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(1)Modeling of SiC Sensor Characteristics for Nuclear Radiation Measurements.

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(3) Igor Królikowski. Modeling of SiC Sensor Characteristics for Nuclear Radiation Measurements. Ph.D. Thesis. Department of Nuclear Energy Faculty of Energy and Fuels AGH University of Science and Technology September 10, 2015, Cracow, Poland.

(4) c Copyright by Igor Królikowski 2015 All Rights Reserved.

(5) Author: Igor Królikowski Department of Nuclear Energy Faculty of Energy and Fuels AGH University of Science and Technology Al. Mickiewicza 30, Cracow 30-059, Poland e-mail: igor@agh.edu.pl. Supervisor: Professor Jerzy Cetnar Department of Nuclear Energy Faculty of Energy and Fuels AGH University of Science and Technology Al. Mickiewicza 30, Cracow 30-059, Poland e-mail: cetnar@ftj.agh.edu.pl. Polish title of the Ph.D. Thesis:.

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(7) TO MY WIFE.

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(9) Acknowledgments I would like to express my gratitude to my supervisor Professor Jerzy Cetnar, who kindly agreed to consider me as his PhD student. I feel very lucky to have him as a supervisor. His positive attitude and continuous support kept me motivated throughout my stay at AGH. During all these years, his door was always open to discuss anything. Thanks to the people in IM2NP at the Aix-Marseille University for their tutoring in semiconductor science and technology during my eight-month stay in their laboratory. It was very nice time we spent together in Marseille. That was a part of my life, which I will never forget. Thanks to the groups of scientist working in the I-SMART project for great cooperation, discussions and nice time spent during our project meetings. Results of your works have been crucial contribution to my research, which cannot be done without yours measurements, electronics and tests performed by you. I would like to acknowledge Prof. Teresa Grzybek, Prof. Stefan Taczanowski, Prof. Jerzy Janczyszyn, Prof. Ludwik Pieńkowski, Dr. Grażyna Domańska and Dr. Mariusz Kopeć for discussions on all issues and their support in different scientific matters. My special thanks for friends from my department, Mikołaj Oettingen, Paweł Gajda, Przemysław Stanisz, Grzegorz Kępisty, Michał Orliński, Mateusz Malicki, Katarzyna Skolik for providing a nice working atmosphere. Thanks to my colleagues from my office, Jakub Szczurowski, Rafał Baran, Radosław Dębek for funny lunch time. Thanks to KIC PhD students Jan Krawczyk, Łukasz Uruski, Piotr Babiński, Grzegorz Tomaszewicz, Paweł Wajss and Kun Zheng for time spent together in KIC conferences and workshops. Lastly, I want to send my gratitude to my family for relaxing time during weekends, it was very nice break in the research.. Igor Królikowski.

(10) The presented work has been carried out within the I-SMART project, which is a part of the KIC InnoEnergy R&D program. The PhD has been part of the KIC InnoEnergy PhD School, which has organized inspiring workshops and interesting conferences. Numerical calculations have been performed using the supercomputer ZEUS at ACK Cyfronet AGH..

(11) Contents DEDICATION. v. ACKNOWLEDGMENTS. vii. ABSTRACT. xi. STRESZCZENIE. xiii. I Topic overview, Thesis Statements and Basic Theory. 1. Introduction. 3. 2. I-SMART Project. 7. 3. PhD Thesis 11 3.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2. Purpose of the PhD research . . . . . . . . . . . . . . . . . . 13 4. Basic Theory 4.1. Radiation . . . . . . . . . . . . . . . 4.2. Radiation Interactions . . . . . . . . 4.2.1. Interaction of Heavy Charged 4.2.2. Interaction of Fast Electrons 4.2.3. Interaction of Gamma Rays . 4.2.4. Interaction of Neutrons . . . 4.3. Semiconductor Detectors . . . . . . .. . . . . . . . . . . . . Particles . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. 5. Software. 15 15 16 17 24 27 30 34 39. II PhD Research 6. SiC Sensor 6.1. Sensor Structure . . . . . . . . . . . . 6.2. Sensor Operation . . . . . . . . . . . . 6.2.1. Application of External Voltage 6.2.2. Operation Temperature . . . . ix. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 43 43 48 49 52.

(12) x. CONTENTS 6.2.3. Radiation Interactions with SiC Sensors . . . . . . . . 52 6.2.4. Electronics and Signal . . . . . . . . . . . . . . . . . . 56. 7. Modeling Method of SiC Sensor Characteristics 7.1. Forward problem . . . . . . . . . . . . . . . . . . . 7.1.1. Integrated Approach . . . . . . . . . . . . . 7.1.2. Analytic approach . . . . . . . . . . . . . . 7.2. Inverse problem . . . . . . . . . . . . . . . . . . . . 7.3. Precision, accuracy and libraries . . . . . . . . . . 8. Results 8.1. Basic Analyses . . . . . . . . . . . . . . . . 8.1.1. Range of Reaction Products . . . . . 8.1.2. Energy of Reaction Products . . . . 8.1.3. Reaction Rates . . . . . . . . . . . . 8.2. Response Matrix Functions for SiC Sensors 8.3. Responses of Neutron Converter . . . . . . 8.4. Analysis of Measured Signals . . . . . . . . 8.4.1. Thermal Neutrons . . . . . . . . . . 8.4.2. Fast Neutrons . . . . . . . . . . . . . 8.4.3. Thermal and Fast Neutrons . . . . . 8.5. Sensor Improvement . . . . . . . . . . . . . 8.6. Sensor Response Processing . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . .. . . . . .. 57 57 58 59 64 66. . . . . . . . . . . . .. 71 71 71 73 75 77 97 99 100 106 115 118 122. 9. Conclusions and Future Directions. 135. REFERENCES. 137. LIST OF FIGURES. 151. LIST OF TABLES. 153.

(13) ABSTRACT. The world population constantly increases, thus the demand on electricity grows. Nuclear energy has to compete with other energy sources and must be more and more safe, therefore we need detailed knowledge of nuclear reactor core behavior and radiation monitoring in nuclear media. Instrumentation used in nuclear energy are based on safe, efficient but still conservative technologies. Future reactors will need complete new on-line instrumentations and innovative advanced measurements methodologies, which will increase safety of the reactors and give necessary information for their designing. Sensors based on silicon carbide (SiC) are highly suitable for spectroscopic measurements of nuclear radiation due to advantages of the 4H-SiC polytype. Its ability to operate in elevated temperatures, the increased radiation resistance and the wide band gap (3.25 eV) allow it to work in harsh radiation environments. Such detectors may be applied in the nuclear energy and in the measurement while drilling. The SiC sensors are based on a p-n junction created using silicon carbide semiconductor layers. The sensors include several layers with various thicknesses depending on the structure. Silicon carbide interacts with neutrons, photons and electrons, it produces electron-hole pairs, which generate the sensor response in the form of count distribution over channels. In order to detect thermal neutrons, a neutron converter basing on 10 B is applied since thermal neutrons do not produce the response through direct interactions with the SiC material. Boron atoms creating the neutron converter interact highly with thermal neutrons producing charged particles, which create the sensor response. The 3D computer modeling, which is the topic of the PhD thesis, allows us to study phenomenon such as a response creation within the SiC sensors under radiation. The computer modeling is applied to solve two crucial issues related to the responses of SiC sensors under radiation. The first one is the forward simulation of detector signal formation in the filed of primary neutrons and secondary radiations, whereas the second one is the inverse problem of finding a representation of a primary radiation, basing on the measured detector signals. Even if the forward problem can be solved using an integrated approach, in which no intermediate functions or distributions.

(14) xii. CONTENTS. are produced nor displayed and only the final signal would be presented, this approach is not appropriate since it would be of no big use for the solution of the inverse problem, which is of a grater importance for the applicability of the developed sensors. In the presented PhD thesis, the new method allowing to get the characteristics of SiC sensors is shown. The characteristics is described using response matrix functions, which are applied to solve both the forward and the inverse problem. The response matrix functions are also used to analyze the sensor response under given radiation. In the thesis, the characteristics of sensors obtained using a computer tool, which is based on the new method, are presented. These characteristics have been used for analyses of the sensor responses and their structures. In order to perform the required calculations, the computer tool has been created by the author. The computer tool was created using MATLAB and the supercomputer ZEUS at ACK Cyfronet AGH. Simulations of particle transport through the matter, which were needed to create the characteristics have been performed using the well known codes: Geant4 and MCNP/MCNPX. Presented method has been validated using several measurements of thermal and fast neutrons collected by a few different structures of SiC sensors. The experimental data have been compared with the numerical responses obtained using the computer tool in order to validate the new method. Then, the detailed analyses of the experimental responses were done using the computer tool. Validated computer tool basing on the new method has been used to optimize the SiC sensor structure, which may be used for simultaneous detection of both fast and thermal neutrons. Several ideas of improved structures of SiC sensors are presented in the thesis. The PhD research is a part of the I-SMART project within the framework of KIC InnoEnergy..

(15) STRESZCZENIE Ludzka populacja rozwija się nieustannie, co skutkuje rosnącym zapotrzebowaniem na energię elektryczną. Z tego powodu, energetyka jądrowa musi konkurować z nowymi technologiami przy pomocy których pozyskiwana jest energia elektryczna. Aparatura pomiarowa stosowana w energetyce jądrowej jest oparta na bezpiecznych, wydajnych jednak wciąż konwencjonalnych technologiach. Reaktory przyszłości wymagają innowacyjnych metod pomiarowych oraz zaawansowanych narzędzi do ich przeprowadzenia. Nowoczesna aparatura pozwoli otrzymać istotne informacje, które podniosą bezpieczeństwo przyszłych reaktorów jądrowych oraz dostarczą niezbędnej wiedzy do ich zaprojektowania. Półprzewodnikowe detektory oparte na materiale SiC mogą zostać wykorzystane do spektralnych pomiarów promieniowania jądrowego. Właściwości materiałowe węglika krzemu 4H-SiC takie jak zdolność do pracy w wysokiej temperaturze, podwyższona odporność na promieniowanie oraz szeroka przerwa energetyczna dla półprzewodnika (3.25eV) pozwalają na pracę w silnym polu promieniowania oraz w wysokiej temperaturze. Detektory SiC mogą zostać wykorzystane do pomiarów promieniowania jądrowego w energetyce jądrowej oraz branży wiertniczej, gdzie wykorzystuje się pomiary strumienia neutronów do określania składu gleby podczas przeprowadzania odwiertów. Detektory SiC bazują na złączu p-n, które zbudowane jest z półprzewodników opartych na węgliku krzemu. Detektor może zawierać kilka warstw, których grubości wahają się od kilku do kilkuset mikrometrów w zależności od konstrukcji. Materiał SiC wchodzi w interakcje z elektronami, fotonami oraz neutronami w wyniku czego tworzone są pary elektron-dziura, które generują odpowiedź detektora zbieraną w formie zliczeń na kanał. W celu detekcji neutronów termicznych, które słabo produkują sygnał poprzez bezpośrednie oddziaływanie z SiC, wprowadzono do konstrukcji detektora konwerter neutronów. Wykorzystuje on izotop boru 10, który silnie oddziałuje z neutronami termicznymi emitując przy tym cząstki naładowane wykorzystane do tworzenia sygnału. Metody numeryczne wsparte superkomputerami dają możliwości badania nowych zjawisk fizycznych takich jak tworzenie odpowiedzi detektora SiC wystawionego na działanie promieniowania jądrowego. W przedstawionych badaniach modelownie komputerowe wykorzystane jest do rozwiązania dwóch podstawowych problemów związanych z detektorami SiC. Pierwszym z nich jest wygenerowanie odpowiedzi detektor wystawionego na działanie zdefiniowanego promieniowania jądrowego. Drugim ważniejszym aspektem jest znalezienie spektrum opisującego pierwotne promieniowanie przy pomocy odpowiedzi detektora, która została zebrana podczas interakcji detektora z tym promieniowanie..

(16) W pracy przedstawiono nową metodę pozwalającą uzyskać charakterystykę detektorów SiC w formie macierzowych funkcji odpowiedzi detektora. Funkcje pozwalają rozwiązać dwa wymienione problemy oraz umożliwiają przeprowadzenie szczegółowej analizy tworzenia się sygnału wewnątrz detektora. W pracy przedstawiono charakterystyki detektorów otrzymane dzięki narzędziu komputerowemu, które bazuje na opracowanej metodzie. Charakterystyki zostały wykorzystane do analizy odpowiedzi detektorów. W celu zastosowania opisanej metody stworzono narzędzie komputerowe pozwalające przeprowadzić wszystkie niezbędne obliczenia. Narzędzie komputerowe zostało stworzone przy pomocy oprogramowania MATLAB oraz superkomputera ZEUS w ACK Cyfronet AGH. Obliczenia transportu cząstek przez materię wymagane do stworzenia charakterystyk detektorów zostały przeprowadzone przy użyciu znanych kodów opartych na metodzie Monte Carlo: Geant4 oraz MCNP/MCNPX. Zaprezentowana metoda została zweryfikowana za pomocą rzeczywistych pomiarów, które zebrano wykorzystując różne konstrukcje detektorów SiC wystawione na działanie promieniowania. Pomiary eksperymentalne zostały porównane z numerycznymi odpowiedziami detektorów w celu weryfikacji nowej metody. W następnym kroku przeprowadzono szczegółową analizę zebranych odpowiedzi detektorów przy pomocy stworzonego narzędzie komputerowego. Sprawdzone narzędzie komputerowe zostało wykorzystane do zoptymalizowania konstrukcji detektora, który zostanie wykorzystany do równoczesnych pomiarów neutronów prędkich oraz termicznych. Przedstawiono kilka wariantów ulepszonych konstrukcji detektorów, które zostały wykorzystane w przedstawionych badaniach. Praca doktorska w całości jest częścią projektu I-SMART prowadzonego w ramach KIC InnoEnergy..

(17) PART ONE. Topic Overview, Thesis Statements And Basic Theory. Chapter I: Introduction Chapter II: I-SMART Project Chapter III: PhD Thesis Chapter IV: Basic Theory Chapter V: Software.

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(19) 3. Part I. Topic overview, Thesis Statements and Basic Theory 1. Introduction Human population grows constantly, thus people need more and more energy due to increasing number of human beings and a higher quality of life. Therefore, power production efficiency and fossil fuel production must be enhanced and increased. However, reservoirs of fossil fuels are finite and their amount continually decreases. Moreover, access to new reservoirs is more and more difficult due to their deeper locations. Regarding enhancements of the power sector, silicon carbide sensors may be used in nuclear energy and gas-oil drilling process to improve global energy production. The sensors applied as a nuclear instrumentation allow us to enhance reactor safety and to optimize its operation, whereas in the case of oil prospecting, the sensors support a measurement while drilling, which provides information about material composition around a borehole and this allows us to identify a fossil fuel reservoir. Instrumentation used in nuclear energy is based on safe, efficient but still conservative technologies. Nuclear energy has to compete with other energy sources and must be more and more safe, thus we need detailed knowledge of nuclear reactor core behavior and better radiation monitoring in nuclear media. Future research reactors like the International Jules Horowitz Reactor, ITER and generation IV reactors will need complete new on-line instrumentations and innovative advanced measurement methodologies. Experiments and measurements in such facilities have to be more instrumented than in the past especially with real-time analysis devices. Technological breakthrough allows us to design the SiC sensors, which can operate at elevated temperatures in harsh environment such as in the nuclear reactor core or in the measurement while drilling. The SiC sensors coupled with the electronics and tools for signal processing and analysis create advanced measurement technologies giving opportunities to increase performances and satisfy market needs. A more efficient instrumentation.

(20) 4. 1. INTRODUCTION. allows us to optimize the reactor operation and the efficiency, which have a positive economical impact and increase the nuclear reactor safety. On-line selective and simultaneous detection of both fast and thermal neutron flux and high energy gamma flux is an important issue for: • Nuclear experimental and power reactors • Nuclear fuel cycle • Safeguards • Homeland security • Boron neutron capture therapy • Measurement while drilling Nowadays, there is a need in the market for the on-line instrumentation to measure radiation at elevated temperatures and in harsh environment. Main goal of the I-SMART project is to solve this problem. Final expected result of the project is a prototype of a system including the sensor, the electronics and software for the signal analysis. The PhD thesis: Modeling of SiC sensor characteristics for nuclear radiation measurements is a part of the I-SMART project. The 3D computer modeling, which is the topic of the PhD thesis, helps to design and to optimize the structure of sensors. The structure is important since it significantly impacts on the sensor signal. The computer simulations aim in developing of a tool for detailed analysis of the sensor response, which is generated by fast and thermal neutrons and high energy gammas. The thesis is divided in two parts. Part One: Topic Overview, Thesis Statements and Basic Theory includes eight chapters (Chapter 1-8), whereas Part Two: PhD Research comprises five chapters (Chapter 9-13). Chapter 1 - Introduction - gives some preliminary information about the topic of the PhD research. Chapter 2 - I-SMART project - describes motivation and objectives of the project and its impact on the market. The PhD research is the part of this project. Chapter 3 - PhD Thesis - shows the motivation and the objectives of the PhD research..

(21) 5 Chapter 4 - Basic Theory - explains the basic physical phenomena which are required to understand the research presented in the thesis. Chapter 5 - Software - describes the software used for calculations performed in the PhD research. Chapter 6 - SiC Sensor - presents structure of the SiC sensors and crucial information about their operation. These sensor have been manufactured within the I-SMART project and they have been used in the measurements performed in the research. Chapter 7 - Modeling Method of SiC Sensor Characteristics - presents the new method, which is the key of the PhD research. Chapter 8 - Results - shows crucial results obtained in the PhD research. Chapter 9 - Conclusions and Future Directions - summarize the PhD research..

(22) 6. 1. INTRODUCTION.

(23) 7. 2. I-SMART Project Presented PhD research is the part of the I-SMART Project: Innovative Sensor for Material Ageing and Radiation Testing, which is three-year R&D pilot project (2012-2014). The project had many participants, which are listed below: • AGH / Poland / University • AMU (Aix Marseille University) / Alps Valleys / University • AREVA / Alps Valleys / Industry • CEA / Alps Valleys / Research center • GRAIN2/GRAVIT / Alps Valleys / Innovation Infrastructure • Grenoble INP / Alps Valleys / University • INSA2 / France / Research institute • KIT / Germany / Research center • KTH / Sweden / University • SCKCEN / Belgium / Research center • UiO / Norway / University The fundamental aim of the project is to enhance safety of nuclear power installations and as such in fertilizing the use and development of nuclear power business in Europe and worldwide. The uptake of the R&D and innovation results of the project is considered for both existing and new business processes. Influence on existing business Nuclear instrumentation can somehow appear as a very conservative area where progresses need much longer time (comparing with the race on the rest of the sensor/IT technology highways) before being considered as a proven method to be used in nuclear facilities. As a result there is.

(24) 8. 2. I-SMART PROJECT. a serious gap between public expectations for enhanced nuclear radiation monitoring using advances in modern technology and the actual instrumentation used in the existing installations. To face these challenges, significant efforts have been made recently in order to strengthen research and development activities regarding innovative in-pile instrumentation and associated measurement methods. Highlighting the effort a number of novel detector systems were developed, e.g. fast neutron flux detection system -FNDS- using fission chambers with 242 Pu deposit, an improved self-powered detector performing selective measurements of the gamma radiation level, an optical system based on the Fabry-Perot principle and designed to perform in-pile dimensional measurements of material samples under irradiation, an acoustical instrumentation for the online characterization of fission gas release in pressurized water reactor fuel rods, etc. Nevertheless, selective and simultaneous - called ”spectroscopic” - detection of both fast and thermal neutron fluxes as well as gamma radiations operating at elevated temperatures is by now a real instrumentation challenge for the nuclear power industries in terms of direct (on-line) nuclear ageing and fuel cycle monitoring. Moreover, such detection system may be used by other businesses in a number of fields ranging from medical applications to the homeland security thus creating additional impacts of the project. Accounting for all theses challenges I-SMART consortium suggests developing and commercializing such spectroscopic detector system made of silicon carbide (SiC), which is known to be radiation hard material suitable for high temperature application. Summarizing, the realization of our Innovative Sensor for Material Ageing and Radiation Testing made of SiC as a result of the present I-SMART proposal is anticipated to have a fundamental impact on the existing business processes. Influence on new business As introduced above and to the best of our knowledge, there is no system available for spectroscopic radiation monitoring at elevated temperatures (up to 600 ◦ C). Hence the timing for launching a focused I-SMART European innovative project toward solving this problem is excellent also in terms of possible impact on spinning off new businesses and/or conquering.

(25) 9 new markets by relevant existing SMEs or bigger companies. Indeed, on behalf of relative readiness of SiC technology that our consortium suggests to use as a platform to build the system satisfying demands of radiation hardness and high temperature operation, the realization of new business processes is considered to be feasible. The effort is going to result in a fabrication of an outstanding radiation detector system calibrated for operation in nuclear facilities specified by end-users. At this point, the commercialization of the I-SMART detection system is considered to be economically justified. Moreover, we foresee more of new long-term business opportunities for the I-SMART detector also in the field of ITER blanket developments taking into account a host of trade-offs when choosing a detector system for making spectroscopic monitoring of neutron, electromagnetic radiations, but also charged energetic particles, ions, that will enter and leave the plasma. A high temperature together with high flux of particles and radiations set severe limitations for the properties of detector materials and SiC is probably one of the only semiconductor to consider for this application. Summarizing, the outlooks for new business processes as a result of I-SMART realization is fully in accordance with the spirit of the present KIC INNO call in terms of possible impacts on spinning off new businesses and/or conquering new markets by relevant existing SMEs or bigger companies. Motivation and Project Objectives Most of up-today radiation instrumentations routinely used in the present nuclear installations are based on safe, predictive, but somehow conservative concepts not taking up in a full scale the progress achieved in modern semiconductor technology that readily deliver real-time information detection/treatment in many other industrial applications. Importantly, the nuclear energy production competitiveness (including safety issues) may be significantly enhanced providing more accurate monitoring of the present and future nuclear fission reactors and nuclear fuel facilities as well as when integrating detectors into fusion reactor blankets. Silicon carbide sensors, which are intensively studied and used in many applications, give the nuclear instrumentation technology opportunities to.

(26) 10. 2. I-SMART PROJECT. create innovative detector system able to operate in extremely harsh environments in term of radiation and temperature exposures, where traditional semiconductor detectors, e.g. silicon-based, lose all functionalities..

(27) 11. 3. PhD Thesis 3.1. Motivation As was descried in previous chapters, SiC Sensors are considered to be a promising candidate detectors for high temperature and harsh radiation environment applications. This is due to properties of the 4H-SiC material such as large bandgap, high thermal conductivity, high breakdown field, and higher radiation resistance [1–14]. This offers a significant advantage of the SiC sensors over conventional semiconductor detectors and classifies them as a radiation hard semiconductor detectors. Technological breakthrough allows us to design the SiC sensors based on highly pure SiC material, which can operate at elevated temperature in a harsh radiation environment such as in the nuclear reactor core. In the literature, we may find technological processes allowing to manufacture various SiC diodes, which may be basis of the radiation sensors. These didoes may include the neutron converter basing on the boron 10 isotope or the lithium 6 isotope to detect thermal neutrons [15]. In order to create a system for radiation measurements, the diodes are connected with the electronics consisting of a preamplifier/amplifier and a multichannel analyzer. The systems including the SiC sensors and the electronics have been tested to check their electrical and temperature stability. Results, which have been obtained in tests, are presented in available articles [16–18]. The senors have been applied to detect different types of radiation, sensor responses collected in experiments have been published in journals and at conferences [19–22]. The SiC sensors coupled with the electronics create an advanced measurement system for simultaneous measurement of fast and thermal neutron flux and optionally the gamma radiation. Such systems, which are a topic of research at various institutions, require a computer tool for signal processing and analysis. Till now, there is no method available to fully describe the characteristics of the SiC sensors, that would allow us to study and to analyze the sensor response to the radiation field. In order to achieve the SiC capability of simultaneous spectroscopic measurements of neutrons and gamma-rays an appropriate methodology of the detector signal modeling and its interpretation must be adopted..

(28) 12. 3. PHD THESIS. The process of detector simulation can be divided into two basically separate but actually interconnected sections. The first one is the forward simulation of detector signal formation in the filed of primary neutrons and secondary radiations, whereas the second one is the inverse problem of finding a representation of the primary radiation, basing on the measured detector signals. Even if the forward problem can be solved using an integrated approach, in which no intermediate functions or distributions are produced nor displayed and only the final signal would be presented, this approach is not appropriate since it would be of no big use for the solution of the inverse problem, which is of a grater importance for the applicability of the developed sensors. In the PhD research, the new methodology has been studied to specify the functions that are needed to solve the forward and the inverse problem. The method uses response matrix functions describing characteristics of the SiC sensors, which would quantitatively represent the detector system ability for solving the inverse problem with the requested level of energy spectrum resolution. These functions are recognized and produced using a computer tool created by the author. The tool was validated by means of the responses collected in measurements with thermal and fast neutrons. The measured responses have been analyzed and the part of the response coming from the neutron converter has been separated. Obtained results allow us to find crucial parameters of the neutron converter, which are used to optimize its structure. The method presented in the PhD thesis gives opportunities to create the characteristics of the radiation sensors. The characteristics define the response of the sensor under given radiation and supply information significant for the response processing. The method may be adopted for other types of radiation detectors. Therefore, the presented research are contribution to knowledge of the spectral radiation measurements..

(29) 3.2. Purpose of the PhD research. 13. 3.2. Purpose of the PhD research General purposes of the PhD research: • scientific description of the new method defining the characteristic of the semiconductor sensors for spectral radiation measurements, which allows us to solve the forward and the inverse problem • creation of the computer tool able to apply the new method for the modeling of the SiC sensor characteristics • generation of the response matrix functions for the SiC sensor structure manufactured and used in the PhD research • solving of the forward problem for neutrons, photons and electrons using the computer tool basing on the presented method • validation of the studied method using the measurements obtained in the experiments with fast and thermal neutrons • analysis of the experimental measurements by means of the computer tool basing on the presented method • separation of the responses coming from fast and thermal neutrons • finding of the important parameters of the neutron converter influencing the sensor response • optimization of the neutron converter to enhance simultaneous detection of thermal and fast neutrons • solving the inverse problem by means of the characteristic of the sensors.

(30) 14. 3. PHD THESIS.

(31) 15. 4. Basic Theory Purpose of this chapter is to present basic theory closely related to the field of research presented in the PhD thesis. More details or additional information about phenomena can be found in the books [23–27], which are used to write this chapter.. 4.1. Radiation Radiations originate in nuclear or atomic processes which can be divided into four following categories:. Fast electrons category takes into account positive and negative beta particles coming from nuclear decay and energetic electrons generated by any other process. Heavy charged particles include energetic ions with mass of one atomic mass unite or greater, such as protons, alpha particles, fission products and other products of nuclear reactions. The electromagnetic radiation contains X-rays emitted in the rearrangement of electron shells of atoms, and gamma rays coming from transitions within the nucleus itself. Neutrons are produced in many nuclear processes and they are the most significant category, which is divided into two subcategroies: slow/thermal neutrons and fast neutrons. The radiation energy range taken into account in presented research is from 10 eV to 15 MeV except the neutron energy, which is from 0.001 eV to 15 MeV in order to cover energy of the thermal neutrons. Thermal neutrons are significant due to their technological importance in nuclear energy, since they are used in nuclear reactors to generate fission. The lower energy bound (10 eV) is defined by the minimum energy needed to ionize typical materials by radiation or secondary products of its interaction, which is classified as ionizing radiation. The upper bound (15 MeV) is determined by the maximum radiation energy linked with applications of the SiC sensor..

(32) 16. 4. BASIC THEORY. 4.2. Radiation Interactions Structures of detectors and their operation generally depend on the way how the measured radiation interacts with the detector material. Therefore, analysis of the response coming from a specific detector is based on the knowledge of the fundamental mechanisms by which radiation interacts with the matter and deposit its energy. To make the following discussions clear, it is helpful to organize the four major categories of radiation:. The radiation in the left column is the charged particle radiation, these particles with the electric charge continuously interact by the coulomb forces with electrons present in the matter. The right column represents the uncharged particle radiation. These types of radiation do not have the electric charge and therefore do not interact through the coulomb forces. The uncharged radiation interacts by ”catastrophic” interaction often involving the nucleus of atoms. These interactions transfer full or part of energy to electrons or nuclei of atoms, or to charged particles, which are products of nuclear reactions. The arrows in the scheme above illustrate such catastrophic interactions, the uncharged radiation produces through the catastrophic interactions the charged radiation. X-rays and gamma rays may transfer part or full energy to electrons and those electrons interact with the matter like the fast electrons. Detectors to measure both the X-rays and the gamma rays use such interactions and their structures enable them to stop the secondary electrons and therefore their energy may contribute to the output response. Regarding neutrons, reactions caused by them produce secondary charged particles which actively form the detector response. Characteristic lengths in the scheme are order-of-magnitude numbers for the characteristic distance of penetration, it is range or mean free path in solids for the radiation of its typical energy..

(33) 4.2. Radiation Interactions. 17. 4.2.1. Interaction of Heavy Charged Particles Heavy charged particles interact mainly with the matter by the coulomb forces between their positive charges and the negative charges of orbital electrons of the matter atoms. However, the charged particles may interact with nuclei (Rutherford scattering or alpha-particle induced reactions) but probability of such interactions is not high and therefore their contribution to the signal is low. The charged particle entering the matter interacts with many orbital electrons in its vicinity, the electrons feel an impulse generated by the coulomb forces. If this impulse is sufficient, the electron jumps to a higher shell in the atom (excitation) or escapes completely from the atom (ionization). The energy transferred to the electron comes from the charged particle and therefore its velocity decreases. The maximum energy that is possible to transfer from the charged particle of mass m and energy E to the electron of mass m0 in a single event equals 4Em0 /m. This is a small portion of energy compared to the total energy of the charged particle, therefore a single charged particle causes many such events before deposits all its energy. Figure 4.1 presents representative paths of the charged particles in the matter during their slowing down process. The paths except their end are quite straight during penetration because the interactions between the charged particles and the matter occur in all possible directions simultaneously.. Figure 4.1. Paths of the charged particles in the matter[23].. The interactions of the charged particles yield finally either ion pairs or excited atoms. The ion pairs are composed of a free electron and an ion with positive charge formed from an atom of the matter, from which the free electron was removed. The ions have a tendency to recombine to neu-.

(34) 18. 4. BASIC THEORY. tral atoms. The electrons that are called delta rays may have enough kinetic energy to produce ions further. The delta rays are the indirect means by which the charged particles lose the energy in the matter and their range is smaller than the range of the charged particles. Many events of the ion pairs creation are continuously formed along the path. Therefore, the ionization occurs close to the path of the charged particles. Stopping Power The linear stopping power (S) for the charged particles crossing the matter is defined as follows: S=−. dE dx. (4.1). where dE is the differential energy loss for the particle in the matter and dx is the corresponding differential path length. The energy loss in air for various charged particles as a function of particle energy is shown Fig. 4.2.. Figure 4.2. The energy loss in air for various particles as a function of the charged particle energy [23]..

(35) 4.2. Radiation Interactions. 19. The Bragg Curve Figure 4.3 presents a Bragg curve describing the energy loss of the charged particle along its path. Presented curves concern an alpha particle of a few MeV initial energy. The energy loss increases roughly as 1/E. As alpha particles have the electric charge of +2, curves fall down at the end of track because their charge is reduce by electrons pickup. The plot shows two curves, the first one for a single alpha particle, whereas the second one for the average behavior of a parallel beam of alpha particles with the same initial energy. We observe differences between curves due to the straggling effect.. Figure 4.3. The energy loss of an alpha particle along its path [23].. Energy Straggling The microscopic interactions of any specific particles behave somewhat randomly, so the energy loss is a stochastic process. Therefore, the energy spread appears after the beam of monoenergetic charged particles passing through the matter. Figure 4.4 presents energy distributions F (E, X) of the monoenergetic beam with the initial energy E0 in several points along its range (X). At the beginning (X = 0), the energy distribution is narrow and close to the initial energy, while the distribution is wider and skewed with the distance of penetration, which shows increasing influence of the energy straggling. At the end of the range, the energy distribution is narrow due to high reduction of the mean particle energy..

(36) 20. 4. BASIC THEORY. Figure 4.4. Plots of energy distribution of a beam of initially monoenergetic charged particles at various penetration distances. E is the particle energy and X is the distance along the track [23].. Particle Range To define the particle range, we use the theoretical experiment presented in Fig. 4.5. A detector counts monoenergetic collimated alpha particles crossing through a material block of variable thickness. The plot in Fig. 4.5 shows the detection results.. Figure 4.5. An alpha particle transmission experiment. I is the detected number of alpha particles through an absorber thickness T , whereas I0 is the number detected without the absorber. The mean range Rm , and extrapolated range Re are indicated [23].. In the case of small thickness, the alpha particles loss only part of their energy in the material. Therefore, the number of particle reaching the detector is constant because the tracks of the alpha particles through the material are quite straight forward. There is no decrease of I/I0 until the.

(37) 4.2. Radiation Interactions. 21. material thickness is lower than the shortest track of the alpha particles. If the thickness increases, we observe that the number of detected particles drops rapidly. We can use the presented curve to determine the range of the alpha particles in the material. The mean range (Rm ) equals the thickness of the material that reduces I/I0 to 50%, whereas the extrapolated range is calculated by linear extrapolation of the curve to zero. The range is a unique property of the specific material and depends on the type of the charged particle and its energy.. Figure 4.6. Range-energy curves calculated for different charged particles in silicon. The near-linear behavior of the log-log plot over the energy range shown suggests an empirical relation to the form R = aE b , where the slope-related parameter b is not greatly different for the various particles [23].. Figures 4.6 and 4.7 present the mean range of different charged particles in various detector materials of interest. Detectors used to measure the full incident energy of charged particles must have thickness of the active region greater than the range of particles in the detector material. Therefore, data presented in Fig. 4.6 and 4.7 are used to design such detectors. We observe the range straggling of the charged particles caused by stochastic behavior of these particles. The range straggling is the fluctu-.

(38) 22. 4. BASIC THEORY. Figure 4.7. Range-energy curves calculated for alpha particles in different materials. Units of the range are given in mass thickness to minimize the differences of these curves [23].. ation of the range for particles of the same initial energy. The straggling may achieve the level of a few percent of the mean range for heavy charged particles (protons, alpha particles). Energy Loss in Thin Absorbers The energy deposited by given charged particles passing through thin absorbers or detectors is as follows: ∆E = −. dE dx. T. (4.2). avg. where −(dE/dx)avg is the average linear stopping power and T is the thickness of the absorber. If the energy loss is mall, the value of −(dE/dx)avg is averaged over the particle energy during penetration through the absorber. Fig. 4.8 and 4.9 present some values of −(dE/dx)avg for different charged particles and absorbing materials..

(39) 4.2. Radiation Interactions. 23. Figure 4.8. The energy loss calculated for various charged particles in silicon [23].. Figure 4.9. The energy loss calculated for alpha particles in different materials. Values are normalized by the density of the absorber material [23].. Regarding absorber thicknesses where the energy loss is not small, calculations of correct −(dE/dx)avg value are not simple. In order to obtain the energy deposition, it is useful to use data shown in Fig. 4.6 and 4.7 and the method presented in Fig. 4.10. R1 is the full range of the particle.

(40) 24. 4. BASIC THEORY. with energy E1 within the absorber. The value of R2 defining the range of particles that cross the absrober is calculated by subtracting the absorber thickness T from R1 . The E2 energy corresponding to R2 and describing the energy of particles transmitted from the absorber is used to calculate the deposited energy: ∆E = E1 − E2 .. Figure 4.10. Method for calculation of the energy loss [23].. 4.2.2. Interaction of Fast Electrons Fast electrons compared to the heavy charged particles deposit their energy at a lower rate and their tracks through material are very tortuous. Several probable tracks of the fast electrons emitted from a monoenergetic source are shown in Fig. 4.11.. Figure 4.11. Probable electron tracks in the matter [23].. The electron path deviation is high since it interacts with orbital electrons of the same mass, therefore they may lose large fraction of their energy in single encounter. Electron Range and Transmission Curve Fig. 4.12 shows the experiment of the electron beam attenuation which is similar to the experiment in the Fig. 4.5 describing the attenuation of the alpha particle beam. In the case of fast electrons, even the absorber with.

(41) 4.2. Radiation Interactions. 25. small thickness leads to a decrease of the electron flux measured by the detector since the electron scattering removes a part of the electrons from the beam measured by the detector. Therefore, the curve plotted in Fig. 4.12 describing the I/I0 starts to decrease from low thickness and approaches zero for large thickness of the absorber. For big thickness absorbers, detected are only electrons whose initial directions have not been changed much during the penetration.. Figure 4.12. Transmission curve for monoenergetic electrons. Re is the extrapolated range, I is the detected number of electrons through an absorber thickness T , whereas I0 is the number detected without the absorber. [23].. Figure 4.13. Range-energy plots for electrons in silicon and sodium iodide. If units of mass thickness (distance × density) are used for the range as shown, values at the same electron energy are similar even for materials with widely different physical properties or atomic number [23]..

(42) 26. 4. BASIC THEORY. The total length of the electron paths is greater than the penetration distance along the vector of initial velocity. Generally, the electron range is calculated by linear extrapolation to zero using the transmission curve as shown in Fig. 4.12. It allows us to ensure that almost no electrons can go through the absorber. The energy loss of the electrons compared to the heavy charged particles is much lower thus the length of the electron path is hundreds of times greater. In a simple estimation, electron range is about 2 mm per MeV in materials of low density while roughly 1 mm for moderate density materials. Curves describing the range of the electrons in two materials commonly used in detectors are shown in Fig. 4.13 Absorption of Beta Particles. Figure 4.14. Transmission curves for beta particles from of 0.43 MeV) [23].. 185. W (endpoint energy. The transmission curve describing the beta particles emitted from a radioisotope source is significantly different from the curve for the monoenergetic electrons due to a continuous energy distribution of the electrons. The beta particles of low energy are immediately stopped even in a very thin absorber thus the attenuation curve decreases rapidly as shown in Fig. 4.14. The figure shows experimental data, the curve shapes are almost exponential functions..

(43) 4.2. Radiation Interactions. 27. 4.2.3. Interaction of Gamma Rays Gamma rays may interact with the matter by many well-known interactions, but only three are significant for radiation measurements: photoelectric absorption, Compton scattering, and pair production. These processes cause partial or full transfer of the gamma energy to an electron or a pair of electron-positron. After the energy transfer, the photon disappears, if the full gamma energy is transfer to the electron, otherwise is scattered. Photoelectric Absorption A photon interacts with an atom, which absorbs the photon. After absorption, the atoms ejects an energetic photoelectron from one of its bound shells, it is mainly K shell. Energy of the photoelectron is defined as follows:. Ee− = hν − Eb. (4.3). where hν is energy of the photon causing the electron emission, and Eb is the binding energy of the interacting electron in the shell. In the case of the photons with energy higher than a several hundred keV, most of the photon energy is carried off by the photoelectron. Additionally, the photoelectric absorption creates an ionized atom having a vacancy in one of its bound shell. In order to fill this vacancy, the atom captures a free electron from the matter and/or rearranges electrons on shells. During rearrangement of electrons, the atom may generate one or more X-ray photons or an Auger electron. The photoelectric effect is the dominant interaction of gamma rays of low energy. Materials with high atomic number Z enhance the photoelectric effect. Compton Scattering The Compton scattering process, which is shown in the in Fig. 4.15, is an interaction between the photon and an electron within the matter. The photon after the interaction with the electron changes its direction, which is defined by angle θ. Part of the photon energy is transferred to the electron,.

(44) 28. 4. BASIC THEORY. which is called a recoil electron. Amount of the energy transferred from the photon to the electron may vary from zero to a big fraction of the photon energy, since all values of the scattering angle are possible.. Figure 4.15. The Compton scattering [23].. Energy of the photon after the Compton scattering may be calculated using equations of the conservation of energy and momentum: hν. hν 0 = 1+. hν (1 − cos θ) m0 c2. (4.4). where m0 c2 equals 0.511 MeV and is the rest-mass energy of electron. If the scattering angle θ is small, the transferred energy is very small. The graphical angular distribution of scattered photons is presented in Fig. 4.16, which shows that high energy photons have tendency to scatter forward.. Figure 4.16. A polar plot of the number of photons (incident from the left) Compton scattered into a unit solid angle at the scattering angle θ. The curves are shown for the indicated initial energies [23].. The Compton scattering similarly to the photoelectric absorption is enhanced in materials with high atomic number Z, because the probability of.

(45) 4.2. Radiation Interactions. 29. the Compton scattering increases with the number of electrons, which may become scattering targets. Pair Production The pair production process is possible, if the gamma-ray energy is at least 1.02 MeV, this is double the rest-mass energy of electron. The probability of the pair production of the photon with energy a little bit higher than 1.02 MeV is low. Thus, to strengthen the pair production, the photon energy must exceed a level of a few MeV and because of that, the pair production is dominant process for the photons with high energy. In the process, the photon with sufficient energy in the coulomb filed of a nucleus disappears and a pair comprising electron and positron is produced. The energy of 1.02 MeV is used for the pair production, whereas the rest of the photon energy is shared between the positron end the electron as a kinetic energy. The positron slows down in the matter and annihilates generating two annihilation photons. These photons are significant for the response of gamma-ray detectors.. Figure 4.17. The relative importance of the three major types of gamma-rays interaction. The lines show the values of Z and hv for which the two neighboring effects are just equal [23].. The significance of the three major interactions of the gamma-rays for various materials and different photon energies is shown in Fig. 4.17. The right curve represents the energy of the photon for which the probability of.

(46) 30. 4. BASIC THEORY. the Compton effect equals the probability of the pair production, whereas the left line symbolizes the situation in which the photoelectric effect and the Compton effect are equally probable. 4.2.4. Interaction of Neutrons Neutrons having no electric charge do not interact with the coulomb force, which is dominant process of the energy loss for the charged particles. The neutrons interact directly with nuclei of the matter in which they move. Their paths through the matter may reach even tens of centimeters, since they may travel in the matter without any interaction. Therefore, they can be invisible to ionization detectors. As a result of the neutron interaction with a nucleus, the neutron may be absorbed by the nucleus, which produces secondary radiations after absorption, or the neutron energy and direction is changed during a collision with a nucleus. Several neutron interactions such as elastic scattering, inelastic scattering, radiative capture, charged-particle reactions, neutron-producing reactions and fission are described below. Elastic Scattering The neutron hits the nucleus in material and is scattered while the nucleus during the collision does not change its state. The neutron in this process is elastically scattered by the nucleus in the reaction, of which the symbol is (n,n). Inelastic Scattering Inelastic scattering is similar to elastic scattering except that the neutron gives part of its energy to the nucleus causing its excitation. The reaction symbol is (n,n’). The excited nucleus decays into ground state by emission of gamma-rays called inelastic gamma rays. Radiative Capture In this process, the nucleus captures the neutron and as a result single or a cascade of gamma-rays is emitted. This is an absorption reaction - (n,γ)..

(47) 4.2. Radiation Interactions. 31. Reactions with Charged-Particle Emission As with the radiative capture, the neutron is captured by the nucleus, however after that a charged particle such as alpha or proton is emitted by the nucleus. The reaction symbols are (n,α) and (n,p), respectively. Neutron-Producing Reactions Reactions (n,2n) and (n,3n) take place with energetic neutrons. After these reactions, additional neutrons are emitted from the nucleus. Fission During fission the neutron collides with the nucleus causing the nucleus splits into smaller parts. These parts are lighter nuclei and usually two free neutrons, a few gamma rays and neutrinos are emitted. Regarding the secondary radiations coming from the neutron interactions, heavy charged particles carrying most of the energy may be the products of neutron induced reactions or the nuclei of the material, which gain the energy in neutron collisions. Neutron detectors very often use the neutron converter, which is the material applied to convert the neutrons into secondary charged particles. To describe the neutron interactions with the matter, the cross-section is commonly used, which represents the probability of different types of neutron interactions with various material. The probability changes significantly with neutron energy. In order to present behavior of the neutrons, they are divided into two group depending on their energy: slow neutrons and fast neutrons, where the dividing energy is at about 0.5 eV. Slow neutron interactions Slow neutrons have small kinetic energy, therefore they transfer very little energy to the nucleus by elastic scattering. Consequently, elastic scat-.

(48) 32. 4. BASIC THEORY. tering cannot be used for thermal neutron detection. However, the neutrons loss their energy by elastic scattering and this process brings them into thermal equilibrium with the matter. Energy of neutrons linked with thermal equilibrium is about 0.025 eV and therefore many of slow neutrons have energy, which is near this value, so they are called thermal neutrons. The most important interactions of the slow neutrons are neutron induced reactions that produce secondary radiations with energy, which is sufficient for detection. The Q-value of these reactions must be positive, because energy of slow neutrons is very low. Mostly, the radiative capture reactions, which are used for the indirect detection of the neutrons, occur in the matter. Regarding slow neutron detection, reactions generating charged particles are the most attractive. Fast Neutron Interactions The fast neutron-induced reactions are useful for the neutron detection since usually a charged particle emission occurs with it but their probabilities decreasing with neutron energy. In the most cases, they are to low to play an important role. The most of such reactions may be initialized only by the neutrons with energy which is higher than the energy threshold of the reaction. For that neutrons, the scattering may become more important concerning detection since the neutron is able to transfer more energy in one collision. The result of such interactions are recoil nuclei with energy, which is sufficient for detection. Additionally, the recoil nuclei may be excited in the inelastic scattering. Neutron Cross Sections. Figure 4.18. Neutron beam striking a target [24]..

(49) 4.2. Radiation Interactions. 33. The neutron cross sections describe probabilities of interaction between neutrons and nuclei. The cross section concept is explained in Fig. 4.18, where the beam of monoenergetic neutrons passes through a thin target of area A and thickness T. The number of neutrons in 1 cm3 in the beam is n and their speed equals v, thus the intensity of the neutron beam is as follows: I = nv. (4.5). The value of nvA = IA is the number of neutrons striking the target per second and the I value is the number of neutrons hitting the target per second and per cm2 . The target is very thin and nuclei are very small, therefore the most of the neutrons pass through the target without interactions. The number of collision C is proportional to the atom density N, the beam intensity I, the thickness T and the area A of the target. It can be described by the equation: C = σIN AT. (4.6). where σ is cross-section and N AT defines the total number of nuclei in the target. Therefore, σI is the number of collisions per second per nucleus and σ is the number of collisions per second per nucleus per unit intensity. The unit of neutron cross-sections is barn (b), where one barn equals 10−24 cm2 . Reaction Rate Reaction rate R is another useful parameter, which defines the number of specific reactions in material volume per second. Reaction rate (1/(cm3 s)) is defined as follows: R = ΣΦ. (4.7). where Φ is the neutron flux (1/(cm2 s)) and Σ is the macroscopic cross section (1/cm) of the reaction defined as follows: Σ = Nσ. (4.8).

(50) 34. 4. BASIC THEORY. N is the atomic density: N=. ρNA M. (4.9). where ρ is the density of material (kg/m3 ), NA is the Avogadro constant (1/mole) and M is the molar mass of the material (kg/mol).. 4.3. Semiconductor Detectors Many types of detectors are used to measure nuclear radiations, where the most known are ionization chambers, proportional counters, GeigerMueller counters, scintillation detectors, photomultiplier tubes and semiconductors. Structures of these detectors and their applications are different, therefore only basic information about the semiconductor detectors required to understand the PhD thesis results is described. Semiconductor Detector Structure. Figure 4.19. Space charge region within the p-n junction. Semiconductor detectors are based very often on a p-n junction, the scheme of such detectors is presented in Fig. 4.19. The detector includes a p-type and a n-type semiconductor that are merged together in order to create a p-n junction. The n-type semiconductor has the electron concentration higher than the hole concentration in its structure, and therefore the negative charge of electrons is dominant so the semiconductor is called.

(51) 4.3. Semiconductor Detectors. 35. n-type. In contrast to the n-type semiconductor, the p-type semiconductor has larger holes concentration, which means that positive charge of holes is dominant so it is called p-type semiconductor. If both the n-type and the p-type semiconductors are merged together, the electrons from the n-type region diffuse to the p-type region and positive donors are left in the n-type region and likewise the holes move from the p-type region to the n-type region and negative acceptors are left in the ptype region. The electrons meet together with the holes and disappear due to recombination thus the negative charged ions are created in the p-type region as the positive charged ions in the n-type region. In consequence, electric filed is created within the p-n junction. This field creates the force, which stops the continued exchange of the electrons and the holes. The region, where the electrons and the holes have diffused away and only the charged ions are left is called the space charge region (SCR). If the electric filed stops the diffusion of the electrons and the holes, the SCR reaches the equilibrium and its equilibrium dimension. The electric filed that stops the diffusion is called the build-in voltage and is defined as follows [26, 27]: kT ln Vbi = q. . NA ND Ni2. (4.10). where NA is acceptor concentration, ND is donor concentration, Ni is intrinsic carrier concentration, T is temperature, q is elementary charge and k is Boltzmann constant. To increase the width of the SCR, the external voltage may be applied and in this case the width of the SCR equals [26, 27]: s W =. 2εε0 (ND + NA ) (Vbi + V ) qND NA. (4.11). where ε is dielectric constant, ε0 is vacuum permittivity and V is external voltage. Detector Response Interactions between the semiconductor detectors and the radiations depend on the semiconductor material and the radiation type. Various materials may be used to create the semiconductor detector, where the most.

(52) 36. 4. BASIC THEORY. common are silicon (Si), germanium (Ge), gallium arsenide (GaAs) and diamond. Silicon carbide (SiC) is one of the novel material which may be applied for the semiconductor detectors, which are investigated now in may institutions. Different types of radiation interact with this material on many ways, all of these processes finally lead to ionization.. Figure 4.20. Signal processing of semiconductor detectors by the electronics. Changes of the voltage (A), detector response in the form of count distribution per channel (B).. As a result of the ionization, electron-hole pairs are generated within the volume of semiconductor detector. Generation of the electron-hole pairs impacts on the voltage and the current in the detector, however, only the electron-hole pairs generated in the space charge region may influence the response of the detector. In order to measure the radiation, the sensor system is needed that comprises the semiconductor detector connected with a few electronic devices such as a fast preamplifier, a spectroscopic amplifier, a multi-channel analyzer and a digital oscilloscope. Changes of the voltage shown in the Fig. 4.20-A are monitored by the electronics. Each peak of the voltage is linked with a single event in the detector. The area under the peak corresponds to the energy of the reaction, which is deposited in the SCR. The energy is calculated by the electronics and used to create the response in the form of counts per channel as shown in Fig. 4.20-B. Each.

(53) 4.3. Semiconductor Detectors. 37. calculated value of the deposited energy produces a single count which is located in the specific channel, which corresponds to the deposited energy. The channels are defined by upper and lower channel energies. Additionally, the upper energy is a label of the channel. For instance the channel C2 is defined by the lower energy E1 and the upper energy E2 . A count occurs in the Ei channel, if a particle deposits Ex energy satisfying the following condition Ei−1 < Ex ≤ Ei . The width and the number of the channels impact on the signal shape since the number of counts in channels depends on the channel width. Higher number of the channels means higher resolution of the signal but also its bigger uncertainty due to lower number of the counts in narrower channels. Changing the channel width, two energy scales may be applied: linear or logarithmic depending on specific needs. The next important parameter which influences the signal is the collection time. It is obvious that if the time is longer the number of the counts is higher. The number of counts per channels also is linked with the spectrum of radiation, which forms the signal..

(54) 38. 4. BASIC THEORY.

(55) 39. 5. Software In presented PhD thesis, many various computer calculations have been done in which several codes have been used. These codes are listed and described below. Because these codes are well-known the description is very brief and includes only general information. MCNP/MCNPX MCNP is a general-purpose Monte Carlo N-Particle code for transport calculation of neutron, photon, electron or coupled neutron/photon/electron through the matter. MCNPX similarly to MCNP is a Monte Carlo radiation transport code, which is eXtended, which means that it allows taking into account particles such as protons, deuterons, tritons and alphas [28–31]. MCB MCB is Monte Carlo Continuous Energy Burn-up Code for calculation of a nuclide density time evolution (after burn-up or decay). The code allows performing eigenvalue calculations of critical and sub-critical systems as well as neutron transport calculations in fixed source mode to obtain reaction rates and energy deposition that are necessary for evaluation of burn-up. MCB internally integrates MCNP [32, 33]. GEANT4 Geant4 is a toolkit to simulate the passage of particles through the matter. It is dedicated code for modeling of detectors, the code may be used for high energy, nuclear and accelerator physics, as well as studies in medical and space science [34]. MATLAB MATLAB is a commercial software pachage, which is a high-level language and interactive environment for numerical computation, visualization,.

(56) 40. 5. SOFTWARE. and programming. It allows users to analyze data, develop algorithms, and create models and applications [35]. SRIM/TRIM SRIM/TRIM is a group of programs to calculate the stopping power and range of ions in the matter using a quantum mechanical treatment of ion-atom collisions [36]..

(57) PART TWO. PhD Research. Chapter VI: SiC Sensor Chapter VII: Modeling Method of SiC Sensor Characteristics Chapter VIII: Results Chapter IX: Conclusions and Future Directions.

(58)

(59) 43. Part II. PhD Research In this part, the work done by the author of the thesis is presented. The most of calculations, curves, figures, simulations and numerical models have been done by the author except those works for which information about other authors is given.. 6. SiC Sensor Many different sensors have been produced for testing and radiation measurements by the French group of scientists during the I-SMART project [15–17, 37–39]. Structures of the sensor have been evolving during research with broadening our knowledge about the sensor operation. The sensors producing high quality and clear signals during measurements and satisfying electrical tests have been used for modeling and studying of their behavior. The sensors have been based on silicon carbide (SiC) since this material is highly suitable for spectroscopic measurements in nuclear energy and for the measurement while drilling due to advantages given by the 4HSiC polytype. Its ability to operate in elevated temperature, the increased radiation resistance and the wide band gap (3.25 eV) allow it to work at elevated temperatures in harsh radiation environments [1–14].. 6.1. Sensor Structure Three types of the sensor structure based on the p-n junction have been used in computer modeling, in order to study behavior of the SiC sensor under radiation. The structures are defined by two major features: the area and the layered structure. The area of the sensor may be circle, square or rectangle and the structure may include several layers consisting different materials. The neutron converter may be applied in the sensor but it is not required for its operation. All structures have been realized on n+ -type 4H-SiC wafers and include the n-type epitaxial layer and the p+ epitaxial layer. Some of them contains.

(60) 44. 6. SIC SENSOR. Figure 6.1. Structure of S1 sensor.. Figure 6.2. Structure of S1B sensor.. the p++ epitaxial layer and the metal contact made of aluminum. Moreover, some of the sensor structures have the neutron converter. The first sensor has been made in two versions: S1 without the neutron converter and S1B with the neutron converter, the structures of which are presented in Fig. 6.1 and 6.2. These structures were fabricated with three.

(61) 6.1. Sensor Structure. 45. different areas: 4, 10 and 25 mm2 but only the biggest sensor was analyzed due to the highest sensitivity. The structure includes five layers starting from the base layer of the 4H-SiC n+ substrate of 350 µm thickness. The n-type epitaxial layer with 80 µm thickness and low nitrogen doping concentration of ∼ 2 × 1020 m−3 was used on the substrate and was covered by two p-type epitaxial layers: p+ and p++ . Both p+ and p++ have thickness 1 µm and are doped using aluminum with concentration of 2 × 1023 m−3 and 2 × 1025 m−3 , respectively. At the top of the p++ layer, the 4 µm aluminum metallic contact was used.. Figure 6.3. Distribution of SRIM/TRIM.. 10. B in the metallic contact of S1B calculated by. In case of S1B, ions of 10 B have been implanted directly into the metallic contact with 2 MeV energy and a dose of 5 × 1015 cm−2 , Fig. 6.3 shows the distriubtion of 10 B in the metallic contact calculated by SRIM/TRIM [36]. Boron is located in thin layer, which thickness is roughly 0.5 µm - boundaries of the layer are marked in Fig. 6.2 and 6.3. Concentration of boron and atoms number density of aluminum, which is 6.04 × 1028 3 give us the atomic m fraction of boron in the metallic contact. The maximal value of the boron atomic fraction is about 0.029%. The second structure is the next generation of the first sensor (S1/S1B), two versions of the sensor: S2 without the neutron converter and S2B with the neutron converter are shown in Fig. 6.4 and in 6.5. The sensors with the biggest area were used due to the highest sensitivity. Diameters of fabricated sensors are from 330 µm to 1180 µm. The 350 µm 4H-SiC n+ substrate is covered by 20 µm n-type epitaxial layer with low nitrogen concentration of.

(62) 46. 6. SIC SENSOR. Figure 6.4. Structure of S2 sensor.. Figure 6.5. Structure of S2B sensor.. ∼ 2×1020 m−3 . Single 1 µm p+ epitaxial layer with 1×1025 m−3 concentration of Al doping and the 1 µm aluminum metallic contact are located at the top of the sensor. Regarding the S2B sensor including the neutron converter, boron was implanted into the metallic contact with 180 keV energy and the dose of.

(63) 6.1. Sensor Structure. Figure 6.6. Distribution of SRIM/TRIM.. 47. 10. B in the metallic contact of S2B calculated by. Figure 6.7. Structure of S3B sensor.. 5 × 1015 cm−2 , the boron distribution calculated by SRIM/TRIM is shown in Fig. 6.6. The maximal atomic fraction of 10 B for S2B is about 0.069%. The atomic concentration and the atomic fraction of 10 B in case of S2B are higher than in S1B. Two parameters influence the atomic concentration: the boron dose and the size of the volume where boron ions are implanted. The higher dose means higher concentration, whereas bigger volume means.

(64) 48. 6. SIC SENSOR. lower concentration. The volume size is a result of the implantation process. Smaller volume in the case of S2B compared to S1B is responsible for its higher concentration of boron.. Figure 6.8. Distribution of 10 B in the SiC layer of S3B calculated by SRIM/TRIM.. The third structure of the sensor is presented in Fig. 6.7. The sensor with the biggest area with 1 mm diameter includes the 350 µm 4H-SiC n+ substrate and the 15 µm n-type epitaxial layer with low nitrogen concentration of ∼ 3 × 1021 m−3 . The 0.5 µm p+ epitaxial layer with 1 × 1025 m−3 concentration of Al doping and the 0.2 µm of SiC with boron implantation were applied in this structure. Boron atoms are implanted with energy of 50 keV and a dose of 1015 cm−2 . The maximal atomic fraction of boron for S3B is about 0.046%. The atomic concentration and the atomic fraction of boron in case of S3B is higher than in S1B and lower than in S2B. Five times lower boron dose used for S3B has been compensated by smaller boron volume and as a result, a similar value of the concentration was achieved.. 6.2. Sensor Operation In order to perform the radiation measurements, the sensor system must be prepared and adjusted to the specific needs of the experiment. In order to protect the sensor from mechanical damage, the sensors with the wiring have been placed in aluminum boxes where BNC connectors have been applied to connect the sensor, which is shown in Fig. 6.9. Various size and shape of.

(65) 6.2. Sensor Operation. 49. aluminum boxes were used depending on space available in the experiments. Packaging shown in Fig. 6.9 have been assembled by the French group of scientists [15–17, 37–39]. Presented packaging has been used in the experiments, where the box was located in given position in the experimental setup. The sensor has been connected with the preamplifier/amplifier and the multichannel analyzer in order to collect the signals.. Figure 6.9. Packaging: SiC sensor (A) with wiring (B) in aluminum box (C) with BNC connector (D).. 6.2.1. Application of External Voltage Regarding the response shape, the width of the SCR has strong influence on it, therefore its value during the measurements must be well known. External voltage (V ) may be applied for the SiC sensors to increase the SCR. The width of the SCR is defined by Eq. 6.1, which was proved by [26, 27]: s W =. 2εε0 (ND + NA ) (Vbi + V ) qND NA. (6.1).

(66) 50. 6. SIC SENSOR. where Vbi is the built-in voltage defined as follows: kT NA ND Vbi = ln q Ni2. (6.2). Quantities used in Eq. 6.1 and 6.3 for various sensors are presented in Tab. 6.1. Table 6.1 Comparison of SiC material properties for different sensors.. The SCR, the volume where the signal is created and collected, is formed on the boundary between the n-type epitaxial layer and the p+ layer. We can distinguish two volumes of the SCR, the first one inside n-type epitaxial layer whereas the second one in the p+ layer. The ratio of those volumes is proportional to the ratio of ND and NA , as shown in Eq. 6.3. The SCR volume in the n-type epitaxial layer is denoted by Vn− , whereas Vp+ is the volume of the SCR in the p+ layer. The SCR is located mainly in the n-type epitaxial layer due to significant difference between ND and NA . V − NA = n ND Vp+. (6.3). Figure 6.10 shows curves describing the width of the SCR as a function of the external voltage for different sensor structures and three values of temperature. Curves for S1, S1B, S2 and S2B are similar because the level of ND , which significantly influences the width, is the same. The width of the SCR for S3B is lower than in case of S1, S1B, S2 and S2B. Temperature impact on the SCR width is not strong, higher differences in the width caused by temperature are observed in the region of low voltage. The impact of temperature decreases with the external voltage..