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The role of self-trapped excitons in radiation-damage processes in insulators
Nuclear Instruments North-Holland
and Methods
in Physics
Research
207
846 (1990) 207-21.5
Section III. Alkuli halides THE ROLE OF SELF-TRAPPED IN INSULATORS
EXCITONS
IN RADIATION-DAMAGE
PROCESSES
We review current studies on defect formation induced by valence-electron excitation in insulators. Emphasis IS placed on the role of self-trapped excitons In damage processes. First we classify the processes into a few cases. based on categorization of materials in terms of energy localization and on the density of excitation. Then defect formation in alkali halides. which is a typical example of single-excitation process, is discussed to clarify the origin of the dependence of the efficiency on materials. Finally. the effects of the density of excitation on defect formation are discussed. presenting some pieces of evidence that excitation of the self-trapped exciton and the interaction of free excitons and self-trapped excitons produce Frenkel pairs in materials which are highly resistive to single-excitation
processes.
1. Introduction The interaction between nonmetallic solids and radiation results in three types of electronic excitation: (i) core-electron excitation. (ii) ordinary valence-electron excitation and (iii) dense valence-electron excitation. The core-electron excitation generates holes in core orbitals and electrons in the conduction band. while the latter two types of excitation generate holes in the valence band and electrons in the conduction band. We differentiate the types (ii) and (iii), since the interaction between single-excitation events causes specific effects when the density of excitation is sufficiently high. Electronic excitation of each of the three types described above induce specific atomic processes. such as defect formation [1.2]. defect migration [3], crystal-toamorphous transformation [4,5] and ejection of constituent atoms at surfaces [6]. Contrary to the atomic processes induced by elastic collisions. the processes induced by electronic excitation are featured by a strong dependence of their efficiency both on the materials being investigated and on the type of excitation. For example, under ordinary valence-electron excitation. no atomic process is induced in most of the semiconductors, whereas defects are created with a high efficiency in some insulators like the alkali halides. Furthermore. there are several materials which are highly resistive under ordinary valence-electron excitation, but are subjected to radiation effects under dense electronic excitation [5.7-91 and/or core excitation [lo]. Even in the regime of valence-electron excitation. which is dealt with in this paper. the efficiency varies strongly. depending both on materials and on the density of excitation. Extensive studies on the defect formation due to electron-hole recombination in alkali halides have re0168-583X/90/$03.50
(North-Holland)
7’ Elsevier
Science Pubhshers
B.V.
vealed that there are three crucial steps in the process of forming defects from electronic excited states [1,2]: the first is the localization of the electronic-excitation energy. the second is instability of the system, by which localized electronic energy is transformed to the kinetic energy of the atomic system for inducing atomic displacement. and the third is the probability of populating the state(s) having instability. Hereafter we shall call such states the reactive states. Self-trapping of excitons or holes is the most important mechanism which causes the energy localization. The instability appears to be induced in the relaxation process from an exciton (or an electron-hole pair) to the self-trapped exciton (STE) and the probability of populating the state having the instability is governed by the branching ratio in the relaxation process. The fact that the efficiencies of the lattice-defect formation are distributed indicates that these important factors depend strongly on materials and on the density of excitation. Electrons, holes and excitons in nonmetallic solids have two ways of stabilization: delocalization through intersite transfer and localization through coupling with the lattice [ll]. The bandwidth 2B is a measure of the strength of the stabilization through intersite transfer. and the lattice relaxation energy E,, is a measure of the strength of the stabilization through coupling with the lattice. Whether an electron, for example. in a solid is delocalized or localized is determined by the relative magnitude of E, n against B [ll]. In view of the primary importance of the energy localization in the defect-formation process. we categorize nonmetallic solids into two types, as shown in table 1 [12]. in terms of localization of charge carriers and excitons. Since the occurrence of self-trapped electrons seems to be rarer than that of self-trapped holes or excitons, we mainly consider holes and excitons. The III. ALKALI
HALIDES
Table
1
Categorization
of nonmrtallic
solids
with
respect
to
self-trap-
ping of rxcrtons and holes Self-trapping
Type 1 2
2a Zb
Examples
Exciton
Hole
no yes yes
no no yes
MgO. ZnO. GaP. Si SiO,. MgF, alkali
halldes
C-aF,. KM&F,
Type 1 are solids with weak electron-lattice coupling: excitons and holes remain to be free state. The Type 2 are solids with strong electron-lattice coupling; excitons are self-trapped. Depending on whether holes are delocalized or localized. solids of Type 2 are further classified into subgroups 2a and 2b. although the distinction of Type 2 into subgroups is less important in view, of energy localization. Typical examples of these solids are also given in table 1. It is presumed that the efficiency of defect formation induced by electronic excitation in Type 1 materials is substantially lower than in nonmetals of Type 2. In fact. there has been no experimental result indicating formation of lattice defects by an intrinsic mechanism under electronic excitation in Type 1 materials. Even in materials where excitons are self-trapped. the efficiency still varies significantly: the yields range from near unity to several orders of magnitude lower [13]. The purpose of this paper is to discuss the origin of the dependence of the yields of defect formation on materials and on the density of excitation in solids with strong electron-lattice coupling. The origin of the instability and the factors governing the probability of populating the reactivje state are discussed. emphasizing their relevance to materials and the density of excitation. We first describe the properties of the STEs which play a crucial role in the defect-formation process under valence-electron excitation. Since extensive reviews have already been published [14], we describe only the properties related to the instability and the probability of populating the reactive state. Then we focus our attention on defect formation under ordinary excitation, particularly the dependence of the yield of the F centers on materials. Finally. we discuss the high-density effects for defect formation. and point out that the origin of the instability and the probability of populating the state having instability are altered significantly through interaction of single-excitation events.
2. Self-trapped
excitons
The STE is essentially a localized electron-hole pair associated with large lattice relaxation. Although details of the relaxed configuration depend on the nature of the
atomic orbital responsible for the valence band and on the crystal structures [15], there exist a few important common features. One of these features is that the relaxed configuration is often associated with motecular-bond formation. In halides. except AgCI [16,17]. the hole of an STE is stabilized in the form of XT. where X denotes a halogen [1X-20]. Also. it has been shown that an STE in oxides comprises an oxygen molecule [21.23]. Another important feature is the fact that the STE in the lowest triplet state has an off-center configuration in which the molecular ion is displaced as a whole [14]. The most typical example is the STE in alkaline-earth fluorides. In this crystal. the self-trapped hole (STH) is the F,-. molecular ion oriented along a (100) direction [23]. but the STE comprises an F; molecular ion displaced to be oriented along a (1 II) axis. and forming a nearby vacancy where an electron is localized [19,24]. Recently. it has been shown theoretically that the lowest triplet STE in alkali halides has an off-center configuration. where the XT molecular ion is displaced along a (110) direction [14.25527]. Although definite experimental evidence has not yet been obtained. abundant experimental results obtained for the STEs in alkali halides are better explained in terms of the off-center relaxation of the STE [14]. The features of the STE configuration described above indicate clearly that the STE at the lowest excited state has inherently the instability which results in the displacement of the molecular ion. However. there is a barrier against further separation of the molecular ion to form a distant vacancy-interstitial pair. As a result, the lowest triplet STE remains as a metastable state which decays radiativety at tow temperatures. The lowjest triplet STE is generated through deexcitation of an electron--hole pair or an exciton. The deexcitation process consists of a series of nonradiative transitions between several excited states. Besides the deexcitation to the lowest triplet STE. there are other channels of deexcitation; de-excitation to the ground state. involving either radiative (singlet-luminescence) or nonradiative transition. and defect formation [2X]. The probability of deexcitation to these several channels is governed by branching ratios from each of the excited states to tow-lying states. Experimental values of the yield of the lowest STE are usually smatter than unity, and the magnitude depends strongly on the materials [29]. as shown later. The results indicate that the pathways of deexcitation are strongly dependent on materials. In general, the yield of the lattice defects is dependent not only on the degree of the instability of the reactive state(s). but also on the probability of populating the state(s) during deexcitation. Therefore. characterization of the excited states of the STE and ctarification of the deexcitation pathways are essential for understanding the origin of the dependence of the defect yield on materials and on the density of excitation.
(e-h)* 77
K!
(f.e + f h) I --\ ““”
EG
-3
a = %TE
-4
-.Cl=&)
Fig. 1. Energy levels of the STE in KI. together with the transient absorption spectrum (ref. [18]) and luminescence spectrum due to the lowest trlplet STE. Symbols e*. h* and (e + h) * stand for the electron-excited. hole-excited and bulkexcited states of the STE, respectively.
Since the STE is a two-particle system in solids. three types of excited states are evident: electron-excited states, hole-excited states and host-excited states associated with an STE. An exciton perturbed by an STE belongs to the last class of the excited states and its existence in alkali iodides has been demonstrated by Williams and Kabler [30]. In alkali halide and alkaline-earth fluoride crystals, the structure of the STE is such that an election is trapped by a potential formed by an STH and surrounding cations. while a hole forms a halogen-halogen molecular bond. Thus the electron-excited states have features similar to the hydrogenic series in which some orbital degeneracies are removed by low local symmetry associated with lattice relaxation due to self-trapping. On the other hand. the hole-excited states have features similar to the excited states of the halogen molecular ions. Three types of excited states can be clearly demonstrated in an optical-absorption spectrum of the STE in the lowest triplet state [31]. In fig. 1 we portray the absorption spectrum of the STEs and the associated energy-level diagram in Kl. It has been shown that the optical-absorption spectrum due to the 1, molecular ion (STH) has three prominent peaks at 3.1, 2.8 and 1.9 eV [32,33]. A similar three-peak structure is clearly observed for the absorption spectrum due to the STE. and these peaks correspond to transitions to the holeexcited states. On the other hand. the strongest peak at
the lowest energy at 1.1 eV is characteristic of the STE. and has been assigned to the electron transition from the lowest to a higher electron orbital. The sharp peak at 5.75 eV has been ascribed to the optical transition to create excitons perturbed by the STEs. In order to specify each of the excited states more clearly. we adopt mainly the irreducible representation of the DZh symmetry for convenience. The lowest state of the STE possesses the electron at the ls(a,) orbital and the hole at as B3,,. (f.e + f.h) the b,, orbital and is designated denotes the state for a pair comprising a free electron and a free hole. And e * and h* denote the electron- and hole-excited states, respectively. Only the electron orbitals are denoted by e*. The lowest triplet state ‘B,,(a,: h,,,) is known to emit the 71 luminescence. The singlet luminescence. u luminescence. has been considered to be emitted not from the lowest, but from a higher singlet state ‘B,,(a,*; b,,). here a,* denotes a 2s-like orbital. It is also useful to classify the excited states according to the energy of the states. Referring to the energy of an excited state of the STE as E. and the band-gap energy as E,;, those with E < E,; are populated under ordinary valence-electron excitation. but those with E > E, cannot be reached from a single excitation. The latter type can be generated when at least two excitation events interact and/or the lowest STE is excited optically with sufficient energies. The bulk-excited state associated with the STE and some of the hole-excited states fall in this category. The classification of the excited states with respect to the energy is useful to discuss the contribution of a specific excited state to defect formation under irradiation of several types. Incident energetic ions cause the creation of two neighboring excitations in the process of deceleration. Therefore. excited states with E > E,; will be generated with a high probability. On the other hand. under ionizing irradiation, the formation of excited states with E -c if,; dominates. although the yield of two consecutive excitations due to low-energy secondary electrons is not negligible [34.35]. Irradiation of insulators with intense laser pulses of photon energies below E, shows specific features, namely generation of highly excited STEs, since the lowest triplet STEs generated by multi-photon band-toband excitation have chance to absorb photons. Therefore, the excited states with E > E,;. not easily accessible by ordinary valence-electron excitation, can be generated by intense laser irradiation.
3. Defect formation
by a single exciton
As a typical example of the lattice-defect formation induced by ordinary valence-electron excitation, we discuss here the defect formation in alkali halides. ExtenIII. ALKALI
HALIDES
sive experimental and theoretical studies have been carried out on the atomic processes which are involved in the evolution of a Frenkel pair from an exciton. It is known that the process is essentially an isomeric transformation from an STE to a Frenkel pair comprising a vacancy with an electron (the F-center) and an interstitial atom in the form of XT occupying an anion site (the H-center) [l.Z]. As already described in section 2. the STE at the lowest triplet state has an instability to displace the X; molecular ion from the on-site configuration as well as a barrier for further separation of the Xi from the vacancy. Therefore. the yield of the defect formation can be understood as a result of competition between the degree of the instabllity and the magnitude of the barrier. First we mainlq concern ourselves with the defect formation at low temperatures where thermally activated transformation from an STE to an F-H pair on the potential surface of the lowest triplet state [36] is not active. The dependence of the yield of the stable F-centers generated by continuous ionizing irradiation on materials has been characterized well in terms of the Rabin-Klick parameter S/D. where S is defined as the separation of the two adjacent halide ions along a (1 IO) direction minus twice the halide-ion radius. and D is the diameter of a halogen atom [37]. The yield of the stable F-centers plotted as a function of S/D is shown in fig. 2. Although the data points are scattered considerably, the overall dependence is such that the yield ix constant for materials with S/D larger than 0.5. whereas the yield decreases sharply with S/D decreasing from 0.5. In the same figure we have plotted the yields of the IT luminescence and the D luminescence [29]. These represent the yields of the lowest triplet STE and the excited singlet STE, respectively. It is clear that the yield of the lowest triplet STE shows anticorrelation with the yield of the F centers. On the other hand, the yield of the singlet STE is constant irrespectively of the magnitude of S/D. The anticorrelation between the yields of the lowest triplet STE and the F-centers suggests strongly that the competition associated with defect formation occurs in the triplet manifold. and that the material-dependent yield of stable F-centers is a direct consequence of the competition which takes place during relaxation leading to the lowest triplet state. Time-resolved measurements which utilize a pulsedelectron beam [40] or a pulsed-laser light [41] have revealed formation of the transient F-H pairs, as well as stable ones at low temperatures. For example. in KCI. more than 90% of the instantaneously produced F-centers by a pulsed-electron irradiation at 5 K are annihilated by pair recombination within 0.1 ms after irradiation [40]. The formation of transient F centers in the nanosecond regime has also been observed in RbCl [42]. KBr and RbBr [31.40]. This group of materials is
\
1030+--p--ylo~ S/D
Fig. 2.
The Rabin-Klick
required (double mental triangles
diagram
to form an F-center
at 4 K showing the energir.\
and a photon of IJ luminescence
circles), and are of 7: luminescence results for F-center
formation
and open circles were taken
[37]. Hughes et al. [3X], and IkezaNa Luminescence
(crosseh). Experi-
shown hy solid circleb. from
Rabin
and Klick
et al. [39]. respectively.
data were from Pooleq and Runchlmann
[29].
situated at the middle part of the S/D axis. On the other hand. in LiF and NaF, both of which are situated at a similar region in the Rabin-Klick diagram and show a similar magnitude of efficiencies in the formation of stable F-centers, no such transient F-centers are produced: the F-centers produced within the width of a pulsed electron beam of 20 ns remain stable over several seconds or more at 5 K [43]. Therefore, it appears that the Rabin-Klick diagram is not sufficient to characterize the efficiency of the defect formation of transient defects annihilated in the nanosecond regime. We consider that some other properties which are related to S/D may govern the competition between the instability and the barrier in the defect formation process. It is of interest to measure the formation of the transient F-H pairs for NaF and LiF in the picosecond regime. It has been controversial that defect formation is governed by the competition on the potential surface either of a higher excited state of the STE [44.45] or of the lowest excited state of STE [27.46.47]. At present definite experimental results capable of determining Mhich is the case have not yet been obtained. From the theoretical point of view. on the other hand, Song et al. have described the Rahin-Klick diagram for the stable F-center yields in terms of off-center STE relaxation on the potential surface of the lowest state of STE [47]: as the degree of off-center increases. the F-center yield
increases because of larger kinetic energy imparted for the off-center relaxation. Detailed description and critical discussions on both types of models have been given in a recent review [48]. So far we have argued the dependence of the F-center yield on materials in terms of instability. This factor certainly explains the overall dependence of the yield, but the large scatter of the experimental data is evident in fig. 2. Although this scatter might be partly due to experimental error. we consider that the probability of populating the reactive state affects the yield. Since in alkali halides the hole self-trapping occurs prior to self-trapping of excitons, the excited states passed through during deexcitation are mainly the electron-excited states described in section 2. Therefore the deexcitation pathways at these states are essential for determining the probability of populating reactive state(s). and hence the yield of the F-centers. The present authors have studied the nonradiative deexcitation from electron-excited states of the STE by means of the cascade-excitation technique in which a specimen populated with the lowest triplet STE is excited further by a light pulse from a tunable-dye laser to generate a given type of excited state selectively [28]. The yields, qF of the transient F-centers from each of the electron-excited states of the STE. to which optical transition from the lowest state is allowed, have been determined. Fig. 3 shows the results for KC1 and KBr. respectively. In the figure. thin solid curves represent the absorption spectra to excited states at which the electron occupies one of the Zp-like orbitals. and the broken curve, to higher states. The results shown in fig. 3 indicate two important features: (1) the yield qF depends on the nature of the excited state of the STE, (2) the yield for excited states with similar electronic nature in different materials shows a strong dependence on the materials. The first feature is evident from the results of different magnitudes qf for different excited states in both KC1 and KBr, and the second feature is clear from the fact that the np-excited state does not show any F-center formation in KBr. whereas in KCI it shows the highest yield. These features are interpreted in terms of the difference in the probability of populating the reactive state. and hence the selective nonradiative transitions at the excited states of the STE [28]. Thus the deexcitation pathway during relaxation of the STE in a highly excited state is also essential for understanding the dependence of the yield of the defect formation on materials. The mechanism of selective nonradiative transitions at the excited states of STEs remains unclear. 4. Multiple-excitation
processes
In the previous section, we discussed the lattice-defect production under ordinary valence-electron excita-
OL-
0.2-
0
I 15
20 PHOTON
ENERGY
25 ( eV )
Fig. 3. Yields of F-centers from photo-generated elrctron-rxcited states of the STE in KCI and KBr. Data shown by double circles. squares and open circles are for B,,. .A, and B,, substates of the Zp-excited state, respectively. The solid circles are for the up-excited states (II > 2). The solid curve shows the absorption spectrum due to the lowest triplet STE. Thin solid and broken curves show the ahborption due to transitions to 2p- and np-excited states.
tion. When the density of excitation becomes higher, the interaction between (or among) the single-excitation events cannot be neglected. In this situation. effects of the interaction on the relaxation of electronic excitations will be significant. In fact. there are several experimental results which indicate such high-density effects: these include the decrease of the luminescence yield [49.50] and the superlinear increase of the yield of defect production with an increase of the density of excitation [4.7-91. These results have been obtained mainly by high-energy ion irradiation. The primary processes which result in these high-density effects have remained unclear. Recently the present authors have studied the luminescence and defect formation by laser irradiation in RbI which shows a small efficiency (10~5-10-h per electron-hole pair) of the F-center under ordinary valence-electron excitation. They observed a decrease in the n luminescence yield with increasing laser intensity and the superlinear increase of the yield of the stable defects in proportion to the square of the density of excitation [8]. Further details of the experimental results are explained with reference to fig. 4. A specimen was irradiated with 308 nm laser light from a XeCI-excimer laser. The two-photon absorption process generates electron-hole pairs in this case. For weak excitation, the intensity of the 77 luminescence, 111. ALKALI
HALIDES
LASER
FLUX
(arb units )
Fig. 4. The magnitude of the stable component of the opticalabsorption change measured at 726 nm (sohd circles), and the intensity of the 71 luminescence (open circles), Induced by a 308 nm laser pulse as a function of excitation intensity.
which monitors the concentration of the lowest triplet STE. increases linearly with increasing density pe, of excitation. However, it saturates at higher pcx. On the other hand, the optical density at 726 nm measured after 0.2 ms of laser-pulse irradiation is essentially independent of p,, for weak excitation, but it increases abruptly above the value of pi, at which saturation of the n-luminescence intensity becomes significant. On subtraction of the intensity-independent component, the magnitude of optical-absorption change was found to increase in proportion to the square of prx. as shown by the broken lines in the figure. We showed the opticalabsorption spectrum of this superlinear component to be the F-band. Although the laser irradiation excites the holes of the lowest triplet STE, formed by two-photon absorption, it has been confirmed experimentally that hole excitation does not contribute to the formation of the stable F-centers in Rbl. Therefore, it is clear that the stable F-centers are generated by the interaction of two single-excitation events in this case. The results obtained by Tanimura and Itoh [8] strongly suggest that the interaction between two single-excitation events (excitons or electronhole pairs) either creates a new state having instability that is not formed under single excitation and/or enhances the probability of populating the reactive state, which is responsible for generating F-centers under single exci-
tation. Below we give general discussions on the mechanism of defect formation under dense electronic excitation. In a substance of Type 1, the important process under dense electronic excitation is the interaction among free excitons and/or free carriers. The interaction leads to formation of biexcitons and if the density is extremely high, an electron-hole plasma. On the other hand. in substances of Type 2. where holes and/or excitons are self-trapped. such free multiparticle complexes are not formed. mainly due to the short lifetimes of free carriers and excitons against self-trapping. The dense electronic excitation for this type of materials will form a mixture of free excitons and STEs. At this stage, collisions of free excitons with STEs dominate [51] and the collision will form a complex. a free exciton (FE) interacting with an STE, since the interaction has been shown to be attractive [30]. We call this complex the FE-STE pair. Evidently the mobility of free excitons is a crucial factor for determining the yield of FE-STE pairs and. if it is extremely low, we expect only the interaction between STEs for extremely dense excitation. From the arguments above. it is clear that the deexcitation of the FE-STE pairs governs the high-density effects in defect formation in solids of Type 2. Since an FE-STE pair is already localized, the crucial point is whether there are states having instability specific to the FE-STE pair. Recently Tanimura and Itoh have obtained the most direct information on the relaxation processes of the FE-STE pair in RbI [52]. In RbI, the optical-absorption band due to the creation of excitons perturbed by the STEs is situated at 5.61 eV [30]. to which a KrCl-excimer laser resonates almost exactly. Therefore. by using the cascade-excitation technique, in which a specimen populated with STEs is excited further by a light pulse of 222 nm. the FE-STE pairs are generated directly, and measurements of the resulting changes in optical absorption and luminescence have given the direct consequences of the generation of FE-STE pairs. The results by the present authors for optical-absorption changes induced by sequential irradiation with an electron pulse and a light pulse are shown in fig. 5. In the figure, curve (a) shows the optical-absorption spectrum measured 5 KS after an electron pulse. The peaks were ascribed to the lowest triplet STE from a comparison of the spectrum with that obtained by Williams and Kabler [31] and of the decay time of the band with the lifetime of STEs. Curve (b) is the spectrum measured after I7 shots of the electron pulse, while curve (c) is the spectrum measured after 17 cycles of the sequential irradiation with an electron pulse and a light pulse. In the latter experiments, each cycle consists of an electron pulse followed by a light pulse with a 5 ps delay. About 30% of the lowest triplet STEs were de-
PHOTON
ENERGY
( eV )
Fig. 5. Optical-absorption spectra measured (a) at 5 ps after irradiation of an electron pulse. (b) after 16 electron pulse shots and (c) after 16 cycles of sequential irradiation of an electron pulse and a light pulse of 222 nm. The arrow show the peak energies of the F and H bands. The inset shows the relation between the peak height of optical absorption at 726 nm and the number of cycles of sequential irradiation.
stroyed by the light pulse in each cycle. It is clear that no absorption band is produced by the irradiation with electron pulses only. but the sequential irradiation produces the F absorption band. the peak of which is shown by an arrow. The inset of fig. 5 shows the relation between the height of the F band induced and the number of cycles of the sequential irradiation. The proportional relation is evident. The results shown in fig. 5 give unambiguous evidence that stable F centers are formed during relaxation of the FE-STE pairs. By using Smakula’s equation, they obtained 0.041 for the conversion yield from a FE-STE to a stable F-center. They have also found another important relaxation channel of the FE-STE pairs: that is conversion to the excited singlet STE responsible for the o luminescence from the FE-STE pair. The yield of this conversion, which can be regarded as exciton fusion, was 0.38. Their results have revealed two important aspects of the high-density effects on the lattice defect formation. One is that a FE-STE pair possesses a new type of instability for generating lattice defects. As described in section 3. the yield of the stable F-centers due to the single-exciton mechanism in RbI is as low as 10m5-10. ’ per electron-hole pair, while the conversion yield from FE-STE pairs is as high as 0.04. This magnitude is almost the same as or larger than the yield of F-H pairs by a single-exciton mechanism in NaF. which shows the highest yield of defect formation under ordinary valence-electron excitation. The second important aspect is concerned with the generation of highly excited states of the STE from an FE-STE pair through exciton fusion. Since an FE-STE pair possesses an energy which is almost twice the band-gap energy E,;. highly excited states of the STE. which are not populated
under ordinary excitation. can be populated. If one of these highly excited states of the STE is a reactive state. then the exciton fusion can be a cause of lattice-defect formation. In this aspect. we point out here some features of the radiation effects which occur under intense laser irradiation. When solids with strong electron-lattice coupling are exposed to intense laser light having a photon energy h v smaller than E,. the primary process is multiphoton absorption generating electron-hole pairs followed by formation of STEs. Because of long lifetimes of the lowest triplet STE and high photon fluxes. excited states with energies as high as hv + E,,, (where is the energy of the lowest STE) are highly popuEsrn lated. If hv+ Esrb exceeds E,;. the excited states that cannot be populated under ordinary valence-electron excitation are produced. Therefore. the effects under intense laser irradiation may be essentially similar to those under high-density excitation. in the sense that the highly excited states (with E > E,,) having an instability can be populated under both of these types of excitation. The example of the lattice-defect formation in such a situation has been demonstrated by the present authors [53]. They have studied relaxation in the lattice of CaF, caused by excitation of STEs by means of cascade-excitation spectroscopy. CaF, is known as one of the materials that shows low F-center yields under ordinary valence-electron excitation [54,55]. Fig. 6 shows the optical-absorption changes in CaF, induced by sequential irradiation with an electron pulse at t, and a light pulse at 1,. measured at 365 nm which is close to the F-band maximum. The result shown in fig. 6a is the consequence of electron excitation of the STE by a 2.61 eV laser pulse, whereas that in fig. 6b is the consequence of hole excitation of the STE by a 4.03 eV laser pulse. Hole excitation generates a hole-excited state, in which the hole occupies the bonding orbital (a,). and hence the F1- molecular ion is an antibonding state. It is clear from the figure that the combination of pulsed-electron and pulsed-laser irradiation to generate the electron-excited states of the STE produces only the transient component. On the other hand. upon generation of the hole-excited state of the STE. significant amounts of the stable and transient components are generated. Spectroscopic measurements have confirmed that the stable component consists of F-centers. Therefore, it is evident that the hole-excited state of the STE in CaFz produces stable F-centers. Consideration of the energetics has shown that the hole-excited state is located above the ionization continuum at the self-trapped exciton configuration, so that the state has almost no chance of being populated under ordinary valence-electron excitation. Thus. the results attained for CaF, have provided a typical example of the lattice-defect formation induced by the modification of the population of III. ALKALI HALIDES
214
(a)
02 1
i
i
te
tl TIME
Fig. 6. Oscilloscope traces of the optical-absorption changes at 365 nm in CaF, induced by sequential irradiation with an electron pulse at f, and a light pulse at f,; (a) for the light pulse of 2.61 eV dye-laser pulse, and (b) for the light pulse of 4.03 eV excimer-laser pulse.
curs during deexcitation at the excited states of the STE. based on the experimental results for the state-dependent yield of the F-center formation in KC1 and KBr. The general understanding of the rule which governs the branching is highly desired. Then we have discussed the instability at the highly excited states that are not produced by the single-exciton process and the probability of populating these highly excited states. Based on recent experimental results by the present authors, the importance of FE-STE pairs for the high-density effects of lattice-defect formation has been stressed. The two important factors that govern the high-density effects are the instability possessed by FE-STE pairs and the probability of populating the states having an instability. The similarity of the defect formation process under intense UV laser irradiation and the effect of the dense electronic excitation has also been pointed out. Throughout this paper, we have emphasized that the STEs play crucial roles. directly or indirectly, in the process of lattice-defect formation in nonmetallic solids with strong electron-lattice coupling. The role of selftrapped excitons in the formation of latent tracks of heavy energetic ions in non-metallic solids has been treated separately [5X].
References
the reactive states. Similar results have also been obtained in MgFz [56]. The mechanism described here is presumed to have close correlation to the recent experimental results showing efficient formation of the F-centers in CaF, and MgF,, when irradiated with subpicosecond intense UV laser pulses [57].
5. Summary
In this paper we have described the primary processes of defect formation induced by electronic excitation in solids with strong electron-lattice coupling. The emphasis has been placed on understanding the origin that induces significant differences in the efficiencies of lattice-defect formation over the types of materials and the mode of excitation. Our viewpoint is that the difference is governed by the existence of the state having an instability, and the probability of populating the state having the instability under a given mode of excitation. As a typical example of the defect-formation process which occurs under ordinary valence-electron excitation, where the single-exciton mechanism is exclusive, we have discussed the material dependence of the Fcenter yields at low temperatures in alkali halides. We also discussed the importance of branching which oc-
[II M.N. Kahler and R.T. Williams,
Phys. Rev. BlX (1978) 194x. PI N. ltoh, Adv. Phya. 31 (1982) 491. [31 J.D. Weeks, J.C. Tully and L.C. Kimering, Phys. Rev. B12 (1975) 3286. and L.W. Hobbs, Radiat. 141 M.R. Pacuccl. J.L. HutchInson Eff. 74 (19X3) 219. F. Joliet, Y. Langevin and E. Dooryhee. [51 J.P. Duraud. Nucl. Instr. and Meth. 832 (1988) 248. [61 N. Itoh. Nucl. Instr. and Meth. B27 (1987) 155. Proc. SPIE 541 (1985) 3X. [71 D.L. Griscom, and N. Itoh, Phys. Rev. Lett. 60 (1988) 2753. PI K. Tanimura Nucl. Instr. and Meth. 813 191 N. Itoh and T. Nakayama. (19X6) 550. and P.J. Feibelman, Phys. Rev. Lett. 40 [1W M.L. Knotech (1978) 964. Y. Toyozawa and E. U]l M. Ueta. H. Kanzaki. K. Kohayashi, Hanamura, Excitonic Processes in Solids (Springer. Berlin. 1986) chap. 4, p. 203. and N. ltoh, Nucl. Instr. and Meth. B33 [I21 K. Tanimura (1988) 815 and 832 (1988) 211. Radiat. Eff. 98 (1986) 269. P31 N. Itoh and K. Tanimura, [I41 R.T. Williams and K.S. Song, J. Phys. Chem. Solids, in press. Semicond. and Insul. 5 (1983) 175. [I51 Y. Toyozawa, R.T. Williams and M.N. Kabler, Solid U61 C.L. Marquardt, State Commun. 9 (1971) 2285. Insul. 5 (1983) 533. [I71 W. Hayes, Semicond.
K. Tunmura,
IV. Itoh / Self-trapped
[1X] M.J. Marrow, F.W. Patten and M.N. Kabler, Phys. Rev. Lett. 31 (1973) 467: A. Washiela. G. Ascarelli and Y. Merle d’Aubigne. ibid., p. 994. [19] P.J. Call. W. Hayes and M.N. Kabler. J. Phys. C8 (1975) L60. [20] D. Block. A. Wasiela and Y. Merle D’Aubigne, J. Phys. Cl1 (1978) 4201. [21] W. Hayes, M.J. Kane. 0. Salminen. R.L. Wood and S.P. Doherty. J. Phys. Cl7 (1984) 2943. [22] W. Hayes, M.J. Kane. 0. Salminen and A.I. Kuznetsov,. J. Phys. Cl7 (1984) L383. [23] W. Hayes and J.W. Twidell, Proc. Phys. Sot. London 79 (1962) 1295. [24] R.T. Williams, M.N. Kabler, W. Hayes and J.P. Stott. Phys. Rev. B14 (1976) 725. [25] KS. Song and C.H. Leung, J. Phys. Cl2 (1979) L67. [26] G.B. Brunet, C.H. Leung and KS. Song. Solid State Commun. 53 (1985) 607; C.H. Leung, B. Brunet and K.S. Song, J. Phys. Cl8 (1985) 4459. [27] R.T. Williams. KS. Song, W.L. Faust and C.H. Leung, Phys. Rev. B33 (1986) 7232. [2X] K. Tanimura and N. Itoh, J. Phys. Chem. Solids 45 (1984) 323. [29] D. Pooley and W.A. Runchiman, J. Phys. C3 (1970) 1815. [30] R.T. Williams and M.N. Kabler. Solid State Commun. 10 (1972) 49. [31] R.G. Fuller, R.T. Williams and M.N. Kabler. Phys. Rev. Lett. 25 (1979) 446; R.T. Williams and M.N. Kabler, Phys. Rev. B9 (1974) 1897. [32] C.J. Delbecq. W. Hayes and P.H. Yuster, Phys. Rev. 121 (1961) 1043. [33] R.B. Murray and F.J. Keller, Phys. Rev. 153 (1967) 993. [34] J.H.O. Varley, J. Phys. Chem. Solids 23 (1962) 985. [35] N. Itoh, Phys. Status Solidi 30 (1968) 199. 1361 R.T. Williams, Phys. Rev. Lett. 52 (1984) 1709.
exc’rtons tn dumugr processes
215
[37] H. Rabin and C.C. Klick, Phys. Rev. 117 (1960) 1005. [38] A.E. Hughes. D. Pooley. H.U. Rahman and W.A. Runciman. AERE-Report R5604 (1967). [39] M. Ikezawa. K. Shirahata and T. Kojima. Sci. Rep. Tohoku Univ. 1. Lll (1969) 45. [40] M. Hirai, Y. Kondo, T. Yoshinari and M. Ueta. J. Phys. Sot. Jpn. 30 (1971) 440: Y. Kondo. M. Hirai and M. Ueta. J. Phya. Sot. Jpn. 33 (1972) 151. (411 R.T. Wtlliams, J.N. Bradford and W.L. Faust, Phys. Rev. B18 (1978) 7038. [42] B. Mizuno. K. Tanimura and N. Itoh, J. Phys. Sot. Jpn. 55 (1986) 3258. [43] K. Tanimura. unpublished (1988). [44] N. ltoh and M. Saidoh. J. Phys. (Paris) 34 (1973) C9-101. [45] M.N. Kabler. in: Radiation Damage Processes in Materials. ed. C.H.S. Dupy (Noordhoff. Leiden. 1975) p. 171. [46] Y. Toyozawa, J. Phys. Sot. Jpn. 44 (197X) 482. [47] K.S. Song. C.H. Leung and R.T. Williams, J. Phys. Condens. Matter 1 (1989) 683. [48] N. Itoh and K. Tanimura. J. Phys. Chem. Solids. in press. [49] K. Kimura and M. Iwamura. Phys. Lett. A67 (1978) 159. [50] N. Matsunami. T. Ohwaki, N. Itoh and H. Horino, Nucl. Instr. and Meth. 194 (1982) 39. [51] K. Tammura, T. Eshita and N. Itoh, J. Phys. Sot. Jpn. 53 (1984) 2145. [52] K. Tanimura and N. Itoh, to be published. [53] K. Tanimura, T. Katoh and N. Itoh. Phys. Rev. B40 (1989) 1282. [54] D.A. Patterson and R.G. Fuller. Phys. Rev. Lett. 18 (1967) 1123. [55] P.J. Call, W. Hayes, J.P. Stott and A.E. Hughes, J. Phya. C7 (1974) 2417. [56] K. Tanimura and N. Itoh. Nucl. Instr. and Meth. 832 (1988) 211. [57] K. Hata, M. Watanabe and S. Watanabe, to appear in Appl. Phys. B. [58] N. Itoh. Radiat. Eff. and Def. in Solids, in press.
III. ALKALI
HALIDES
and Methods
in Physics
Research
207
846 (1990) 207-21.5
Section III. Alkuli halides THE ROLE OF SELF-TRAPPED IN INSULATORS
EXCITONS
IN RADIATION-DAMAGE
PROCESSES
We review current studies on defect formation induced by valence-electron excitation in insulators. Emphasis IS placed on the role of self-trapped excitons In damage processes. First we classify the processes into a few cases. based on categorization of materials in terms of energy localization and on the density of excitation. Then defect formation in alkali halides. which is a typical example of single-excitation process, is discussed to clarify the origin of the dependence of the efficiency on materials. Finally. the effects of the density of excitation on defect formation are discussed. presenting some pieces of evidence that excitation of the self-trapped exciton and the interaction of free excitons and self-trapped excitons produce Frenkel pairs in materials which are highly resistive to single-excitation
processes.
1. Introduction The interaction between nonmetallic solids and radiation results in three types of electronic excitation: (i) core-electron excitation. (ii) ordinary valence-electron excitation and (iii) dense valence-electron excitation. The core-electron excitation generates holes in core orbitals and electrons in the conduction band. while the latter two types of excitation generate holes in the valence band and electrons in the conduction band. We differentiate the types (ii) and (iii), since the interaction between single-excitation events causes specific effects when the density of excitation is sufficiently high. Electronic excitation of each of the three types described above induce specific atomic processes. such as defect formation [1.2]. defect migration [3], crystal-toamorphous transformation [4,5] and ejection of constituent atoms at surfaces [6]. Contrary to the atomic processes induced by elastic collisions. the processes induced by electronic excitation are featured by a strong dependence of their efficiency both on the materials being investigated and on the type of excitation. For example, under ordinary valence-electron excitation. no atomic process is induced in most of the semiconductors, whereas defects are created with a high efficiency in some insulators like the alkali halides. Furthermore. there are several materials which are highly resistive under ordinary valence-electron excitation, but are subjected to radiation effects under dense electronic excitation [5.7-91 and/or core excitation [lo]. Even in the regime of valence-electron excitation. which is dealt with in this paper. the efficiency varies strongly. depending both on materials and on the density of excitation. Extensive studies on the defect formation due to electron-hole recombination in alkali halides have re0168-583X/90/$03.50
(North-Holland)
7’ Elsevier
Science Pubhshers
B.V.
vealed that there are three crucial steps in the process of forming defects from electronic excited states [1,2]: the first is the localization of the electronic-excitation energy. the second is instability of the system, by which localized electronic energy is transformed to the kinetic energy of the atomic system for inducing atomic displacement. and the third is the probability of populating the state(s) having instability. Hereafter we shall call such states the reactive states. Self-trapping of excitons or holes is the most important mechanism which causes the energy localization. The instability appears to be induced in the relaxation process from an exciton (or an electron-hole pair) to the self-trapped exciton (STE) and the probability of populating the state having the instability is governed by the branching ratio in the relaxation process. The fact that the efficiencies of the lattice-defect formation are distributed indicates that these important factors depend strongly on materials and on the density of excitation. Electrons, holes and excitons in nonmetallic solids have two ways of stabilization: delocalization through intersite transfer and localization through coupling with the lattice [ll]. The bandwidth 2B is a measure of the strength of the stabilization through intersite transfer. and the lattice relaxation energy E,, is a measure of the strength of the stabilization through coupling with the lattice. Whether an electron, for example. in a solid is delocalized or localized is determined by the relative magnitude of E, n against B [ll]. In view of the primary importance of the energy localization in the defect-formation process. we categorize nonmetallic solids into two types, as shown in table 1 [12]. in terms of localization of charge carriers and excitons. Since the occurrence of self-trapped electrons seems to be rarer than that of self-trapped holes or excitons, we mainly consider holes and excitons. The III. ALKALI
HALIDES
Table
1
Categorization
of nonmrtallic
solids
with
respect
to
self-trap-
ping of rxcrtons and holes Self-trapping
Type 1 2
2a Zb
Examples
Exciton
Hole
no yes yes
no no yes
MgO. ZnO. GaP. Si SiO,. MgF, alkali
halldes
C-aF,. KM&F,
Type 1 are solids with weak electron-lattice coupling: excitons and holes remain to be free state. The Type 2 are solids with strong electron-lattice coupling; excitons are self-trapped. Depending on whether holes are delocalized or localized. solids of Type 2 are further classified into subgroups 2a and 2b. although the distinction of Type 2 into subgroups is less important in view, of energy localization. Typical examples of these solids are also given in table 1. It is presumed that the efficiency of defect formation induced by electronic excitation in Type 1 materials is substantially lower than in nonmetals of Type 2. In fact. there has been no experimental result indicating formation of lattice defects by an intrinsic mechanism under electronic excitation in Type 1 materials. Even in materials where excitons are self-trapped. the efficiency still varies significantly: the yields range from near unity to several orders of magnitude lower [13]. The purpose of this paper is to discuss the origin of the dependence of the yields of defect formation on materials and on the density of excitation in solids with strong electron-lattice coupling. The origin of the instability and the factors governing the probability of populating the reactivje state are discussed. emphasizing their relevance to materials and the density of excitation. We first describe the properties of the STEs which play a crucial role in the defect-formation process under valence-electron excitation. Since extensive reviews have already been published [14], we describe only the properties related to the instability and the probability of populating the reactive state. Then we focus our attention on defect formation under ordinary excitation, particularly the dependence of the yield of the F centers on materials. Finally. we discuss the high-density effects for defect formation. and point out that the origin of the instability and the probability of populating the state having instability are altered significantly through interaction of single-excitation events.
2. Self-trapped
excitons
The STE is essentially a localized electron-hole pair associated with large lattice relaxation. Although details of the relaxed configuration depend on the nature of the
atomic orbital responsible for the valence band and on the crystal structures [15], there exist a few important common features. One of these features is that the relaxed configuration is often associated with motecular-bond formation. In halides. except AgCI [16,17]. the hole of an STE is stabilized in the form of XT. where X denotes a halogen [1X-20]. Also. it has been shown that an STE in oxides comprises an oxygen molecule [21.23]. Another important feature is the fact that the STE in the lowest triplet state has an off-center configuration in which the molecular ion is displaced as a whole [14]. The most typical example is the STE in alkaline-earth fluorides. In this crystal. the self-trapped hole (STH) is the F,-. molecular ion oriented along a (100) direction [23]. but the STE comprises an F; molecular ion displaced to be oriented along a (1 II) axis. and forming a nearby vacancy where an electron is localized [19,24]. Recently. it has been shown theoretically that the lowest triplet STE in alkali halides has an off-center configuration. where the XT molecular ion is displaced along a (110) direction [14.25527]. Although definite experimental evidence has not yet been obtained. abundant experimental results obtained for the STEs in alkali halides are better explained in terms of the off-center relaxation of the STE [14]. The features of the STE configuration described above indicate clearly that the STE at the lowest excited state has inherently the instability which results in the displacement of the molecular ion. However. there is a barrier against further separation of the molecular ion to form a distant vacancy-interstitial pair. As a result, the lowest triplet STE remains as a metastable state which decays radiativety at tow temperatures. The lowjest triplet STE is generated through deexcitation of an electron--hole pair or an exciton. The deexcitation process consists of a series of nonradiative transitions between several excited states. Besides the deexcitation to the lowest triplet STE. there are other channels of deexcitation; de-excitation to the ground state. involving either radiative (singlet-luminescence) or nonradiative transition. and defect formation [2X]. The probability of deexcitation to these several channels is governed by branching ratios from each of the excited states to tow-lying states. Experimental values of the yield of the lowest STE are usually smatter than unity, and the magnitude depends strongly on the materials [29]. as shown later. The results indicate that the pathways of deexcitation are strongly dependent on materials. In general, the yield of the lattice defects is dependent not only on the degree of the instability of the reactive state(s). but also on the probability of populating the state(s) during deexcitation. Therefore. characterization of the excited states of the STE and ctarification of the deexcitation pathways are essential for understanding the origin of the dependence of the defect yield on materials and on the density of excitation.
(e-h)* 77
K!
(f.e + f h) I --\ ““”
EG
-3
a = %TE
-4
-.Cl=&)
Fig. 1. Energy levels of the STE in KI. together with the transient absorption spectrum (ref. [18]) and luminescence spectrum due to the lowest trlplet STE. Symbols e*. h* and (e + h) * stand for the electron-excited. hole-excited and bulkexcited states of the STE, respectively.
Since the STE is a two-particle system in solids. three types of excited states are evident: electron-excited states, hole-excited states and host-excited states associated with an STE. An exciton perturbed by an STE belongs to the last class of the excited states and its existence in alkali iodides has been demonstrated by Williams and Kabler [30]. In alkali halide and alkaline-earth fluoride crystals, the structure of the STE is such that an election is trapped by a potential formed by an STH and surrounding cations. while a hole forms a halogen-halogen molecular bond. Thus the electron-excited states have features similar to the hydrogenic series in which some orbital degeneracies are removed by low local symmetry associated with lattice relaxation due to self-trapping. On the other hand. the hole-excited states have features similar to the excited states of the halogen molecular ions. Three types of excited states can be clearly demonstrated in an optical-absorption spectrum of the STE in the lowest triplet state [31]. In fig. 1 we portray the absorption spectrum of the STEs and the associated energy-level diagram in Kl. It has been shown that the optical-absorption spectrum due to the 1, molecular ion (STH) has three prominent peaks at 3.1, 2.8 and 1.9 eV [32,33]. A similar three-peak structure is clearly observed for the absorption spectrum due to the STE. and these peaks correspond to transitions to the holeexcited states. On the other hand. the strongest peak at
the lowest energy at 1.1 eV is characteristic of the STE. and has been assigned to the electron transition from the lowest to a higher electron orbital. The sharp peak at 5.75 eV has been ascribed to the optical transition to create excitons perturbed by the STEs. In order to specify each of the excited states more clearly. we adopt mainly the irreducible representation of the DZh symmetry for convenience. The lowest state of the STE possesses the electron at the ls(a,) orbital and the hole at as B3,,. (f.e + f.h) the b,, orbital and is designated denotes the state for a pair comprising a free electron and a free hole. And e * and h* denote the electron- and hole-excited states, respectively. Only the electron orbitals are denoted by e*. The lowest triplet state ‘B,,(a,: h,,,) is known to emit the 71 luminescence. The singlet luminescence. u luminescence. has been considered to be emitted not from the lowest, but from a higher singlet state ‘B,,(a,*; b,,). here a,* denotes a 2s-like orbital. It is also useful to classify the excited states according to the energy of the states. Referring to the energy of an excited state of the STE as E. and the band-gap energy as E,;, those with E < E,; are populated under ordinary valence-electron excitation. but those with E > E, cannot be reached from a single excitation. The latter type can be generated when at least two excitation events interact and/or the lowest STE is excited optically with sufficient energies. The bulk-excited state associated with the STE and some of the hole-excited states fall in this category. The classification of the excited states with respect to the energy is useful to discuss the contribution of a specific excited state to defect formation under irradiation of several types. Incident energetic ions cause the creation of two neighboring excitations in the process of deceleration. Therefore. excited states with E > E,; will be generated with a high probability. On the other hand. under ionizing irradiation, the formation of excited states with E -c if,; dominates. although the yield of two consecutive excitations due to low-energy secondary electrons is not negligible [34.35]. Irradiation of insulators with intense laser pulses of photon energies below E, shows specific features, namely generation of highly excited STEs, since the lowest triplet STEs generated by multi-photon band-toband excitation have chance to absorb photons. Therefore, the excited states with E > E,;. not easily accessible by ordinary valence-electron excitation, can be generated by intense laser irradiation.
3. Defect formation
by a single exciton
As a typical example of the lattice-defect formation induced by ordinary valence-electron excitation, we discuss here the defect formation in alkali halides. ExtenIII. ALKALI
HALIDES
sive experimental and theoretical studies have been carried out on the atomic processes which are involved in the evolution of a Frenkel pair from an exciton. It is known that the process is essentially an isomeric transformation from an STE to a Frenkel pair comprising a vacancy with an electron (the F-center) and an interstitial atom in the form of XT occupying an anion site (the H-center) [l.Z]. As already described in section 2. the STE at the lowest triplet state has an instability to displace the X; molecular ion from the on-site configuration as well as a barrier for further separation of the Xi from the vacancy. Therefore. the yield of the defect formation can be understood as a result of competition between the degree of the instabllity and the magnitude of the barrier. First we mainlq concern ourselves with the defect formation at low temperatures where thermally activated transformation from an STE to an F-H pair on the potential surface of the lowest triplet state [36] is not active. The dependence of the yield of the stable F-centers generated by continuous ionizing irradiation on materials has been characterized well in terms of the Rabin-Klick parameter S/D. where S is defined as the separation of the two adjacent halide ions along a (1 IO) direction minus twice the halide-ion radius. and D is the diameter of a halogen atom [37]. The yield of the stable F-centers plotted as a function of S/D is shown in fig. 2. Although the data points are scattered considerably, the overall dependence is such that the yield ix constant for materials with S/D larger than 0.5. whereas the yield decreases sharply with S/D decreasing from 0.5. In the same figure we have plotted the yields of the IT luminescence and the D luminescence [29]. These represent the yields of the lowest triplet STE and the excited singlet STE, respectively. It is clear that the yield of the lowest triplet STE shows anticorrelation with the yield of the F centers. On the other hand, the yield of the singlet STE is constant irrespectively of the magnitude of S/D. The anticorrelation between the yields of the lowest triplet STE and the F-centers suggests strongly that the competition associated with defect formation occurs in the triplet manifold. and that the material-dependent yield of stable F-centers is a direct consequence of the competition which takes place during relaxation leading to the lowest triplet state. Time-resolved measurements which utilize a pulsedelectron beam [40] or a pulsed-laser light [41] have revealed formation of the transient F-H pairs, as well as stable ones at low temperatures. For example. in KCI. more than 90% of the instantaneously produced F-centers by a pulsed-electron irradiation at 5 K are annihilated by pair recombination within 0.1 ms after irradiation [40]. The formation of transient F centers in the nanosecond regime has also been observed in RbCl [42]. KBr and RbBr [31.40]. This group of materials is
\
1030+--p--ylo~ S/D
Fig. 2.
The Rabin-Klick
required (double mental triangles
diagram
to form an F-center
at 4 K showing the energir.\
and a photon of IJ luminescence
circles), and are of 7: luminescence results for F-center
formation
and open circles were taken
[37]. Hughes et al. [3X], and IkezaNa Luminescence
(crosseh). Experi-
shown hy solid circleb. from
Rabin
and Klick
et al. [39]. respectively.
data were from Pooleq and Runchlmann
[29].
situated at the middle part of the S/D axis. On the other hand. in LiF and NaF, both of which are situated at a similar region in the Rabin-Klick diagram and show a similar magnitude of efficiencies in the formation of stable F-centers, no such transient F-centers are produced: the F-centers produced within the width of a pulsed electron beam of 20 ns remain stable over several seconds or more at 5 K [43]. Therefore, it appears that the Rabin-Klick diagram is not sufficient to characterize the efficiency of the defect formation of transient defects annihilated in the nanosecond regime. We consider that some other properties which are related to S/D may govern the competition between the instability and the barrier in the defect formation process. It is of interest to measure the formation of the transient F-H pairs for NaF and LiF in the picosecond regime. It has been controversial that defect formation is governed by the competition on the potential surface either of a higher excited state of the STE [44.45] or of the lowest excited state of STE [27.46.47]. At present definite experimental results capable of determining Mhich is the case have not yet been obtained. From the theoretical point of view. on the other hand, Song et al. have described the Rahin-Klick diagram for the stable F-center yields in terms of off-center STE relaxation on the potential surface of the lowest state of STE [47]: as the degree of off-center increases. the F-center yield
increases because of larger kinetic energy imparted for the off-center relaxation. Detailed description and critical discussions on both types of models have been given in a recent review [48]. So far we have argued the dependence of the F-center yield on materials in terms of instability. This factor certainly explains the overall dependence of the yield, but the large scatter of the experimental data is evident in fig. 2. Although this scatter might be partly due to experimental error. we consider that the probability of populating the reactive state affects the yield. Since in alkali halides the hole self-trapping occurs prior to self-trapping of excitons, the excited states passed through during deexcitation are mainly the electron-excited states described in section 2. Therefore the deexcitation pathways at these states are essential for determining the probability of populating reactive state(s). and hence the yield of the F-centers. The present authors have studied the nonradiative deexcitation from electron-excited states of the STE by means of the cascade-excitation technique in which a specimen populated with the lowest triplet STE is excited further by a light pulse from a tunable-dye laser to generate a given type of excited state selectively [28]. The yields, qF of the transient F-centers from each of the electron-excited states of the STE. to which optical transition from the lowest state is allowed, have been determined. Fig. 3 shows the results for KC1 and KBr. respectively. In the figure. thin solid curves represent the absorption spectra to excited states at which the electron occupies one of the Zp-like orbitals. and the broken curve, to higher states. The results shown in fig. 3 indicate two important features: (1) the yield qF depends on the nature of the excited state of the STE, (2) the yield for excited states with similar electronic nature in different materials shows a strong dependence on the materials. The first feature is evident from the results of different magnitudes qf for different excited states in both KC1 and KBr, and the second feature is clear from the fact that the np-excited state does not show any F-center formation in KBr. whereas in KCI it shows the highest yield. These features are interpreted in terms of the difference in the probability of populating the reactive state. and hence the selective nonradiative transitions at the excited states of the STE [28]. Thus the deexcitation pathway during relaxation of the STE in a highly excited state is also essential for understanding the dependence of the yield of the defect formation on materials. The mechanism of selective nonradiative transitions at the excited states of STEs remains unclear. 4. Multiple-excitation
processes
In the previous section, we discussed the lattice-defect production under ordinary valence-electron excita-
OL-
0.2-
0
I 15
20 PHOTON
ENERGY
25 ( eV )
Fig. 3. Yields of F-centers from photo-generated elrctron-rxcited states of the STE in KCI and KBr. Data shown by double circles. squares and open circles are for B,,. .A, and B,, substates of the Zp-excited state, respectively. The solid circles are for the up-excited states (II > 2). The solid curve shows the absorption spectrum due to the lowest triplet STE. Thin solid and broken curves show the ahborption due to transitions to 2p- and np-excited states.
tion. When the density of excitation becomes higher, the interaction between (or among) the single-excitation events cannot be neglected. In this situation. effects of the interaction on the relaxation of electronic excitations will be significant. In fact. there are several experimental results which indicate such high-density effects: these include the decrease of the luminescence yield [49.50] and the superlinear increase of the yield of defect production with an increase of the density of excitation [4.7-91. These results have been obtained mainly by high-energy ion irradiation. The primary processes which result in these high-density effects have remained unclear. Recently the present authors have studied the luminescence and defect formation by laser irradiation in RbI which shows a small efficiency (10~5-10-h per electron-hole pair) of the F-center under ordinary valence-electron excitation. They observed a decrease in the n luminescence yield with increasing laser intensity and the superlinear increase of the yield of the stable defects in proportion to the square of the density of excitation [8]. Further details of the experimental results are explained with reference to fig. 4. A specimen was irradiated with 308 nm laser light from a XeCI-excimer laser. The two-photon absorption process generates electron-hole pairs in this case. For weak excitation, the intensity of the 77 luminescence, 111. ALKALI
HALIDES
LASER
FLUX
(arb units )
Fig. 4. The magnitude of the stable component of the opticalabsorption change measured at 726 nm (sohd circles), and the intensity of the 71 luminescence (open circles), Induced by a 308 nm laser pulse as a function of excitation intensity.
which monitors the concentration of the lowest triplet STE. increases linearly with increasing density pe, of excitation. However, it saturates at higher pcx. On the other hand, the optical density at 726 nm measured after 0.2 ms of laser-pulse irradiation is essentially independent of p,, for weak excitation, but it increases abruptly above the value of pi, at which saturation of the n-luminescence intensity becomes significant. On subtraction of the intensity-independent component, the magnitude of optical-absorption change was found to increase in proportion to the square of prx. as shown by the broken lines in the figure. We showed the opticalabsorption spectrum of this superlinear component to be the F-band. Although the laser irradiation excites the holes of the lowest triplet STE, formed by two-photon absorption, it has been confirmed experimentally that hole excitation does not contribute to the formation of the stable F-centers in Rbl. Therefore, it is clear that the stable F-centers are generated by the interaction of two single-excitation events in this case. The results obtained by Tanimura and Itoh [8] strongly suggest that the interaction between two single-excitation events (excitons or electronhole pairs) either creates a new state having instability that is not formed under single excitation and/or enhances the probability of populating the reactive state, which is responsible for generating F-centers under single exci-
tation. Below we give general discussions on the mechanism of defect formation under dense electronic excitation. In a substance of Type 1, the important process under dense electronic excitation is the interaction among free excitons and/or free carriers. The interaction leads to formation of biexcitons and if the density is extremely high, an electron-hole plasma. On the other hand. in substances of Type 2. where holes and/or excitons are self-trapped. such free multiparticle complexes are not formed. mainly due to the short lifetimes of free carriers and excitons against self-trapping. The dense electronic excitation for this type of materials will form a mixture of free excitons and STEs. At this stage, collisions of free excitons with STEs dominate [51] and the collision will form a complex. a free exciton (FE) interacting with an STE, since the interaction has been shown to be attractive [30]. We call this complex the FE-STE pair. Evidently the mobility of free excitons is a crucial factor for determining the yield of FE-STE pairs and. if it is extremely low, we expect only the interaction between STEs for extremely dense excitation. From the arguments above. it is clear that the deexcitation of the FE-STE pairs governs the high-density effects in defect formation in solids of Type 2. Since an FE-STE pair is already localized, the crucial point is whether there are states having instability specific to the FE-STE pair. Recently Tanimura and Itoh have obtained the most direct information on the relaxation processes of the FE-STE pair in RbI [52]. In RbI, the optical-absorption band due to the creation of excitons perturbed by the STEs is situated at 5.61 eV [30]. to which a KrCl-excimer laser resonates almost exactly. Therefore. by using the cascade-excitation technique, in which a specimen populated with STEs is excited further by a light pulse of 222 nm. the FE-STE pairs are generated directly, and measurements of the resulting changes in optical absorption and luminescence have given the direct consequences of the generation of FE-STE pairs. The results by the present authors for optical-absorption changes induced by sequential irradiation with an electron pulse and a light pulse are shown in fig. 5. In the figure, curve (a) shows the optical-absorption spectrum measured 5 KS after an electron pulse. The peaks were ascribed to the lowest triplet STE from a comparison of the spectrum with that obtained by Williams and Kabler [31] and of the decay time of the band with the lifetime of STEs. Curve (b) is the spectrum measured after I7 shots of the electron pulse, while curve (c) is the spectrum measured after 17 cycles of the sequential irradiation with an electron pulse and a light pulse. In the latter experiments, each cycle consists of an electron pulse followed by a light pulse with a 5 ps delay. About 30% of the lowest triplet STEs were de-
PHOTON
ENERGY
( eV )
Fig. 5. Optical-absorption spectra measured (a) at 5 ps after irradiation of an electron pulse. (b) after 16 electron pulse shots and (c) after 16 cycles of sequential irradiation of an electron pulse and a light pulse of 222 nm. The arrow show the peak energies of the F and H bands. The inset shows the relation between the peak height of optical absorption at 726 nm and the number of cycles of sequential irradiation.
stroyed by the light pulse in each cycle. It is clear that no absorption band is produced by the irradiation with electron pulses only. but the sequential irradiation produces the F absorption band. the peak of which is shown by an arrow. The inset of fig. 5 shows the relation between the height of the F band induced and the number of cycles of the sequential irradiation. The proportional relation is evident. The results shown in fig. 5 give unambiguous evidence that stable F centers are formed during relaxation of the FE-STE pairs. By using Smakula’s equation, they obtained 0.041 for the conversion yield from a FE-STE to a stable F-center. They have also found another important relaxation channel of the FE-STE pairs: that is conversion to the excited singlet STE responsible for the o luminescence from the FE-STE pair. The yield of this conversion, which can be regarded as exciton fusion, was 0.38. Their results have revealed two important aspects of the high-density effects on the lattice defect formation. One is that a FE-STE pair possesses a new type of instability for generating lattice defects. As described in section 3. the yield of the stable F-centers due to the single-exciton mechanism in RbI is as low as 10m5-10. ’ per electron-hole pair, while the conversion yield from FE-STE pairs is as high as 0.04. This magnitude is almost the same as or larger than the yield of F-H pairs by a single-exciton mechanism in NaF. which shows the highest yield of defect formation under ordinary valence-electron excitation. The second important aspect is concerned with the generation of highly excited states of the STE from an FE-STE pair through exciton fusion. Since an FE-STE pair possesses an energy which is almost twice the band-gap energy E,;. highly excited states of the STE. which are not populated
under ordinary excitation. can be populated. If one of these highly excited states of the STE is a reactive state. then the exciton fusion can be a cause of lattice-defect formation. In this aspect. we point out here some features of the radiation effects which occur under intense laser irradiation. When solids with strong electron-lattice coupling are exposed to intense laser light having a photon energy h v smaller than E,. the primary process is multiphoton absorption generating electron-hole pairs followed by formation of STEs. Because of long lifetimes of the lowest triplet STE and high photon fluxes. excited states with energies as high as hv + E,,, (where is the energy of the lowest STE) are highly popuEsrn lated. If hv+ Esrb exceeds E,;. the excited states that cannot be populated under ordinary valence-electron excitation are produced. Therefore. the effects under intense laser irradiation may be essentially similar to those under high-density excitation. in the sense that the highly excited states (with E > E,,) having an instability can be populated under both of these types of excitation. The example of the lattice-defect formation in such a situation has been demonstrated by the present authors [53]. They have studied relaxation in the lattice of CaF, caused by excitation of STEs by means of cascade-excitation spectroscopy. CaF, is known as one of the materials that shows low F-center yields under ordinary valence-electron excitation [54,55]. Fig. 6 shows the optical-absorption changes in CaF, induced by sequential irradiation with an electron pulse at t, and a light pulse at 1,. measured at 365 nm which is close to the F-band maximum. The result shown in fig. 6a is the consequence of electron excitation of the STE by a 2.61 eV laser pulse, whereas that in fig. 6b is the consequence of hole excitation of the STE by a 4.03 eV laser pulse. Hole excitation generates a hole-excited state, in which the hole occupies the bonding orbital (a,). and hence the F1- molecular ion is an antibonding state. It is clear from the figure that the combination of pulsed-electron and pulsed-laser irradiation to generate the electron-excited states of the STE produces only the transient component. On the other hand. upon generation of the hole-excited state of the STE. significant amounts of the stable and transient components are generated. Spectroscopic measurements have confirmed that the stable component consists of F-centers. Therefore, it is evident that the hole-excited state of the STE in CaFz produces stable F-centers. Consideration of the energetics has shown that the hole-excited state is located above the ionization continuum at the self-trapped exciton configuration, so that the state has almost no chance of being populated under ordinary valence-electron excitation. Thus. the results attained for CaF, have provided a typical example of the lattice-defect formation induced by the modification of the population of III. ALKALI HALIDES
214
(a)
02 1
i
i
te
tl TIME
Fig. 6. Oscilloscope traces of the optical-absorption changes at 365 nm in CaF, induced by sequential irradiation with an electron pulse at f, and a light pulse at f,; (a) for the light pulse of 2.61 eV dye-laser pulse, and (b) for the light pulse of 4.03 eV excimer-laser pulse.
curs during deexcitation at the excited states of the STE. based on the experimental results for the state-dependent yield of the F-center formation in KC1 and KBr. The general understanding of the rule which governs the branching is highly desired. Then we have discussed the instability at the highly excited states that are not produced by the single-exciton process and the probability of populating these highly excited states. Based on recent experimental results by the present authors, the importance of FE-STE pairs for the high-density effects of lattice-defect formation has been stressed. The two important factors that govern the high-density effects are the instability possessed by FE-STE pairs and the probability of populating the states having an instability. The similarity of the defect formation process under intense UV laser irradiation and the effect of the dense electronic excitation has also been pointed out. Throughout this paper, we have emphasized that the STEs play crucial roles. directly or indirectly, in the process of lattice-defect formation in nonmetallic solids with strong electron-lattice coupling. The role of selftrapped excitons in the formation of latent tracks of heavy energetic ions in non-metallic solids has been treated separately [5X].
References
the reactive states. Similar results have also been obtained in MgFz [56]. The mechanism described here is presumed to have close correlation to the recent experimental results showing efficient formation of the F-centers in CaF, and MgF,, when irradiated with subpicosecond intense UV laser pulses [57].
5. Summary
In this paper we have described the primary processes of defect formation induced by electronic excitation in solids with strong electron-lattice coupling. The emphasis has been placed on understanding the origin that induces significant differences in the efficiencies of lattice-defect formation over the types of materials and the mode of excitation. Our viewpoint is that the difference is governed by the existence of the state having an instability, and the probability of populating the state having the instability under a given mode of excitation. As a typical example of the defect-formation process which occurs under ordinary valence-electron excitation, where the single-exciton mechanism is exclusive, we have discussed the material dependence of the Fcenter yields at low temperatures in alkali halides. We also discussed the importance of branching which oc-
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III. ALKALI
HALIDES