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UBC Theses and Dissertations

A gallium arsenide CCD X-Ray detector Patten, Scott 1997

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A G A L L I U M A R S E N I D E C C DX - R A Y  DETECTOR  By Scott P a t t e n B . Sc. (Physics) Simon Fraser University, 1994  A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R 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 F A C U L T Y OF G R A D U A T E STUDIES D E P A R T M E N T O F 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 i n partial fulfilment of the requirements for an advanced degree at the University of B r i t i s h C o l u m b i a , I agree that the L i b r a r y 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. financial  It is understood that copying or publication of this thesis for  gain shall not be allowed without my written permission.  Department of Physics & A s t r o n o m y T h e University of B r i t i s h C o l u m b i a 6224 A g r i c u l t u r a l R o a d Vancouver, B . C . , C a n a d a V 6 T 1Z1  Date:  Abstract  A one dimensional buried channel C C D w i t h a 30 /urn thick intrinsic layer was manufactured 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 w i t h energies ranging from 8 K e V to 60 k e V 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. T h e 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. T h e spectrum from an  2 4 1  A m source was also studied to determine the detector's response to  a multi-energetic source.  ii  Table of Contents  Abstract  ii  Table of Contents  iii  List of Tables  vi  List of Figures  vii  1  2  3  Introduction  1  1.1  Motivation  1  1.2  Work Done i n this Study  2  1.3  Outline  2  The C C D  4  2.1  Overview  4  2.2  T h e Structure of the C C D  5  2.3  T h e potential underneath a gate i n the C C D  7  2.4  Movement of charge from pixel to pixel  12  Interactions of Particles in G a A s  14  3.1  Introduction  14  3.2  T h e Interaction of an X - R a y w i t h G a A s  14  3.3  T h e Photo-electric Effect  3.4  Creation of electron-hole pairs  .  15 19  iii  4  5  6  3.5  Interactions of electrons i n G a A s  20  3.6  Escape of particles from the detector  21  E l e c t r o n Transport  24  4.1  Introduction  24  4.2  Electrostatic fields i n the C C D  25  4.3  Initial 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  Experiment  36  5.1  Experimental Setup  36  5.2  Analysis of oscilloscope traces  39  5.2.1  40  T h e Choice of N  s i g n a  i  5.3  Tests w i t h known input pulses  41  5.4  Response of the detector to Characteristic X - R a y s  45  5.5  The  47  2 4 1  A m spectrum  Results and Discussion  50  6.1  Overview  50  6.2  The Noise Peak  51  6.3  T h e Signal Peak  53  6.3.1  53  C a l i b r a t i o n of the C C D Energy Scale  6.4  T h e High-Energy Peak  6.5  The Escape Peak  55  . .  '. iv  57  Escape of Secondary X - R a y s  58  6.5.2  Escape of photo-electrons  61  6.5.3  Experiment  67  6.6  T h e Field-Free Peak  67  6.7  F u l l Spectrum Analysis  69  6.8  The  A m Spectrum  71  6.8.1  Theory  71  6.8.2  Experiment  73  6.9 7  6.5.1  2 4 1  Charge Sharing  75  Conclusion  76  7.1  Future Work  76  7.2  Conclusions  78  Bibliography 8  Appendix:  80 Spectra  84  v  List of Tables  2.1  Constants for G a A s used i n calculating J  9  3.2  Chance of absorption of the K  5.3  T h e parameters of the peaks for T b data w i t h differing N  5.4  The K  6.5  Noise peak data for X - R a y s on C C D 1  6.6  T h e resolution for X - R a y s on C C D 2 , analyzed using N j  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 - R a y s from the C C D  61  6.9  Range and chance of escape of photo-electrons i n G e  64  s  a  a  X-Rays  17  s i g n a l  's  energies of the elements used i n this study  41 46 52  s  g n a  i = 3 and 5 . .  55  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  72  6.13 Peak data for the  2 4 1  2 4 1  Am  A m X - R a y s on C C D 2  73  6.14 Comparison of the 60 k e V resolution to some other detectors  74  6.15 Range i n the x-direction and charge sharing for electrons i n G e  75  vi  List of Figures  2.1  A schematic diagram of the C C D  6  2.2  T h e well created under the C C D  6  2.3  T h e band diagram w i t h V ^ j  2.4  T h e band diagram w i t h V  2.5  T h e voltages on the phases of a pixel of the C C D  13  2.6  T h e potential beneath the wells of the C C D  13  3.7  T h e C o m p t o n and photo-electric cross-sections of X - R a y s i n G a A s . . . .  16  3.8  T h e angular distribution of ejected photo-electrons  18  3.9  T h e mean path length for an electron i n G e  22  b  i  a g  a  s  = 0V  8  = -7 V . . .  11  4.10 A time-line of the creation and collection of electron hole pairs i n the C C D 26 4.11 T h e linear e.h.p. density and diffusion time for a 60 keV photo-electron .  28  4.12 T h e charge that has diffused to the depletion region V s . time  33  5.13 A typical oscilloscope trace  37  5.14 T h e spectra of T b X - R a y s analyzed w i t h N  s i g n a  i = 3, 5, 7 and 9  42  5.15 A histogram of the count rate for a 3 1 m V input pulse  43  5.16 T h e charge deposited i n the C C D by known input pulses  44  5.17 T h e 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 T h e charge deposited i n a C C D by M o , N  48  vii  s i g n a  i=5  5.21 T h e charge deposited i n C C D 2 by T b , N 5.22 T h e charge deposited i n C C D 1 by  2 4 1  s i g n a l  =5  48  A m X-Rays, N  s i g n a  i = 5 and 7  . . .  49  6.23 T h e noise peaks for A g spectra  52  6.24 T h e signal peaks for R b , M o and A g  53  6.25 Signal peak positions of X - R a y s for C C D 1 and C C D 2 w i t h N  s i g n a  i = 5 . .  6.26 Comparison of the C u and T b spectra  54 56  6.27 B a and T b spectra on C C D 2 analyzed w i t h 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 M o n t e C a r l o simulation . . . .  63  6.30 T h e energy deposited by an escaped photo-electron  65  6.31 T h e energy deposited by an escaped photo-electron  66  6.32 T h e energy deposited for escaped X-rays and electrons  66  6.33 B a and T b K  68  6.34 T b K  Q  Q  X - R a y s on C C D 2 fit w i t h signal and escape peak  spectrum fitted w i t h signal, escape and field-free peaks  6.35 Theoretical  2 4 1  A m spectrum i n 30 /xm of G a A s  6.36 T h e spectrum of  2 4 1  A m on C C D 2  69 72 74  8.37 R b , 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 R b , B a and T b spectra on C C D 2  88  viii  Chapter 1  Introduction  1.1  Motivation  T h e Charge Coupled Device ( C C D ) was first conceptualized by Boyle and S m i t h [1] i n 1970, and was experimentally verified using S i , i n the same year, by A m e l i o [2]. Since then, C C D s have been used i n a large and varied number of applications, w i t h the two major areas being imaging[3, 4, 5, 6] and digital signal processing[7, 8, 9]. A l t h o u g h S i 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 S i because its larger Z value  increases the detection efficiency of X - R a y s . Also, G a A s device structures are inherently more radiation hard than those made on Si[16, 17]. T h e m o b i l i t y of electrons in G a A s is larger than i n S i , m a k i n g G a A s devices potentially faster.  Finally, the large band  gap of G a A s makes it usable at room temperature, unlike S i and G e based detectors. These properties would make a G a A s detector useful i n many different environments. T h e detection efficiency of G a A s would make it useful i n 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 i n such high particle flux environments as the L H C (Large Hadron Collider) [18]. 1  2  1.2  W o r k D o n e in this S t u d y  T h e C C D s used i n this study were originally used as transient digitizers i n the Brookhaven N a t i o n a l 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 w i t h a 30 yum thick epitaxial layer was fabricated at the G a A s Micro-structure L a b o r a t o r y at T R I U M F . T h e purpose of this study was to find the response of the G a A s C C D detector to X - R a y s w i t h energies ranging from 8 to 60 k e V . In order to do this, an X - R a y source which emitted the K  a  X - R a y s of either C u , R b , M o , A g , B a or T b was used. T h e K  were shone on the C C D and the resulting spectra found. A n  2 4 1  a  X-Rays  A m source was used as  well to study the detector's response to more complex spectra. T h e spectra from the K  Q  X - R a y s were not single peaks, but instead exhibited a number of features. T h e features arose from escape of photons and electrons from the detector's volume, noise sources in the detector and deposition of charge i n areas of the detector that had little or no drift field. In order to understand these features, several simulations of the microscopic interactions and transport of photons and electrons w i t h i n the detector were made. U s i n g the results from the simulations, each peak i n each i n d i v i d u a l spectrum was assigned to a phenomenological source. F r o m 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 - R a y s was found.  1.3  Outline  T h e thesis is divided into seven chapters, the first being the introduction. T h e second chapter introduces the structure and operation of the C C D . In the t h i r d chapter, the interactions of particles i n G a A s and the creation of electron hole pairs are discussed.  3  The fourth chapter details the transport of electrons from their i n i t i a l creation to the time they enter the potential wells under the C C D gates. T h e fifth chapter details the experimental work done i n this study and shows some of the spectra obtained. T h e sixth chapter discusses and analyzes the data obtained and shows the results of simulations done to help explain the spectra. T h e final chapter discusses possible work that could be done i n the future and makes conclusions. A n appendix shows a l l of the single energy X - R a y spectra that were taken i n 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  w i t h a broad area bias n o r m a l to the surface, three dimensional potential wells can be formed where electrons w i l l be trapped.  B y changing the gate voltages i n sequence,  charge can be transferred from pixel to pixel. T h e 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 i n a pixel consists of a periodic train of pulses w i t h fixed phase w i t h respect to each other. Figure 2.6 shows the voltages on the four gates of a pixel i n the C C D used i n this study. T h e effect of these pulse sequences is to move a packet of electron charge from one pixel to the next. T h e creation of electron hole pairs (e.h.p.s) i n the C C D and their collection under one of the pixels of the C C D is shown i n figure 4.10. W h e n an X - R a y enters a C C D , it interacts w i t h the semiconductor substrate of the C C D , creating electron-hole pairs. T h e number of electron-hole pairs created i n the C C D is directly proportional to the energy of the incident X - R a y .  T h e electrons created by the X - R a y are accelerated by  the vertical field i n the C C D , which drives them into the potential wells under the gates. 4  5  T h e electrons i n the potential wells are then transferred from pixel to pixel to the output of the C C D by the gate pulses shown i n figure 2.6. T h e 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  T h e Structure of the C C D  T h e C C D used i n this study (see Figure 2.1) is a buried channel resistive gate C C D comprised of 128 pixels. E a c h 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.  T h e gates  are i n ohmic contact w i t h a 0.1 /xm thick sheet of Cermet ( C r - S i O ) , a resistive dielectric w i t h a sheet resistance of -1 M Q / D at this thickness. T h e Cermet makes a Schottky contact w i t h the G a A s below it. T h e 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). T h i s avoids problems associated w i t h trapping of the electrons i n the well by the surface states inherent i n G a A s . T h e Cermet also ensures that the voltage between gates varies linearly along the surface of the C C D , providing an electric field that helps i n the transfer of electrons from pixel to pixel[20] (see Figure 2.6). T h e channel of the C C D , the region where the potential wells i n 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 . T h i s 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  16  cm  - 3  . Below this is a second epitaxially grown, 30 fim thick layer of  semi-insulating G a A s , which is p-type w i t h a nominal doping of N A < 1 0  14  cm  - 3  . This  layer is called the active layer as this is where the X - R a y s interact w i t h the G a A s to form  6  Cermet 0.1 j i m : 0.27 u.m  30u,m  Active Region, Semi-Insulating, nominally doped atNA= 1 0 c m 1 4  650 um  3  Substrate, doped at NA = 1 0 c m " 1 8  ^  3  ! Vsubstrate  Figure 2.1: A schematic diagram of the C C D used i n 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 i q u i d Encapsulated Czochralski ( L E C ) method, and doped at N A = 1 0  18  cm  - 3  . T h e b o t t o m of the C C D has an ohmic contact made to it. T h i s  contact is kept at a negative voltage while the C C D is being used as a detector.  2.3  T h e potential underneath a gate in the C C D  Figure 2.3 shows the band diagram underneath one of the gates i n the active area of the C C D w i t h a l l the gates at ground. T h e device consists of three junctions, a p - p ~ +  junction, a p ~ - n j u n c t i o n and a Schottky junction between the n layer and the Cermet. T h e p ~ - n j u n c t i o n and the n - C e r m e t j u n c t i o n act together to form a potential well w i t h a flat m i n i m u m from 0.1 jim. to 0.27 yum deep i n the C C D . T h e depletion region is ~4 iim deep, leaving a field-free region 26 / m i deep. W h e n a negative voltage is put on the b o t t o m contact of the device, the p - p ~ and the +  p ~ - n junctions act as reverse-biased diodes, and the n - C e r m e t j u n c t i o n acts as a forward biased Schottky diode. To find the depletion depth i n the active region under reverse bias conditions, a number of approximations are made. T h e abrupt j u n c t i o n approximation assumes that the changes i n doping are step functions.  T h e second approximation is  that there is a well defined depletion region outside of which a l l fields are zero. T h e next step is to find how much voltage is dropped across each j u n c t i o n . To do this, a current continuity equation is set-up. T h e current density through a p n j u n c t i o n diode[21] or a Schottky diode[22] at a  8  Active region  a  ,  s  x  ^  field free region  region  u  Substrate 1.5  n N  J  T  j  /  i  0.7 eV  /  1  !  0.5 !  ]  m  3  I  E, 0  (3  -0.5  ]  -1 Cermet  I  !  1  0  5  10  15  20  25  30  35  -1.5  Depth(|im)  Figure 2.3: T h e band diagram under a pixel of the C C D w i t h V ^ j  = 0 V  a g  temperature T is given by the Schockley equation,  J = J (e^  - 1)  kBT  s  (2.1)  Where V is the bias voltage across the j u n c t i o n , and is defined to be positive for forward bias and negative for reverse bias. J is the saturation current density, and ks s  is B o l t z m a n n ' s constant. For a pn j u n c t i o n , J is given by[21] s  J -  j  s  Where D  p  and D  n  +  (2.2)  j  are the hole and electron diffusion constants, and L  p  and L  p  are  the hole and electron diffusion lengths, given by  L  n  — \JT D n  n  , L  p  — \jip~Dp  (2.3)  9  Table 2.1: Constants for G a A s used i n calculating the saturation current density i n p n and Schottky junctions.[21],[22] Parameter  D D L L  Value  n  222 c m / s  p  10.4 c m / s  2  2  n p  14.58 3.16 pm ~ 10" s ~ 10- s 1.79xl0 c m " 8  T  N  8  T  P  Hi m* 4>B  6  0.067 m 0.7 e V  3  0  n o and p o are the electron and hole minority concentrations on the p and n side of p  n  the junction, respectively. T h e y can be found using the fact that the electron and hole density, n and p i n a doped semiconductor are related to the intrinsic electron density, rii by  np = n  2  (2.4)  Table 2.1 gives values for the parameters named i n the above equations. T h e saturation current density has two components added together. T h e first is linearly dependent on the hole concentration on the n side of the j u n c t i o n , and the second on the electron concentration on the p side of the junction. For a Schottky diode w i t h a barrier energy of 4>B running at a temperature T, the  10  saturation current density is given by[22]  J = AT exp  (2.5)  2  s  where A is  A =  (2.6)  m* is the effective mass of an electron i n G a A s , 0.067m ( m being the electron mass), 0  0  and h is Planck's constant. For the p - n junction, n  3> p , so the saturation current for this junction, J ,  _  p0  n0  Spn  w i l l be given by  J  *  Spn  For the p - p +  _  junction, p  ~ 10-  1 4  A/m  (2.7)  2  is given by the doping density i n the p~ region, so the  n0  saturation current density through this junction, J  Svv  J  Spp  «  is  ~ 10 A/m 3  (2.8)  2  For the Schottky j u n c t i o n at 3 0 0 ° K , the saturation current density, J  SSchottky  Js  = AT exp 2  Schottky  ~ 10- A/m 9  2  is  (2.9)  T h e saturation current for the p ~ - n j u n c t i o n is much smaller than the saturation current for the other two junctions, so the current through the p ~ - n junction w i l l be the  11  Active region A i >•  N-Type atSxltf" \  field free region  d e p l e , l o n  region i  i i i i  i /  -  /  1  /  /  4 1  Substrate  i  /  9  > I—  E  - J —  Ev"  ~  /  -t  5  /  /  7 6  /  / / 1  8  m  i  /  <D  -1 1 1 1  / /  /  / /  /  !  3  j  2  / /  ill  •  0.7 eV~$ II  10  15  20  25  30  1 0  i  Cermet  <  -1 35  -2  Depth(nm)  Figure 2.4: T h e band diagram under a pixel of the C C D w i t h V ^ j  a s  = -7 V  l i m i t i n g current, and a l l the applied voltage w i 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 w i t h the voltage at the b o t t o m of the C C D set to -7 V , the voltage used during this study. T h e depletion w i d t h is -11 / i m , leaving a field free region i n the active region of 20 fim. T h e m a x i m u m field i n the device is 15 k V / c m , much less than the breakdown field of G a A s of 300 k V / c m [ 2 1 ] . T h e 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 j u n c t i o n . _  12  2.4  M o v e m e n t of charge from pixel to pixel  If the gates i n 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 i n synchronism w i t h an input clock signal. In this experiment, the clock signal was run at 10 M H z . fa and fax were set at - 0 . 5 V and - 1 . 5 V , respectively. T h e fa electrode alternated between 2.5V and - 2 . 5 V 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 i n the clock cycle.  T h e 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 = t 2 , the charge has a l l moved to the fa electrode. A t t , the voltages on fax and fa go negative, and the charge starts 3  moving towards the fa gate of the next pixel, fa>. T h e 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 , t i , t and t . A n electron "packet" is also shown being transferred from one pixel to the next. 0  2  3  Chapter 3  Interactions of Particles in GaAs  3.1  Introduction  A n X - R a y i n G a A s w i l l interact w i t h the G a A s by ejecting an energetic electron from one of the atoms through either the C o m p t o n or photo-electric process. B o t h of these processes leave an excited atom, which w i l l relax to its ground state by either emitting 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 w i t h another atom, liberating another electron. T h i s w i l l result i n two energetic electrons (with energies from 10 to 50 keV) i n the G a A s . These electrons, as they move through the crystal, w i l l interact w i t h the G a and A s atoms to create further electron-hole pairs. T h e electrons w i l l continue generating e.h.p.s until 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 w i t h material i n three ways: pair production, C o m p t o n and photo-electric interactions[23],[24]. P a i r 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 C o m p t o n interaction involves a photon scattering from an atom, causing the atom to eject a " C o m p t o n " 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 C o m p t o n and photo-electric processes, the atom is left i n an excited state. T h e X - R a y s used to irradiate the G a A s C C D i n this study ranged i n energy from 8keV to 60keV, much less than the 1.02 M e V needed to create an electron-positron pair. T h e cross-sections for C o m p t o n and photo-electric interactions for incident photons i n G a A s w i t h energies ranging from 1 k e V to 100 k e V are shown i n Figure 3.7. T h e crosssections were calculated using the "photocoeff" program published by A p p l i e d Inventions Corp. Software. T h e photo-electric interaction is more likely i n this energy range, and for photon energies below 30 k e V the chance of a C o m p t o n 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 Photo-electric Effect  Since a photon is completely absorbed i n a photo-electric interaction, the chance, p(z) of the photon being absorbed w i t h i n a distance dz at a given depth z i n a material is given by  p(z)dz = A exp(—\z)dz  (3.10)  16  1e+07 1e+06  Photo-electric Compton  F  E100000 V CO  C  10000 r  o cu CO  1000  o  CO  co o  100 10 1 1  10 Energy (keV)  100  Figure 3.7: T h e C o m p t o n and photo-electric cross section for X - R a y s of energies from 1 to 100 keV i n G a A s where A is the linear absorption coefficient of the X - R a y i n 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. T h e 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  (3.11)  P(z) = 1 - e x p ( - A z )  T h e chance that a K  a  photon from the six elements used i n this work w i l l be absorbed  i n 30 fim of G a A s , the depth of the active region i n the C C D , is shown i n table 3.2 W h e n a photon interacts w i t h an atom by the photo-electric effect, an electron is ejected from one of the inner shells. T h i s ejected electron, the photo-electron, has an energy of E — E , where E is the energy of the incident photon, and E s  s  is the binding  energy of the shell that the electron has been ejected from. T h e photon has an -80%  17  Table 3.2: Chance for absorption i n 30//m of G a A s of a K used i n this work. Element K X - R a y energy (keV)[25] Linear photo-electric absorption coefficient, A (1/cm) Chance of absorption a  Q  X - R a y from the elements  Cu 8.047  Rb 13.394  Mo 17.489  Ag 22.162  Ba 32.19  Tb ' 44.17  352.95  649.11  320.32  166.93  58.54  23.02  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 B o r n approximation gives the partial cross section for an electron to be ejected i n a direction given by 9 and <fi as [27]  (l-/?cos(0))  4  (3.12)  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 distribution can be treated as being independent of 9. Figure 3.8 shows the angular distributions i n <p, w i t h 9 = 0, for a photo-electron ejected w i t h small energy (3 = 0) and for a photo-electron w i t h E = 50 k e V (3 = 0.414). T h e excited atom can relax to its ground state i n two ways. T h e first is for an electron from an outer shell to take the place of the ejected electron, emitting an X - R a y of energy E — E , where E is the energy of the outer shell involved i n the process. T h i s X - R a y is s  0  0  18  Figure 3.8: T h e angular distribution i n <j> (with 6 = 0) of ejected photoelectrons for /3 = 0 and for j3 = 0.414, normalized so that the m a x i m u m probability is 1.  called a secondary X - R a y . T h e second method is an Auger process, i n which an electron "falls" from an outer shell into the vacancy i n the K - s h e l l , ejecting another outer shell electron of energy E — E  0  i n the process [28]. T h e 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-shell are [29]. G a - 50.7% A s - 56.2%  19  3.4  Creation of electron-hole pairs  T h e photo-electron and the secondary electron created i n 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. T h e process continues until the energy of the ionized electron-hole pairs is a few e V . These low energy electron-hole pairs are unable to cause further ionization, but instead lose energy to lattice vibrations, eventually cooling down to ambient temperature.  T h e average number of electron-hole pairs, N h , created in this cascade e  p  of electrons by an electron of energy E can be described by the ratio w = E/N ^ . e  p  The  accepted value of w for G a A s is 4.2 eV/e.h.p.[14]. T h a t is, on average it takes 4.2 e V to create a relatively long-lived electron-hole-pair i n G a A s . T h e 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. T h e variance i n N h e  p  is proportional to N h [30]. T h e constant of proportionality, called the Fano factor, is e  p  a function of the material w i t h i n which the electron interacts. T h e 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 -/V hp = wE. e  a  2  = /iV p. e h  T h e variance of this distribution would be  T h e X - R a y s used i n this study had energies from -10 keV to -60 k e V ,  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  Interactions of electrons i n G a A s  T h e photo-electrons and Auger electrons created by the incident X - R a y have energies from -1 k e V to -50 k e V . These electrons interact w i t h 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 w i t h loosely bound conduction electrons i n the solid. Faster secondary electrons can also be created through this method, or by interactions w i t h the inner shell electrons of the solid. A n o t h e r type of interaction, plasmon scattering, occurs when the C o u l o m b field of the incident electron disturbs the long range correlation i n the C o u l o m b field of the conduction band electrons, exciting collective oscillations of these electrons, called plasmons. A l l of these interactions are included i n the phenomenological "continuous energy loss approximation" of Bethe[32]. T h i s gives the energy loss of an electron per distance traveled, dE/dx,  i n a material w i t h 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 i n 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 - keV 3  (3.14)  B y integrating dx/dE from (3.13) from the i n i t i a l energy of the electron, E, to 0, one can find the mean distance traveled by an electron of energy E i n G a A s . T h i s distance is the mean distance the electron would travel i f it d i d not change its direction of travel through the interactions. T h e actual displacement of the electron from its starting position w i 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 G e . T h e calculation was done for G e because its atomic number (Z = 32) is in-between that of G a and A s (Z = 31 and Z = 33), and its density is the same as G a A s .  3.6  Escape of particles f r o m the detector  Not a l l of the energy of the photon is always absorbed by the detector. T h i s is because the detector has a finite volume, so some of the electrons and photons created i n 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]. T h i s 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 Energy(keV)  35  40  45  50  Figure 3.9: T h e mean path length of an electron i n Ge, calculated using the continuous energy loss approximation of Bethe.  W h e n recording the number of electrons, N, collected i n 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 w i l l result i n a peak at TV = E/w.  W h e n an X - R a y escapes, a l l of the energy of the X - R a y  escapes the detector. T h e escape of X - R a y s of energy E  s  N = (E — E )/w. s  w i l l result i n a second peak at  In contrast, the escape of an electron does not always result i n the  same energy loss; the loss depends on how far the electron has traveled before it leaves the detector. T h e 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). T h e distribution of the number of electrons deposited i n the detector due to electron escape processes w i l l therefore have a t a i l at lower N . T h e shape of this t a 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  E l e c t r o n Transport  4.1  Introduction  Figure 4.10 shows a time-line of the creation and collection of electron hole pairs i n the C C D . T h e i n i t i a l interaction between the photon and solid (Figure 4.10-a) and the creation of electron hole pairs (Figure 4.10-b) were discussed i n sections 3.2 and 3.5. T h i s chapter w i l l discuss the transport of the e.h.p.s after the i n i t i a l distribution has been created (Figure 4.10-c and -d). For the purpose of this discussion, two different regimes w i l l be studied: that where a l l of the e.h.p.s were created i n the depletion region, and that where a l l the e.h.p.s were created i n the field-free region. The high energy photo-electron created by an incident X - R a y w i l l leave a high density track of electron hole pairs i n its wake. A t first, the electron-hole pairs w i l l spread by ambi-polar diffusion (Figure 4.10-c). W h a t happens next w i l l depend on whether the charge was deposited i n the field-free or depletion region. If the charge is i n the field-free region, the charge w i l l continue to diffuse until it enters the depletion region, recombines or is trapped. If, however, the charge is i n the depletion region, then after -400 ps the field w i l l fully penetrate the charge distribution and the electrons and holes w i l l start 24  25  to drift towards the top and b o t t o m 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 b o t t o m of the depleted region. A t this point, the electrons become trapped i n one of the pixels and they w i 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 i n a straight line through the C C D . This, of course, is not what w i l l happen. T h e electron w i l l be scattered by numerous collisions during its travel. T h e effects of this scattering on the shape of the distribution were modelled by a Monte C a r l o simulation, which is discussed i n 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 i n the C C D w i l l be zero except for i n the depleted regions near the p - p , p - n and n - C e r m e t junctions. T h e field that electrons w i l l drift i n is created by +  _  _  the p - n j u n c t i o n (see Figure 2.4). W i t h a bias on the substrate of -7 V , the depleted _  region is 11 tim deep. T h e field w i l l increase linearly from the zero at the b o t t o m of the depletion region, to a m a x i m u m field of E  = 1.5 x 10 V / c m at the p ~ - n junction 4  max  and w i l l then decrease rapidly (within 1 /mi) to zero field.  26  (a) 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.  (b)  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  W h e n the electron-hole pairs created by the incident X - R a y have a l l cooled down to room temperature, to a good approximation they are distributed i n a Gaussian cylinder w i t h a radius of a = -0.1 / i m along the path of the photo-electron that created them[35]. T h e density of the electron-hole pairs i n the cylinder is approximately Gaussian i n the radial direction outward from the axis of the cylinder. T h e density of e.h.p.s per unit length, i V , can be found by dividing the energy loss of the electron per unit length, 0  dE/dx,  (equation (3.13)) by the average energy needed to create an electron-hole pair  in G a A s , w = 4.2 e V . T h e number of e.h.p.s created i n 1 / i m by a 30 k e V electron i n G a A s is 685. T h e density of e.h.p.s along the axis of the cylinder of charge created by this electron is 1.1 x 1 0  16  cm  - 3  (from equation (4.16)). Figure 4.11 shows a plot of N  0  as a function of x. A s the energy of the electron gets lower, the linear density of e.h.p.s increases, until the last 10 k e V of energy is deposited i n 1 / i m . T h i s last m i c r o n of charge is so much denser than the rest that a better model of the charge distribution is a -0.1 //m thick Gaussian cylindrical t a i l w i t h a length dependent on the i n i t i a l energy of the photo-electron, followed by a Gaussian b a l l of charge roughly 0.25 / i m i n radius. If the photo-electron has an i n i t i a l energy of less than 10 k e V , then there w i l l be no tail.  A simplified picture for the electron m o t i o n 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  cm  - 3  i n our case.  Electrons and  28  Ball Region  Tail Region  5000  2000  4500 (-  1800  4000  1600  3500  1400  1 3000  1 1200  q- 2500  - 1000 £  4 2000  - 800  1500  600  1000  400  500  200  2  0  0  10  15  20  25  x(|im) Figure 4.11: T h e linear e.h.p. density (N ) and the time (t) required for the i n i t i a l distribution to diffuse to an on-axis density of 1 0 c m for a 60 keV photo-electron as a function of the distance traveled by the photo-electron. 0  14  - 3  holes outside of the radius of penetration of the field w i l l be swept towards the top and b o t t o m of the C C D , respectively. Electrons and holes inside of the radius of penetration w i l l undergo ambipolar diffusion. T h e speed of the diffusion is given by the ambipolar diffusion constant, D , which is related to the electron and hole diffusion constants,  D  Ap  n  and D , i n the l i m i t where the electron and hole concentrations are much greater than p  the donor or acceptor density, by [36]  _  2D D n  p  (4.15)  D +D n  For  GaAs, D  n  and D  p  p  for an electron or hole density of 1 0  1 6  cm  3  are 222 c m / s  and 10.4 c m / s , respectively[21]. T h i s gives an ambipolar diffusion constant of D  2  2  a  p  =  29  19.8 c m / s . For the track section of the e.h.p. distribution, the electron-hole pair den2  sity, Pehp,cyi(?~, t) at a radius r and time t is found by solving the diffusion equation i n a cylindrical co-ordinate system to get N Peh ,cyi(r, t) = P  • °£  (! +  where N i  ax S  exp[-r /(2a 2  + AD t)]  2 0  (4.16)  ap  ^ f )  is the on-axis density of the e.h.p. track at t = 0, and o is the i n i t i a l radius 0  of the distribution, 0.1 fim. N  is related to the linear density of e.h.p.s, 7V , by  axis  0  N  = -  axis  \  (4.17)  T h e time for the distribution to diffuse w i l l be the largest at the point where the t a 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. T h e distribution w i l l diffuse to an on-axis density of 1 0  1 4  cm  - 3  after -400 ps, and w i l l  have a w i d t h of -1.25 /zm at this time. T h e e.h.p.  density i n the ball section of the distribution is found by solving the  diffusion problem i n a spherical co-ordinate system. T h e solution is  Peh baii(r, t) = P)  M  |  J  a p t  ^  exp[-r /(2a 2  / 9  2  + AD t)}  (4.18)  ap  In this case, -/V is the concentration of e.h.p.s at r = 0 and t = 0, and a 0  0  = 0.25p:m.  Solving this equation, it was found that the distribution would take -320 ps to diffuse to the background density, and the w i d t h of the distribution at this time is -1 um. A l t h o u g h a very simplified model has been assumed, we can conclude that the time taken for the applied field to start i m p a r t i n g 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 electrons  Once the electric field has penetrated to the centre of the electron track, a l 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 m o b i l i t y of the electrons and  E is the electric field acting on them. W h e n the voltage applied to the substrate is -7 V , the depleted region is xj = 11 /zm deep, and the m a x i m u m field, E , max  is 15 k V / c m .  T h i s field is larger than the saturation field of G a A s , so / / w i l l not be constant. Using e  the values of v  ift  dr  as a function of drift field, E, found by R u t h and Kino[37], the drift  time across the depleted region,t ift, was found by dr  (4.19)  tdrift  was found for the values for the fields and drift depths given i n section 4.2. Because  the field is zero at x = 0, and no diffusion was incorporated i n this simple model, the drift time is highly dependent on the value for XQ. For x = 1 ^m, 0  tdrift  —  XQ  = 0.1 / m i ,  tdrift  = 96 ps. For  74 ps. These times are of the same order as the time for the initial  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 i n the charge column, then each pixel w i l l collect a l l the charge that is created i n a 20 / m i region (the length of a pixel) directly  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. T h i s is called charge sharing. To make an estimate of the amount of charge sharing i n the device due to the length of the initial charge distribution, the scattering of the electron must be taken into account. T h i s is done using a M o n t e C a r l o simulation and discussed i n section 6.5.2. A second k i n d of charge sharing can occur i f a large charge is introduced into the C C D . Too many electrons can affect the potential i n the pixels under the C C D , effectively m a k i n g the wells shallower for additional electrons. If enough charge is added, the electrons w i l l spill over into neighbouring pixels. Additionally, a l l of the charge i n a pixel may  not be transferred to an adjacent pixel during the charge transfer process i f the  charge i n the pixel is large. T h i s second k i n d of charge sharing is much more noticeable w i t h the C C D s used i n this study than charge sharing caused by the length of the i n i t i a l electron distribution (see section 6.9).  4.5  Electrons created in the  field-free  region  Electrons and holes created i n 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 u n t 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 fieldfree region to the depletion region. T h i s calculation is, i n general, quite complicated, so a number of simplifications were made. First, it was assumed that the field-free region was  32  infinitely deep. T h i s avoids complications arising from electrons piling up at the  field-free  - substrate interface. Recombination was ignored, even though it w i l l be a large factor considering the time-scales involved (see section 4.6). Finally, only the ball section of the e.h.p. distribution was considered. Using these assumptions, the time it would take for a percentage of the ball of charge to diffuse to the depletion region was calculated. A t most half of the charge w i l l be collected, as the other half w i l l diffuse i n the opposite direction. T h e Gaussian half w i d t h , a, of the b a l l as a function of time, t, is  (4.20)  T h e fraction of charge, F, from a ball deposited at a i n i t i a l distance d from the depletion region, which has travelled into the depletion region by time t is given by  F = 1/2(1 -  Erf(d/tr(r)))  (4.21)  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 ball. T h e effects of these e.h.p.s on the spectra seen by the C C D are discussed in section 6.6.  33  40 60 Time(us)  100  Figure 4.12: T h e fraction of the total charge of the ball that has diffused into the depletion region as a function of time for d = 1,5,10 and 15 jj,m. T h e curves approach 0.5 asymptotically as at most half of the total charge w i l l diffuse into the depletion region. 4.6  Recombination  A c c o r d i n g to Nelson and Sobers [38], the radiative recombination lifetime  T&  tron i n G a A s w i t h an equilibrium electron and hole concentration of n  and p ,  0  ra  of an elec-  0  respec-  tively, is Trad  B(n  0  (4.22)  +po + A n )  where A n is the concentration of excess electron hole pairs and B is the radiative recombination coefficient. Nelson and Sobers found B to be 3 . 7 x l 0  - 1 0  c m / s . There are 3  two different densities at which recombination could i n principle be important.  The  first corresponds to the i n i t i a l diffusion of the distribution from its i n i t i a l density of A n ~10  16  cm  - 3  to the background density, and the second corresponds to the diffusion of  34  e.h.p.s i n the field-free region w i t h A n ~ 1 0 10  16  cm  - 3  i n G a A s doped at N  A  = 10  14  1 4  cm  cm  - 3  ,  - 3  . For an excess electron population of  T  rad  = 250 ns. T h i s time is large com-  pared to the time for the electron-hole pairs to diffuse from their i n i t i a l distribution to the background hole concentration, so recombination should not be a factor during the ambipolar diffusion of the i n i t i a l distribution of the e.h.p.s or the drift of the e.h.ps i n the depletion region. T h e radiative recombination lifetime for e.h.p.s at a concentration of A n = 1 0  14  cm  i n the field free region is -14 ps.  - 3  A s discussed i n section 4.5, this  is s m a l l compared to the diffusion time for the e.h.p.s created at depths greated than 11 pm i n the device (see figure 4.12). Recombination w i l l therefore be a large factor for e.h.p.s created i n the field-free region.  4.7  Summary of transport  processes  T h e important length scale i n the C C D is the pixel pitch of 20 pm. If the ball of charge is deposited i n the drift region, then it w i l l have a w i d t h of o ~ 1.5 pm, which is not significant compared to the pixel w i d t h . If however, the b a l l is deposited i n the field-free region, then it w i l l have a w i d t h of up to a few pixel lengths by the time an appreciable fraction of the charge in the ball enters the depletion region. There are three important time-scales i n the C C D . T h e first is the clock period of 0.1 ps. T h e second is the frequency of X - R a y events i n the C C D of -1 H z . T h e t h i r d is the radiative recombination lifetime of electron-hole pairs, ranging from 250 ns at an e.h.p. concentration of 1 0  16  cm  - 3  to 14 ps at an e.h.p. concentration of 1 0  14  cm  - 3  . If the e.h.p.s  35  are deposited i n the depletion region, they w i l l be quickly swept into the well of the C C D and then transported to the output. T h i s w i l l a l l occur w i t h i n -500 ps, much smaller than all of the relevant time-scales. If, on the other hand, the e.h.p.s are deposited i n the fieldfree region, there w i 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 b o t h the clock period and the recombination lifetimes, but are still 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 i n the field-free region w i l l contribute to the spectra i n the C C D .  Chapter 5  Experiment  5.1  Experimental Setup  T h e C C D is run at room temperature at a frequency of 10 M H z , w i t h a substrate voltage of - 7 V . T h i s substrate voltage was chosen as it was the largest that was believed to be usable without harming the C C D . T h e output of the C C D w i t h no input signal consisted of a square wave centred around zero volts w i t h a peak to peak voltage of 620 m V . T h e 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 . T h e output of the C C D was sent to a Tektronix D S A 602 digital sampling oscilloscope. D a t a 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. T h e 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 T b 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 m V , and a typical signal ranged from 5 m V to 45 m V 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 X-Ray from Tb. Q  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 C C D ' 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 C C D ' 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 C C D ' 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  T h e Choice of N  The choice of  N  s i g n a  i  s i g n a l  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 T b 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 C C D ' 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 h C  a r g  ed,  then for  N  s i g n a l  > N  c h a  r ed> g  there should be  41  Table 5.3: The area (A), width (w) and position (x) of the first and third peaks for T b data analyzed with N 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 s i g n a  ^signal  A  3 5 7 9  21 40 9.6 9.8  First Peak x w (CU.) (CU.) 662 269 790 481 744 281 810 305  Third Peak w A x (CU.) (CU.) 214 37 1051 226 129 1090 47 1156 239 257 48 1206  ratio (%)  57 31 20 20  Resolution (keV) 12.4 13.0 13.8 14.8  no change in the signal charge calculated by the analysis program. The change in the shape of the spectra from Nsignai  N j S  g n a  i  =  3 to  N i S  g n  ai =  5 is quite large, and the change for  larger than 5 is much smaller. This suggests that the charge in a signal from a T b  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 trade-off between the decrease in resolution as the area of peak 1 as  5.3  N  s i g n a  i  N j S  g n a  i  N j s  g n a  i  =  5, a choice that was a  was increased and the increase of  was decreased.  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  i  r~.  1  1  600  r  Data — Fit •••••••• Peaki 1 Peak 2 — Peak 3 —  % 100  (b)  500 o | 400 E  Data Fit Peaki Peak 2 Peak 3  g. 80 c  D 0  1300  60  8 200  0 40  o  20 0  100 0  200 400 600 800 1000120014001600 Charge units (C.U.)  0 180  200 400 600 800 1000120014001600 Charge units (C.U.) 1  1  1  160 Data — Fit Peaki Peak2— Peak 3 —  140 o | 120 £ 100 CD  w 80 o 60 0  1  1  1  — —  j' •  lift  §! | |[/ ! |; I | | I  1 ;  40 20 200 400 600 800 1000120014001600 Charge units (C.U.)  00  Figure 5.14: The spectra of T b X-Rays analyzed with N figures (a), (b), (c) and (d) respectively.  200 400 600 800 1000120014001600 Charge units (C.U.) s i g n a l  = 3, 5, 7 and 9 shown in  43  450  0  2 0 0 4 0 0 6 0 0 800 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 m V to 44 m V 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 m V is shown in Figure 5.15.  The histograms were then fitted to Gaussians with an area A , position x and width, 0  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 2  nd  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 -  CD  600 -  'E  D) CO  JC  O  400 200 0 0  5  10  15 20 25 30 Input voltage (mV)  35  40  45  Figure 5.16: The charge deposited in C C D 2 by a known input pulse as a function of the height of the pulses, analyzed with N j 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 S  gna  2  The resolution of the detector at each input voltage is found by  R  AE  (5.23)  E  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, x , on the histogram. A plot of the 0  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 = 96P-  0 8 9  (5.24)  45  data ° Fit - -  c o o  CO CD  rr  1000 Charge Units  Figure 5.17: The resolution of the charge deposited in C C D 2 by a known input pulse as a function of the height of the pulses. The data was analyzed with N i = 5. s i g n a  Assuming the charge injected into the C C D is constant for a given input voltage, equation (5.24) gives the maximum resolution of the C C D under the operating conditions.  5.4  Response of the detector to Characteristic 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 X-Ray energy) Cu, Rb, Mo, A g , B a and Tb. The energies of the K  a  a  X-Rays of these elements range from 8.047 keV for C u to 44.47 keV for Tb. Table 5.4 shows a listing of the K energies for all six elements[25]. The source was shone on the Q  46  Table 5.4: The K energies of the elements used in this study a  Element K X-Ray Energy (keV)[25] Q  Cu 8.047  Rb 13.394  Mo 17.489  Ag 22.162  Ba 32.19  Tb 44.17  A i  Aluminum shielding  Am  Figure 5.18: A schematic of the source used to create characteristic X-Rays. The Am is an annulus. X-Rays emitted by the A m are absorbed by the foil, and the foil emits a characteristic X-Ray. Any X-Rays emitted by the A m that do not strike the foil will be absorbed by the Aluminum shielding. 2 4 1  2 4 1  2 4 1  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 C C D s that will be referred to as C C D 1 and C C D 2 . A run of 20,000 events was taken with each of the X-Ray energies. Figure 5.20 shows the spectrum for Mo K X-Rays on C C D 1 and a  47  CCD Chip D S A 6 0 2 digital C C D Card  ^  sampling oscilloscope  CCD Output Ceramic Lid  Waveforms that triggered events  Electrician's Tape  Emitted <X-Ray  IBM PC  Source  Figure 5.19: A schematic of the experimental setup used to study the X-Ray spectra. CCD2.  Figure 5 . 2 1 shows the spectrum for Tb K X-Rays on Q  were made with  5.5  The  2  4  1  N i S  A m  g n a  j =  CCD2.  A l l the histograms  5.  spectrum  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 7 2 0 0 0 counts was taken. Figure  5.22  Nsignai =  5  shows the histogram of the  2 4 1  and 7 . The two values of N  energies in the  2 4 1  s  i  A m spectrum found using C C D 2 analyzed with g  n  a  i  were used to make sure that the increased  A m spectrum did not create charge sharing among more than five pixels,  thereby increasing the value needed for N the peaks was not large, so N  s  i  g n  ai  S  i  g n  ai-  The change in the relative intensities of  did not need to be increased.  48  1000  ~I  900  J  !  i  T"  (a)  800 | 700 | 600  1500  I  400  D  5 300 200 100 0  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 ) C C D l and (b)CCD2 by the characteristic X-Rays of Mo, analyzed with N i = 5. s i g n a  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 ig i = 5. s  na  49  0  200 400 600 800 10001200 14001600 Charge units (C.U.)  0 200 400 600 800 1000120014001600 Charge units (C.U.)  Figure 5.22: The charge deposited in C C D 1 by X-Rays from an with N  s i g n a  i = (a) 5 and (b)7.  241  Am source, analyzed  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 C C D 1 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 A g 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 B a and T b runs on C C D 1 , 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 T b 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  T h e 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 C C D ' s waveform, rather than triggers from actual events in the C C D . Figure 6.23 shows the spectrum of A g for CCD1 and C C D 2 . The runs with C C D 2 show no evidence of the noise peak. This is because the noise levels in the C C D waveform in C C D 2 were larger, causing the trigger level to be raised much higher in the C C D 2 runs than the C C D 1 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 C C D 2 was also run with the trigger level set lower. A small noise peak is evident in the Rb and B a 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 spectra obtained with C C D 1 . Q  52  0  200 400 600 800 1000120014001600 Charge units (C.U.)  0 200 400 600 800 1000120014001600 Charge units (C.U.)  Figure 6.23: The spectra for the K X-Rays from A g on ( a ) C C D l and (b)CCD2. The spectrum for CCD1 shows the noise peak, while that for C C D 2 doesn't. Q  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 i i = 5. The areas are in units of 1000 Charge Unit Counts, while x and w are expressed in Charge Units. S  Element Rb Mo Ag Ba Tb  A 51 68 40 25 26  X  172 161 207 200 160  w  111 99 131 142 89  g n a  53  1800  Charge units ( C U . )  Figure 6.24: The signal peaks, indicated by arrows, for the K X-Rays of Rb, Mo and A g on C C D 2 . 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. Q  6.3  T h e Signal Peak  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 A g incident on C C D 2 . 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 Scale  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 C C D 1 and C C D 2 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  -  r  i  i  1  1  1  1200  1  (a)  800  !  1  1  -T  "1 • • • |  /  1100 • (b)  /  JOOO  ^ 700  p  ^600  1  ^ 900  A  •  c  A  o 2w 500 o £ 400  § 800  Data ° Fit -----  A' °  •  /'  1 700 Q. « 600  (8  CD  A  0  Q- 300  A  200  500  1  Data ° Fit  cr'  400 i  100 10  15  i  20  i  i  i  i  25 30 35 40 X-Ray Energy(keV)  i  45  300  50  10  Figure -6.25: Signal peak positions of the known and (b)CCD2 from the data analyzed with N i ting function of the peak position, P as a function dent X-Ray is P = -6.1C.U.+19C.U./keV E. For P = 197 C.U.+20 C.U./keV E. s i g n a  i  i  i  15  20  25 30 35 40 X-Ray Energy(keV)  45  50  energy X-Rays for ( a ) C C D l = 5. For C C D 1 , the fitof the energy E of the inciC C D 2 , the fitting function is  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 rays from the five elements studied, Q  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 at higher energies.  s i g n a l  = 3 than 5, but setting N j i = 3 creates artefacts s  gna  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 i = 3 and 5. s i g n a  Element Rb 13.4 K X-Ray energy (keV) 424 N i g a i = 3 position ( C U . ) N g i g n a i ^ resolution 36.7% N ^ n a i ^ position ( C U . ) 461 57% N ignai=5 resolution  Mo 17.5 493 36% 554 46%  a  S  n  S  6.4  Ag 22.2 556 36% 615 42%  Ba 32.2 783 24% 845 28%  Tb 44.2 1083 14% 1092 28%  2 4 1  Am 60 -  1325 13.6%  The High-Energy Peak  The A g 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 C u and Rb spectra taken using C C D 2 . The Rb spectrum shows both a signal and high-energy peak, while C u shows only the high-energy peak. The C u K X-Rays were not only low in intensity, but Q  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 C u and Rb match almost perfectly. The HEPs of Mo and A g 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 C u and Rb Spectra for runs on CCD2 analyzed with N i = 5. The y-axis was rescaled for the Rb data to allow a direct comparison of the shape of the spectra. s i g n a  Table 6.7 shows the areas, positions and widths of the HEPs for X-Ray spectra on C C D 2 . Using the calibration made in section 6.3.1 for C C D 2 , the high-energy peak was found to be at 50 keV, which is more energetic than any of the K X-Rays studied, but a  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 C C D 2 analyzed with N j i = 5. The areas are in units of 1000 Charge Unit Counts, while x and w are expressed in Charge Units. S  Element Cu Rb Rb (run 2) Mo Ag Ba Ba (run 2)  6.5  A 98 156 76 33 14 35 32  x 1160 1169 1071 1226 1227 1189 1195  gna  w 387 388 509 541 450 381 335  T h e Escape Peak  Both the B a and Tb spectra from C C D 1 and C C D 2 showed a similiar low-energy shoulder whose position varied linearly with the energy of the X-Ray. Figure 6.27 shows the B a and T b spectra on C C D 2 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  i  1  600  r  Data Signal  (b)  600  500  <B 500 +-» c E 400  — —  Shoulder  3 400 \ g_ 300  <D  a  to  » 300 c  g 200 r O  O 200  100 100 00  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 X-Rays on C C D 2 analyzed with N i g 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. Q  S  n  deposited in the detector by electrons that escaped from the detector.  6.5.1  Escape of Secondary  X-Rays  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) = e x p ( - A P )  (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 30Lim  30-x r •  50|im 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 P{X) = —  r  r*  2w  d9  4TT JO  JO  -» d(f) sin (f>exp[-\R(X,e,(t))}  (6.27)  The secondary X-Ray is emitted from the position that the incident X-Ray interacted with either a G a 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. f  30 0  PM = ° J  dxf™dyexp[-\'x}P(X)  7oi° T^Zr' J dxf dyexp[-X'x} 30  (6-28)  50  0  The probability of escape of secondary X-Rays from the C C D was calculated for the KQ, X-Rays of G a and As for incident X-Ray energies from Cu, Rb, Mo, A g , B a and T b 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 = where Pa  a  (P apGaF G  Ga  APGaAs  +  A  As  and PA are the probabilities for an escape by a K S  an As atom, respectively.  PGaAs, PGa  and  p  As  (6.29)  P spAsF )  a  X-Ray from a G a or  are the densities of GaAs, G a and As.  F d a n d FA are the fluorescence ratios of G a and As, 50.7% and 56.2%, respectively. S  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 K X-Ray Energy (keV)[25] Chance of escape Q  Cu 8.047 0.25  Rb 13.394 0.25  Mo 17.489 0.25  Ag 22.162 0.25  Ba 32.19 0.25  Tb 44.17 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, da i(9), was used to find the scattering e  angle of the electron, 9, the angle between the initial and final direction of motion of the electron. da i(9) gives the cross-section for an electron with a relativistic wavelength of e  A in a solid with atomic number Z to be scattered into a solid angle dQ = 2TT sin(9)d9. , do (9) = el  K  )  AZ 4  dn  2  6 4 7 r 4  , . (6.30) ^ * / f  -—r-s-  -n  «o[sin (^/2) 5] 2  2  + (  n n  where a is the Bohr radius and 8 is the screening parameter which is numerically equal 0  to 8 = 3.4 x 10~ Z /E 3  2/3  (E in keV)  (6.31)  A is given by  (2m E(l +  A  0  E/2m x )y/ 2  2  0  where h is Planck's constant, m is the rest mass of the electron and E is the energy of 0  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 Y(fim)  1  2  3  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 K X-Ray from T b traveling in the negative x direction and interacting with an atom at the origin. a  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 G a or As atom by a T b 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 K X-Ray energy (keV)[25] Photo-electron energy (keV) Mean path length (pm) Electron range (/dm) Range/(Mean path length) Chance of escape a  Rb 13.394 3.4 0.17 0.047 .276 <1%  Mo 17.489 7.5 0.57 0.161 .282 <1%  Ag 22.162 12.2 1.27 0.394 .310 0.011  Ba 32.19 22.2 3.52 1.231 0.35 0.039  Tb 44.17 34.2 7.47 2.85 0.38 0.083  Am 59.54 49.5 14.38 5.97 0.42 0.20  2 4 1  (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 Gaussian 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 Energy Deposited (keV)  32  34  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 T b  run on C C D 2 . 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 Energy Deposited(keV)  50  60  Figure 6.31: The energy deposited by a 44 keV photo-electron that escapes from the detector. 160  i  .  .  0  10  20  .  .  30 40 Energy(keV)  .  1  50  60  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  Experiment  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 G a 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 T b K  a  X-Rays incident on C C D 2 . 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 B a spectrum in figure 6.33-a is fit well by the escape, signal and high-energy peaks. The T b spectrum shown in figure 6.33-b is not. Another peak had to be postulated for the T b spectrum.  6.6  T h e Field-Free Peak  In order to obtain a good fit for the Tb spectra on C C D 2 , a third peak was postulated. The third peak was a Gaussian at lower energies than the first two, and is tentatively  68  600  1  I  1  1  1  1  i  i  (b) 500 Data — Escape — Signal Fit -  § 400 g. 300  Si U #/ u i / ' / ; ll fll  \  •  w  § 200 0 100 jr  i  0 0  200 400 600 800 1000120014001600 Charge units (C.U.)  0  —  .  .  -  \  '  \  i  *M  200 400 600 800 1000120014001600 Charge units (C.U.)  Figure 6.33: The spectra for (a)Ba and (b)Tb K X-Rays incident on C C D 2 fit with a signal and escape peak. a  identified as the field-free peak. Figure 6.34 shows the spectrum for T b K X-Rays on a  C C D 1 and C C D 2 fitted with the signal, escape and field-free peaks analyzed with N j i s  gna  = 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  Data Fit Noise Field-Free Escape Signal  0  1  —  —  200 400 600 800 1000120014001600 Charge units (CU.)  0  200 400 600 800 1000120014001600 Charge units (CU.)  Figure 6.34: The spectrum for T b K X-Rays on ( a ) C C D l and (b)CCD2 analyzed with N i g n a i = 5 fitted with noise, signal, escape and field-free peaks. a  S  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  Full Spectrum  Analysis  In tables 6.10 and 6.11 the positions, areas and widths for the peaks assigned to all of the spectra taken for C C D 1 and C C D 2 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 j i = 5. The areas are in units of 1000 Charge Unit Counts, while x and w are expressed in Charge Units. S  Element Rb Mo Ag Ba Tb  A 51 68 40 25 26  Noise x 172 161 207 200 160  w 111 99 131 142 89  A  Field Free x w  53  357  293  A  14 26  Escape x w  397 604  105 150  gna  Signal A 101 Ul 48 41 78  X  244 312 399 577 794  w 72 88 100 158 203  High Energy A X w 29 782 476 6 859 436 2.3 853 355 9.4 873 230  Table 6.11: The peak positions (x), areas (A) and widths (w) of the peaks in the spectra from characteristic X-Rays impinging on C C D 2 analyzed with N j 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. S  Element Cu Rb Rb (run 2) Mo Ag Ba Ba (run 2) Tb Tb (run 2)  A  Field-Free X w  40 20  790 619  481 232  Escape A  48 48 43 51  X  625 632 891 858  gna  Signal w  A  X  w  220 214 222 187  41 122 196 213 14 142 120 153  458 392 551 614 825 836 1091 1102  157 192 171 176 206 200 226 245  High Energy A X w 98 1160 387 156 1169 388 76 1071 509 33 1226 541 14 1227 450 35 1189 381 32 1195 335  71  6.8  The  6.8.1  2 4 1  2 4 1  A m  Spectrum  Theory  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 unimpeded. 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 probability 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 Am  linear absorption coefficient (1/cm)  probability of absorption in 30 //m of GaAs  probability of event from this energy  0.81 13 0.33 20.2 5.2 2.4 0.12 35.7  886.22 586.96 416.68 270.2 194.62 103.01 53.61 9.76  .930 .828 .714 .555 .442 .266 .149 .029  0.028 0.399 0.009 0.416 0.085 0.024 0.001 0.038  2 4 1  11.871 13.927 15.861 18.611 20.977 26.345 33.192 59.5364  0  10  20  Figure 6.35: Theoretical  2 4 1  30 40 50 Energy (keV)  60  70  80  A m spectrum in 30 tim of GaAs  73  Table 6.13: Peak data for the A m X-Rays on C C D 2 analyzed with N i = 5. The x-axis was calibrated using the C C D 2 5 peak calibration. The areas are in units of keV Counts, while x and w are expressed in keV. 2 4 1  s i g n a  Peak Name 13 keV 18 keV Field Free Escape 60 keV  6.8.2  A (keV Counts) 4201 4450 5631 906 2719  X  w  (keV) 13.1 17.9 43.5 45.8 55.6  (keV) 6.1 12.1 16.0 7.1 8.0  Experiment  Figure 6.36 shows the data obtained from shining an The N  s i g n a  2 4 1  A m source on the top of CCD2.  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] McGregor et. al.[41] Bencivelli et. al.[42] Bertuccio et. al.[15] Bertuccio et. al.[15] Hesse et. al. [43] This Work  L E C GaAs L E C GaAs L E C GaAs L E C GaAs L E C GaAs epitaxial GaAs GaAs C C D  -10 R.T. R.T. 20 -30 R.T. R.T.  7.5 37 7.5 28 3.7 4.3 16  4.5 22 4.5 16.8 2.2 2.6 9.6  75  Table 6.15: Range in the x-direction and chance of charge sharing for photoelectrons in Ge Element K X-Ray energy (keV) Photo-electron energy (keV) range of the electron in the X-direction, I (/nn) Chance for charge sharing Q  6.9  Charge  Ba 32.19 22.2 0.682  Tb 44.17 34.2 2.86  0.035  0.075  Am 59.54 49.5 3.08  2 4 1  0.15  Sharing  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 T b 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 W o r k  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 C C D s 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 T b 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 c m 14  - 3  to 10  13  c m , the active region would be fully depleted at - 3  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 K  a  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 K  a  spectra with an energy  of 50 keV. Its origin has been tentatively assigned to an X-Ray event caused by backscattered 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 CCD.  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 Technical Journal 4 9 (1970) 593. [3] A . R . Walker " B V I C C D astronomy of galactic globular clusters. II. M68" Astronomical Journal, 1 0 8 (1994) 555. [4] C.S. Barth et. al. 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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 G e V / c pions, kaons and protons" Phys. Rev. B 18 (1978) 1039.  Chapter 8  Appendix:  Spectra  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.)  0 250  200 400 600 800 1000120014001600 Charge units (CU.) -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 C C D 1 analyzed with N characteristic X-Rays of (a)Rb, (b)Mo, (c)Ag and (d)Ba.  s i g n a  i = 5 for the  86  350  I  '  1  0  200  400  1  1  1  !  r  1  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 ; characteristic X-Rays of Tb s  250  400  (a)  350  200  +<D3^  I  Data Fit High-Energy 1 High-Energy 2  150  0)  a  I 100 0  .(b)  1  1  1  i = 5 for the  1  1  1  1  D * -  Signal . High-Energy 1 — High-Energy 2 -----  i  If i  | 250 £200 w § 150  o 0  3  0  I  g n a  100  50  •• /A\f i/-A \ •  50 0  0 0  200 400 600 800 1000120014001600 Charge units (C.U.)  0  200 400 600 800 1000120014001600 Charge units (C.U.)  Figure 8.39: Spectra for X-rays impinging in CCD2 analyzed with N characteristic X-Rays of (a)Cu and (b)Rb.  s i g n a  i = 5 for the  87  200 400 600 800 1000120014001600 Charge units (CU.) 700  1  (c)  600 $ 500  1  1  1  . k J ^1 1  1  1  200 400 600 800 1000120014001600 Charge units (CU.)  1  Data — Fit -----. Escape Signal — High •  C  £ 400  a <2 300 c 3  0 200 100 0 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 characteristic X-Rays of (a)Mo, (b)Ag, (c)Ba and (d)Tb.  s i g n a  i = 5 for the  88  Figure 8.41: Spectra for a second set of X-Rays impinging on C C D 2 analyzed with N = 5 for the characteristic X-Rays of (a)Rb, (b)Ba and (c)Tb.  s i g n a  i  

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