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UBC Theses and Dissertations

A gallium arsenide CCD X-Ray detector 1997

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A G A L L I U M A R S E N I D E C C D X - R A Y D E T E C T O R B y Scott Patten B . Sc. (Physics) Simon Fraser University, 1994 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF S C I E N C E in T H E FACULTY OF G R A D U A T E STUDIES D E P A R T M E N T OF PHYSICS & A S T R O N O M Y We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH C O L U M B I A October 1997 © Scott Patten, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Br i t i sh Columbia , I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics & Astronomy The University of Br i t i sh Columbia 6224 Agricul tura l Road Vancouver, B . C . , Canada V 6 T 1Z1 Date: Abstract A one dimensional buried channel C C D with a 30 /urn thick intrinsic layer was manufac- tured at T R I U M F for use as a radiation detector. In order to characterize the detector's response to radiation, six discrete X - R a y sources wi th energies ranging from 8 K e V to 60 keV were impinged on the device. A n algorithm was developed to convert events detected by the C C D into spectra characteristic of each X - R a y source. The range of energies detectable and the energy resolution of the detector at different energies were studied.A model was developed and used to explain the shape of each spectrum. The spectrum from an 2 4 1 A m source was also studied to determine the detector's response to a multi-energetic source. i i Table of Contents Abstract ii Table of Contents iii List of Tables v i List of Figures vii 1 Introduction 1 1.1 Mot ivat ion 1 1.2 Work Done in this Study 2 1.3 Outline 2 2 The C C D 4 2.1 Overview 4 2.2 The Structure of the C C D 5 2.3 The potential underneath a gate in the C C D 7 2.4 Movement of charge from pixel to pixel 12 3 Interactions of Particles in G a A s 14 3.1 Introduction 14 3.2 The Interaction of an X - R a y wi th G a A s 14 3.3 The Photo-electric Effect . 15 3.4 Creation of electron-hole pairs 19 i i i 3.5 Interactions of electrons in G a A s 20 3.6 Escape of particles from the detector 21 4 Electron Transport 24 4.1 Introduction 24 4.2 Electrostatic fields in the C C D 25 4.3 Init ial distribution of e.h.p.s 27 4.4 Drift of electrons 30 4.5 Electrons created in the field-free region 31 4.6 Recombination 33 4.7 Summary of transport processes 34 5 Experiment 36 5.1 Experimental Setup 36 5.2 Analysis of oscilloscope traces 39 5.2.1 The Choice of N s i g n a i 40 5.3 Tests with known input pulses 41 5.4 Response of the detector to Characteristic X - R a y s 45 5.5 The 2 4 1 A m spectrum 47 6 Results and Discussion 50 6.1 Overview 50 6.2 The Noise Peak 51 6.3 The Signal Peak 53 6.3.1 Cal ibrat ion of the C C D Energy Scale 53 6.4 The High-Energy Peak 55 6.5 The Escape Peak . . ' . 57 iv 6.5.1 Escape of Secondary X-Rays 58 6.5.2 Escape of photo-electrons 61 6.5.3 Experiment 67 6.6 The Field-Free Peak 67 6.7 Fu l l Spectrum Analysis 69 6.8 The 2 4 1 A m Spectrum 71 6.8.1 Theory 71 6.8.2 Experiment 73 6.9 Charge Sharing 75 7 Conclusion 76 7.1 Future Work 76 7.2 Conclusions 78 Bibliography 80 8 Appendix: Spectra 84 v List of Tables 2.1 Constants for G a A s used in calculating Js 9 3.2 Chance of absorption of the K a X - R a y s 17 5.3 The parameters of the peaks for T b data wi th differing N s i g n a l ' s 41 5.4 The K a energies of the elements used in this study 46 6.5 Noise peak data for X - R a y s on C C D 1 52 6.6 The resolution for X-Rays on C C D 2 , analyzed using N s j g n a i = 3 and 5 . . 55 6.7 High-energy peak data for X - R a y s on C C D 2 57 6.8 Chance of escape of the secondary X-Rays from the C C D 61 6.9 Range and chance of escape of photo-electrons in Ge 64 6.10 Peak data for characteristic X - R a y s on C C D 1 70 6.11 Peak data for characteristic X - R a y s on C C D 2 70 6.12 X - R a y s emitted by 2 4 1 A m 72 6.13 Peak data for the 2 4 1 A m X - R a y s on C C D 2 73 6.14 Comparison of the 60 keV resolution to some other detectors 74 6.15 Range in the x-direction and charge sharing for electrons in Ge 75 v i List of Figures 2.1 A schematic diagram of the C C D 6 2.2 The well created under the C C D 6 2.3 The band diagram wi th V ^ j a g = 0 V 8 2.4 The band diagram wi th V b i a s = -7 V . . . 11 2.5 The voltages on the phases of a pixel of the C C D 13 2.6 The potential beneath the wells of the C C D 13 3.7 The Compton and photo-electric cross-sections of X-Rays in G a A s . . . . 16 3.8 The angular distribution of ejected photo-electrons 18 3.9 The mean path length for an electron in Ge 22 4.10 A time-line of the creation and collection of electron hole pairs in the C C D 26 4.11 The linear e.h.p. density and diffusion time for a 60 keV photo-electron . 28 4.12 The charge that has diffused to the depletion region V s . time 33 5.13 A typical oscilloscope trace 37 5.14 The spectra of T b X-Rays analyzed wi th N s i g n a i = 3, 5, 7 and 9 42 5.15 A histogram of the count rate for a 31mV input pulse 43 5.16 The charge deposited in the C C D by known input pulses 44 5.17 The resolution of C C D 2 as a function of energy 45 5.18 A schematic of the source used to create characteristic X - R a y s 46 5.19 A schematic of the experimental setup used to study the X - R a y spectra. 47 5.20 The charge deposited in a C C D by M o , N s i g n a i = 5 48 v i i 5.21 The charge deposited in C C D 2 by T b , N s i g n a l =5 48 5.22 The charge deposited in C C D 1 by 2 4 1 A m X-Rays , N s i g n a i = 5 and 7 . . . 49 6.23 The noise peaks for A g spectra 52 6.24 The signal peaks for R b , M o and A g 53 6.25 Signal peak positions of X-Rays for C C D 1 and C C D 2 wi th N s i g n a i = 5 . . 54 6.26 Comparison of the C u and T b spectra 56 6.27 B a and T b spectra on C C D 2 analyzed wi th N s ; g n a i = 5 58 6.28 A cross section of the C C D 59 6.29 Five typical electron tracks created by the Monte Car lo simulation . . . . 63 6.30 The energy deposited by an escaped photo-electron 65 6.31 The energy deposited by an escaped photo-electron 66 6.32 The energy deposited for escaped X-rays and electrons 66 6.33 B a and T b K Q X - R a y s on C C D 2 fit wi th signal and escape peak 68 6.34 T b K Q spectrum fitted wi th signal, escape and field-free peaks 69 6.35 Theoretical 2 4 1 A m spectrum in 30 /xm of G a A s 72 6.36 The spectrum of 2 4 1 A m on C C D 2 74 8.37 Rb , M o , A g and B a spectra on C C D 1 85 8.38 A T b spectrum on C C D 1 86 8.39 C u and R b spectra on C C D 2 86 8.40 M o , A g , B a and T b spectra on C C D 2 87 8.41 Rb , B a and T b spectra on C C D 2 88 v i i i Chapter 1 Introduction 1.1 Motivation The Charge Coupled Device ( C C D ) was first conceptualized by Boyle and Smith [1] in 1970, and was experimentally verified using Si , in the same year, by Amel io [2]. Since then, C C D s have been used in a large and varied number of applications, with the two major areas being imaging[3, 4, 5, 6] and digital signal processing[7, 8, 9]. Al though Si C C D s have been used to detect X-Rays[10, 11, 12] and single element G a A s particle and X - R a y detectors have been built[13, 14, 15], few, if any G a A s C C D detectors have been made. G a A s has advantages over Si because its larger Z value increases the detection efficiency of X-Rays . Also, G a A s device structures are inherently more radiation hard than those made on Si[16, 17]. The mobil i ty of electrons in G a A s is larger than in S i , making G a A s devices potentially faster. Final ly , the large band gap of G a A s makes it usable at room temperature, unlike Si and Ge based detectors. These properties would make a G a A s detector useful in many different environments. The detection efficiency of G a A s would make it useful in X - R a y astronomy for detection of X - R a y s from 10 - 100 keV[10], while the radiation hardness of G a A s would make these detectors useful in such high particle flux environments as the L H C (Large Hadron Collider) [18]. 1 2 1.2 Work Done in this Study The C C D s used in this study were originally used as transient digitizers in the Brookhaven Nat ional Laboratories Experiment 787[19]. It was thought that by simply increasing the depth of the epitaxial layer of G a A s on which the C C D s were fabricated, the C C D s would be useful for directly detecting radiation. A wafer of C C D s wi th a 30 yum thick epitaxial layer was fabricated at the G a A s Micro-structure Laboratory at T R I U M F . The purpose of this study was to find the response of the G a A s C C D detector to X-Rays wi th energies ranging from 8 to 60 keV. In order to do this, an X - R a y source which emitted the K a X -Rays of either C u , R b , M o , A g , B a or T b was used. The K a X-Rays were shone on the C C D and the resulting spectra found. A n 2 4 1 A m source was used as well to study the detector's response to more complex spectra. The spectra from the K Q X - R a y s were not single peaks, but instead exhibited a number of features. The features arose from escape of photons and electrons from the detector's volume, noise sources in the detector and deposition of charge in areas of the detector that had litt le or no drift field. In order to understand these features, several simulations of the microscopic interactions and transport of photons and electrons wi thin the detector were made. Using the results from the simulations, each peak in each individual spectrum was assigned to a phenomenological source. From the positions and widths of the peaks arising from the the deposition of the full energy of a single X - R a y of known energy into the C C D ' s wells, the energy response and resolution of the G a A s C C D to X-Rays was found. 1.3 Outline The thesis is divided into seven chapters, the first being the introduction. The second chapter introduces the structure and operation of the C C D . In the thi rd chapter, the interactions of particles in G a A s and the creation of electron hole pairs are discussed. 3 The fourth chapter details the transport of electrons from their in i t i a l creation to the time they enter the potential wells under the C C D gates. The fifth chapter details the experimental work done in this study and shows some of the spectra obtained. The sixth chapter discusses and analyzes the data obtained and shows the results of simulations done to help explain the spectra. The final chapter discusses possible work that could be done in the future and makes conclusions. A n appendix shows al l of the single energy X - R a y spectra that were taken in this study. Chapter 2 The C C D 2.1 Overview Figure 2.1 shows a diagram of a Charge Coupled Device ( C C D ) . It consists of a number of metal contacts, or gates, on top of a semiconductor substrate. Four of the gates act together to form a "pixel" . B y putting different voltages on the four gates, together wi th a broad area bias normal to the surface, three dimensional potential wells can be formed where electrons wi l l be trapped. B y changing the gate voltages in sequence, charge can be transferred from pixel to pixel. The broad area bias localizes the pixels to the near-surface region and also attracts electrons from the bulk area of the C C D into the pixels. In normal C C D operation, the voltage on each of the four gates in a pixel consists of a periodic train of pulses wi th fixed phase wi th respect to each other. Figure 2.6 shows the voltages on the four gates of a pixel in the C C D used in this study. The effect of these pulse sequences is to move a packet of electron charge from one pixel to the next. The creation of electron hole pairs (e.h.p.s) in the C C D and their collection under one of the pixels of the C C D is shown in figure 4.10. When an X - R a y enters a C C D , it interacts wi th the semiconductor substrate of the C C D , creating electron-hole pairs. The number of electron-hole pairs created in the C C D is directly proportional to the energy of the incident X-Ray . The electrons created by the X - R a y are accelerated by the vertical field in the C C D , which drives them into the potential wells under the gates. 4 5 The electrons in the potential wells are then transferred from pixel to pixel to the output of the C C D by the gate pulses shown in figure 2.6. The voltage generated at the output when the charge is output from the C C D should therefore provide a measure of the X - R a y ' s energy. 2 . 2 The Structure of the C C D The C C D used in this study (see Figure 2.1) is a buried channel resistive gate C C D comprised of 128 pixels. Each pixel of the C C D consists of four metal gates which are 2 fj,m wide and spaced by 3 fj,m, giving a pixel length, or pitch, of 20 fim. The gates are in ohmic contact wi th a 0.1 /xm thick sheet of Cermet (Cr-S iO) , a resistive dielectric wi th a sheet resistance of -1 M Q / D at this thickness. The Cermet makes a Schottky contact wi th the G a A s below it. The Cermet serves two purposes. First , the Schottky barrier moves the potential well away from the surface of the G a A s (see Figure 2.2). This avoids problems associated wi th trapping of the electrons in the well by the surface states inherent in G a A s . The Cermet also ensures that the voltage between gates varies linearly along the surface of the C C D , providing an electric field that helps in the transfer of electrons from pixel to pixel[20] (see Figure 2.6). The channel of the C C D , the region where the potential wells in the C C D exist, is 50 / /m wide and 2.5 m m long (128 pixels x 20 ^m) . Below the gate contacts and the Cermet is a wafer of G a A s . This wafer consists of three layers. O n top is an epitaxially grown 0.27 pirn thick layer of n-type G a A s doped at N D = 5 x 10 1 6 c m - 3 . Below this is a second epitaxially grown, 30 fim thick layer of semi-insulating G a A s , which is p-type wi th a nominal doping of N A < 10 1 4 c m - 3 . This layer is called the active layer as this is where the X-Rays interact wi th the G a A s to form 6 0.1 j i m : Cermet 0.27 u.m 30u,m Active Region, Semi-Insulating, nominally doped a tNA= 1 0 1 4 c m - 3 650 um Substrate, doped at NA = 1 0 1 8 c m " 3 ^ ! Vsubstrate Figure 2.1: A schematic diagram of the C C D used in this study, showing a single pixel. 7 electron-hole pairs (e.h.p.s). Below the epitaxial layers is a 650 fj,m thick substrate of p-type G a A s grown by the L iqu id Encapsulated Czochralski ( L E C ) method, and doped at N A = 10 1 8 c m - 3 . The bottom of the C C D has an ohmic contact made to it. This contact is kept at a negative voltage while the C C D is being used as a detector. 2.3 The potential underneath a gate in the C C D Figure 2.3 shows the band diagram underneath one of the gates in the active area of the C C D wi th al l the gates at ground. The device consists of three junctions, a p + - p ~ junction, a p ~ - n junction and a Schottky junction between the n layer and the Cermet. The p ~ - n junction and the n-Cermet junction act together to form a potential well wi th a flat min imum from 0.1 jim. to 0.27 yum deep in the C C D . The depletion region is ~4 iim deep, leaving a field-free region 26 /mi deep. When a negative voltage is put on the bottom contact of the device, the p + - p ~ and the p ~ - n junctions act as reverse-biased diodes, and the n-Cermet junct ion acts as a forward biased Schottky diode. To find the depletion depth in the active region under reverse bias conditions, a number of approximations are made. The abrupt junction approximation assumes that the changes in doping are step functions. The second approximation is that there is a well defined depletion region outside of which a l l fields are zero. The next step is to find how much voltage is dropped across each junction. To do this, a current continuity equation is set-up. The current density through a pn junction diode[21] or a Schottky diode[22] at a 8 Active region a , s x ^ u region field free region Substrate N n J / j i / ! 0.7 eV ] ! T I ] Cermet I 1 ! 1.5 1 0.5 m 3 (3 E, 0 -0.5 -1 -1.5 0 5 10 15 20 25 30 35 Depth(|im) Figure 2.3: The band diagram under a pixel of the C C D with V ^ j a g = 0 V temperature T is given by the Schockley equation, J = Js(e^kBT - 1) (2.1) Where V is the bias voltage across the junction, and is defined to be positive for forward bias and negative for reverse bias. Js is the saturation current density, and ks is Boltzmann's constant. For a pn junction, Js is given by[21] Js - j + j (2.2) Where Dp and Dn are the hole and electron diffusion constants, and Lp and Lp are the hole and electron diffusion lengths, given by Ln — \JTnDn , Lp — \jip~Dp (2.3) 9 Table 2.1: Constants for G a A s used in calculating the saturation current density in pn and Schottky junctions.[21],[22] Parameter Value Dn 222 c m 2 / s Dp 10.4 c m 2 / s Ln 14.58 Lp 3.16 pm TN ~ 10" 8 s TP ~ 1 0 - 8 s Hi 1 .79x l0 6 c m " 3 m* 0.067 m 0 4>B 0.7 eV npo and pno are the electron and hole minority concentrations on the p and n side of the junction, respectively. They can be found using the fact that the electron and hole density, n and p in a doped semiconductor are related to the intrinsic electron density, rii by np = n2 (2.4) Table 2.1 gives values for the parameters named in the above equations. The satura- t ion current density has two components added together. The first is linearly dependent on the hole concentration on the n side of the junction, and the second on the electron concentration on the p side of the junction. For a Schottky diode wi th a barrier energy of 4>B running at a temperature T, the 10 saturation current density is given by[22] Js = AT2 exp (2.5) where A is A = (2.6) m* is the effective mass of an electron in G a A s , 0.067m 0 ( m 0 being the electron mass), and h is Planck's constant. For the p _ - n junction, np0 3> pn0, so the saturation current for this junction, JSpn, wi l l be given by JSpn * ~ 1 0 - 1 4 A / m 2 (2.7) For the p + - p _ junction, pn0 is given by the doping density in the p~ region, so the saturation current density through this junction, JSvv is JSpp « ~ 1 0 3 A / m 2 (2.8) For the Schottky junction at 300°K, the saturation current density, JSSchottky is JsSchottky = AT2 exp ~ 1 0 - 9 A / m 2 (2.9) The saturation current for the p ~ - n junction is much smaller than the saturation current for the other two junctions, so the current through the p~-n junction wi l l be the 11 Active region N-Type A i >• a t S x l t f " d e p l e , l o n \ region field free region Substrate i i i i 1 > — E i i / i / I ~ - J — Ev" 4 / / 1 / / - / / 1 / / -t / / i -1 / / 1 / / ! 1 / / 1  / / j 0.7 eV~$ i l l • Cermet II i m 9 8 7 6 5 <D 3 < 2 1 0 -1 -2 10 15 20 Depth(nm) 25 30 35 Figure 2.4: The band diagram under a pixel of the C C D with V ^ j a s = -7 V l imi t ing current, and al l the applied voltage wi l l be dropped across this junction. Using this information, the band diagram under the C C D was calculated for negative voltages applied to the bottom of the C C D . Figure 2.4 shows the band diagram underneath one of the gates wi th the voltage at the bottom of the C C D set to -7 V , the voltage used during this study. The depletion width is -11 / im , leaving a field free region in the active region of 20 fim. The maximum field in the device is 15 k V / c m , much less than the breakdown field of G a A s of 300 kV/cm[21]. The field w i l l vary linearly from zero at the deepest part of the depletion region to 15 k V / c m at the p _ - n junction. 12 2.4 Movement of charge from pixel to pixel If the gates in a pixel are named, from left to right, fa, fax, 4>2 and fax (see figure 2.1), the voltages on fa and fax are constant, while the voltages on fa and ^ 1 A change between two levels in synchronism wi th an input clock signal. In this experiment, the clock signal was run at 10 M H z . fa and fax were set at -0.5V and -1 .5V, respectively. The fa electrode alternated between 2.5V and -2.5V and the fax electrode alternated between 0 V and - 4 V . Figure 2.5 shows the signals on the gates of a C C D pixel . Figure 2.6 shows the corresponding electron potential beneath the pixel at four different times in the clock cycle. The figure also shows how a small packet of charge is moved from its original position under fa to a position under the fa gate of the next pixel to the right. A t t= t 0 , the signal charge is under fa. A t a time t i , the voltages on fax and fa go positive, and the charge starts to move towards the fa electrode. A t t=t2, the charge has al l moved to the fa electrode. A t t 3 , the voltages on fax and fa go negative, and the charge starts moving towards the fa gate of the next pixel, fa>. The charge has been moved from one pixel to the next. In this study, the C C D was used in the continuous operation mode: the clock signal is constantly input to the C C D , and charge is moved from one pixel to the next at a rate equal to the clock's frequency. 13 Figure 2.6: A diagram showing the potential along the C C D at times t 0 , t i , t 2 and t 3 . A n electron "packet" is also shown being transferred from one pixel to the next. Chapter 3 Interactions of Particles in GaAs 3.1 Introduction A n X - R a y in G a A s w i l l interact wi th the G a A s by ejecting an energetic electron from one of the atoms through either the Compton or photo-electric process. Bo th of these processes leave an excited atom, which wi l l relax to its ground state by either emitt ing a secondary X - R a y or, through an Auger process, an energetic electron. If a secondary X - R a y is released, it w i l l then interact wi th another atom, liberating another electron. This w i l l result in two energetic electrons (with energies from 10 to 50 keV) in the G a A s . These electrons, as they move through the crystal, w i l l interact with the G a and A s atoms to create further electron-hole pairs. The electrons wi l l continue generating e.h.p.s unti l their kinetic energies are too low to cause further ionization. 3.2 The Interaction of an X-Ray with GaAs In general, an X - R a y photon can interact wi th material in three ways: pair production, Compton and photo-electric interactions[23],[24]. Pair production occurs when a photon disappears, creating an electron-positron pair. In order for this to happen, the photon 14 15 must have at least the rest mass energy of the electron and position, 1.02 M e V . A Compton interaction involves a photon scattering from an atom, causing the atom to eject a "Compton" electron and a photon of lower energy. In the photo-electric interaction, a photon is completely absorbed by an atom, and a "photo-electron" is ejected by the atom. In the Compton and photo-electric processes, the atom is left in an excited state. The X-Rays used to irradiate the G a A s C C D in this study ranged in energy from 8keV to 60keV, much less than the 1.02 M e V needed to create an electron-positron pair. The cross-sections for Compton and photo-electric interactions for incident photons in G a A s wi th energies ranging from 1 keV to 100 keV are shown in Figure 3.7. The cross- sections were calculated using the "photocoeff" program published by Appl ied Inventions Corp. Software. The photo-electric interaction is more likely in this energy range, and for photon energies below 30 keV the chance of a Compton interaction is negligible. For the rest of this study, it w i l l be assumed that a l l photon-solid interactions are photo-electric. 3.3 T h e P h o t o - e l e c t r i c E f f e c t Since a photon is completely absorbed in a photo-electric interaction, the chance, p(z) of the photon being absorbed wi th in a distance dz at a given depth z in a material is given by p(z)dz = A exp(—\z)dz (3.10) 16 1e+07 1e+06 F Photo-electric Compton E100000 V CO C 10000 r o o cu CO 1000 CO co o 100 10 1 1 10 Energy (keV) 100 Figure 3.7: The Compton and photo-electric cross section for X - R a y s of energies from 1 to 100 keV in G a A s where A is the linear absorption coefficient of the X - R a y in the material. Table 3.2 shows the photo-electric linear absorption coefficient for six different X - R a y energies calculated using the "photocoeff" software. The chance, P(z), that a photon has been absorbed by the time it reaches a depth z is given by integrating 3.10 to get The chance that a K a photon from the six elements used in this work w i l l be absorbed in 30 fim of G a A s , the depth of the active region in the C C D , is shown in table 3.2 When a photon interacts wi th an atom by the photo-electric effect, an electron is ejected from one of the inner shells. This ejected electron, the photo-electron, has an energy of E — Es, where E is the energy of the incident photon, and Es is the binding energy of the shell that the electron has been ejected from. The photon has an -80% P(z) = 1 - e x p ( - A z ) (3.11) 17 Table 3.2: Chance for absorption in 30//m of G a A s of a K Q X - R a y from the elements used in this work. Element C u R b M o A g B a T b ' K a X - R a y energy (keV)[25] 8.047 13.394 17.489 22.162 32.19 44.17 Linear photo-electric absorption coefficient, 352.95 649.11 320.32 166.93 58.54 23.02 A (1/cm) Chance of absorption 0.653 .857 .617 .394 .161 .067 chance of ejecting an electron from the inner-most, or K , shell and -19% chance of exciting an electron from the next higher shell, the L shell[26]. The angular distribution of the photoelectrons depends on the velocity, v, of the electron relative to the speed of light, c. If 3 = vI'c, then the non-relativistic Born approximation gives the partial cross section for an electron to be ejected in a direction given by 9 and <fi as [27] (3.12) (l- /?cos(0)) 4 where 9 is the angle between the polarization of the incident photon and the direction of travel of the incident photon, and <p is the angle between the direction of travel of the incident photon and the ejected photo-electron. For a non-polarized beam of photons, the angle 9 is random, so the angular distr ibution can be treated as being independent of 9. Figure 3.8 shows the angular distributions in <p, wi th 9 = 0, for a photo-electron ejected wi th small energy (3 = 0) and for a photo-electron wi th E = 50 keV (3 = 0.414). The excited atom can relax to its ground state in two ways. The first is for an electron from an outer shell to take the place of the ejected electron, emitt ing an X - R a y of energy Es — E0, where E0 is the energy of the outer shell involved in the process. This X - R a y is 18 Figure 3.8: The angular distribution in <j> (with 6 = 0) of ejected photoelectrons for /3 = 0 and for j3 = 0.414, normalized so that the maximum probability is 1. called a secondary X-Ray . The second method is an Auger process, in which an electron "falls" from an outer shell into the vacancy in the K-shel l , ejecting another outer shell electron of energy E — E0 in the process [28]. The ratio of secondary X - R a y s to Auger electrons emitted by a given atom is independent of the energy of the incident X - R a y and is called the fluorescent yield. For G a and A s , the fluorescent yields for the K-shel l are [29]. G a - 50.7% A s - 56.2% 19 3 .4 C r e a t i o n o f e l e c t r o n - h o l e p a i r s The photo-electron and the secondary electron created in the photo-electric interaction lose their energy through multiple scattering interactions, creating a large number of electron-hole pairs (see section 3.5). These other electron-hole pairs also scatter and create more e.h.p.s. The process continues unti l the energy of the ionized electron-hole pairs is a few eV. These low energy electron-hole pairs are unable to cause further ion- ization, but instead lose energy to lattice vibrations, eventually cooling down to ambient temperature. The average number of electron-hole pairs, N e h p , created in this cascade of electrons by an electron of energy E can be described by the ratio w = E/Ne^p. The accepted value of w for G a A s is 4.2 eV/e.h.p.[14]. That is, on average it takes 4.2 eV to create a relatively long-lived electron-hole-pair in G a A s . The creation of electron-hole pairs is a statistical process, so the number of electron hole pairs created by an electron of energy E w i l l not be constant. The variance in N e h p is proportional to N eh p[30]. The constant of proportionality, called the Fano factor, is a function of the material wi th in which the electron interacts. The Fano factor, / , for G a A s as room temperature is quoted as being < 0.18[31]. If none of the energy of an incident photon of energy E escaped from the detector, then the number of electrons seen by the detector would be a Gaussian distribution around a number of electrons -/Vehp = wE. The variance of this distribution would be a2 = / i V e h p . The X-Rays used in this study had energies from -10 keV to -60 keV, 20 corresponding to the creation of -2300 - -14 000 electron-hole pairs. Using a Fano factor of / = 0.18, this gives Gaussian line-widths, 2cr, of -41 and -100 e.h.p.s, respectively. 3 .5 I n t e r a c t i o n s o f e l e c t r o n s i n G a A s The photo-electrons and Auger electrons created by the incident X - R a y have energies from -1 keV to -50 keV. These electrons interact wi th the electrons and nucleus of the G a A s through many different processes. Elastic interactions occur between the electron and the partially shielded nucleus of the solid's atoms. Slow secondary electrons can be created through interactions wi th loosely bound conduction electrons in the solid. Faster secondary electrons can also be created through this method, or by interactions with the inner shell electrons of the solid. Another type of interaction, plasmon scattering, occurs when the Coulomb field of the incident electron disturbs the long range correlation in the Coulomb field of the conduction band electrons, exciting collective oscillations of these electrons, called plasmons. A l l of these interactions are included in the phenomenological "continuous energy loss approximation" of Bethe[32]. This gives the energy loss of an electron per distance traveled, dE/dx, in a material wi th atomic number Z, density p and atomic mass A as (3.13) 21 where E is the energy of the electron and J is defined as the average energy lost in an interaction. A n expression for J is given by Berger and Seltzer as[32] J = (9.76Z + 5 8 . 5 Z - 1 1 9 ) 1 0 - 3 keV (3.14) B y integrating dx/dE from (3.13) from the in i t ia l energy of the electron, E, to 0, one can find the mean distance traveled by an electron of energy E in G a A s . This distance is the mean distance the electron would travel i f it did not change its direction of travel through the interactions. The actual displacement of the electron from its starting position wi l l be much less, because of the many scatterings the electron undergoes. Figure 3.9 shows a plot of electron path length, from integrating (3.13), as a function of energy for electrons in Ge. The calculation was done for Ge because its atomic number (Z = 32) is in-between that of G a and As (Z = 31 and Z = 33), and its density is the same as G a A s . 3.6 E s c a p e o f p a r t i c l e s f r o m t h e d e t e c t o r Not a l l of the energy of the photon is always absorbed by the detector. This is because the detector has a finite volume, so some of the electrons and photons created in the active region may escape. If we look at the distribution of the number of electrons deposited in a detector for an ensemble of incident photons of equal energy, then the escape of particles w i l l affect the shape of this distribution[34]. This escape of energy can occur through a number of different processes. Either a secondary X - R a y , the photo-electron or an Auger electron can escape from the device. 22 0 5 10 15 20 25 30 35 40 45 50 Energy(keV) Figure 3.9: The mean path length of an electron in Ge, calculated using the continuous energy loss approximation of Bethe. When recording the number of electrons, N, collected in a pixel of the C C D due to the absorption of an incident X - R a y of energy E, events where no particles escape wi l l result in a peak at TV = E/w. When an X - R a y escapes, al l of the energy of the X - R a y escapes the detector. The escape of X - R a y s of energy Es w i l l result in a second peak at N = (E — Es)/w. In contrast, the escape of an electron does not always result in the same energy loss; the loss depends on how far the electron has traveled before it leaves the detector. The energy lost ranges from zero (the electron never leaves the detector) to the total energy of the photo or Auger electron (the electron is created right at the edge of the detector and escapes right away). The distribution of the number of electrons deposited in the detector due to electron escape processes wi l l therefore have a ta i l at lower N . The shape of this ta i l depends on the geometry of the detector, the angle at 23 which the photons are incident upon the detector, and the material of which the detector is made (see section 6.5.2 for further discussion). Chapter 4 Electron Transport 4.1 Introduction Figure 4.10 shows a time-line of the creation and collection of electron hole pairs in the C C D . The ini t ia l interaction between the photon and solid (Figure 4.10-a) and the creation of electron hole pairs (Figure 4.10-b) were discussed in sections 3.2 and 3.5. This chapter wi l l discuss the transport of the e.h.p.s after the in i t ia l distribution has been created (Figure 4.10-c and -d). For the purpose of this discussion, two different regimes wi l l be studied: that where a l l of the e.h.p.s were created in the depletion region, and that where al l the e.h.p.s were created in the field-free region. The high energy photo-electron created by an incident X - R a y wi l l leave a high density track of electron hole pairs in its wake. A t first, the electron-hole pairs w i l l spread by ambi-polar diffusion (Figure 4.10-c). Wha t happens next w i l l depend on whether the charge was deposited in the field-free or depletion region. If the charge is in the field-free region, the charge wi l l continue to diffuse unti l it enters the depletion region, recombines or is trapped. If, however, the charge is in the depletion region, then after -400 ps the field w i l l fully penetrate the charge distribution and the electrons and holes wi l l start 24 25 to drift towards the top and bottom of the C C D , respectively (Figure 4.10-d). It takes -100 ps for the electrons to drift to the top of the C C D from the bottom of the depleted region. A t this point, the electrons become trapped in one of the pixels and they wi l l then be moved towards the output of the C C D , pixel by pixel . The discussion above makes a simplification: it assumes that the high-energy electron moves in a straight line through the C C D . This , of course, is not what w i l l happen. The electron wi l l be scattered by numerous collisions during its travel. The effects of this scattering on the shape of the distribution were modelled by a Monte Carlo simulation, which is discussed in section 6.5.2. For now, the simplified picture of the electron moving in a straight line is adequate. 4.2 Electrostatic fields in the C C D The vertical fields in the C C D w i l l be zero except for in the depleted regions near the p + - p _ , p _ - n and n-Cermet junctions. The field that electrons wi l l drift in is created by the p _ - n junction (see Figure 2.4). W i t h a bias on the substrate of -7 V , the depleted region is 11 tim deep. The field w i l l increase linearly from the zero at the bottom of the depletion region, to a maximum field of Emax = 1.5 x 104 V / c m at the p ~ - n junction and w i l l then decrease rapidly (within 1 /mi) to zero field. 26 (a) (b) The X-Ray enters the CCD and interacts with an atom of the GaAs substrate via the photo-electric effect. Straight lines represent electrons while curved lines represent X-Rays. The electron hole pair distribution is created by the photo-electron and either a secondary photon or an Auger electron. The e.h.p. distribution spreads by ambipolar diffusion until the concentration is low enough so that the drift field can act upon it. The electrons drift towards the wells in the drift field, while the holes drift in the opposite direction. (e) The electrons are fully collected underneath the well Figure 4.10: A time-line of the creation and collection of electron hole pairs in the C C D 27 4 . 3 I n i t i a l d i s t r i b u t i o n o f e . h . p . s When the electron-hole pairs created by the incident X - R a y have al l cooled down to room temperature, to a good approximation they are distributed in a Gaussian cylinder wi th a radius of a = -0.1 / im along the path of the photo-electron that created them[35]. The density of the electron-hole pairs in the cylinder is approximately Gaussian in the radial direction outward from the axis of the cylinder. The density of e.h.p.s per unit length, i V 0 , can be found by dividing the energy loss of the electron per unit length, dE/dx, (equation (3.13)) by the average energy needed to create an electron-hole pair in G a A s , w = 4.2 eV. The number of e.h.p.s created in 1 / im by a 30 keV electron in G a A s is 685. The density of e.h.p.s along the axis of the cylinder of charge created by this electron is 1.1 x 10 1 6 c m - 3 (from equation (4.16)). Figure 4.11 shows a plot of N0 as a function of x. A s the energy of the electron gets lower, the linear density of e.h.p.s increases, unti l the last 10 keV of energy is deposited in 1 / im. This last micron of charge is so much denser than the rest that a better model of the charge distr ibution is a -0.1 / /m thick Gaussian cylindrical ta i l wi th a length dependent on the in i t ia l energy of the photo-electron, followed by a Gaussian bal l of charge roughly 0.25 / im in radius. If the photo-electron has an in i t ia l energy of less than 10 keV, then there w i l l be no ta i l . A simplified picture for the electron motion assumes that the e.h.p.s effectively screen the interior of the distribution from the applied field when the e.h.p. density exceeds the background doping density of the G a A s , - 1 0 1 4 c m - 3 in our case. Electrons and 28 5000 Tail Region Ball Region 4500 (- 4000 3500 1 3000 q- 2500 4 2000 2 1500 1000 500 0 2000 1800 1600 1400 1 1200 - 1000 £ - 800 600 400 200 0 10 15 x(|im) 20 25 Figure 4.11: The linear e.h.p. density (N0) and the time (t) required for the in i t ia l distribution to diffuse to an on-axis density of 10 1 4 c m - 3 for a 60 keV photo-electron as a function of the distance traveled by the photo-electron. holes outside of the radius of penetration of the field w i l l be swept towards the top and bottom of the C C D , respectively. Electrons and holes inside of the radius of penetration wi l l undergo ambipolar diffusion. The speed of the diffusion is given by the ambipolar diffusion constant, DAp, which is related to the electron and hole diffusion constants, Dn and Dp, in the l imi t where the electron and hole concentrations are much greater than the donor or acceptor density, by [36] _ 2DnDp Dn + Dp (4.15) For G a A s , Dn and Dp for an electron or hole density of 10 1 6 cm 3 are 222 c m 2 / s and 10.4 c m 2 / s , respectively[21]. This gives an ambipolar diffusion constant of D a p = 29 19.8 c m 2 / s . For the track section of the e.h.p. distribution, the electron-hole pair den- sity, Pehp,cyi(?~, t) at a radius r and time t is found by solving the diffusion equation in a cylindrical co-ordinate system to get N • Peh P ,cyi(r , t) = °£ e x p [ - r 2 / ( 2 a 0 2 + ADapt)] (4.16) ( ! + ^ f ) where NaxiS is the on-axis density of the e.h.p. track at t = 0, and o0 is the in i t ia l radius of the distribution, 0.1 fim. Naxis is related to the linear density of e.h.p.s, 7V0, by Naxis = - \ (4.17) The time for the distribution to diffuse wi l l be the largest at the point where the ta i l of the distribution enters the ball . A t this point, the linear e.h.p. density is -1000 e.h.p./p:m. The distribution wi l l diffuse to an on-axis density of 10 1 4 c m - 3 after -400 ps, and wi l l have a width of -1.25 /zm at this time. The e.h.p. density in the ball section of the distribution is found by solving the diffusion problem in a spherical co-ordinate system. The solution is Peh P ) baii(r , t) = M | J a p t ^ / 9 e x p [ - r 2 / ( 2 a 2 + ADapt)} (4.18) In this case, -/V0 is the concentration of e.h.p.s at r = 0 and t = 0, and a0 = 0.25p:m. Solving this equation, it was found that the distribution would take -320 ps to diffuse to the background density, and the width of the distribution at this time is -1 um. Although a very simplified model has been assumed, we can conclude that the time taken for the applied field to start impart ing a drift velocity on the electron cloud is on 30 the order of a few hundred picoseconds. 4 . 4 D r i f t o f e l e c t r o n s Once the electric field has penetrated to the centre of the electron track, al l of the electrons drift towards the top of the C C D , while the holes drift towards the substrate. The electrons move at a speed Vdrift = PeE, where jj,e is the mobil i ty of the electrons and E is the electric field acting on them. When the voltage applied to the substrate is -7 V , the depleted region is xj = 11 /zm deep, and the maximum field, Emax, is 15 k V / c m . This field is larger than the saturation field of G a A s , so / / e w i l l not be constant. Using the values of vdrift as a function of drift field, E, found by R u t h and Kino[37], the drift time across the depleted region,t d rift, was found by tdrift was found for the values for the fields and drift depths given in section 4.2. Because the field is zero at x = 0, and no diffusion was incorporated in this simple model, the drift t ime is highly dependent on the value for XQ. For XQ = 0.1 /mi , tdrift = 96 ps. For x0 = 1 ^ m , tdrift — 74 ps. These times are of the same order as the time for the ini t ia l distribution to diffuse to a point where the field can penetrate the distribution. The electrons created by an X - R a y w i l l not necessarily a l l drift into the same pixel. If we ignore the diffusion of the electrons created in the charge column, then each pixel w i l l collect a l l the charge that is created in a 20 /mi region (the length of a pixel) directly (4.19) 31 below it. If the line of charge is created below two pixels, then two pixels w i l l have charge drift into them. This is called charge sharing. To make an estimate of the amount of charge sharing in the device due to the length of the ini t ia l charge distribution, the scattering of the electron must be taken into account. This is done using a Monte Carlo simulation and discussed in section 6.5.2. A second k ind of charge sharing can occur i f a large charge is introduced into the C C D . Too many electrons can affect the potential in the pixels under the C C D , effec- tively making the wells shallower for additional electrons. If enough charge is added, the electrons wi l l spi l l over into neighbouring pixels. Addit ional ly, al l of the charge in a pixel may not be transferred to an adjacent pixel during the charge transfer process i f the charge in the pixel is large. This second k ind of charge sharing is much more noticeable with the C C D s used in this study than charge sharing caused by the length of the in i t ia l electron distribution (see section 6.9). 4 . 5 E l e c t r o n s c r e a t e d i n t h e field-free r e g i o n Electrons and holes created in the field free region w i l l not have an electric field to drift in , but instead w i l l only diffuse outward unt i l they either enter the depletion region, recombine or become trapped. A calculation was made of the time it would take for charge to diffuse from the field- free region to the depletion region. This calculation is, in general, quite complicated, so a number of simplifications were made. First , it was assumed that the field-free region was 32 infinitely deep. This avoids complications arising from electrons pi l ing up at the field-free - substrate interface. Recombination was ignored, even though it wi l l be a large factor considering the time-scales involved (see section 4.6). Final ly , only the bal l section of the e.h.p. distribution was considered. Using these assumptions, the time it would take for a percentage of the bal l of charge to diffuse to the depletion region was calculated. A t most half of the charge wi l l be collected, as the other half w i l l diffuse in the opposite direction. The Gaussian half width, a, of the bal l as a function of time, t, is The fraction of charge, F, from a ball deposited at a in i t ia l distance d from the depletion region, which has travelled into the depletion region by time t is given by where Erf(x) is the error function. Figure 4.12 shows F as a function of time for four different deposition depths, d, of the charge bal l . The effects of these e.h.p.s on the spectra seen by the C C D are discussed in section 6.6. (4.20) F = 1/2(1 - Erf(d/tr(r))) (4.21) 33 40 60 Time(us) 100 Figure 4.12: The fraction of the total charge of the bal l that has diffused into the deple- tion region as a function of time for d = 1,5,10 and 15 jj,m. The curves approach 0.5 asymptotically as at most half of the total charge wi l l diffuse into the depletion region. 4 . 6 R e c o m b i n a t i o n According to Nelson and Sobers [38], the radiative recombination lifetime Tra& of an elec- tron in G a A s with an equil ibrium electron and hole concentration of n 0 and p0, respec- tively, is Trad B(n0 +po + A n ) (4.22) where A n is the concentration of excess electron hole pairs and B is the radiative re- combination coefficient. Nelson and Sobers found B to be 3 . 7 x l 0 - 1 0 c m 3 / s . There are two different densities at which recombination could in principle be important. The first corresponds to the in i t ia l diffusion of the distribution from its in i t ia l density of A n ~10 1 6 c m - 3 to the background density, and the second corresponds to the diffusion of 34 e.h.p.s in the field-free region wi th A n ~ 1 0 1 4 c m - 3 . For an excess electron population of 10 1 6 c m - 3 in G a A s doped at N A = 10 1 4 c m - 3 , Trad = 250 ns. This time is large com- pared to the time for the electron-hole pairs to diffuse from their in i t ia l distribution to the background hole concentration, so recombination should not be a factor during the ambipolar diffusion of the in i t ia l distribution of the e.h.p.s or the drift of the e.h.ps in the depletion region. The radiative recombination lifetime for e.h.p.s at a concentration of A n = 10 1 4 c m - 3 in the field free region is -14 ps. A s discussed in section 4.5, this is small compared to the diffusion time for the e.h.p.s created at depths greated than 11 pm in the device (see figure 4.12). Recombination wi l l therefore be a large factor for e.h.p.s created in the field-free region. 4 . 7 S u m m a r y o f t r a n s p o r t p r o c e s s e s The important length scale in the C C D is the pixel pitch of 20 pm. If the bal l of charge is deposited in the drift region, then it wi l l have a width of o ~ 1.5 pm, which is not significant compared to the pixel width. If however, the bal l is deposited in the field-free region, then it wi l l have a width of up to a few pixel lengths by the time an appreciable fraction of the charge in the bal l enters the depletion region. There are three important time-scales in the C C D . The first is the clock period of 0.1 ps. The second is the frequency of X - R a y events in the C C D of -1 Hz . The thi rd is the radiative recombination lifetime of electron-hole pairs, ranging from 250 ns at an e.h.p. concentration of 10 1 6 c m - 3 to 14 ps at an e.h.p. concentration of 10 1 4 c m - 3 . If the e.h.p.s 35 are deposited in the depletion region, they wi l l be quickly swept into the well of the C C D and then transported to the output. This w i l l a l l occur within -500 ps, much smaller than all of the relevant time-scales. If, on the other hand, the e.h.p.s are deposited in the field- free region, there wi l l be a period of diffusion before any of the electrons encounter the drift field. These diffusion times of -100 ps are long compared to both the clock period and the recombination lifetimes, but are s t i l l smaller than the X - R a y event frequency. Because the diffusion times are large compared to the recombination times, the charge that w i l l make it to the wells of the C C D w i l l be greatly reduced. Because the diffusion times are large compared to the C C D clock's period, the charge that does make it to the well w i l l be spread over hundreds of pixels. These two factors make it unlikely that any charge that is deposited at any depth larger than a micron in the field-free region wi l l contribute to the spectra in the C C D . Chapter 5 Experiment 5.1 Experimental Setup The C C D is run at room temperature at a frequency of 10 M H z , with a substrate voltage of -7 V . This substrate voltage was chosen as it was the largest that was believed to be usable without harming the C C D . The output of the C C D with no input signal consisted of a square wave centred around zero volts wi th a peak to peak voltage of 620 m V . The frequency of the pulses was the same as the input clock, 10 M H z . The area of each pulse above a threshold represented a signal proportional to the charge transferred out of the last pixel of the C C D . The output of the C C D was sent to a Tektronix D S A 602 digital sampling oscilloscope. Da ta was acquired using a Personal Computer that was connected to the oscilloscope by means of an I E E E 488 interface. The computer set the trigger level on the oscilloscope using an algorithm described below, waited for a number of traces to be read into the oscilloscope's memory, and then down-loaded the traces off of the oscilloscope. The trigger level on the oscilloscope was then reset, and the whole process repeated. The oscilloscope's voltage settings were set to 5 m V / d i v i s i o n , and the time scale was 36 37 800 1200 Time(ns) Figure 5.13: A typical oscilloscope trace for an event triggered by a 44 keV X-Ray from a Tb foil. There are 20 peaks shown in the trace, and the signal peak is the 11th peak shown. Peaks 1 and 22 from the original trace were trimmed off by the analysis software. set to 50 nS/div. The voltage was offset so that only the bottom of the C C D waveform was viewed. This is because the peak-to-peak voltage of the waveform was 620 mV, and a typical signal ranged from 5 mV to 45 mV for the 10-60 keV X-Rays used in this study. A l l of the analysis was done with a more negative voltage denoting a larger signal on the C C D . The trigger point was set so that exactly 22 pulses showed on each trace. Figure 5.13 shows a typical oscilloscope trace triggered by a 44 keV K Q X-Ray from Tb. The trigger level of the oscilloscope had to be carefully set for a number of related reasons. First, the event rate (-1 Hz) was much smaller than the clock rate of the C C D (10 MHz). Secondly, the peak to peak voltage of the C C D output drifted appreciably during the two to six hours needed to sample 20,000 events. Thirdly, the size of the 38 signals on the C C D (5 - 45 mV) was much smaller than the peak to peak voltage of the CCD's output waveform (620 mV). Putting all these factors together meant that the trigger level had to be above the level of the CCD's output when there were no events, but not so high as to discriminate against low energy events. The trigger level also had to be high enough to avoid falling into the noise if the CCD's output drifted higher, and was therefore reset periodically to take into account the drift. The trigger level was determined by first setting it low enough that the oscilloscope would be triggered on every pulse from the C C D . A n envelope of 512 scope traces was taken. This envelope showed the range of the voltages for each point on the oscilloscope over the 512 traces that were taken. Because the rate of the C C D was much larger than the rate of events from the sources, this gave an envelope of the pulses from the C C D without any events. The maximum height of each peak on the trace was found, and these maxima were averaged. By using this average, a measure of the top of the C C D waveform was found. A n offset, either positive or negative, was then added onto this average. The offset was chosen so that the maximum trigger rate was achieved without triggering off of non-event peaks (see section 6.2). The offset also had to be large enough that any drift of the CCD's output levels would not cause the oscilloscope to trigger off of every pulse from the C C D . The trigger level of the oscilloscope was then set to the result. After the trigger level was set, the oscilloscope was instructed to take 900 readings (the maximum number of traces that it could hold in memory at the resolution used was 39 912). After the readings were done, the traces were loaded into the computer, the trigger level was reset using the same procedure as above, and the process was repeated. The resetting of the trigger level was done to reduce the effects of drift in the absolute C C D voltage level. The time between settings of the trigger varied from 2 minutes to 25 minutes depending on the event rate, and hence on the X-Ray source used to irradiate the C C D . 5.2 Analysis of oscilloscope traces Each individual oscilloscope trace was analyzed to find the charge deposited in the C C D , as represented by that trace. The first and last peak were discarded, leaving twenty pulses to analyze. The charge of each peak was found by integrating the voltage over the whole peak. Each peak was denoted as either being part of the signal or part of the background. The time-base on the oscilloscope was set so that peak 12 was the peak that triggered the oscilloscope. Because of this, Peak 12 was defined as the central signal peak, and a number of peaks on either side of it could also be considered as signal peaks. If the number of signal peaks, N s i g n a i , was chosen to be 5, then peaks 10-14 were considered signal peaks. The peaks that were not signal peaks were considered background peaks. The background level was found by finding the average charge of the background peaks. The net signal contained in a trace was found by summing the charge of the signal peaks, and then subtracting the background. Problems in the above algorithm occurred when any of the peaks in the trace went off 40 the screen of the oscilloscope. A 7-bit number was used to store the position of each point on an oscilloscope trace, with the top of the screen set to read 127 and the bottom of the screen 0. When the peak went off the top of the screen, the 8-bit number "rolled-over", becoming a large negative number. This caused the peak finding routine to find spurious peaks, which, in turn, caused the traces in the rest of the file to be read improperly. To avoid this problem, any traces that had peaks within 5 units of the top of the screen were discarded, with 128 units being the full extent of the screen. The final step in the analysis was to create a histogram of the charges deposited in the C C D . The bin size of the histogram was set to five charge units (C.U.), with the scale of the histogram going from 0 C .U. to 2000 C .U. The charge unit scale is essentially arbitrary, and should only be used to compare different spectrum on the same C C D , obtained using the same system parameters. 5.2.1 The Choice of N s i g n a l The choice of N s i g n a i can have a large effect on the shape of the spectrum found by the C C D . Figure 5.14 shows the the spectrum from the characteristic X-Rays of Tb analyzed from the same raw data using N s i g n a i = 3,5,7 and 9. The reduced data was fit to three peaks, labelled peak 1, peak 2 and peak 3, whose parameters are shown in table 5.3. If the charge in a single event were contained in one pixel of the CCD's output, changing Nsignai would have little effect on the shape of the spectra. In fact, if the number of pixels that contain charge from an event is N C h a r g e d , then for N s i g n a l > N c h a r g e d > there should be 41 Table 5.3: The area (A), width (w) and position (x) of the first and third peaks for Tb data analyzed with N s i g n a i = 3, 5, 7 and 9. The areas are expressed in units of 1000 Charge Units counts. The ratio between the area of the first and third peaks and the resolution of the third peak are also shown First Peak Third Peak ^signal A x w A x w ratio Resolution (CU. ) (CU. ) (CU. ) (CU. ) (%) (keV) 3 21 662 269 37 1051 214 57 12.4 5 40 790 481 129 1090 226 31 13.0 7 9.6 744 281 47 1156 239 20 13.8 9 9.8 810 305 48 1206 257 20 14.8 no change in the signal charge calculated by the analysis program. The change in the shape of the spectra from N S j g n a i = 3 to N S i g n a i = 5 is quite large, and the change for Nsignai larger than 5 is much smaller. This suggests that the charge in a signal from a Tb X-Ray is contained in at most five pixels, and that some events have more than three pixels with charge in them. The data was analyzed with N s j g n a i = 5, a choice that was a trade-off between the decrease in resolution as N S j g n a i was increased and the increase of the area of peak 1 as N s i g n a i was decreased. 5.3 Tests with known input pulses This experiment studied the relationship between the charge deposited in the C C D and the number of charge units found by the analysis of the oscilloscope traces. A known input pulse was applied to the first gate finger of the C C D , in order to introduce a charge into the active layer under the first pixel. The charge pulses were 4 ns wide, and ranged 42 160 140 % 100 g. 80 c D 0 0 60 40 20 0 i r~. 1 1 r Data — Fit •••••••• Peaki 1 Peak 2 — Peak 3 — 200 400 600 800 1000120014001600 Charge units (C.U.) 600 500 o | 400 E 1300 8 200 o 100 0 180 160 140 o | 120 £ 100 CD w 80 o 60 0 40 20 0 (b) Data Fit Peaki Peak 2 Peak 3 0 200 400 600 800 1000120014001600 Charge units (C.U.) 1 1 1 1 1 1 — — j' • Data — lift Fit § ! | Peaki | [ / ! P e a k 2 — | ; I Peak 3 — | | I 1 ; 200 400 600 800 1000120014001600 Charge units (C.U.) 0 200 400 600 800 1000120014001600 Charge units (C.U.) Figure 5.14: The spectra of Tb X-Rays analyzed with N s i g n a l = 3, 5, 7 and 9 shown in figures (a), (b), (c) and (d) respectively. 43 450 0 200 400 600 800 1 0 0 0 1 2 0 0 1 4 0 0 1600 Charge units (C.U.) Figure 5.15: A histogram of the count rate for a 31mV input pulse from 0 mV to 44 mV in height. The signals were then analyzed as described above, and histograms for each input voltage were made. A histogram for an input voltage of 31 mV is shown in Figure 5.15. The histograms were then fitted to Gaussians with an area A , position x0 and width, w = 2a, where a is the half-width of the Gaussian. A plot of the charge units deposited in the C C D as a function of the input voltage is shown in figure 5.16. A 2nd order, concave up polynomial fit was made to the data. It is not known whether or not this non-linearity arises from the input or the output, but the linearity of the charge deposited in the C C D as a function of X-Ray energy (see section 6.3.1) points to the input as the source of the non-linearities. 44 1400 r 1200 - b 1000 - o m 800 - 'E CD 600 - D) CO JC O 400 - 200 - 0 - 0 5 10 15 20 25 30 35 40 45 Input voltage (mV) Figure 5.16: The charge deposited in CCD2 by a known input pulse as a function of the height of the pulses, analyzed with N S j g n a i = 5. The error bars are the Gaussian widths of the peaks. The fitting equation of Q in Charge Units as a function of the input voltage V is Q = 214 C U . + 3.7 V + 0.47 V 2 The resolution of the detector at each input voltage is found by AE R E (5.23) where AE is the width, 2a, of the Gaussian fit to the peaks on the histogram, and E is the position of the maximum of the Gaussian, x0, on the histogram. A plot of the resolution of the C C D as a function of the position of the peak is shown in figure 5.17 for the known input pulses. A linear fit was made to the plot of log(i?) as a function of the Log of the peak position, log(P). Raising each side to the power of 10 gives the power relation between R and P (with P expressed in C U . ) of R = 9 6 P - 0 8 9 (5.24) 45 data ° Fit - - 1000 Charge Units Figure 5.17: The resolution of the charge deposited in CCD2 by a known input pulse as a function of the height of the pulses. The data was analyzed with N s i g n a i = 5. Assuming the charge injected into the C C D is constant for a given input voltage, equa- tion (5.24) gives the maximum resolution of the C C D under the operating conditions. 5 . 4 R e s p o n s e o f t h e d e t e c t o r t o C h a r a c t e r i s t i c X - R a y s The response of the detector to the characteristic X-Rays from six elements was studied. A schematic diagram of the source used to create these X-Rays is shown in figure 5.18. The X-Rays from an 2 4 1 A m source were shone on a foil of one of six different elements. The element then emitted its characteristic X-Rays. The six elements used were (in order of increasing K a X-Ray energy) Cu, Rb, Mo, Ag, Ba and Tb. The energies of the Ka X-Rays of these elements range from 8.047 keV for Cu to 44.47 keV for Tb. Table 5.4 shows a listing of the K Q energies for all six elements[25]. The source was shone on the c o o CO CD rr 46 Table 5.4: The Ka energies of the elements used in this study Element Cu Rb Mo Ag Ba Tb K Q X-Ray Energy (keV)[25] 8.047 13.394 17.489 22.162 32.19 44.17 A i Aluminum shielding Am Figure 5.18: A schematic of the source used to create characteristic X-Rays. The 2 4 1 A m is an annulus. X-Rays emitted by the 2 4 1 A m are absorbed by the foil, and the foil emits a characteristic X-Ray. Any X-Rays emitted by the 2 4 1 A m that do not strike the foil will be absorbed by the Aluminum shielding. C C D from the top. The C C D was covered with a ceramic lid, which had a hole milled in it to allow the X-Rays to impinge on the C C D . The hole was covered with electrical tape to prevent ambient light from shining on the C C D . Figure 5.19 shows a schematic of the setup used to study characteristic X-Rays. Tests with the single X-Ray energy source were done with two different CCDs that will be referred to as CCD1 and CCD2. A run of 20,000 events was taken with each of the X-Ray energies. Figure 5.20 shows the spectrum for Mo K a X-Rays on CCD1 and 4 7 CCD Chip CCD Card DSA 602 digital ^ sampling oscil loscope CCD Output Ceramic Lid Electrician's Tape Waveforms that triggered events Emitted <X-Ray IBM PC Source Figure 5 .19 : A schematic of the experimental setup used to study the X-Ray spectra. C C D 2 . Figure 5 .21 shows the spectrum for Tb K Q X-Rays on C C D 2 . A l l the histograms were made with N S i g n a j = 5. 5.5 T h e 2 4 1 A m s p e c t r u m The response of the detector to the X-Rays emitted by an 2 4 1 A m source was also studied. The X-Rays were shone on the top of the C C D , and a run of 72 0 0 0 counts was taken. Figure 5 .22 shows the histogram of the 2 4 1 A m spectrum found using C C D 2 analyzed with Nsignai = 5 and 7 . The two values of N s i g n a i were used to make sure that the increased energies in the 2 4 1 A m spectrum did not create charge sharing among more than five pixels, thereby increasing the value needed for N S i g n a i - The change in the relative intensities of the peaks was not large, so N s i g n a i did not need to be increased. 48 1000 900 800 | 700 | 600 1500 I 400 D 5 300 200 100 0 ~I J ! i T" (a) 0 200 400 600 800 1000120014001600 Charge units (CU.) 0 200 400 600 800 1000120014001600 Charge units (CU.) Figure 5.20: The charge deposited in (a)CCDl and (b)CCD2 by the characteristic X-Rays of Mo, analyzed with N s i g n a i = 5. 600 200 400 600 800 10001200 14001600 Charge units ( C U . ) Figure 5.21: The charge deposited in CCD2 by the characteristic X-Rays of Tb, analyzed with N s ig n a i = 5. 49 0 200 400 600 800 10001200 14001600 0 200 400 600 800 1000120014001600 Charge units (C.U.) Charge units (C.U.) Figure 5.22: The charge deposited in C C D 1 by X-Rays from an 2 4 1 A m source, analyzed with N s i g n a i = (a) 5 and (b)7. Chapter 6 Results and Discussion 6.1 Overview The histograms resulting from the known input pulse studies resulted in single peaks with Gaussian profiles. The histograms for the characteristic X-Rays were not as simple. The histograms for CCD1 all showed at least two peaks. The peak at the low end of the scale stayed at the same position for all the X-Ray energies. This peak, denoted the noise peak, was assumed to arise from events that were caused by triggers due to random noise in the CCD's waveform, rather than triggers from actual events in the C C D . The histograms for Rb, Mo and Ag showed a second peak that, as will be shown in this chapter, varied linearly in position as the energy of the incident X-Ray was changed. This peak was therefore denoted the signal peak. A broad peak at high energies was also evident. It was not considered to be an artifact of the triggering, but instead a result of some higher energy X-Rays being released by the source (see section 6.4). It was called the high energy peak. For the Ba and Tb runs on CCD1, the picture was still more complicated. The noise peak was still evident, but in these cases there were two peaks whose position varied linearly with energy. In section 6.5.1 we present evidence that the 50 51 second, lower energy signal peak arises from the escape of secondary X-Rays from the C C D (see section 6.5.2). This second, lower energy peak was therefore denoted the escape peak. The histogram for the Tb X-Ray showed yet another peak, tentatively identified as the field-free peak (see section 4.5) resulting from The escape of photo-electrons from the depletion region of the C C D . 6.2 The Noise Peak A l l of the histograms for CCD1 showed at least two peaks. The peak at the low end of the scale stayed at the same position for all the X-Ray energies. This peak was assumed to arise from events that were caused by triggers due to random noise in the CCD's waveform, rather than triggers from actual events in the C C D . Figure 6.23 shows the spectrum of Ag for CCD1 and CCD2. The runs with CCD2 show no evidence of the noise peak. This is because the noise levels in the C C D waveform in CCD2 were larger, causing the trigger level to be raised much higher in the CCD2 runs than the CCD1 runs. This change in the trigger level could have been large enough to avoid any triggers in the C C D waveform, causing the loss of the noise peak in the spectra. A second set of runs for CCD2 was also run with the trigger level set lower. A small noise peak is evident in the Rb and Ba runs, showing that the noise peak is present on CCD2, with its strength depending on the setting of the trigger level. Table 6.5 shows the peak positions and widths for the noise peaks of the K Q spectra obtained with CCD1. 52 0 200 400 600 800 1000120014001600 0 200 400 600 800 1000120014001600 Charge units (C.U.) Charge units (C.U.) Figure 6.23: The spectra for the K Q X-Rays from Ag on (a)CCDl and (b)CCD2. The spectrum for CCD1 shows the noise peak, while that for CCD2 doesn't. Table 6.5: The peak positions (x), areas (A) and widths (w) of the noise peaks in the spectra arising from characteristic X-Rays impinging on CCD1 analyzed with N S i g n a i = 5. The areas are in units of 1000 Charge Unit Counts, while x and w are expressed in Charge Units. Element A X w Rb 51 172 111 Mo 68 161 99 Ag 40 207 131 Ba 25 200 142 Tb 26 160 89 53 1 8 0 0 Charge units (CU.) Figure 6.24: The signal peaks, indicated by arrows, for the K Q X-Rays of Rb, Mo and Ag on CCD2. The spectra have been scaled vertically to make comparison easier. The higher energy feature, which is present in all the spectra but most prominent for the Rb spectrum, is discussed in section 6.4. 6 .3 T h e S i g n a l P e a k The signal peak was, as expected, evident in all the spectra. Figure 6.24 shows the signal peaks for the K Q X-Rays of Rb, Mo and Ag incident on CCD2. The positions of the signal peaks, as is shown below, vary linearly with the energy of the incident X-Ray. 6 . 3 . 1 C a l i b r a t i o n o f t h e C C D E n e r g y S c a l e The positions of the signal peaks for the known energy X-Rays were used to calibrate the energy scale of the C C D . Plots of signal peak position in charge units as a function of incident X-Ray energy were made for the runs on CCD1 and CCD2 with N s i g n a i = 5. The plots are shown in figure 6.25, and the positions are tabulated in Table 6.6. The plots 54 900 800 ^ 700 p ^600 c o 2 500 w o £ 400 (8 CD Q- 300 200 100 - r i i (a) 1 1 1 1 / • A A Data ° Fit ----- A i i i i i i i 1200 1100 JOOO ^ 900 § 800 1 700 Q. « 600 0 1 500 400 300 1 ! 1 • (b) 1 -T "1 • • • | / • A' ° / ' Data ° Fit A cr' i i i 10 15 20 25 30 35 40 45 50 X-Ray Energy(keV) 10 15 20 25 30 35 40 45 50 X-Ray Energy(keV) Figure -6.25: Signal peak positions of the known energy X-Rays for (a)CCDl and (b)CCD2 from the data analyzed with N s i g n a i = 5. For CCD1, the fit- ting function of the peak position, P as a function of the energy E of the inci- dent X-Ray is P = -6.1C.U.+19C.U./keV E. For CCD2, the fitting function is P = 197 C.U.+20 C.U./keV E. are linear, showing that the output of the C C D is linearly proportional to the charge in a pixel and that the charge collection efficiency is constant over this energy region. The resolutions for the signal peaks of the K Q rays from the five elements studied, analyzed using three and five peaks as the signal peaks, are also shown in table 6.6. The resolution decreases as the energy increases, but the width of the peaks is not constant. The resolution is also better for N s i g n a l = 3 than 5, but setting N s j g n a i = 3 creates artefacts at higher energies. 55 Table 6.6: The resolution and position of the signal peaks of the five different incident X-Ray energies from the runs on CCD2, analyzed using N s i g n a i = 3 and 5. Element Rb Mo Ag Ba Tb 2 4 1 A m K a X-Ray energy (keV) 13.4 17.5 22.2 32.2 44.2 60 N S i g n a i=3 position (CU.) 424 493 556 783 1083 - N g i g n a i ^ resolution 36.7% 36% 36% 24% 14% - N ^ n a i ^ position (CU.) 461 554 615 845 1092 1325 N S ignai=5 resolution 57% 46% 42% 28% 28% 13.6% 6 .4 T h e H i g h - E n e r g y P e a k The Ag spectrum in figure 6.24 also exhibits a broad feature at higher energies (between -900 - 1600 C.U.). A l l of the low energy K Q X-Ray spectra (Cu, Rb, Mo and Ag) contained this feature, denoted the high-energy peak (HEP). It is believed that this H E P peak is likely also present in the higher energy K Q spectra, but at higher energies the larger intensity of the signal peak masks it. Figure 6.26 shows a comparison of the high energy peak in the Cu and Rb spectra taken using CCD2. The Rb spectrum shows both a signal and high-energy peak, while Cu shows only the high-energy peak. The Cu K Q X-Rays were not only low in intensity, but their energy was of the same order as the noise in the C C D , so they were discriminated against, leaving only the high-energy events. The HEPs for Cu and Rb match almost perfectly. The HEPs of Mo and Ag do not match as well, but there are relatively fewer counts in this region of the spectrum for these energies, as the signal peak was much more intense. 56 Figure 6.26: Comparison of the high energy region for the Cu and Rb Spectra for runs on CCD2 analyzed with N s i g n a i = 5. The y-axis was rescaled for the Rb data to allow a direct comparison of the shape of the spectra. Table 6.7 shows the areas, positions and widths of the HEPs for X-Ray spectra on CCD2. Using the calibration made in section 6.3.1 for CCD2, the high-energy peak was found to be at 50 keV, which is more energetic than any of the Ka X-Rays studied, but lower than the calibrated energy of the 60 keV 2 4 1 A m X-Ray (see section 6.8.2). The high energy peak could result from back-scattered 60 keV 2 4 1 A m X-Rays. At 60 keV, both the Compton and coherent scattering cross-sections are -7% of the photo-electric cross-section. 57 Table 6.7: The peak positions (x), areas (A) and widths (w) of the high-energy peaks in the spectra arising from characteristic X-Rays impinging on CCD2 analyzed with N S j g n a i = 5. The areas are in units of 1000 Charge Unit Counts, while x and w are expressed in Charge Units. Element A x w Cu 98 1160 387 Rb 156 1169 388 Rb (run 2) 76 1071 509 Mo 33 1226 541 Ag 14 1227 450 Ba 35 1189 381 Ba (run 2) 32 1195 335 6 .5 T h e E s c a p e P e a k Both the Ba and Tb spectra from CCD1 and CCD2 showed a similiar low-energy shoulder whose position varied linearly with the energy of the X-Ray. Figure 6.27 shows the Ba and Tb spectra on CCD2 fit with signal peaks. The position of the signal peak as well as the peak that creates the shoulder are indicated. The differences between the signal and shoulder position are the same for both spectra. It was postulated that this shoulder arose from the escape of photo-electrons and secondary X-Rays from the C C D . To help assign this feature, the escape of secondary X-Rays and photo-electrons was modeled. The escape of secondary X-Rays was studied by finding the chance of escape of an X - Ray interacting at any position in the active area of the C C D . To study the escape of photo-electrons, a Monte-Carlo simulation of the scattering of the photo-electron in the detector was made. This simulation allowed one to determine the spectrum of energies 58 700 600 <B 500 +-» c E 400 <D a » 300 c O 200 100 0 i 1 r 600 500 3 400 \ g_ 300 to g 200 r O 100 0 (b) Shoulder Data — Signal — 0 200 400 600 800 1000 1200 1400 1600 Charge units (C.U.) 0 200 400 600 800 1000 1200 1400 1600 Charge units (C.U.) Figure 6.27: The spectrum for (a)Ba and (b)Tb K Q X-Rays on CCD2 analyzed with N S i g n a i = 5, fitted with the signal peaks. The positions of the signal and the gaussian creating the shoulder have been labeled with vertical lines. The shoulder has also been indicated with an arrow. deposited in the detector by electrons that escaped from the detector. 6 . 5 . 1 E s c a p e o f S e c o n d a r y X - R a y s The active area of the C C D is a 30 pm x 50 pm x 2.5 mm block of GaAs. If a photon of energy E is a distance R from the edge of the active region, then its chance of escape, P(R), is given by P(A, R) = exp(-AP) (6.25) where A is the linear absorption coefficient of a photon of energy E in GaAs. The distance —* R is dependent on the initial position of the photon, X, and its direction of travel, defined 59 i X r 50-y 30-x r 50|im • 30Lim Figure 6.28: A cross section of the C C D , showing x, y and 9. The z-axis is out of the page, and <f> is the angle from the z-axis. by two angles, 9 and <f>. We can write R as R = R(X,9,(f)) (6.26) Figure 6.28 shows a cross-section of the C C D . The figure shows how 9 and <j> are defined, and also shows the components of X, x and y. The third component of X is ignored as it is along the 2.5 mm long axis of the C C D , and is effectively infinite for the photon energies considered here. We can now write R as R(x,y,9,<j>). The photon must escape from one of the four sides of the rectangle (top, bottom, left or right). The chance that a photon will escape from an initial position X, P{X), is found by integrating over all angles 8 and <f> for that position, and normalizing by the integration over all solid angles. Assuming that the X-Ray has an equal chance of being 60 emitted in any direction, then - 1 r2w r* -» P{X) = — d9 d(f) sin (f>exp[-\R(X,e,(t))} (6.27) 4TT JO JO The secondary X-Ray is emitted from the position that the incident X-Ray interacted with either a Ga or As atom through the photo-electric effect. The incident X-Ray has an equal probability of being anywhere in the y direction. The X-Ray will not, however, be equally deposited at all depths. As shown in equation (3.10), the probability of deposition of an X-Ray with a linear absorption coefficient of A' as a function of the depth, x, is given by A' exp(—X'x). The probability of escape is found by integrating P(X) over the —* area of the C C D , weighted by the probability that the secondary X-Ray originated at X. f030 dxf™dyexp[-\'x}P(X) J30dxf050dyexp[-X'x} PM =  J° 7oi° T^Zr' (6-28) The probability of escape of secondary X-Rays from the C C D was calculated for the KQ, X-Rays of Ga and As for incident X-Ray energies from Cu, Rb, Mo, Ag, Ba and Tb K a X-Rays. The total chance for a secondary X-Ray to escape from any one event in GaAs, V is given by V = (PGapGaFGa + PAspAsFAs) (6.29) APGaAs where Paa and PAS are the probabilities for an escape by a K a X-Ray from a Ga or an As atom, respectively. PGaAs, PGa and pAs are the densities of GaAs, Ga and As. F d a n d FAS are the fluorescence ratios of Ga and As, 50.7% and 56.2%, respectively. Table 6.8 shows the results for the calculations done for six different incident K Q X-Ray 61 Table 6.8: Chance of escape of the secondary X-Ray from the C C D for various incident X-Ray energies Element Cu Rb Mo Ag Ba Tb K Q X-Ray Energy (keV)[25] 8.047 13.394 17.489 22.162 32.19 44.17 Chance of escape 0.25 0.25 0.25 0.25 0.25 0.25 energies. The chance of escape is quite high, -25% , for all the incident X-Ray energies. The insensitivity to incident X-Ray energies is because the chance of escape depends only slightly on the linear absorption coefficient of the incident X-Ray, A'. A plot showing the effect of secondary X-Ray escape on the spectra of energies deposited into the C C D by a 44 kev X-Ray is shown in figure 6.32. The effect on the spectra of escaping secondary X-Rays is significant. 6.5.2 Escape of photo-electrons Figure 3.9 shows the mean path length for an electron in Ge calculated using Bethe's continuous energy loss formula[32]. For a 10 keV electron in GaAs, the mean path length is 0.9 fim. The chance of escape of an electron of this energy from the detector is negligible if the electron starts more than 1 /j,m away from the edge of the detector. For a 50 keV electron, however, the mean path length is -15 yum. The electron will always be within its mean path length of the edge of the detector. The chance of escape of a high energy photo-electron from the detector must therefore be taken into account when discussing the spectrum of energies deposited in the detector by an X-Ray with energy greater than 62 22 keV. A Monte-Carlo simulation was done to do a more realistic study of the creation of electrons in the detector. The code used was taken from Advanced Scanning Electron Microscopy and X-Ray Microanalysis[24]. The simulation used Bethe's formula (3.13) to find the path length of the electron. The path length was then divided up into 50 equal segments, and an elastic scattering event was generated for each of these segments. The differential cross-section for elastic scattering, daei(9), was used to find the scattering angle of the electron, 9, the angle between the initial and final direction of motion of the electron. daei(9) gives the cross-section for an electron with a relativistic wavelength of A in a solid with atomic number Z to be scattered into a solid angle dQ = 2TT sin(9)d9. , A 4 Z 2 dn / f , n n . doel(9) = - — r - s - -n (6.30) K ) 6 4 7 r 4 « o [ s i n 2 ( ^ / 2 ) + ( 5 ] 2 ^ * where a0 is the Bohr radius and 8 is the screening parameter which is numerically equal to 8 = 3.4 x 10~3Z2/3/E (E in keV) (6.31) A is given by A (2m0E(l + E/2m0x2)y/2 where h is Planck's constant, m 0 is the rest mass of the electron and E is the energy of the electron. The probability for a scattering angle of 9 is then found using 6.30 and the procedure outlined in [39]. 63 3 Incident X-Ray -3 -3 -2 -1 0 1 2 3 Y(fim) Figure 6.29: Five typical electron tracks created by the Monte Carlo simulation. The tracks were made by a 34 keV photo-electron, created by a 44 keV Ka X-Ray from Tb traveling in the negative x direction and interacting with an atom at the origin. Figure 6.29 shows a run of 5 electron paths in Ge with an electron energy of 34 keV (the energy of the photo-electron ejected from a Ga or As atom by a Tb K Q X-Ray). The initial direction of travel of the electron was found by finding the most probable angle of ejection of the photo-electron from equation (3.12), assuming the X-Ray was incident normal to the surface of the C C D . The simulation was used to find the range of the photo-electrons, the actual distance the electron travels from its starting point. 10 000 electron paths were simulated, and the average and standard error of the range recorded. Table 6.9 shows the range, mean path length and the ratio of the range to the mean path length for electrons of various energies in Ge. The simulation was also used to study the escape of photo-electrons from the detector 64 Table 6.9: Range and chance of escape of photo-electrons in Ge for various electron energies Element Rb Mo Ag Ba Tb 2 4 1 A m Ka X-Ray energy (keV)[25] 13.394 17.489 22.162 32.19 44.17 59.54 Photo-electron energy (keV) 3.4 7.5 12.2 22.2 34.2 49.5 Mean path length (pm) 0.17 0.57 1.27 3.52 7.47 14.38 Electron range (/dm) 0.047 0.161 0.394 1.231 2.85 5.97 Range/(Mean path length) .276 .282 .310 0.35 0.38 0.42 Chance of escape <1% <1% 0.011 0.039 0.083 0.20 (see Table 6.9). In order to do this, the starting position of the electrons had to be chosen randomly. The deposition depth of the photons was chosen using equation (3.10), while the position in the lateral direction was equally distributed over the width of the C C D . The electrons were divided into two different populations, those that escaped from the detector and those that did not. The number of electrons that escaped was found, as well as the energy that was deposited in the detector by each escaped electron. Figure 6.30 shows a histogram of the energy deposited in the C C D by the 58390 escaped electrons created by 700 000 incident 44 keV X-rays (giving a photo-electron energy of 34 keV). The curve was fitted to an exponential rise, F(E), as a function of deposited energy, E, with a rise energy of t and amplitude A F(E) = Aexp(E/t) (6.33) The shape of the spectra from escaped photo-electrons is found by convolving a Gaus- sian with the distribution of energies deposited in the C C D by the escaping electrons. Figure 6.31 shows the distribution of the energies deposited by escaped electrons that 65 3000 2800 2600 2400 2200 | 2000 <§ 1800 1600 1400 1200 1000 800 18 20 22 24 26 28 30 32 34 Energy Deposited (keV) Figure 6.30: A histogram of the energy, E , deposited by a 34 keV photo-electron that escapes from the detector. A fit of Counts = 275 Exp(E/15.1 keV) was made. would be expected for the 44 keV X-Ray from Tb. A n exponential with a rise energy, t (defined in (6.33)), of 15.1 keV was convolved with a Gaussian with a half-width, <7, of 6.3 keV. The Gaussian's width was taken from the N s i g n a i = 5 analysis of the Tb run on CCD2. Since the simulation showed that 8.3% of the photo-electrons escaped, the distribution for the energy deposited for all electrons would consist of 8.3% of the photo-escape peak plus 87.7% of the non-escape peak. The theoretical spectra for the energy deposited in the detector with and without taking the escape of photo-electrons into account is shown in figure 6.32. There is a small difference between the two cases at lower energies, but this difference is not significant compared to the statistical noise in the detector. Therefore, the escape of electrons does not appear to be a significant factor in determining the shape of the spectra in these CCDs. 66 50 0 10 20 30 40 50 60 Energy Deposited(keV) Figure 6.31: The energy deposited by a 44 keV photo-electron that escapes from the detector. 160 i . . . . . 1 0 10 20 30 40 50 60 Energy(keV) Figure 6.32: The spectrum of energies deposited in the detector for electron and secondary X-Ray escape. The incident X-Ray has an energy of 44 keV. The escape X-Ray has an energy of 10 keV, and 25% of the secondary X-Rays escape. Approximately 8% of the photo-electrons escape, and the energy deposited in the detector by them is shown in figure 6.30. See sections 6.5.1 and 6.5.2 67 6 . 5 . 3 E x p e r i m e n t Figure 6.32 shows the theoretical spectrum for a 44 keV X-Ray for three different analyses: when no escape of particles is taken into account, when the escape of secondary X-Rays is taken into account, and when the escape of photo-electrons is taken into account. The figure shows that the escape of secondary X-rays will significantly affect the shape of the spectrum, while the escape of photo-electrons will not. Modelling the spectrum as two peaks, the signal peak and the secondary X-Ray escape peak, should result in the spectrum containing two Gaussian peaks, with the second peak 10 keV (the K Q X-Ray energy of Ga and As) lower in energy, with the same width and containing 1/3 of the events of the first. Figure 6.33 shows the spectrum for Ba and Tb Ka X-Rays incident on CCD2. The spectrum was then fit with two Gaussians. The first Gaussian corresponding to the signal peak, and the second to the escape. The escape peak was constrained to be 10 keV below and have 1/3 the area of the signal peak. The Ba spectrum in figure 6.33-a is fit well by the escape, signal and high-energy peaks. The Tb spectrum shown in figure 6.33-b is not. Another peak had to be postulated for the Tb spectrum. 6 .6 T h e F i e l d - F r e e P e a k In order to obtain a good fit for the Tb spectra on CCD2, a third peak was postulated. The third peak was a Gaussian at lower energies than the first two, and is tentatively 68 0 200 400 600 800 1000120014001600 Charge units (C.U.) 600 500 § 400 g. 300 w § 200 0 100 0 1 I 1 1 1 1 (b) i i Data — Si U Escape — # / u Signal i / ' / ; ll Fit - fll \ • j r \ i — . . - ' \ i *M 0 200 400 600 800 1000120014001600 Charge units (C.U.) Figure 6.33: The spectra for (a)Ba and (b)Tb Ka X-Rays incident on CCD2 fit with a signal and escape peak. identified as the field-free peak. Figure 6.34 shows the spectrum for Tb Ka X-Rays on CCD1 and CCD2 fitted with the signal, escape and field-free peaks analyzed with N s j g n a i = 5. The field-free peak appears at the same position for all of the analyses of CCD2, within error (see section 5.2.1). This position is equivalent to an energy deposition in the C C D of 26 ± 3 keV. In section 4.5, the possibility of charge that was deposited in the field-free region contributing to the spectrum was discussed. The conclusion was that this would not happen. The field-free peak hypothesis does not agree with our analysis. It is thought, instead, that photo-electron escape could account for the field-free peak. The fact that the field-free region was so large was not found until after the Monte-Carlo simulations 69 350 T 1 1 1 Data — Fit Noise Field-Free — Escape Signal 0 200 400 600 800 1000120014001600 Charge units (CU.) 0 200 400 600 800 1000120014001600 Charge units (CU.) Figure 6.34: The spectrum for Tb Ka X-Rays on (a)CCDl and (b)CCD2 analyzed with N S igna i = 5 fitted with noise, signal, escape and field-free peaks. of the photo-electron escape were made. It is possible that by redoing these simulations with an active detection area only 10 pm deep, the low energy tail created would account for the shape of the Tb spectra. 6 . 7 F u l l S p e c t r u m A n a l y s i s In tables 6.10 and 6.11 the positions, areas and widths for the peaks assigned to all of the spectra taken for CCD1 and CCD2 are tabulated. A l l of the spectra tabulated here are shown in the appendix. 70 Table 6.10: The peak positions (x), areas (A) and widths (w) of the peaks in the spectra from characteristic X-Rays impinging on CCD1 analyzed with N S j g n a i = 5. The areas are in units of 1000 Charge Unit Counts, while x and w are expressed in Charge Units. Element Noise Field Free Escape Signal High Energy A x w A x w A x w A X w A X w Rb 51 172 111 101 244 72 29 782 476 Mo 68 161 99 U l 312 88 6 859 436 Ag 40 207 131 48 399 100 2.3 853 355 Ba 25 200 142 14 397 105 41 577 158 9.4 873 230 Tb 26 160 89 53 357 293 26 604 150 78 794 203 Table 6.11: The peak positions (x), areas (A) and widths (w) of the peaks in the spectra from characteristic X-Rays impinging on CCD2 analyzed with N S j g n a i = 5. The areas are in units of 1000 Charge Unit Counts, while x and w are expressed in Charge Units. For the Cu and Rb spectra, only the High Energy 2 peak was included in the table. Element Field-Free Escape Signal High Energy A X w A X w A X w A X w Cu 98 1160 387 Rb 41 458 157 156 1169 388 Rb (run 2) 122 392 192 76 1071 509 Mo 196 551 171 33 1226 541 Ag 213 614 176 14 1227 450 Ba 48 625 220 14 825 206 35 1189 381 Ba (run 2) 48 632 214 142 836 200 32 1195 335 Tb 40 790 481 43 891 222 120 1091 226 Tb (run 2) 20 619 232 51 858 187 153 1102 245 71 6.8 T h e 2 4 1 A m S p e c t r u m 6 . 8 . 1 T h e o r y 2 4 1 A m emits both ai-particles and X-Rays. The 2 4 1 A m source used in this study was shielded so that the o;-particles would be absorbed, but the X-Rays would emerge unim- peded. Because the source emits a large number of X-Rays at different energies and intensities, the spectrum for 2 4 1 A m had to be calculated. The energies and probabilities of each different X-Ray transition of 2 4 1 A m are shown in table 6.12[25]. Also shown in this table are the linear absorption coefficients of each of those X-Rays in GaAs. The linear absorption coefficients were then used to calculate the probability that each of the X-Ray energies would be absorbed in 30 pm of GaAs, using equation (3.10). The proba- bility of absorption was then multiplied by the probability of an emission of that energy from the 2 4 1 A m source to get the probability of an event in the C C D at that energy. Using the results shown in Table 6.12, the spectrum of 2 4 1 A m was calculated. For each energy there was a Gaussian distribution with a fixed width and an area given by the probability of an event from that energy. The Gaussians were then added, and the result called the theoretical 2 4 1 A m spectrum (see figure 6.35). Significant peaks are expected at 13.9, 18.6 and 59.5 keV. This spectrum does not take into account any escape of secondary X-Rays or photoelectrons, but gives an idea of what the spectrum should look like. 72 Table 6.12: X-Rays emitted by A m , and their probability of absorption in 30//m of GaAs. Multiplying these two probabilities give the probability that an event from this energy of X-Ray will be seen in the C C D . X-Ray energy (keV) Probability of emission from 2 4 1 A m linear absorption coefficient (1/cm) probability of absorption in 30 //m of GaAs probability of event from this energy 11.871 0.81 886.22 .930 0.028 13.927 13 586.96 .828 0.399 15.861 0.33 416.68 .714 0.009 18.611 20.2 270.2 .555 0.416 20.977 5.2 194.62 .442 0.085 26.345 2.4 103.01 .266 0.024 33.192 0.12 53.61 .149 0.001 59.5364 35.7 9.76 .029 0.038 0 10 20 30 40 50 60 70 80 Energy (keV) Figure 6.35: Theoretical 2 4 1 A m spectrum in 30 tim of GaAs 73 Table 6.13: Peak data for the 2 4 1 A m X-Rays on CCD2 analyzed with N s i g n a i = 5. The x-axis was calibrated using the CCD2 5 peak calibration. The areas are in units of keV Counts, while x and w are expressed in keV. Peak Name A X w (keV Counts) (keV) (keV) 13 keV 4201 13.1 6.1 18 keV 4450 17.9 12.1 Field Free 5631 43.5 16.0 Escape 906 45.8 7.1 60 keV 2719 55.6 8.0 6.8.2 Experiment Figure 6.36 shows the data obtained from shining an 2 4 1 A m source on the top of CCD2. The N s i g n a i = 5 data was fit with five Gaussian peaks, each of them corresponding to an expected peak. The peaks were the 13 keV, 18 keV, 60 keV and the escape and field-free peaks corresponding to the 60 keV peak. The fit of the escape peak was constrained to be 10 keV below the 60 keV peak and have one third the area. The results of this are shown in figure 6.36 and table 6.13. The resulting fit shows the 13 keV and 18 keV peaks to be where they were expected, and the 60 keV peak to be centred at 57 keV on the calibration scale. The ratio of the areas of the 60 keV peak to the 13 and 18 keV peaks is much larger than predicted in Section 6.8.1. The resolution of the C C D at 60 keV is 9.6 keV F W H M . Table 6.14 shows a comparison of this resolution to some other studies using single element GaAs detectors. 74 j i Table 6.14: Comparison of the GaAs C C D X-Ray detector's resolution at 60 keV to some other GaAs detectors. Authors Detector Type Temperature (°C) FWHM[%] FWHM[keV] Holland et. al.[40] L E C GaAs -10 7.5 4.5 McGregor et. al.[41] L E C GaAs R.T. 37 22 Bencivelli et. al.[42] L E C GaAs R.T. 7.5 4.5 Bertuccio et. al.[15] L E C GaAs 20 28 16.8 Bertuccio et. al.[15] L E C GaAs -30 3.7 2.2 Hesse et. al. [43] epitaxial GaAs R.T. 4.3 2.6 This Work GaAs C C D R.T. 16 9.6 75 Table 6.15: Range in the x-direction and chance of charge sharing for photoelectrons in Ge Element Ba Tb 2 4 1 A m K Q X-Ray energy (keV) 32.19 44.17 59.54 Photo-electron energy (keV) 22.2 34.2 49.5 range of the electron in the X-direction, I (/nn) 0.682 2.86 3.08 Chance for charge sharing 0.035 0.075 0.15 6 .9 C h a r g e S h a r i n g The Monte Carlo simulation was also used to examine charge sharing in the C C D (see section 4.4). The extent of the initial photo-electron's track in the x-direction was found. The chance of charge sharing, P(x), for a track with an extent in the x-direction of I microns in a C C D with an anode pitch of A is given by P(l) — I/A. The chance of charge sharing for X-rays of 59 keV, 44 keV and 32 keV was calculated. The average range in the x-direction and the chance for charge sharing for these three energies are shown in table 6.15. Because the photo-electron's path length is always less than the pixel spacing (20 A*m), there is essentially no chance of charge sharing into more than two pixels. The fact that a value of N s i g n a i of 5 had to be used for the Tb and higher energy spectra shows that some charge sharing occured. This could be caused by charge "spilling" from one pixel into another, as discussed in section 4.4. Chapter 7 Conclusion 7.1 Future Work There are a number of possibilities for further research and development of the C C D X-Ray detector. These possibilities include methods for increasing the resolution of the detector, better characterizing the detector, and increasing the types of particles studied. The top priority should, however, be an analysis of the sources of noise in the device. One likely source is the output circuitry on the CCDs used in the study. The output circuitry on the CCDs used for the B N L 787 experiment has been greatly improved since the two wafers of CCDs used for this study were fabricated. A second fabrication using this improved output circuitry should greatly reduce the noise of the baseline of the C C D . A second method of increasing the resolution may be to cool the C C D . A study[15] using a bulk L E C grown GaAs detector detected the 60 keV 2 4 1 A m X-Ray with a resolution of 28% at 20°C. By cooling the detector to -30°C, the resolution was increased to 3.6%. Further increases in resolution might also be obtained by characterizing individual pixels of the C C D . If it was known which pixel an X-Ray deposited charge into, then the known characteristics of that pixel could be used to further reduce the variance of the charge 76 77 read out. A further study of the field-free region would also be useful. Knowledge of the true depth of the depletion region would allow a proper analysis of the effect of the escape of photo-electrons on the shape of the spectra for Tb X-Rays through further Monte Carlo simulations. This knowledge would further test the assignation of the field-free peak to the escape of photo-electrons from the depletion region. Holland et. al.[40] suggest that measuring the count rate of 60 keV 2 4 1 A m X-Rays as a function of bias would give a measure of the depth of the actual depletion region. Another possible direction for future research would be to increase the depth of the depletion region. This should allow a greater detection efficiency and should also lower the relative intensities of the field-free and escape peaks. In order to increase the depth of the field-free region without increasing the bias voltage, the purity of the intrinsic GaAs would have to be increased. The depth of the depletion region is inversely proportional to the square root of the doping density in the active region. If the intrinsic doping density was decreased from 10 1 4 c m - 3 to 10 1 3 c m - 3 , the active region would be fully depleted at a bias voltage of 7 V . The ability of the C C D detector to detect X-Rays also implies that it should be able to detect other particles. A minimum ionizing particle in GaAs will lose energy at a rate of dE/dx = 5.6 MeV/cm[44]. In 30 //m, a minimum ionizing particle will deposit 16.8 keV, or 4000 e.h.p.s, in the C C D , roughly equivalent to the 17.5 keV deposited by a Mo Ka X-Ray. This number of e.h.p.s is detected by the detector, implying that electrons 78 and a rays will be seen by the detector. Detectors used for detecting minimum ionizing particles would be much more useful if they could also be used to detect the position and direction of travel of the particles. In order to detect position, the pixel that the charge was deposited into by the particle would have to be known. The direction of travel of the particle could be found by finding the position of the particle as it traveled through several detectors. In order for this to be feasible, the energy lost by the particle as it traversed each detector would have to be low. In the detector as it is now, a minimum ionizing particle will lose -350 keV in the L E C substrate of the detector. This could be lowered if the substrate was made thinner than its current 650 /mi. 7.2 Conclusions The response of a buried channel GaAs C C D detector to X-Rays ranging in energy from 8 to 60 keV was studied. The spectra from single-energy X-Ray sources were not simple Gaussians, but generally contained a number of different peaks. Five different peak types, the noise, signal, escape, high-energy and field-free peaks, were identified. The mechanisms for their creation have been either established or tentatively assigned. The noise peak results from triggers due to noise in the C C D waveform rather than X-Ray caused events. The signal peak is the expected peak resulting from full deposition of the X-Ray's energy in the detector. The position of the signal peak was found to be linear as a function of incident X-Ray energy for X-Ray energies ranging from 14 keV to 44 keV. The resolution of the detector varied from 57% at 14 keV to 16% at 60 keV. The 79 escape peak results from the escape of secondary X-Rays from the detector. Simulations were made to estimate the relative intensity of the escape peak to the signal peak. This intensity was then used to make fits to the experimental spectra. The high-energy peak was found to be constant in energy and shape for all the Ka spectra with an energy of 50 keV. Its origin has been tentatively assigned to an X-Ray event caused by back- scattered 60 keV 2 4 1 A m X-Rays leaked from the source. The field-free peak is believed to result from the escape of photo-electrons from the depletion region. The resolution of the detector is larger (worse) than that of other single element GaAs X-Ray detectors, but it is believed that improvements in the resolution can be made, as outlined in section 7.1. These studies showed that X-Rays were detectable, and that the energy deposited in the C C D by a minimum ionizing particle would be detectable by the C C D . Bibliography [1] W.S. Boyle and G.E. Smith "Charge Coupled Semiconductor Devices" Bell Systems Technical Journal 4 9 (1970) 587. [2] G.F. Amelio "Experimental Verification of the C C D Concept" Bell Systems Tech- nical Journal 4 9 (1970) 593. [3] A .R . Walker "BVI C C D astronomy of galactic globular clusters. II. M68" Astro- nomical Journal, 1 0 8 (1994) 555. [4] C.S. Barth et. al. " C C D imaging of N G C 4861:ionized gas properties and stellar formation" Astronomical Journal 1 0 8 (1994) 2069. [5] C.S. Burley et. al. "A precisely aligned C C D mosaic" Astronomical Society of the Pacific 1 0 8 (1994) 1024. [6] W.P. Acker et. al. "The use of a charge-coupled device and position sensitive anode detector for multi-order spontaneous Raman spectroscopy from Silicon" JAP 6 4 (1988) 2263. [7] M . H . Abd-el-Barr and Z.G. Vranesic "Charge coupled device implementation of multi-valued logic systems" IEE Proc. E Computers and Digital Techniques 1 3 6 (1989) 306. [8] A . H . Baher "Design of finite duration impulse response digital and charge coupled device filters with arbitrary attenuation characteristics" IEE Proc. G Electronic Circuits and Systems 1 3 2 (1985) 193. [9] R. Hayes and D.L . Heidtman "Dual channel charge coupled device for high speed signal acquisition" Optical Engineering 2 6 (1987) 829. [10] A . J . Holland et. al. "The X-Ray polarization sensitivity of CCDs" Nucl. Instr. and Meth. A 3 5 5 (1995) 526. [11] K . J . McCarthy et. al. "Modeling the X-Ray response of charge coupled devices" Nucl. Instr. and Meth. A 3 6 2 (1995) 538. [12] K . J . McCarthy and A . Wells, Proc 10th Symp. on Photo-electric Imaging Devices, Institute of Physics Conference Series 121 (1992) 17. 80 81 E. Bertolucci et. al. "X-ray imaging using a pixel GaAs detector" Nucl. Instr. and Meth. A 3 6 2 (1995) 547. L. Berlutti et. al. "Gallium Arsenide particle detectors: a study of the active region and charge-collection efficiency" Nucl. Instr. and Meth. A 3 5 4 (1995) 364. G. Bertuccio et. al. "Performance of SI L E C GaAs detectors at 20°C and -30°C for X - and 7-ray spectroscopy" Nucl. Instr. and Meth. A 3 7 9 (1996) 152. R. Bertin et. al. "A preliminary study of GaAs solid state detectors for high energy physics" Nucl. Instr. and Meth. A 2 9 4 (1990) 211. S.P. Beaumont et. al. "GaAs solid state detectors for particle physics" Nucl. Instr. and Meth. A 3 2 2 (1992) 472. K . M . Smith "GaAs detector performance and radiation hardness" Nucl. Instr. and Meth. A 3 6 8 (1995) 220. D.A. Bryman et. al. "500 MHz transient digitizers based on GaAs CCDs" submitted to Nucl. Instr. and Meth. 3.-1. Song et. al. "GaAs C C D readout for engineered bandgap detectors" Proc. SPIE 1 3 0 8 (1990) 254. S.M. Sze, Physics of Semiconductor Devices, 2nd edition. John Wiley (Toronto) 1981. M.S. Tyagi "Physics of Schottky barrier junctions" in Metal Semiconductor Schottky Barrier Junctions and Their Applications (B.L. sharma, ed.) Plenum (New York) 1984. D.E. Newbury in SEM Microcharacterization of Semiconductors (D.B. Holt and D.C. Joy, eds) Academic Press, (Toronto) 1989. D.E. Newbury "Modeling Electron Beam-Specimen Interactions" in Advanced Scan- ning Electron Microscopy and X-Ray Microanalysis (D.E. Newbury, ed) Plenum, (New York) 1986. N .G . Gusev and P.P. Dmitrev, Quantum Radiation of Radioactive Nuclides, Pergam- mon (New York) 1979. H. He et. al, "A detailed study of the interaction mechanisms for Si(Li) detector response functions by the direct Monte Carlo approach" Nucl. Instr. and Meth. A 2 7 2 (1988) 847. Condon and Odishaw, Handbook of physics, 2nd edition. McGraw-Hill (New York) 1967. 82 E.J . McGuire "Auger and Coster-Kronig Transitions" in Atomic Inner Shell Pro- cesses, B Vol 1 (B. Crasemann, ed.) (1975) 293-330. M.O. Krause "Atomic radiative and radiationless yields for K and L shells" J. Phys. Chem. Ref. Data. 8 (1979) 307. J.L. Blakenship and W.F . Mruk Bull. Amer. Phys. Soc. 9 (1964) 49. J .E. Eberhardt et. al. "Evaluation of epitaxial n-GAs for nuclear radiation detection" Nucl. Instr. and Meth. 9 4 (1971) 463. H.A. Bethe and J. Ashkin in Experimental Nuclear Physics, Vol 1 (E Segre, ed) John Wiley, (New York) 1953. J . Shah et. al., "Determination of intervalley scattering rates in GaAs by subpicosec- ond luminescence spectroscopy", Phys. Rev. Lett. 5 9 (1987) 2222. R.P. Gardner et. al. "An investigation of the possible interaction mechanisms for Si(Li) and Ge detector response functions by Monte Carlo simulation" Nucl. Instr. and Meth. A 2 4 2 (1986) 399. G.C. Messenger, "Collection of charge on junction nodes from ion tracks", IEEE TNS, N S - 2 9 (1982) 2024. M . Shur et. al., "Charge collection by drift during single particle upset", IEEE TNS, N S - 3 3 (1986) 1140. J .G. Ruth and G.S. Kino "Measurement of the velocity field characteristic of Gallium Arsenide" Appl. Phys. Lett. 10 40. R .J . Nelson and R .G . Sobers "Minority carrier lifetime and internal quantum effi- ciency of surface-free GaAs" J. Appl. Phys. 4 9 (1978) 6103. L. Reimer, Scanning Electron Microscopy, Springer-Veriag, (Berlin) 1985. A . D . Holland et. al. "X-Ray detection using bulk GaAs" Nucl. Instr. and Meth. A 3 4 6 (1994) 366. D.S. McGregor et. al. "Bulk GaAs room temperature radiation detectors" Nucl. Instr. and Meth. A 3 2 2 (1992) 487. W. Bencivelli et. al. "Some new results on semi-insulation GaAs detectors for low energy X-rays" Nucl. Instr. and Meth. A 3 5 5 (1995) 425. K . Hesse et. al. "Room-Temperature GaAs gamma detectors" Nucl. Instr. and Meth. 101 (1972) 39. 83 H . Esbensen et. al. "Random and channeled energy loss in thin Germanium and Silicon crystals for positive and negative 2-15 GeV/c pions, kaons and protons" Phys. Rev. B 18 (1978) 1039. C h a p t e r 8 A p p e n d i x : S p e c t r a A l l of the single-energy spectra taken during this study are reproduced here with all curve fits. The areas, widths and positions of the peaks shown in the spectra are tabulated in tables 6.10 and 6.11. 84 85 ~I I ! I I I Data — Fit Noise Signal — High-Energy ----- 200 400 600 800 1000120014001600 Charge units (CU.) 0 200 400 600 800 1000120014001600 Charge units (CU.) 250 - i 1 1 1 1 r Data Fit Noise Escape Signal High-Energy 200 400 600 800 1000120014001600 Charge units (CU.) 0 200 400 600 800 1000120014001600 Charge units (CU.) Figure 8.37: Spectra for X-rays impinging on CCD1 analyzed with N s i g n a i = 5 for the characteristic X-Rays of (a)Rb, (b)Mo, (c)Ag and (d)Ba. 86 350 I ' 1 1 1 1 ! 1 r 0 200 400 600 800 1 0 0 0 1 2 0 0 1 4 0 0 1600 Charge units (C.U.) Figure 8.38: Spectra for X-rays impinging on CCD1 analyzed with N s ; g n a i = 5 for the characteristic X-Rays of Tb 250 200 <D +̂  3 I 150 0) a I 100 3 0 0 50 0 (a) Data Fit High-Energy 1 High-Energy 2 0 200 400 600 800 1000120014001600 Charge units (C.U.) 400 350 | 250 £200 w § 150 o 0 100 50 0 I 1 1 1 1 . ( b ) D * - 1 1 1 Signal . High-Energy 1 — If i High-Energy 2 ----- i • A /-A \ • • / \f i 0 200 400 600 800 1000120014001600 Charge units (C.U.) Figure 8.39: Spectra for X-rays impinging in CCD2 analyzed with N s i g n a i = 5 for the characteristic X-Rays of (a)Cu and (b)Rb. 87 200 400 600 800 1000120014001600 Charge units (CU.) 700 600 $ 500 C £ 400 a <2 300 c 3 0 200 100 0 1 1 1 (c) 1 1 1 1 . Data — k Fit -----. J Escape ^ 1 Signal — 1 High • 200 400 600 800 1000120014001600 Charge units (CU.) 0 200 400 600 800 1000120014001600 Charge units (CU.) 200 400 600 800 1000120014001600 Charge units (CU.) Figure 8.40: Spectra for X-rays impinging on C C D 2 analyzed with N s i g n a i = 5 for the characteristic X-Rays of (a)Mo, (b)Ag, (c)Ba and (d)Tb. 88 Figure 8.41: Spectra for a second set of X-Rays impinging on CCD2 analyzed with N s i g n a i = 5 for the characteristic X-Rays of (a)Rb, (b)Ba and (c)Tb.

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