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Photodarkening of amorphous selenium
Journal of Non-Crystalline Solids 70 (1985) 359-366 North-Holland, Amsterdam
PHOTODARKENING
OF AMORPHOUS
359
SELENIUM
R.T. P H I L L I P S * Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, Great Britain
Received 6 July 1984 Revised manuscript received 31 August 1984
Various parameters associated with photodarkening of amorphous selenium have been measured at 100 K. The spectral response of photodarkening shows a step at the absorption edge indicating that electron-hole pair creation is a basic feature of the process. It is shown that the slope of the Urbach edge decreases during photodarkening, and it is found that the change in the optical joint-density-of-statespeaks in the region of photon energy between 2.0 and 2.5 eV. A film of a-Se subjected to ion bombardment at 100 K does not then show photodarkening, and this and the other observations are discussed in terms of a model of local change in atomic arrangement.
3. Introduction Several m e a s u r e m e n t s of p h o t o d a r k e n i n g of a m o r p h o u s selenium have been r e p o r t e d [1-3], a n d there have b e e n m a n y m e a s u r e m e n t s of p h o t o i n d u c e d changes in c h a l c o g e n i d e glasses c o n t a i n i n g selenium or sulphur [4]. These p r e v i o u s e x p e r i m e n t s have shown that p h o t o d a r k e n i n g can p r o c e e d following a n y i n t e r b a n d optical t r a n s i t i o n a t the f u n d a m e n t a l a b s o r p t i o n edge. Subb a n d g a p i l l u m i n a t i o n often reduces the p h o t o - d a r k e n i n g , as does increasing the t e m p e r a t u r e to near the glass transition. T h e r m a l a n n e a l i n g at j u s t b e l o w the glass t r a n s i t i o n t e m p e r a t u r e results in r e m o v a l of the i n d u c e d a b s o r p t i o n , which is a p p a r e n t l y c o m p l e t e l y reversible. Below an a b s o r p t i o n coefficient, a, of 2 - 3 × 10 4 c m -1, a b s o r p t i o n varies e x p o n e n t i a l l y with p h o t o n energy, E, giving logea = F ( E - E0) in selenium. F is the s l o p e of the edge, E the p h o t o n energy a n d E 0 a constant. This b e h a v i o u r - the spectral U r b a c h rule - gives w a y to a w e a k e r d e p e n d e n c e of a on E at higher E , where a E ~x ( E - Ea), with E 1 a n o t h e r constant. This linear v a r i a t i o n o f mE w o u l d arise for excitation b e t w e e n two b a n d s of c o n s t a n t density-of-states, in the a b s e n c e of strong v a r i a t i o n of m a t r i x elements for different electronic transitions. T h e energy E~ can be used to define an " o p t i c a l b a n d g a p " , a n d clearly for p h o t o n energies near E t it is to be expected * Present address: Department of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, Great Britain. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
360
R.T. Phillips / Photodarkeningof amorphous selenium
that the behaviour of the absorption coefficient will be sensitive to states near the band edges. This region is difficult to interpret because of the possible effects of the coulomb interaction on the final state, and indeed the origin of the Urbach region in amorphous systems is not yet resolved [5,6]. The experimental work described here covers the absorption edge of a-Se across the two regions described above, and is discussed in terms of previously proposed models for the origin of photodarkening.
2. Experimental work Thin films of a-Se were prepared by thermal evaporation, from a tungsten basket, of material which had been purified by the quenching method [7]. The original material was specified to be 99.9999% pure with respect to heavy elements. The vacuum system used a mercury diffusion pump and attained a pressure of - 3 × ]0 -9 Torr before evaporation of the films used for the present experiments. Typically, a rise in pressure of about two orders of magnitude occurred during deposition of films. Superpolished spectrosil discs were used as substrates, and these were mounted in a copper block held at a temperature of about 290 K during film growth, which proceeded at about 0.3-0.5 n m s -1. After deposition, specimens were quickly transferred (in air) to a Displex coldfinger mounted in the target chamber of a heavy-ion accelerator in which optical properties could be measured. Reflectance, R, and transmittance, T, of the film-and-substrate combination were measured at normal incidence. For these experiments on a-Se the specimens were held at 100 K in a background pressure of < 5 x 10 -s Torr, and were always cooled in the dark from a thermally annealed state at 290-300 K. For a homogeneous film of constant thickness, the refractive index, n-ik, may be obtained directly from the measured values of R and T by numerical solution of the appropriate equations [8]. This permits a derivation of the absorption coefficient, a, taking into account interference within the film and the presence of the substrate. The optical joint density of states has also been obtained from the measured n-ik [9].
3. Discussion of results Fig. 1 shows the absorption edge of a film of a-Se 137 nm thick, deposited at 291 K at a mean rate of 0.43 nm s-l, and measured at 100 K before and after exposure for 30 min to the white light emitted by a 150 W tungsten lamp at a distance of 20 cm. The spectral Urbach rule is clearly shown at low values of a, where a marked change in absorption occurs during exposure (photodarkening). Over the energy range from about 2.4 to 3.2 eV only one series of points is shown, since the absorption edges are very close when log a is plotted.
R.T. Phillips / Photodarkening of amorphous selenium i
361
i
/ E cJ
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Fig. 1. The optical absorption edges of amorphous selenium at 100 K in the annealed (+) and photodarkened (O) states described in the text.
Though scatter in the data becomes apparent below a --- 6 - 7 × 10 3 cm -1 it seems clear that the photodarkening has not only shifted the absorption edge but also caused a decrease in the slope F of the Urbach region. A change in slope from about 16 eV -1 to 11 eV - ] (measured at a = 10 4 cm - ] ) occurs for illumination with light of 2.2 eV. A change of this type has been measured for a-As4SesGe and a-As4SeaS3Ge by Utsugi and Mizushima [10]. Fig. 2 illustrates the spectral dependence of the variable E04 (the energy at which a = 10 4 cm -1) plotted in the form A E 0 4 = E 0 4 (illuminated)-E04 (annealed) versus photon energy. In this case the data were obtained in the region where A E04 is insensitive to the total number of absorbed photons, and lengths of exposure were chosen to control the total number of absorbed photons to within about a factor of three, except for the point at 1.96 eV. For this point a 2 mW helium-neon laser was used, and no detectable shift in the
R.T. Phillips / Photodarkening of amorphous selenium
362
0.10
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2.3
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absorption edge occurred even for very long exposures. The decline in the efficiency of photodarkening above 2.5 eV appears to be a genuine effect, and is in agreement with the observations of Tanaka and Odajima [3]. The lack of any photodarkening of films under irradiation by the He-He laser may be due to the small absorption coefficient at this energy, which is well within the Urbach region. The data therefore seem to indicate that the efficiency of photodarkening rises at the same energy as the absorption edge. At 2.1 eV the step in the efficiency of photodarkening appears to be essentially complete, and yet at this energy the absorption is only about 5 x 103 cm -1 in the un-irradiated film (at 100 K). There is no gap between the absorption edge and spectral response of photodarkening, as there is for photoconduction. Photodarkening may therefore occur even if geminate recombination of photoexcited electron-hole pairs takes place, and it seems likely that the shift in the absorption edge is simply associated with the occurrence of an interband transition. Interpretation of the photodarkening is further aided by studying the change in the optical jointdensity-of-states. In fig. 3 the value of AJDS is plotted versus photon energy, where the change in the joint-density-of-states z~JDS = 4.6 x 1 0 - 4 VATOM X E[c2b(E) - c2a(E)] and the atomic volume, VATOM= 31.4 A3 (corresponding to a density of 4.3 g cm-1). The imaginary part of the dielectric function after photodarkening c2b(E ) at photon energy E is compared with a value interpolated from the data for c2a(E ) for the annealed film. The oscillator strength has been set to unity. This method of displaying the change associated with photodarkening makes it clear that the transitions near the absorption edge are
R.T. Phillips
/
Photodarkening o f amorphous selenium
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Fig. 3. The change in the opticaljoint-density-of-statesdeduced from the measurementsof R and T, showing a peak between 2.0 and 2.5 eV. The shaded region is discussed in the text.
the ones which are being altered most dramatically. The data for E > 2.5 eV cannot be interpreted as indication of a definite change in c 2 because of the inherent inaccuracy of the measurement i n this region of high absorption. The integrated change in joint-density-of-states from 2.0 to 2.5 eV (filled area in fig. 3, arbitrarily chosen to span the peak) given a change of about 2.7 × 10 -4 states per atomic volume per unit oscillator strength. It is difficult to extract from this value the parameter of interest to structural modelling of photoinduced changes - the number of atoms involved. This stems from the problems associated with estimating an appropriate oscillator strength for a range of transition energies spanning the " U r b a c h " and "interband" regions. Dunstan's recent arguments [6] would support the much-used assumption of only a slow variation of matrix elements with energy, which helps to overcome this obstacle. By treating the region of the c 2 spectrum from the absorption edge to the pronounced minimum near 7 eV as being due to transitions involving 2 p-lone pair electrons being excited into the conduction band [11] it is possible to assign an effective strength to the transitions in the region 2-2.5 eV. Use of the sum rule for the effective number of electrons taking part in the transitions in the region 2.0-2.5 eV gives an estimate of one extra transition for several hundred atoms in the specimen. This corresponds to a reasonable value of 0.1 for the oscillator strength. The data therefore suggest that if a structural change is assumed to accompany photodarkening, it is likely to involve a few tenths of a per cent of the atoms present. If this change involves movement of -
R.T. Phillips / Photodarkening of amorphous selenium
364
6
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Fig. 4. The effect of heavy-ion bombardment on the absorption edge of a-Se at 100 K. ( + ) is for the annealed state, (O) after bombardment and (zx) after subsequent exposure to bright white light. Photodarkening is suppressed.
selenium atoms to metastable configurations of higher energy than those occupied in the annealed state, then the saturation of the shift in the absorption edge presumably reflects an upper limit on the density of the sites which can be excited in this way. This is also shown by the measurement of the absorption edge following intense ion-bombardment, shown in fig. 4. In this case the specimen was exposed at 100 K to a total dose of 2 x 1012 S°Se+ ions cm -2 at 100 keV energy. Since the film is not homogeneous after such a bombardment, a is deduced from ( T / 1 - R ) = e x p ( - a d ) . The similarity between the shift of the absorption edge in this case (induced by ion bombardment) and that associated with photodarkening illustrates that for photoexcitation and ion bombardment the changes in the density of states near the band edges are comparable (assuming that this plays a direct part in determining the optical absorption). Some relaxation of the heavy disorder induced by the ion
R.T. Phillips / Photodarkeningof amorphous selenium
365
beam can be produced by exposure to white light as shown in fig. 4 (photoannealing) but photodarkening of bombarded material does not occur, and a bombarded and illuminated film gives the same absorption edge as illuminated pristine material (within the crude approximation used for calculating a for the inhomogeneous layer).
4. Conclusion The photodarkening of amorphous selenium involves changes in the optical absorption edge in both the region of photon energy associated with the interband transition and in the region of " U r b a c h " behaviour. The decrease in the slope of the exponential region during photodarkening would be interpreted as an increase in mean strength of the microscopic electric field in Dow and Redfield's theory. Various other models are also consistent with this observation - for example those involving changes in band tails. There is no gap between the onset of absorption (as the photon energy increases) and the onset of photodarkening, as there is for photoconduction at low electric fields. It therefore appears that even if carriers recombine without diffusing apart the optical response may still be changed. Measurement of n - ik before and after illumination has made it possible to estimate roughly the number of atoms which would be involved in the photoinduced structural change presumed to accompany photodarkening. This suggests that one atom in several hundred may be involved in configurational change of the type outlined by Tanaka [4], in which an atom may be subject to a double-well potential as the configuration is varied. Since the effect of optical excitation is to introduce a hole in the high-lying lone pair states it is clear that illumination can lead to a change in the interaction of the lone pair (now singly occupied) with second-nearest atomic neighbours. A change in configuration brought about as a result of this is likely to lead to a shifting of the final state if the atom remains at a metastable structural configuration after recombination. It is not clear how this model explains changes in the Urbach region, which is not well understood even for annealed material. This work has been supported by the Science and Engineering Research Council. I would like to thank J.H. Davies, W.Y. Liang and A.D. Yoffe for many enlightening comments.
References [1] R. Chang, Mat. Res. Bull. 2 (1967) 145. [2] V .L. Averianov,A.V. Kolobov,B.T. Kolomietsand V.M. Lyubin, Phys. Stat. Sol. a57 (1980) 81. [3] K. Tanaka and A. Odajima, Solid St. Commun. 43 (1982) 961.
366
R.T. Phillips / Photodarkeningof amorphous selenium
[4] K. Tanaka, in: Amorphous Semiconductor Technologies and Devices, ed., Y. Hamakawa (OHM-North Holland, Amsterdam, 1982) p. 227. [5] J.D. Dow and D. Redfield, Phys. Rev. 85 (1972) 594. [6] D.J. Dunstan, J. Phys. C 15 (1982) L419. [7] P.T. Kosyrev, Inorg. Mater. 2 (1967) 1419. [8] R.T. Phillips, J. Phys. D16 (1983) 489. [9] W.Y. Liang and A.R. Beal, J. Phys. C 9 (1976) 2823. [10] Y. Utsugi and Y. Mizushima, J. Appl. Phys. 51 (80) 1773. [11] N.F. Mort and E.A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd Ed. (Clarendon, Oxford, 1979) p. 528.
PHOTODARKENING
OF AMORPHOUS
359
SELENIUM
R.T. P H I L L I P S * Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, Great Britain
Received 6 July 1984 Revised manuscript received 31 August 1984
Various parameters associated with photodarkening of amorphous selenium have been measured at 100 K. The spectral response of photodarkening shows a step at the absorption edge indicating that electron-hole pair creation is a basic feature of the process. It is shown that the slope of the Urbach edge decreases during photodarkening, and it is found that the change in the optical joint-density-of-statespeaks in the region of photon energy between 2.0 and 2.5 eV. A film of a-Se subjected to ion bombardment at 100 K does not then show photodarkening, and this and the other observations are discussed in terms of a model of local change in atomic arrangement.
3. Introduction Several m e a s u r e m e n t s of p h o t o d a r k e n i n g of a m o r p h o u s selenium have been r e p o r t e d [1-3], a n d there have b e e n m a n y m e a s u r e m e n t s of p h o t o i n d u c e d changes in c h a l c o g e n i d e glasses c o n t a i n i n g selenium or sulphur [4]. These p r e v i o u s e x p e r i m e n t s have shown that p h o t o d a r k e n i n g can p r o c e e d following a n y i n t e r b a n d optical t r a n s i t i o n a t the f u n d a m e n t a l a b s o r p t i o n edge. Subb a n d g a p i l l u m i n a t i o n often reduces the p h o t o - d a r k e n i n g , as does increasing the t e m p e r a t u r e to near the glass transition. T h e r m a l a n n e a l i n g at j u s t b e l o w the glass t r a n s i t i o n t e m p e r a t u r e results in r e m o v a l of the i n d u c e d a b s o r p t i o n , which is a p p a r e n t l y c o m p l e t e l y reversible. Below an a b s o r p t i o n coefficient, a, of 2 - 3 × 10 4 c m -1, a b s o r p t i o n varies e x p o n e n t i a l l y with p h o t o n energy, E, giving logea = F ( E - E0) in selenium. F is the s l o p e of the edge, E the p h o t o n energy a n d E 0 a constant. This b e h a v i o u r - the spectral U r b a c h rule - gives w a y to a w e a k e r d e p e n d e n c e of a on E at higher E , where a E ~x ( E - Ea), with E 1 a n o t h e r constant. This linear v a r i a t i o n o f mE w o u l d arise for excitation b e t w e e n two b a n d s of c o n s t a n t density-of-states, in the a b s e n c e of strong v a r i a t i o n of m a t r i x elements for different electronic transitions. T h e energy E~ can be used to define an " o p t i c a l b a n d g a p " , a n d clearly for p h o t o n energies near E t it is to be expected * Present address: Department of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, Great Britain. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
360
R.T. Phillips / Photodarkeningof amorphous selenium
that the behaviour of the absorption coefficient will be sensitive to states near the band edges. This region is difficult to interpret because of the possible effects of the coulomb interaction on the final state, and indeed the origin of the Urbach region in amorphous systems is not yet resolved [5,6]. The experimental work described here covers the absorption edge of a-Se across the two regions described above, and is discussed in terms of previously proposed models for the origin of photodarkening.
2. Experimental work Thin films of a-Se were prepared by thermal evaporation, from a tungsten basket, of material which had been purified by the quenching method [7]. The original material was specified to be 99.9999% pure with respect to heavy elements. The vacuum system used a mercury diffusion pump and attained a pressure of - 3 × ]0 -9 Torr before evaporation of the films used for the present experiments. Typically, a rise in pressure of about two orders of magnitude occurred during deposition of films. Superpolished spectrosil discs were used as substrates, and these were mounted in a copper block held at a temperature of about 290 K during film growth, which proceeded at about 0.3-0.5 n m s -1. After deposition, specimens were quickly transferred (in air) to a Displex coldfinger mounted in the target chamber of a heavy-ion accelerator in which optical properties could be measured. Reflectance, R, and transmittance, T, of the film-and-substrate combination were measured at normal incidence. For these experiments on a-Se the specimens were held at 100 K in a background pressure of < 5 x 10 -s Torr, and were always cooled in the dark from a thermally annealed state at 290-300 K. For a homogeneous film of constant thickness, the refractive index, n-ik, may be obtained directly from the measured values of R and T by numerical solution of the appropriate equations [8]. This permits a derivation of the absorption coefficient, a, taking into account interference within the film and the presence of the substrate. The optical joint density of states has also been obtained from the measured n-ik [9].
3. Discussion of results Fig. 1 shows the absorption edge of a film of a-Se 137 nm thick, deposited at 291 K at a mean rate of 0.43 nm s-l, and measured at 100 K before and after exposure for 30 min to the white light emitted by a 150 W tungsten lamp at a distance of 20 cm. The spectral Urbach rule is clearly shown at low values of a, where a marked change in absorption occurs during exposure (photodarkening). Over the energy range from about 2.4 to 3.2 eV only one series of points is shown, since the absorption edges are very close when log a is plotted.
R.T. Phillips / Photodarkening of amorphous selenium i
361
i
/ E cJ
l+ e+
o
4-
e+ • + + + • +
0
•
•
4
+
•
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+
÷ 4-
•
÷ •
3
+
i
i
J
2.0
2.5
3.0
35
Photon energy / eV
Fig. 1. The optical absorption edges of amorphous selenium at 100 K in the annealed (+) and photodarkened (O) states described in the text.
Though scatter in the data becomes apparent below a --- 6 - 7 × 10 3 cm -1 it seems clear that the photodarkening has not only shifted the absorption edge but also caused a decrease in the slope F of the Urbach region. A change in slope from about 16 eV -1 to 11 eV - ] (measured at a = 10 4 cm - ] ) occurs for illumination with light of 2.2 eV. A change of this type has been measured for a-As4SesGe and a-As4SeaS3Ge by Utsugi and Mizushima [10]. Fig. 2 illustrates the spectral dependence of the variable E04 (the energy at which a = 10 4 cm -1) plotted in the form A E 0 4 = E 0 4 (illuminated)-E04 (annealed) versus photon energy. In this case the data were obtained in the region where A E04 is insensitive to the total number of absorbed photons, and lengths of exposure were chosen to control the total number of absorbed photons to within about a factor of three, except for the point at 1.96 eV. For this point a 2 mW helium-neon laser was used, and no detectable shift in the
R.T. Phillips / Photodarkening of amorphous selenium
362
0.10
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2.2
2.3
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Fig. 2. The spectral response of the change in optical gap measured at ct = 104 c m - 1 for a-Se at 100 K.
absorption edge occurred even for very long exposures. The decline in the efficiency of photodarkening above 2.5 eV appears to be a genuine effect, and is in agreement with the observations of Tanaka and Odajima [3]. The lack of any photodarkening of films under irradiation by the He-He laser may be due to the small absorption coefficient at this energy, which is well within the Urbach region. The data therefore seem to indicate that the efficiency of photodarkening rises at the same energy as the absorption edge. At 2.1 eV the step in the efficiency of photodarkening appears to be essentially complete, and yet at this energy the absorption is only about 5 x 103 cm -1 in the un-irradiated film (at 100 K). There is no gap between the absorption edge and spectral response of photodarkening, as there is for photoconduction. Photodarkening may therefore occur even if geminate recombination of photoexcited electron-hole pairs takes place, and it seems likely that the shift in the absorption edge is simply associated with the occurrence of an interband transition. Interpretation of the photodarkening is further aided by studying the change in the optical jointdensity-of-states. In fig. 3 the value of AJDS is plotted versus photon energy, where the change in the joint-density-of-states z~JDS = 4.6 x 1 0 - 4 VATOM X E[c2b(E) - c2a(E)] and the atomic volume, VATOM= 31.4 A3 (corresponding to a density of 4.3 g cm-1). The imaginary part of the dielectric function after photodarkening c2b(E ) at photon energy E is compared with a value interpolated from the data for c2a(E ) for the annealed film. The oscillator strength has been set to unity. This method of displaying the change associated with photodarkening makes it clear that the transitions near the absorption edge are
R.T. Phillips
/
Photodarkening o f amorphous selenium
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Fig. 3. The change in the opticaljoint-density-of-statesdeduced from the measurementsof R and T, showing a peak between 2.0 and 2.5 eV. The shaded region is discussed in the text.
the ones which are being altered most dramatically. The data for E > 2.5 eV cannot be interpreted as indication of a definite change in c 2 because of the inherent inaccuracy of the measurement i n this region of high absorption. The integrated change in joint-density-of-states from 2.0 to 2.5 eV (filled area in fig. 3, arbitrarily chosen to span the peak) given a change of about 2.7 × 10 -4 states per atomic volume per unit oscillator strength. It is difficult to extract from this value the parameter of interest to structural modelling of photoinduced changes - the number of atoms involved. This stems from the problems associated with estimating an appropriate oscillator strength for a range of transition energies spanning the " U r b a c h " and "interband" regions. Dunstan's recent arguments [6] would support the much-used assumption of only a slow variation of matrix elements with energy, which helps to overcome this obstacle. By treating the region of the c 2 spectrum from the absorption edge to the pronounced minimum near 7 eV as being due to transitions involving 2 p-lone pair electrons being excited into the conduction band [11] it is possible to assign an effective strength to the transitions in the region 2-2.5 eV. Use of the sum rule for the effective number of electrons taking part in the transitions in the region 2.0-2.5 eV gives an estimate of one extra transition for several hundred atoms in the specimen. This corresponds to a reasonable value of 0.1 for the oscillator strength. The data therefore suggest that if a structural change is assumed to accompany photodarkening, it is likely to involve a few tenths of a per cent of the atoms present. If this change involves movement of -
R.T. Phillips / Photodarkening of amorphous selenium
364
6
i
i
i
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E o
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3.0 3.5 Photon energy/eV
Fig. 4. The effect of heavy-ion bombardment on the absorption edge of a-Se at 100 K. ( + ) is for the annealed state, (O) after bombardment and (zx) after subsequent exposure to bright white light. Photodarkening is suppressed.
selenium atoms to metastable configurations of higher energy than those occupied in the annealed state, then the saturation of the shift in the absorption edge presumably reflects an upper limit on the density of the sites which can be excited in this way. This is also shown by the measurement of the absorption edge following intense ion-bombardment, shown in fig. 4. In this case the specimen was exposed at 100 K to a total dose of 2 x 1012 S°Se+ ions cm -2 at 100 keV energy. Since the film is not homogeneous after such a bombardment, a is deduced from ( T / 1 - R ) = e x p ( - a d ) . The similarity between the shift of the absorption edge in this case (induced by ion bombardment) and that associated with photodarkening illustrates that for photoexcitation and ion bombardment the changes in the density of states near the band edges are comparable (assuming that this plays a direct part in determining the optical absorption). Some relaxation of the heavy disorder induced by the ion
R.T. Phillips / Photodarkeningof amorphous selenium
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beam can be produced by exposure to white light as shown in fig. 4 (photoannealing) but photodarkening of bombarded material does not occur, and a bombarded and illuminated film gives the same absorption edge as illuminated pristine material (within the crude approximation used for calculating a for the inhomogeneous layer).
4. Conclusion The photodarkening of amorphous selenium involves changes in the optical absorption edge in both the region of photon energy associated with the interband transition and in the region of " U r b a c h " behaviour. The decrease in the slope of the exponential region during photodarkening would be interpreted as an increase in mean strength of the microscopic electric field in Dow and Redfield's theory. Various other models are also consistent with this observation - for example those involving changes in band tails. There is no gap between the onset of absorption (as the photon energy increases) and the onset of photodarkening, as there is for photoconduction at low electric fields. It therefore appears that even if carriers recombine without diffusing apart the optical response may still be changed. Measurement of n - ik before and after illumination has made it possible to estimate roughly the number of atoms which would be involved in the photoinduced structural change presumed to accompany photodarkening. This suggests that one atom in several hundred may be involved in configurational change of the type outlined by Tanaka [4], in which an atom may be subject to a double-well potential as the configuration is varied. Since the effect of optical excitation is to introduce a hole in the high-lying lone pair states it is clear that illumination can lead to a change in the interaction of the lone pair (now singly occupied) with second-nearest atomic neighbours. A change in configuration brought about as a result of this is likely to lead to a shifting of the final state if the atom remains at a metastable structural configuration after recombination. It is not clear how this model explains changes in the Urbach region, which is not well understood even for annealed material. This work has been supported by the Science and Engineering Research Council. I would like to thank J.H. Davies, W.Y. Liang and A.D. Yoffe for many enlightening comments.
References [1] R. Chang, Mat. Res. Bull. 2 (1967) 145. [2] V .L. Averianov,A.V. Kolobov,B.T. Kolomietsand V.M. Lyubin, Phys. Stat. Sol. a57 (1980) 81. [3] K. Tanaka and A. Odajima, Solid St. Commun. 43 (1982) 961.
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[4] K. Tanaka, in: Amorphous Semiconductor Technologies and Devices, ed., Y. Hamakawa (OHM-North Holland, Amsterdam, 1982) p. 227. [5] J.D. Dow and D. Redfield, Phys. Rev. 85 (1972) 594. [6] D.J. Dunstan, J. Phys. C 15 (1982) L419. [7] P.T. Kosyrev, Inorg. Mater. 2 (1967) 1419. [8] R.T. Phillips, J. Phys. D16 (1983) 489. [9] W.Y. Liang and A.R. Beal, J. Phys. C 9 (1976) 2823. [10] Y. Utsugi and Y. Mizushima, J. Appl. Phys. 51 (80) 1773. [11] N.F. Mort and E.A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd Ed. (Clarendon, Oxford, 1979) p. 528.