by combining segmented fitting with weighted splicing for depth-carrier concentration sample data at different frequencies and different test conditions. The fitting model generates local optimal fitting models in the left half, right half and middle transition area of ​​the sample curve respectively, and achieves natural and seamless connection between the segmented models based on the weighted fusion of the Bayesian information criterion, solving the fitting faults and discontinuities that are prone to occur in traditional segmented fitting. Based on this complete fitting model, it is possible to perform unified interpolation and reconstruction on DLCP data of different frequencies under a unified depth coordinate system, and accurately obtain the carrier concentration value corresponding to any depth point, thereby effectively avoiding the spatial mismatch error caused by the inconsistency of depth points extracted at different frequencies in traditional methods. At the same time, the smoothness and robustness of the complete fitting model greatly suppress the local abnormal fluctuations introduced by the nonlinearity and noise of the CV curve, and significantly improve the stability of the carrier concentration curve and the rationality of the physical interpretation. Relying on this high-precision and continuous fitting model, the present application further constructs an interactive analysis and three-dimensional visualization platform for large-scale multi-frequency DLCP data. Based on a complete fitting model, the platform achieves unified depth coordinate alignment of data under different frequency, bias, and AC amplitude conditions and frequency differential extraction of defect state density, ensuring the accuracy and consistency of defect state information. Furthermore, the platform allows users to dynamically adjust frequency intervals, fitting parameters, and depth mapping strategies, updating analysis results in real time, improving the automation and flexibility of data processing.

[0138] In order to verify the superiority of the DLCP defect state density extraction method based on mathematical modeling proposed in this application, Figure 7 , the original depth-carrier concentration data at two frequencies of 10kHz and 500kHz were selected as the basis for comparison. Due to the spatial misalignment of the depth data measured at different frequencies, the traditional differential method directly subtracts the concentration data with mismatched depth coordinates, resulting in large errors and fluctuations in the defect state density extraction results, and a lack of stability and physical rationality. The comparison results show that the defect state density curve of the traditional differential method exhibits obvious noise and discontinuity, while the defect state density curve extracted by the modeling method of the present application is smooth and has good physical interpretation, which significantly improves the accuracy and reliability of defect state analysis. This comparative analysis fully proves that the DLCP defect state density extraction method based on the combination of mathematical modeling and frequency differential in the present application can effectively solve the defect extraction errors caused by depth misalignment and data noise in the traditional method, and improves the overall performance and application value of DLCP data processing.

[0139] Figure 8 This is a structural block diagram of a DLCP data analysis system based on mathematical modeling and human-computer interaction visualization provided by an embodiment of the present application. The system includes at least the following modules:

[0140] The data acquisition module is used to obtain the output data of the DLCP experiment, invert the data pairs of depth and corresponding carrier concentration, and generate a sample data set sorted by depth;

[0141] The segmented fitting module is used to generate a depth-concentration sample curve based on the sample data set. The corresponding mathematical model library is constructed for the left half, right half, and middle transition part of the depth-concentration sample curve, and the parameters of the segmented model are determined and fitted based on the random consistency sampling method and adaptive fitting strategy.

[0142] The weighted splicing module is used to perform weighted splicing on the segmented models fitted on the left half, right half and middle transition part of the depth-concentration sample curve by weighted fusion to generate a complete fitting model;

[0143] The visualization interaction module is used to build a multi-frequency DLCP data analysis and interactive 3D visualization platform based on the complete fitting model of the depth-concentration sample curve.

[0144] For relevant details, please refer to the above method embodiment.

[0145] Figure 9 4 is a block diagram of an electronic device provided in one embodiment of the present application. The device includes at least a processor 401 and a memory 402. The memory stores a program that is loaded and executed by the processor to implement the DLCP data analysis method based on mathematical modeling and human-computer interaction visualization of the above method embodiment.

[0146] Optionally, the present application also provides a computer-readable storage medium, in which a program is stored. The program is loaded and executed by a processor to implement the DLCP data analysis method based on mathematical modeling and human-computer interaction visualization of the above method embodiment.

[0147] The above embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A DLCP data analysis method based on mathematical modeling and human-computer interaction visualization, characterized in that: The method comprises: Obtain the output data of the DLCP experiment, invert the data pairs of depth and corresponding carrier concentration, and generate a sample data set sorted by depth; A depth-concentration sample curve is generated based on a sample data set, and corresponding mathematical model libraries are constructed for the left half, right half and middle transition part of the depth-concentration sample curve, and the parameters of the segmented model are determined and fitted based on a random consistency sampling method and an adaptive fitting strategy, including: generating a depth-concentration sample curve based on a sample data set sorted by depth; each sample data is represented as a set of binary value pairs (x, y), where x represents the normalized depth and y represents the carrier concentration after logarithmic transformation; corresponding to the left half, right half and middle transition part of the depth-concentration sample curve, a first-segment model library, a second-segment model library and a third-segment model library are constructed respectively; for the left half and right half of the depth-concentration sample curve, the first-segment model library and the second-segment model library are called respectively, and the optimal model parameters are determined based on the random consistency sampling method and a fitting model is generated; for the middle transition part of the depth-concentration sample curve, the third-segment model library is called, and the optimal model parameters are determined based on the adaptive fitting method and a fitting model is generated; The first segment model library includes a logarithmic function model 1, a skewed normal distribution model 2, and a logarithmic normal distribution model 3; the second segment model library includes a logarithmic function model 4, a skewed normal distribution model 5, and a logarithmic normal distribution model 6; Logarithmic function model 1 is: ; in, 、 、 are all parameters of the logarithmic function model 1 to be solved; The skewed normal distribution model 2 is: ; in, 、 、 are the parameters of the skewed normal distribution model 2 to be solved; Lognormal distribution model 3 is: ; in, 、 are the parameters of the lognormal distribution model 3 to be solved; Logarithmic function model 4 is: ; in, 、 、 are all parameters of the logarithmic function model 4 to be solved; The skewed normal distribution model 5 is: ; in, 、 、 are the parameters of the skewed normal distribution model 5 to be solved; The lognormal distribution model 6 is: ; in, 、 are the parameters of the lognormal distribution model 6 to be solved; The segmented models fitted on the left half, right half and middle transition part of the depth-concentration sample curve are weightedly spliced ​​by weighted fusion to generate a complete fitting model; A multi-frequency DLCP data analysis and interactive three-dimensional visualization platform was constructed based on a complete fitting model of the depth-concentration sample curve.

2. The DLCP data analysis method based on mathematical modeling and human-computer interaction visualization according to claim 1 is characterized in that: The method of calling the first segment model library and the second segment model library for the left half and the right half of the depth-concentration sample curve respectively, determining the optimal model parameters based on the random consistency sampling method and generating the fitting model includes: Call the pre-built first and second segment model libraries. For the left half of the depth-concentration curve, select the fitting sample subset according to the sample set index range [1:i]. For the right half of the depth-concentration curve, select the fitting sample subset in the index range [ni:n], where n represents the total number of samples in the entire depth-concentration sample curve. For each mathematical model in the model library, the following parameter fitting process is performed: the maximum number of iterations K and the initial optimal mean square error RMSE_best are set. In each iteration j, a fixed number of sample points are randomly selected from the fitting sample subset to obtain the current parameter combination param(j). The corresponding mean square error RMSE(j) is calculated based on the current parameter combination param(j). If the mean square error RMSE(j) is less than the initial optimal mean square error RMSE_best, the current parameter combination param(j) is updated to the optimal model parameter, and the iteration is repeated until the maximum number of iterations K is reached. After completing all iterations, the optimal parameter combination and its fitting error under the current mathematical model are obtained, and the next mathematical model in the model library is traversed, and the parameter fitting process is repeated. Among all the combinations of mathematical models and optimal parameter combinations, the group with the smallest mean square error is selected as the optimal mathematical model and its optimal model parameters for this part of the curve.

3. The DLCP data analysis method based on mathematical modeling and human-computer interaction visualization according to claim 1 is characterized in that: The third segment model library includes an exponential model 7 and a polynomial function model 8. The exponential model 7 is: ; in, 、 、 are the parameters of the exponential model 7 to be solved; The polynomial function model 8 is: ; in, 、 are all parameters of the polynomial function model 8 to be solved.

4. The DLCP data analysis method based on mathematical modeling and human-computer interaction visualization according to claim 3 is characterized in that: The method of calling the third segment model library for the intermediate transition portion of the depth-concentration sample curve, determining the optimal model parameters based on the adaptive fitting method, and generating a fitting model includes: Based on the boundary information of the left and right halves that have been fitted, let the right boundary sample index of the left half be p and the left boundary sample index of the right half be q. The theoretical boundary interval of the middle transition segment is determined to be the index interval [p,q]. The sample set for the middle segment fitting is constructed by extending the index p to the left by r sample points and the index q to the right by r sample points. The index range is extended to [pr,q+r]. Traverse the mathematical models in the third section of the model library and perform the following adaptive fitting process in sequence: set the maximum number of iterations K and the initial optimal mean square error RMSE_best. In each iteration j, randomly select m groups of sample points from the expanded fitting sample set as the current training subset, use the selected model to perform parameter fitting, and obtain the current parameter combination param(j). Based on the current parameter combination param(j), calculate the corresponding mean square error RMSE(j). If the mean square error RMSE(j) is less than the initial optimal mean square error RMSE_best, update the current parameter combination param(j) to the optimal model parameters, and repeat the iteration until the maximum number of iterations K is reached; After completing all iterations, the optimal parameter combination and fitting error under the current mathematical model are obtained; continue to traverse the next mathematical model in the third segment model library and repeat the parameter fitting process. Among all the combinations of mathematical models and optimal parameter combinations, the one with the smallest mean square error is selected as the candidate optimal model and optimal model parameters for the middle segment; The mean square error of the candidate optimal model is compared with the preset threshold. If it is less than the preset threshold, the candidate optimal model is determined as the optimal mathematical model of the intermediate transition section; if it is greater than or equal to the preset threshold, the fitting process is repeated until the mean square error is less than the preset threshold.

5. The DLCP data analysis method based on mathematical modeling and human-computer interaction visualization according to claim 1 is characterized in that: The weighted fusion method is used to perform weighted splicing on the segmented models fitted on the left half, right half, and middle transition part of the depth-concentration sample curve to generate a complete fitting model, including: A transition region is defined between the left half and the middle part, and between the middle part and the right half. For each transition region, the Bayesian information criterion is used. The fitting quality of the two models in the transition region is measured. The specific calculation formula is as follows: ； in, is the number of parameters of the fitting model, n represents the number of samples in the current transition region, Indicates the maximum likelihood value corresponding to the model; the calculation formula of the maximum likelihood value is as follows: ； in, Indicates the The observed value of the sample, Indicates the The predicted value of the sample, Represents the standard deviation between the observed values ​​of all sample points and the model predicted values, For all The average value of the BIC value of different models is used to perform normalization operations to calculate the weight coefficient of each model. The solution formula for the weight coefficient is: ； in, Indicates the The weight of each model in the spliced ​​region, is the number of models involved in the splicing; within the splicing area, based on the output values ​​of the two fitting models and their weight coefficients, the fitting results of each sample point are weighted summed to generate a splicing fitting segment; Repeat the processing of the two splicing areas on the left and right, and splice the three segmented models by splicing the fitting segments to generate a complete fitting model.

6. A DLCP data analysis system based on mathematical modeling and human-computer interaction visualization, characterized in that: include: The data acquisition module is used to obtain the output data of the DLCP experiment, invert the data pairs of depth and corresponding carrier concentration, and generate a sample data set sorted by depth; A segmented fitting module is used to generate a depth-concentration sample curve based on a sample data set, and to construct corresponding mathematical model libraries for the left half, right half, and middle transition part of the depth-concentration sample curve, and to complete parameter determination and fitting of the segmented model based on a random consistency sampling method and an adaptive fitting strategy, including: generating a depth-concentration sample curve based on a sample data set sorted by depth; each sample data is represented as a set of binary value pairs (x, y), where x represents the normalized depth and y represents the carrier concentration after logarithmic transformation; constructing a first segment model library, a second segment model library, and a third segment model library corresponding to the left half, right half, and middle transition part of the depth-concentration sample curve; for the left half and right half of the depth-concentration sample curve, calling the first segment model library and the second segment model library respectively, determining the optimal model parameters based on the random consistency sampling method, and generating a fitting model; for the middle transition part of the depth-concentration sample curve, calling the third segment model library, determining the optimal model parameters based on the adaptive fitting method, and generating a fitting model; The first segment model library includes a logarithmic function model 1, a skewed normal distribution model 2, and a logarithmic normal distribution model 3; the second segment model library includes a logarithmic function model 4, a skewed normal distribution model 5, and a logarithmic normal distribution model 6; Logarithmic function model 1 is: ; in, 、 、 are all parameters of the logarithmic function model 1 to be solved; The skewed normal distribution model 2 is: ; in, 、 、 are the parameters of the skewed normal distribution model 2 to be solved; Lognormal distribution model 3 is: ; in, 、 are the parameters of the lognormal distribution model 3 to be solved; Logarithmic function model 4 is: ; in, 、 、 are all parameters of the logarithmic function model 4 to be solved; The skewed normal distribution model 5 is: ; in, 、 、 are the parameters of the skewed normal distribution model 5 to be solved; The lognormal distribution model 6 is: ; in, 、 are the parameters of the lognormal distribution model 6 to be solved; The weighted splicing module is used to perform weighted splicing on the segmented models fitted on the left half, right half and middle transition part of the depth-concentration sample curve by weighted fusion to generate a complete fitting model; The visualization interaction module is used to build a multi-frequency DLCP data analysis and interactive 3D visualization platform based on the complete fitting model of the depth-concentration sample curve.

7. An electronic device, characterized in that: The device includes a processor and a memory; the memory stores a program, and the program is loaded and executed by the processor to implement a DLCP data analysis method based on mathematical modeling and human-computer interaction visualization as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that The storage medium stores a program, which, when executed by a processor, is used to implement a DLCP data analysis method based on mathematical modeling and human-computer interaction visualization according to any one of claims 1 to 5.

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