Applied thermoluminescence dosimetry

D DIM
COURSES
APPLIED
THERMOLUMINESCENCE
DOSIMETRY
Edited by
M Oberhofer and A Scharmann
Published for the Commission of the European Communities
by Adam Hilger

As the use of nuclear energy
increases, so too does the need for
methods of radiation detection and
dose assessment for a variety of
purposes, the most important being
personnel dosimetry and
environmental monitoring.
Thermoluminescence dosimetry
(TLD) is an important technique in
these areas and has also found
application in a wide range of
different fields in medicine and
biology, and industry and
archaeology.
The present volume, intended to
become the new standard reference
on TLD and its applications, arose out
of two courses held at the Joint
Research Centre, Ispra, in 1977 and
1979. The edited texts of twenty
lectures given by sixteen leading
experts in TLD are presented. The
book is divided into two parts, part I
dealing with fundamentals and part II
with applications.
Part I contains chapters on the
historical development of TLD; theory;
instrumentation; materials and their
properties; measurement; and
comparison of TLD to other solid state
methods in dosimetry. Part II covers
areas of application of TLD including
personnel dosimetry; environmental
monitoring; neutron dosimetry; glow-
curve analysis; medicine; biology
and related fields; high-level photon
dosimetry in industry; reactor
engineering; archaeology; and
dose standardisation and
intercomparison. An appendix is also
included which explains the system
of units adopted recently in radiation
and dosimetry.

Applied Thermoluminescence Dosimetry

Ispra Courses
Applied Thermoluminescence
Dosimetry
Lectures of a course held at the Joint Research Centre,
Ispra, Italy, 12-16 November 1979
EDITED BY M OBERHOFER
AND A SCHARMANN
Published for the Commission of the European Communities by
Adam Hilger Ltd, Bristol
EUftOP. Blblfoth.

© ECSC, EEC, EAEC, Brussels and Luxembourg 1981
Published for the Commission of the European Communities,
Directorate-General Information Market and Innovation,
Luxembourg.
EUR 6990 EN
LEGAL NOTICE
Neither the Commission of the European Communities nor any
person acting on behalf of the Commission is responsible for the use
which might be made of the following information.
British Library Cataloguing in Publication Data
Applied thermoluminescence dosimetry.
1. Thermoluminescence - Congresses
I. Oberhofer, M II. Scharmann, A
III. Commission of the European Communities
5 35'.35 QC479
ISBN 0-85274-544-3
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system or transmitted in any form or by any
means, electronic, mechanical, photocopying, recording or otherwise,
without prior permission of the copyright holder.
Published by Adam Hilger Ltd, Techno House,
Redcliffe Way, Bristol, BS1 6NX.
The Adam Hilger book-publishing imprint is owned by
The Institute of Physics.
Printed in Great Britain by J W Arrowsmith Ltd, Bristol.
Lectures of a course held at the Joint Research Centre of the
Commission of the European Communities, Ispra (Varese), Italy, in
the framework of Ispra Courses.

Contents
List of contributors ix
Preface xi
Part I: Fundamentals
1 History 3
A SCHARMANN
2 Theory
M BOHM AND A SCHARMANN 11
11
11
16
18
21
24
26
30
32
36
39
39
40
48
52
53
64
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
Introduction
Excitation by radiation
Thermal excitation and recombination
Phenomenological analysis
Kinetic models
Determination of trap parameters
Additional parameters
Computer simulation
Comparison with experiment
Conclusions
3 Instrumentation
H W JULIUS
3.1
3.2
3.3
3.4
3.5
3.6
Introduction
The heating system
The light detecting system
Special items
TLD readers and systems
Address list

vi Contents
4 Accessory instrumentation 67
M OBERHOFER
67
67
69
70
71
74
74
75
75
76
77
79
80
83
83
83
86
88
89
91
93
94
95
5.10 Tribothermoluminescence (or triboluminescence) 95
6 Preparation and properties of principal TL products 97
G PORTAL
97
97
106
109
111
115
118
123
123
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
Introduction
Heating planchets
Gas flushing
Reference light sources
Powder dispensers
Mechanical tweezers
Vacuum tweezers
Sieves
Ultrasonic cleaners
Annealing furnaces
Annealing stands
Irradiators
Literature
5 General characteristics of TL materials
G BUSUOLI
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Introduction
Linearity
Response to photons
Response to beta rays
Response to neutrons
Fading
Annealing procedures
Stability and reproducibility
Dose rate dependence
6.1
6.2
6.3
6.4
6.5
6.6
6.7
Introduction
Lithium fluoride
Lithium borate
Beryllium oxide
Calcium fluoride
Calcium sulphate
Aluminium oxide
7 Operational aspects
D F REGULLA
7.1 Introduction

Contents vii
7.2 Parameters affecting precision 124
7.3 Conclusion 140
8 Precision and accuracy of TLD measurements 143
G BUSUOLI
8.1 Introduction 143
8.2 Definitions 143
8.3 Assessment of random and systematic uncertainties 143
8.4 Sources of errors in TLD 145
8.5 Precision of TL measurements 146
8.6 Accuracy of TL measurements 149
8.7 Accuracy in low-dose measurements 150
9 Reference to other solid-state methods 151
E PITT AND A SCHARMANN
9.2 Radiophotoluminescence (RPL) 153
9.3 Colouring 155
9.4 Photographic processes 156
9.5 Stimulated exoelectron emission 157
9.6 Track detection 159
9.7 Change of resistance in silicon diodes 161
9.8 Scintillation dosemeter 163
9.9 Conclusions 163
Part II: Applications
10 Application of TLD to personnel dosimetry 167
E PIESCH
10.2 Performance specifications 168
10.3 Detector materials and specific requirements 170
10.4 Personnel dosemeter systems 177
10.5 Special applications 182
10.6 Future trends 192
11 Application of TLD systems for environmental monitoring 197
E PIESCH
11.2 Performance specifications 198
11.3 Properties of commercial TLD systems 198

viii Contents
11.4 Calibration technique for dosemeter batch and reader 214
11.5 Reproducibility and overall uncertainty of measurement 219
11.6 Interpretation of field exposures 220
11.7 Practical application 224
12 Applications of TL materials in neutron dosimetry 229
J A DOUGLAS
12.2 Neutrons and dosimetry 229
12.3 Thermal neutron detectors 232
12.4 Intermediate and fast neutron dosemeters 241
12.5 Possible future developments 253
13 Glow-curve analysis 259
A C LUCAS
13.2 Recording of glow curves 259
13.3 Measurement of neutron dose equivalent 261
13.4 Beta-ray measurement 265
13.5 Fading correction 266
13.6 Determination of time from exposure 268
13.7 Verification of data 269
14 Application of TLD in medicine 271
A F McKINLAY
14.1 Radiotherapy measurements 271
14.2 Diagnostic radiology measurements 271
14.3 Factors in the choice of dosemeters for clinical use 273
14.4 Radiotherapy absorbed dose measurements 279
14.5 Examples of the use of TL dosemeters in radiotherapy 283
14.6 Diagnostic radiology absorbed dose measurements 284
15 Application of TLD in biology and related fields 289
M OBERHOFER
15.2 Animal experiments 289
15.3 Bone dosimetry 290
15.4 Photon radiation quality measurements 291
15.5 Toxicity determinations 292
15.6 General biology and biochemistry 293
15.7 Ecology 293
15.8 Animal habit studies 295

Contents ix
16 High-level photon dosimetry with TLD materials 297
M OBERHOFER
16.2 Lithium fluoride 298
16.3 Lithium borate 306
16.4 Calcium fluoride 308
16.5 Other TLD phosphors 308
16.6 Final remarks 310
17 Application of TLD in reactor engineering 315
JRALAKEY
17.2 A survey of the application of TL in reactor environments 316
17.3 Application to neutron dosimetry 327
17.4 Environmental monitoring 331
17.5 Miscellaneous applications 333
Appendix 17.1 Calculation of gamma photon absorbed dose 333
Appendix 17.2 Cavity ionisation theory 337
Appendix 17.3 The intrinsic TL response per absorbed neutron 340
18 Application of TLD for dating: a review 347
G A WAGNER
18.2 Dating method 347
18.3 Dating applications 352
18.4 Conclusion 355
19 TL dating: techniques and problems 361
M J AITKEN
19.2 Application 365
19.3 Recent research and outstanding problems 369
20 Application of TL dosemeters in dose standardisation and intercomparison 383
G SCARPA
20.2 Dissemination of standards 383
20.3 Direct intercomparison methods 384
20.4 Characteristics of TL dosemeters used for mailed intercomparisons 386
20.5 Practical examples of mailed intercomparisons 386
20.6 Conclusions 390

x Contents
Appendix The new radiological (si) units and their conversion to the units
previously used 39 j
Index 3 9 3

List of contributors
Dr M J Aitken
Research Laboratory for Archaeology and the History of Art,
Oxford University, 6 Keble Road, Oxford 0X1 3QJ, UK
Dr M Bohm
Justus-Liebig-Universitat Giessen,
I Physikalisches Institut,
Heinrich-Buff-Ring 16, D-6300 Giessen, FRG
Dr G Busuoli
Comitato Nazionale per l'Energia Nucleare,
Laboratorio Fisica Sanitaria,
Via Mazzini, 2,1-40138, Bologna, Italy
Dr J A Douglas
Environmental and Medical Sciences Division,
AERE, Harwell, Oxfordshire 0X11 ORA, UK
Dr H W Julius
Radiologische Dienst TNO,
Utrechtsweg 310, N-6812 AR, Arnhem, The Netherlands
Professor J R A Lakey
Department of Nuclear Science and Technology,
Royal Naval College, Greenwich,
London SE10 9NN, UK
Dr A Lucas
Crystal and Electronic Products Department, The Harshaw Chemical Company
6801 Cochran Road, Solon, Ohio 44139, USA
Dr A F McKinlay
National Radiological Protection Board,
Chilton, Didcot, Oxfordshire 0X11 ORQ, UK

xii List of contributors
Dr M Oberhofer
Commission of the European Communities, Joint Research Centre,
Ispra Establishment, Applied Dosimetry Research,
1-21020 Ispra (Varese), Italy
Dipl. Phys. E Piesch
Kernforschungszentrum Karlsruhe GmbH, Hauptabteilung Sicherheit,
Postfach 3640, D-7500 Karlsruhe 1, FRG
Dr E Pitt
Dr G Portal
Commissariat a l'Energie Atomique,
Institut de Protection et de Surete Nucleaire,
Departement de Protection,
BP No. 6, 92260, Fontenay-aux-Roses, France
Dr D F Regulla
Gesellschaft fur Strahlen- und Umweltforschung mbH Miinchen,
Institut fur Strahlenschutz,
Ingolstadter Landstrasse 1, D-8042 Neuherberg, FRG
Professor G Scarpa
Comitato Nazionale per l'Energia Nucleare,
Centro di Studi Nucleari della Casaccia,
Laboratorio di Dosimetria e Biofisica,
SJ?. Anguillarese km 1 + 300,1-00100 Rome, Italy
Professor Dr A Scharmann
Dr G A Wagner
Max-Planck-Institut fiir Kernphysik,
Abt. Kosmochemie,
Saupfercheckweg 1, D-6900 Heidelberg 1, FRG

Preface
With the ever increasing use of nuclear energy, particularly for power production, there is
more and more need for radiation detection and dose assessment for a variety of pur-
poses. Two of these are environmental dose control and personnel dose determination.
These types of measurements are essential for ensuring the radiological safety of the
population as a whole and of individual radiation workers. Additionally they may have
great importance with respect to the legal aspects of nuclear energy.
Many radiation detectors and measuring devices have been developed over the last few
decades and some are being used routinely for environmental and personnel dose control.
One of them is based on the fact that some materials emit light when heated after
exposure to radiation. This technique is known as thermoluminescence dosimetry (TLD).
Because of its simplicity and suitability for automation much research and development
work has been put into this type of dosimetry, which has also turned out to be useful in
fields other than radiation protection.
The results of this research and development have been published in different scientific
journals, in various conference proceedings (like the proceedings of the International
Luminescence Meetings at Palo Alto, Gatlinburg, Riso, Krakow and Sao Paulo in 1965,
1968, 1971, 1974 and 1977, respectively), in some books on radiation protection and
solid-state dosimetry and in the only bibliography on the subject by J R Cameron,
N Suntharalingam and G N Kenney, which was published in 1968 by the University
of Wisconsin under the title Thermoluminescent Dosimetry.
According to the authors of this latter publication the book was 'designed to be a
comprehensive introduction to the technique giving much useful information as to
instrumentation, phosphor characteristics and applications'.
For many years this was considered as the standard reference book on the subject and
hence made use of by nearly all students and newcomers to the field. However, for some
years now there has been an increasingly felt need for an up-dated version of the book,
which sadly has not been produced.
Thus the idea was born at the Joint Research Centre (JRC) of the Commission of the
European Communities, Ispra Establishment, to collect all available material in the field
of TLD by organising a course.
Such a course was held within the framework of the Education and Training Program
of the JRC, 14-18 November 1977 in collaboration with the I Physikalisches Institut of
the Justus-Liebig-Universitat, Giessen. From the outset this Institute has contributed to
the understanding of the phenomenon of TL and to the development of TLD and is still
today actively engaged in many aspects of TLD research. Thirteen outstanding experts in

xiv Preface
the field of TLD agreed to present the latest state of the art. The course was such a success
that it was decided to repeat the course with the aim of perfecting the material with
regard to its content and presentation so that it would be suitable for later publication.
Only minor refinements in the course program needed to be made, including the addition
of lectures on subjects which had been missing in the first course, in order to have a com-
plete treatment of the field. The second course was held at the JRC, Ispra, 12-16 Novem-
ber 1979 and the contents now seemed to be worth presenting to a much larger audience
than the one which attended the course.
This book contains all the lectures given at the courses in sequence of their original
presentation with some changes in order to avoid too much overlap and repetition, which
understandably could not be eliminated completely. This was also not desirable in order
not to lose the independent character of each chapter. A number of cross-references have
been inserted into the texts to give maximum information on certain aspects of TLD.
The book starts with the historical development of TLD in chapter 1. In this first
chapter the reader's attention is drawn to the fact that TL is a widespread phenomenon
which has been known for a very long time. Of 3000 minerals, for example, three-quarters
exhibit this effect. The use of TL as a means for measuring radiation exposures or doses
actually started from the observation that many minerals exhibit natural TL and also from
the known uv sensitivity of manganese-activated calcium sulphate. In the late 1940s
much effort was put into the development of suitable TL dosemeters, mostly for military
purposes, and by 1950 many of the TL phosphors presently in use had already been dis-
covered and/or rediscovered for dosimetric applications. During the 1960s a second
generation of materials became available and a wide variety of commercial TLD systems
were developed to more and more sophisticated levels, taking advantage of rapid progress
in computer technology.
In chapter 2 an attempt is made to treat the phenomenon of TL theoretically on the
basis of general physics and with the help of the energy band model of solids. It is shown
that TL intensities can be simulated without any assumptions, but that other properties
of the material of interest need to be studied as well in order to obtain an overall picture
of the electronic processes occurring in the solid.
TLD instrumentation is the subject of chapter 3. The rather simple experimental
devices used for measuring the TL from various phosphors at the very beginning of TL
work have been developed into very sophisticated computerised TL readers which allow
hundreds or even thousands of TL dosemeters to be read fully automatically and also
include data processing. The most important common components of such a TL reader
system are described and examples of commercial instruments are given without going into
details of the electronics. The chapter ends with an address list of TLD instrumentation
manufacturers.
Besides some basic instrumentation, TLD work requires a number of accessories, like
powder dispensers, annealing stands, furnaces, etc, which are the subject of chapter 4.
This completes the instrumental aspects of TLD.
Chapter 5 is dedicated to the general requirements to be fulfilled by TLD materials
when intended to be used as dosemeters, in particular when worn in personal dosemeters.
Among other requirements, those discussed are the sensitivity of the phosphor, its energy
dependence, fading characteristics and the reproducibility obtainable.
There then follows, in chapter 6, a detailed description of each single phosphor of
current interest, starting in each case with a short historical review of its actual role in the

Preface xv
field of TLD. In this chapter the reader is informed about the preparation of the phosphor
and its thermal treatment afterwards, specific models are used to explain the physical
properties like glow curve and emission characteristics, and the actual dosimetric proper-
ties are discussed.
The aim of chapter 7 is to make the user of the materials described in chapter 6
familiar with the possibilities and limits of TL dosimetry. Experimental results obtained
with currently used techniques are reported and analysed to show the sources and magni-
tudes of errors. The author of this chapter shows that, besides the dependence of TL on
the energy and direction of the incident radiation, operational features such as the read-
out device, reading geometry, annealing cycle and dosemeter handling technique may be
major factors influencing the results. At the same time suggestions are made how to
minimise these effects in order to achieve maximum reliability in TL dosimetry.
While the main object of chapter 7 is to make the student familiar with sources of
error in TLD measurements, chapter 8 was written to clarify the difference between
accuracy and precision, to give examples and to show how error analyses are dealt with
mathematically.
Before concluding the first part of the book, reference is made in chapter 9 to other
solid-state methods such as radiophotoluminescence, coloration effects, the photographic
effect, exoelectron emission, track detection, neutron-induced defects and scintillation
which are used with success in the field of dosimetry. It turns out that, compared to all
the other solid-state methods, TLD is the best developed system.
Summarising, one can say that most of the fundamentals of TL which are needed for a
reasonable understanding of this phenomenon, its suitability and its advantages for dosi-
metric applications are discussed in the first part of the book.
The second part of the book has been compiled with the idea of showing where TL
already has been and is being applied successfully. Personnel dosimetry is such a field of
application. The near-tissue equivalence for the detection of photons, the low fading and
the high accuracy of a number of TL materials, coupled with the possibility of evaluating
a large number of dosemeters using automatic reader systems, proved to be very advant-
ageous. In chapter 10 the particular requirements for this field of application are discussed
and a comprehensive survey of TLD systems and dosemeter designs for routine personnel
dose control are given. Future trends of the development in this special field of applica-
tion are indicated.
Environmental monitoring is another application of TLD where interest is growing
rapidly. This subject is treated in chapter 11. TL dosemeters with low fading charac-
teristics, low zero reading and high accuracy are very well suited and mostly much cheaper
than other systems for monitoring the natural radiation background level and short-term
or long-term influences of nuclear installations. Proper individual calibration of the dose-
meters is of prime importance if high accuracy is to be achieved. Thus this chapter con-
tains a short section on calibration techniques.
Much work has also been put into the assessment of neutron doses using TL phosphors.
A review of this work is given in chapter 12.
Some knowledge of the complex processes involved when neutrons interact with
matter is required for a good understanding of the neutron response of TL materials. The
chapter therefore starts with a categorisation of the neutron reactions involved, a dis-
cussion of the appropriate parameters necessary to monitor the effects of neutrons and
some definitions of terms used throughout the chapter. The response of common TL

xvi Preface
materials to thermal neutrons and the factors affecting the measurement are dealt with in
more detail than in earlier chapters.
Methods of separating the- neutron component in a mixed radiation field and of pro-
ducing a high thermal neutron response by mixing a phosphor with non-luminous 6
Li salt
are discussed. Furthermore, techniques for increasing the intermediate and fast neutron
response of phosphors by the use of proton radiators, fission foils and moderators are
surveyed. The practical applications and limitations of these techniques in dosimetry are
assessed and the feasibility of using the neutron activation of a constituent of a phosphor
for dosimetry in therapy work or activity accidents is examined.
Finally, possible future developments in fast neutron dosimetry are considered.
In all cases treated in the last three chapters valuable additional information on the
type of radiation or the time since exposure, for instance, may be obtained from the glow
curves. The importance of this topic is underlined by the insertion into the course of a
lecture on glow-curve analysis, which is reproduced in chapter 13. It is shown there that
various analytical methods exist for complementing internal TL data with glow-curve
shape analysis. The chapter enumerates five such methods.
Many advantages of TLD over other dosimetric methods have favoured its application
in the medical field, where TL dosemeters are often preferred to ionisation dosemeters,
for example, mainly due to their small size and thus ease of placing them singly or in large
numbers within body cavities. The extent to which TL dosemeters are used today in
medicine is shown in chapter 14.
Biology is another field in which TLD has been applied successfully from the beginning.
Although this type of application was not included in the course the subject is treated
briefly, together with related ones, in this book in chapter 15 for the sake of completeness.
The possibility of assessing very high doses of 106
R or more with TL phosphors sug-
gests their application for certain dosimetric problems in technological fields (material
testing, electrical component testing, radiation sterilisation, etc), in the chemical indus-
tries (radiation chemistry, cracking of hydrocarbons, polymerisation, vulcanisation of
rubber, etc) and in food processing, for example. In chapter 16 an attempt has been made
to collect TL data relevant to high dose assessment. Some other TL-related phosphor
features, which in some cases may be useful for high dose measurements, have been
included in the text of chapter 16.
There have been a surprisingly large number of applications of TLD in the field of
reactor engineering. The published articles are widely dispersed in the literature and so are
not readily available. This is why this topic is summarised in chapter 17. Many practical
examples are described, such as reactor shield testing, fast reactor core measurements,
reactor gamma-heat measurements, problems associated with reactor neutrons, accumu-
lated activity transfer studies, etc. For a better understanding of certain peculiarities
associated with TLD in reactor engineering three appendices are added. These deal with
the calculation of gamma photon absorbed dose, an introduction to the cavity ionisation
theory and a short description of the intrinsic TL response per absorbed neutron and its
calculation.
In recent years a number of new 'atomic' tools, like radiocarbon dating, neutron
activation analysis and neutron radiography, have enabled archeologists to reveal new data
about ancient civilisations. A 'dating' method has been developed in parallel with these,
which takes advantage of the fact that many materials exist which show TL when exposed

Preface xvii
to radiation. Materials such as rocks, ceramics, slags, bones and meteorites, for instance,
can acquire significant levels of TL from 'natural' radiation. By measuring this TL the
radiation dose can be determined and from that the age of the object can be obtained.
This is the theme of the next two chapters which contain the contents of two unco-
ordinated lectures. Chapter 18, which was presented in the 1979 course, gives a summary
of the subject for the interested reader, while chapter 19, which was in the 1977 course,
gives the more specialised reader full details of the various techniques and their associated
problems. Although there is some overlap and repetition, the editors do not consider this
a drawback bearing in mind the much higher information content of both works taken
together.
The book concludes with a chapter on the applications of TL dosemeters in dose
standardisation and intercomparison. This is a field where TL detectors are increasingly
used as a consequence of the ease with which TL measurements can be performed and
also because their small size is an advantage, especially for postal intercomparisons.
Most authors refer to literature up to mid-1978, though in some instances literature
references up to the 6th International Conference on Solid State Dosimetry in Toulouse,
France, from 1-4 April 1980, have been inserted into the texts during the reviewing
period.
While writing their texts all of the authors were aware of the recent introduction of
the Systeme International d'Unites (si) and of the adoption, by the 10th General Confer-
ence of Weights and Measures, of special names for some units of this system used in the
field of ionising radiation and dosimetry. In spite of this, throughout the book the 'old'
units have been retained, such as the roentgen (R), the rad, the rem and the Curie (Ci).
This is because those units are still widely used and will continue to be used for a while,
together with the new units. They are also retained because many of the graphs selected
by the authors were drawn some time ago using the old units and could not be redrawn
economically and in a reasonable time using the new units. To convert from old to new
units, coulomb per kilogram (Ckg-1
), gray (Gy), sievert (Sv) and becquerel (Bq), the
reader is referred to the Appendix.
The editors wish to thank all the authors who contributed to the courses and thus to
the realisation of this book. Without their ready acceptance of the invitation to lecture at
the courses and to prepare lecture notes this book could not have been published.
Furthermore, the editors would like to express their gratitude to Mr B Henry, Manager,
Education and Training Program of the JRC, Ispra, who fully supported the course series
and the publication of these proceedings, and to the Ispra Courses Secretarial staff for
their assistance in the organisation of the courses.
We are also grateful to Adam Hilger Ltd, and in particular to its Managing Editor, Mr
K J Hall, for having accepted the material of the courses for publication and for having
prepared an edition, which hopefully will be widely distributed throughout the world.
Ispra Martin Oberhofer
May, 1980 Arthur Scharmann

Applied Thermoluminescence Dosimetry. Eds M Oberhofer and A Scharmann
© 1981 ECSC, EEC, EAEC, Brussels and Luxembourg
1
History
ASCHARMANN
Even prehistoric cavemen probably observed an effect which was surely known to the
medieval alchemists. Certain minerals, such as fluorite, exhibit a transient glow when they
are heated in darkness [1]. This phenomenon, today called thermoluminescence, is the
basis of one of the most important methods of modern integrating dosimetry.
One of the founders of modern chemistry, Sir Robert Boyle, described this effect. On
28 October 1663, he reported to the Royal Society in London the observation of a
strange 'glimmering light' when he warmed a diamond in the dark of his bedroom. He
said: i also brought it to some kind of glimmering light by taking it into bed with me,
and holding it a good while upon a warm part of my naked body'. Boyle also did some
other experiments on the shining of diamonds. He rubbed a diamond on several bodies
and held it near to the flame of a candle or a piece of hot iron.
In 1705 Oldenberg [2] described the phenomenon of thermoluminescence in the
mineral, fluorite. Besides this, other properties of such phosphors were also studied. In
1830 Pearsall [3] gave a description of the effects of electricity upon minerals which
phosphoresce upon heating.
Henri Becquerel [4] described in his work on measurements of infrared spectra in
1883 the effect of thermoluminescence, too: 'En chauffant dans l'obscurite une substance
phosphorescente a longue persistance, prealablement exposee a la lumiere, on voit la
phosphorescence s'aviver, puis s'eteindre ensuite rapidement'. This means: If you heat in
darkness a phosphorescent sample which was previously exposed to light, you can first
see the phosphorescence becoming brighter and then being extinguished rapidly. In this
work he remarked that the influence of red and infrared radiation was the same as that
of a rise in temperature. In 1842, his father E Becquerel [5] had already discovered
a new property of this radiation. The phosphorescence might be destroyed by red or
infrared light. An explanation of these results was given by the later measurements that
he carried out in the following way. Because of the influence of red and infrared radiation
the stored light is released very quickly as luminescence and therefore the usually slow
phosphorescence decay is no longer visible.
The fact that the spectrum consists of a part which leads to a rise in temperature was
found as early as 1800 by William Herschel [6] when he performed the following
experiment. He projected sunlight onto a thermometer bulb and noticed that there was a
different increase of temperature in the different regions of the spectrum. The blue
radiation showed only a small heating effect but, when moving towards the red, the effect
became more pronounced. Even in a region beyond the visible he was able to observe
maxima and minima of the heating effect.

4 A Scharmann
When it was known that there is an invisible region in the spectrum of the Sun beyond
the red, the other end of the spectrum was also examined and UV radiation was discovered
by its property of reducing silver salts (Ritter, Inglefield and Wollaston).
Since the time of BecquereFs first publication in 1883 on the phenomenon of lumi-
nescence, several research workers, mostly physicists, have devoted their whole scientific
careers to the investigation of 'fluorescence' and 'phosphorescence' [7]. The difference
between the two types of behaviour lies in the decay characteristic of light emission.
'Fluorescence' has only a short lifetime, whereas 'phosphorescence' consists of a slowly
decaying afterglow.
Much work was done in the field of cathodoluminescence (luminescence excited by
bombardment with cathode rays), in the field of electroluminescence (luminescence
excited by the application of electric fields), in the field of chemiluminescence and
biological processes, in the field of triboluminescence, where luminescence is stimulated
by mechanical stresses, and finally in the field of photoluminescence, stimulated by the
absorption of light.
The features common to all these forms of luminescence are:
(i) the existence of some process whereby an atom, molecule, or centre is excited to
higher energy states, and
(ii) the radiative transition to the ground state via the emission of a photon of appro-
priate energy after a certain time delay.
As early as 1895 the physical process for the thermal release of stored radiation-
induced luminescence (thermoluminescence) was used for the detection of ionising
radiation by Wiedemann and Schmidt [8] in Erlangen. They irradiated a great number of
minerals and inorganic compounds with cathode rays and found, among other things, that
natural fluorite and manganese-activated calcium fluorite in particular show a very
intense luminescence when they are heated in darkness, and there is no decay of the
stored luminescence even after storage for a few weeks. Both substances are still used as
thermoluminescent phosphors in solid-state dosimetry.
In the same year Rontgen [9] announced the discovery of x-rays and even in his first
preliminary communication [10] he reported on the sensitivity of photographic plates to
this new radiation. They enable the fixation of some phenomena and therefore a decep-
tion might be better detected and 'you can take exposures with a plate covered by the
paper envelope in a bright room'. Concerning the quantitative measurements he said: 'In
order to get some relation between transmission and thickness of the absorbing lay:r, I
took a number of exposures with photographic plates covered to some extent with tinfoil
of a gradually increasing number of leafs'.
As was shown, the first measurements were done on the effect of x-rays on photo-
graphic emulsions. But the influence of this radiation on thermoluminescence was
reported, too. In 1925 Wick [11], from Vassar College, gave a description of the effects of
x-rays in producing and modifying thermoluminescence. He observed in many substances
considerable changes in TL when irradiated with x-rays. Some materials which usually
showed no natural TL became thermoluminescent when excited by x-rays. He also found
out that the TL after x-irradiation normally started at lower temperatures and showed
higher intensities than the natural thermoluminescence of the same materials.

History 5
Today, one knows that the stability of the metastable states responsible for TL is
greater for higher values of the energy necessary for the system to release charge carriers
from these states. When a relatively low thermal energy is sufficient to release the charge
carriers, i.e. when the observed maximum temperature is near to the excitation tempera-
ture, then the charge carriers responsible for this maximum may be thermally liberated
due to longer storage at the exciting temperature. Consequently, in the following glow
curve this maximum cannot be observed. However, when the thermoluminescence experi-
ment is performed directly after excitation this maximum can also be measured. This
effect was observed by Wick but without any explanation. In 1928 he reported, together
with his coworker Slattery [12], further measurements of TL in synthetic materials previ-
ously excited by x-rays.
Thermoluminescence measurements in the modern sense were carried out for the first
time in the Przibram Institute in Vienna by Urbach and Frisch [13]. Urbach [14]
described in 1930 the luminescence of alkali halides. As well as the description of the
measurement he also reported the first results of a theory. The theory for the calculation
of model glow curves which is now used to estimate the trapping parameters was given in
1945 by Randall and Wilkins [15] and in 1948 by Garlick and Gibson [16]. These
theories will be discussed in more detail in chapter 2.
The thermoluminescence method was hardly used for dosimetric purposes up to this
time. In this field the film dosemeter reigned supreme. In the beginning the photographic
dose measurement was used less in radiological protection than in other problems of
medical dosimetry [10]. The reason for this is that little importance was attached to
radiological protection, and the sensitivity of the available photomaterials was too small
to detect the small doses then in use. Behnken [17], indeed, tried in 1922 to intensify the
radiation effect on the film by means of fluorescent foils. He found, however, that there
was a long-term error due to the contribution of light to the total density of the photo-
graphic emulsion.
In 1926 Quimby [18] studied scattered and secondary radiation in radiation labora-
tories by photographic methods, and in 1928, with increasing attention being given to the
safety of the people engaged in radiation research, this method was proposed for personal
dosimetry by Barclay and Cox [19]. In 1929 Eggert and Luft [20, 21] constructed a
badge with several metal filters to be carried on the body of radiation workers and which
was calibrated by known radiation doses. They called it a 'film dosemeter'. Bouwers and
Van Der Tuuk [22] extended the arrangement of Eggert and Luft using different filter
metals. In this way the photographic film was established in personal radiological
protection.
With the rapidly increasing use of radiation sources and reactors in civilian as well as
in military fields after World War II, far-sighted experts quickly realised that the proper-
ties of photographic emulsions as a large-scale long-term dosemeter were rather limited [1].
The main reasons are the inherent problems of a strong energy dependence (film dose-
meters are about 20-50 times more sensitive to 40 keV x-rays than to gamma radiation
and the metal filters only partially compensate for this energy dependence), of pro-
nounced fading at higher temperatures and humidities, high sensitivity to disturbing
agents such as light, pressure and certain chemicals, limited lifetime, dose range and sensi-
tivity, poor reproducibility, and the need for rather complex darkroom processing
procedures including development, fixing and washing, involving many potential sources
of error.

6 A Scharmann
In the USA especially, in the late 1940s, an intensive search therefore began for better
alternatives, more suitable for the dose control of larger military units. Radiophoto-
luminescence (RPL) dosemeters based on silver-activated phosphate glasses were developed
(Weyl et al [23], Schulman et al [24]). The glasses later became the first mass-produced
solid-state dosimetry system. More than a million units were used in the US Navy (Schul-
man et al [25]). In the early 1950s most of the TL phosphors mainly used at present were
discovered or rediscovered and seriously proposed for dosimetric purposes, e.g. LiF by
Daniels [26], CaS04 by Kossel et al [27] and CaF2 by Ginther and Kirk [28].
The idea of dose measurements by means of TL phosphors started in two ways [7]:
(i) Since the beginning of this century, the natural TL of various materials has been
studied, mostly in Europe. In 75% of about 3000 investigated minerals TL was found.
(ii) Since the beginning of this century it has also been known that CaS04:Mn could
be used for the quantitative measurement of ultraviolet radiation. Originally the green
luminescence of CaS04:Mn obtained by heating the material after uv exposure was
evaluated visually. Later use was made of a photomultiplier for evaluation of the phos-
phor. Soon it was found that this method could also be used for measuring x-rays. A
practical application of this method was reported in 1951 by Purcell et al [29]. On
18 November 1948 and 17 February 1949 CaS04 and MnS04 phosphors were carried to
a height of 90 and 79 miles, respectively, by means of a V2 rocket. They were then
exposed to the Sun for about three minutes. Some of the phosphors were naked, while
others were covered with filters of CaF2, LiF and beryllium. Upon their return the differ-
ent phosphor strips were heated and the thermoluminescence was measured by a photo-
multiplier. In every case a glow curve was observed and the intensities registered with the
Be, CaF2 and LiF filters were about 1/10, 1/3 and 1/2 of the naked phosphor, respectively.
The occurrence of thermoluminescence, even in the shielded phosphors, was evidence for
a high-energy region in the Sun's spectrum. At the height where the exposures were done
there was even a component in the x-ray region, proved by the thermoluminescence of
the Be-covered phosphor.
Basic work on CaS04:Mn was also done by Kossel et al [27]. They described in 1954
the development of simultaneous dosimetry of radiation fields in living objects. The
motivation for these investigations came from Bickenbach who was the head of the
hospital in Tubingen at this time. He pointed out the urgent interest in measuring the
dose distribution of radiation sources (radium and hollow anode tubes) which were
introduced into small cavities of the body or even in the tissue.
It was obvious to the authors that they should use for this purpose the classical
method of the light sum which was founded quantitatively by Ltnard and Hausser [30]
in 1912. In this method phosphorescent substances in a low-energy state may store a light
sum which is at most proportional to the exciting radiation. This light sum is measured by
means of a photoelectric detector when the material is later heated. The method was
useful because of the small size of such storage phosphors, which enabled convenient
injection into the cavities of the body and because of the omission of leads necessary for
measurements using ionisation or photocurrent methods and experiments with a counter.
Another advantage of this method is the great number of phosphors which could be
deposited around the radiation source. This allows simultaneous dosimetry at different
places during a single radiation period. The classical phosphor, fluorite, turned out to be
too insensitive to the small doses which are of interest in this special case, but CaS04:Mn,

History 7
which was suggested by Brauer, proved to be very suitabe. With this phosphor simul-
taneous dosimetry could be developed. The reproducibility of the data on intensity
relations was about ± 5%. The method was tested for up to 20 simultaneous working
observation points.
As mentioned above, the idea of dose measurements by means of TL phosphors started
in two ways. One was the early known uv sensitivity of CaS04:Mn and the other was the
natural thermoluminescence observed in many minerals. Natural TL is excited in the
course of geological deposition of stone formations by background radiation, in particular
by naturally occurring radionuclides which are present everywhere in small quantities.
Some of the minerals were more sensitive to radiation than others, i.e. under the same
conditions they showed a higher TL intensity. The phosphor most investigated was the
very sensitive CaF2. So, materials were discovered which were suitable for dosimetric
purposes.
Since there is a close connection between TL and natural radiation, the TL measure-
ments were used to investigate the thermal and radiation history of minerals. A sum-
marising report on the application of thermoluminescence methods, in particular for the
study of the radiation history of natural minerals for the purposes of geology, mineralogy
and geological chronology but also for investigations of ceramic materials, glasses, cata-
lysts, etc, was given for example by Daniels et al in their publication of 1953 Thermo-
luminescence as a research tool [31].
The research work done by Houtermans et al [32] should also be mentioned here.
They described in 1957 an apparatus for the quantitative measurement of glow curves
with a heating rate of about 40-80 K s_1
. This enormous heating rate strongly increased
the TL intensity. The resolution power of the apparatus relative to the separation of the
maxima, however, was nearly the same as at low heating rates. By comparing the natural
glow curves with those after artificial irradiation the natural dose of 'Wolsendorfer'
fluorite could be estimated. If the contents of uranium, thorium and potassium are
known, the dose rate in a mineral of sufficient size could be calculated from the ionisa-
tion energy of the a, 0 and y radiation of these elements. From the known stored radiation
dose and dose rate the period of irradiation could be estimated. But there are still further
results which could be obtained from the glow curves.
By means of annealing experiments information on the thermal history of meteorites
could be obtained. So one can say that the temperature at which the natural glow curve
of the material starts to increase is surely not exceeded for more than a few seconds in its
thermal history during its exposure to natural radiation and in particular during its fall
through the atmosphere.
In some cases it turns out that the glow curve is lower near the surface than in the
interior of the meteorite and that the crust itself, which was heated up to 500 °C or more,
showed no TL signal. This dependence of the natural glow curves on the depth of the
material below the present crust is detectable only in the outermost layers. Deeper than
15 mm no differences between the glow curves could be observed, which proves that
during the passage through the atmosphere the heat wave advanced only up to a depth of
15 mm.
In the 1950s more and more thermoluminescent materials were examined for their
usefulness as dosimetric phosphors. Single crystals activated with metal ions were mostly
examined, beginning with manganese-activated calcium sulphate which was occasionally

8 A Scharmann
used as mentioned above between 1895 and 1954 for radiation and uv dosimetry, e.g.
in rockets. Manganese-activated calcium fluoride was also often suggested [1].
In the late 1940s studies on lithium fluoride, a material of low atomic number and
therefore low energy dependence for x-rays, began at the University of Wisconsin under
the guidance of Daniels. This work was interrupted between 1956 and 1960 because of
the less desirable dosimetric properties of a newer material. Later works of Cameron and
his coworkers in collaboration with the Harshaw Company led to the development of a
material which was mainly activated with magnesium and titanium and which is now
widely distributed under the name 'TLD 100'. Despite some unfavourable properties such
as non-linearity at higher doses and a complex behaviour when heated, it is still the most
popular TLD phosphor, and for many people knowing the field only slightly it is
synonymous with the term 'solid-state dosemeter'.
Further popular TLD phosphors have been developed. Since 1957 special interest has
been shown in natural fluorite, manganese-activated lithium borate, and, recently, beryl-
lium oxide as an alternative to lithium fluoride for energy-independent photon measure-
ments, as well as in dysprosium-activated calcium fluorite and calcium sulphate and
terbium-activated magnesium orthosilicate. Thermoluminescent glasses developed in
various countries, as well as infrared-stimulated detectors, have not been successful so far
in large quantities.
A second generation of materials including greatly improved RPL glasses and TL phos-
phors and a wide variety of commercial systems became available during the 1960s. The
new techniques of exoelectron dosimetry and track etching were also explored during this
period. In about 1965 an explosion of publications began which apparently has not yet
reached its peak (figure 1.1). Our available knowledge on solid-state dosemeters now
doubles every few years which makes it increasingly difficult for individual scientists,
particularly in small institutions or developing countries, to keep their knowledge up to
date. Today, scientists in about 25-30 countries are engaged in problems of solid-state
dosimetry.
Figure 1.1. Approximate number of publications per year
on thermoluminescence (TL) in LiF and in other materials,
on radiophotoluminescence (RPL), track etching and
exoelectron emission. (Based on data by Attix, Fleischer
and Becker.)

History 9
References
1 Becker K and Scharmann A 1975 Einfuhrung in die Festkorperdosimetrie (Miinchen: Verlag Karl
Thiemig)
2 Oldenberg H 1705 Phil. Trans. Abrdg. 3 345
3 Pearsall T J 1830/. R. Inst. 1 267
4 Becquerel H 1883 Ann. Chim. Phys. 5e
serie XXX 5
5 Becquerel E 1842 Bibl. Univ. Geneve-Arch. Set Phys. Nat.
6 HeischelW 1800Phil. Trans.
7 Oberhofer M 1973 Thermoluminescence Dosimetry, Pusat Reactor Atom Bandung PRAB: 335/
HP.40/73
8 Wiedemann E and Schmidt G C 1895 Ann. Phys. Chem. 54 604
9 Röntgen W C 1895 Verhandl. Phys.-Medizin. Akad. Wurzburg
10 Becker K 1962 Filmdosimetrie (Berlin: Springer-Verlag)
11 Wick F G 1925 Phys. Rev. 25 588
12 Wick F G and Slattery M K 1928 7. Opt. Soc. Am. 16 398
13 Scharmann A, Bohm M, Born G, Grasser R and May A 1971 Einfuhrung in die Lumineszenz
(Miinchen: Verlag Karl Thiemig)
14 Urbach F 1930 Wien. Ber. Ila 139 363
15 Randall J T and Wilkins M H F 1945 Proc. R. Soc. A 184 336, 390
16 Garlick G F J and Gibson A F 1948 Proc. Phys. Soc. 60 574
17 Behnken H 1922 Fortschr. Rontgenstr. 29 330
18 Quimby E H 1926 Radiology 7 211
19 Barclay A E and Cox S 1928 Fortschr. Rontgenstr. 38 311
20 Eggert J and Luft F 1929 Rontgenpraxis 1 188
21 Eggert J and Luft F 1929 Rontgenblätter 1 655
22 Bouwers A and Van Der Tuuk J H 1930 Br. J. Radiol. 3 503
23 Weyl W A, Schulman J H, Ginther R J and Evans L W 19497. Electrochem. Soc. 95 70
24 Schulman J H, Ginther R J, Klick C C, Alger R S and Levy R A 1951 7. Appl. Phys. 22 1479
25 Schulman J H, Shurcliff W, Ginther R J and Attix F H 1953 Nucleonics 11 (10) 52
26 Daniels F 1950 Report on 4th Symp. on Chemical Physics and Radiation Dosimetry part I (Edge-
wood, Md: Army Chemical Center) p 148
27 Kossel W, Mayer U and Wolf H 1954 Naturw. 41 209
28 Ginther R J and Kirk R D 1957 7. Electrochem. Soc. 104 365
29 Tousey R, Watanabe K and Purcell J D 1951 Phys. Rev. 83 792
30 Lenard P and Hausser W 1912 Sitzgsber. Heidelberger Akad. Wiss. Math.-Naturw. Kl. 12 Abh.
31 Daniels F, Boyd C A and Saunders D F 1953 Science 117 343
32 Houtermans F G, Jager E, Schon M and Staufer H 1957 Ann. Phys., Lpz. 20 283

Applied Thermoluminescence Dosimetry. Eds M Oberhofer and A Scharmann
© 1981 ECSC, EEC, EAEC, Brussels and Luxembourg
2
Theory
M BOHM AND A SCHARMANN
2.1. Introduction
Thermoluminescence involves two steps. In the first step, the solid is exposed to the
exciting radiation, such as particle or electromagnetic radiation, at a fixed temperature.
In the second step the excitation is interrupted and the sample is heated. One finds that
during the temperature increase the sample emits light. The intensity of luminescence as a
function of temperature, which possibly exhibits several maxima, is called the thermally
stimulated luminescence or thermoluminescence (TL) glow curve. In some cases glow
curves of thermally stimulated conductivity (TSC) and thermally stimulated exoelectron
emission (TSEE) can be observed which are usually correlated to thermoluminescence.
The theory of thermally stimulated phenomena is treated in a two-fold manner. First
the excitation, the thermal stimulation, the luminescence, the electrical conductivity and
the exoelectron emission are considered on the basis of general physics. Secondly, the
phenomena are phenomenologically analysed without considering the various processes,
such as thermal activation or recombination, from a physical point of view and without
considering the atomistic structure of centres. Finally, an experimental example is
theoretically analysed in this way.
2.2. Excitation by radiation
In the following the interaction of radiation with matter and defect creation are studied
more closely. The radiation possibly causes numerous changes in both the indigenous
lattice ion and in the impurities present. The end-products of these changes may be
classified in terms of three categories of defects: (i) electronic defects, which involve
changes in valence states; (ii) ionic defects, which consist of displaced lattice ions; and
(iii) gross imperfections, such as dislocation loops and voids. In the latter case large
macroscopic defects rarely occur and are mostly due to particle irradiation.
As for the electronic defects the valence state of both the impurities and lattice defects
can be changed. The simplest radiation products arise from the impurities which are
present in all samples. Thus the valence states are changed by trapping electrons and holes
created elsewhere in the lattice by radiation. It means that the impurities act as traps for
electrons and holes. The capture cross sections of impurities for electrons and holes vary
with the type of impurity and the nature of the host lattice. The experimental proof of
the change of valence state due to radiation can be obtained by studying the change in
optical, dielectric and magnetic properties. For instance, different optical absorption
bands or spin resonance spectra characteristic of the defect are observed.

12 M Bohm and A Scharmann
As mentioned above, imperfections in crystals can also change their nature by trapping
electrons or holes. More interesting perhaps is the fact that free charges can be trapped
even in perfect crystals. In alkali halides the so-called 'self-trapped holes' are obtained. Their
structure can be investigated by the methods of EPR [1,2] and optical absorption [3-5]
in a performed manner. The configuration of these centres is represented by figure 2.1.
They consist of two nearest-neighbour < 110> halide ions that have captured a hole or have
given up an electron respectively. The halide ions have moved together to form a halide
molecular ion. It should be emphasised that these centres are not lattice defects in the
usual sense of involving a vacancy or interstitial. The two halide ions are, however,
displaced from their normal lattice sites so that they have a smaller spacing than the
normal negatively charged halide ions. Also, it is noted that in order for a self-trapped
hole to be produced, the accompanying electron must be trapped at some other defect,
such as an impurity.
Figure 2.1. Model of the V^ centre in alkali halides.
As for the ionic defects the most important role is played by the vacancies, which are
probably the best-known radiation damage products. In simple elemental crystals (e.g.
metals), all vacancies are equivalent. In compounds and more complicated crystal struc-
tures, there are a number of possible vacancy configurations, depending upon which
elemental species is missing and which of a number of non-equivalent lattice sites are
vacant.
In principle, the energy to form a vacancy can be estimated by imagining that an
atom is removed from the interior of the crystal and then placed upon the surface. In the
first step some energy is required to break a number of bonds; in the second step the
re-establishing of a smaller number of bonds is responsible for energy becoming available.
Because of relaxation of the lattice around the vacancy, it is very difficult to calculate
accurately the formation energy directly from theory. However, a rough value of the
order of 1 eV may be estimated.
In the case of a binary ionic compound, such as NaCl, the vacancies tends to occur in
pairs in order to preserve equal numbers of alkali and halide ions. It is also true that

Theory 13
defects of one kind would leave the crystal charged or would produce high electric fields.
Consequently, positive and negative ion vacancies must occur in pairs in order to guaran-
tee charge neutrality. A pair of such vacancies is known as a 'Schottky defect'.
In polar compounds most of the observations of radiation defects have been made on
negative-ion vacancies. In singly charged compounds, the anion vacancy which contains
an electron is referred to as the F centre [6] (figure 2.2). The centre has the same charge
as the anion originally present there and is consequently uncharged with respect to the
perfect lattice. The electron density of the unpaired electron is not only localised to the
vacancy but extends to neighbouring nuclei. The interaction with these nuclei can be
detected as hyperfine structure (HFS) in the ESR or ENDOR measurements respectively.
Figure 2.2. Model of the F centre in alkali halides.
When another electron is captured by the F centre an F' centre is formed. It has a single
negative charge with respect to the lattice. No ESR absorption or dispersion from an
F' centre can be observed because it is a two-electron centre with a diamagnetic ground
state. In alkali halides containing impurities one nearest-neighbour cation of the F centre
can be replaced by an alkali ion of smaller size. A static perturbation is then applied to
the F centre and the original local symmetry is reduced. The reduction in symmetry
causes a splitting of the three-fold degenerate excited state into two states and therefore a
splitting of the main F absorption band into two components. These centres are called
FA centres [7].
There are also a number of defects which involve a positive-ion vacancy. For instance
the analogue to an F centre consists of a hole located on the site of a cation vacancy [8].
This centre is called a Vjr centre. However, the symmetry of the Vp centre differs greatly
from that of the F centre. The F centre has cubic symmetry in the ground state, and its
wavefunction is substantially s-wave in character. In the case of the VF centre, the hole is
in a p-like state. The degeneracy is removed due to a reduction in symmetry (Jahn-Teller
effect).
In many cases, it is possible to produce groups of vacancies, so-called vacancy aggre-
gates. For instance, aggregates of F centres which consist of two (M centre), three (R
centre) or four (N centre) F centres [9,10].

Other ionic defects are formed by interstitials. A lattice atom or ion is displaced from
its normal site and remains in a position that is not a normal lattice site. The double
defect consisting of the vacancy and interstitial is called a 'Frenkel defect'. Obviously, the
energy to form a Frenkel defect is the sum of the energy to form the interstitial and the
energy to form the vacancy. Such defects might be generated in the interior of the crystal
by thermal vibrations. There are many possible types of interstitial centre. In compounds,
there may be cation and anion interstitial ions or atoms. Moreover, interstitial ions can sit
either at the centre of an interstitial site or may be drawn towards one of the lattice ions
to form a centre of differing configuration such as a molecular ion. An example is shown
in figure 2.3. It consists of an interstitial halide atom that has bonded itself to a lattice
halide ion and shares that ion's lattice site. This molecular ion defect, called an H
centre [2,11], is to be contrasted to the (halide)2-hole centre (Vk centre) in the perfect
lattice, where the two anions have two lattice sites.
Figure 2.3. Model of the H centre in alkali halides.
In the following subsection, the mechanisms by which defects can be created in solids
by radiation will be considered. One can distinguish three generic classes of radiation
damage processes:
(i) electronic processes;
(ii) elastic collisions; and
(iii) radiolysis.
The electronic class includes all processes in which an electronic state is changed or a
charge is moved about by the absorption of radiant energy, but in which no ionic or
atomic defects are formed. The absorption occurs somewhat differently for various types
of radiation.
A heavy, energetic particle passing through matter is usually stripped of some or all of
its electrons and thus represents a rapidly moving point charge which interacts with the
crystal electrons. Similar considerations are valid for fast electrons. However, bombarding

Theory 5
electrons are not distinguishable from the crystal electrons. Moreover, since bombarding
electrons, in contrast to heavy particles, are as light as the crystal electrons, they can lose
an appreciable fraction of their energy in a single collision. The penetration depth of a
particle in a crystal, which is very important in radiation damage, depends on the energy
loss. Since the energy absorbed from a heavy particle is very much greater than that
absorbed from electrons, electrons will penetrate deep into crystals while heavy particles
are stopped near the surface.
Fast neutrons, since they are not charged, do not excite the crystal electronically as do
charged particles. However, when a fast neutron displaces a crystal ion, the ion gives up
some of its kinetic energy to the electronic structure of the crystal.
In some materials, thermal neutrons can be quite effective in producing electronic
excitation indirectly. This comes about when a thermal neutron is captured by a nucleus
and the excited new isotope decays.
Photons with energies in the range obtainable with x-ray or isotope sources can transfer
their energy to the electronic system of a crystal by a number of processes. In the photo-
electric effect, the full photon energy is transformed into ionisation and kinetic energy
of one of the crystal electrons. Energy transfer increases in efficiency as the photon
energy decreases until the energy becomes too small to excite K-shell electrons. If the
photon transfers only a portion of its energy to an electron of the crystal the process is
called the 'Compton effect'. This mechanism of energy transfer becomes important for
photon energies between about 0.1 and 1 MeV. At energies above 1.02 MeV the produc-
tion of electron-positron pairs ('pair production') becomes important.
In order to create defects through elastic collisions, it is necessary for the incident
particle to impart sufficient energy to a lattice atom or ion to displace it through its
neighbours into an interstitial site. Thus the effectiveness of an incident particle in creat-
ing damage depends on the maximum amount of kinetic energy it can transfer to a lattice
ion. This depends, in turn, on the energy and the mass of the incident particle and the
mass of the lattice ion. In general, five types of radiation may produce displaced atoms or
ions by elastic collision. These are:
(i) 7-rays,
(ii) energetic electrons,
(iii) thermal neutrons,
(iv) fast neutrons, and
(v) energetic atoms and ions.
It is clear that the heavier particles will be much more effective in displacing lattice
ions than the lighter ones. In fact, they are so effective that they produce so-called
'cascades'.
Finally, defects are created by radiolysis. This means that in certain ionic materials,
defect creation is highly efficient and is most probably due to the conversion of electronic
excitation energy into a form capable of manufacturing lattice defects rather than into
elastic collisions. Such photochemical processes are most probably involved in the photo-
graphic process and photosynthesis.
When energy is absorbed in a crystal by electronic processes as described in the first
part, it appears in the form of electrons in a normally empty conduction band and holes
in the normally occupied valence bands, or in the form of excitons (electron-hole pairs

bound to each other) at lattice ions, impurity ions, or defects in the crystal. The excita-
tion is only the first step and must be followed by processes that lead to observable
electronic states. This usually involves separation of the electrons and holes, and trapping
of the separated charges at impurities, defects or in the perfect lattice. The capture cross
sections are determined by potential variations near the centres which can be attractive,
neutral or repulsive.
Normally, the crystal as a whole remains neutral, and free electrons and holes are
always created in pairs. For every electron trapping centre formed, there must also be a
corresponding hole centre formed.
2.3. Thermal excitation and recombination
Supposing the solid previously excited is heated, a thermal relaxation then occurs which
is the dominant mechanism in nearly all temperature-dependent processes in solids. It
means that the processes are started and accelerated if energy is supplied in the form of
thermal energy [12]. These thermally stimulated processes can be compared with chemi-
cal reactions. The increase in the rate of such reactions with temperature can usually be
expressed by an Arrhenius equation. This equation leads one to the concept of an activa-
tion energy: an energy barrier which must be overcome in order to reach equilibrium.
In this special case electrons and holes may escape from metastable states during
heating. These levels are known as traps. The probability of thermal excitation of a
carrier, the so-called escape probability a, is assumed to be given by a Boltzmann factor:
ct = a0exp(-E/kT) (2.1)
(a0 = constant, E= thermal activation energy required to liberate a trapped electron,
k = Boltzmann's constant, T = absolute temperature).
Although this expression is well supported by experiment, a detailed theoretical treat-
ment is still lacking. In a semiclassical approach a trapping model with levels equidistant
in energy from each other and a successive absorption of phonons is assumed. Another
model is based on thermodynamic concepts as they are assumed to be valid in chemical
reactions. Finally, this relation can be deduced from a simple model using the law of
detailed balancing.
For this purpose one may consider traps with only one state. There are also H traps
(per unit volume) and many electrons, of which n are in the conduction band and (H— n)
in the traps. Denoting by a the cross section for the capture of an electron in a trap
(= actual area multiplied by the probability of capture) and letting a be the probability
per unit time that it escapes, from the law of detailed balancing a relation between a and
a may be deduced. For a steady state one can write
n2
va=(H-n)a (2.2)
(number of transitions into the traps = number of transitions into the conduction band),
where v is the mean velocity of the electrons.
The concentration n of the free carriers is calculated using the methods of statistical
mechanics. Thus the assumption is made that the crystal is in thermodynamic equilibrium
at a fixed temperature T. With the volume V of the crystal as a second state variable the
equilibrium value of n will then be given by the condition that the free energy F becomes

Theory V ^ T W T E ^ V V
1 7
a minimum:
(W73ii)r=0. | * w
^ ? / / , 0 J (2.3)
Then one obtains
n2
n-nmkTf1
F ^ - ( — ) ^-E/kT) (2
'4>
where E is the energy required to remove an electron from the trap into the conduction
band. Substituting n in equation (2.2) gives
a = a0exp(-E/kT) with a0=ovNc. (2.5)
Nc is an effective density of states for electrons in the conduction band. Substituting v
from (/2)mv2
= (3/2)kT and assuming the effective cross section σ of the order of
10"ls
cm2
one obtains a 0 « 1011
s1
. This preexponential factor is of the order of the
frequency of the lattice vibrations and is called the 'frequency factor'. From this model
its temperature dependence is proportional to T2
(v~T112
, NC~T3
'2
). In most cases it
is neglected. The thermal activation energy, the socalled trap depth, is much smaller than
the optical ionisation energy because the thermal activation, which involves a multi
phonon process, occurs with the removal of ionic polarisation due to trapped carriers,
whereas in the case of optical activation the polarisation does not have enough time to
disappear according the FranckCondon principle.
The thermal release of carriers from traps possibly gives rise to a thermally stimulated
conductivity (TSC) when the sample is placed in an external electric field. Moreover,
electrons liberated from traps into the conduction band also have a chance of leaving the
solid if they are close to the surface and if their energy is sufficient to overcome the
barrier created by the electron affinity. This phenomenon is called thermally stimulated
exoelectron emission (TSEE) and according to this model it is expected to be associated
with TL and TSC.
When electrons (or holes) have been thermally excited into the conduction band (or
valence band) they will be captured by traps again or recombine with opposite carriers.
The retrapping is influenced by the thermal velocity v in the energy band and the effec
tive cross section a. It can be expressed by the transition coefficient ß:
P = ov. (2.6)
If recombination occurs with the emission of light, a TL glow curve can be observed.
Radiationless transitions are also possible. In this process the energy is transferred to
another electron (Auger recombination) or to the lattice in multiphonon processes. As
is known from absorption the energy and momentum must be conserved in each recombi
nation process. Let k be the wavenumber of the carrier in the initial state and k' in the
final state. Then
hk-hk' = h/ (2.7)
or, since the momentum of the photon (h/X, X = wavelength) is small compared with the
smallest momentum of the carrier (h/a,a = lattice constant), the selection rule for optical

transitions is given by
hk-hk' = 0. (2.8)
This states that direct recombination occurs only between carriers with the same wave-
number. In the energy band model the carriers may only make vertical transitions. The
change in momentum and energy due to electron-phonon interactions occurs in a time
that is much smaller than the carriers' mean lifetime. (In other words, the phonon energy
is large compared with the linewidth.) Thus a direct band-band recombination is very
unlikely.
A larger probability of radiative transitions is obtained in the presence of imperfec-
tions such as vacancies, interstitials or impurities. When the optical transition involves an
imperfection the selection rule (2.8) is satisfied even for different wavenumbers in the
conservation of momentum. In connection with luminescence these imperfections are
called activators.
2.4. Phenomenological analysis
The thermally stimulated processes may be phenomenologically analysed. The physical
processes such as interaction with the exciting radiation, thermal activation, charge and
energy transport or recombination are not considered at all. This means that one does not
investigate the kinds of transition involved and the contribution of phonons during
thermal stimulation. One is also not interested in the structure of centres, such as traps
and activators.
Several properties of solids may be explained by the energy band model. It involves
energy states which are allowed or forbidden to be occupied by electrons. These energy
levels are so closely spaced as to constitute a quasicontinuum or energy band. All the
bands which represent the closed electron shells of the individual atoms are always fully
occupied with electrons. The next higher-lying band contains the valence electrons and is
called the valence band. In the case of the insulators in question this valence band is
completely filled by the valence electrons. An energy gap without any allowed states lies
between the highest state in the valence band and the lowest state of the next highest
band called the conduction band. The width of the band gap is greater than 1 eV so that
transitions of electrons across this gap cannot occur at normal temperatures. The conduc-
tion band, normally empty, is responsible for electrical conductivity if an electron reaches
this band from the valence band. For such transitions to be possible more energy from
exciting radiation is necessary.
One can understand the origin of these bands from two limiting cases. In bringing free
atoms together to form a crystal, the discrete levels of these atoms split up into groups of
levels which then form an energy band, or by the influence of the lattice potential the
continuous energy spectrum of a free-electron gas is broken at certain characteristic
energies since electrons with these energies and corresponding momenta on their passage
through the crystal suffer Bragg reflections from the lattice. Both types of description
starting from tightly bound or completely free electrons meet in the band model of
solids.
The simplified energy level scheme is commonly used to describe the non-stationary
processes (figure 2.4). Wherever the perfect periodicity of the crystalline structure is dis-
turbed, it is possible for carriers to take on energies which are forbidden in the perfect

Theory 19
Y
a >E
Ev
Figure 2.4. Energy level diagram for the phenomenological analysis of TL and TSC with
one type of trap level and recombination level.
crystal. The presence of a defect can introduce one or more additional energy levels in
the forbidden gap between the conduction and valence bands; unlike the bands them-
selves, which extend throughout the crystal, the additional level is localised at the crystal
defect. The activators and traps give rise to some discrete levels above the valence band
and below the conduction band, respectively. In the ground state the recombination
levels are occupied by electrons and the trapping levels are empty. After excitation by
energetic radiation electrons or holes can be captured in traps or recombination centres,
respectively. For the sake of simplicity the following consideration deals only with
electrons. If sufficient thermal energy is supplied the trapped electrons may again be
raised to the conduction band. The electrical conductivity can now be measured. From
the bottom of the conduction band the electron may be retrapped by the traps or they
may recombine with empty activators in a radiative manner. The latter process gives rise
to thermoluminescence. The possible transitions are represented by arrows. The simplest
model involves only a single trap level and a single type recombination level. The symbols
used are h, the density of trapped charge carriers, H, the density of trap levels, n, the
density of free charge carriers, and /, the density of recombination levels.
The transition probabilities are replaced by transition coefficients: a, the escape
coefficient for trapped carriers, (3, the retrapping coefficient, and y, the recombination
coefficient.
It is not probable that such a model accurately represents an actual situation occurring
in solids since essential simplifications have been introduced. For instance:
(i) The free carriers are electrons and there is no thermal quenching. This implies that
transitions of electrons from the valence band to the recombination centres are
neglected.
(ii) No interaction exists between centres which excludes donor-acceptor recombina-
tion and trap distributions.

(iii) Only one kind of centre is involved in the recombination process; thus no killer
centres are present,
(iv) Recombination of trapped electrons via excited states of defect centres does not
occur.
The phenomenological analysis now deals with the kinetic balance. Some transition rates
are necessary.
(i) The rate at which trapped carriers are thermally released (the rate of liberation) is
proportional to the number of occupied traps h:
rate of liberation = ah.
(ii) The retrapping rate, which means the number of trapping transitions per unit time
and volume, is proportional to the density of free carriers n in the conduction band
and the density of empty traps (// - h):
rate of retrapping = &n{H — h).
(iii) The recombination rate, which means the number of recombination transitions per
unit time and volume, is proportional to the density of free carriers n in the conduc-
tion band and the density of empty recombination centres/:
rate of recombination = ynf.
In this simple model the kinetic processes involving the change in the density of
trapped and free charge carriers during thermal stimulation are described by the following
system of differential equations.
The rate of change of the density of trapped electrons is given by
dh/dt = -ah+pn(H-h). (2.9)
The rate of change of the density of free electrons is given by
dn/dt = ah-Pn(H-h)-ynf. (2.10)
Since the solid is electrically neutral, the density of carriers in the conduction band must
be equal to the density of empty recombination centres. The condition of charge
neutrality then yields
/=n+A„ (2-11)
The thermoluminescence intensity / is given by the number of radiative transitions per
unit time and volume and is therefore proportional to the recombination rate:
I~ynf. (2.12)
The electrical conductivity a is determined by the free charge carriers in the conduction
band when the mobility ju is assumed to be constant:
a = nen (2.13)
(e = electron charge).
The purpose of phenomenological analysis is to obtain explicit functions of the carrier
density and, by that, explicit functions of the current and luminescence intensities. The

Theory 21
experimental glow curves are then fitted to the calculated ones by variation of some
trapping parameters. This procedure possibly gives some physical quantities such as the
thermal activation energy E and the frequency factor a0. However, all attempts to find
explicit functions have been unsuccessful. Therefore one introduces some approximations
or simplifying models.
2.5. Kinetic models
It is assumed that the lifetime of free carriers in the conduction band is short when com-
pared with the lifetime of trapped carriers [13], which probably holds in high-resistivity
solids [50]. As a result one obtains a small quasistationary electron concentration in the
conduction band. This means that the density of free charge carriers is always much
smaller than the density of trapped charge carriers:
n<h (2.14)
and that the time rate of change of the free carrier density is much less than the time rate
of change of the trapped carrier density:
dn/dt<dh/dt. (2.15)
Also a constant heating rate q is used:
T=T0 + qt or q = dT,'dt (2.16)
(T0 ~ initial temperature).
With these assumptions an analytical solution is obtained only in two special cases. In
the first case the retrapping transitions are neglected (fi = 0) [14]. In the other case the
transition coefficients for retrapping and recombination are equal (fi/y = 1) [15].
Substituting equation (2.16) into (2.9) and (2.10) one obtains the following differen-
tial equations for the first case (fi = 0):
qdhldT=-ah (2.17)
q dnldT=ah-ynf (2.18)
with a = a0exp(—E/kT); the temperature dependence of a0 is neglected. From equation
(2.17) this case corresponds to 'first-order' or 'monomolecular' kinetics.
With the approximation (2.15) and by adding equations (2.17) and (2.18) one obtains:
qdh/dT=-ynf. (2.19)
Since the luminescence intensity is given by equation (2.12) from equations (2.19) and
(2.17)
/ = constant x ah. (2.20)
The density of trapped carriers h is a function of temperature and can be calculated
from equation (2.17). The integration yields
h(T) = h0exp[-f(T)] (2.21a)

with
f(T) = — exp(-E/kT)dT'
VJT„
(h0 = initial density of trapped carriers).
With equation (2.20) the luminescence intensity is explicitly given by
I(T) = constant x a0h0 exp(-E/kT) exp [-f(T)].
(2.21b)
(2.22)
After integration by parts the function f(T) can be represented by an exponential
integral function which is approximately substituted by a series. Since the initial tempera-
ture T0 is far below the peak temperature the limit of integration can be replaced by zero:
I' exp(-*/*r)«- -jl e*p(-£/*r, i <- ir J ^ (2.23)
With four terms of the semiconvergent series a glow curve of thermoluminescence is
calculated from equation (2.22) represented in figure 2.5. The first exponential function
is responsible for the initial increase, the second for the decay of the glow curve. A non-
symmetrical shape with a steep high-temperature tail is obtained.
The error made in approximating the integral by four terms of the series can be
estimated to be less than 1% [50] and is unimportant in the following calculations. This
approximation is avoided by using a hyperbolic heating rate [19-21]:
1 1
= St (5= constant)
T0 T
as can be experimentally realised. Now the integral is integrable in a closed form.
(2.24)
< 10
60 70
TEMPERATURE IK)
Figure 2.5. Glow curves of TL (a) and TSC (b)
calculated from equations (2.22) and (2.27)
with £-=0.13eV, o„ = 2 X 10' s" hJH = 1 and
q = 1 K s 1
.

Theory 23
In this model, however, there are some problems in calculating the conductivity glow
curve. From equation (2.13) the electrical conductivity is proportional to the density of
free carriers n. Using the approximation (2.14) in the condition of neutrality (2.11) one
has
f*>h (2.25)
and from equation (2.19) one obtains
q dh/dT=-ynh. (2.26)
Combining this with equation (2.17) the density of free carriers is found to be
n(T) = (a0/7) exp(-E/kT). (2.27)
The result is physically absurd because there is an exponential increase in the density of
conduction electrons and no maximum occurs (figure 2.5). At sufficiently high tempera-
tures the condition n >h becomes valid. This is in contradiction to the initial assumption
(2.14). To obtain reasonable solutions for the conductivity, too, the model must be
varied, which will be discussed later.
In the second case one expects liberated electrons to be recaptured by traps with some
definite probability since traps are lattice-positive. With the special assumption j3 = y from
equations (2.9), (2.10) and (2.16) one obtains the differential equations
qdh/dT=-ah+yn(H-h) (2.28)
qdn/dT=ah-yn(H-h)-ynf (2.29)
and by adding these equations and using the approximations (2.14) and (2.15)
qdhldT=-ynh. (2.30)
Comparison with equation (2.28) yields
n=ah/yH. (2.31)
With that one may substitute n in equation (2.30) and one obtains
q dh/dT=-ah2
/H. (2.32)
This equation describes 'second-order' or 'bimolecular' kinetics.
The integration of equation (2.32) yields
ho
h (T) = (2.33)
l + (h0IH)f{T)
where f(T) is given by equation (2.21b). From equation (2.20), which is valid in this case
also, the luminescence intensity / can be expressed by an explicit function of temperature:
a0h exp(-E/kT)
I(T) = constant x — — . (2.34)
H [l + (h0IH)f(T)]2
Combining equation (2.32) with equation (2.31), the conductivity a (see equation (2.13))

is given by
a(T) = en
a0h0 exp(-E/kT)
yH [ + (h0/H)f(T)]'
(2.35)
The curves of TL and TSC calculated from this model are shown in figure 2.6. The integral
of function f(T) is again approximated by four terms of the series (2.23). Above the
maximum temperature the TL intensity drops more slowly than in firstorder kinetics, i.e.
the glow peak is more extended and more symmetrical. The conductivity glow curve is
shifted to higher temperatures and shows a very slow decrease after reaching the maximum.
/
/ /
JJ
b
a /■—v^
V
TEMPERATURE(K)
Figure 2.6. Glow curves of TL (a) and TSC (ft)
calculated from equations (2.34) and (2.35)
with £=0.19eV, o0 = 7XlOl !
s'1
, hJH=l,
q = 1 Ks"' and (3/7= 1.
2.6. Determination of trap parameters
The kinetic processes and the transitions of carriers are essentially influenced by the two
quantities E and a0. The thermal activation energy E is of particular interest because of
its importance to the lifetime of the excited state of the solid. According to the above
mentioned models one may derive many methods for the determination of activation
energy and frequency factor. Sometimes additional approximations are used, for instance,
the integral in equation (2.21b) is approximated only by the first term of the series
expansion (2.23).
The methods can be divided into several groups according to the experimental pro
cedure which must be used in order to obtain the parameter. In the first approximation
it is possible to calculate a formula which provides a linear dependence of the trap depth
E and the maximum temperature Tm [14, 16]:
E~75kTm (2.36)
The derivation uses a frequency factor a0 =2.9xl09
s '. The rough formula is quite
useful for a quick first estimation of the trap depth. However, the numerical factor in

Theory 25
equation (2.36) is dependent upon the value of a0, and hence the values of E thus obtained
only have the right order of magnitude. The frequency factor, in fact, may be different
for each trap in the same substance.
The position of the maximum is obtained by differentiating equation (2.22) with
respect to temperature and equating to zero. Then the relation between E, a0 and Tm is
given by
E/kT^ = (a0lq)exp(-E/kT). (2.37)
From this equation the peak position is influenced both by the thermal activation energy
and the frequency factor (figure 2.7). A decrease of a0 or an increase of E, respectively,
gives rise to a shift of the maximum to higher temperatures. If either of the parameters
E and a0 are known equation (2.37) can serve as a transcendental equation which can be
solved numerically for the unknown parameter.
400 500 600
MAXIMUM TEMPERATURE IK)
Figure 2.7. Thermal activation energy E as a function of maximum temperature 7^ of TL
glow peak with the frequency factor a0 as parameter (calculated from equation (2.37) using
a heating rate of 1 K s~')-
By taking the logarithm one obtains from equation (2.37)
n(T^/q)=E/kTm + n(a0k/E). (2.38)
Thus the plot of the left-hand side against 1/Tm is linear, having a slope E/k. E and a0 can
be determined from the slope and intercept [17, 18]. From equation (2.38) we can
eliminate the frequency factor for two different heating rates ql and q2 [22, 23]:
T2
E = k
J m l T,1 -<m2
7mi — T,m2
" ( - % ) ■
Q2TlJ
(2.39)
The glow curve must be measured with two different heating rates q^ and q2 which yield
the different maximum temperatures Tml and 7m 2 [16, 24].

Other methods use different temperatures besides the maximum temperature. If one
lets T be the temperature corresponding to half-intensity, we can write [25]
E=.5kTm~—L
—. (2.40)
Similar relations are obtained if the temperatures are considered where the intensity is
decreased to 1/2 [26, 27], to 2/3 and 4/5 of the maximal height [28]. The inflection
temperature [29] and the half-width [30] may also be utilised.
Frequently, the so-called 'initial rise method' is used to determine E. This technique is
based on the fact that the function f(T) in equation (2.22) is nearly temperature-
independent when the traps begin to empty as the temperature is raised.
Then, in the initial part of the glow curve the intensity is given by / ~ exp(—E/kT) or
lnI=-E/kT+ constant (2.41)
for either type of kinetics. Thus, the plots of In/ against 1/7 are linear, having slopes
equal to —E/k. This provides a quick analysis of the initial ascending part of the glow
peak which yields the value of E without any knowledge of a0 [31-33]. However, the
peaks will become wider and shallower with increasing retrapping. The temperature limit-
ing the validity of equation (2.41) is therefore decreasing [34]. Then the slope will be
equal to — E/k at very low intensities where exact measurements are impossible.
From numerical methods of analysis some initial approximate values of E and a0 are
chosen and they are suitably varied to determine the values giving the best fit to the
experimental data [35-37]. Finally the area under the glow curve can be used for para-
meter determination [38-40].
The methods may be improved by considering the temperature dependence of the
frequency factor a0 [16, 24]. However, its influence on the shape of the glow curve and
on the determination of activation energy is only small. It amounts to about 10% from a
temperature dependence proportional to T1
'2
[41] and T~" {a = 1 or 2) [27], respectively.
A survey of methods from the literature is given in references [42-44].
2.7. Additional parameters
The above-mentioned models are often extended to obtain, on the one hand, a simpler
mathematical treatment and, on the other, better agreement with the experimental
results, mainly with respect to the conductivity glow curve. In this subsection two such
models are considered in detail. Both cases show first-order conditions.
In the first case a constant lifetime of free electrons in the conduction band is assumed.
This corresponds to the assumption that the density of recombination centres remains
approximately constant during the thermal stimulation. So one obtains the new condition
of neutrality (see equation (2.11)) [21, 41, 45-47]
n + h =/o 0* constant) (2.42)
and the balance equations
qdh/dT=-ah (2.43)
q dn/dT = ah - ynf0. (2.44)

Theory 27
By adding the differential equations and considering the approximation (2.15) one
obtains
n=ahhf0. (2.45)
The density of captured carriers h as a function of temperature is calculated by integrat-
ing equation (2.43) (see equation (2.21))
h(T) = h0exp[-f(T)]. (2.46)
Combining equations (2.46) and (2.45) the free carrier density is given by
n = ^y exp(-E/kT) exp [-f(T)]. (2.47)
T/o
Since from equations (2.12), (2.42) and (2.13) both the luminescence and the conducti-
vity are proportional to the density of free carriers we obtain the same temperature
dependence of both intensities as is represented by equations (2.47) or (2.22). Therefore
the glow curves exhibit the same shape as shown in figure 2.5. In this case the maximum
of the two phenomena peaks exactly at the same temperature. This means there is no
shift of the TSC glow curve to higher temperatures.
This model is used to explain the experimental results observed in x-rayed LiF crystals
[48]. X-irradiation creates H centres and V^ centres in addition to other paramagnetic
centres. The concentration of V^ centres is larger than that of H centres by one order of
magnitude. Concerning the behaviour under thermal treatment the H centres disappear
rapidly if the temperature approaches 105 K. This thermal decay is connected with a
relatively small drop in the number of V^ centres [49]. Glow peaks are observed in TL
and TSC measurements at about 107 K which show first-order conditions and nearly no
temperature shift. This might suggest that the H centre decays by emitting an electron,
and thus transforms into an F2 molecule. The electron in turn annihilates a Vk centre.
From the above-mentioned model the observed conductivity is possibly due to this charge
transfer and the thermoluminescence to the electron-hole recombination. Thereby the
density of recombination centres remains approximately constant and the neutrality
condition (2.42) is valid.
In the second model it is assumed that as well as the mentioned traps H there are
additional traps M which are thermally disconnected and act merely as a reservoir for
trapped charge carriers [50-52]. Now one obtains the neutrality condition
f=n+h+M (2.48)
and the rate equations (2.9) and (2.10) change to
qdh/AT=-ah+Pn(H-h) (2.49)
q dnjdT=ah - $n(H- h) - yn(n + h +M). (2.50)
By adding the differential equations and considering the approximations (2.14) and
(2.15) one obtains
qdhldT=-yn(h+M). (2.51)

Substituting q dh/dT from equation (2.19) one obtains the density of free carriers n:
ah
Combining equations (2.51) and (2.52) the following equation results:
(2.52)
dh ah(M + h)
-q — = (2.53)
dT h(l-P/y) + (ply)H + M
The integration of this equation yields
l& PH (M + h i PH (h
- + — In - ( 1 - — In - =/(7) (2.54)
y yMI M + h0) yM< h0J
with/(f) defined by equation (2.21b).
As it is a first-order process, retrapping is neglected and p/y < 1 is valid. In addition
the assumptions H/M> 1 and $H/yM< 1 are made as a way of simulating a changing life-
time of the charge carriers [50]. Then we obtain
-n(h/h0)=f(T) (2.55)
A=A0 exp[-/(r)]. (2.56)
This equation yields a calculation of TL because from equations (2.12) and (2.51) the
intensity is proportional to — dh/dT:
I(T) = constant x a0h0 exp(-E/kT) exp [-f(T)]. (2.57)
It is exactly the same relation as is obtained from a theoretical treatment of a first-order
process without additional parameter M (see equation (2.22)).
In contrast the calculated shape of TSC shows another result. Formerly one finds that
the density of charge carriers increases with constant increasing temperature according to
an exponential law without reaching a maximum, whereas now from the above-mentioned
relations one has
-q dh/dT
n=— (2.58)
y(M + h)
and
7"1
^"1
ao/*oexp(-£'/fc7')exp[-/(7')] t N
" (T) = (2.59)
1 + (z0H/M) exp [ - / ( D ]
where z0 = H/h0 is the fraction of initially filled traps. In the calculation of I(T) and
n(T) from equations (2.57) and (2.59) the function f(T) is approximated by four terms
of the semiconvergent series (2.23).
A TL glow curve and a family of TSC glow curves obtained in this way are shown in
figure 2.8. The temperature function in the denominator of equation (2.59) gives rise to
a shift of the TSC maxima to higher temperatures as compared with the TL maximum
usually obtained by measurement. The shift increases with increasing z0H/M.

Theory 29
130 160
TEMPERATURE(K)
Figure 2.8. Calculated glow curves of TL (I) and TSC (II, III, IV) from equations (2.57)
and (2.59) with E = 0.28 eV, a0 = 1010
s"', q = 0.05 K sM
, and the parameter z0H/M = 1 (II),
10(111), 103
(IV).
For comparison with experiment the glow curves of x-rayed LiF crystals are chosen.
With a heating rate of 0.05 K s"1
the crystal shows a TL maximum at 138 K and a TSC
maximum near 141 K (figure 2.9(a)). With the values of the trap depth E and the
frequency factor a0 revealed from another measurement [32] and with the parameter
z0H/M=3 the calculated glow curves (figure 2.9(b)) defined by equations (2.57) and
(2.59) show good agreement with the experimental results. Because of the influence of the
parameter z0H/M on the magnitude of the temperature shift it is in principle possible to
verify the model by the dependence upon the initial occupancy z0. However, it may be
very difficult to measure the low currents.
If one applies the model with additional traps M to second-order processes, there are
three cases that must be distinguished [50]. In the first case (H/M< l,f3H/yM<: 1) where
a constant lifetime of charge carriers is simulated, the calculated glow curves show once
again a shape similar to those in first-order kinetics and consequently there is no shift of
TL and TSC maxima. In the second case (H/M < 1, (3H/yM> 1) there exist relatively large
half-widths. Even larger half-widths result theoretically from the third case (H/M> 1,
(3H/yM< 1) where the lifetime changes during heating. Moreover, there are large shifts of
TL and TSC maxima and with increasing H/M ratio the TSC shape decreases slower after
reaching the maximum [50, 53].
As well as the above cases many other models are known. For instance, additional
occupied traps and direct recombination of trapped electrons with free holes are con-
sidered by a changed neutrality condition and an effective non-radiative transition [54].
Another model involves the transition between trap and activator in a non-radiative way.
Analytical expressions for both TL and TSC intensities are obtained and the shifts of
maxima can be explained [47, 55]. Now the frequency factor and the activation energy

( 0 )
n rs
'—n—~u
120 UO
TEMPERATURE (Kl
120 HO
TEMPERATURE (Kl
Figure
rate: 0.
eV, a„■■
2.9. (a) Glow peaks of TL and TSC obtained from an xrayed LiF crystal (heating
05 Ks"1
). (b) Calculated glow curves from equations (2.57) and (2.59) with £ = 0.27
= 5 X I O ' V , ? = 0.05Ks"' and z0H/M= 3.
for nonradiative transitions and charge transfer between an excited state and a spatially
separated recombination centre are considered, too. The shape of the glow curve calcu
lated with this model again shows firstorder characteristics.
2.8. Computer simulation
In this subsection the correlated phenomena of TL and TSC will be described in simple
models but without recourse to any simplifying approximations (2.14) and (2.15) and the
results calculated in this way will be compared with approximate solutions. The dif
ferential equations are solved rigorously on an electronic analog computer [57]. When
the equations are amplitude and temperaturescaled the densities of free and captured
carriers can be generated. However, one obtains no analytical solution but a simulation
of TL and TSC intensities against temperature.
A typical solution in the case £"=0.13 eV, ct0 = 2 x 109
s~!
, /20/#=
1 and q = 1 K s"1
is
shown in figure 2.10. In the TL glow curve the maximum temperature differs to some
extent from that curve showing the change in the trapped carrier density (dh/dT) and is
often mistaken for the TL glow curve [18, 25, 5860]. A maximum can clearly be
observed in the TSC glow curve. Moreover the exact calculation gives rise to a shift of
the TSC maximum of about 23 K to a higher temperature when compared with the TL
maximum. The break in the simulation at about 66 K is caused by the maximal limiting
voltage of the analog computer. The TL glow curve calculated approximately with the
abovementioned parameters (figure 2.5) shows the same shape. However, the maxima
are shifted to a somewhat higher temperature.

Theory 31
j
1J
[t
n'

50 60
TEMPERATURE (K)
Figure 2.10. Computer simulation of TL (a),
TSC (b) and the change in density of trapped
carriers (c) with first-order conditions and
£ = 0.12eV, ao = 2xl0's-', hJH=l, q = lKs''
and 7//=0.5 cnvV'.
a
Af
1
50 60
TEMPERATURE [Kl
Figure 2.11. Computer simulation of TL (a)
and TSC (b) with first-order conditions and
additional thermally disconnected traps (A/);
^O.DeV, ao=2xl0's-1
, h0/H=l, q = lKs~l
and H/M = 0.2.
Two special cases with first-order conditions described in §2.7 are also calculated
without making approximations. In the first case, the density of recombination centres
/ and therefore the lifetime of free charge carriers are to be assumed as approximately
constant during the glow experiment. This corresponds directly to the case where addi-
tional thermally disconnected traps M exist and their density is assumed large in com-
parison with the above-mentioned traps H [50]. This yields the neutrality condition
f-n +h +M and the assumption H/M<. 1 is made. Figure 2.11 shows the glow curves
simulated by analog computer calculations, again without the approximations (2.14) and
(2.15). Only if the density of the additional traps is increased by a factor of five do the
two glow curves have the same shape and no shift of maximum temperatures exists, as is
found in the approximate calculation.
In the other case the assumptions H/M> 1 and fiH/yM< 1 are made. With these a
changing lifetime of carriers is simulated (see §2.7). The exact solution of the differential
equations yields the same result as is obtained in approximate calculations. The TSC curve
shows a shift in the maximum temperature and a longer exponential increase at the begin-
ning of the heating because of the increase in the lifetime.
Considering transitions to the traps one obtains the condition |3 = 0. From the special
case with second-order conditions ()3 = 7) calculated approximately in §2.5 the glow
curves of TL and TSC are exactly simulated. As a result the shape of the TSC glow curve is
parallel with that of TL in contrast to the approximate calculation. It also shows a shift to
higher temperatures winch is of the same magnitude as in the case of first-order kinetics

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