An efficient measurement system and method for positron annihilation lifetime for thin film sample characterization

Abstract

The present invention provides a highly efficient positron annihilation lifetime measurement system and method for thin film sample characterization. The system comprises a positron emitter, a detector array, and a thin film sample to be measured. A radioactive source is placed within the positron emitter, and the thin film sample to be measured is positioned between the positron emitter and the positron detectors in the detector array. The system is suitable for use in strong source environments and can comprehensively detect positron annihilation events, fully eliminating positron annihilation events in non-sample areas, thereby achieving highly efficient measurement of the positron annihilation lifetime of thin film samples.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear spectroscopy and nuclear detection technology, and specifically relates to a high-efficiency measurement system and method for positron annihilation lifetime for thin film sample characterization. The system and method are suitable for strong source environments, can perform all-round detection of positron annihilation cases, fully exclude positron annihilation cases in non-samples, and realize efficient measurement of the positron annihilation lifetime of thin film samples. Background Art

[0002] Positron annihilation is a nondestructive, sensitive probe for atomic-scale defects in materials, characterized by its "automatic" defect detection and high sensitivity. As the most representative measurement method in positron annihilation spectroscopy, positron annihilation lifetime measurement can accurately measure the type and concentration of defects in materials. It is also one of the few effective measurement methods for accurately detecting characteristic information such as the free volume size in polymer materials, offering unique advantages and widespread application in materials science research.

[0003] Commonly used in conventional positron annihilation lifetime measurements 22 Na radioactive source, 22 When Na decays, it emits a positron and a gamma photon with an energy of 1.28 MeV. During the measurement, a "sample-source-sample" sandwich configuration is employed to ensure that all positrons are annihilated in the sample. Simultaneously, two gamma detectors are placed in close proximity to the sample. One detector detects the 1.28 MeV gamma photon, using this detection signal as the start signal for the positron annihilation lifetime measurement; the other detector detects the 0.511 MeV gamma photon produced by the positron annihilation, using this detection signal as the stop signal for the positron annihilation lifetime measurement. For thin film samples, since positrons generated by the positron source have a limited range within the material, they may penetrate the sample, significantly reducing the number of valid annihilation events detected in the sample. Furthermore, this detection method means that each detector can only detect one of the 1.28 MeV and 0.511 MeV gamma rays at a time, and events in which both gamma rays simultaneously impinge on a given detector are discarded. Furthermore, the detector structure and geometry determine the maximum count rate. The probability of detector signal pileup is related to the width of the detector signal and the detection count rate. For detectors based on fixed crystals and photoelectric converters, the detection count rate has a limit. For example, BaF2 detectors are commonly used in gamma-ray detectors. Assuming a signal width of 800ns, if the probability of signal pileup does not exceed 1%, the maximum count rate per detector is 12,500 cps.

[0004] Therefore, it is necessary to develop a new detection structure to improve the detection efficiency of annihilation cases, so as to achieve efficient characterization of the positron annihilation lifetime of the microstructure in thin film sample materials. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a high-efficiency measurement system and method for positron annihilation lifetime for thin film sample characterization, which consists of a positron emitter, a detector array, and a thin film sample to be measured; the radiation source is placed in the positron emitter, and the thin film sample to be measured is arranged between the positron emitter and the positron detector in the detector array. The present invention adopts a detector array structure, which is suitable for strong source environments and improves the counting rate of the detector; multiple gamma detectors in the detector array can be flexibly arranged at any placement angle and in any splicing method to maximize the effective detection solid angle and perform all-round detection of positron annihilation cases; positrons other than the thin film sample to be measured can be detected in all directions, and positron annihilation cases in non-samples can be fully excluded; at the same time, the present invention can directly detect the starting moment of the positron, and is suitable for all types of positron radiation sources (such as 68 Ge, 22 Na).

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A high-efficiency positron annihilation lifetime measurement system for thin film sample characterization consists of a positron emitter, a detector array, and a thin film sample to be measured; a radioactive source is placed in the positron emitter, and the thin film sample to be measured is arranged between the positron emitter and the positron detectors in the detector array.

[0008] Furthermore, the positron emitter consists of a plastic scintillator, a fast-response photoelectric converter and a radiation source; the radiation source is placed between the plastic scintillator and the photoelectric converter; when positrons enter the plastic scintillator and deposit energy, they generate fluorescent photons, which are converted into electrical signals by the photoelectric converter and output to the back-end circuit for further processing.

[0009] Furthermore, a reflective layer is provided on the upper surface and side surfaces of the plastic scintillating sheet, which can not only fully transmit the fluorescent photons to the photoelectric converter, but also has a light shielding function to prevent external visible light from interfering with the normal operation of the positron emitter.

[0010] Furthermore, the thickness of the plastic scintillator depends on the positron energy distribution of the selected radiation source. The thickness should be sufficient to allow the positrons to deposit sufficient energy in the plastic scintillator, thereby generating enough fluorescent photons to make the detector signal amplitude higher than the electronic noise and increase the effective counting rate. At the same time, the thickness of the plastic scintillator should not be too thick to ensure that as many positrons as possible pass through the scintillator.

[0011] Furthermore, the detector array is composed of a positron detector and a plurality of gamma detectors; structurally, the positron detector is located at the center of the detector array, and the plurality of gamma detectors are arranged in an array around the central positron detector.

[0012] Furthermore, the positron detector is composed of a plastic scintillator coupled with a fast-response photoelectric converter, and is responsible for detecting positrons that penetrate the thin film sample.

[0013] Furthermore, the thickness of the plastic scintillator depends on the positron energy distribution of the selected radioactive source. It should be thick enough to ensure that the positrons deposit sufficient energy in the plastic scintillator, and accordingly generate enough fluorescent photons, so that the detector signal amplitude is higher than the electronic noise, to meet the complete detection of the incident positrons, thereby achieving complete exclusion of annihilation cases in non-samples; at the same time, the thickness of the scintillator should not be too thick so that the detection efficiency of gamma photons is as low as possible, reducing the erroneous exclusion of positron annihilation cases.

[0014] Furthermore, a reflective layer is provided on the upper surface and side surfaces of the plastic scintillator, which can not only fully transmit the fluorescent photons to the photoelectric converter, but also has a light shielding function to prevent external visible light from interfering with the normal operation of the positron detector.

[0015] Furthermore, the gamma detectors are composed of a scintillator with high time resolution and a fast-response photoelectric converter coupled thereto, which is responsible for fully detecting the gamma photons generated after positron annihilation, thereby achieving full detection of positron annihilation cases; the scintillators include BaF2, LaBr3, LYSO, etc.; the photoelectric converters include silicon photomultiplier tubes, etc.; the outer surface of the gamma detector is encapsulated with a light-proof structural material to prevent external visible light from interfering with the normal operation of the detector.

[0016] Furthermore, the structure of the scintillator in the gamma detector depends on the intensity of the actual positron source and the system's requirements for time and energy resolution. The greater the intensity of the positron source, the smaller the geometric cross-sectional size of the scintillator should be, reducing the solid angle it forms to the positron source, thereby reducing the probability of multiple gamma photons being detected in a short period of time and effectively reducing the probability of signal accumulation. In principle, if the preparation technology permits, the size of the scintillator can be as small as possible to improve the time resolution of positron lifetime detection. The positions of the gamma detectors can be flexibly distributed on a spherical surface centered on the concentrated annihilation area of ​​positrons in the sample. The number of gamma detectors is determined by the requirements for the detection efficiency of positron annihilation cases in actual situations. In principle, the solid angle formed by these gamma detectors to the sample should be as large as possible to achieve all-round detection of annihilated gamma photons and fully improve the collection efficiency of effective positron annihilation cases.

[0017] The present invention also provides a measurement method of a positron annihilation lifetime high-efficiency measurement system for thin film sample characterization, comprising the following steps:

[0018] Step 1: For different types of positrons, a positron emitter detects the positrons entering the thin film sample, a positron detector is set in the detector array to detect the positrons penetrating the thin film sample, and multiple gamma detectors are set in the detector array to detect the gamma photons generated after the positron annihilation;

[0019] Step 2: After the positron emitter detects a positron, it generates a first positron signal; after the positron detector in the detector array detects a positron, it generates a second positron signal; after the gamma detector detects a gamma photon, it generates one or more gamma signals; the signal acquisition module is responsible for collecting the first positron signal, the second positron signal, and the one or more gamma signals, and transmitting the waveform data to the data processing module for processing;

[0020] Step 3: The data processing module performs energy identification, timing, annihilation case selection and lifetime spectrum statistics on the waveform data;

[0021] Furthermore, the step 3 includes, for the first positron signal, setting the energy threshold to the electronic noise level, and generating a start timing signal after timing; for one or more gamma signals, setting the energy threshold to the photoelectric peak of the 0.511 MeV gamma photon, combining signal shape discrimination, screening the gamma photon signal generated by positron annihilation from one or more gamma signals, and generating a stop timing signal after timing; within a certain time window, calculating the time difference between the start timing signal and the stop timing signal as the lifetime of each positron annihilation case; for the second positron signal, setting the energy threshold to the electronic noise level, only When the second positron signal is detected, a discrimination signal will be output, and the discrimination signal will be used as the basis for determining whether the positron annihilation case is recorded or not; when no discrimination signal is output, it means that the case is a valid positron annihilation case in the thin film sample, and a time difference calculation will be performed; and when a discrimination signal is output, it means that the positron in the case is not annihilated in the sample, and the time difference calculation will be suppressed. At the same time, the data processing module directly enters the processing of the next case, thereby excluding positron annihilation cases in non-thin film samples; finally, the time difference corresponding to each valid positron annihilation case will be counted, and after accumulating enough cases, a positron annihilation lifetime spectrum will be generated.

[0022] Beneficial effects:

[0023] (1) The gamma detector used in the present invention has a small solid angle to the positron source, low gamma photon detection efficiency, and can reduce the probability of signal accumulation. It is suitable for positron annihilation detection under strong sources. The multiple gamma detectors arranged in the detector array can be flexibly spliced ​​to ensure that the overall array has a large detection solid angle for gamma photons, thereby improving the system detection count rate.

[0024] (2) The device and method proposed in the present invention have the characteristics of low pile-up probability and all-round detection of positron annihilation cases when detecting under a strong positron source, which can make up for the deficiency of low positron annihilation ratio of thin film samples in the present invention and achieve the purpose of efficient and rapid detection of thin film samples.

[0025] (3) The positron starting signal in the present invention is directly generated by the positron emitter when the positron passes through the plastic scintillator to deposit energy, and is applicable to all types of positron radiation sources (such as 68 Ge, 22 Na), broadening the experimental conditions for positron annihilation lifetime measurements. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagram of a highly efficient positron annihilation lifetime measurement device for thin film sample characterization according to the present invention;

[0027] Figure 2 Schematic diagram of the measuring circuit of the present invention;

[0028] Figure 3 Schematic diagram of the structure of the positron emitter of the present invention;

[0029] Figure 4 Schematic diagram of the detector array structure of the present invention;

[0030] Figure 5 This is a graph showing the variation of positron annihilation intensity with film thickness in different types of thin film materials. DETAILED DESCRIPTION

[0031] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0032] For the rapid characterization of thin film samples, the present invention adopts a detector array structure, which is suitable for strong source environments and improves the detector's limit counting rate; it can maximize the effective detection solid angle through flexible splicing and perform all-round detection of positron annihilation cases; it can accurately identify positrons annihilated outside the thin film sample, fully exclude positron annihilation cases in non-samples, and effectively improve the signal-to-noise ratio; at the same time, the present invention can directly detect the starting moment of positrons and is applicable to all types of positron radiation sources (such as 68 Ge, 22 Na).

[0033] like Figure 1 As shown, the present invention's high-efficiency positron annihilation lifetime measurement system for thin film sample characterization consists of a positron emitter, a detector array, and the thin film sample being measured. Unlike the traditional "sample-radiation source-sample" structure, in this invention, the radiation source is placed inside the positron emitter, and the thin film sample being measured is placed between the positron emitter and the positron detectors in the detector array.

[0034] The direction of positrons generated by the radioactive source is completely random, emitting them randomly throughout space, with only a portion entering the thin film sample. For some positrons with higher energy, they will penetrate the thin film and be annihilated in the detector array. Another portion of positrons never enter the sample, but are annihilated in the positron emitter. For different types of positrons, when the measurement system of the present invention is operating, the positron emitter detects positrons entering the thin film sample. The detector array has two functions: one is to set a positron detector in the center to detect positrons that penetrate the thin film sample; the other is to set multiple gamma detectors around the positron detector to perform all-round detection of gamma photons generated after positron annihilation. Positron annihilation in both the sample and other non-sample materials will produce annihilation gamma photons. The characteristic gamma detection unit used to detect positron annihilation information cannot distinguish whether the detected annihilation gamma photons come from the sample. Therefore, annihilation cases need to be screened during measurement.

[0035] In order to fully exclude the positron annihilation information in non-samples and only retain the positron annihilation components in thin film samples, the present invention designs a measurement circuit based on the detector signal characteristics and processing methods, such as Figure 2 shown.

[0036] When a positron emitter detects a positron, it generates a first positron signal. When a positron detector detects a positron, it generates a second positron signal. When a gamma photon is detected by a multi-gamma detector, it generates one or more gamma signals. The signal acquisition module is responsible for collecting the first positron signal, the second positron signal, and one or more gamma signals, and transmitting the waveform data to the data processing module for processing.

[0037] The data processing module is responsible for energy discrimination, timing, annihilation case selection, and lifetime spectrum statistics of the waveform data. For the first positron signal, the energy threshold is set to the electronic noise level, which fully detects all initial positron energies emitted by the radiation source while avoiding interference from electronic noise. After timing, a start timing signal is generated. For one or more gamma signals, the energy threshold is set to the photopeak of the 0.511 MeV gamma photon to improve time measurement accuracy and eliminate other gamma background interference. Combined with signal shape discrimination, gamma photon signals generated by positron annihilation are filtered out from the one or more gamma signals. After timing, a stop timing signal is generated. Within a certain time window (on the order of hundreds of nanoseconds), the time difference between the start timing signal and the stop timing signal is calculated as the lifetime of each positron annihilation case. For the second positron signal, the energy threshold is set to the electronic noise level. Once the second positron signal is detected, a selection signal is output, which serves as the basis for determining whether the positron annihilation case should be recorded. When no discrimination signal is output, it means that the event is a valid positron annihilation event in the thin film sample, and a time difference calculation will be performed; when a discrimination signal is output, it means that the positron in the event is not annihilated in the sample, and the time difference calculation will be suppressed. At the same time, the data processing module directly enters the processing of the next event, thereby excluding positron annihilation events in non-thin film samples; finally, the time difference corresponding to each valid positron annihilation event will be counted, and after accumulating enough events, a positron annihilation lifetime spectrum will be generated.

[0038] like Figure 3 As shown, the positron emitter consists of a plastic scintillator, a fast-response photoelectric converter, and a radioactive source. The radioactive source is placed between the plastic scintillator and the photoelectric converter. When positrons enter the plastic scintillator and deposit energy, they generate fluorescent photons. The photoelectric converter converts the fluorescence into an electrical signal and outputs it to the back-end circuit for further processing. A reflective layer (such as Teflon or BaSO4) is coated on the upper and side surfaces of the plastic scintillator. This layer effectively transmits the fluorescent photons to the photoelectric converter while shielding against external visible light. The thickness of the plastic scintillator used in the positron emitter should be appropriate, depending on the positron energy distribution of the selected radioactive source. The plastic scintillator should be thick enough to allow positrons to deposit sufficient energy in the scintillator, generating a sufficient number of fluorescent photons. This allows the detector signal amplitude to be higher than the electronic noise, thereby increasing the effective count rate. At the same time, the plastic scintillator should not be too thick to ensure that as many positrons as possible pass through the scintillator.

[0039] In the present invention, the structure of the detector array is as follows Figure 4As shown, the system consists of multiple gamma detectors surrounding a central positron detector. The positron detector, composed of a plastic scintillator coupled to a fast-response photoelectric converter, is responsible for detecting positrons that penetrate the thin film sample. The thickness of the plastic scintillator depends on the positron energy distribution of the selected radiation source. It should be thick enough to ensure that the positrons deposit sufficient energy in the plastic scintillator, generating a sufficient number of fluorescence photons, so that the detector signal amplitude is higher than the electronic noise, ensuring complete detection of incident positrons and thus completely eliminating annihilation cases not in the sample. At the same time, the scintillator should not be too thick to minimize the detection efficiency of gamma photons and reduce the false exclusion of positron annihilation cases.

[0040] The detector array contains multiple gamma detectors, which are responsible for fully detecting the gamma photons produced after positron annihilation. The structure, number and position of the gamma detectors are reasonably set according to the requirements of time resolution, energy resolution and detection efficiency of the specific detection scenario; Figure 4 As shown, gamma detectors are arranged in a square configuration around the positron detector. Alternatively, they can be arranged in a ring or sphere. To ensure accurate detection of positron annihilation lifetimes, gamma detectors utilize high-resolution scintillator detectors. These detectors typically consist of a scintillator with excellent time resolution (such as BaF2, LaBr3, or LYSO) coupled to a fast-response photoelectric converter (such as a silicon photomultiplier tube).

[0041] The outer surfaces of the positron detectors and gamma detectors in the detector array are encapsulated with light-proof structural materials such as reflective layers to prevent external visible light from interfering with the normal operation of the detectors.

[0042] The thickness of the film sample applicable to the present invention is determined by the properties of the material being tested and the structure of the radioactive source. To protect the radioactive source, Kapton film is generally used to encapsulate the source, and the positron annihilation component in the Kapton film is recorded as the source component in the measured positron annihilation lifetime spectrum. Assuming that the radioactive source is wrapped by two layers of 7μm thick Kapton film, and positron annihilation cases in other non-sample materials are completely excluded, Geant4 Monte Carlo software was used to simulate the positron annihilation situation in several typical thin film materials of different thicknesses. The results are as follows: Figure 5 To reduce the influence of source components, if the intensity of positron annihilation events in the sample in the lifetime spectrum is required to be no less than 50%, the minimum measurement thicknesses of the metal Fe, semiconductor Si, and polymer PE films are 10 μm, 28 μm, and 35 μm, respectively.

[0043] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An efficient positron annihilation lifetime measurement system for thin film sample characterization, characterized by: The system consists of a positron emitter, a detector array, and a thin film sample to be measured; the detector array consists of a positron detector and multiple gamma detectors; a radioactive source is placed in the positron emitter, and the thin film sample to be measured is set between the positron emitter and the positron detectors in the detector array; during measurement, the measurement system uses a strong source to increase the count rate of the detector array; multiple gamma detectors are set to maximize the effective detection solid angle and conduct all-round detection of positron annihilation cases; the positron detector accurately identifies positrons annihilated outside the thin film sample, fully excludes positron annihilation cases in non-samples, and improves the signal-to-noise ratio; The positron emitter consists of a plastic scintillator, a fast-response photoelectric converter, and a radioactive source; the radioactive source is placed between the plastic scintillator and the photoelectric converter; when positrons enter the plastic scintillator and deposit energy, they generate fluorescent photons, which are converted into electrical signals by the photoelectric converter and output to the back-end circuit for further processing; a reflective layer is provided on the upper surface and side surfaces of the plastic scintillator, which can not only fully transmit the fluorescent photons to the photoelectric converter but also has a light-shielding function to prevent external visible light from interfering with the normal operation of the positron emitter; the thickness of the plastic scintillator depends on the positron energy distribution of the selected radioactive source. Its thickness ensures that the positrons deposit sufficient energy in the plastic scintillator, correspondingly generating a sufficient number of fluorescent photons, making the detector signal amplitude higher than the electronic noise and increasing the effective counting rate; at the same time, the thickness of the plastic scintillator ensures that as many positrons as possible pass through the scintillator; The detector array is composed of a positron detector and a plurality of gamma detectors. Structurally, the positron detector is located at the center of the detector array, and the plurality of gamma detectors are arranged in an array around the central positron detector. The positron detector is composed of a plastic scintillator coupled to a fast-response photoelectric converter, responsible for detecting positrons that penetrate the thin film sample. The thickness of the plastic scintillator depends on the positron energy distribution of the selected radioactive source. Its thickness ensures that the positrons deposit sufficient energy in the plastic scintillator, correspondingly generating a sufficient number of fluorescent photons, so that the detector signal amplitude is higher than the electronic noise, ensuring the complete detection of incident positrons, thereby achieving complete exclusion of annihilation cases in non-samples. At the same time, the thickness of the scintillator minimizes the detection efficiency of gamma photons, reducing the erroneous exclusion of positron annihilation cases. A reflective layer is provided on the upper surface and side surfaces of the plastic scintillator, which not only fully transmits the fluorescent photons to the photoelectric converter, but also has a light-shielding function, preventing external visible light from interfering with the normal operation of the positron detector. The gamma detectors are composed of a scintillator with high time resolution and a fast-response photoelectric converter coupled with it, which is responsible for fully detecting the gamma photons generated after positron annihilation, thereby achieving sufficient detection of positron annihilation cases; the scintillator includes BaF2, LaBr3 or LYSO; the photoelectric converter includes a silicon photomultiplier tube; the outer surface of the gamma detector is encapsulated with a light-proof structural material to prevent external visible light from interfering with the normal operation of the detector.

2. The positron annihilation lifetime efficient measurement system for thin film sample characterization according to claim 1, characterized in that: The structure of the scintillator in the gamma detector depends on the intensity of the actual positron source and the system's requirements for time and energy resolution. The greater the intensity of the positron source, the smaller the geometric cross-sectional size of the scintillator should be, reducing the solid angle it covers with respect to the positron source, thereby reducing the probability of multiple gamma photons being detected in a short period of time and effectively reducing the probability of signal accumulation. The gamma detectors are arranged on a spherical surface centered on the concentrated annihilation area of ​​positrons in the sample. The number of gamma detectors is determined by the requirements for the detection efficiency of positron annihilation cases in actual conditions, thereby maximizing the effective detection solid angle, with a maximum solid angle of 4π, to detect annihilated gamma photons in all directions, fully improving the collection efficiency of effective positron annihilation cases.

3. The measurement method of a positron annihilation lifetime efficient measurement system for thin film sample characterization according to any one of claims 1-2, characterized in that: The steps include: Step 1: A positron emitter detects positrons entering the thin film sample, a positron detector is set in the detector array to detect positrons penetrating the thin film sample, and multiple gamma detectors are set in the detector array to detect gamma photons generated after positron annihilation; Step 2: After the positron emitter detects a positron, it generates a first positron signal; after the positron detector in the detector array detects a positron, it generates a second positron signal; after the gamma detector detects a gamma photon, it generates one or more gamma signals; the signal acquisition module is responsible for collecting the first positron signal, the second positron signal, and the one or more gamma signals, and transmitting the waveform data to the data processing module for processing; Step 3: The data processing module performs energy identification, timing, annihilation case selection and lifetime spectrum statistics on the waveform data.

4. The measuring method according to claim 3, characterized in that The step 3 includes: for the first positron signal, the energy threshold is set to the electronic noise level, and a start timing signal is generated after timing; for one or more gamma signals, the energy threshold is set to 0.511 The photoelectric peak of MeV gamma photons, combined with signal shape discrimination, is used to screen out gamma photon signals generated by positron annihilation from one or more gamma signals, and a stop timing signal is generated after timing. Within a certain time window, the time difference between the start timing signal and the stop timing signal is calculated as the lifetime of each positron annihilation event. For the second positron signal, the energy threshold is set to the electronic noise level. As long as the second positron signal is detected, a discrimination signal is output, which is used as the basis for determining whether the positron annihilation event is recorded. When no discrimination signal is output, it indicates that the event is a valid positron annihilation event in the thin film sample, and a time difference calculation is performed. When a discrimination signal is output, it indicates that the positron in the event did not annihilate in the sample, the time difference calculation is suppressed, and the data processing module directly proceeds to the processing of the next event, thereby excluding positron annihilation events in non-thin film samples. Finally, the time difference corresponding to each valid positron annihilation event is statistically analyzed, and after sufficient event accumulation, a positron annihilation lifetime spectrum is generated.

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