A full-range calibration method for a microwave photoconductive decay tester

Abstract

The application relates to the technical field of semiconductor material photoelectric detection, and discloses a full-range calibration method of a microwave photoconductive decay tester, which comprises the following steps: steady-state optical calibration, establishing a reference mapping of light intensity to absolute carrier concentration; performing frequency sweep perturbation measurement at each concentration working point to obtain multiple sets of complex response data; adopting a system identification algorithm to separate the instrument transfer function and the sample differential response sensitivity; integrating the differential sensitivity reconstruction curve, converting the anchor point into an absolute calibration model; enabling closed-loop feedback control to lock a specific phase, verifying the model; outputting the absolute calibration model and the instrument transfer function, and making a static reference and a dynamic operator. According to the application, the absolute concentration anchor point is established through steady-state optical calibration, the differential response sensitivity decoupled by dynamic frequency sweep measurement is integrated and reconstructed, and finally the integral constant is determined by using the anchor point, so that the accuracy and reliability of carrier concentration quantitative analysis are improved.

Description

Technical Field

[0001] This invention relates to the field of optoelectronic detection technology for semiconductor materials, specifically a full-process calibration method for a microwave photoconductivity attenuation tester. Background Technology

[0002] Microwave photoconductivity attenuation (TRMC) is a non-contact, highly sensitive measurement method for representing the minority carrier lifetime in semiconductor materials. It generates excess carriers within the sample through transient photoexcitation, causing changes in the sample's absorption or reflectivity to a microwave probe signal. By monitoring the attenuation process of this microwave signal over time, the recombination dynamics of the carriers can be derived.

[0003] In conventional applications, this technique is primarily used to obtain the relative value or characteristic time constant of carrier lifetime. Researchers or engineers typically analyze the acquired decay curves on logarithmic coordinates, extracting their slope to characterize carrier lifetime. The core of this analytical approach lies in focusing on the "shape" of the signal waveform rather than its "absolute amplitude." Therefore, the measurement results are often used for lateral comparisons, such as evaluating which sample series prepared using different processes has a longer carrier lifetime, or studying the performance changes of the same sample under different temperatures or environments.

[0004] However, existing microwave photoconductivity attenuation techniques generally employ the linear assumption that the signal response is proportional to the carrier concentration. This assumption holds only locally under specific injection conditions, and the ambiguity of its applicability introduces significant uncertainty into quantitative analysis. Furthermore, the instrument's own electronic bandwidth limitations distort the true physical signal. For high-performance materials with extremely short carrier lifetimes, the actual rapid attenuation process is smoothed out by the instrument's relatively slow response, leading to distorted measurement results. Moreover, the existing technical framework treats the accuracy of static calibration and the fidelity of dynamic response as two isolated issues, lacking a methodology that intrinsically links them and provides a systematic solution. Therefore, this invention provides a full-process calibration method for microwave photoconductivity attenuation testers to address the shortcomings of existing technologies. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a full-process calibration method for a microwave photoconductivity attenuation tester. This method solves the problems of existing microwave photoconductivity attenuation (TRMC) testing techniques, which rely on simplified linear assumptions or external independent measurements for quantitative analysis of carrier concentration. These methods make it difficult to obtain accurate absolute concentrations covering a wide dynamic range. Furthermore, the limitations of the instrument's own electronic response bandwidth introduce dynamic distortion, especially when measuring high-speed attenuation processes, leading to signal deformation and making it difficult to accurately reflect the intrinsic physical processes of the sample.

[0006] To achieve the above objectives, the present invention provides a full-process calibration method for a microwave photoconductivity attenuation tester, comprising the following steps:

[0007] S100. By simultaneously measuring the photoluminescence intensity, incident photon flux, and corresponding steady-state microwave signal output by the microwave photoconductivity attenuation tester of the sample under different steady-state light intensities, and combining the internal quantum efficiency analysis, a benchmark mapping relationship is established to map the external controllable light intensity to the absolute excess carrier concentration inside the sample.

[0008] S200. Based on the aforementioned reference mapping relationship, multiple steady-state carrier concentration operating points are set, and dynamic response frequency sweep perturbation measurement is performed at each steady-state carrier concentration operating point to obtain multiple sets of complex response data corresponding to each steady-state carrier concentration operating point from the microwave photoconductivity attenuation tester.

[0009] The S300 closed-loop feedback and adaptive control module uses a system identification algorithm to solve and separate the globally unique instrument electronics transfer function from the multiple sets of complex response data, as well as the multi-point sample differential response sensitivity of the microwave photoconductivity attenuation tester and each steady-state carrier concentration operating point.

[0010] S400. Integrate the differential response sensitivity to reconstruct the relative calibration curve, and use the steady-state microwave signal and the absolute excess carrier concentration to form an absolute anchor point, so as to convert the relative calibration curve into an absolute calibration model.

[0011] S500: Enable closed-loop feedback control, lock the specific phase characteristics predicted by the sample physical response parameters, and perform measurements in the locked state to verify the absolute calibration model.

[0012] S600 generates and outputs the verified absolute calibration model and the instrument electronic transfer function model, which serve as the static calibration benchmark for carrier concentration conversion in conventional measurements and the dynamic correction operator for eliminating instrument dynamic response distortion, respectively.

[0013] Preferably, in step S100, the step of establishing a reference mapping relationship that maps external controllable light intensity to the absolute excess carrier concentration inside the sample further includes:

[0014] The relative internal quantum efficiency curve is calculated based on the photoluminescence intensity and the incident photon flux.

[0015] The relative internal quantum efficiency curve is absolutized by fitting the data of the relative internal quantum efficiency curve in the high injection region with the theoretical internal quantum efficiency model;

[0016] Based on the absolutized internal quantum efficiency curve and carrier dynamics equation, the reference mapping relationship is obtained by inverse solution.

[0017] Preferably, in step S200, the frequency sweep perturbation measurement includes applying an AC perturbation optical signal with a continuously sweeping frequency, and simultaneously measuring the complex response of the microwave photoconductivity attenuation tester at each frequency point.

[0018] Preferably, step S300 further includes:

[0019] The total complex response of the microwave photoconductivity attenuation tester is modeled as the cascade product of the transfer function of the sample physical response and the transfer function of the instrument electronics. The transfer function of the sample physical response is a function of the steady-state carrier concentration, and the transfer function of the instrument electronics is independent of the steady-state carrier concentration.

[0020] Multiple sets of complex response data from the microwave photoconductivity attenuation tester are used as input to execute a system identification algorithm. The system identification algorithm utilizes the constraint that the instrument electronic transfer function is a common factor in all data sets and the sample physical response transfer function is a variable factor in different data sets to simultaneously fit all data sets, solve and separate the unique instrument electronic transfer function and the sample physical response parameters corresponding to each steady-state carrier concentration operating point.

[0021] Preferably, the transfer function of the physical response of the sample is:

[0022] ;

[0023] in, The transfer function of the physical response of the sample. For steady-state excess carrier concentration, For the frequency of the alternating perturbation optical signal, The imaginary unit, The differential response sensitivity, The effective carrier lifetime is concentration-dependent.

[0024] Preferably, in step S400, the step of converting the relative calibration curve into an absolute calibration model further includes:

[0025] Using the decoupled multi-point sample differential response sensitivity, a continuous function describing the continuous change of differential response sensitivity with carrier concentration is constructed.

[0026] By integrating the continuous function, a relative calibration curve is generated that describes the functional relationship between the microwave signal and the carrier concentration, but contains an unknown integration constant.

[0027] By using the anchor point formed by the steady-state microwave signal and the corresponding absolute excess carrier concentration, the unknown integral constant is solved and determined to absolutize the relative calibration curve and generate an absolute calibration model.

[0028] Preferably, step S500 further includes:

[0029] Using the sample's physical response parameters, the corresponding target sample response phase is calculated based on the preset key physical states;

[0030] A closed-loop feedback control loop is constructed, which measures the current response phase of the sample in real time and compares it with the calculated target sample response phase to generate an error signal.

[0031] Based on the error signal, the steady-state light intensity is dynamically adjusted through the closed-loop feedback control loop until the error signal converges, thereby accurately locking the physical state of the sample to the key physical state, so as to perform high-precision fixed-point calibration under the key physical state.

[0032] Preferably, the instrument electronics transfer function model is also used to perform deconvolution correction on the original measurement signal, including the following steps:

[0033] The original time-domain measurement signal to be corrected is subjected to Fourier transform to generate a frequency-domain representation;

[0034] In the frequency domain, the obtained instrument electronic transfer function is used as an inverse filter to perform a division operation on the frequency domain representation of the original measurement signal in order to construct the signal spectrum with the instrument dynamic distortion corrected.

[0035] The signal spectrum of the instrument's dynamic distortion, which has been corrected, is subjected to an inverse Fourier transform to generate the final dynamically corrected high-fidelity time-domain signal.

[0036] Preferably, the expression for performing division on the frequency domain representation of the original measurement signal is:

[0037] ;

[0038] in, The frequency domain representation of the real signal. The frequency domain representation of the original measurement signal. This represents the instrument's electronic transfer function.

[0039] A full-process calibration system for a microwave photoconductivity attenuation tester is also provided, including:

[0040] The composite optical path excitation and modulation module is used to generate composite excitation light containing an adjustable DC optical component and a swept AC perturbation optical signal according to control commands;

[0041] The multidimensional response signal acquisition module is used to simultaneously acquire the photoluminescence intensity, incident photon flux, and steady-state or transient microwave response signal output by the microwave photoconductivity attenuation tester of the sample.

[0042] A microwave signal phase-locked demodulation module is used to extract a complex response from the microwave response signal that is at the same frequency as the swept-frequency AC perturbation optical signal;

[0043] The data processing and model identification module is used to receive data from the multidimensional response signal acquisition module and the microwave signal phase-locked demodulation module, and perform calibration, decoupling, reconstruction and modeling operations to generate calibration models, correction operators and real-time analysis results.

[0044] The closed-loop feedback and adaptive control module is used to receive the real-time analysis results and generate control commands to send to the composite optical path excitation and modulation module to construct an adaptive locking closed-loop feedback loop.

[0045] This invention provides a full-process calibration method for a microwave photoconductivity attenuation tester. It has the following beneficial effects:

[0046] 1. This invention establishes an absolute concentration anchor point with clear physical meaning through steady-state optical calibration, and integrates and reconstructs the differential response sensitivity decoupled from dynamic frequency sweep measurements. Finally, this anchor point is used to determine the integration constant. This generates an absolute calibration model covering a wide dynamic range, thereby significantly improving the accuracy and reliability of quantitative carrier concentration analysis.

[0047] 2. This invention utilizes a system identification algorithm to accurately separate the instrument's electronic transfer function from dynamic response data at different operating points, obtaining a mathematical model representing the system's dynamic distortion. This model can serve as a dynamic correction operator, eliminating distortions introduced by instrument bandwidth limitations in the original measurement signal through deconvolution operations. It can realistically restore the sample's intrinsic physical dynamic processes, especially for representing transient characteristics such as rapid decay of short-lived materials.

[0048] 3. This invention utilizes the same set of swept-frequency perturbation measurement datasets to simultaneously identify the static calibration model for absolute concentration conversion and the instrument transfer function for dynamic distortion correction. This integrated design solves the technical problem of static calibration and dynamic correction being mutually exclusive and difficult to balance in traditional technologies, providing a comprehensive and self-consistent quantitative analysis basis for microwave photoconductivity attenuation testing technology. Attached Figure Description

[0049] Figure 1 This is a diagram of the full calibration system architecture of the present invention;

[0050] Figure 2 This is a flowchart of the method of the present invention;

[0051] Figure 3 This is a flowchart of the adaptive locking and verification process of the present invention;

[0052] Figure 4 This is a flowchart of the integral reconstruction and absolute calibration process of the present invention. Detailed Implementation

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Please see the appendix Figure 1 , Figure 1 This is a system architecture diagram of a full-process calibration system according to an embodiment of the present invention. The present invention provides a full-process calibration system for a microwave photoconductivity attenuation tester, used to implement a full-process calibration method for the microwave photoconductivity attenuation tester. Through the coordinated work of various modules, the system completes a closed-loop calibration process from excitation generation, multi-dimensional response acquisition, signal demodulation, model identification to adaptive control, including:

[0055] The composite optical path excitation and modulation module, serving as the excitation source for the calibration process, is responsible for generating excitation light with precisely controllable physical properties. This module integrates a pump source and a probe source, with an acousto-optic modulator incorporated into the pump source's optical path. During operation, the module outputs composite excitation light, which includes a stable DC component and a high-frequency sinusoidally modulated AC component. The intensity of the DC component is used to set a quasi-static excess carrier concentration reference within the semiconductor sample, while the modulation frequency and amplitude of the AC component are precisely controlled by an external driving signal to apply controllable dynamic perturbations to the sample.

[0056] The multidimensional response signal acquisition module, connected to the composite optical path excitation and modulation module and the μ-PCD instrument to be calibrated, is responsible for synchronously acquiring multidimensional physical response signals induced by excitation light. This module integrates a high-precision optical power meter for real-time measurement of the photon flux incident on the sample surface; it also integrates a spectrometer and a photodetector for acquiring and integrating the photoluminescence intensity generated by the sample. The module receives and digitizes the raw microwave reflection signal output from the μ-PCD instrument to be calibrated, forming time-series data.

[0057] A microwave signal phase-locked demodulation module is included. Its signal input is connected to a multi-dimensional response signal acquisition module, and its reference input is synchronized with the signal source driving the acousto-optic modulator. This module accurately separates and extracts the microwave response signal with the same frequency as the excitation light's AC component from the original microwave reflection signal, which contains DC components, AC response, and noise. Its output is the complex information of this specific frequency response signal, namely its amplitude and phase relative to the reference signal. This process effectively demodulates the system's linear response to perturbations from the complex overall signal.

[0058] The data processing and model identification module receives and processes data from the multidimensional response signal acquisition module and the microwave signal phase-locked demodulation module. This module performs the core data analysis tasks of the invention: First, based on steady-state data of photon flux and photoluminescence intensity, it performs internal quantum efficiency analysis to establish a physical benchmark for the absolute excess carrier concentration. Second, based on complex response data obtained from frequency sweep measurements, it executes a system identification algorithm to solve for and separate the instrument's transfer function and the sample's physical response model. Third, it performs integral calculations on the decoupled sample differential response to reconstruct the full calibration curve.

[0059] A closed-loop feedback and adaptive control module, connected to the data processing and model identification module and the composite optical path excitation and modulation module, forms a feedback control loop. This module compares the real-time analysis results from the data processing and model identification module, such as the demodulated sample response phase, with a preset target phase value to generate an error signal. Based on this error signal, the module outputs control commands to the composite optical path excitation and modulation module, dynamically adjusting its output DC light intensity until the sample response phase is locked at the target value. This function is used for high-precision point-to-point calibration at specific physical state points.

[0060] In the overall workflow, the composite optical path excitation and modulation module generates an excitation signal, the multidimensional response signal acquisition module captures the resulting multidimensional physical results, the microwave signal phase-locked demodulation module extracts the key dynamic response, the data processing and model identification module analyzes and models all the data, and finally the closed-loop feedback and adaptive control module can finely adjust the excitation source in reverse according to the analysis results, thereby realizing a complete, accurate and self-consistent calibration closed loop.

[0061] See attached document Figure 2 , Figure 2 This is a flowchart illustrating a full-process calibration method for a microwave photoconductivity attenuation tester according to an embodiment of the present invention. The present invention provides a full-process calibration method for a microwave photoconductivity attenuation tester, comprising the following steps:

[0062] S100 is used for steady-state optical calibration of absolute carrier concentration. By measuring the photoluminescence intensity and incident photon flux of the sample under different steady-state light intensities, and combining the internal quantum efficiency analysis model, a benchmark mapping relationship between light intensity and absolute excess carrier concentration inside the sample is established.

[0063] The S200 performs frequency-sweeping perturbation measurements of the system's dynamic response. At different steady-state carrier concentration operating points determined by the reference mapping relationship, an AC perturbation optical signal with a continuously sweeping frequency is applied, and the complex response of the μ-PCD tester at each frequency point is measured simultaneously.

[0064] The S300 performs decoupling identification of the instrument transfer function and the physical response of the sample. Using complex response data measured at multiple operating points, the system identification algorithm solves and separates the global, concentration-independent instrument electronic transfer function and the sample physical response parameters that vary with concentration.

[0065] S400: Perform integral reconstruction and absolute calibration of the differential sensitivity function; integrate the decoupled sample differential response sensitivity to reconstruct a relative calibration curve covering the entire process, and use the absolute concentration benchmark established in step S100 for anchoring to generate the final absolute calibration model.

[0066] The S500 performs adaptive locking and refined measurement of key physical state points; for the preset carrier concentration region, closed-loop feedback control is enabled to achieve fixed-point calibration of the region by locking specific phase characteristics of the sample response, so as to refine or verify the absolute calibration model.

[0067] The S600 is used to generate and apply calibration models and correction operators; it also solidifies the output absolute calibration model and instrument transfer function model, which are used for carrier concentration conversion in subsequent measurements and for deconvolution correction of the original measurement signal to eliminate instrument-introduced distortion.

[0068] In step S100, steady-state optical calibration of the absolute carrier concentration benchmark is performed. The core objective of this step is to establish a high-confidence physical benchmark based on the photophysical properties of the sample itself, independent of the microwave measurement system to be calibrated. This benchmark, in the form of a function or lookup table, precisely defines the deterministic mapping relationship between the externally measurable steady-state photon flux and the absolute steady-state excess carrier concentration generated inside the sample, providing an absolute concentration anchor point for subsequent dynamic calibration steps. This step can be specifically broken down into the following operations:

[0069] S110 performs synchronous measurements of multiple physical quantities under steady-state excitation. The composite optical path excitation and modulation module is set to pure DC operating mode, i.e., no AC modulation signal is applied. Through program control, the output optical power of the pump source is changed from low to high in preset steps or sequences. At each stable optical power setpoint, two key measurements are simultaneously performed by the multi-dimensional response signal acquisition module:

[0070] Firstly, by utilizing its internal optical power meter, the pump photon flux incident on the effective region of the sample can be accurately measured. ;

[0071] Secondly, using its internal spectrometer and photodetector, it collects the photoluminescence (PL) spectrum generated by the sample under the current excitation, and integrates the spectral signal to obtain the total photoluminescence intensity. By performing a series of measurements at different optical powers, a set of discrete data pairs was obtained. .

[0072] S120 establishes a physical model and calculates the relative internal quantum efficiency. The data processing and model identification module models the data based on the acquired data pairs and the fundamental principles of semiconductor carrier dynamics. Under steady-state conditions, the photogenerated carrier generation rate per unit volume is calculated. With total recombination rate Equal. Production rate Determined by the incident photon flux:

[0073] ;

[0074] in, The light absorption efficiency of the sample material at the pump light wavelength is a known parameter that can be obtained through independent measurement or by consulting literature. This represents the incident photon flux; The effective thickness of the semiconductor sample.

[0075] Total recombination rate It is the sum of the rates of the three main recombination mechanisms, plus the steady-state excess carrier concentration. Related:

[0076] ;

[0077] in, It represents the total rate at which excess carriers recombine and disappear within a unit volume; The nonradiative Shockley-Read-Hall (SRH) recombination coefficient. The radiative recombination coefficient, is the Auger composite coefficient.

[0078] Measured photoluminescence intensity With radiative recombination rate Proportional, proportionality coefficient Let be the optical collection efficiency constant of the system. Therefore, .

[0079] Internal quantum efficiency (IQE) is defined as the ratio of radiative recombination rate to total recombination rate. Because... and Proportional to Therefore, there is a proportional relationship between IQE and measurable quantities:

[0080] ;

[0081] in, It represents the ratio of the radiative recombination rate to the total recombination rate; This represents the steady-state excess carrier concentration. This represents the rate of recombination of charge carriers per unit volume via radiation. It represents the total rate at which excess carriers recombine and disappear within a unit volume; This indicates the intensity of light (photons) emitted by the sample under illumination.

[0082] Based on this relationship, the data processing and model identification module performs analysis on each collected data pair. Calculate the ratio to obtain a relative IQE curve that has the same shape as the true IQE curve but whose magnitude is unknown, denoted as . .

[0083] S130 performs an absolute scaling of the relative internal quantum efficiency. To obtain the absolute IQE value, it is necessary to... The curve is calibrated. This process utilizes the physical properties of semiconductor recombination mechanisms under high injection conditions. At high injection levels, SRH recombination ( The contribution of ) compared to radiation recombination ( ) and Auger complex ( This can be ignored. In this case, the expression for IQE is approximately:

[0084] ;

[0085] in, The radiative recombination coefficient; The Auger composite coefficient; This represents the steady-state excess carrier concentration.

[0086] For the target semiconductor material, the recombination coefficients B and C are its intrinsic physical constants, possessing relatively definite values ​​or ratios. The data processing and model identification module will collect data from the high injection region. The data is then fitted to the theoretical IQE model described above. Through this fitting process, the specific IQE can be uniquely determined. Convert to absolute The required scaling constant is used to complete the absolute representation of the entire IQE curve.

[0087] S140, inverse solution generates a concentration-light intensity baseline mapping relationship. This is used to obtain the absolute... Following the curve, for each measurement point, the data processing and model identification module possesses a complete set of equations. That is, for any given photon flux... The corresponding absolute carrier concentration The following two equations must be satisfied simultaneously:

[0088] ;

[0089] ;

[0090] in, Indicates light absorption efficiency; This represents the steady-state photogenerated carrier generation rate; Represents the total recombination rate .

[0091] By numerically solving this system of equations, the flux of each photon can be accurately determined. The corresponding unique absolute excess carrier concentration After calculating all data points, a high-precision benchmark mapping relationship covering the entire measurement range is generated. This relationship can be stored as a look-up table or fitted to an analytical function. This mapping relationship is the absolute concentration benchmark that is ultimately output in this step and used in subsequent calibration procedures.

[0092] After completing the absolute concentration benchmark calibration, the method proceeds to steps S200 and S300. By applying dynamic perturbations and analyzing the system's frequency response, two coupled components are precisely represented and separated: one is the physical response characteristics of the semiconductor sample itself, which vary with carrier concentration; the other is the electronic transfer function inherent to the testing instrument, independent of the sample state. This approach solves the problem that traditional calibration cannot assess and compensate for the dynamic performance limitations of the instrument. This stage can be specifically broken down into the following operations:

[0093] S210: Set the operating point and apply a frequency-sweeping perturbation excitation. The data processing and model identification module selects a series of discrete pump light DC photon flux values. And utilize the generated baseline mapping relationship ,in, This represents the generated baseline mapping relationship, which is used to calculate the unique steady-state excess carrier concentration operating point corresponding to each luminous flux value. .

[0094] For each selected work point The composite optical path excitation and modulation module, in addition to outputting the corresponding DC light intensity, applies a constant and minute sinusoidal AC light intensity modulation. The frequency of this AC modulation... Instead of a fixed value, continuous or stepped scanning is performed within a preset frequency range that covers the instrument's main response bandwidth (e.g., from kilohertz to tens of megahertz). This perturbation amplitude is small enough to ensure that the system response remains in the linear region.

[0095] S220 performs phase-locked acquisition of the system's complex response. The microwave signal phase-locked demodulation module operates continuously throughout the entire process of applying the frequency sweep perturbation excitation. For each operating point... Each scan frequency point below This module accurately extracts the frequency from the composite microwave signal output by the μ-PCD tester. The response components were measured, and their amplitudes were measured. and phase shift relative to the excitation light modulation .

[0096] After completing a full frequency scan, a set of descriptions of the system at that operating point can be obtained. Complex response data of the dynamic behavior of the system. This set of data is known in engineering as the system's empirical Bode plot. This process is repeated, traversing all preset operating points, to ultimately obtain a set (N) of total system frequency response datasets corresponding to different carrier concentrations. ,in It is a complex quantity consisting of amplitude and phase.

[0097] S310, construct the system cascaded transfer function model. The data processing and model identification module performs physical modeling on the acquired frequency response data. The overall transfer function of the entire test system. It is modeled as the sample physical response transfer function. Instrumentation Electronics Transfer Function The cascade, that is, the product of the two:

[0098] ;

[0099] in, This represents the overall transfer function of the entire test system; Represents the transfer function of instrument electronics; Indicates the frequency of the AC perturbation signal; This represents the physical response of the sample itself; its dynamic characteristics are mainly determined by the carrier recombination process and can be effectively approximated as a first-order low-pass filter model.

[0100] ;

[0101] in, The transfer function of the physical response of the sample. For steady-state excess carrier concentration, For the frequency of the alternating perturbation optical signal, The imaginary unit, For differential response sensitivity, The effective carrier lifetime is concentration-dependent. The differential response sensitivity of the sample at this operating point, which is the ratio of the change in microwave signal to the change in carrier concentration, has the following physical meaning: exist The slope of the point is the core parameter required to finally construct the calibration curve. The effective carrier lifetime at this concentration determines the cutoff frequency of the sample response. Both parameters vary with carrier concentration. It changes with the changes.

[0102] Instrumentation Electronics Transfer Function This represents the combined frequency response of all electronic components, from the microwave cavity and detector to the amplifier circuit and signal output port. Its key characteristic is that it is only the frequency response. The function of the carrier concentration inside the sample Irrelevant.

[0103] S320 executes the system identification algorithm to achieve decoupling. This step is crucial for achieving separation. The data processing and model identification module executes the system identification algorithm, which is essentially a global optimization fitting process involving multiple variables and multiple datasets. This system identification algorithm is used to find a globally unique, concentration-independent function. And N sets of concentration-related parameters This allows the theoretical total response calculated by substituting these parameters into the aforementioned cascaded transfer function model to be obtained. , and all experimental data obtained from actual measurements The overall error between them is the smallest.

[0104] Due to the different carrier concentration operating points, The form (by changes) and The decisions are significantly different, and As common factors are present across all measurement datasets, this data diversity allows the algorithm to uniquely extract these common factors. and the changes in each group The parameters provide sufficient constraints. The algorithm can be implemented using iterative optimization based on nonlinear least squares.

[0105] After completing this step, two key results will be output:

[0106] Operating point at each concentration The precise differential response sensitivity value This dataset will be used directly for subsequent calibration curve reconstruction;

[0107] A globally unique instrument transfer function model that represents the instrument's own dynamic characteristics. The instrument's transfer function model will be used to generate correction operators for subsequent measurement data.

[0108] See attached document Figure 4 , Figure 4 This is a flowchart of integral reconstruction and absolute calibration according to an embodiment of the present invention.

[0109] In step S400, the full-range calibration curve is reconstructed and absolutized. The purpose of this step is to transform the discrete, differential system response information obtained in the previous steps into a continuous, integral, and absolutely physically meaningful full-range calibration model. This full-range calibration model ultimately establishes a precise correspondence between the macroscopic microwave signal output by the μ-PCD analyzer and the absolute excess carrier concentration within the semiconductor sample. This step can be specifically broken down into the following operations:

[0110] S410, perform continuous fitting of the differential response sensitivity function. The data processing and model identification module receives discrete data points from step S320, i.e., operating points at different carrier concentrations. Below, the decoupled sample differential response sensitivity To perform integration, these discrete points need to be transformed into a continuous function. The data processing and model identification module uses numerical fitting methods, such as polynomial fitting or piecewise spline interpolation, to process the dataset and generate an analytical function that accurately describes the continuous change of differential sensitivity with carrier concentration. This parsing function This represents the situation at any carrier concentration. Microwave signal The rate of change of carrier concentration, i.e. ,in Let be the differential response sensitivity analytical function. For any carrier concentration, It is a microwave signal. This indicates that at any carrier concentration Microwave signal Regarding carrier concentration The rate of change.

[0111] S420 performs integration to reconstruct the relative calibration curve. A continuous differential sensitivity function is obtained. Subsequently, the data processing and model identification module retrieves the microwave signal by numerical integration. With arbitrary carrier concentration The functional relationship between them. The expression for this integral operation is:

[0112] ;

[0113] in, Indicates the relative calibration curve; The sensitivity function representing the continuous differential response; For the integration variable, the lower limit of integration is usually taken as zero, which represents the state where there are no excess carriers. The integral constant corresponds to the background microwave signal value of the system at zero excess carrier concentration (i.e., in the dark state). Since this integral constant is only relevant when only differential information is available... Since it is unknown, the integral operation directly produces a relative calibration curve with a correct shape but an undetermined vertical axis position. .

[0114] The S430 uses an optical reference for absolute anchoring. This is to determine the integration constant. The relative calibration curve is then converted into an absolute calibration curve, utilizing the additional information obtained during the steady-state calibration phase. During steady-state measurement in step S110, the multidimensional response signal acquisition module acquires the photon flux. and photoluminescence intensity Simultaneously, the DC microwave signal value output by the μ-PCD meter under this steady-state light intensity was also recorded. Combined with the generated baseline mapping relationship The system actually possesses one or more sets of anchor point data that can directly correlate absolute carrier concentration with absolute microwave signal. .

[0115] The data processing and model identification module selects one of the high-confidence anchor points, substitutes it into the equation of the relative calibration curve, and then directly solves for the integral constant. :

[0116] ;

[0117] in, It is the integration constant; This represents the microwave signal value at the anchor point; This indicates the excess carrier concentration at the anchor point; This represents the function value of the relative calibration curve at the anchor point; This represents the differential response sensitivity function.

[0118] To improve robustness, multiple anchor points can be selected, and an optimal integration constant can be calculated using optimization algorithms such as the least squares method. This is to minimize the deviation between all anchor points and the final calibration curve.

[0119] Once the integration constant Once uniquely determined, the final end-to-end absolute calibration model can be obtained. This end-to-end absolute calibration model accurately describes the one-to-one correspondence between the output signal value of the μ-PCD tester and the absolute excess carrier concentration inside the sample across the entire range from low to high injection, thus achieving the core objective of the entire calibration process.

[0120] See attached document Figure 3 , Figure 3 This is an adaptive locking and verification flowchart according to an embodiment of the present invention.

[0121] In step S500, adaptive locking and refined measurement of key physical state points are performed. This step is optional but significantly improves calibration accuracy. Its purpose is to verify the entire calibration model with high confidence, or to perform targeted, ultra-high-precision point calibration of specific carrier concentration regions with drastic changes in physical characteristics. This process transforms the open-loop measurement process into a closed-loop intelligent control process based on real-time feedback, capable of actively searching for and stabilizing at specific physical state points. This step can be specifically broken down into the following operations:

[0122] S510, Set the target physical state and calculate its corresponding phase characteristics. First, based on the known physical properties of the semiconductor sample or calibration requirements, determine one or more key physical states that require fine calibration. These states typically correspond to regions where the carrier recombination mechanism changes significantly, such as the transition region from SRH recombination dominance to radiative recombination dominance, which usually corresponds to the vicinity of the peak point of the internal quantum efficiency curve. This physical state can be determined by a specific effective carrier lifetime value. To provide a unique representation.

[0123] The data processing and model identification module uses the sample physical response model decoupled in step S320, i.e. phase part Calculate when the effective carrier lifetime is At a fixed modulation frequency with a high signal-to-noise ratio, The theoretical phase response that the sample should exhibit. .Should This refers to the target setpoint that the closed-loop control system needs to track and lock.

[0124] S520, enables and executes the closed-loop feedback control process. The closed-loop feedback and adaptive control module is activated and begins executing real-time feedback control algorithms, such as proportional-integral-derivative (PID) control algorithms. This module operates at a preset fixed frequency. The driving composite optical path excitation and modulation module generates AC perturbations.

[0125] In each step of the control loop, the system performs the following operations: the microwave signal phase-locked demodulation module measures the system's frequency in real time. The total response phase below The data processing and model identification module receives this value and subtracts the identified, constant instrument response phase at that frequency. Thus, the true response phase of the current sample is obtained. .

[0126] The closed-loop feedback and adaptive control module will calculate the real-time sample phase. With the target phase set in step S510 Compare and generate an error signal The error signal is input to a PID controller, which calculates a control output based on the magnitude, historical accumulation, and trend of the error. This output is then converted into an adjustment command for the DC intensity of the pump source in the composite optical path excitation and modulation module, thereby altering the steady-state carrier concentration in the sample. This adjustment affects the effective carrier lifetime. The change in the phase of the sample's response alters the phase of the response. This forms a complete negative feedback closed loop. This process continues until the error signal... When the convergence reaches zero, the physical state of the sample is precisely and stably locked at the target state. superior.

[0127] The S530 performs high-precision differential sensitivity measurements in the locked state. Once the system is stably locked onto the target phase, the data processing and model identification module triggers a high-precision measurement. In this stable state, the microwave signal phase-locked demodulation module performs a long-term average measurement of the system response amplitude to obtain a high signal-to-noise ratio differential response sensitivity measurement. Because the system is precisely clamped at a known physical state point, this measurement... It has a very high confidence level.

[0128] S540 performs verification or local correction of the calibration model. The obtained refined measurement values... The corresponding carrier concentration point (which can be obtained by converting the DC light intensity stabilized during locking via the S100 reference relationship) and the fitted continuous differential sensitivity function The values ​​at this point are compared. If the two values ​​match closely, the accuracy of the full-range calibration model is strongly verified. If a minor deviation exists, the measurement point can be refined. As data points with high weights, the original differential sensitivity function Local corrections or refitting are performed to further improve the final generated end-to-end absolute calibration model. Precision in this critical area.

[0129] In step S600, the calibration model and correction operator are generated and applied. This step solidifies the core results of the entire calibration process and clarifies their application in subsequent routine μ-PCD measurements. The method of this invention not only provides a static signal-concentration conversion relationship but also a dynamic signal correction tool, jointly ensuring the accuracy and fidelity of routine measurement results. This step can be specifically broken down into the following operations:

[0130] The S610 module solidifies and outputs the full-process absolute calibration model and the instrument transfer function model. The data processing and model identification module performs final processing and storage on the two core data results generated.

[0131] Firstly, it involves using a fully absolute calibration model. This data is then converted into an efficient, directly callable data format. One implementation is to discretize it into a high-density look-up table, which stores a series of absolute excess carrier concentration values ​​and their corresponding ideal microwave signal values. Another implementation is to store it as the coefficients of an analytic function that fits the curve, such as the coefficients of a polynomial function.

[0132] Secondly, it involves identifying a globally unique instrument electronics transfer function model. The instrument's electronic transfer function model describes the instrument's amplitude and phase response at different frequencies and can be stored as a series of complex pairs corresponding to frequency points, or a set of coefficients for a digital filter. This model forms the basis for subsequent dynamic correction operators.

[0133] The S620 employs a full-range absolute calibration model for carrier concentration conversion. During routine transient photoconductivity attenuation measurements, the μ-PCD meter outputs a time-varying curve of the original microwave signal attenuation. To obtain the curve of excess carrier concentration decaying over time. The data processing and model identification module calls the calibration model fixed in step S610. Through... By performing a reverse lookup on each data point on the curve (interpolating in a lookup table or solving analytical equations), the corresponding absolute excess carrier concentration can be calculated point by point, ultimately generating a carrier concentration decay curve. .

[0134] The S630 uses an instrument response correction operator to correct distortion in the measured signal. The original signal obtained from a conventional measurement... Inevitably, distortion is included due to the dynamic characteristics of the instrument, such as its limited electronic bandwidth. To eliminate this distortion and restore a signal that more closely approximates the true physical processes of the sample, it is necessary to apply a method based on the instrument's electronic transfer function. The correction operator.

[0135] This correction process is implemented in the frequency domain through deconvolution. Specifically, the data processing and model identification module first processes the original signal in the time domain... Perform a Fast Fourier Transform (FFT) to obtain its representation in the frequency domain. The measured signal is the actual physical response signal of the sample. Instrumentation Electronics Transfer Function The result of convolution is represented as a product in the frequency domain:

[0136] ;

[0137] Therefore, the correction operator is the inverse of the instrument transfer function, i.e., an inverse filter. The distortion-free true signal spectrum can be obtained by performing division in the frequency domain.

[0138] ;

[0139] in, The frequency domain representation of the real signal. The frequency domain representation of the original measurement signal. This represents the electronic transfer function of the instrument.

[0140] Subsequently, the calculated By performing an inverse fast Fourier transform (IFFT), a more faithful time-domain signal attenuation curve can be obtained after dynamic correction. . This Substituting the values ​​into the calibration model from step S620 for concentration conversion yields the most accurate carrier dynamics decay curve.

[0141] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A full-process calibration method for a microwave photoconductivity attenuation tester, characterized in that, Includes the following steps: S100. By simultaneously measuring the photoluminescence intensity, incident photon flux, and corresponding steady-state microwave signal output by the microwave photoconductivity attenuation tester of the sample under different steady-state light intensities, and combining the internal quantum efficiency analysis, a benchmark mapping relationship is established to map the external controllable light intensity to the absolute excess carrier concentration inside the sample. S200. Based on the aforementioned reference mapping relationship, multiple steady-state carrier concentration operating points are set, and dynamic response frequency sweep perturbation measurement is performed at each steady-state carrier concentration operating point to obtain multiple sets of complex response data corresponding to each steady-state carrier concentration operating point from the microwave photoconductivity attenuation tester. The S300 closed-loop feedback and adaptive control module uses a system identification algorithm to solve and separate the globally unique instrument electronics transfer function from the multiple sets of complex response data, as well as the multi-point sample differential response sensitivity of the microwave photoconductivity attenuation tester and each steady-state carrier concentration operating point. S400. Integrate the differential response sensitivity to reconstruct the relative calibration curve, and use the steady-state microwave signal and the absolute excess carrier concentration to form an absolute anchor point, so as to convert the relative calibration curve into an absolute calibration model. S500: Enable closed-loop feedback control, lock the specific phase characteristics predicted by the sample physical response parameters, and perform measurements in the locked state to verify the absolute calibration model. S600 generates and outputs the verified absolute calibration model and the instrument electronic transfer function model, which serve as the static calibration benchmark for carrier concentration conversion in conventional measurements and the dynamic correction operator for eliminating instrument dynamic response distortion, respectively.

2. The full-process calibration method for a microwave photoconductivity attenuation tester according to claim 1, characterized in that, In step S100, the step of establishing a reference mapping relationship that maps external controllable light intensity to the absolute excess carrier concentration inside the sample further includes: The relative internal quantum efficiency curve is calculated based on the photoluminescence intensity and the incident photon flux. The relative internal quantum efficiency curve is absolutized by fitting the data of the relative internal quantum efficiency curve in the high injection region with the theoretical internal quantum efficiency model; Based on the absolutized internal quantum efficiency curve and carrier dynamics equation, the reference mapping relationship is obtained by inverse solution.

3. The full-process calibration method for a microwave photoconductivity attenuation tester according to claim 1, characterized in that, In step S200, the frequency sweep perturbation measurement includes applying an AC perturbation optical signal with a continuously sweeping frequency, and simultaneously measuring the complex response of the microwave photoconductivity attenuation tester at each frequency point.

4. The full-process calibration method for a microwave photoconductivity attenuation tester according to claim 1, characterized in that, The steps of S300 further include: The total complex response of the microwave photoconductivity attenuation tester is modeled as the cascade product of the transfer function of the sample physical response and the transfer function of the instrument electronics. The transfer function of the sample physical response is a function of the steady-state carrier concentration, and the transfer function of the instrument electronics is independent of the steady-state carrier concentration. Multiple sets of complex response data from the microwave photoconductivity attenuation tester are used as input to execute a system identification algorithm. The system identification algorithm utilizes the constraint that the instrument electronic transfer function is a common factor in all data sets and the sample physical response transfer function is a variable factor in different data sets to simultaneously fit all data sets, solve and separate the unique instrument electronic transfer function and the sample physical response parameters corresponding to each steady-state carrier concentration operating point.

5. The full-process calibration method for a microwave photoconductivity attenuation tester according to claim 4, characterized in that, The transfer function of the physical response of the sample is: ； in, The transfer function of the physical response of the sample. For steady-state excess carrier concentration, For the frequency of the alternating perturbation optical signal, The imaginary unit, The differential response sensitivity, The effective carrier lifetime is concentration-dependent.

6. The full-process calibration method for a microwave photoconductivity attenuation tester according to claim 1, characterized in that, In step S400, the step of converting the relative calibration curve into an absolute calibration model further includes: Using the decoupled multi-point sample differential response sensitivity, a continuous function describing the continuous change of differential response sensitivity with carrier concentration is constructed. By integrating the continuous function, a relative calibration curve is generated that describes the functional relationship between the microwave signal and the carrier concentration, but contains an unknown integration constant. By using the anchor point formed by the steady-state microwave signal and the corresponding absolute excess carrier concentration, the unknown integral constant is solved and determined to absolutize the relative calibration curve and generate an absolute calibration model.

7. The full-process calibration method for a microwave photoconductivity attenuation tester according to claim 1, characterized in that, The steps of S500 further include: Using the sample's physical response parameters, the corresponding target sample response phase is calculated based on the preset key physical states; A closed-loop feedback control loop is constructed, which measures the current response phase of the sample in real time and compares it with the calculated target sample response phase to generate an error signal. Based on the error signal, the steady-state light intensity is dynamically adjusted through the closed-loop feedback control loop until the error signal converges, thereby accurately locking the physical state of the sample to the key physical state, so as to perform high-precision fixed-point calibration under the key physical state.

8. The full-range calibration method for a microwave photoconductivity attenuation tester according to claim 1, characterized in that, The instrument's electronic transfer function model is also used to perform deconvolution correction on the original measurement signal, including the following steps: The original time-domain measurement signal to be corrected is subjected to Fourier transform to generate a frequency-domain representation; In the frequency domain, the obtained instrument electronic transfer function is used as an inverse filter to perform a division operation on the frequency domain representation of the original measurement signal in order to construct the signal spectrum with the instrument dynamic distortion corrected. The signal spectrum of the instrument's dynamic distortion, which has been corrected, is subjected to an inverse Fourier transform to generate the final dynamically corrected high-fidelity time-domain signal.

9. The full-process calibration method for a microwave photoconductivity attenuation tester according to claim 8, characterized in that, The expression for performing a division operation on the frequency domain representation of the original measurement signal is as follows: ； in, The frequency domain representation of the real signal. The frequency domain representation of the original measurement signal. This represents the electronic transfer function of the instrument.

10. A full-range calibration system for a microwave photoconductivity attenuation tester, applied to the full-range calibration method for a microwave photoconductivity attenuation tester according to any one of claims 1-9, characterized in that, include: The composite optical path excitation and modulation module is used to generate composite excitation light containing an adjustable DC optical component and a swept AC perturbation optical signal according to control commands; The multidimensional response signal acquisition module is used to simultaneously acquire the photoluminescence intensity, incident photon flux, and steady-state or transient microwave response signal output by the microwave photoconductivity attenuation tester of the sample. A microwave signal phase-locked demodulation module is used to extract a complex response from the microwave response signal that is at the same frequency as the swept-frequency AC perturbation optical signal; The data processing and model identification module is used to receive data from the multidimensional response signal acquisition module and the microwave signal phase-locked demodulation module, and perform calibration, decoupling, reconstruction and modeling operations to generate calibration models, correction operators and real-time analysis results. The closed-loop feedback and adaptive control module is used to receive the real-time analysis results and generate control commands to send to the composite optical path excitation and modulation module to construct an adaptive locking closed-loop feedback loop.

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