MAGNETIC FIELDS AND THERMAL GRADIENTS
8.6.8 Location of the peaks in thermoluminescent intensity
How can the depths o f the electron traps below the conduction band be studied from the thermoluminescent glow curve?
When intensity of emission / is measured as a function of tem perature 7 as the temperature is swept at a fixed rate, peaks in the intensity will corrcspon to the depth of electron traps below the conduction band.
1 7 8 Electrical and thermal properties o f materials
Temperature (°C)
Fig. 8.9 Thermoluminescence glow curve for TLD 100 dosimeter with several intensity peaks corresponding to several depths of electron traps. Reprinted from N u c l. T r a c a n d R a d ia tio n M ea s., II, R. K. Bull, p. 108, copyright 1986, with kind permission from Pergamon Press Ltd, Oxford, UK.
An empirical relationship has been given between the depth AE in electron volts (eV) and the peak temperature T * in Kelvin (K) by Urbach [9]
8.6.9 A p p lic a tio n s o f therm olum inescence
How is thermoluminescence used in its primary applications o f radiation dosimetry antf'archaelogical dating?
/T h e r m o lu m in e s c e n c e fin d s a p p lic a tio n s in ra d ia tio n d o s im e tr y [ 1 0 ] , g e o lo g ic a l, a n d c o s m o lo g ic a l d a tin g a n d in th e in v e s tig a tio n o f r a d ia tio n d a m a g e i n s o lid s - T h e th e rm o lu m in e s c e n t g lo w c u rv e gives in fo rm a tio n a b o u t th e t o t a l r a d i a t i o n dose a b s o rb e d b y th e m a te ria l. F o r d o s im e try th is is a ll th a t is r e q u ire d .
T h e elapsed tim e since fo r m a tio n o f a s o lid ca n be c a lc u la te d f o r d a t i n g p u rp o s e s a s s u m in g a c e rta in average b a c k g ro u n d r a d ia tio n in te n s ity o v e r a p e rio d o f tim e , a n d a ssu m in g the m a te ria l has n o t been h e a te d in th e in t e r im - I f th e m a te ria l has been heated th is w o u ld e m p ty so m e o r a ll o f th e e le c tr o n tra p s , e ffe c tiv e ly re s e ttin g th e th e rm o lu m in e s c e n t c lo c k .
A useful re v ie w o f th e rm o lu m in e s c e n c e and its a p p lic a tio n s has b e e n g iv e n b y B u ll [ 11] , Thermoluminescent ra d ia tio n d e te cto rs are d iscu sse d in s e c tio n 16.5.
R E F E R E N C E S
b Brillouin, L.(1953) W a v e P ro p a g a tio n in P erio d ic S tr u c tu re , Dover Press, New York.
2 Anderson, J. C. (1964) D ie le c tric s, Chapman and Hall, London.
3. Solymar, L. and Walsh, D. (1984) L e c tu re s on th e E le c tr ic a l P r o p e r tie s o f M a t e r i a l s ,
Oxford University Press.
4. Mort, J. and Pfister, G. (1982) Electronic Properties of Polymers, ). Wiley & Sons, New York.
5. Kittel, C. and Krocmcr, H. (1980) Thermal Physics, 2nd edn, W. H. Freeman, San Francisco.
Tye, R. P. (1969) Thermal Conductivity, Academie Press.
7. Garlick, G. F. J. and Gibson, A. F. (1984) Proc. Phys. Soc., ¿60, *74;
8. Randall, J. T. and Wilkins, M. H. F. (1945) Proc. Roy. Soc., A184, 366.
9. Urbach, F. (1930) Wiener Berichte, IIA, 139, 363. . . 10. McKinlay, A. F. (1981) Thermoluminescence Dosimetry, Adam i ger, ris o H. Bull, R. K. (1986) Nucl. Tracks Radiation Meas., Il, 105.
Exercises 1 7 9
FUR THER r e a d i n g
Anderson, J. C„ Leaver, K. D., Rawlings, R. D. a n d A l e x a n d e r , J. M. (1990) Materials Science, 4th edn, Chapman and Hall, London, Chapters . Verlae Berlin Hummel, R. (1993) Electronic Properties of Materials, 2nd edn. Spring
Parts 11 and V. j ccin W II Freeman. San
K it t e l, C. and K r o c m e r , H. (1980) Thermal Physu.'. - na L ’
Francisco. Crystalline Materials,
Mott, N. F. and Davis, E. A. (1971) Electronic Processes in Non C )
Clarendon Press, Oxford. . v w
Tye, R. P. (1969) Thermal Conductivity, Academic Press, New _ Ziman, J- M. (1960) Electrons and Phonons, Oxford Univers >
e x e r c i s e s ^
E x e r c i s e 8 .1 D r i f t v e l o c i t y o f c o n d u c t i o n e l e c " ° ” sv Thf ^ f r ® iTm .C alculate m in iu m is 12eV and its electrical resistance at 3UU 1S .. velocity in the m e a n free path of the conduction electrons and their mea ^ 700k -3^
afield of 103 V m ' l . (Atomic weight of aluminium = 27,densi y
E x e r c i s e 8 . 2 C o n d u c t i v i t y in i n t r i n s i c a n d e x t r i n s i c s e n i i c o n d u c Estimate of n-type germanium contains 1023 ionized donors per cu *c to thal 0f the ratio at room temperature of the conductivity o is .ômis 0.7 eV.
high purity intrinsic germanium. Assume the band gap in germa
E x e r c i s e 8 . 3 T h e r m o l u m i n e s c e n c e a n d li f e t i m e /7? i ^ y e a rs),
time of trapped electrons in a particular ceramic at 2 - is . Qf the and if the frequency parameter s = 4.64 x 10- s 1 ca cu to e the depth o ^ electron traps below the conduction band. Then ca cu a e calculate at which the peak occurs in the thermoluminescence glow curve, ‘
the lifetime of the same electrons in the same traps at a temperature o
O ptical Properties of M aterials
We have touched briefly on the optical properties of materials in the early chapters, but here we must bring together the concepts of electron structure and the known optical properties of materials. This is done by identifying the allowed energy transitions which determine the main features of the optical spectrum. This mean that we need to connect measured optical properties with the allowed electro energy levels. The major classification_gfxlectron transiimS-is between transi
tions within the same band ( intrabaafl) and transitions between different ban ( interband) The former are lower_energy.±ransitions which lead to the hign rTfl^thnfv of metals in the visible spectrum. The latter are h j g h e t ^ n ^ ^ r ^ i J i o n S which can lead to specific colours in materials. Various methods for measuring the optical properties are discussed including both conventional static optica measurements and differential techniques under external modulation o f field, temperature or stress. Finally the specialized topics o f photoluminescence ana electroluminescence are discussed.
9 OPTICAL PROPERTIES
X What quantities need to be measured to completely determine the optical properties o f a material9
In previous chapters we have shown that the optical properties of materials can be described in terms of two constants. These are the refractive index n a n d
the extinction coefficient k. Alternatively we can choose the real and imaginary components e, and t 2 of the dielectric ‘constant’ or complex permittivity. The reflectance R can be expressed in terms of either of these two pairs of parameters D I
9 .1 .1 P e n e t r a t i o n d e p t h 6, a n d a t t e n u a t i o n c o e ffic ie n t a
How can we describe empirically the reduction in intensity of light when it passes through a material?
When discussing the electronic transitions in materials which arise from the absorption of photons we should remember that these do not necessarily take
Optical properties 181 place throughout the bulk of the specimen. The depth of penetration of incident light depends on the frequency of the light and the optical constants of the material. The depth at which the intensity of the incident electromagnetic wave is attenuated to \/e of its value is called the penetration depth 3. This is expressed by the following equation,
/ = 70e x p (- z/3)
where z is the distance into the material. Replacing 1 /3 by the attenuation coefficient a, which is also widely used to characterize materials, gives the relation,
/ = /0exp(— az).
In transparent materials, such as various different types of glass, 3 is large, being of the order of 0.1-0.3 m, while in metals <5 is very small, being of the order of 10“ 8 m.
9.1.2 Physical significance of the optical constants n and k
H ow do the observed optical constants relate to the absorption o f a wave in a m aterial medium?
The solution of the wave equation in a material w'ith optical constants n and k leads to the following equation for the electric vector £ [2]
$ , ( * ) = £0 e x p ( - " - ) e x p ( i w j t - ^
incident \ /d am p in g \ /un d am p ed \ amplitude/ V term / \ oscillation /
Here, & is the electric field component parallel to the surface, co is the frequency of the incident radiation, z is the distance normal to the surface of the material,
* is a direction parallel to the surface of the material and c is the velocity of the incident light wave. The optical constants n and k have been defined in sections 1.4.1 and 1.4.2. Since io/c = 2n/?, this equation can be expressed alternatively in terms of the wavelength X
9.1.3 Dielectric constants of materials
H ow are the optical constants o f a material related to the dielectric constants:’
The above equation for the parallel component of q as a function of depth r contains two terms, an exponentially decaying term which is dependent on k
182 O p t i c a l p r o p e r t i e s o f m a te r ia ls and an undamped wave term which k a
phase o f the light wave in the material e* f ndem on n. T h e r e fo r e n affects the propert^s can 5e expressed equajlv in * affects its amplitude. T h e optical e d,electric constant er as follow s, em iS ° f the ^ea, and im aginary parts o f
Wbj hC ,h e ,o ta l d ieiectric co n sta n t fc X ^ + ^
h‘ ' mens"> 'of * * ■ , h dI to s , is then given by,.
and from this equation we can use the definition of the penetration depth 3 as the distance required to decrease the intensity by a factor of l/e
Notice that 3 depends on k but not on n. Some typical values of extinction Coefficient k and penetration depth c> in the visible range of the spectrum are
given in Table 9.1.
We see therefore, that while optical properties of materials such as w ater and glass are the result of a bulk measurement, in graphite and gold they are restricted to measurements made over a few tens of nanometers at the surface.
This is shown in Fig. 9.1. Once again the fact that light only penetrates a few Under these conditions the penetration depth <5 is,
y s = — = ~
2a>k 4nk and the attenuation coefficient is
a = 2(ok/c = ---- . /
Table 9.1 Values of extinction coefficient (k) and penetration d rpth (<$) for various materials in the visible range of the spectrum
Material k <5 M
Water Glass Graphite Gold
1.4 x 1 0 '7 1.5 x 10“ 7
0.8
3.2
0.32 0.29 60 x 10"9
15 x 10"9
Interpretation oj optical properties 183
Fig. 9.1 R e f r a c t i o n a n d r e f l e c t i o n o f l i g h t b y a m a t e r i a l m e d i u m .
nanometers in some materials implies that those materials must have high reflectance. Reflectance measurements on metals are highly sensitive to the surface condition (e.g. presence of oxide coating) and a question also remains whether a surface measurement under these conditions is representative of bulk material.