Al AZHAR UNIVERSITY FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINEERING
Development of Quantum Devices and Algorithms for Radiation Detection and Radiation Signal Processing
Thesis Submitted For the Degree of Doctoral of Philosophy in Electrical Engineering (Electronics and Communications) Faculty of Engineering Al Azhar University
By Mohamed El Sayed Mohamed El Sayed El Tokhy Lecturer Assistant at Engineering Department Nuclear Research Center Egyptian Atomic Energy Authority
Supervised By
Prof. Dr. Hussein Ahmed Konber Prof. Dr. Imbaby Ismail Mahmoud Professor of Electrical Communications Head of Engineering Department Faculty of Engineering Nuclear Research Center Al Azhar University Atomic Energy Authority
2012 CAIRO EGYPT ﺟﺎﻣﻌﺔ ﻷزض١ ﺟﺎﻣﻌﺔ ﻛ ﻠ ﺒ ا ﺔﻟ ﻬ ﻨ ﺪ ﺳﺔ ﻛ ﻠ ﺒ ﺔ ﻗ ﺴ ﻢ ^—اﻟﻬﻔﺪﻣﺲ اﻟﻜﻬﺮﺑﻴﺔ ^—اﻟﻬﻔﺪﻣﺲ ﻗ ﺴ ﻢ
ﺗﻄﻮﻳﺮ ﻧﺒﺎﺋﻂﻛﻤﻴﺔ وﺧﻮارزﻣﻴﺎت ﻟﻜﺸﻒ اﻻﺷﻌﺎع وﻣﻌﺎﻟﺠﺔ اﻻﺷﺎرات وﻣﻌﺎﻟﺠﺔ اﻻﺷﻌﺎع ﻟﻜﺸﻒ وﺧﻮارزﻣﻴﺎت ﻛﻤﻴﺔ ﻧﺒﺎﺋﻂ ﺗﻄﻮﻳﺮ اﻻﺷﻌﺎﻋﻴﺔ
ر ﺳﺎﻟﺔ ﻣﻘﺪﻣﺔ ﻣﻦ اﻟﻤﻬﻨﺪس ﻣ ﺤ ﻤ ﺪ اﻟ ﺴﻴﺪ ﻣﺤﻤﺪ اﻟﺴﻴﺪاﻟ ﻄﻮ ﺧﻰ ﻣﺎﺟﺴﺘﻴﺮ ﻫﻨﺪﺳﺔ اﻻﻟﻜﺘﺮوﻧﻴﺎت واﻻﺗﺼﺎﻻتاﻟﻜﻬﺮﺑﻴﺔ ﻣﺪرس ﻣﺴﺎﻋﺪ ﺑﻬﻴﺌﺔ اﻟﻄﺎﻗﺔ اﻟﺬرﻳﺔ اﻟﻄﺎﻗﺔ ﺑﻬﻴﺌﺔ ﻣﺴﺎﻋﺪ ﻣﺪر س
ﻟﻠﺤﺼﻮل ﻋﻠﻰ درﺟﺔ اﻟﻌﺎﻟﻤﻴﺔ (دﻛﺘﻮراه اﻟﻔﻠﺴﻔﺔ) ﻓﻰ اﻻﻟﻜﺘﺮوﻧﻴﺎتواﻻﺗﺼﺎﻻت اﻻﻟﻜﺘﺮوﻧﻴﺎت اﻟﻜﻬﺮﺑﻴﺔ
ﺗﺤﺖإﺷﺮاف ﺗﺤﺖ ا.د ﺣﺴﻴﻦ أﺣﻤﺪ ﻗﻨﺒﺮ د٠ا إﻣﺒﺎض إﺳﻤﺎﻋﻴﻞﻣﺤﻤﻮد إﺳﻤﺎﻋﻴﻞ إﻣﺒﺎ ض أﺳﺘﺎذ اﻻﺗﺼﺎﻻتاﻟﻜﻬﺮﺑﻴﺔ رﺋﻴﺲ ﻗﺴﻢ اﻟﻬﻨﺪﺳﺔ- ﻣﺮﻛﺰ اﻟﺒﺤﻮث ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔ- ﺟﺎﻣﻌﺔ اﻷزﻫﺮ اﻟﻨﻮوﻳﺔ-ﻫﻴﺌﺔ اﻟﻄﺎﻗﺔ اﻟﺬرﻳﺔ اﻟﻄﺎﻗﺔ ﻫﻴﺌﺔ اﻟﻨﻮوﻳﺔ-
2 ١ 20 ١ 2 اﻟﻘﺎﻫﺮة- ﻣﺼﺮ اﻟﻘﺎﻫﺮة- Acknowledgement
I present all thanks for my "GOD" for helping me to finish this thesis.
My great thanks to Prof. Dr. Hussein A. Konber for his supervision, support and sincere help.
My appreciation is expressed to Prof. Dr Imbaby I. Mahmoud for his supervision, introducing block diagram programming using VisSim, encouragement, and continuous help.
This work is partially supported by International Atomic Energy
Authority (IAEA) grant under Coordinated Research Project contract Number CRP (16409/R0).
MOHAMED EL SAYED EL TOKHY
i LIST OF ABBREVIATION
LIST OF ABBREVIATION
ABBREVIATIONS MEANING ADC Analog-To-Digital Converter CaTe Cadmium Telluride CaZnTe Cadmium Zinc Telluride CdSe Cadmium Selenide 60 Co Cobalt-60 CRT Cathode Ray Tube 137 Cs Cesium-137 CsI Cesium Iodide DAS Data Acquisition System DMYER Discrete Meyer FIR Finite Impulse Response FWHM Full Width at Half Maximum Ge Germanium GM Geiger-Muller GUI Graphical User Interface HgI Mercuric Iodide HRGS High-Resolution Gamma-Ray Spectroscopy IR Infrared IWT Inverse Wavelet Transform LEDs Light Emitting Diodes LiI Lithium Iodide LLD Lower Level Discriminator MCA Multichannel Analyzer NaI(TI) Thallium-Doped Sodium Iodide NDA Non-Destructive Assay PbS Lead Sulfide PC Personal Computer PDS Parallel Direct Search Algorithm PL Peak Photoluminescence PMT Photomultiplier Tube QD Quantum Dot QDIP Quantum Dot Infrared Photodetectors Rbior1.1 Reverse Biorthogonal1.1 RMS Root Mean Square SCA Single Channel Analyzer SCH Separate Confinement Heterostructure Si Silicon Si (Li) Lithium Drifted Silicon SNR Signal To Noise Ratio ULD Upper Level Discriminator WL Wetting Layer WT Wavelet Transform ZnS Zinc Sulfide
v CONTENTS
Acknowledgement …………………………………………………………………………..... i Abstract …………………………………………………………………………...... ii List of Abbreviation ………………………………………………………………………….. v
CHAPTER (1) INTRODUCTION 1.1 Introduction………………………………………………………………………...... 1 1.2 Objective of the Thesis……………………………………………………………….. 4 1.3 Organization of the Thesis………………………………………………………...... 6
CHAPTER (2) OVERVIEW OF GAMMA-RAY SPECTROSCOPY 2.1 Introduction…………………………………………………………………………… 7 2.2 Gamma Radiation Detection………………………………………………………….. 7 2.2.1 Gas-filled detectors…………………………………………………………… 8 2.2.2 Solid-state detectors…………………………………………………………... 9 2.2.3 Scintillator detectors………………………………………………………….. 10 2.2.3.1 Quantum dot technology for gamma radiation detection…………... 11 2.3 Spectrum Analysis……………………………………………………………………. 13 2.3.1 Analysis of spectra with peaks………………………………………………... 13 2.3.1.1 Spectral features…………………………………………………….. 14 2.3.1.1.1 The full energy photopeak……………………………… 14 2.3.1.1.2 Compton background continuum………………………. 14 2.3.1.1.3 The Compton edge……………………………………… 15 2.3.1.1.4 The Compton valley……………………………………. 15 2.3.1.1.5 Back scatter peak………………………………………... 15 2.3.1.1.6 Excess energy region…………………………………… 15 2.3.1.1.7 Low energy rise………………………………………… 15 2.4 Single Channel Analyzer……………………………………………………………… 15 2.4.1 Multiple single channel analyzers…………………………………………….. 16 2.5 Multichannel Analyzer………………………………………………………………... 18 2.5.1 Principle of operation of MCA……………………………………………….. 18 2.5.2 Basic components of gamma ray spectroscopy………………………………. 18
vi CONTENTS
2.5.3 General MCA characteristics …………………………………………………. 20 2.5.3.1 Number of channels required……………………………………….. 20 2.5.3.2 Calibration of spectrometers………………………………………... 22 2.6 MCA Problems……………………………………………………………………….. 22 2.6.1 MCA dead time……………………………………………………………….. 22 2.6.2 MCA pileup…………………………………………………………………… 23
CHAPTER (3) MODELS OF QUANTUM DOT DEVICES FOR GAMMA RADIATION DETECTION 3.1 Introduction………………………………………………………………………….... 25 3.2 VisSim Simulator……………………………………………………………………... 26 3.3 QD Devices as a Detector…………………………………………………………….. 27 3.4 The Proposed Models of Quantum Dot Devices……………………………………... 28 3.4.1 The proposed simulator of quantum dot source under gamma radiation……... 28 3.4.1.1 The proposed simulator of carriers densities of quantum dot gamma ray detection………………………………………………………… 28 3.4.1.2 Proposed simulator of optical wavelength……….…………………. 31 3.4.2 Block diagram models of QDIP………………………………………………. 32 3.4.2.1 Dark current density block diagram model of QDIP…..…………… 33 3.4.2.2 Photocurrent density block diagram model of QDIP……………….. 35 3.4.2.3 Detectivity block diagram model of QDIP……...... 36 3.5 Results and Discussion………………………………………………………………... 39 3.5.1 Results of QD sources………………………………………………………… 39 3.5.1.1 Carrier densities and population inversion of QD devices results….. 39 3.5.1.2 Emission wavelength results………………………………………... 43 3.5.2 Results of QDIPs……………………………………………………………… 44 3.5.2.1 Dark current result...……………………………………………...…. 44 3.5.2.2 Photocurrent result...……………………………………………..…. 47 3.5.2.3 Detectivity result……………………………………………………. 49
vii CONTENTS
CHAPTER (4) THE PROPOSED DIGITAL GAMMA-RAY SPECTROSCOPY ALGORITHMS 4.1 Introduction…………………………………………………………………………… 51 4.2 System Component…………………………………………………………………… 52 4.3 Signal Preprocessing Algorithms……………………………………………………... 53 4.3.1 Background correction………………………………………………………... 53 4.3.2 Afterpulse removal……………………………………………………………. 53 4.3.3 Noise elimination algorithm based on wavelet transform………………..…… 54 4.4 Algorithms of Problems Correction for Digital Gamma-Ray Spectroscopy Signal….. 55 4.4.1 Pile up correction……..………………………………………………………. 55 4.4.1.1 Pileup recovery using deconvolution……………………………….. 56 4.4.1.2 Direct search pileup recovery algorithm……………………………. 56 4.4.1.3 Least square fitting pileup recovery algorithm……………………... 59 4.4.1.4 First derivative with maximum peak search pileup recovery algorithm…………………………………………………………..... 60 4.4.1.5 First derivative with matrix division pileup recovery algorithm...... 61 4.4.1.6 Comparison between the algorithms…………………………...... 62 4.4.2 Dead time correction algorithm due to radiation detector……….……………. 62 4.5 Spectrum Drawing and Evaluation Flow…...…………………………………………. 64 4.6 Energy Calibration……………………………………………………………………. 65 4.7 Activity Measurements……………………………………………………………….. 66
CHAPTER (5) DIGITAL GAMMA-RAY SPECTROSCOPY RESULTS 5.1 Introduction………………………………………………………………………….... 67 5.2 Signal Preprocessing Results…………………………………………………………. 68 5.2.1 Background correction result...………………………………………………... 68 5.2.2 Smoothing algorithm result..………………………………………………….. 68 5.2.3 Noise removal result using wavelet transform……………..…………………. 69 5.3 Problems Correction of Gamma-Ray Spectroscopy………………………………….. 71 5.3.1 Pileup recovery and correction results………………………………………... 71 5.3.2 Pileup recovery using hypothetical signal……………………………………. 72
viii CONTENTS
5.3.2.1 Direct search algorithm result …... ………………………………….. 72 5.3.2.2 Least square fitting algorithm result…...……………………………. 74 5.3.2.3 First derivative with maximum peak search algorithm result………. 76 5.3.2.4 First derivative with matrix division algorithm result………………. 77 5.3.2.5 Gaussian noise handling……………………………………………. 79 5.3.2.6 Registration and rejection of the peak height………………………. 80 5.3.2.7 Comparison between the algorithms and discussion for hypothetical signal………………...... 80 5.3.3 Experimental comparison among pileup recovery algorithms for digital gamma-ray spectroscopy……………………………………………………… 83 5.3.3.1 Direct search algorithm result…...……………………………….. 83 5.3.3.2 Least square fitting algorithm result………..……………………. 84 5.3.3.3 First derivative with maximum peak search algorithm result……. 86 5.3.3.4 Comparison between algorithms and discussion for real signal…. 88 5.3.4 Dead time correction results due to radiation detector………………………... 89 5.4 Spectrum Drawing and Evaluation Results…………………………………………... 90 5.4.1 Spectrum of 137 Cs……………………………………………………………... 90 5.4.2 Spectrum of 60 Co……………………………………………………………… 91 5.4.3 Effect of pileup recovery algorithms on spectrum evaluation………………... 93 5.4.4 The Compton interaction……………………………………………………... 96 5.5 Energy Calibration Results…………………………………………………………… 97 5.6 Activity Measurement Results………………………………………………………... 98
CHAPTER (6) CONCLUSION 6.1 Conclusion……………………………….……………………………………………. 99 6.2 Future Work…………………………………………………………………………... 101
References …………………………………………………………………………………...... 102 List of Publications …………………………………………………………………………… 115 Arabic Summary ……………………………………………………………………………... 117
ix ABSTRACT
ABSTRACT
The main functions of spectroscopy system are signal detection, filtering and amplification, pileup detection and recovery, dead time correction, amplitude analysis and energy spectrum analysis. Safeguards isotopic measurements require the best spectrometer systems with excellent resolution, stability, efficiency and throughput. However, the resolution and throughput, which depend mainly on the detector, amplifier and the analog to digital converter (ADC), can still be improved. These modules have been in continuous development and improvement. For this reason we are interested with both the development of quantum detectors and efficient algorithms of the digital processing measurement. Therefore, the main objective of this thesis is concentrated on both 1. Study quantum dot (QD) devices behaviors under gamma radiation 2. Development of efficient algorithms for handling problems of gamma ray spectroscopy For gamma radiation detection, a detailed study of nanotechnology QD sources and infrared photodetectors (QDIP) for gamma radiation detection is introduced. There are two different types of quantum scintillator detectors, which dominate the area of ionizing radiation measurements. These detectors are QD scintillator detectors and QDIP scintillator detectors. By comparison with traditional systems, quantum systems have less mass, require less volume, and consume less power. These factors are increasing the need for efficient detector for gamma ray applications such as gamma ray spectroscopy. Consequently, the nanocomposite materials based on semiconductor quantum dots has potential for radiation detection via scintillation was demonstrated in the literature. Therefore, this thesis presents a theoretical analysis for the characteristics of QD sources and infrared photodetectors (QDIPs). A model of QD sources under incident gamma radiation detection is developed. A novel methodology is introduced to characterize the effect of gamma radiation on QD devices. The rate equations of the QD devices under gamma radiation are studied. The effect of incident gamma radiation on the optical gain, power, and output photon densities are investigated. Moreover, block diagram models were derived to express implicitly the performance of QDIPs. These models are used to calculate different characteristics of these devices. Block diagram programming through VisSim environment is used to
ii ABSTRACT implement models for those devices. The roles that the parameters of fabrication can play in the characteristics of QD sources and QDIPs are discussed through developed models implemented by VisSim environment. Implicit solutions of dynamic equations governing quantum detectors provide exact handling of the device performance. In this methodology, we used the VisSim environment along with the block diagram programming procedures. The benefits of using this modeling language are the simplicity of carrying out the performance's measurement through computer simulation instead of setting up a practical procedure which becomes expensive as well as the difficulty of its management. The implemented models can help designers and scientists to optimize their devices to meet their requirements. In order to confirm our models and their validity on the practical applications, a comparison between the results obtained by proposed models and that published in the literature are conducted and full agreement is observed. These demonstrate the strength of implementation of block diagram models through VisSim. Secondly, we present algorithms to evaluate and improve the performance of gamma ray spectroscopy. Spectra from both 137 Cs and 60 Co radioisotopes are acquired using sodium iodide doped with thallium (NaI(TI)) scintillator detectors. In this thesis, an algorithm for noise elimination of the detected gamma ray spectroscopy signals is studied. Background correction and afterpulse removal of gamma ray spectroscopy measurement experiment is preprocessed using MATLAB environment. Since, the photomultiplier tube (PMT) anode signal is very noisy, a de noising algorithm is required. A de noising algorithm based on the wavelet transform (WT) is implemented to reduce the effect of noise introduced by the noisy analog channel and by the PMT. Reconstruction of the original detected signal is obtained by applying the inverse wavelet transform (IWT) to the transformed wavelet signal. Consequently, a 5 level de noising algorithm based on discrete Meyer (dmyer) and reverse biorthogonal1.1 (rbior1.1) wavelet functions was implemented. Another scope of this thesis is the treatment of main problems of digital gamma ray spectroscopy. Algorithms for overcoming a common problem of gamma ray spectroscopy, namely peak pileup problem is presented. Four different approaches are studied and evaluated within a spectroscopy system using hypothetical and real signals. The first approach is a direct search based on Nelder Mead technique without any derivatives in order to find the local minimum points. This algorithm is evaluated by the means of parameters error and fitting error calculations. The second algorithm
iii ABSTRACT is based on the nonlinear least square method. A simple and improved algorithm to resolve overlapped asymmetric pulses into its component peaks using nonlinear least square fitting method is evaluated. The objective of curve fitting is to find a mathematical equation that describes a set of data. The third approach is a proposed one. This algorithm is based on a maximum peak search method combined with the first derivative method to determine peak position of each pulse. The maximum peak is determined using the maximum peak search routine. This routine search and find local maxima in the overlapping peaks. Additional fourth algorithm is presented. This algorithm is based on first derivative method for determining the peak position of each pulse in conjunction with inverse matrix method. For all algorithms, a Gaussian shape in conjunction with the peak and position of each peak are used to construct the pulse. Using hypothetical and real signals, the main pulse parameters such as peak height, position and width can be determined for all algorithms. By using the inverse matrix algorithm, the maximum amplitude is measured and compared with the true amplitude with maximum error of 0.3585%. The main advantage of this algorithm is their high execution time in comparison with other algorithms. These results enhance the performance of the spectrometer. Comparison among these approaches is conducted in terms of parameters errors. The pulse parameters have been calculated and compared with the actual one. Consequently, higher isotope identification can be achieved. Dead time correction algorithm is studied using the decaying source method. This time was calculated assuming paralyzable model is applicable. Also, the dead time percent was computed by this algorithm. The true rate was calculated using Lambert W function numerical technique. The spectrum drawing and evaluation algorithm is another objective. Different spectrums are drawn for both cesium 137 ( 137 Cs) and cobalt 60 ( 60 Co) radiation point sources. Furthermore, Compton energy was computed. Moreover, energy calibration is another major target in this thesis. It was implemented for the collected spectra using the mentioned isotopes. Least square fitting method is used to fit the obtained data to make the spectrometer available for larger number of channels. These algorithms have the advantages of simplicity and ease of processing. MATLAB environment is used for these purposes. This will allow a further characterization of γ rays beyond what is possible with current detector systems.
iv Chapter (1) Introduction
CHAPTER (1)
INTRODUCTION
1.1 Introduction Gamma ray spectroscopy is the quantitative study of the energy spectra of gamma ray sources and used to identify radiological gamma sources. It utilizes proven and sensitive detectors, to capture gamma photons and convert them to measurable energy and form a spectrum. Unique algorithms are applied to interpret specific emission energies or peaks in the spectrum, shielding characteristics as well as other spectral features necessary to pin point the source of radiological gamma isotope. A gamma spectroscopy system consists of a detector, digital electronics to collect and process the signals produced by the detector, and a computer with processing software to generate, display, and store the spectrum. Gamma spectroscopy detectors are passive materials that wait for a gamma interaction to occur in the detector volume. The most important interaction mechanisms are the photoelectric effect, the Compton effect and pair production. The photoelectric effect is preferred. Since, it absorbs all of the energy of the incident gamma ray. Full energy absorption is possible when a series of these interaction mechanisms take place within the detector volume. The energy of the gamma rays being detected is an important factor in the efficiency of the detector. The use of quantum devices as gamma radiation detector has been reported as a new and active field of research as in [1]. Gamma rays are used for nondestructive quantitative analysis of nuclear material [2]. Knowledge of both the energy of the gamma ray and its rate of emission from the unknown mass of nuclear material is required to interpret most measurements of nuclear material quantities. Therefore, detection of gamma rays for nondestructive analysis of nuclear materials requires both spectroscopy capability and knowledge of absolute specific detector response [3]. The development of room temperature quantum detectors for gamma ray spectroscopy is limited by position and energy resolution. To overcome the processes that deteriorate their resolution, we must understand and reproduce the physics from the initial gamma ray interaction down to measurable signals. Thus, a detailed study of various radiation
١ Chapter (1) Introduction detectors is introduced. Here, analytical and simulation models of the semiconductor QD gamma ray detectors is presented. Quantum confinement of electrons in one, two and three dimensions is a topic that has attracted sustained attention for several years. Quantum devices are emerging as a new class of fluorescent probes for spectroscopy applications and gamma radiation detectors [4]. They have unique optical and electronic properties such as size tunable light emission, improved signal brightness, resistant against photobleaching and simultaneous excitation of multiplex fluorescence colors [5]. By comparison with traditional systems, a quantum photodetectors system has less mass, requires less volume, and consumes less power. These factors are increasing the need for efficient detector for gamma ray applications such as gamma ray spectroscopy, infrared spectroscopy for chemical analysis, remote sensing and atmospheric communications. Hence, provides the driving force to develop improved infrared (IR) radiation detectors such as QDIPs. Therefore, a means of improving these devices characteristics are essential. Consequently, we are interested with enhancing the device performance of quantum photodetectors through modeling by simulation solutions using VisSim environment. This thesis discusses the application of both QDs sources and QDIP as scintillator detectors for gamma ray spectroscopy [6]. Therefore, we focused on improving the characteristics of QD confined structures. The parameters that have a large effect on the performance of it through the developed models are utilized. Experimental Setups for measuring the characteristics of QDIPs in previous works [7 8] are reported in the following chapters. However, it shows difficulties in tuning and cost much. In this thesis block diagram models are used to overcome the above mentioned complexity. Models are designed for describing the main characteristics for the mentioned devices. Block diagram models are implemented by VisSim describing the detection characteristics of QDIPs . Proposed programs for modeling and simulation of QDIPs behavior is partially implemented in VisSim environment. VisSim is a visual block diagram for nonlinear dynamic simulation [9 11]. The basic part of this diagram is based on what is known as a block. This block allows users to create their corresponding one in C/C++. In this environment, the system is modeled by the graphical interconnection of function blocks [12]. For flexibility, variables are used to denote system parameters and then are assigned values in a separate compound blocks. Once the underlined problem was represented by its group of
٢ Chapter (1) Introduction blocks, it is ready to be evaluated through the VisSim which is internally programmed. The program can be distributed with VisSim viewer or through generated C code from VisSim block diagram, which means that it doesn't depend on the VisSim environment [9]. Generally, this modeling presents an easy way for the physicists to achieve the QDIPs designs by making the values of the parameters to be varied. The ultimate goal of nuclear spectrometry signal processing is to produce digital signals that exactly describe the properties of radiation and radiation induced events. In a typical nuclear spectrometry experiment, the energy of radiation, or a charged particle, is measured in such a way that its energy is absorbed in solid state, proportional or scintillation detector, and converted into a pulse of electrical charge [13]. In all cases, the electrical pulse is degraded and contaminated with noise during its passage through non ideal front end electronic components. Many random signal processing applications involve digital pulse height analysis. Height estimation is one of the most important tasks on nuclear systems [14]. All the information of a gamma ray event can be extracted by measuring the height of electronic pulses [15]. An important example is a system used to analyze the amplitude distribution of the voltage spectrum of pulses developed by a nuclear radiation detector [16]. Gamma ray spectroscopy systems can be divided into two classes according to whether they use single channel analyzer (SCA) or multichannel analyzer (MCA). The function of the single channel analyzer is to analyze the input signal pulse height distribution (to measure the pulse repetition rate of pulses whose amplitudes lie within the predetermined voltage interval). The thesis introduces a comparison among different algorithms of gamma ray spectroscopy for determining the pulse height distribution. These algorithms based on a reference signal from radiation point sources 137 Cs and 60 Co acquired by data acquisition system (DAS). Effects of signal background and afterpulse problems in the gamma ray spectrometer are illustrated. These signal preprocessing is essential step, and enhances the spectrum accuracy. There are many applications of radiation detection and measurement which are constrained by the finite time resolution of the radiation detector [17]. As a consequence of the fundamentally random nature of detected radiation events, there exists the potential for multiple events to arrive at the detector simultaneously. These effects are generally called pileup . Pileup distortion is a common problem for high counting rates radiation spectroscopy in many fields such as industrial, nuclear and
٣ Chapter (1) Introduction medical applications [18 19 ]. That is caused by finite response time of radiation detectors. Furthermore, pulse pileup caused by the non zero response time of the detection system. The fact that pulses from a radiation detector are randomly spaced in time can lead to interfering effects between pulses when counting rates are not low [20 21]. These pileup effects can be minimized by making the total width of the pulses as small as possible [22]. Signals from these two pileup pulses and the pulse height analyzer would not see them at their true heights, leading degradation in the energy resolution of the detector [14 16]. The losses of pulses in gamma ray spectroscopy due to pulse pileup are a major problem in quantitative gamma ray spectroscopy [23]. Pileup in the amplifier is the classical case of extending dead time. Pileup phenomena are of two types [24]. The first type is known as tail pileup and involves the superposition of pulses on the long duration tail from a preceding pulse [25 26]. That is the arrival of a second pulse on the tail of the first increases the time that the counting system is busy. Since the ADC live time is well compensated by the circuitry, any additional losses may be approximated if pileup alone is the dominant effect, or equivalently the losses have the same mathematical dependence on count rate [27]. Tails can persist for relatively long periods of time so that tail pileup can be significant event at relatively low counting rates. A second type of pileup is the peak pileup, which occurs when the mutual pulse spacing between the two overlapping pulses is less than approximately τ R/2, τR is the total mean width of all pulses. There have been many attempts to correct spectral data obtained from a multichannel analyzer counting system for counting losses due to pulse pileup [27]. In this thesis, we propose different approaches for recovery of pileup in gamma ray spectroscopy using MATLAB environment. These approaches were tested in resolving pileup with very small error between the original and recovered pulse. Moreover, different algorithms are studied for spectrum drawing and evaluation, energy calibration and activity measurements for digital gamma ray spectroscopy. Energy calibration is an important algorithm for every run time. These algorithms are measure to the accuracy of the isotope identifications.
1.2 Objective of the Thesis The main objectives of the thesis are the following: 1. Study and development QD devices behavior under gamma radiation.
٤ Chapter (1) Introduction
2. Development of efficient algorithms for handling problems of gamma ray spectroscopy. In this thesis, we enhanced the detection of gamma radiation through the development of QD devices. Therefore, QD radiation detector characteristics are being analyzed. There are two different types of QD scintillator detectors, which dominate the area of ionizing radiation measurements. These detectors are QD sources scintillator detectors and QDIPs scintillator detectors. Therefore, a detailed study of these nanotechnology QD devices for gamma radiation detection is introduced. This study is based on physical analysis of the factors determining their operation. To determine these factors, we use block diagram models based on VisSim environment. Furthermore, this thesis introduces different algorithms of treatment of gamma ray spectroscopy problems. These algorithms are preprocessing, problems corrections and spectrum drawing algorithms. The objective of this research is to provide a flexible and accurate technique for automated spectroscopy for multichannel pulse height spectra while limiting human interaction to only prior defined parameters and functions. This minimizes the demands on user’s time, human error and the subjectivity of the result. Spectra from both 137 Cs and 60 Co radioisotopes are acquired using NaI(TI) scintillator detectors. Effects of signal background and afterpulse problems in the gamma ray spectrometer are corrected. Signal de noising is one of the main goals in the thesis. Furthermore, algorithms for overcoming the most common problem of gamma ray spectroscopy, namely the pileup and dead time due to radiation detectors are presented. Different approaches are studied and evaluated within a spectroscopy system. Another goal was to develop algorithms that could be used in spectrum drawing and evaluation of gamma ray spectrometers. Furthermore, we are interested with determining the energy calibration for digital signal processing. Energy calibration is one of the scopes in this thesis. It was implemented for the collected spectra using 137 Cs and 60 Co radioisotopes. These algorithms are measure to the accuracy of the isotope identifications. This will allow a further characterization of gamma rays beyond what is possible with current detector systems. Such features open a new window in medical and industrial gamma ray applications. MATLAB environment is used for these purposes. These algorithms have the advantages of simplicity and ease of processing.
٥ Chapter (1) Introduction
1.3 Organization of the Thesis The thesis is organized into six chapters as follows: Chapter 1 presents the introduction chapter. Chapter 2 is devoted to the basic structures of gamma ray spectroscopy. This chapter introduces an introduction governing the basic elements of gamma ray spectrometry, basics of gamma radiation detection, description of SCA and MCA, discussion of pulse height analysis, and the problems associated with gamma ray spectroscopy. Chapter 3 introduces QD devices as detectors, the proposed models of QD sources for gamma radiation detection, theoretical study of QDIP used for gamma radiation detection. It includes basics of these quantum devices, the proposed block diagram models by VisSim, and the obtained results for these devices. The proposed algorithms of gamma ray spectroscopy are summarized in chapter 4. These algorithms are preprocessing, problems overcoming, spectrum drawing and evaluation, energy calibration and activity measurements algorithms. Chapter 5 gives the results of gamma ray spectroscopy algorithms. Moreover, comparison among the considered algorithms is presented. Conclusions of the results with future work are illustrated in chapter 6.
٦ Chapter (2) Overview of Gamma-Ray Spectroscopy
CHAPTER (2)
OVERVIEW OF GAMMA RAY SPECTROSCOPY
2.1 Introduction A measurement of the differential pulse height spectrum from a radiation detector can yield important information on the nature of the incident radiation or the behavior of the detector itself. Consequently, it is one of the most important functions to be performed in nuclear measurements. Therefore, the subject of this chapter is the function and operation of the gamma ray spectrometry system. It is known that the output pulse amplitude from most gamma ray detectors is proportional to the energy deposited by the gamma ray [28]. The pulse height spectrum from such detector contains a series of full energy peaks superimposed on a continuous Compton background [29]. Although, the spectrum can be quite complicated and thereby difficult to analyze, it contains much useful information about the energies and relative intensities of the gamma rays emitted by the source. The information that is important for the quantitative non destructive assay (NDA) of nuclear material is contained in the full energy peaks. The purpose of the electronic equipment that follows the detector is to acquire an accurate representation of the pulse height spectrum and to extract the desired energy and intensity information from that spectrum. Gamma ray spectroscopy systems can be divided into two classes; SCAs and MCAs [30]. This chapter provides a relatively brief introduction to wide variety of instrumentation used in the gamma ray spectroscopy of nuclear materials. It emphasizes the function of each component and provides information about important aspects of instrument operation. This chapter is organized as follows: Section 2.2 presents the gamma radiation detection. Spectrum analysis and evaluation are summarized in Section 2.3. Single channel analyzer is illustrated in Section 2.4 . Multichannel analyzers are represented in Section 2.5 . Various problems of gamma ray spectroscopy are studied in Section. 2.6 .
2.2 Gamma Radiation Detection In order for a gamma ray to be detected, it must interact with matter and this interaction must be recorded. Fortunately, the electromagnetic nature of gamma ray
٧ Chapter (2) Overview of Gamma-Ray Spectroscopy
photons allows them to interact strongly with the charged electrons in the atoms of all matter [31]. The key process by which a gamma ray is detected is ionization, where it gives up part or all of its energy to an electron. The ionized electrons collide with other atoms and liberate many more electrons. The liberated charge is collected, either directly (as with a proportional counter or a solid state semiconductor detector) or indirectly (as with a scintillation detector), in order to register the presence of the gamma ray and measure its energy. The final result is an electrical pulse whose voltage is proportional to the energy deposited in the detecting medium [32]. Some general information on different types of gamma ray detectors that are used in gamma ray spectroscopy of nuclear materials is discussed. Many different detectors have been used to register the gamma ray and its energy. In NDA, it is usually necessary to measure not only the amount of radiation emanating from a sample but also its energy spectrum. Thus, the detectors of most use in NDA applications are those whose signal outputs are proportional to the energy deposited by the gamma ray in the sensitive volume of the detector [32]. A detailed study of different radiation detectors presented in the following subsections.
2.2.1 Gas filled detectors The most common type of radiation detector is a gas filled radiation detector. This instrument works on the principle that as radiation passes through air or a specific gas, ionization of the molecules in the air occurs. When a high voltage is placed between two areas of the gas filled space, the positive ions will be attracted to the negative side of the detector (the cathode) and the free electrons will travel to the positive side (the anode) as depicted in Fig. 2.1 [33]. These charges are collected by the anode and cathode which form a very small current in the wires going to the detector. A very sensitive current measuring device is placed between the wires from the cathode and anode. Therefore, small current measured and displayed as a signal. The more radiation which enters the chamber, the more current displayed by the instrument. The most common types of gas filled detectors are the ion chamber used for measuring large amounts of radiation and the Geiger Muller (GM) detector used to measure very small amounts of radiation [33]. An ionization chamber is a gas filled counter for which the voltage between the electrodes is low enough that only the primary ionization charge is collected. The electrical output signal is proportional to the energy deposited in the gas volume.
٨ Chapter (2) Overview of Gamma-Ray Spectroscopy
If the voltage between the electrodes is increased, the ionized electrons attain enough kinetic energy to cause further ionizations. One then has a proportional counter that can be tailored for specific applications by varying the gas pressure and the operating voltage. The output signal is still proportional to the energy deposited in the gas by the incident gamma ray photon and the energy resolution is intermediate between NaI (TI) scintillation counters and germanium (Ge) solid state detectors. Proportional counters have been used for gamma rays spectroscopy whose energies are low enough (a few tens of keV) to interact with reasonable efficiency in the counter gas. Voltage Source
Electrical Current Anode Measuring Device
Cathode Fig. 2.1 Schematic diagram of a gas filled detector If the operating voltage is further increased, charge multiplication in the gas volume increases (avalanches) until the space charge produced by the residual ions inhibits further ionization. As a result, the amount of ionization saturates and becomes independent of the initial energy deposited in the gas. This type of detector is known as the GM detector. A GM tube gas counter does not differentiate among the kinds of particles [34], it counts only the number of particles entering the detector.
2.2.2 Solid state detectors The most recent class of detector developed is the solid state detector. These detectors convert the incident photons directly into electrical pulses [35]. These devices work on the principle that they collect the charge generated by ionizing radiation in a solid. These detectors are made of semiconducting material and are operated much like a solid state diode with a reverse bias as shown in Fig. 2.2 . Semiconductor diodes employ reverse biased P N junctions where the absorbed radiation creates electrons and holes that are separated by the junction field. Thereby, a direct electrical response is produced [36]. The applied high voltage generates a thick depletion layer and any charge created by the radiation in this layer is collected at an electrode. The charge collected is proportional to the energy deposited in the detector. Therefore, these
٩ Chapter (2) Overview of Gamma-Ray Spectroscopy
devices can yield information about the energy of individual particles or photons of radiation [37]. Solid state detectors are fabricated from a variety of materials including; germanium (Ge), silicon (Si), cadmium telluride (CaTe), mercuric iodide (HgI), and cadmium zinc telluride (CaZnTe). The best detector for a given application depends on several factors. For instance, germanium detectors have the best resolution. However, it requires liquid nitrogen cooling which makes them impractical for portable applications. Signal
Solid Sate Crystal N
Depletion Region C R
Solid Sate Crystal P
High Voltage
Fig. 2.2 Typical arrangement of components in a solid state detector
The reverse bias diode configuration of a germanium solid state detector results in very low currents in the detector. This leakage current can be further reduced from its room temperature value by cryogenic cooling of solid state medium, typically to liquid nitrogen temperature (77 0K). This cooling reduces the thermally generated electrical noise in the crystal that constitutes the main disadvantage of such detectors [32]. On the other hand, silicon needs no cooling, but is inefficient in detecting photons with energies greater than a few tens of keV. Another popular solid state detector material for photon spectroscopy is lithium drifted silicon, Si (Li) [38]. Silicon detectors are most heavily used in charged particle spectroscopy and are used for spectroscopy of high energy gamma rays.
2.2.3 Scintillator detectors The sensitive volume of a scintillation detector is a luminescent material (a solid, liquid, or gas) that is viewed by a device that detects the gamma ray induced light emissions. The scintillation material may be organic or inorganic. Examples of organic scintillators are anthracene, plastics and liquids. The latter two are less efficient than anthracene. Some common inorganic scintillation materials are sodium iodide (NaI), cesium iodide (CsI), zinc sulfide (ZnS) and lithium iodide (LiI). The most common scintillation detectors are solid and the most popular are the inorganic crystals NaI and CsI.
١٠ Chapter (2) Overview of Gamma-Ray Spectroscopy
When gamma rays interact in scintillator material, ionized (excited) atoms in the scintillator material relax to a lower energy state and emit photons of light. In a pure inorganic scintillator crystal, the return of the atom to lower energy states with the emission of a photon is an inefficient process. Furthermore, the emitted photons are usually too high in energy to lie in the range of wavelengths to which the PMT is sensitive. Small amounts of impurities (called activators) are added to all scintillators to enhance the emission of visible photons. The scintillation light is emitted isotropically. Therefore, the scintillator is typically surrounded with reflective material to minimize the loss of light and then is optically coupled to the photocathode of a PMT. Scintillation photons incident on the photocathode liberate electrons through the photoelectric effect and these photoelectrons are accelerated by a strong electric field in the PMT. As these photoelectrons are accelerated, they collide with electrodes in the tube (known as dynodes) releasing additional electrons. This increased electron flux is accelerated to collide with succeeding electrodes, causing a large multiplication (by a factor of 10 4 or more) of the electron flux from its initial value at the photocathode surface. Finally, the amplified charge burst arrives at the output electrode (the anode) of the tube. Furthermore, by virtue of the physics of the photoelectric effect, the initial number of photoelectrons liberated at the photocathode is proportional to the amount of light incident on the phototube, which in turn is proportional to the amount of energy deposited in the scintillator by the gamma ray (assuming no light loss from the scintillator volume). Thus, an output signal is produced that is proportional to the energy deposited by the gamma ray in the scintillation medium. However, the spectrum of deposited energies is quite varied, because of the occurrence of the photoelectric effect, Compton effect [39], and various scattering phenomena in the scintillation medium and statistical fluctuations associated with all of these processes. There are two different types of QD scintillator detectors that dominate the area of ionizing radiation measurements. These detectors are QD sources scintillator detectors and QDIP scintillator detectors [32]. These radiation detectors are described in the following subsection.
2.2.3.1 Quantum dot technology for gamma radiation detection Quantum dots may serve as suitable scintillator materials for the development of high resolution room temperature gamma ray detectors [40]. Such detectors have potential
١١ Chapter (2) Overview of Gamma-Ray Spectroscopy
applications in gamma radiation detection, medical imaging, environmental monitoring and security [41]. Contemporary approaches to gamma ray detection carry several drawbacks. It still employs a PMT and NaI crystal as a scintillator, which is limited in size and offers an energy resolution of only approximately 6% at 1 MeV. Alternatively, a semiconductor detector such as germanium offers much better energy resolution than the scintillation [42 43] approach. However, it requires cryogenic cooling and is subject to radiation damage. Quantum dots offer an improvement on scintillator technology in that the size of the phosphorescent material would not be restrained by crystal growth. Also, the dots would be suspended in a transparent matrix that could be as large as desired. Moreover, the output of the quantum dots is a function of their dimensions. So, they could be produced to emit light at wavelengths suitable for detection by avalanche photodiodes. Therefore, it offers higher quantum efficiencies than PMT. Thus, the sensitivity of the scintillation detector increases. The results indicate that QD scintillation detectors should offer an energy resolution of approximately 2%, between that of traditional scintillation and cooled semiconductor instruments for gamma ray detection. Gamma ray standards are used to investigate the linearity of the scintillation output in the composite material. The semiconductor dots display a relatively small Stokes shift [44]. So, the light they emit in response to stimulation by incoming radiation tends to be absorbed by other dots. Consequently, the resulting output is lost. Also, the low atomic number of the cadmium selenide (CdSe)/zinc sulfide (ZnS) dots translates into a low stopping power. It will be necessary to employ types of dots with a higher atomic number such as lead sulfide (PbS). For applications that involve exposure of light sources to ionizing radiation, it is important to know the levels of irradiation that would degrade their optical properties. Several metal chalcogenides such as ZnS and CdSe/ZnS are known to be highly efficient scintillators [45]. Concerns related to the use of these commercially available inorganic compounds include their low solubilities in organic and polymeric matrices. Their preparation is in inorganic matrices, results in non transparent gels, thus, lowering their efficiency as scintillating devices. By reducing their particle sizes from commonly used micrometer into nanometer size, their optical properties and solubilities in both polar and nonpolar solvents can be controlled. The combination of sol gel technique and the chemistry of inorganic nanocrystalline quantum dots are
١٢ Chapter (2) Overview of Gamma-Ray Spectroscopy
demonstrated as a powerful method in preparing scintillating devices [46]. To our knowledge, still models describing QD as gamma detection are not devised yet. Another semiconductor scintillation detector based on QD was proposed in which high energy radiation produces electron hole pairs in a direct gap semiconductor material that subsequently undergo interband recombination, producing IR light to be registered by a photodetector [36,47,48,49]. Therefore, QDIPs can be used for this purpose. Scintillators are not normally made of semiconductor material. The key issue in implementing a semiconductor scintillator is how to make the material essentially transparent to its own IR light. So that photons generated deep inside the semiconductor slab could reach its surface without tangible attenuation.
2.3 Spectrum Analysis A gamma ray spectrometer determines the energies of gamma ray photons emitted by the source. Radioactive nuclei commonly emit gamma rays in the energy range from a few keV to approximately 10 MeV, corresponding to the typical energy levels in nuclei. Most radioactive sources produce gamma rays of various energies and intensities. When these emissions are collected and analyzed with a gamma ray spectroscopy system, a gamma ray energy spectrum can be produced. A gamma ray spectrum is a graph showing the number of gamma rays detected versus the energy of those gamma rays. A detailed analysis of this spectrum is typically used to determine the identity and quantity of gamma emitters present in the source. The gamma spectrum is characteristic of the gamma emitting nuclides contained in the source [50 51].
2.3.1 Analysis of spectra with peaks The task of peaking out statistical significant peaks that rise above smoothly varying continuum appears deceptively simple. When implemented in software the search process must be relatively sophisticated to avoid the sensing of false peaks that results from statistical fluctuation in the background and at the same time remain highly efficient for finding true peaks of low intensity. The problem is further complicated by the fact that too closely lying peaks may not be fully separated in the spectrum and the program must be able to distinguish such partially resolved doublets from single peaks [28].
١٣ Chapter (2) Overview of Gamma-Ray Spectroscopy
2.3.1.1 Spectral features A more realistic representation of a detector generated gamma ray spectrum from a monoenergetic gamma ray flux is shown in Fig. 2.3. The spectral features are explained in more details below [32].
Full Energy
Photopeak
Excess Low Compton Background energy Energy Continuum region Rise Back Scatter Compton Peak Edge Compton
Number of Pulses per Channel Valley
Gamma Ray Energy (MeV) E0 Fig. 2.3 Gamma ray spectroscopy spectrum analysis
2.3.1.1.1 The full energy photopeak This peak represents the pulses that arise from the full energy due to photoelectric interactions in the detection medium. Some counts also arise from single or multiple Compton interactions that are followed by a photoelectric interaction. Its width is determined primarily by the statistical fluctuations in the charge produced from the interactions plus a contribution from the pulse processing electronics. Its centroid represents the photon energy (E). Its net area above background represents the total number of full energy interactions in the detector and is usually proportional to the mass of the emitting isotope.
2.3.1.1.2 Compton background continuum These pulses distributed smoothly up to a maximum energy (Ec) and come from interactions involving only partial photon energy loss in the detecting medium. Compton events are the primary source of background counts under the full energy peaks in more complex spectra.
١٤ Chapter (2) Overview of Gamma-Ray Spectroscopy
2.3.1.1.3 The Compton edge This is the region of the spectrum that represents the maximum energy loss by the incident photon through Compton scattering. It is a broad asymmetric peak corresponding to the maximum energy (E c) that a gamma ray photon of energy (E) can transfer to a free electron in a single scattering event. This corresponds to a head on collision between the photon and the electron. These electron moves forward and the gamma ray scatter backward through 180°.
2.3.1.1.4 The Compton valley For a monoenergetic source, pulses in this region arise from either multiple Compton scattering events or from full energy interactions by photons that have undergone small angle scattering before entering the detector. Unscattered photons from a monoenergetic source cannot produce pulses in this region from a single interaction in the detector. In more complex spectra, this region can contain Compton generated pulses from higher energy photons.
2.3.1.1.5 Back scatter peak This peak is caused by gamma rays that have interacted by Compton scattering in one of the materials surrounding the detector.
2.3.1.1.6 Excess energy region For a monoenergetic source, events in this region are from high energy gamma rays, cosmic ray in the natural background and from pulse pileup events if the count rate is high enough. In a more complex spectrum, counts above a given photopeak are primarily Compton events from the higher energy gamma rays.
2.3.1.1.7 Low energy rise This feature of the spectrum is near the zero pulse height amplitude region and arises typically from low amplitude electronic noise in the detection system that is processed like low amplitude detector pulses. This noise tends to be at rather high frequency and appears as high count rate phenomenon. Electronic noise is usually filtered out of the analysis electronically. Hence, this effect does not usually dominate the displayed spectrum.
2.4 Single Channel Analyzer The differential discriminator can be used to record a steady state pulse height spectrum [55]. The window is set to a small width H. It can be moved stepwise over
١٥ Chapter (2) Overview of Gamma-Ray Spectroscopy
the pulse height range of interest. Also, the number of output pulses produced over a measurement period is recorded as N. Sequential measurements of N/ H plotted at the midpoint H value of the window will trace out the shape of the distribution. The function of the SCA is to analyze the input signal pulse height distribution. On other words, to measure the pulse repetition rate of pulses whose amplitudes lie within the predetermined voltage interval E and E+ E, where E is called the base line and E is the channel (window) width. If E and E are adjustable, the equipment can be used to measure the pulse height spectrum, which indicates the pulse repetition rate associated with the pulse height (E) within the interval E. Figure 2.4 shows input output relation in SCA [16]. The SCA consists of two voltage discriminator circuits whose discrimination (threshold) levels are different by a small adjustable amount ( E) [56] such that signals whose amplitudes lie between E and E+ E exceed the discrimination level of one discriminator but not the other.
Signal Pulse Height Ui
(Time (t U٠
Time (t) Fig. 2.4 Input output relation in single channel analyzer.
The system contains a counter to count the repetition rate of the selected pulse train coming from the SCA circuit. Also, a timer is necessary to measure the accumulation period. The timer should possess a predetermined time facility so that processing lasts for a certain adjustable predetermined period. The counter and the timer should be synchronized to start and stop simultaneously at the beginning and end of the counting interval. This serial process is inefficient, in that most pulses are ignored during a given measurement since they lie outside the specific window chosen [28].
2.4.1 Multiple single channel analyzers A multiple SCA is in principle equivalent to many SCA with their windows arranged contiguously [16,28]. A better approach is to employ multiple SCA as in Fig. 2.5. Here, the measurement is converted from one that is serial to one that is parallel.
١٦ Chapter (2) Overview of Gamma-Ray Spectroscopy
Every pulse can now contribute to the measured spectrum. All the inputs are connected together and each output to a separate counter. The lower level of the SCA at the bottom of the stack is set to zero, and that for the top SCA is set to correspond to the largest pulse height of interest. The lower level of the intermediate SCA is arranged at equal intervals between these extremes. The window width of each SCA is identical and is set equal to the spacing between adjacent discrimination levels. Thus, this arrangement provides a series of contiguous pulse height windows of equal width as illustrated in Fig. 2.6 [28]. An input pulse presented to this array will fall into one and only one of the multiple windows set by the SCA. Therefore, each input pulse increments the corresponding SCA counter by one count. A small pulse will correspond to a window near the bottom of the stack. However, a large pulse will fall into a window near the top at the end of the measurement period. The sum of all counters will equivalent the total number of pulses presented to the input.
SCA D Counter D A B C D SCA N/ H Window SCA C Counter C Input
SCA B Counter B
SCA A Counter A
Cannel Cannel Cannel Cannel 1 2 3 4 Fig. 2.5 An Array of stacked SCA, Fig. 2.6 A pointwise representation of the windows A, B, C,… are assumed to be differential pulse height distribution contiguous and of equal width H, with A obtained from the stacked SCA array of at the bottom of the pulse height scale Fig. 2.5
If we plot the number of recorded pulses ( N) in each counter divided by the window width ( H), versus the average pulse height for each window, a discrete representation of the differential pulse height distribution is derived. Therefore, each window is conventionally called a channel and is numbered in increasing order from left to right. The lowest channel corresponds to the pulse height window at the bottom of the range and records only those pulses whose amplitude is very small. The largest channel numbers is plotted at the right of the horizontal axis and record only the pulses of largest amplitude [28]. This process of sorting successive signal pulses into parallel amplitude channels is commonly called multichannel pulse height analysis. As a practical matter, schemes
١٧ Chapter (2) Overview of Gamma-Ray Spectroscopy
based on stacked independent SCAs are seldom attractive because of complications introduced by drifts in the various discrimination levels and window widths. These drifts can lead to overlapping or noncontiguous channels whose width may not be constant [28]. As a result other approaches have evolved for accomplishing the same purpose. The standard device designed to carry out this function is known as a MCA. The following sections discuss some general properties and functions of these instruments.
2.5 Multichannel Analyzer 2.5.1 Principle of operation of MCA The basic function of the MCA involves only the ADC and the memory. Its operation is based on the principle of converting an analog signal (the pulse amplitude) to an equivalent digital number. As a result, the ADC is a key element in determining the performance characteristics of the analyzer [28]. Once this conversion has been accomplished, there is extensive technology available for the storage and display of digital information. The flash and sub ranging ADCs produce a continuous series of digital output values of a fixed clock frequency. In contrast, the ADCs intended for use in MCAs operate in a deferent mode. These are designed to produce only a signal output value for each pulse presented to their input that is proportional to the peak amplitude of the pulse. Therefore, they are often called peak sensing ADCs [28]. The input circuitry for these ADCs must include a capability to sense the arrival of an input pulse and to sample and hold the maximum amplitude of the pulse for a time needed to carry out the conversion to a digital value. The output of the ADC appears in a register that is used to address standard digital memory that has many addressable locations as the maximum number of channels into which the spectrum can be subdivided. The number of memory locations is normally made a power of 2, with memories of 1024 to 8192 being common choices [28].
2.5.2 Basic components of gamma ray spectrometers The MCA is comprised of the basic components as illustrated in Fig. 2.7 . The memory is arranged as a vertical stack of addressable locations that ranging from the first address (or channel number 1) at the bottom through the maximum location number at the top. Once a pulse has been processed by the ADC, the analyzer control
١٨ Chapter (2) Overview of Gamma-Ray Spectroscopy
circuit seeks out the memory location corresponding to the digitized amplitude stored in the addressed register and the contents of that location incremented by one count. The net effect of this operation can be thought of as one in which the pulse to be analyzed passes through the ADC and is stored into a memory location that corresponds to most closely to its amplitude. This function is identical to that described earlier for the stacked SCA illustrated in Fig. 2.5 . Neglecting dead time, each input pulse increments an appropriate memory location by one count. Therefore, the total accumulated number of counts over all memory is simply the total number of pulse presented to the analyzer during the measurement period. A plot of the contents of each channel versus the channel number will be the same reorientation of the differential pulse height distribution of the input pulse as discussed earlier for the stacked SCA [28]. As illustrated in Figure 2.7 , an input gate is usually provided to block pulses from reaching the ADC during the time it is busy digitizing a previous pulse. The ADC provides a logic signal level that holds the input gate open during the time it is not occupied. Since, the ADC can be relatively slow, high counting rates will result in situations in which the input gate is closed for much of the time. Therefore, some fraction of the input pulses will be lost during this dead time. So, any attempt to measure quantitatively the number of pulses presented to the analyzer must take into account those lost during the dead time [28]. To overcome this problem, most MCAs provide an internal clock whose output pulses are routed through the same input gate and are stored in a special memory location. The clock output is a train of regular pulses synchronized with an internal crystal oscillator. If the fraction of time the analyzer is dead is low. Then, the fraction of clock pulses that is being clocked by the input gate is the same as the fraction of pulses blocked by the same input gate. Therefore, the number of clock pulses accumulated is a measure of the live time of the analyzer or the time over which the input gate held open. Therefore, absolute measurements can be based on a fixed value of live time, which eliminates the need for an explicit dead time correction to the data. Further discussion of the dead time problem of the MCAs [28] is given latter in this chapter. Also, many MCAs are provided with another linear gate that is controlled by a SCA. The input pulses are presented in parallel to the SCA, and after passing through a small fixed delay to the linear pulse input of this gate. If the input pulse meets the amplitude criteria set by the SCA, the gate is opened and the pulse is passed on to the reminder of the MCA circuitry. The purpose of this step is to allow rejection of input
١٩ Chapter (2) Overview of Gamma-Ray Spectroscopy
pulses that are either smaller or larger than the region of interest set by the SCA limits. These limits often referred as lower level discriminator (LLD) and upper level discriminator (ULD) [57] are chosen to exclude very small noise pulses at the lower end and very large pulses beyond the range of interest at the upper end. Thus, these uninteresting pulses never reach the ADC and consequently do not use valuable conversion time, which would otherwise increase the fractional dead time [28]. If an MCA is operated at relatively high fractional dead time (greater than 30 or 40%), distortions in the spectrum can arise because of greater probability of input pulses that arrive at the input gate just at the time it is either opening or closing. Hence, it is often advisable to reduce the counting rate presented to the input gate as much as possible by excluding noise and other insignificant small amplitude events with the LLD. Therefore, all of the commonly used gamma ray detectors require a high voltage bias supply to provide the electric field that accelerates and collects the charge generated by the gamma ray interaction in the detector [58].
Memory Delay Liner ADC 4 Input Gate Input 3 gate 2 (Open 1 when Ch. SCA ADC is not busy) Live Time Live Time Clock
Display Fig. 2.7 Functional block diagram of a typical MCA
The contents of the memory after a measurement can be displayed or recorded in a number of ways. All MCAs provide a cathode ray tube (CRT) display of the content of each channel as the Y displacement versus the channel number as the X displacement. Consequently, this display is a graphical representation of the pulse height spectrum. The display can be either on a linear vertical, or, a logarithmic scale to show detail over a wider range of channel content.
2.5.3 General MCA characteristics 2.5.3.1 Number of channels required In any pulse height distribution measurement, two factors dominate the choice of the number of channels that should be used for the measurement; the degree of resolution required and the total number of counts that can be obtained [55]. If arbitrarily large
٢٠ Chapter (2) Overview of Gamma-Ray Spectroscopy
number of counts can be accumulated, there is a need in making the number of channels as large as one wish. By providing a large number of channels, the width of any channel can be made very small and the resulting discrete spectrum will be a close approximation to the continuous distribution that is shown in Fig. 2.8(a ).
a c
Continuous 50 Channel
Spectrum
Count Count
Pulse Height Channel Number d b 500 Channel
10 Channel
Count Count
Channel Number Channel Number Fig. 2.8 An illustration of the effect of varying the number of channels used to record the differential distribution
If peaks are present in the spectrum, this requirement translates into specifying that at least four or five channels should be provided over a range of pulse height corresponding to the full width at half maximum (FWHM) of the peak [28,55]. Figure 2.8(b) shows hypothetical differential distributions taken under conditions in which the number of channels is too small to meet the criterion of the resulting distribution and lose of resolution in the spectrum are obvious. Also, the channels requirements can be expressed in terms of detector resolution (R). Both H and FWHM can be expressed in terms of number of channels. For a peak with a main pulse height (H): FWHM FWHM R = or H = (2.1) H R The position of H in units of channels is obtained by the following relation: 5 Channels Peak Position H= (2.2) R Therefore, a detector whose energy resolution is 5% requires a minimum of 100 channels. However, a detector with 0.2% resolution would require 2500 channels.
٢١ Chapter (2) Overview of Gamma-Ray Spectroscopy
The above arguments would suggest that one should always use the maximum number of channels possible. However, a second factor arises, when the available measurement time limits the total number of pulses that contribute to the recorded spectrum. Since, the number of events that fall within any channel will vary in a proportion to its width. The content of a typical channel varies inversely with the total number of channels provided over the spectrum. Choosing a larger number of channels will cause the relativity statistical uncertainty of each content to increase. Also, the channel to channel fluctuation of the data over smooth portions of the spectrum will become more noticeable. If these fluctuations are large enough, they can begin to interfere with the ability to discern small features in the spectrum. Very small peaks can become lost in statistical noise. These effects are illustrated in Fig. 2.8 (c d) [28].
2.5.3.2 Calibration of spectrometers A gamma spectrometer is used for identifying samples of unknown composition [28]. Its energy scale must be calibrated first. Calibration is performed by using the peaks of known sources such as 137 Cs and 60Co. Since, the channel number is proportional to energy, the channel scale can then be converted to an energy scale.
2.6 MCA Problems 2.6.1 MCA dead time The dead time of an MCA is usually comprised of two components; the processing time of the ADC and the memory storage time [59]. The latter time is a variable time that is proportional to the channel number in which the pulse is stored. The processing time per channel is simply the period of the clock oscillator. Once the pulse has been digitized, an additional fixed time of a few microseconds is generally required to store the pulse in the proper location in the memory. Thus, the dead time of an MCA using an ADC of this type can be written as: T=N + B υ (2.3) where υ, N and B denote the frequency of the clock oscillator, channel number in which the pulse is stored and the pulse storage time, respectively. The analyzer control circuits will hold the input gate closed for a period of time that equals this dead time. A dead time meter is often driven by the input gate to indicate the fraction of time the gate is closed, as a guide to the experimenter [28,55]. One normally tries
٢٢ Chapter (2) Overview of Gamma-Ray Spectroscopy
to arrange experimental conditions, so that the fractional dead time in any measurement does not exceed 30 or 40% to prevent possible spectrum distortions. The atomic live time operation of an MCA described earlier is usually quite satisfactory for making routine dead time corrections. However, circumstances can arise, in which the built in live time correction is not accurate. When the fractional dead time is high, errors can enter because the clock pulses are not generally of the same shape and duration as signal pulses. There are different techniques that used for dead time corrections such as pulser technique, harms technique and loss free counting technique [28,55].
2.6.2 MCA pileup The fact that pulses from a radiation detector are randomly spaced in time can lead to interfering effects between pulses when counting rates are not low [21,26,60]. These effects are generally called pileup and can be minimized by making the total width of the pulses as small as possible. Other consideration of ballistic deficit and signal to noise ratio (SNR) prevent reduction of the pulse width beyond a certain point. Therefore, the effects of pulse pileup at high rates are often very significant. Pileup phenomena are of two general types that have different effects on pulse height measurements [21,60]. The first type is known as tail pileup and involves the superposition of pulses on the long duration tail or undershoots from a proceeding pulse as shown in Fig. 2.9 . Tails or undershoot can persist for relatively long periods of time. Therefore, tail pileup can be significant event at relatively low counting rates. The effect on the measurement is to worsen the resolution by adding wings to the recorded peaks in the pulse height spectrum as illustrated in Fig. 2.9 . The remedy for tail pileup is to eliminate residual tails or undershoot through the use of pole zero cancellation technique. A second type of pileup generally called peak pileup. It occurs when two pulses are sufficiently close together. Therefore, they are treated as a single pulse by the analysis system. As shown in Fig. 2.10, the superposition of pulses were relatively flat tops and will lead to a combine pulse with apparent amplitude equal to the sum of two individual amplitudes. Lesser degrees of overlap will give a combined pulse with amplitude somewhat less than the sum. Since, peak pileup leads to the recording of one pulse in place of two, the total area under the recorded spectrum is smaller than the total number of pulses presented to the system during its live time [28].
٢٣ Chapter (2) Overview of Gamma-Ray Spectroscopy
dN/dH
V (t) H Time Tail
dN/dH
V (t)
H Overshoot Time
Fig. 2.9 Pileup from the tail or undershoot of a preceding pulse. Both are
categorized as tail pileup
V (t)
Time Fig. 2.10 Peak pileup, in which two closely spaced signal pulses combine to form one distorted pulse
The seriousness of peak pileup for a given situation can be estimated from the counting rate and the effective width of the signal pulses [26]. For pileup to be avoided, the interval following each pulse must be greater than the effective pulse width. At higher rates, any pileup that occurs can result only in total amplitude that is an integral multiple of single pulse amplitude. Therefore, the effect of pileup would be introducing sum peaks that would appear only at uniformly spaced position in the recorded spectrum. From these, the double sum peaks corresponding to the simple pileup of two pulses will be the most intense and will appear at a position corresponding to twice the basic amplitude.
٢٤ Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
CHAPTER (3)
MODELS OF QUANTUM DOT DEVICES FOR GAMMA RADIATION DETECTION
3.1 Introduction Quantum dots have attracted tremendous interest over the last few years for a large variety of applications ranging from optoelectronic through photocatalytic to biomedical, including applications as nanophosphors in light emitting diodes (LEDs) [61]. Quantum dots have been suggested as scintillators for detection of alpha particles and gamma rays [41,61,62,63]. Quantum dots offer an improvement on scintillator technology in that the size of the phosphorescent material would not be restrained by crystal growth. The dots would be suspended in a transparent matrix that could be as large as desired. Moreover, the output of the QDs is a function of their dimensions. Therefore, they could be produced to emit light at wavelengths suitable for detection by avalanche photodiodes that offer higher quantum efficiencies than PMT. Therefore, the sensitivity of the scintillator detector is increased [40]. To our knowledge, still models describing QD sources as gamma detection are not devised yet. In this chapter, we report on the effects of gamma irradiation on the different properties of CdSe/ZnS QDs. These characteristics are optical gain, power, population inversion and photon density. Furthermore, a new semiconductor scintillator detector was studied in which high energy gamma radiation produces electron hole pairs in a direct gap semiconductor material that subsequently undergo interband recombination, producing IR light to be registered by a photodetector [36]. Therefore, QDIPs can be used for this purpose. This chapter presents a method to evaluate, study, and improve the performance of QD sources and QDIPs as gamma radiation detection. This chapter is organized as follows: Section 3.2 presents the basics of VisSim simulator. QD devices as a detector are illustrated in Section 3.3 . The proposed models of QD devices as detectors are represented in Section 3.4. Discussion and results are summarized in Section 3.5.
25 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
3.2 VisSim Simulator VisSim simulation is one of the most widely used environments in operations research and management science, and by all indications its popularity is on the increase. The goal of using VisSim modeling and analysis is to give an up to date treatment of all the important aspects of a simulation study including modeling, simulation languages, validation and output data analysis. However, most real world systems are too complex to allow realistic models to be evaluated analytically. These models must be studied by means of VisSim simulation. In VisSim a computer was used to evaluate a model numerically over a time period of interest, and data are gathered to estimate the desired true characteristics of the model. In addition we have tried to represent the operation of the QD sources and photodetectors in a manner understandable to a person having only a basic familiarity with its main behaviors such as optical gain, power, output photon densities, dark current, photocurrent and detectivity. It can be a powerful supplement to traditional design techniques. System engineering program such as Mathsoft’s VisSim employ the Graphical User Interface (GUI) concept. The following are some possible reasons for the widespread popularity of the VisSim simulation [9 12]: 1. Most complex, real world systems with stochastic elements cannot be accurately described by a mathematical model which can be evaluated analytically. Thus, VisSim simulation is often the main type of investigation possible. 2. VisSim Simulation allows one to estimate the performance of an exciting system under some projected set of operation conditions. 3. Alternative proposed system designs (or alternative operating policies for a single system) can be compared via VisSim simulation to see which best meets specified requirements. 4. In VisSim simulation we can maintain much better control over experimental conditions than would generally be possible when experimenting with the system itself. 5. VisSim Simulation allows us to study a system with along time frame, or alternatively to study the detailed workings of a system in expanded time. Our goal in this chapter is to evaluate the performance of QD devices by using VisSim environment along with the block diagram programming procedures.
26 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
3.3 QD Devices as a Detector Quantum dots have been used in a wide variety of applications. A key advantage of these particles is that their optical properties depend predictably on size, which enables tuning of the emission wavelength [64]. Quantum dot devices as a source and infrared photodetectors can be used to detect gamma radiation [36,41,63]. Moreover, the ability of semiconductor QDs to convert alpha radiation into visible photons was demonstrated in [41]. In this chapter, we report on the scintillation of QDs sources and infrared photodetectors under gamma ray irradiation. Semiconductor scintillation gamma radiation detector based on QD will be discussed in which the gamma ray absorbing semiconductor body is impregnated with multiple small direct gap semiconductor inclusions of band gap slightly narrower than that of the body. If the typical distance between them is smaller than the diffusion length of carriers in the body material, the photo generated electrons and holes will recombine inside the impregnations and produce scintillating radiation to which the wide gap body is essentially transparent [36]. Furthermore, the QD sources under gamma radiation are characterized by changes in threshold current, external slope efficiency and light output [65]. For IR detection, most of QDIPs are based on vertical heterostructures consisting of two dimensional arrays of QDs separated by the barrier layers. The QD structures serving as the photodetector active region, where IR radiation is absorbed, are sandwiched between heavily doped emitter and collector contact layers. The active region can be either doped (with dopants of the same type as the contact layers) or undoped. Schematic view of vertical QDIP device structures is in [66]. The absorption of IR is associated with the electron intersubband transitions from bound states in QDs into continuum states above the barriers or into excited quasi bound states near the barrier top. The bound to continuum transitions or bound to quasi bound transitions followed by fast escape into the continuum result in the photoionization of QDs and the appearance of mobile electrons. Bound electrons accumulated in QDs can create a significant space charge in the active region. In this chapter, we extended the same physical characteristics to study QD devices under gamma radiation.
27 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
3.4 The Proposed Models of Quantum Dot Devices 3.4.1 The proposed simulator of quantum dot source under gamma radiation Improved radiation detection using QD semiconductor composites is demonstrated [63]. The quantum confinement effects enabled the QDs to be used with a wide variety of detectors. The inorganic nanocrystalline QDs will be demonstrated as a powerful method in preparing scintillating devices. In gamma ray detection, our goal is to employ nanomaterials in the form of QD based mixed matrices to achieve scintillation output several times over that from NaI(Tl) crystals. Moreover, block diagram models are used to represent carrier densities in the subbands, population inversion process, optical power and gain. The objective of this study is to obtain device that has high performance with optimal operating conditions.
3.4.1.1 The proposed simulator of carriers densities of quantum dot gamma ray detection The main objective of this subsection is to develop model of QD devices for incident gamma radiation detection. A novel methodology is introduced to characterize effect of gamma radiation on QD detectors. In this methodology, VisSim environment along with block diagram programming was used. The roles that the parameters of fabrication can play in the characteristics of QDs devices are discussed through developed models implemented by VisSim environment. The rate equations of QD devices under gamma radiation are studied. The effect of incident gamma radiation on the optical gain, power and output photon densities is investigated.
τ τwe s SCH (N s)
WL (N W) τe τe τdj τ wr QD j (N j) τe S τ p Figure 3.1 Energy diagram of the active region, diffusion, recombination and relaxation process
Solving the rate equations for carrier and photon is accurate way to deal with the source characteristics. Figure 3.1 depicts the energy diagram of the conduction band
28 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
of the QD active region, diffusion, relaxation, recombination and escape process of carriers. An exciton model is considered. Therefore, both electron and hole relax into the ground state simultaneously to form an exciton. According to this model, a single discrete electron and hole ground state is formed inside the QD and the charge neutrality always holds in each QD [67]. The rate equations of the QD devices are written as follows [67 69]:
dNs N ssw N N =Ri − − + (3.1) dt ts t sr t we dNNN NNN ws=+∑ j −−− www (3.2) dt tsj tD eg t wr t we td dN NN jNw Gj j j cG ()1 = −− − ∑ g S m (3.3) dt tdj t r tD eg n r m βN dSm j cG ()1 S m = +∑ g S m − (3.4) dttnr rm t p where N s, N w, N j, S m, R i, G j, q, D g, β, τ s, τ sr , τ we , τ wr , τ dj , and τ r denote the carrier number in separate confinement heterostructure (SCH) layer, wetting layer (WL), j th QDs group, the photon number of the m th mode, where m=1,2,…2M+1, the pumping rate of incident radiation, fraction of the j th QDs group type within an ensemble of different dot size populations, the electron charge, the degeneracy of the QD ground state without spin, the spontaneous emission coupling efficiency to the lasing mode, diffusion in the SCH region, carrier recombination in the SCH region, carrier reexcitation from the WL to the SCH region, carrier recombination in the WL, carrier relaxation into the j th QDs group and carrier recombination in the QDs (photon life time in the cavity), respectively. The average carrier relaxation time td is given by [67]:
−1 − 1 − 1 td=∑ tG dnn = ∑ τ o()1 − PG nn (3.5) n n where τ o is the initial relaxation carrier relation time. The photon life time in the cavity is given by:
c 1 1 t −1 =α + ln (3.6) p i nr2 L cav RR1 2 where R 1, R 2, Lcav , c, n r and α i denote the cavity mirror reflectivities, cavity length, light speed, refractive index and the internal loss, respectively. The linear optical gain
29 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
which the j th QDs group gives to the m th mode photons is represented by the following equation [67,70]:
2 2 P σ ()1 2pq hN D CV gmj =2 ()()2 PGBEEj − 1 jCV m − j (3.7) cnro e m o E CV
σ 2 where PCV , h, Ej, ND and E cv denote the transition matrix element, height of QD, the energy of the j th QDs group (where j=1,2,….2M+1) the volume density of QDs and the interband transition energy, respectively. The linear optical gain shows the homogeneous broadening of a Lorentz shape as follows [70]: hγ CV π BCV() E m− E j = 2 2 (3.8) E− E + hγ ()m j ()CV where γ cv and h denote the scattering rate and the reduced Plank's constant, respectively. The transition matrix element is given by:
σ 2 2 2 PCV= I CV M (3.9) where I cv represents the overlap integral between the envelope functions of an electron and a hole and M is derived by the first order interaction between the conduction and valence band [67]:
2 m Eg( E g + ) M 2 = o (3.10) 12 m * E + 2 e g 3 * where E g, m e and denote the band gap of bulk material, the electron effective mass, and the spin orbit interaction energy of the QD material, respectively. The source output power of the m th mode is also given by: h ωmcS m 1 Im = ln (3.11) 2Lcav R where ωm and R denote the emitted photon frequency and cavity mirrors R 1 and R 2, respectively. This subsection presents a method for modeling QD devices for gamma radiation detection. Their block diagram models are devised. VisSim environment is used to achieve this purpose. Block diagram model describing the rate equations of QD gamma radiation is proposed as depicted in Fig. 3.2.
30 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
+r-l td_dash Parameters Gain I l / q r Bcv_Em_Ej PcvSegma2 M2 tp + Ns l / - ts r 1/S Ns - h_Gamma_cv Plot Ns l + / g 2 tsr r 1 Nw l / twe r 0 Ns l r / -1 ts g2 -1e-16 .09216 .18432 .27648 l Nw g3 r / + twr - l Nw - r / 1/S Nw twe - Nw l / + td_dash r Relation Between Gain and Energy at different Matrix Element Nj l / te r hbar * * Dg w * Nw c * Gi l * / tdj r + l Nj - Sm r / tr - 1/S Nj * Im_Power - Nj l / te r * 1 l Dg r / ln R l c * r / G l Lcav 2 / nr r Beta * Nj l g * / * tr r Sm c Beta * * G l Nj l / / nr2 r + tr r g * + 1/S Sm2 c * Sm - G l r / Sm l nr + / tp r g * + 1/S Sm Sm - Sm l / tp r Fig. 3.2 Block diagram model describing the carrier densities of QD devices at different states for gamma radiation detection
3.4.1.2 Proposed simulator of optical wavelength This subsection introduces a useful block diagram model to predict effect of incident gamma radiation on QD emission wavelength. The QDs semiconductor composite is designed so that ionizing radiation produces excitations predominantly in the semiconductor QDs. These excitations are subsequently Förster transferred to organic material. For scintillators, the composite material must be transparent to the emitted photon, and the large Stokes shift of the organic material is essential. For charge collection devices the composite material must be trap free to allow efficient charge collection. Trap free and conjugated organic materials are available [63]. Pure QDs solids are impractical radiation detection materials because they are not transparent to their emission wavelength and have significant charge carrier trapping. If the peak photoluminescence (PL) photon emission energy, E , is always lower PL than the 1s–1s absorbance peak energy, E , by an energy shift ( E ~ 0.14 eV + abs AP 0.074 x E or E ~0.025 eV for CdSe QDs when 2 eV < E < 2.5 eV), then the abs AP abs wavelength of the PL peak, λ , can be calculated as follows [71] PL hc λPL = (3.12) E+X − E gR AP 7 where h, X denote plank's constant and X = 0.82x10 eV cm for CdSe, respectively. If all Cd precursors have been consumed, the average nanocrystal radius reaches the
31 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
completion radius, R , and PL emission occurs at a completion wavelength, λ , that is c c given by
λc= λ PL (3.13) R= R c +r-l Parameters Values
Eg + Energy l X l / lamd_LP / + r R r Delta_E_AP - Energy 1e6 Plot lamd_LP 10 -9 3 -10 Co * 10 vm l -11 r / pow R 10 4 -12 10 pi * lamd_LP2 0 .5 1 1.5 Neff lamd_LP3
Fig. 3.3 Block diagram model that describes the effect of incident gamma energy on emission wavelength.
Growth of the average QD radius can be written as [71] 1 3 3C0 V m Rc = (3.14) 4π N eff where C 0, Neff , and V m denote the original molar concentration of Cd in the batch (in 3 moles cm ), the effective number of spherical nanocrystals that would contain the number of moles of Cd that have been consumed and the molar volume, respectively. Block diagram model that describe the effect of gamma energy on the emission wavelength is depicted in Fig. 3.3 .
3.4.2 Block diagram models of QDIP A new scintillation type semiconductor detector was studied in which high energy radiation produces electron hole pairs in a direct gap semiconductor material that subsequently undergo interband recombination, producing IR light to be registered by a QDIP. Scintillators are not normally made of semiconductor material. The key issue in implementing a semiconductor scintillator is how to make the material essentially transparent to its own IR light. Consequently, the photons generated deep inside the semiconductor slab could reach its surface without tangible attenuation. In this subsection, different treatments are applied to model the characteristics of QDIPs than that in [72 73] under gamma radiation. Furthermore, we will utilize a new
32 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
block diagram model to consider the characteristics of a QDIP for gamma radiation detection under dark and illumination condition.
3.4.2.1 Dark current density block diagram model of QDIP If the numbers of electrons in QDs are sufficiently large, we may assume that these numbers are approximately the same for all QDs in a particular QD array,
i, j Nk= N k where i and j are the in plane indices of QDs,
∂2 ∂ 2 ∂ 2 4πq ++=ϕN δδδ xx − yy − zz −− ρ 2 2 2 ∑ 11()i 11 () j⊥ () kD (3.15) ∂xyz ∂ ∂ æ i, j , k where q is the electron charge, æ is the dielectric constant of the material from which the QD is fabricated, δ11 (x ) , δ11 ( y ) , and δ⊥ (z ) are the QD form factors in lateral (in the QD array plane) and transverse (growth) directions, respectively, x i and y j are the th in plane QD coordinates, z k = kL is the coordinate of the k QD array (where k = 1, 2, 3, . . . , M and M is the number of the QD arrays in the QDIP), L is the transverse spacing between QDs and ρ D is the donor concentration in the active region. The form factors correspond to the lateral and transverse sizes of QDs equal to a QD and lQD , respectively. The boundary condition supplementing Eq. 3.15 is given by [72]:
ϕ z =0 = 0 and ϕ z=() M + 1 L =V (3.16) where z= (M + 1)L is the width of the active region and V is the applied voltage.
When, V > V 0, V 0 denotes the doubled modulus of the potential at its minimum, the injected current is controlled by a potential barrier formed by a series of the potential hills belonging to the QD array located near the emitter contact. Apart from the charges of electrons occupying the first QD array, the charges of remote QDs and donors participate in the formation of this barrier. The potential barrier height has maxima at QDs and minima between them. These minima form the punctures through which the main part of the injected current flows. To calculate the current, the height of the potential barrier as a function of the in plane coordinates using Eq. 3.15 with Eq. 3.16 was calculated. Considering the effect of different charges on the punctures, we discriminate the average contribution of distant QDs, donors and the immediate
33 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
contribution of the charges of four QDs of the first QD array surrounding each puncture. Thus, the potential of the first QD array can be presented in the form [72]: ϕ= ϕ +Ψ−Ψ( ) (3.17)
Here and below, the potential is φ k = φ(x, y, kL). Averaging Eq. 3.15 in the lateral direction, it takes the following form [72]:
d 2 ϕ 4πq M
2 =∑QD N∑δ⊥ () zkL −− ρ D (3.18) dz æ k =1 where Σ QD denotes the density of QDs in each QD array. In QDIPs, the transverse size of QDs, l QD , is smaller than their lateral size, a QD , and both of them are smaller 1/2 than the transverse and lateral spacing between QDs, L and L QD = (Σ QD ) ,
−1/2 respectively. Considering QDIPs with aQD<< L QD = Σ QD , for ψ near the puncture at the point (x i = 0, yj = 0, z1 = L) and for ψ , we obtain [72]:
4 2q 1 2 2 Ψ=−N ΣQD1 +Σ QD () x + y (3.19) æ 2 where x and y are the in plane coordinates, and the averaging value is given by:
LQD L QD 1 2 2 Ψ=− Ψ dxdy (3.20) 2 ∫ ∫ LQD L L −QD − QD 2 2 The average number of electrons can be expressed by the following equation [72]:
NQD E QD N= VV +++D () M 1 (3.21) VQD q where N QD , E QD , V D and V QD denote the maximum number of electrons can occupy the QDs, the ionization energy of the quantum level in the QD and the characteristic 2πq voltages that given by the following relations V=ρ LMM2 () + 1 , Dæ D
2πq 2 2 ξ VQD= MM()() +Σ1 QD L 1 − η N QD , where, η = . The current through æ π ML ΣQD each puncture is proportional to J m exp (q ϕ/k BT), where J m is the maximum current density which can be supplied by the emitter contact, K B denotes the Boltzmann constant and T is the temperature. Hence, the average current density J is given by
[74 ]:
LQD L QD 2 2 qϕ JJ= Σ edxdyKB T (3.22) m QD ∫ ∫ L L −QD − QD 2 2
34 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
Therefore, block diagram model that describes the relation between dark current density and structural parameters is implemented through VisSim as depicted in Fig. 3.4. Solving the average dark current through VisSim introduces a better result that is comparable to analytical results in [74 75].
+ur-l FOR SECOND VARIATION FOR FIRST VARIATION PARAMETERS FOR FIRST PARAMETERS FOR SECOND
jm * SegmaQD LQD/2 u 1/S -LQD/2 l LQD/2 u 1/S average JQD -LQD/2 l
V Plot average JQD 10 -8 m * K -9 * average JQD2 10 T * aQD pow -10
Dark Current (A) Dark Current 10 l 0 .5 1 3.14 / V (Volt) * r hbar N1 + + average JQD * P * * NQD + l ln average N - r / l q * r / average N G * SegmaQD * NQD
1 + + 3.14 pow * l aQD r / 2 * aB Fig. 3.4 Dark current density block diagram model of QDIPs
3.4.2.2 Photocurrent density block diagram model of QDIP We calculate the photocurrent density in QDIPs using a developed device model of [72]. This model takes into account the space charge and the self consistent electric potential in the QDIP active region, the activation character of the electron capture and its limitation by the Pauli principle, the thermionic electron emission from QDs, thermionic injection of electrons from the emitter contact into the QDIP active region and the existence of the punctures between QDs. The developed model yields the photocurrent density in a QDIP as a function of its structural parameters. The photocurrent density of QDIP is given by [72 73]:
qϕ
KB T JPhoto= J m e (3.23) where J m is the maximum current density which can be supplied by the emitter contact and the potential ( ϕ ) is given by the relation [72]:
ϕ= ϕ +( ψ − ψ ) (3.24)
35 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
+ur-l PUSH OF PARAMETERS FOR PHOTO CURRENT FOR DARK CURRENT
jpoto * SegmaQD LQD/2 u 1/S -LQD/2 l LQD/2 u 1/S average jpoto V Plot l -8 -LQD/2 10 Photocurrent Current (A) average jpoto Dark Current (A) average jpoto * Pk average JQD l 10 -9 q * r / average N segma * I * -10 SegmaQD 10 0 .2 .4 .6 .8 1 jd V (Volt) * SegmaQD LQD/2 u 1/S -LQD/2 l LQD/2 u 1/S average JQD -LQD/2 l m * K * T * aQD pow
l 3.14 / * r hbar N2 + + average JQD * P * * NQD + l ln average N2 - r / l q * r / average N2 G * SegmaQD * NQD
1 + + 3.14 pow * l aQD r / 2 * aB2 Fig. 3.5 Photocurrent density block diagram model of QDIPs
By substitution from Eqs. 3.19, 3.20 and 3.22 into Eq. 3.27 , we get an equation for the potential of the first QD array. The average photocurrent density of QDIP is given by [72 73]:
LLQD QD LLQD QD 22 22 qϕ J=Σ JdxdyJ =Σ edxdyKB T (3.25) Photo QD∫∫ Photo m QD ∫∫ LL LL −−QD QD −−QD QD 22 22 Block diagram model through VisSim environment was used to implement photocurrent density. Therefore, block diagram model describes the relation between photocurrent density and structural parameters are implemented through VisSim as illustrated in Fig. 3.5.
3.4.2.3 Detectivity block diagram model of QDIP The specific detectivity, D, used to characterize QDIPs [76], was calculated from the noise density spectra and the peak responsivity [77]. The balance equation to equate the rates of electrons capture into and emission from the QDs under dark conditions is given by [78]:
qΣQD Jdark=() G k + G tun (3.26) PK where P K, G k, and G tun denote the capture probability, the rate of thermionic emission and the rate of field assisted tunneling emission, respectively. The expressions for these parameters are [74,78,79,80]:
36 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
−q2 N N− N QD CQD K B T PK= P o e (3.27) N QD π 2 N E h − QD * 2 KB T m KB Ta QD Gk = Ge0 e (3.28) 3 π 2 N 4 2m* q φ 2 h − B − E * 2 K T m K Ta GGe= 3 h E eB e B QD tun ot (3.29)
* 2 8ε0æ where C, C QD , ϕ , P o, G 0, m , G ot , E, a B, a , and ε 0 denote C= a , the QD B QD π QD
ε0æ 2 EQD − E capacitance CQD= 4 a QD , the potential barrier height ϕB = , the capture aB q probability for uncharged number of electrons which can occupy each QD, the thermionic emission rate constant, the effective mass of the electrons, the field assisted tunneling emission rate constant, the electric field across the device, the Bohr radius, the QD lateral area, and the permittivity, respectively. Because the electron transport across the active region under the effect of sufficiently strong electric field is associated with the drift, the balance equation can be presented in a form much like that for QWIPs [72]: J PK= G K + σ IN (3.30) qΣQD where J , σ and I denote the current density average in lateral directions, the cross section of electron photoescape from QDs and the intensity (photon flux) of incident IR radiation, respectively. By solving Eq. 3.26 and Eq. 3.30 for N , at I=0, we get
3 E 5.6mqφ 2 KT+ 3 EhE −QD − 0.33 B B 2 K TGot hEK T 2 Nπ h +ln eB + eB mKTa 0 B QD Go N= − 8 aε æ (3.31) B 0 3 8πεaæ−+−h22 h 4 πε2 h 2 aæaq + 2 π ma ( B 0 () QD0 B QD ) When photo excitation of electrons from QDs dominates their thermionic emission, the photocurrent density can be determined by the following equation [78]:
δq N ΣQD φ S J Photo = (3.32) PK where δ and φS denote the electron capture cross section coefficient and the photon flux density incident on a detector, respectively. By substituting from Eqs. 3.27 and 3.31, into Eq. 3.32 we get:
37 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
−8δqaB ε0 æQ Σ QD φ S N QD J Photo = 2 (3.33) q aB Q π aB ε 0 æQ SaQD K B T SPNo QD + 8 e S 3 h2 22 h 2 2 * where S=8πε aæB 0 ( −+− h) 4 πε aæaqmasQD0 + B π QD , and
3 * 2 EQD 5.6mqφ KT+ 3 EhE −G − 0.33 B B QN=π h2 +ln eKB T + ot e hEKB T mKTa* 2 . 0 B QD Go The responsivity is the ratio of the detector photocurrent to the incident photon power and it can be defined by the following formula [78]: J R = Photo (3.34) φS h υ where υ denotes the optical frequency. By substituting from Eq. 3.33 into Eq. 3.34 , we get an equation for the responsivity. Also, the detectivity of QDIP is determined as in [78,81,82,83] using the following equation:
R A D = (3.35) 4 q Jdark g where A and g denote the QDIP area and the QDIP photo gain, respectively. Block diagram model through VisSim environment was used to implement detectivity characteristic. Therefore, block diagram model describes the relation between detectivity and structural parameters are implemented through VisSim as illustrated in Fig. 3.6 . url PUSH OF PARAMETERS FOR PHOTO CURRENT Responsivity V Plot gQD Average N Pc FOR DARK CURRENT Average_N2 Detectivity 1e-6 20 15 jpoto * SegmaQD 10 LQD/2 u 1/S -LQD/2 l LQD/2 u 1/S average jpoto 5 l -LQD/2 0 0 .5 1 1.5 2 Detectivity (cm Hz.5/W) jd V (Volt) * SegmaQD LQD/2 u 1/S -LQD/2 l LQD/2 u 1/S average JQD -LQD/2 l
Responsivity * A * sqrt f
4 * q l * / Detectivity average JQD r * gQD
* sqrt Deltaf Fig. 3.6 Detectivity block diagram model of QDIPs
38 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
3.5 Results and Discussion In this thesis, we calculated different characteristics of QD sources and detectors that can be used as a scintillator for the detection of gamma radiation. The values of the calculations are taken from various references as in [67,74,78,79,84,85,86,87].
3.5.1 Results of QD sources 3.5.1.1 Carrier densities and population inversion of QD devices results The relation between optical gain and homogenous broadening at different dipole matrix element and refractive index is depicted in Figs. 3.7 3.8, respectively. The optical gain is peaked and decayed around 0.0031MeV as shown in Fig. 3.7. Also, higher optical gain is obtained for larger dipole matrix element. Since, the oscillator strength increases with the coupling between the two excited states. Such efficient coupling will produce high population inversion. Thus, high gain is achieved. The optical gain increases with the refractive index as illustrated in Fig. 3.8. We noticed that as the refractive index is increased, the beam is refracted with small divergence and high coupling occur inside the cavity with small dissipation. Consequently, better optical confinement is obtained along with high gain. The optical power against pumping rate is shown in Fig. 3.9. From this figure, the output power increases with the pumping rate. The alignment between the excited states increases with pumping. Hence, satisfied population inversion and high photons emission are produced. The dead period is needed for overcoming the threshold portion. After the threshold, the optical power increases with the pumping rate. Furthermore, the output power from QD devices increases with the incident ionizing gamma radiation. The incident radiation energy is greater than the energy gap between the two excited states. Consequently, more electrons are excited into higher energy levels. Then, the electrons return to the ground state with more radiated photons. Hence, the output power increases as shown in Figs. 3.10 3.11 . Moreover, the output power increases with cavity length as illustrated in Fig. 3.10 . We concluded that high population inversion is achieved using larger cavity length. Consequently, high differential efficiency is achieved. As this length increases, more electrons are amplified on the QD device under gamma radiation. Therefore, larger population inversion is achieved. Moreover, there is a limitation for increasing the length of the structure depending on
39 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
1. Complexity of the device 2. Saturation that may be occurs on the gain 3. Capability of the pumping source 4. Increasing the scattering rates However, the optical power decreases with the mirror length as depicted in Fig. 3.11 . Since, the mirrors absorb much photons and as a result more photons is dissipated. Relation between the power and photon density is shown in Fig. 3.12 . The number of output photons increase with the photons density. Therefore, the output power increases. The population inversion between the excited levels increases with the incident gamma radiation as shown in Fig. 3.13 . From this figure, as the incident gamma energy increases, the number of electrons in the upper subband increases and this in turn leads to enhance the population inversion. As a consequence of this, the number of photons will be raised and the QD characteristics will be improved. The results of the underlined figure exhibit a threshold region. After threshold the carrier densities will be further increased with incident energy. The output photon densities against the incident gamma radiation at different refractive index and photon life time are shown in Figs. 3.14 3.15 , respectively. The photon density increases with refractive index as illustrated in Fig. 3.14 . As the refractive index increases, high coupling between states is obtained. Consequently, better optical confinement is obtained along with high output photons. However, the photon density is inversely proportional to the photon life time, τ p, as depicted in Fig.
3.15 . The output photon density against radiative life time, τ r, is shown in Fig. 3.16 . The output photons increase with the radiative life time of the electrons. The output photon density against number of carriers in the WL is depicted in Fig. 3.17 . The population inversion increases with the number of carriers in the wetting layer. Therefore, the photon density increases.
40 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
σ 2 −6 Pcv =6.1 × 10 nm
2
) σ −6 1 Pcv =3.1 × 10 nm 2 m σ −6 6 Pcv =1.1 × 10 nm Gain (10
Homogenous Broadening (MeV) Fig. 3.7 Gain against homogenous broadening at different transition matrix element
nr=5
) 1 Power (W)
n =3.5
Gain (m r
Homogenous Broadening (MeV) Pumping Rate (cm 3s 1) Fig. 3.8 Gain against homogenous Fig. 3.9 Power against pumping rate of broadening at different refractive index incident gamma radiation
Lcav =900 m
Lcav =800 m
Lcav =700 m R=5nm Lcav =600 m R=15 nm Power (W) Power (W) R=60 nm
Gamma Energy (MeV) Gamma Energy (MeV) Fig. 3.10 Power against incident gamma Fig. 3.11 Power against incident gamma ray energy at different cavity lengths ray energy at different mirror reflectivity
41 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
Power (W)
Population Inversion
3 Sm (cm ) Gamma Energy (MeV) Fig. 3.12 Power against photon density Fig. 3.13 Population inversion against incident gamma energy
nr=4.5 τp=8ps
τp=12ps
) τp=16ps ) 3 3 (cm
(cm τp=20ps m
m n =3.5 r S S
Gamma Energy (MeV) Gamma Energy (MeV) Fig. 3.14 Photon density against incident Fig. 3.15 Photon density against incident gamma ray energy at different refractive gamma ray energy at different τ p index
)
3 ) 3 (cm m (cm S m S
3 τr (ps) Nw (cm )
Fig. 3.16 Photon density against τ r Fig. 3.17 τ r against incident N w
42 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
3.5.1.2 Emission wavelength results The emission wavelength against incident gamma energy is shown in Fig. 3.18 . The wide range of emission wavelength is one of the main advantages of QD devices. The emission wavelength increases with the incident gamma energy as depicted in Fig. 3.18 . Also, the emission wavelength against incident gamma energy at different
Neff and V m is depicted in Figs. 3.19 3.20 , respectively. If N eff increases, the emission wavelength decreases as depicted in Fig. 3.19 . However, the emission wavelength increases with the molar volume as shown in Fig. 3.20 . From this study we are concluded that the emission wavelength of QD is wide. Therefore, QD can be used as an efficient device for gamma radiation detection. Furthermore, the intraband free carrier absorption coefficient in doped semiconductors is roughly proportional to λ 2, which translates into larger optical waveguide losses at the longer wavelengths.
29 3 Neff =10 cm
30 3 Neff =10 cm
31 3 Neff =10 cm Wavelength (m) Wavelength (m)
Energy (MeV) Energy (MeV) Fig. 3.19 Emission wavelength against Fig. 3.18 Emission wavelength against incident gamma energy at different values incident gamma energy of N eff
3 Vm=33.34 cm /Mole
3 Vm=20 cm /Mole
3 Vm=10 cm /Mole Wavelength (m)
Energy (MeV) Fig. 3.20 Emission wavelength against incident gamma energy at different values of molar volume
43 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
3.5.2 Results of QDIPs 3.5.2.1 Dark current result The change of the dark current with the bias voltage is depicted in Fig. 3.21 . From this figure, the dark current increases with the bias voltage. As the applied bias voltage increases more electrons are accelerated into the continuum. Consequently, the potential barrier due to the space charge that accumulated in the active region vanishes. The thermionic effect of the injected current is increased. Therefore, the dark current is increased. Moreover, high agreement between both VisSim and published results [75] is obtained. The variation of dark current with a number of QD layers at different spacing between QD layers and bias voltage is depicted in Figs. 3.22 3.23, respectively. As depicted in Fig. 3.22 , the dark current decreases with the number of QD layers, M. If the number of QD layers increases the detector volume increases. Hence, the absorption coefficient of incident photons increases and consequently the losses of electrons decrease. Hence, the dark current reduces. From the figure, in the range of a number of QD layers M < 20, strong increase in dark current is observed. Increasing spacing between QD layers from 60 nm to 100 nm results in decreasing dark current more than one order of magnitude. Additionally, the dark current decreases with increases the spacing between the dots, L. The main reason for this dependence may be caused by increasing the barrier width. Consequently, the tunneling of electrons between QDs decreases. So, the wave function overlap between QDs decreases. Therefore, the dark current reduces. The previous published results [78] are in a good agreement with the obtained theoretical results. Figure 3.23 depicts the change of dark current with a number of QD layers at different bias voltage. From the result of this figure, dark current increases with the bias voltage. As the bias voltage increases, the space charge accumulated in the active region decreases. The injected current from the emitter through the active region is in thermionic origin. Therefore, the dark current increases. Also, at higher bias voltage, the electron space charge accumulated in QDs becomes fixed. In such a regime, the dark current in QDIPs becomes limited by the space charge of the injected mobile electrons, eventually tending to the saturation value of J m [72]. Figures 3.24 3.26 show the change of dark current with donor concentration in the barrier density at different bias voltage, transverse spacing between the dot layers and temperature, respectively. The dark current decreases with the increases of donor
44 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
concentration in the barrier as depicted in Fig. 3.24 . Subsequently, the injected current is controlled. Apart from the charges of donors participate in the formation of a potential barrier. The potential barrier height has maxima at QDs and minima between them. However, the dark current increases with bias voltage. As illustrated in Fig. 3.25 , the dark current reduces with the increases of both the donor concentration and spacing between the dots. Figure 3.26 shows that the dark current decreases with the increases of the donor concentration in the barrier and decreases the temperature. From this figure, the dark current increases with the temperature, because the energy of dissipated electrons increases with the temperature. Hence, thermionic transition occurs. On other words, the rapid increase of the dark current density of QDIP with temperature is mainly due to its exponential dependence on temperature and the thermionic emission of the electrons confined in the QDs.
-8 x 10 2 Published Results 1.8 VisSim Results A)
8 1.6
1.4
1.2
1
0.8
Dark Current (x10 0.6
0.4 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5
Bias Voltage (V) Fig. 3.21 Dark current and bias voltage for theoretical, VisSim and published results [75]
L=50 nm A) 8 Dark Current (x10
L= 100 nm
Number of Quantum Dot Layers Fig. 3.22 Dark current and number of QD layers at different transverse spacing between QD layers
45 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
V=0.3 V Dark Current (A) V=0.1 V
Number of Quantum Dot Layers Fig. 3.23 Dark current and number of QD layers at different bias voltage
V=0.3 V Dark Current (A)
V=0.1 V
Donor Concentration Density (x10 10 cm 3) Fig. 3.24 Dark current against donor concentration in the barrier density at different bias voltage
L=10 nm Dark Current (A)
L=30 nm
Donor Concentration Density (x10 10 cm 3) Fig. 3.25 Dark current against donor concentration in the barrier density at different transverse spacing between the dots layers
46 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
T=90 K A) 8
T=70 K Dark Current (x10
T=50 K
Donor Concentration Density (x10 10 cm 3) Fig. 3.26 Dark current against donor concentration in the barrier density at different temperature
3.5.2.2 Photocurrent result Figure 3.27 depicts the relation between photocurrent with the number of QD layer at different transverse spacing between the dot layers. From this figure, we observe that smaller photocurrent is achieved with increasing both the number of QD layer and transverse spacing between the dots. As the spacing between dots layers increases, the wave function overlapping between QDs decreases. Therefore, the dark current reduces and the photocurrent decreases. Moreover, smaller photocurrent is achieved with increases the number of QD layer, because small amount of electrons reaches the collector.
L=10 nm
L=15 nm Photocurrent (A)
Number of QD Layer Fig. 3.27 Photocurrent against number of QD layer at different transverse spacing between QD layers
47 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
NQD =15
NQD =10
NQD =5 Photocurrent (A)
Number of QD Layers Fig. 3.28 Photocurrent against number of QD layers at different number of electrons occupied by each QD
V=6 V
V=4 V Photocurrent (A)
Spacing Between QD Layers (nm) Fig. 3.29 Photocurrent against L at different bias voltage
Also, Fig. 3.28 depicts the relation between photocurrent of QDIP and number of the QD arrays in the QDIP at different maximum number of electrons occupied by each
QD, N QD . We can see that the photocurrent decreases with increases the number of QD layers, M. Also, it is increases with the number of electrons occupied by each QD due to large number of electrons that will reach the collector terminal. Photocurrent of QDIP against transverse spacing between the dots layers at different bias voltage is shown in Fig. 3.29 . As shown in this figure, we observe that the photocurrent increases with the bias voltage. The potential barrier height that formed due to the space charge in the active region will be vanished. Consequently, more electrons will
48 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
be excited from their bound states in the dot into the continuum. Hence, larger photocurrent is generated.
3.5.2.3 Detectivity result Detectivity against QD density is shown in Fig. 3.30. It is obvious that increasing QD density results in increasing detectivity. Since, both the active detector’s area and the absorption coefficient are increase. Also, high agreement between our results with the published results is obtained [78]. Figures 3.31 3.32 depict the variation of detectivity of QDIP against bias voltage at different maximum number of electrons occupied by each QD, N QD , and number of QD layers, M, respectively. As expected from Fig. 3.31, a rapid increase in detectivity occurs with increases the maximum number of electrons occupied by each QD due to excitation of large number of bound electrons. Therefore, the detectivity increases. Detectivity against bias voltage at different number of QD layers is shown in Fig. 3.32. From this figure, the detectivity increases with M. The detector volume increases with the number of QD layers and therefore the absorption coefficient increases. Consequently, the detectivity increases.
6.5
Published Results
/W) 6 Theoretical Results 1/2
5.5 cmHz 7 7
5 (x10
4.5
4 Detectivity
3.5
3 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
10 2 ΣQD (x10 cm )
Fig. 3.30 Detectivity of QDIP against ΣQD for both theoretical and published results [78]
49 Chapter (3) Models of Quantum Dot Devices for Gamma Radiation Detection
/W) 1/2 cmHz 6 NQD =10 (x10
NQD =8 Detectivity
Bias Voltage (V) Fig. 3.31 Detectivity against bias voltage at different maximum number of electrons occupied by each QD
/W) 1/2 cmHz 6 M=15 (x10
M=10 Detectivity
Bias Voltage (V) Fig. 3.32 Detectivity against bias voltage at different number of QD layers
50 Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
CHAPTER (4)
THE PROPOSED DIGITAL GAMMA RAY SPECTROSCOPY ALGORITHMS
4.1 Introduction Digital pulse processing for gamma ray spectroscopy is a signal processing technique in which detector signals are directly digitized and processed to extract quantities of interest [88]. Spectroscopic gamma ray detectors are used for many research, industrial, medical and homeland security applications [19,89,90,91]. They are being developed in many laboratories all over the world [92], because they offer several significant advantages compared to their analog counterparts [93 94]. These advantages are reflected in the possibilities of implementation of complex algorithms, simple and rapid modification of algorithms used for signal processing [94]. Thallium doped sodium iodide NaI(Tl) scintillation crystals coupled to PMT provide medium resolution spectral data about the surrounding environment. These effects are hardware dependent and have strong effects on the radioisotopic identification capability of NaI(Tl) based systems. However, high resolution gamma ray spectroscopy (HRGS) is used routinely in passive gamma ray assays of nuclear materials and radioactive waste. HRGS provides the capability to identify radionuclides from complex gamma ray spectra and to accurately determine the full energy response of selected gamma rays [95]. Height estimation is one of the most important tasks on nuclear systems [14]. All the information of a gamma ray event can be extracted by measuring the height of electronic pulses [15]. An important example is a system used to analyze the amplitude distribution of the voltage spectrum of pulses developed by a nuclear radiation detector [16]. The objective of this chapter is to provide flexible, accurate, and scalable algorithms for digital gamma ray spectroscopy for multichannel pulse height spectra. This chapter is organized as follows: Section 4.2 presents the spectroscopy system components. Signal preprocessing algorithms are studied in Section 4.3 . The more interesting
٥١ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
characteristics of pileup recovery algorithms, registration or rejection of the peak height and comparison between different algorithms are represented in Section 4.4 . Spectrum evaluation flow is summarized in Section 4.5 . Energy calibration is shown in Section 4.6 . We terminate the study by activity measurements in Section 4.7 .
4.2 System Components In this system, the components of the system for signal preprocessing algorithms, evaluation of different pileup recovery algorithms, dead time correction algorithm, spectrum drawing and evaluation algorithm, energy calibration and activity measurement algorithms are described. It contains the following elements: • Cesium 137 ( 137 Cs) and cobalt 60 ( 60 Co) radiation point sources, • Scintillator detector, • Amplifier, • ADC, • Connection to a desktop personal computer (PC). Figure 4.1 depicts a block diagram of the pulse height analysis system. However, the system components are shown in Fig. 4.2 . Scintillation detector with NaI(TI) is used to detect the radiation signal from 137 Cs and 60 Co point sources. This detector is connected to amplifier through coaxial cable which in turn connected to the PC through ADC. MATLAB environment is used to perform these algorithms. MATLAB is commercially available software that offers a large set of tool kits for processing and presentation of digital data [96].
Point Sources Scintillation Data Acquisition PC Station 137 60 Cs/ Co Detector system
Fig. 4.1 Schematic diagram of the pulse height analysis system
Fig. 4.2 System components
٥٢ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
4.3 Signal Preprocessing Algorithms To determine the spectroscopy with high accuracy, the signal should be processed without noise. Therefore, the data preprocessing steps are carried out using the MATLAB environment. These steps include background correction and afterpulse removal. Furthermore, the PMT anode signal is very noisy. Consequently, a de noising algorithm is required. These algorithms are explained below.
4.3.1. Background correction In this subsection, we are interested with removing the existing background radiation. It is the level of the signal before the measurements of the radiation source. As a consequence of, the cosmic rays radiation continuously bombarding the earth's atmosphere and the existence of natural radioactivity in the environment, all radiation detectors record some background signal [28]. Gamma rays from various radioactive sources, such as 40 K found in concrete walls, can often contribute to these spectra. The amount of this background varies greatly with the size, type of detector and with the extent of shielding that may be placed around it. Background level is important in those applications involving radiation sources of low activity. Since, the magnitude of the background signal is ultimately determines the minimum detectable radiation level. A useful technique can be applied to reduce background radiation in low level counting as follows:
Bc= M s − B r (4.1) where M s, Br and B c denote the measured signal from the radiation source, the background radiation signal and the background correction signal, respectively.
4.3.2. Afterpulse removal Afterpulse was originated from single or few count of pulses [28]. Here, we are concerned with elimination of the fluctuations resulting from counting statistical noise. Removing the afterpulse is priority in gamma ray spectroscopy because it has a great effect on the number of counts in the gamma ray spectroscopy. Consequently, it affects on the isotope identification. Therefore, we focus on removing afterpulse problem in the gamma ray spectroscopy. It is performed with a finite impulse response (FIR) filter with the following transfer function: 1+z−1 + z − 2 + z − 3 H() z = (4.2) 4 where z is in frequency domain.
٥٣ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
4.3.3 Noise elimination algorithm based on wavelet transform Since, the PMT anode signal is very noisy and timing features highly depend on the signal at specific times. A de noising algorithm is required. Therefore, the evaluation and studying the performance of signal de noising using WT algorithms of gamma ray spectroscopy is necessary. Wavelet de noising which is a non linear filtering operation that analyzes the signal at different time resolution levels and then removes the noise components by thresholding signal components in one or more levels. Depending on the application, the level and threshold should be modified to remove the noise while keeping the important frequency components of the signal. Also, the rescaling in wavelet decomposition is performed using level dependent estimation of the noise level [97]. We are interested with reducing the white Gaussian noises in gamma ray spectroscopy due to both analog channel and system readout. In order to de noise the signal and not to lose important information, an approach based on the WT is used. Wavelet analysis has the potential to benefit over other approaches due to the fact that the signal can simultaneously be analyzed over multiple scales, thus eliminating potential false isotope identifications from artifacts such as the Compton edge and backscatter peaks. An algorithm for signal de noising of gamma ray spectroscopy that based on WT is shown in Fig. 4.3 .
1) 137 Cs / 60 Co Point Sources 2) Scintillator Detector 3) Amplifier 4) ADC 5) Do Wavelet Transform Using dmyer and rbior1.1 6) Determine the Signal Approximation and Details 7) Reconstruct the Or iginal Signal from the Approximation Using Inverse Wavelet Transform 8) De Noise Output Signal Fig. 4.3 Signal de noising algorithm using WT
In order to determine the accuracy of this algorithm, a comparison between different wavelets approaches such as dmyer and rbior1.1 wavelets are studied. Then, reconstruction of the signals by IWT is presented. This comparison is based on a reference signal from 137 Cs and 60 Co acquired by DAS. This signal is stored in excel file and processed by MATLAB. Starting from the approximation, cA j, and detail,
٥٤ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
1 cD j, coefficients at level j, the IWT reconstructs cAj , inverting the decomposition step by inserting zeros and convolving the results with the reconstruction filters as depicted in Fig. 4.4 .
Approximation Apply IDW Inverting the Convolving the and Detail transform Decompositi results with the 1 Coefficients Level reconstructs cAj on Step reconstruction filters
Fig. 4.4 Schematic diagram showing the reconstruction step using single level (1 D) IWT
4.4 Algorithms of Problems Correction for Digital Gamma Ray Spectroscopy Signal 4.4.1 Pileup correction In many applications as much as 80% of information can be lost due to the effects of pulse pileup and dead time [17]. Pulse pileup distortion is a common problem for radiation spectroscopy measurements at high counting rates [91,98]. Moreover, pileup is one of the most delicate problems of any spectrometric method that is related to the extraction of the correct information out of the experimental spectra. The process of the spectroscopic measurement results in an inaccurate representation of the spectrum due to the interfering presence of the detector which perturbs the measurement [99]. Furthermore, the effects of pulse pileup in applications of nuclear techniques include the following issues; imposing a fundamental limit on detector throughput decreases the spectral accuracy and resolution, reduced peak to valley ratios due to false detection of pulses and causing significant detector dead time in the system [17]. Therefore , without a correction on the response function of the detector system , incorrect physical data are obtained from an analysis of measured spectra [99]. The deconvolution methods are widely applied in various fields of data processing and various approaches can be employed [99]. Furthermore, it must decompose completely the overlapping peaks while preserving as much as possible their heights, positions, areas and widths. Subsequently, the performances of various pileup recovery algorithms were evaluated. These algorithms are direct search, least square fitting, first derivative with maximum peak search algorithms and first derivative with inverse matrix algorithms. Our primary focus is the analysis of pileup signals collected from detector systems to obtain high accuracy of the spectroscopy. Also, the influence of white Gaussian noise
٥٥ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
on the recovery performance of these algorithms is discussed. Pileup corrections of gamma ray spectroscopy using these different algorithms are studied.
4.4.1.1 Pileup recovery using deconvolution [28] Deconvolution is sometimes used for the process of resolving or decomposing a set of overlapping peaks into their separate components by different techniques. If the counting rate is too high, a means of reducing it is needed to achieve maximum throughput [27]. Several methods for improving counting rate performance, such as shortening of the effective pulse width and pileup correction have been investigated [28]. Radiation particles are emitted from a source following the interval distribution as shown below [28,91,100]:
−λn t f( tdt) = λn e dt (4.3) where λ n, t and dt denote the true average emission rate of the radiation, the time interval between the current time pulse stamp and the relative origin of the time axis and the infinitely small time interval between t and t+dt, respectively. The probability P (N) for one pulse to occur without pileup with subsequent pulses may be estimated by:
P( t > τ ) = e −λn τ (4.4) where τ denotes the first pulse width. In the following, four different algorithms for the pileup recovery are investigated.
4.4.1.2 Direct search pileup recovery algorithm Here, we are interested in resolving or decomposing a set of overlapping peaks into their separate components. Nelder Mead modified simplex technique is used for this purpose. Direct search is a method for solving optimization problems that does not require any information about the gradient of the objective function. A direct search algorithm searches a set of points around the current point, looking for one where the value of the objective function is lower than the value at the current point. We can use direct search to solve problems for which the objective function is not differentiable or even continuous [101]. Direct search is used to describe sequential examination of trial solutions involving comparison of each trial solution with the "best" obtained up to that time together with a strategy for determining what the next trial solution will be [102]. It remains
٥٦ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
popular because of their simplicity, flexibility and reliability. Examples of direct search methods are the Nelder Mead Simplex method, Hooke and Jeeves' pattern search, the box method, and Dennis and Torczon`s Parallel Direct Search Algorithm (PDS) [103]. The simplex algorithm is one of the earliest and best known optimization algorithms. This algorithm solves the linear programming problems. The algorithm moves along the edges of the polyhedron defined by the constraints, from one vertex to another, while decreasing the value of the objective function at each step. A modified simplex method for finding a local minimum of a function of several variables has been devised by Nelder and Mead [104]. The Nelder Mead modified simplex algorithm succeeds in obtaining a good reduction in the function value using a relatively small number of function evaluations. This method finds the minimum of a function of several variables [105], starting at an initial estimate. This is generally referred to unconstrained nonlinear optimization. Search methods that use only function evaluations (the simplex search of Nelder Mead) are most suitable for problems that are very nonlinear or have a number of discontinuities. Thus, it is a direct method that does not use numerical or analytic gradients [101]. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder Mead algorithm [106]. For two variables, a simplex is a triangle, and the method is a pattern search that compares function values at the three vertices of a triangle. The worst vertex, where the function value is largest, is rejected and replaced with a new vertex. A new triangle is formed and the search is continued. The process generates a sequence of triangles (which might have different shapes), for which the function values at the vertices get smaller and smaller. The size of the triangles is reduced and the coordinates of the minimum point are found. This algorithm is stated using one time the term simplex (a generalized triangle in N dimensions) and other time Nelder Mead to find the minimum of a function of N variables. It is effective and computationally compact [104]. In other words, if n is the length of vector, x, a simplex in n dimensional space is characterized by the n+1 distinct vectors that are its vertices. A simplex is a triangle in two space. However, it is a pyramid in three space. At each step of the search, a new point in or near the current simplex is generated. Usually, one of the vertices is replaced by the new point that giving a new simplex. This step is repeated until the
٥٧ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
diameter of the simplex is less than the specified tolerance [101]. The MATLAB implementation of this algorithm finds both local minimum and maximum for a function without derivative [101].
1) Input Pileup Signal Containing Overlapping Peaks
2) Adding White Gaussian Noise to the Input Signal in the
Hypothetical Case Only
3) Applying Nelder Mead Modified Simplex Technique
A) Do Iterative Fit Routine
B) Determine the Parameters of the Noisy Input Signal
4) Apply Recovery Peaks Routine
5) Detect Illusive Pulses (If Exist)
6) Register Actual Peaks
Fig. 4.5 Pileup recovery using the Nelder Mead direct search algorithm
Fig. 4.6 Flowchart of the iterative methodology Figure 4.5 depicts the algorithm for pileup recovery peaks using Nelder Mead direct search method. From the figure, this algorithm is applied to hypothetical and real overlapping peaks. Moreover, in the hypothetical case, white Gaussian noise is added to these peaks to test the accuracy of the algorithm. Nelder Mead algorithm is essentially a way of organizing and optimizing the changes in parameters to shorten the time required to fit function to the required degree of accuracy. The most general
٥٨ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
way of fitting any model to a set of data is the iterative method. Consequently, iterative fit is performed. Iterative methods proceed in the following general way as depicted in Fig. 4.6 . This figure is illustrated as in the following [105] 1) Selects a model for the data 2) First guesses of all the non linear parameters are made 3) A computer program computes the model and compares it to the data set and calculating a fitting error 4) If the fitting error is greater than the required fitting accuracy, the program systematically changes one or more of the parameters and loops back around to step 3. The overlapped peak was assumed to be a convolution of its component peaks. It was characterized by Gaussian shape [107]. Therefore, the obtained coefficients are fitted the input pileup peaks and the overlapping peaks are recovered.
4.4.1.3 Least square fitting pileup recovery algorithm For resolving pileup overlapping peaks, the standard least square technique is used [108]. Least square curve fitting is used because it is easy to implement. It provides effective results in many fields of applications like signal processing and noise cancellation. The least square analysis is used to fit a set of m observations with a model that is non linear in n unknown parameters (m > n). Solution of least square fitting problem is an iterative process, whose convergence speed is problem dependent. This technique is employed for initial guessing of peak parameters. These parameters are peak height, position and width. The objective of curve fitting is to find a mathematical equation that describes a set of data. A simple and improved algorithm to resolve overlapped asymmetric pulses into its component peaks using nonlinear least square fitting method is reported in [100,109,110]. Figure 4.7 illustrates this algorithm. Considering voltage waveform with n overlapping peaks are characterized by the following equation after applying the fitting procedure:
2 2 2 2 Tb−− Tb Tb − Tb − −−()1() 2 −()n−1 − ()n cc c c 1 2 n−1 n VTae() =1 + ae 2 ++... aen− 1 + ae n (4.5)
where V(T), a1,2,..,n b 1,2,..,n and c 1,2..,n denote the voltage waveform of n overlapping peaks as a function of time, the amplitude, position and the width of 1,2,..,n 1,n recovered peaks, respectively. The overlapped peak was assumed to be a convolution
٥٩ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
of its component peaks. It was characterized by Gaussian shape. Therefore, the obtained coefficients are fitted to match the input peaks.
1) Input Pileup Signal Containing Overlapping Peaks
2) Adding White Gaussian Nois e to the Input Signal in the
Hypothetical Case Only
3) Applying Nonlinear Least Square Fitting Technique
A) Do Iterative Fit with Gaussian model
B) Determine the Parameters of the Noisy Input Signal 4) Apply Recovery Peaks Routine 5) Detect Illusive Pulses (If Exist) 6) Register Actual Peaks
Fig. 4.7 Pileup recovery using nonlinear least square fitting algorithm
4.4.1.4 First derivative with maximum peak search pileup recovery algorithm The third algorithm for pileup recovery is a proposed one that is presented in Fig. 4.8 . The detection of the peak and determination of the peak position can be realized in successive steps that independent of each other. This algorithm is based on first derivative of peak overlapping peaks and a MATLAB routine implementing the maximum peak search algorithm [108,111,112]. The differentiation of signals is used to facilitate the detection and location of partially overlapped Gaussian peaks in a multi component signal [113]. First derivative method has been used because it has the capability of spectral discrimination [114 116].
1) Input Pileup Signal Containing Overlapping Peaks 2) Adding White Gaussian Noise to the Input Signal in Hypothetical Case Only 3) Do the 1st Derivative Process to Determine Peaks Positions 4) Do Maximum Peak Search Routine to Determine Peaks Heights 5) Develop a Gaussian Pulses Shape Using the Obtained Parameters 6) Apply Recovery Peaks Routine 7) Detect Illusive Pulses (If Exist) 8) Register Actual Peaks Fig. 4.8 Pileup recovery using first derivative with maximum peak search algorithm The maximum peak is determined using the maximum peak search routine. This routine search and find local maxima in the overlapping peaks. For signal recovery step, the overlapped peak was assumed to be a convolution of its component peaks. It
٦٠ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
was characterized by Gaussian shape as in [114,115,117,118]. Therefore, the obtained coefficients are fitted with the input peaks. Consequently, the overlapping peaks are recovered. As a final stage in Fig. 4.8 , the recovered peaks can be rejected or accepted as described latter.
4.4.1.5 First derivative with matrix division pileup recovery algorithm The fourth algorithm is another proposed one. It is a new approach for recovery of multiple overlapping peaks in gamma ray spectroscopy using first derivative method in conjunction with the matrix division approach.
1) Input Pileup Signal Containing Overlapping Peaks 2) Adding White Gaussian Noise to the Input Signal in Hypothetical Case Only 3) Do the 1st Derivative Process to Determine Peaks Positions 4) Create a Matrix with n Rows (n is the Number of Derivative Peaks), Each Row Represents the Width and Position of the Peaks 5) Divide the Pulse by the Matrix 6) Estimate the Peak Height of each Pulse Individually using Matrix Division 7) Develop a Gaussian Pulses Shape Using the Obtained Parameters 8) Apply Recovery Peaks Routine 9) Detect Illusive Pulses (If Exist) 10) Register Actual Peaks Fig. 4.9 Pileup recovery using first derivative with matrix division algorithm
This algorithm is shown in Figure 4.9. In the hypothetical case, white Gaussian noise is added to the signal to test the accuracy of this approach. In this approach the first derivative method is used to determine the peaks positions. This method has the advantage of accurately determining the peak position. In this method the first order difference can be calculated between adjacent points in a time space based on the relationship between pulse rise time and digitization sample interval [100]. Then, a matrix is created that contains rows equal to the number of derivative peaks. Each row in this matrix is approximated by Gaussian shape with definite position and width. The amplitude of each pulse is obtained by dividing the pileup signal on the matrix. Consequently, the peak amplitude of each pulse is obtained. The resulting amplitude is multiplied by the corresponding row in the matrix. Consequently, all peaks are recovered.
٦١ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
4.4.1.6 Comparison between the algorithms In this subsection, comparison between the underlined algorithms is presented. This comparison is based on the input pileup peaks and the recovered peaks. The error is found by the following relation:
Error= Oi − S i (4.6) where O i and S i denote the input pileup signal and the sum of the recovered peaks, respectively. In order to represent the accuracy and validity of these algorithms, comparison between both the 137 Cs and 60 Co input and sum of recovered peaks are done.
4.4.2 Dead time correction algorithm due to radiation detector In nearly all detection systems, there will be a minimum amount of time that must separate two events in order that they are recorded as two separate pulses. This minimum time is usually called the dead time. Because of the random nature of radioactive decay, there is always some probability that a true event will be lost because it occurs too quickly following a preceding event. These dead time losses can become rather serve when high counting rates are encountered and any accurate counting measurements made under these conditions must include some correction for these losses. In this subsection, we focus on correcting dead time problem. Consequently, a study is presented to addresses these limitations. High counting rate causes a high fractional dead time in the MCA. It decreases rapidly during the measuring time. Several authors proposed corrections by means of additional electronic circuits while other elaborated some mathematical solutions for this problem [91,119]. Two models of dead time behavior of counting systems have come into common usage; paralyzable and nonparalyzable response [28]. These models relate the observed counting rate to the true counting rate. The observed counting rate (m) is given by [19,28,98] m= ne −nτ (4.7) where n and τ is the true counting rate and the dead time, respectively. The relation between true and measured rate for paralyzable response at different dead time values
٦٢ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
is depicted in Fig. 4.10 . From this figure, the measured rate decreases with increases the dead time.
4 x 10 8 τ=50 s 6
4 τ=15 s
τ=10 s
Measured rate (C/s) 2 τ=5 s
0 0 2 4 6 8 10 5 True rate (C/s ) x 10 Fig. 4.10 True count rate against measured count rate at different dead time
137 60 1) Cs and Co Radiation Point Sources
2) Scintillator Detector
3) Amplifier
4) Signal Digitization
5) Peak Height Search
6) Accumulate the Number of Peaks within Each Channel
7) Measure the Count Rate
8) Calculate the Dead Time Using Paralyzable Model
9) Calculate the True Rate using Lambert W Function
10) Calculate the Number of Lost Pulses Fig. 4.11 Dead time algorithm using paralyzable model
In order to make dead time corrections using paralyzable response, important knowledge of the dead time is required. One of the most known techniques of dead time corrections is the decaying source method. In this technique, the departure of the observed counting rate from the known exponential decay of the source can be used to calculate the dead time. An algorithm illustrating the dead time correction is depicted in Fig. 4.11. This algorithm is based on the known behavior of the true rate as follows:
٦٣ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
−λt n= n0 e (4.8) ln (2) where n denotes the true rate at the beginning of the measurement, λ = is the 0 T 2 decay constant of the isotope used for the measurement, and T/2 is the half life time of the 137 Cs/60 Co radio isotope. By substituting from Eq. (4.9) into Eq. (4.8), the dead time can be calculated by the following equation:
ln(n0 ) − ln ( m) − λ t τ = −λt (4.9) n0 e The true counting rate can be obtained by solving Eq. (4.8 ) for the true counting rate using Lambert W function as follows: −1 n= Lambert − W() − m τ (4.10) τ Consequently, the number of lost pulses during the course of measurement represents the difference between the true and measured counts. The number of lost pulses can be determined by taking the exposure time (t) into account as follows: L=( nmt − ) (4.11)
4.5 Spectrum Drawing and Evaluation Flow In any pulse height distribution measurement, two factors dominate the choice of the number of channels that should be used for the measurement : the degree of required resolution and the total number of counts that can be obtained [28]. By providing a large number of channels, the width of any channel can be made very small and the resulting discrete spectrum will be a close approximation to the continuous distribution. The true distribution should not change drastically over the width of one channel. If peaks are present in the spectrum, this requirement translates into specifying that at least four or five channels should be provided over a range of pulse height corresponding to the FWHM of the peaks. The algorithm of spectrum drawing is illustrated in Fig. 4.12.
٦٤ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
1) Gamma Radiation Signal Acquired by Scintillation Detector 2) Determine the Peak Height of Interest in the Spectrum 3) Divide the Peak Amplitude into Equal Widths 4) Channel Widths obtained by Dividing Max. Peak on number of Channels 5) Count the Number of Peaks that Located at each Channel 6) Accumulate the Number of Peaks Within Each Channel 7) Plot the Content of each channel (Y axis) Versus the Channel Number (X axis) Fig. 4.12 Spectrum drawing algorithm of gamma ray spectroscopy
4.6 Energy Calibration Another important consideration is the energy calibration. It is necessary to calibrate the system every time we wish to make a run. Calibration is important because it ensures that the channels which the events of decay are recorded correspond to the proper energy levels. Therefore, the energy calibration specifies the relationship between peak position in the spectrum (channel number) and the corresponding gamma ray energy. Figure 4.13 illustrates an algorithm for the calculation of the energy calibration. This is accomplished by measuring the spectrum of a source emitting gamma rays of precisely known energy and comparing the measured peak position with energy irrespective of the number of nuclides present in the source. For any source, it should be ensured that the calibration energies cover the entire range over which the spectrum is to be used. In practice, the spectrum should be measured long enough to achieve good statistical precision for the peaks to be used for calibration [120].
1) 137 Cs and 60 Co Radioisotopes
2) Analyze the Input Signals
3) Draw the Spectrum of each Radioisotope
4) Identify the Channel Number Corresponding to Each Photopeak
5) Draw Relation between the Known Energy Against Channel Number
6) Take this Figure as a Reference for any Future Measurement Using the
Same System
Fig. 4.13 Energy calibration algorithm
٦٥ Chapter (4) The Proposed Digital Gamma-Ray Spectroscopy Algorithms
4.7 Activity Measurements To accurately determine the activity of the detectable radionuclides, one must measure the count rate for the signatures of the sample and determine the probability of observing those signatures. The observation probability depends not only on the signature intensity but also on the absolute efficiency of the detectors and on the possibility that multiple photons simultaneously incident on the same detector impact the observed counting rate [121]. In measuring radionuclide concentrations using gamma spectrometers, it is also important to derive most suitable calibration factors for measurement efficiency, self absorption effect, geometric effect and coincidence summing effect [122]. The activity of the isotope sources will be measured. The isotope source, which is point like to a good approximation, will be located at a known distance depending on source activity and the energy spectrum will be recorded during a known exposure time. An algorithm for activity measurement is shown in Fig. 4.14 . Because the source to detector distance and diameter of the detector is known, it is possible to calculate the geometric efficiency, which is fraction of all gamma that are emitted by source and arrived at the detector surface. Since, the linear attenuation coefficient of NaI(Tl) and thickness of the NaI(Tl) crystal are known, it is possible to calculate fraction of the gamma that will be absorbed in NaI(Tl) and create a detectable count (intrinsic efficiency). Therefore, if the number of counts in the recorded energy spectrum is N, then the source activity will be determined as follows [123]: N A = (4.12) εgeom ε int C i t where ε geom and εint denote the geometric efficiency and the intrinsic efficiency, respectively. Source activities are measured for 137 Cs and 60 Co sources. From the measurement of this experiment, the date of manufacture of the 137 Cs and 60 Co sources was calculated.
1) 137 Cs and 60 Co Radioisotopes
2) Analyze the Input Signals
3) Accumulate Each Count at the Corresponding Channel
4) Calculate Count Rate 5) Compute Geometry Efficiency 6) Compute Activity Fig. 4.14 Activity measurement algorithm
٦٦ Chapter (5) Gamma-Ray Spectroscopy Results
CHAPTER (5)
GAMMA RAY SPECTROSCOPY RESULTS
5.1 Introduction Evaluation of different algorithms of gamma ray spectroscopy was discussed in this chapter. These algorithms are signal preprocessing, problems correction, spectrum drawing and evaluation, energy calibration and activity measurements algorithms. Radiation signals from 137 Cs and 60 Co were acquired by DAS. Signal preprocessing is a fundamental step in digital gamma ray spectroscopy. It includes, background correction, afterpulse removal and noise removal. Also, the influence of white Gaussian noise on the recovery performance in these algorithms is discussed. These algorithms of digital gamma ray spectroscopy measurement experiment are preprocessed using the MATLAB environment. Our primary focus is the analysis of pileup signals collected from detector systems to obtain high accuracy of the spectroscopy. Hence, efficient pileup recovery algorithms of digital gamma ray spectroscopy signals are presented in this chapter. The objective of this chapter is to study different algorithms implementing these problems. Therefore, we discuss the performances of different pileup recovery algorithms; direct search, least square fitting, first derivative with maximum peak search and first derivative with matrix division algorithms. These algorithms have the advantages of decomposition of multiple overlapping events into their original peaks. Dead time correction algorithms are another scope in this chapter. Also, the spectrum drawing and evaluation algorithm is another objective in this chapter. Different spectrums are drawn for different number of sources. Furthermore, evaluation of the spectrum is one of scopes of this study. This chapter is organized as follows: Section 5.2 presents the signal preprocessing results. Problems correction of gamma ray spectroscopy results are studied in Section 5.3. Spectrum drawing and evaluation results are summarized in Section 5.4. Energy calibration results are shown in Section 5.5. We terminate the study by activity measurement results in Section 5.6.
٦٧ Chapter (5) Gamma-Ray Spectroscopy Results
5.2 Signal Preprocessing Results In this section, signal preprocessing was performed. It is necessary for accurate signal analysis and better isotope identification. It includes background correction, afterpulse removal and noise elimination algorithms. Results of these algorithms are discussed in further details as follows.
5.2.1 Background correction result In nuclear spectroscopy, spectra of a combination of radioactive sources may be frequently found, not only as a result of the experimental needs but also due to background signals. As a result, it is often important to have in advance a picture of the spectrum expected from the assumed gamma ray source [124 ]. The measured signal from the radiation source is depicted in Fig. 5.1 (a). By using the mentioned algorithm, the obtained background correction signal is illustrated in Fig. 5.1 (b). This signal is used for further analysis.
Original Signal 200
100 a
0
0 1000 2000 3000 4000 5000
Background Corrected Signal 200 Amplitude (x0.03V)
100 b
0 0 1000 2000 3000 4000 5000
Time (x1.25ms) Fig. 5.1 Background correction signal
5.2.2 Smoothing algorithm result Finite impulse response filter with order 3 is used. The choice of a filter of order 3 is to guarantee the smoothing of the measured data and avoid the complexity problems associated with higher order filters. Applying this filter removes single pulse noise.
The output of the filter C f (n) can be expressed as:
٦٨ Chapter (5) Gamma-Ray Spectroscopy Results
1 Cnf () =() CnCn()()()() + −+1 Cn −+ 2 Cn − 3 (5.1) 4 where C (n) is the filter input as depicted in Fig. 5.1 (b). The result of this step is shown in Fig. 5.2 .
30
25
20
15
Amplitude (x0.03V) 10
5 0 1000 2000 3000 4000 5000
Time (x1.25ms) Fig . 5.2 Afterpulse correction signal
5.2.3 Noise removal result using wavelet transform This subsection presents a method to evaluate and study the performance of signal de noising using WT algorithms of gamma ray spectroscopy. A de noising algorithm based on the WT is implemented to reduce the effect of noise introduced by the noisy analog channel and by the PMT. The decomposition process can be iterated with successive approximations that are being decomposed. Consequently, each signal is broken down into many lower resolution components. This is called the wavelet decomposition tree. Five approximation and detailed coefficients of different WT is studied. Reconstruction of the fifth approximation by IWT is demonstrated. In order to determine the accuracy of this algorithm, a comparison between different wavelets approaches such as dmyer and rbior1.1 wavelets are prepared. Then, reconstructions of the signals by IWT techniques are introduced. Here, a 5 level de noising algorithm based on dmyer wavelet function was performed. The input signal, first approximation and detailed coefficients using dmyer and rbior1.1 are shown in Figs. 5.3 5.4 , respectively. Reconstruction of the first 5 levels using dmyer and rbior1.1 techniques are illustrated in Figs. 5.5 5.6 , respectively. Furthermore, we concluded
٦٩ Chapter (5) Gamma-Ray Spectroscopy Results
that using the rbior1.1 introduces better results over dmyer WT preprocessing of gamma ray spectroscopy as illustrated in Table 5.1 .
Original Signal 400
200 0 0 1000 2000 3000 4000 5000 First Approximation Wavelet Transform 500
0 -500 0 1000 2000 3000 4000 5000
Amplitude (x0.03V) First Detail Wavelet Transform 10 0
-10 0 1000 2000 3000 4000 5000
Time (x1.25ms)
Fig. 5.3 Input signal and both first approximation and detailed coefficients using dmyer
Table 5.1 Comparison between both discrete Meyer and reverse biorthogonal Discrete Meyer Wavelet Reverse Biorthogonal Wavelets Error 3.5428x10 4 8.5265 x10 14 1st Approximation Error 0.0014 3.1264 x10 13
Original Signal 400
200 0 0 1000 2000 3000 4000 5000 First Approximation Wavelet Transform 400 200 0 0 1000 2000 3000 4000 5000 Amplitude (x0.03V) First Detail Wavelet Transform 50
0
-50 0 1000 2000 3000 4000 5000
Time (x1.25ms) Fig. 5.4 Input signal and both first approximation and detailed coefficients using rbio1.1
٧٠ Chapter (5) Gamma-Ray Spectroscopy Results
Reconstructed Signal Using 1st Level Approximation by Inverse Wavelet Transform 500 0 -500 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Reconstructed Signal Using 2nd Level Approximation by Inverse Wavelet Transform 500 0 -500 0 500 1000 1500 2000 2500 Reconstructed Signal Using 3rd Level Approximation by Inverse Wavelet Transform 1000 0 -1000 0 200 400 600 800 1000 1200 1400 Reconstructed Signal Using 4th Level Approximation by Inverse Wavelet Transform 1000 0
Amplitude (x0.03V) -1000 0 100 200 300 400 500 600 700 800 Reconstructed Signal Using 5th Level Approximation by Inverse Wavelet Transform 1000 0 -1000 0 100 200 300 400 500 600
Time (x1.25ms)
Fig. 5.5 Reconstruction of first 5 levels using dmyer that based on IWT
Reconstructed Signal Using 1st Level Approximation by Inverse Wavelet Transform 400 200 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Reconstructed Signal Using 2nd Level Approximation by Inverse Wavelet Transform 400 200 0 0 500 1000 1500 2000 2500 Reconstructed Signal Using 3rd Level Approximation by Inverse Wavelet Transform 1000 500 0 0 200 400 600 800 1000 1200 Reconstructed Signal Using 4th Level Approximation by Inverse Wavelet Transform 1000 500
Amplitude (x0.03V) 0 0 100 200 300 400 500 600 Reconstructed Signal Using 5th Level Approximation by Inverse Wavelet Transform 1000 500 0 0 50 100 150 200 250 300
Time (x1.25ms) Fig . 5.6 Reconstruction of first 5 levels using rbio 1.1 that based on IWT
5.3 Problems Correction of Gamma Ray Spectroscopy 5.3.1 Pileup recovery and correction results Figure 5.7 shows the probability curve of absence of pileup against true rate at different pulse widths. As illustrated in this figure, for applications where counting rate can be kept very low, pulse pileup distortion is not a problem. Also, the probability of absence of pileup decreases with increases the width of the first pulse. From the figure, we observe the dependency of pileup probability on both pulse width
٧١ Chapter (5) Gamma-Ray Spectroscopy Results
and true rate. In the following, four different algorithms results for the pileup recovery are investigated.
1
0.8 Pulse Width =5 s 0.6 Pulse Width =10 s Pulse Width =15 s Pulse Width =20 s 0.4
Probability of absence of Pileup 0.2
0 0 2 4 6 8 10 True Rate (C/ s) 5 x 10 Fig. 5.7 Probability of absence of pileup with the true counting rate at different pulse widths
5.3.2 Pileup recovery using hypothetical signal 5.3.2.1 Direct search algorithm result In this subsection, we are interested with resolving or decomposing a set of overlapping peaks into their separate components. Nelder Mead modified simplex technique is used for this purpose. The pulse parameters; peak position, height and width are determined using this Nelder Mead modified simplex algorithm. The pulse shape is constructed using its peak shape as Gaussian shape [114,115,117,18]. Consequently, the original peaks are recovered. Finally, the recovered peaks are registered as described in the following subsection. This algorithm is applied to two hypothetical overlapping peaks as depicted in Fig. 5.8 (a) . Two nonlinear parameters; peak position and width are determined using this algorithm. A Gaussian shape in conjunction with the peak and its position of each pulse are used to construct each pulse. The recovered two peaks with the input pileup peak are shown in Fig. 5.8 (b) . However, these two peaks are illustrated separately in Fig. 5.8 (c). The pulse parameters for the two recovered peaks are calculated as depicted in Table 5.2 . These parameters are the pulse position, maximum amplitude, FWHM and the
٧٢ Chapter (5) Gamma-Ray Spectroscopy Results
pulse area. The obtained results showed that peak parameters were able to be recovered within 0.24% deviations.
10 a 0 Input Pileup Peaks
-10
Amplitude (a. u) 0 100 200 300 400 500
10 Recovered Peaks with Envelop b 0
-10 0 100 200 300 400 500 Amplitude (a. u) 10
Recovered Peaks
5 c
0 0 100 200 300 400 500 Time (a. u) Amplitude (a. u) Fig. 5.8 Peaks recovery using direct search algorithm
150
Position 100
50
Width
0
Parameter Error (%)
-50 Height
-100 7 7.5 8 8.5 9 Fitting Erro r (%) Fig. 5.9 Percent fitting error against percent parameter error for first peak
Figures 5.9 5.10 depict the relation between the percent parameters errors (the difference between the actual parameters and the parameters of the best fit model) against percent fitting error (the root mean square (RMS) difference between the model and the data) for both the first and second peaks, respectively. The values of
٧٣ Chapter (5) Gamma-Ray Spectroscopy Results
these errors are determined as explained in Fig. 4.6 . The variability of the fitting error is caused by random small variations in the first guesses and by noise in the signal.
-55
Position
-60
Height \\\ Parameter Error (%)
Width
-65 7 7.5 8 8.5 9 Fitting Error (%) Fig.5.10 Percent fitting error against percent parameter error for second peak
Table 5.2 Average measured parameters for recovery of double overlapping peaks Estimated Parameters Max. Peak Position Pulse Width Area 1st Recovered Peak 4.9840 99.8769 100.2060 527.011 5 100 100 527 2nd Recovered Peak 2.9954 250.0082 200.0181 636.6072 3 250 200 636
5.3.2.2 Least square fitting algorithm result The least square fitting method can be used for extracting the original overlapping peaks. The two overlapping peaks are characterized by the following equation after applying the fitting procedure
2 2 Tb− Tb − −()1 − () 2 c c 1 2 VT() = ae1 + ae 2 (5.2)
where V(T), a1,2 , b 1,2, and c 1,2 denote the voltage waveform of two overlapping peaks as a function of time, the amplitude, position and the width of the first and second recovered peaks, respectively. For signal recovery, the overlapped peaks were assumed to be a convolution of its component peaks. It was characterized by Gaussian shape [114,115,117,118]. Therefore the obtained coefficients are fitted with the input
٧٤ Chapter (5) Gamma-Ray Spectroscopy Results
two peaks. Consequently, the two overlapping peaks are recovered. As a final stage the recovered peaks can be rejected or accepted as described in the following subsection. Figure 5.11 shows both the input two overlapping peaks and the fitting Gaussian shape. The two recovered peaks with the original overlapping peaks are shown in Fig. 5.12 . The calculated mean square error between the input pileup and recovered peaks of this algorithm was found to be 4.7306x10 12 .
6
Amplitude vs. Time
5 fit 1
4
3
Amplitude (a. u) 2
1
0 0 100 200 300 400 500 Time (a. u) Fig. 5.11 Comparison between both the input pileup and the fitting Gaussian shape using the least square fitting algorithm
6 Input Pileup Peak 5
Recovered Peaks 4
3
Amplitude (a. u) 2
1
0 0 100 200 300 400 500 Time (a. u)
Fig. 5.12 Input pileup signal and the recovered two overlapping peaks
٧٥ Chapter (5) Gamma-Ray Spectroscopy Results
5.3.2.3 First derivative with maximum peak search algorithm result The first derivative method in junction with the maximum peak search algorithm has been used for overcoming the pileup problem of gamma ray spectroscopy. First derivative method has been used because it has the capability of spectral discrimination [114 115].
6
4 a
2 Amplitude (a. u) 0 0 100 200 300 400 500
0.2 b 0.1
0 0 50 100 150 200 250 300
Derivative Amplitude (a.u) Time (a. u)
Fig . 5.13 Input pileup signal and f irst deri vative result of overlapping peak
1.4
1.2
1
0.8
0.6
Amplitude (a. u) 0.4
0.2
0 0 100 200 300 400 500 600 Time (a. u) Fig. 5.14 Detection of maximum peaks of input pileup signal
٧٦ Chapter (5) Gamma-Ray Spectroscopy Results
2 Input Pileup Peaks 1
0 Amplitude (a. u)
0 100 200 300 400 500 2 Recovered Signals with Envelop 1
0 Amplitude (a. u) 0 100 200 300 400 500
2 Recovered Peaks 1
0
Amplitude (a. u) 0 100 200 300 400 500
Time (a. u) Fig. 5.15 Peaks recovery using first derivative with maximum peak search algorithm
Figure 5.13 (a) shows the input pileup signal against time. However, the first derivative of both peaks is shown in Fig. 5.13 (b). From this figure, the derivative is the slope of the input signal. The derivative of the signal is positive as the signal slopes up. However, the derivative of the signal is negative as the signal slopes down. If a signal has zero slopes, its derivative is zero. Consequently, the location of the maximum in a peak signal can be computed precisely by computing the location of the zero crossing in its first derivative. The maximum peak amplitude of the signal is determined by using a maximum peak search routine as depicted in Fig. 5.14 . Two hypothetical overlapping peaks are depicted in Fig. 5.15 (a). The recovered peaks with the input overlapping peaks are illustrated in Fig. 5.15 (b). However, the recovered peaks are shown separately in Fig. 5.15 (c).
5.3.2.4 First derivative with matrix division algorithm result Another approach for recovery of pileup peaks in gamma ray spectroscopy using first derivative method in conjunction with the matrix division approach is presented. This algorithm has the advantage of accurately determining the peak position. In this algorithm the first order difference can be calculated between adjacent points in a time space based on the relationship between pulse rise time and digitization sample
٧٧ Chapter (5) Gamma-Ray Spectroscopy Results
interval [100]. Then, a matrix is created that contains two rows equal to the number of derivative peaks. Each represents the width and position of the peaks. Each row in this matrix is approximated by Gaussian shape with definite position and width.
6
5
4
3
2
Amplitude (a. u) 1
0
-1 0 50 100 150 200 250 300 350 400 450 500 Time (a. u) Fig . 5.16 Input pileup signal with white Gaussian noise
Input Pileup Peak 6
5 Recovered Peaks
4
3
2
Amplitude (a. u) 1
0
-1 0 100 200 300 400 500 Time (a. u) Fig. 5.17 Recovered peaks with their envelope using matrix division algorithm
The amplitude of each pulse is obtained by dividing the pileup signal on the matrix. Consequently, the peak amplitude of each pulse is obtained. Then, the resulting amplitude is multiplied by the corresponding row in the matrix. Therefore, all pulses are recovered. By using the proposed algorithm, the overlapping peaks depicted in
٧٨ Chapter (5) Gamma-Ray Spectroscopy Results
Fig. 5.16 are recovered and enclosed by input pileup signal as shown in Fig. 5.17 . These recovered peaks are individually illustrated in Fig. 5.18 .
5 1st Recovered Peak
4 2nd Recovered Peak
3
2 Amplitude (a. u)
1
0 0 100 200 300 400 500 Time (a. u) Fig. 5.18 The individual recovered peaks using matrix division algorithm
5.3.2.5 Gaussian noise handling
8 Direct Search Algorithm
Least Square Fitting Algorithm
6 Maximum Peak Search Algorithm
Matrix Division Algorithm
4
Maximum Error 2
0 0 10 20 30 40 50 60
SNR (%)
Fig. 5.19 Maximum error between recovered peaks and input pileup against SNR for the algorithms Here, white Gaussian noise is added to the overlapping peaks to test the accuracy of the algorithms. The effect of white Gaussian noise on the algorithms is studied. The variation between SNR and the maximum error between both the recovered and original peak is depicted in Figure 5.19 . As shown in this figure, the proposed
٧٩ Chapter (5) Gamma-Ray Spectroscopy Results
algorithms (maximum peak search and matrix division) are robust enough to noise at low SNR. However, the direct search algorithm introduces better results at high SNR over maximum peak search algorithm. Consequently, signal preprocessing is essential to achieve low error with the direct search algorithm. However, the pulse width error is the main reason of high error that originated with the least square fitting algorithm. As a final conclusion, the matrix division algorithm gives satisfactory results in noisy environment. In contrast, the direct search and least square fitting algorithms show high sensitivity with noise. Therefore, noise cancellation presented in section 5.2 is essential with both algorithms.
5.3.2.6 Registration and rejection of the peak height The occurrence time of the pulse is defined to be the time point where the leading edge voltage reaches the threshold. Naturally, the time interval between two adjacent pulses can be defined as the difference of the occurrence time for these two peaks. It is clear that pulse pileup occurs whenever the time interval of two adjacent pulses is less than the pulse width of the first pulse [28 91]. On other hand, for pileup to be avoided, the interval following each pulse must be greater than the effective pulse width. The peak amplitude is registered if the difference between the two overlapping peaks is grater than the pulse width otherwise the peak is neglected as follows. FWHM FWHM T− T >1 + 2 (5.3) 2 1 2 2 where FWHM 1, FWHM 2, T 1, and T 2 denote the first pulse width, the second pulse width, the position of the first peak and the position of the second peak, respectively. This means that both recovered peaks will be registered for all algorithms.
5.3.2.7 Comparison between the algorithms and discussion for hypothetical signal In order to represent the accuracy and validity of these algorithms, comparison between both the input pileup and the sum of recovered peaks is carried out. Figures 5.20 5.23 (a) show the difference between the input pileup signal and the sum of recovered peaks for direct search, least square fitting, maximum peak search and matrix division algorithms, respectively. On other hand, Figures 5.20 5.23 (b) show
٨٠ Chapter (5) Gamma-Ray Spectroscopy Results
the error between the input pileup peak and the recovered peaks for these algorithms, respectively. From these results, we notice that the inverse matrix algorithm has high accuracy for identifying both peak height and position of the overlapping peaks than other algorithms. The direct search algorithm introduces the best recovered pulse width result. However, the direct search one introduces better results in clean environment. Therefore , it overcomes this problem when combined with noise cancellation procedure that described previously. However, least square algorithm achieves the highest pulse width error than other algorithms. Furthermore, the estimated parameters error of the recovered two peaks for the considered algorithms is depicted in Table 5.3 . Also, the estimated parameters values of the recovered two peaks in comparison with true values for the considered algorithms are depicted in Table 5.4 .
6
Input Pileup Signal 4 Recovered Signal a 2
Amplitude (a. u) 0 0 100 200 300 400 500 0.02
0 b
Error -0.02
-0.04 0 100 200 300 400 500 Time (a. u) Fig. 5.20 Accuracy of direct search algorithm a) The input pileup signal and sum of recovered peaks and b) The error that represent difference between them
Table 5.3 Estimated parameters errors of the underlined three algorithms Parameters Error Height Error Position Error Width Error Direct Search algorithm 0.0024 0.0006 0.0005 Least Square Algorithm 0 0 0.3994 Maximum Peak Search Algorithm 0.6645 0.0110 0.2244
The main strength of the proposed maximum peak search and matrix division algorithms is their capability of resolving the original peaks in noisy environment. Moreover, matrix division algorithms proved to be satisfactorily robust against
٨١ Chapter (5) Gamma-Ray Spectroscopy Results
increasing level of noise. From the obtained results of the proposed matrix division algorithm, the maximum amplitude is measured and compared with true amplitude and maximum deviation error of 0.3585% is achieved.
6
Input Pileup Signal a 4 Recovered Signal
2
Amplitude (a. u) 0 0 100 200 300 400 500 2
1 b
Error
0 0 100 200 300 400 500 Time (a. u) Fig. 5.21 Accuracy of least square algorithm a) The input pileup signal and sum of recovered peaks and b) The error that represent difference between them
666 Input Pileup Signal a
444 Recovered Signal
222
000 000 100 200 300 400 500
Amplitude (a. u) 2
1
b
0
Error -1 0 100 200 300 400 500
Time (a. u) Fig. 5.22 Accuracy of maximum peak search algorithm a) The input pileup signal and sum of recovered peaks and b) The error that represent difference between them
٨٢ Chapter (5) Gamma-Ray Spectroscopy Results
a
Amplitude (a. u)
b
Error
Time (a. u)
Fig. 5.23 Accuracy of matrix division algorithm a) The input pileup signal and sum of the recovered peaks and b) The error that represent difference between them
Table 5.4 Input and estimated parameters of both the input pileup and recovered peaks Peak Height Position Width 1st 2nd Peak 1st 2nd 1st 2nd Peak Peak Peak Peak Peak Input parameters 5 3 100 250 100 200 Estimated Value of Direct Search 5.0127 3.0025 100.28 251.43 100.51 198.93 algorithm Estimated value of Least Square 5 3 100 250 60.06 120.1 Algorithm Estimated Value of Maximum Peak 5.6642 3.0107 104 247 Search Algorithm Estimated Value of Inverse Matrix 4.9893 2.9952 104 247 Algorithm
5.3.3 Experimental comparison among pileup recovery algorithms for digital gamma ray spectroscopy 5.3.3.1 Direct search algorithm result This algorithm is applied to multiple overlapping peaks from 137 Cs radiation point source of the experimental setup as depicted in Fig. 5.24 . Two nonlinear parameters; peak position and width are determined using this algorithm. A Gaussian shape in conjunction with the peak and its position of each pulse are used to construct each pulse [114,115,117,118]. The recovered peaks with both the input pileup peaks and sum of the recovered peaks are shown in Fig. 5.24 . However, the individual recovered peaks are shown in Fig. 5.25 .
٨٣ Chapter (5) Gamma-Ray Spectroscopy Results
150 A
B
100 C D
E
50 F
Amplitude (x0.03V) G
H 0 0 2 4 6 8 10 12 14 16
Time (x1.25ms) Fig. 5.24 137 Cs input pileup signal, sum of the recovered peaks and recovered peaks using direct search algorithm, where the Acronyms A refers to 137 Cs input pileup signal, B denotes the sum of recovered peaks and the other alphabetically characters referred to the order number of recovered peaks
150
A
B 100
C
D 50 E
Amplitude (x0.03V) F 0 0 2 4 6 8 10 12 14 16 Time (x1.25ms) Fig. 5.25 Peaks recovery using direct search algorithm. The alphabetically characters referred to the order number of recovered peaks
5.3.3.2 Least square fitting algorithm result This algorithm is employed for initial guessing of peak parameters. These parameters are peak height, position and width. Considering voltage waveform, multiple overlapping peaks are characterized by the following equation after applying the fitting procedure.
T− b T − b T− b T− b T− b ()1() 2 − ()3 ()4 − ()5 − − c − c VT() = aec1 + ae c 2 + ae3 + aec 4 + ae 5 (5.4) 1 2 3 4 5
٨٤ Chapter (5) Gamma-Ray Spectroscopy Results
where V(T), a 1:5 , b 1:5, and c 1:5 denote the voltage waveform of multiple overlapping peaks as a function of time, the amplitude, position and the width of the first to the fifth recovered peaks, respectively.
120 A 100 B
80 C
60 D E 40 F 20 Amplitude (x0.03V) G 0 0 2 4 6 8 10 12 14 16 Time (x1.25ms) Fig. 5.26 137 Cs input pileup signal, sum of the recovered peaks, and recovered peaks, using nonlinear least square algorithm, where the Acronyms A refers to 137 Cs input pileup signal, B denotes the sum of recovered peaks and the other alphabetically characters referred to the order number of recovered peaks
120
A 100 B C D 80 E 60
40
Amplitude (x0.03V) 20
0 0 2 4 6 8 10 12 14 16
Time (x1.25ms)
Fig. 5.27 Peaks recovery using nonlinear least square algorithm. The alphabetically characters referred to the order number of recovered peaks
For signal recovery step, the overlapped peaks were assumed to be a convolution of its component peaks. It was characterized by Gaussian shape [114,115,117,118]. Therefore, the obtained coefficients are fitted to match the input signal. Consequently, the multiple overlapping peaks are recovered. As a final stage the recovered peaks can be rejected or accepted as described in the following subsection. Figure 5.26 shows the 137 Cs input pileup signal, sum of recovered peaks and the recovered peaks. The
٨٥ Chapter (5) Gamma-Ray Spectroscopy Results
individual recovered peaks are shown in Fig. 5.27 . However, the main disadvantage of least square fitting, it does not converge because of the difficulty to provide good initial parameter values for severely overlapping peaks [125].
5.3.3.3 First derivative with maximum peak search algorithm result The 137 Cs input signal is shown in Fig. 5.28 (a). Figure 5.28 (b) shows the pulse derivative amplitude against time for multiple peaks.
100 a 137Cs Input Signal 50
0 Amplitude (x0.03V) 0 2 4 6 8 10 12 14 16
30 First Derivative Signal 20 b
(x0.03V) 10
Derivative Amplitude 0
0 2 4 6 8 10 12 14 16
Time (x1.25ms) 137 Fig. 5.28 a) Cs input signal and b ) First deri vative result of overlapping peaks
120
100
80 137Cs Input Signal Maximum Peak Height 60
40
Amplitude (x0.03V) 20
0 0 5 10 15 20 Time (x1.25ms) 137 Fig. 5.29 Cs input signal with detected maximum peak heights
٨٦ Chapter (5) Gamma-Ray Spectroscopy Results
The peak amplitude of the signal is determined by using a maximum peak search routine as depicted in Fig. 5.29 . The detected overlapping peaks, the sum of recovered peaks and the recovered peaks are illustrated in Fig. 5.30 . However, these peaks are shown individually in Fig. 5.31 .
140 A
120 B 100 C
80 D
60 E
F 40 Amplitude (x0.03V) G 20 H 0 0 2 4 6 8 10 12 14 16
Time (x1.25ms) Fig. 5.30 137 Cs input pileup signal, sum of the recovered peaks and recovered peaks using first derivative with maximum peak search algorithm, where the Acronyms A refers to 137 Cs input pileup signal, B denotes the sum of recovered peaks and the
other alphabetically characters referred to the order number of recovered peaks
120 A 100
B 80 C 60
D 40 E Amplitude (x0.03V) 20 F
0 0 2 4 6 8 10 12 14 16 Time (x1.25ms) Fig. 5.31 Recovered peaks using first derivative with maximum peak search algorithm. The alphabetically characters referred to the order number of
recovered peaks
٨٧ Chapter (5) Gamma-Ray Spectroscopy Results
5.3.3.4 Comparison between algorithms and discussion for real signal In order to represent the accuracy and validity of these algorithms, comparison between both the 137 Cs input pileup and the sum of recovered peaks are performed. Figures 5.32 5.34 (a) represent the difference between input pileup signal and sum of recovered peaks for direct search, least square fitting algorithm, maximum peak search and matrix division algorithms, respectively. On other hand, Figures 5.32 5.34 (b) show the error between the input pileup signal and the sum of recovered peaks for the underlined algorithms. From these results, we notice that the proposed maximum peak search algorithm has high accuracy for identifying both peak height and position of multiple overlapping peaks than other algorithms. Furthermore, the error signal is smaller than that of other algorithms. On other words, the performance of all algorithms is evaluated in terms of error between recovered and input pileup signals. From Figures 5.32 5.34 (b), the proposed algorithm shows better average error performance of 27.1238. However, the worst case error was slightly in flavor of other algorithms. Consequently, better isotope identification can be achieved by the proposed algorithm.
150
100 a 137Cs Input Pileup Signal 50 Sum of the Recovered Peaks
0
Amplitude (x0.03V) 0 2 4 6 8 10 12 14 16 50
b 0
Error
-50 0 2 4 6 8 10 12 14 16
Time (x1.25ms) Fig. 5.32 Accuracy of direct search algorithm a) The 137 Cs input pileup signal and sum of recovered peaks and b) The error that represents the difference between the original detected and recovered peaks
٨٨ Chapter (5) Gamma-Ray Spectroscopy Results
150 100 a 50 A
B 0 0 2 4 6 8 10 12 14 16
Amplitude (x0.03V) 100
50
0 Error b
-50 0 2 4 6 8 10 12 14 16
Time (x1.25ms) 137 Fig. 5.33 Accuracy of least square algorithm a) The Cs input pileup signal and sum of recovered peaks, where the Acronyms A refers to 137 Cs input pileup signal while B denotes the sum of recovered peaks and b) The error that represents the difference between origin al detected and recovered peaks
150
100 a A 50 B
0 0 2 4 6 8 10 12 14 16 Amplitude (x0.03V) 200
100
b 0
Error -100 0 2 4 6 8 10 12 14 16
Time (x1.25ms) Fig. 5.34 Accuracy of maximum peak search algorithm a) The 137 Cs input pileup signal and sum of recovered peaks, where the Acronyms A refers to 137 Cs input pileup signal while B denotes the sum of recovered peaks and b) The error that represents the difference between original detected and recovered peaks
5.3.4 Dead time correction results due to radiation detector For paralyzable response, the computed dead time is 96.449 s as depicted in Table 5.5. The number of lost pulses is equal to 223. The advantage of this algorithm is the simplicity of dead time percent calculation without the need of complexity mathematical model in [126]. For paralyzable response, the dead time percent was calculated and equal to 0.0294%.
٨٩ Chapter (5) Gamma-Ray Spectroscopy Results
Table 5.5 Results of paralyzable dead time algorithm m (KC/s) n (KC/s) τ ( s) Lost Pulses Dead Time Percent 2.8422 96.449 223.4531 0.0294 ٢ ١٦٠٨ Paralyzable
5.4 Spectrum Drawing and Evaluation Results The identification of peaks is the first step of the analysis of the nuclear spectrum system. The identification of relatively narrow peaks either on smoothly varying background or after its removal is important task. The main problem lies in distinguishing true peaks from statistical fluctuations, Compton edges, background and other undesired spectrum features [127]. Consequently, previous preprocessing steps are very important for overcoming these problems. The results of spectrum drawing algorithm are illustrated in the following subsections.
5.4.1 Spectrum of 137 Cs The spectrum of 137 Cs for 16 , 32 and 1024 channels is shown in Figs. 5.35 5.37, respectively. The number of events that fall within any one channel will vary in proportion to its width. The channels content with smaller number of channels is larger than that with larger number of channels. For 137 Cs, the content of a typical channel varies inversely with the total number of channels provided over the spectrum as depicted in Figs. 5.35 5.37.
500 450
400
350
300
250 Counts 200
150
100
50
0 0 2 4 6 8 10 12 14 16 Channel Number Fig. 5.35 Channels content versus 16 channel for 137 Cs
٩٠ Chapter (5) Gamma-Ray Spectroscopy Results
450 400
350
300
250
Counts 200
150
100
50 0 0 5 10 15 20 25 30 35 Channel Number 137 Fig. 5.36 Channels content versus 32 channel for Cs
700
600
500
400
Counts 300
200
100
0 0 100 200 300 400 500 600 700 800 900 1000
Channel Number Fig. 5.37 Channels content versus 1024 channel for 137 Cs
5.4.2 Spectrum of 60 Co The spectrum of 60 Co for 16, 32 and 1024 channel numbers are depicted in Figs. 5.38 5.40, respectively. For 60 Co, the content of a typical channel varies inversely with the total number of channels provided over the spectrum as shown in Figs. 5.38 5.40.
٩١ Chapter (5) Gamma-Ray Spectroscopy Results
120
100
80
60 Counts
40
20
0 0 2 4 6 8 10 12 14 16
Channel Number Fig. 5.38 Channels content versus 16 channel for 60 Co
70
60
50
40
Counts 30
20
10
0 0 5 10 15 20 25 30 35
Channel Number Fig . 5.39 Channels content versus 32 channel for 60 Co
٩٢ Chapter (5) Gamma-Ray Spectroscopy Results
120
100
80
60 Counts
40
20
0 0 200 400 600 800 1000 1200
Channel Number Fig. 5.40 Channels content versus 1024 channel for 60 Co
5.4.3 Effect of pileup recovery algorithms on spectrum evaluation Effects of pileup recovery algorithms on spectrum evaluation are studied at both small and large number of data points. Firstly, for smaller number of data points, spectrums of 137 Cs for 4 8 and 16 channel number for direct search, least square, maximum peak search and inverse matrix algorithms are depicted in Fig. 5.41 5.43, respectively. For each spectrum, four different cases are illustrated with pileup recovery algorithms and without pileup correction.
6 Spectrum Using Direct Search Algorithm Spectrum Using Least Square Fitting Algorithm 5 Spectrum Using Maximum Peak Search Algorithm Spectrum Without Pileup Correction 4
3
Counts 2
1
0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Channel Number Fig. 5.41 Channel content versus 4 channel number of 137 Cs for all algorithms
٩٣ Chapter (5) Gamma-Ray Spectroscopy Results
6
5 Spectrum Using Direct Search Algorithm Spectrum Using Least Square Fitting Algorithm
4 Spectrum Using Maximum Peak Search Algorithm Spectrum Without Pileup Correction 3
Counts 2
1
0 0 1 2 3 4 5 6 7 8 9
Channel Number 137 Fig. 5.42 Channel content versus 8 channel number of Cs for all algorithms
For each spectrum, the photopeak corresponds to channel number four, eight, and sixteen as shown in Figs. 5.41 5.43, respectively . From the obtained experimental results, the proposed algorithm proves superior performance for spectrum evaluation. Therefore, this algorithm demonstrates efficient solution of isotope identification. However, the worst spectrum evaluation is obtained using the least square fitting algorithm.
6
5 Spectrum Using Direct Search Algorithm Spectrum Using Least Square Fitting Algorithm 4 Spectrum Using Maximum Peak Search Algorithm Spectrum Without Pileup Correction
3
Counts 2
1
0 0 2 4 6 8 10 12 14 16 18
Channel Number 137 Fig . 5.4 3 Channel content versus 16 channel number of Cs for all algorithms
The number of events that fall within any one channel will vary in proportion to its width. The content of a typical channel varies inversely with the total number of channels provided over the spectrum. The channels content with smaller number of
٩٤ Chapter (5) Gamma-Ray Spectroscopy Results
channels is larger than that with larger number of channels. Moreover, from Figs. 5.41 5.43 , we notice that the resolution enhances with increases the number of channels. As the number of channels increases, the FWHM decreases. Resolution represents the FWHM with respect to position peak of the centroid. Consequently, good resolution is obtained. Therefore, resolution enhancement is an essential contribution especially at small number of channels.
137 Fig. 5.44 Real Cs signal and 512 channel number spectrum with Matlab viewer The effect of the pileup recovery algorithms on four, eight and sixteen channel spectrum is depicted in Table 5.6. From this table, the maximum number of counts at photopeak of each algorithm is demonstrated. Also, the proposed algorithm proves superior performance of isotope identification. Table 5.6 Maximum number of detected counts at photopeak Number of Counts at Direct Search Least Square Fitting Maximum Without Photopeak Algorithm Algorithm Peak Search Pileup Algorithm Correction Four Channels 2 2 6 3 Eight Channels 3 1 6 3 Sixteen Channels 2 1 6 2
Secondly, these algorithms are applied to multiple data points. The proposed maximum peak search algorithm shows better results than other algorithms. The acquired signal for 512 and 1024 channel spectrum with Matlab viewer is illustrated in Figs. 5.44 5.45, respectively . However, the least square algorithm introduces bad results with large number of data points. Moreover, the consuming time is very large
٩٥ Chapter (5) Gamma-Ray Spectroscopy Results
to converge with multiple data points. Also, the direct search algorithm is very complex to deal with multiple data points. Therefore, it is unpractical to use direct search and least square algorithms with multiple data points.
Fig. 5.45 Real 137 Cs signal and 1024 channel number spectrum with Matlab viewer
5.4.4 The Compton interaction The energy of the scattered gamma can be determined by solving the energy and momentum equations for this collision. The solution for these equations in terms of the scattered gamma can be written approximately as follows [128]
E γ E γ ` ≅ (5.5) 1+ 2E γ () 1 − cos θ where E γ ` θ and E γ denote the energy of the scattered gamma in MeV, the scattering angle for γ` and the incident gamma ray energy in MeV, respectively. If θ=180 0 due to a head on collision in which γ` is scattered directly back. Therefore, Eq. 5.5 becomes as follows
E γ E γ ` ≅ (5.6) 1+ 4 E γ
The energy of the recoil electron, E e, for this collision would be
Ee = Eγ − E γ ` (5.7)
٩٦ Chapter (5) Gamma-Ray Spectroscopy Results
The position of the Compton edge is the maximum energy that can be imparted to an electron by the Compton interaction. It can be calculated as depicted in Table 5.7.
Table 5.7 Energy, scattered energy and energy of the recoil electron under Compton scattering for both 137 Cs and 60 Co Source Energy (MeV) Scattered Energy (MeV) Recoil Electron Energy (MeV) 137 Cs 0.661 0.1815 0.4795 60 Co 1.173 0.206079 0.966921 60 Co 1.332 0.21049 1.12151
5.5 Energy Calibration Results The object of energy calibration is to derive a relationship between peaks position in the spectrum and the corresponding gamma ray energy. This is normally performed before measuring the sample. It is essential every run time. Whatever source is used, it is wise to ensure that the calibration energies cover the entire range over which the spectrometer is to be used. Experience suggests that the linearity of modern ADCs is extremely good [123]. Consequently, the energy calibration is a simple but critical step.
2.5
2
1.5
Energy (MeV) 1
0.5 0 200 400 600 800 1000
Channel Number Fig. 5.46 Energy calibration curve for 1024 channel number
Figure 5.46 represents a linear relation between energy and channel number for 1024 channel numbers. From this figure, energy against channel number relationship was derived using least square approximation method. The line intercepts the y axis at energy of 0.662 MeV (137 Cs energy). The obtained data is fitted by the following linear polynomial equation.
E = pC1 + p 2 (5.8)
٩٧ Chapter (5) Gamma-Ray Spectroscopy Results
where C denotes the channel number corresponding to the photopeak, E is the energy,
P1 and P 2 are constants. The values of these constants are p1= 0.001405 (MeV/channel number) and p 2= 0.5905 (MeV). Moreover, sum square error of 0.000186 is obtained, which the maximum permissible channel error is four.
5.6 Activity Measurement Results Another aim of gamma spectrometric analysis is to determine the activity concentration of gamma ray emitting radionuclide [123]. The activity measurement was done and based on the efficiency measurement. The measured activities of both 137 Cs and 60 Co radiation point sources are calculated as depicted in Table 5.8.
Table 5.8 Activity measurement of 137 Cs and 60 Co radiation point sources Measured Activity ( Ci) 137 Cs 0.70408 60 Co 0.24456
٩٨ Chapter (6) Conclusion
CHAPTER (6)
CONCLUSION
6.1 Conclusion The objectives of the thesis are to study quantum devices behavior under gamma radiation and the development of efficient algorithms for handling problems of gamma ray spectroscopy. We have studied various radiation detectors that based on QD nanotechnology under gamma radiation. There are two different types of QD scintillator detectors, which dominate the area of ionizing radiation measurements. These detectors are QD sources and QDIP as scintillator detectors. Therefore, a detailed study of nanotechnology QD sources and QDIP for gamma radiation detection is introduced. One of the objectives of the thesis is to develop a model of QD sources and QDIPs for incident gamma radiation detection. Therefore, a methodology is introduced to characterize the effect of gamma radiation on QD detectors. In this methodology, VisSim environment along with the block diagram programming procedures was used. Block diagram models of QD devices as gamma detectors are presented. These models are used to study the effect of device parameters on performance characteristics of the QDs within user friendly graphical environment. The resulting performance characteristics and comparison among them are presented in this work. Therefore, comparison between the results obtained by proposed VisSim models and that published in the literature are conducted and good agreement is observed. These demonstrate the strength of implementation of block diagram models. Results show the effectiveness of methodology introduced. Additionally, various algorithms for digital gamma ray spectroscopy that implemented using MATLAB environment were developed. These algorithms are signals preprocessing, signal treatment, spectrum drawing and evaluation, energy calibration and activity measurements algorithms. These algorithms based on a reference signals from 137 Cs and 60 Co radiation point sources acquired by DAS. From the obtained results, signal preprocessing is an essential step and enhances the
99 Chapter (6) Conclusion
accuracy of isotope identification. Algorithms for overcoming the pileup problem of gamma ray spectroscopy are presented. Four different algorithms are studied for pileup recovery using hypothetical and real signals. The first one is a direct search algorithm based on Nelder Mead simplex method. The second is the least square fitting algorithm. The third algorithm is a proposed one which based on the first derivative of the signal combined with maximum peak search. The fourth algorithm is another proposed one which based on first derivative with inverse matrix method. The main strength of the proposed algorithms is their capability of resolving the overlapping peaks in noisy environment. Additionally, these algorithms have the advantages of simplicity than other algorithms. The accuracy of the algorithms is determined in terms of fitting accuracy and parameters error calculation. From the obtained results of the hypothetical signal, the inverse matrix algorithm has high accuracy for identifying both peak height and position of the overlapping peaks than other algorithms. The direct search algorithm introduces the best recovered pulse width result. However, the least square algorithm achieves the highest pulse width error than other algorithms. The effect of white Gaussian noise on the algorithms is presented. Both the proposed maximum peak search and matrix division algorithms are robust enough to noise at low SNR. However, the direct search algorithm introduces better results at high SNR over maximum peak search algorithm. Therefore , when it combined with noise cancellation procedure that described previously it overcomes this problem. From the obtained results of the proposed matrix division algorithm, the maximum amplitude is measured and compared with true amplitude and maximum deviation error of 0.3585% is achieved. Moreover, this algorithm proved to be satisfactorily robust against increasing level of noise. From the obtained experimental results, the proposed maximum peak search algorithm has high accuracy for identifying both peak height and position of multiple overlapping peaks than other algorithms. Furthermore, the error signal is smaller than other algorithms. On other words, the performance of all algorithms is evaluated in terms of error between recovered signal and actual signal. The proposed algorithm shows better average error performance. However, the worst case error was slightly in flavor of other algorithms. Furthermore, these algorithms are applied to multiple data points. However, the least square algorithm introduces bad results with large number of data points. Also, the direct search algorithm is very complex to deal with multiple data points. Therefore, it
100 Chapter (6) Conclusion
is unpractical to use direct search and least square algorithms with multiple data points. However, the proposed maximum peak search algorithm shows better spectrum performance than other algorithms. Dead time, due to radiation detector, correction algorithm based on paralyzable response is considered. For paralyzable response, the true counting rate was calculated using Lambert W function numerical technique. From the obtained results, the number of corrected pulses is equal to 224 pulses. The calculated dead time value is equivalent to 96.449 s. Moreover, the dead time percent is computed and equal to 0.0294%. The advantage of this algorithm is the simplicity of dead time percent calculation without the need of sophisticated mathematical calculation in [126]. Moreover, algorithms that could be used in spectrum drawing and evaluation of gamma ray spectrometers were developed. Therefore, spectrum drawing, energy calibration and activity measurement algorithms are studied. The spectrum is evaluated for different number of channels. The obtained result confirms that the resolution increases with the number of channels. Therefore, resolution enhancement is an essential step especially at small number of channels . An algorithm for energy calibration of digital gamma ray spectroscopy is studied. Least square fitting method is used to represent the relation between channel number and energy. Linear relation between energy and channel number is deduced. In order to give complete spectrometer, accurate determinations for the sources activities were achieved. These algorithms are a measure to the accuracy of the isotope identifications. Therefore, complete gamma ray spectroscopy system is studied and evaluated.
6.2 Future Work We plan to develop more algorithms for treatment of further associated gamma ray spectroscopy problems. These algorithms are resolution enhancement and coincidence summing. Algorithms describing different types of efficiency will be performed. In addition, we will apply the same algorithms for neutron and alpha spectroscopy. Performing these algorithms using hardware implementation will be significant scope in the future. Moreover, our research will continue with advanced quantum detectors for gamma radiation detection.
101 ـا ــ ــ ـــ
آ و ارز ت ا ع و ا رات ا
ا ه ل ا ا أن ف ر س ا ع و ع ا ا . ف ا ا ا آ ا رة، ا ، ا ، آ و ا رات ا اآ ، ا ا ، ا و ا . . ن ا ف ا ه درا و آ ا وإ اد ارز ت ف وي ر ص . إ إ اد ار ز ت أ ي ا آ ا د . . ا ن ا ا ا م آ ا ه ا ا آ و ا ا ا ا اء . إ ء ذج ا ا ا وذ ام ا آ ا . ه ا ذج ا وا إ ام ا دوات ا آ ا ه ا ا . آ أ ر ا ذج ا و و ا ى ا رة ا ور ت و ا ق آ ه ا ، وا ه أه إ ام ذج ا آ ا و أداء ا ا آ ا آ ذج ا ا . و م و آ ا ا ا ام ا آ ة ا . . أ ا ارز ت ا و ف ا ، آ ا رات ا اآ و ا ا ، ة ا و س ا ط ا أداء ف ا . . و إ ء ا ارز ت ا اء ا ا و رة ا ا ل دا ا وا ا ا ، "Afterpulse" و إزا ا ء ا أ د أ ب ا وذ ام ا ب . . أ م ه ا ا ارز ت دة أآ ا آ ا ا ، وه ا رات ا اآ . در أر ارز ت و وا ر . ا ن ا ف ا ه ا ارز ت ه إ ع ا رات ا ا رات ا اآ ل أ د س ، وذ ام ا رة ا ا او ي ( م ١٣٧ ، وآ )٦٠ وا ا ل أ ة س . ارزم ا ول ه ا ا وا ى ر دون إ ام أي ت أ ا ا ط ا ذات ا ا د . و ا ارزم ا أ . و ه ا ا ارزم ه ا و ا ى أ ب ا أ إ أ ب ا ا و ن أ . أ ا ارزم را ا ا و ن أ ا أ ب ا ا . ام ه ا ارز ت أدوات آ أ ، ن أ ، ض ا . و ا ل ه ا دوات إ ع ا رة ا وا و . آ أ ر و ا ارز ت ب ا ا ي ا ق ا دوات ا وا دوات ا إ . . و ا ا ا أ ب ا ر ا ا ذج paralyzable ام ا ا ا د " ت ،" و ب ل ا ت ا ، ا و ا دة . و ا د ارزم ء ف ا ا ( م ١٣٧ ، وآ )٦٠ و ه ا ا ف وا ى أ ا ه اف ا
116 ه ا . ر د ا ات ا م ١٣٧ وا .٦٠ إ ب آ ن، و ة ا ى ا ا د ا ات ذروة ف ا ، وذ أى ى ى د ا ات ام ا ف . إ ا م ب و ه ا ارز ت . ا ن ه ا ارز ت آ ف ا . أ ه ا ارز ت ز و أداء ا ف ا . و ا ا د . .
ت ا ا إ ل : : ا ا ول : ه ا ا إ ء ة ف ا ا م ا وأه ، و ا ا ام ا رات ر و ت ا ا وا ب ا م ا وا ف ا و .
ا ا : م ه ا ا درا وا آ آ ا ا وأ اع ه ا ا و ، ف ا ا م ا وأه ، دى ا ة ، د ا ات و ا آ ا دة ا د ا ات . .
ا ا : رس ه ا ا ا ا ا ا ا آ ا ا ا آ و ا ا ا اء ا . آ و آ ا ا ا ى ر آ ا ء ذج و . إ ض ه ا ا . .
ا ا ا : ه ا ا ا دوات ا ا إ ا ا ل ا رات ا . و ا اد ا ارز ت ا ا ز ف ا ارز ت ا رات وا ى ا ا ، إزا ا ا وإزا ا ء ا أ ب ا . أ ا اد ارز ت آ ا ارز ت ا رات ا اآ و ارز ت ا ا . وة ذ ا ارز ت ا ى و ا ف آ ر م ١٣٧ وآ ٦٠ ٦٠ ام ا ا ات . و ا اد ارزم ة ا وا ط ا ا وذ ى رة ا ا ا ى م . .
ا ا : ه ا ا م ا ارز ت ا دة ا ا . .
ا ا دس : م ه ا ا ء ا ، إ آ ا ا ع ا ا ، وآ ض ارز ت ا درا ا وا ر ، و ا ا اح ارز ت أ ى آ ا ى ارزم ا ، ا ا و أ درا ا ف اع ا ى ا أ و ون . . و أ ا ا ا ا إ ا و أ ا ى ا .
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