Quasi Fermi level splitting imaging method based on photocarrier radiation measurement

Abstract

The invention belongs to the technical field of laser imaging, and particularly relates to a quasi Fermi level splitting imaging method based on photocarrier radiation measurement. According to the invention, a photocarrier radiation measurement (PCR) technology is combined with a frequency sweeping and phase locking amplification technology, a laser pumping material is modulated, a carrier radiation composite signal is accurately recorded by using an InGaAs detector, and the amplitude and phase processing of the radiation signal are normalized, so that the detection precision is improved. And the corresponding relation between the radiation intensity signal and the radiation photon number is established through relative calibration, and a single photon counter is not needed to record all photon numbers, so that quasi Fermi level splitting (QFLS) measurement can be realized without an integrating sphere, the system cost is reduced, and the structure is simplified.

Description

Technical Field

[0001] This invention belongs to the field of laser imaging technology, specifically relating to a quasi-Fermi level splitting imaging method based on optical carrier radiation measurement. Background Technology

[0002] In the field of semiconductor material and device performance characterization, accurate measurement of carrier transport parameters (such as carrier lifetime, diffusion coefficient, and surface recombination rate) is the core foundation for analyzing material physical properties and optimizing device performance. Photocarrier radiative recombination (PCR) technology, as a highly efficient carrier characterization method, is based on the physical phenomenon of "photoinduced carrier radiative recombination": a intensity-modulated laser is used as a pump source to periodically excite the semiconductor sample material, generating non-equilibrium photogenerated carriers (electron-hole pairs) within the sample; these non-equilibrium carriers undergo radiative recombination during relaxation, releasing photons of specific energies.

[0003] Quasi-Fermi level splitting (QFLS) is a core concept in semiconductor non-equilibrium physics and a key indicator for evaluating the performance of semiconductor optoelectronic devices. In thermal equilibrium, the distribution of electrons and holes within a semiconductor follows statistical laws of thermal equilibrium, sharing the same "Fermi level." At this point, carrier generation and recombination are in dynamic equilibrium, with no net carrier transport or energy conversion process. However, in non-equilibrium states (such as those caused by light excitation or electrical injection), external energy input disrupts the equilibrium distribution of carriers—electrons are excited to the conduction band, while holes remain in the valence band. Their statistical distributions are no longer uniform and must be described separately using "electron quasi-Fermi levels" and "hole quasi-Fermi levels."

[0004] The degree of splitting of quasi-Fermi levels (i.e., the energy difference between electron and hole quasi-Fermi levels) is directly positively correlated with the concentration of non-equilibrium carriers: the greater the degree of splitting, the more non-equilibrium carriers accumulate and the higher the separation efficiency, reflecting a more significant deviation of the semiconductor from thermal equilibrium. From a fundamental research perspective, QFLS can reveal the carrier transport paths, recombination dynamics, and energy transfer mechanisms within semiconductors, providing direct evidence for deriving key parameters such as carrier lifetime and mobility. From an application perspective, QFLS plays a decisive role in the performance of optoelectronic devices—it determines the upper limit of the open-circuit voltage of photovoltaic devices (such as solar cells) (open-circuit voltage is positively correlated with QFLS), the luminous quantum efficiency of light-emitting diodes (LEDs) (the larger the QFLS, the higher the radiative recombination probability), and the energy conversion efficiency of photocatalysts. Therefore, it is known in the industry as the "gold standard" for evaluating the performance of optoelectronic devices.

[0005] In practical applications, QFLS measurements can characterize the surface and interface states of semiconductor thin films (such as surface and interface defect density and carrier separation efficiency), providing crucial guidance for optimizing the performance of optoelectronic devices (such as perovskite solar cells and GaN-based LEDs). This has significant theoretical and practical value for technological breakthroughs in clean energy, solid-state lighting, and photocatalysis. This patent will utilize PCR technology to achieve QFLS measurement and imaging.

[0006] Currently, among the characterization techniques for QFLS of semiconductor materials, steady-state photoluminescence (steady-state PL) is the most widely used and closest to the objective of this invention (QFLS measurement). Steady-state PL is based on the photoluminescence effect. It continuously excites a semiconductor sample using a steady-state light source (such as a continuously output laser or LED), generating a large number of non-equilibrium photogenerated carriers within the sample. When the carrier generation rate and recombination rate reach dynamic equilibrium, the non-equilibrium carrier distribution enters a "steady state." At this point, electrons and holes follow quasi-Fermi statistics, and the photons released by their radiative recombination form a "steady-state PL spectrum." QFLS is calculated by fitting the high-energy tail of the spectrum. To ensure measurement accuracy, the experimental system for steady-state photon (PL) technology must meet the requirement of "all-photon collection": since QFLS calculations rely on spectral analysis of "all photogenerated photons" (requiring accurate acquisition of the intensity distribution and peak energy of the PL spectrum), the system must be equipped with an integrating sphere (a spherical optical element with a highly reflective inner wall). Through the multi-angle reflection characteristics of the integrating sphere, all photogenerated photons emitted from all directions on the sample surface are collected into the spectrometer. At the same time, to distinguish the PL signal from external stray light, the system also needs to be equipped with a filter element. However, the traditional filtering scheme of steady-state PL technology can only initially filter external ambient light and cannot completely isolate the interference of excitation light.

[0007] Although steady-state PL technology is currently the mainstream solution for QFLS characterization, it has significant drawbacks in system cost, structural complexity, signal processing efficiency, and measurement function scalability. These drawbacks directly limit its application in low-cost, high-efficiency, and multi-parameter characterization scenarios, as manifested in:

[0008] 1) The experimental system relies on an integrating sphere, which results in high cost and complex structure.

[0009] One of the core drawbacks of steady-state photonics (PL) technology is its reliance on an integrating sphere. Since QFLS calculations require analysis of the spectra of "all photogenerated photons" (obtaining the absolute intensity and complete spectral distribution of the PL signal), the absence of an integrating sphere causes photogenerated photons in some directions to escape, leading to distorted spectral intensity measurements and consequently affecting the accuracy of QFLS calculations. However, as a high-precision optical element, the integrating sphere is not only expensive to manufacture (especially high-reflectivity integrating spheres adapted to a wide spectral range), but also requires precise optical path integration with the spectrometer and light source. This results in a large and complex experimental system, hindering low-cost deployment and miniaturization.

[0010] 2) The excitation light and thermal radiation signals interfere significantly, and the signal processing flow is complex.

[0011] Traditional steady-state photoluminescence (PL) filtering schemes have limitations: they can only filter stray light from the external environment and cannot completely prevent the detector from receiving excitation light (some laser / LED light not absorbed by the sample will be directly reflected to the detector); at the same time, the continuous excitation of the steady-state light source will cause the sample temperature to rise, generating thermal radiation signals (which belong to broadband background noise), and these thermal radiation signals will be superimposed on the PL signal and collected by the detector. The mixing of excitation light and thermal radiation signals results in a large amount of noise in the raw PL signal, which needs to be processed by complex signal denoising algorithms (such as multi-band background subtraction and spectral fitting correction). This not only increases the workload of data processing, but may also affect the accuracy of QFLS measurements due to algorithm errors.

[0012] 3) It can only characterize QFLS individually and cannot simultaneously measure carrier transport parameters.

[0013] The limitations of steady-state photoconductivity (PL) technology are obvious: its core objective is only to measure the quantum flux density (QFLS), and it cannot simultaneously obtain key transport parameters such as carrier lifetime, diffusion coefficient, and surface recombination rate. However, in the research and development of semiconductor materials and devices, QFLS and carrier transport parameters are strongly correlated (e.g., carrier lifetime directly affects the accumulation of non-equilibrium carriers, thus altering QFLS). Obtaining these parameters requires the construction of additional experimental systems (such as time-resolved PL systems and microwave photoconductivity attenuation systems), resulting in cumbersome and inefficient measurement procedures that fail to meet the need for simultaneous characterization of multiple parameters. Summary of the Invention

[0014] To address the above problems, this invention provides a quasi-Fermi level splitting imaging method based on photocarrier radiation measurement.

[0015] The technical solution adopted in this invention is as follows:

[0016] A quasi-Fermi level splitting imaging method based on optical carrier radiation measurement includes the following steps:

[0017] S1. After setting the initial measurement position of the sample to be tested, within the preset frequency range, control the laser light source to emit adaptive light signals of different frequencies to the sample to be tested, measure the laser spot area at the test position by the knife-edge method, and at the same time excite the sample to generate non-equilibrium charge carriers, and the charge carriers radiative recombination release fluorescence signals.

[0018] S2. Acquire fluorescence signals and convert them into electrical signals. The amplitude and phase values ​​of the demodulated signal, where The laser modulation angular frequency ω is related to the carrier AC diffusion length and can be expressed by the formula... It indicates that different Each has a corresponding different angular frequency ω, among which It is the AC diffusion length of charge carriers, which characterizes the diffusion distance of non-equilibrium charge carriers under modulated light excitation. Since the radiative recombination of charge carriers mainly occurs within their diffusible space, almost no effective signal is generated in the region beyond the AC diffusion length. Therefore, the AC diffusion length of charge carriers can be equivalent to the absorption thickness of charge carriers and the corresponding measured thickness of the sample. Thus, the corresponding angular frequency ω can be calculated based on the measured thickness of the sample.

[0019] S3. Change the measurement position of the sample to be tested, and remeasure the amplitude and phase values ​​at the current measurement position according to the method of S1-S2. Repeat this step until the amplitude and phase values ​​of all set measurement positions are obtained. Acquire the frequency sweep data for each measurement position. The frequency sweep data refers to the amplitude and phase values ​​corresponding to different measurement thicknesses of the sample obtained by controlling the frequency change of the laser light source. It is expressed as frequency-amplitude and frequency-phase relationship data. Here, the frequency is the modulation frequency, defined as... The relationship between this parameter and the laser modulation angular frequency ω is as follows: ;

[0020] S4. Fit the data from the sweep frequency data at each measurement location:

[0021] The expression for the electrical signal is ,

[0022] ,

[0023] in , , and

[0024] , ,

[0025] ( The total thickness of the sample. Doping concentration, The DC component, For the purpose of exchanging quantities, To stimulate light intensity, The reflectivity of the front surface of the sample to the excitation light is denoted as . The quantum efficiency of charge carrier generation. It is Planck's constant. To excite photon frequency, Let be the absorption coefficient of the sample to the excitation light. Where is the diffusion coefficient. For carrier lifetime, (For surface recombination rate.) The swept frequency data is based on... The amplitude and phase are fitted to obtain the carrier lifetime corresponding to the measurement position. With diffusion coefficient D;

[0026] S5. Based on the given measured thickness and the carrier lifetime obtained in S4 The modulation frequency corresponding to the measured thickness can be calculated from the diffusion coefficient D using the relationships between the measured thickness and modulation angular frequency, and between the modulation angular frequency and modulation frequency in S2 and S3. Set the laser modulation frequency to The sample was replaced with a copper sheet, and the power of the laser source was gradually increased. The signal amplitude measured at different laser powers was recorded. At the same time, the optical power incident on the sample was measured using an optical power meter. The absolute number of photons reflected by the copper sheet was calculated using the spot area measured in S1. Multiple data points showing the change in photon number with power were recorded and fitted into a linear function (using...). For standard format, The variable is the signal amplitude. The variable is the absolute photon number. and This refers to the constant to be fitted. By inputting multiple sets of signal amplitude minus absolute photon number, the constant can be fitted. and The value of is used to obtain the fitting function. This establishes a calibration relationship between "signal amplitude and absolute photon number": Input the signal amplitude The absolute number of photons can then be obtained. That is, the number of photons produced by the corresponding radiation. ;

[0027] S6. Calculate the Quasi-Fermi Level Splitting (QFLS) value:

[0028] Through the Lambert-Bill model Calculate the thin film absorptivity of the sample at the measurement point, where It is the thin film absorptivity, which characterizes the proportion of photons with energy E that the sample absorbs. It is the surface reflectance of the sample; It is the absorption coefficient of the sample; It is the absorption thickness, as described in S2, and this parameter also corresponds to the carrier AC diffusion length. ;

[0029] Calculate the number of photons produced by radiation Combined with the calibration relationship of "signal amplitude - absolute photon number": The amplitude value of the demodulated signal is converted into the number of photons generated by radiation at the measurement location, that is, the total number of photons released by carrier radiative recombination.

[0030] Based on the non-thermal radiation generalized Kirchhoff model, through the formula Establish The correlation with QFLS leads to the QFLS value, where the blackbody radiation constant is... ,in It is the Boltzmann constant; This is the sample temperature, obtained by measuring the ambient temperature during the experiment. It is Planck's constant; It's the speed of light;

[0031] The QFLS values ​​of all measurement points are stitched together according to their position coordinates on the sample surface to generate a QFLS image of the sample; the QFLS value and carrier lifetime of each measurement point are also output. Diffusion coefficient D.

[0032] Furthermore, in S1, a periodic electrical signal with a set frequency range is output by a function generator to control the power of the laser source.

[0033] Furthermore, in S2, a photodetector collects fluorescence signals, and a lock-in amplifier demodulates the signals.

[0034] Furthermore, in S3, the method for changing the measurement position of the sample to be tested is to place the sample to be tested on an electric displacement stage, and use a PLC to control the position of the electric displacement stage to change the measurement position of the sample to be tested.

[0035] The beneficial effects of this invention are as follows:

[0036] 1) The optical carrier radiation measurement (PCR) technique combined with frequency sweeping and lock-in amplification techniques was adopted. By modulating the laser pump material, the carrier radiation recombination signal was accurately recorded using an InGaAs detector. The amplitude and phase of the radiation signal were normalized, and the correspondence between the radiation intensity signal and the number of radiation photons was established through "relative calibration". It is not necessary to use a single photon counter to record all the photons. Therefore, quasi-Fermi level splitting (QFLS) measurement can be realized without integrating sphere, which reduces system cost and simplifies the structure.

[0037] 2) Introducing a long-pass filter in the experiment avoids the detector receiving excitation light, eliminates thermal radiation signal interference, greatly simplifies the signal processing flow, and improves measurement accuracy.

[0038] 3) Based on the amplitude and phase frequency curves obtained from frequency scanning, and combined with theoretical model fitting, parameters such as carrier lifetime, diffusion coefficient, and surface recombination rate can be measured accurately at the same time. A new model for calculating carrier parameters is derived by combining the photocarrier radiation model, the non-thermal radiation generalized Kirchhoff model, and the Lambert-Beer model. ), thus obtaining The values ​​enable simultaneous characterization of multiple parameters, such as carrier lifetime, diffusion coefficient, surface recombination rate, and QFLS. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the imaging system structure in an embodiment;

[0040] Figure 2 This is a flowchart illustrating an embodiment;

[0041] Figure 3 This is a schematic diagram of amplitude-frequency fitting and phase-frequency fitting. Detailed Implementation

[0042] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0043] Example:

[0044] like Figure 1 As shown, based on the method of this invention, the imaging system built in this example includes a function generator 1, a continuous-wave fiber laser 2, an attenuator 3, a reflector 4, an off-axis parabolic mirror 5, a sample 6, an electric displacement stage 7, a long-pass filter 8, a photodetector 9, a lock-in amplifier 10, a computer 11, and a PCL 12. In the imaging system, the function generator 1 modulates the continuous-wave fiber laser 2 to generate periodic light intensity. After passing through the adjustable attenuator 3 and the reflector 4, the sample 6 is excited. The fluorescence signal is collected by the off-axis parabolic mirror 5, and the excitation light is filtered out by the long-pass filter 8. The signal amplitude and phase are demodulated by the near-infrared photodetector 9 and the lock-in amplifier 10. Specific measurement settings include: controlling the function generator via computer to output a specific frequency range (the frequency range used in this example). (e.g., z) is a periodic electrical signal (used to modulate laser intensity). The signal parameters need to be adapted to the sample to be measured (e.g., perovskite thin films need to avoid excessive power to prevent material damage).

[0045] Spot measurement: The laser output from the laser is guided to the sample position through an attenuator and a reflector, and the laser spot area at that position is measured using the knife-edge method (to lay the foundation for subsequent photon count calibration).

[0046] Detector and lock-in amplifier debugging: Ensure that the long-pass filter is installed in place (to filter out the excitation light), and that the photodetector and lock-in amplifier are connected normally. Confirm that the lock-in amplifier can stably demodulate the signal amplitude and phase through a pre-excitation test.

[0047] The processing flow in this example is as follows: Figure 2 As shown, starting from the photocarrier radiation model, the generalized Kirchhoff's laws for non-thermal radiation, and the Lambert-Beer model, the relationship between carrier radiation and QFLS is derived. Key carrier parameters are fitted / calculated, a mapping relationship between absorption and diffusion is established, and finally, the QFLS value is obtained. Figure 2 In this model, Model A represents the photocarrier radiation model, Model B represents the Lambert-Beer model, and Model C represents the non-thermal radiation generalized Kirchhoff model. (The photocarrier radiation model is a dynamic characterization model based on the non-equilibrium carrier radiation recombination effect in semiconductors. Its core is to achieve accurate analysis of the carrier transport characteristics of semiconductor materials through the logic of modulating light to excite semiconductor materials, detecting radiation signals, and inverting parameters. The non-thermal radiation generalized Kirchhoff model describes how, in non-thermal equilibrium, the absorptivity and emissivity of an object are no longer simply equal, but are related through non-equilibrium microscopic processes such as carrier transport and energy level population. The Lambert-Beer model describes how the intensity of monochromatic light decreases with medium concentration and propagation distance when passing through a uniform, non-scattering absorbing medium.) The specific process is as follows:

[0048] The sample to be measured (such as a perovskite thin film) is placed on an electric displacement stage, and the computer controls the electric displacement stage to move to the first measurement point. The frequency sweep function of the function generator is activated: the laser modulation frequency is continuously changed within a preset frequency range. At each frequency, the excitation laser outputs a laser with a corresponding intensity modulation, which excites the sample to generate non-equilibrium charge carriers. The charge carriers radiative recombination releases a fluorescence signal. The fluorescence signal is collected by an off-axis parabolic mirror, filtered by a long-pass filter, and then converted into an electrical signal by a photodetector. The amplitude and phase values ​​of the signal are demodulated by a lock-in amplifier and transmitted to the computer in real time.

[0049] Repeat the above steps to complete the frequency sweep data acquisition for all measurement points on the sample surface (each measurement point will obtain a set of "frequency-amplitude" and "frequency-phase" data).

[0050] Fitting key carrier parameters: The amplitude-frequency / phase-frequency data at each measurement point were fitted using numerical analysis software (see reference). Figure 3 (Fitting curve), to obtain the carrier lifetime at that point ( ) and diffusion coefficient (D);

[0051] Once the film thickness is determined, it can be considered as the AC diffusion length, and can be calculated using the formula... The modulation frequency f when carriers diffuse to a certain depth can be calculated.

[0052] (Parameter explanation:)

[0053] : Carrier AC diffusion length, characterizing the diffusion distance of non-equilibrium carriers under modulated optical excitation;

[0054] D: Carrier diffusion coefficient, a carrier transport parameter obtained through fitting;

[0055] : Carrier lifetime, the carrier transport parameters obtained by fitting;

[0056] ω: Laser modulation angular frequency, calculated from the modulation frequency f (ω=2πf);

[0057] Photon number calibration (establishing the relationship between signal amplitude and absolute photon number)

[0058] This method establishes a correspondence between the lock-in amplifier signal and the number of radiated photons through "relative calibration": the sample to be measured is replaced with a highly reflective copper sheet (the copper sheet does not generate radiative recombination signals, but only reflects the excitation light); at the previously determined modulation frequency f, the excitation laser power is adjusted and gradually increased, and the signal amplitude of the lock-in amplifier demodulated at this time is recorded sequentially. At the same time, the incident light power is measured using an optical power meter. The absolute number of photons reflected by the copper sheet can be calculated using the previously measured spot area. Multiple data points of photon count change with power are recorded, fitted into a function, and then a calibration relationship of "lock-in amplifier signal amplitude - absolute photon count" is established (when measuring the sample later, the signal amplitude can be converted into the absolute number of radiated photons through this relationship).

[0059] Data processing and QFLS calculation (multi-parameter fitting and final value derivation):

[0060] Based on the collected amplitude / phase frequency data, and combined with the optical carrier radiation model, the non-thermal radiation generalized Kirchhoff model, and the Lambert-Beer model, the QFLS value is calculated through the following steps:

[0061] Calculation of thin film absorptivity: using the Lambert-Beer model Calculate the thin film absorption rate of the sample at the measurement point:

[0062] (Parameter explanation:)

[0063] a(E): Thin film absorptivity, characterizing the proportion of photons with energy E absorbed by the sample;

[0064] R: Sample surface reflectance;

[0065] The absorption coefficient of the sample and known material parameters;

[0066] d: Absorption thickness, here taken as the carrier AC diffusion length. (Because charge carriers mainly diffuse and radiatively recombine within this range).

[0067] E: Photon energy;

[0068] Calculate the number of photons produced by radiation ( ): Combining the photon number calibration relationship, the signal amplitude value demodulated by the lock-in amplifier is converted into the number of radiation-generated photons at the measurement point, that is, the total number of photons released by carrier radiative recombination;

[0069] Derivation of QFLS value: Based on the non-thermal radiation generalized Kirchhoff model, through the formula Establish The correlation with QFLS leads to the derivation of the QFLS value. Among these, the blackbody radiation constant...

[0070] (Parameter explanation:)

[0071] The number of photons produced by radiation is obtained by signal amplitude conversion;

[0072] Blackbody radiation constant, which describes the radiation characteristics of a blackbody under thermal equilibrium;

[0073] QFLS: Quasi-Fermi level splitting, a core indicator to be determined, reflecting the accumulation and separation efficiency of non-equilibrium carriers;

[0074] Boltzmann constant;

[0075] T: Sample temperature, obtained from the experimental ambient temperature measurement;

[0076] h: Planck's constant;

[0077] c: speed of light;)

[0078] QFLS Imaging and Result Output: The QFLS values ​​of all measurement points are stitched together according to their position coordinates on the sample surface to generate a QFLS image of the sample; the QFLS value and carrier lifetime of each measurement point are also output. Parameters such as diffusion coefficient (D).

[0079] By measuring multiple points on the perovskite thin film, the QFLS corresponding to different locations can be calculated, the upper limit of the open-circuit voltage can be predicted, and the film quality can be evaluated through the film's uniformity. Below are two sets of QFLS measurement data for a perovskite thin film with a band gap of 1.55 eV, as shown in Table 1. The QFLS values ​​between depths and the experimental measurements in Table 2 are obtained from the film surface to depth. QFLS values ​​between depths:

[0080] Table 1. Experimental measurements of the film surface to... QFLS values ​​between depths

[0081] Table 2 shows the experimental measurements obtained from the film surface to... QFLS values ​​between depths

[0082] The experimentally measured QFLS values ​​for different film thicknesses conform to the standard values ​​of 0.6 eV to 1.5 eV obtained by other methods. As can be seen from the table, at the same point... QFLS value relative The value is relatively small, which is due to the nonradiative recombination of charge carriers caused by surface defects. However, the difference in QFLS value at the same depth is not significant, indicating that the film is relatively uniform in the transverse direction and the film quality is good.

Claims

1. A quasi-Fermi level splitting imaging method based on photocarrier radiation measurement, characterized in that, Includes the following steps: S1. After setting the initial measurement position of the sample to be tested, within the preset frequency range, control the laser light source to emit adaptive light signals of different frequencies to the sample to be tested, measure the laser spot area at the test position by the knife-edge method, and at the same time excite the sample to generate non-equilibrium charge carriers, and the charge carriers radiative recombination release fluorescence signals. S2. Acquire fluorescence signals and convert them into electrical signals. The amplitude and phase values ​​of the demodulated signal, where The laser modulation angular frequency ω is related to the carrier AC diffusion length and can be expressed by the formula... It indicates that different For different angular frequencies ω, where It is the AC diffusion length of charge carriers, which characterizes the diffusion distance of non-equilibrium charge carriers under modulated light excitation. The AC diffusion length of charge carriers is equivalent to the absorption thickness of the charge carriers and the corresponding measured thickness of the sample, so as to calculate the corresponding angular frequency ω based on the measured thickness of the sample. S3. Change the measurement position of the sample to be tested, and remeasure the amplitude and phase values ​​at the current measurement position according to the method of S1-S2. Repeat this step until the amplitude and phase values ​​of all set measurement positions are obtained. Acquire the frequency sweep data for each measurement position. The frequency sweep data refers to the amplitude and phase values ​​corresponding to different measurement thicknesses of the sample obtained by controlling the frequency change of the laser light source. It is expressed as frequency-amplitude and frequency-phase relationship data. Here, the frequency is the modulation frequency, defined as... The relationship between this parameter and the laser modulation angular frequency ω is as follows: ; S4. Fit the data from the sweep frequency data at each measurement location: The expression for the electrical signal is , ， in , , and: ， ， in, The total thickness of the sample. Doping concentration, The DC component, For the purpose of exchanging quantities, To stimulate light intensity, The reflectivity of the front surface of the sample to the excitation light is denoted as . The quantum efficiency of charge carrier generation. It is Planck's constant. To excite photon frequency, Let be the absorption coefficient of the sample to the excitation light. The diffusion coefficient is... For carrier lifetime, For surface recombination rate; the swept frequency data is based on The amplitude and phase are fitted to obtain the carrier lifetime corresponding to the measurement position. With diffusion coefficient D; S5. The required sample thickness and carrier lifetime obtained from S4. Using the diffusion coefficient D, the modulation frequency corresponding to this measured thickness is calculated through the relationships between the measured thickness and modulation angular frequency, and between the modulation angular frequency and modulation frequency in S2 and S3. Set the modulation frequency of the laser to The sample was replaced with a copper sheet, and the power of the laser source was gradually increased. The signal amplitude measured at different laser powers was recorded. At the same time, the optical power incident on the sample was measured using an optical power meter. The absolute number of photons reflected by the copper sheet was calculated using the spot area measured in S1. Multiple data points of photon number change with power were recorded, fitted into a linear function, and a calibration relationship of "signal amplitude - absolute photon number" was established. Input the signal amplitude The absolute number of photons can then be obtained. That is, the number of photons produced by the corresponding radiation. ; S6. Calculate the Quasi-Fermi Level Splitting (QFLS) value: Through the Lambert-Bill model Calculate the thin film absorptivity of the sample at the measurement point, where It is the thin film absorptivity, which characterizes the proportion of photons with energy E that the sample absorbs. It is the surface reflectance of the sample; It is the absorption coefficient of the sample; It is the absorption thickness, which corresponds to the AC diffusion length of charge carriers. ; Calculate the number of photons produced by radiation Combined with the calibration relationship of "signal amplitude - absolute photon number": The amplitude value of the demodulated signal is converted into the number of photons generated by radiation at the measurement location, that is, the total number of photons released by carrier radiative recombination. Based on the non-thermal radiation generalized Kirchhoff model, through the formula Establish The correlation with QFLS leads to the QFLS value, where the blackbody radiation constant is... ,in It is the Boltzmann constant; This is the sample temperature, obtained by measuring the ambient temperature during the experiment. It is Planck's constant; It's the speed of light; The QFLS values ​​of all measurement points are stitched together according to their position coordinates on the sample surface to generate a QFLS image of the sample; the QFLS value and carrier lifetime of each measurement point are also output. Diffusion coefficient D.

2. The quasi-Fermi level splitting imaging method based on photocarrier radiation measurement according to claim 1, characterized in that, In S1, a periodic electrical signal with a set frequency range is output by a function generator to control the power of the laser source.

3. The quasi-Fermi level splitting imaging method based on photocarrier radiation measurement according to claim 1, characterized in that, In S2, a photodetector collects fluorescence signals, and a lock-in amplifier demodulates the signals.

4. The quasi-Fermi level splitting imaging method based on photocarrier radiation measurement according to claim 1, characterized in that, In S3, the method to change the measurement position of the sample to be tested is to place the sample to be tested on an electric displacement stage, and the position of the electric displacement stage is controlled by the PLC to change the measurement position of the sample to be tested.

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