- Email: [email protected]
Excited state phenomena
634
Excited state phenomena Augustin
KS Song
Recent
in theoretical
induced
progress
by electronic
contributed
excitation
to our understanding
of the exciton
self-trapping,
radiation
defect
between
defects
creation,
simulations
of processes
in insulating
solids
has
of some of the basic
recombination
steps
luminescence,
photo-desorption
and interaction
in various large bandgap
materials.
It is
hoped that these examples will stimulate further progress in other systems, many of which have potential practical applications.
Addresses Department of Physics, University of Ottawa, Ottawa, Ontario, Kl N 6N5, Canada; e-mail:[email protected] Current Opinion in Solid State & Materials l:834-040
Science
1996,
0 Current Chemistry Ltd ISSN 1359-0286 Abbreviations APES adiabatic potential energy surface CNDO complete neglect of differential overlap F-H pair Frenkel defect pair HF Hartree-Fock INDO intermediate neglect of differential overlap LDA local density approximation MD molecular dynamics STE self-trapped exciton
Introduction An electronic excitation has a lifetime which may vary typically between a nanosecond and a millisecond. During this relatively short lifetime, the balance of forces between the atoms in a solid can be broken locally, and as a consequence a number of processes, which are not observed in the ground state, can occur. Recent progress in ultrafast spectroscopic techniques has made it possible to explore many processes which involve the excited states. In this review, I will not cover processes which take place in semiconductors. There are interesting systems, such as the DX centers etc., which offer some similarities to those that will be discussed. The principal feature shared by these centers is the characteristic large lattice distortion. Although allusions will be made, it is felt that semiconductors should be treated separately. I will concentrate on processes induced by electronic excitation in large bandgap materials. In many of the large gap materials, the excitation energy is localized in space either around pre-existing defects and impurities, or, more interestingly, can be localized spontaneously (self-trapped) as a result of strong electron-lattice interaction. An energy package of perhaps several electron-volts can become concentrated within a space of the order of an atomic volume. As this is accompanied by a local breakdown of the balance of forces, a large-scale atomic
rearrangement can follow. The details depend on the nature of the chemical bonding and coordination in the lattice. Examples are found in radiation-induced lattice defect formation and atomic desorption in ionic halide crystals, in quartz and even in rare gas solids. The latent image formation in silver halide crystals, familiar to us for over a century, is also an example of this. In many radiation-related devices, for example X-ray storage phosphors and scintillation detectors, the ionizing radiation creates electron-hole pairs which are trapped at some centers at or below room temperature until they can be released to produce signals at the time of reading. In recent years, in parallel with the progress in the new sophisticated computaexperimental techniques, tional methods have been developed and applied to the atomistic studies of processes taking place in excited insulators. While the studies of the ground state have been extensively based on the density functional approaches [l], in particular on the local density approximation (LDA) [2,3*], the excited state studies rely on other approaches. Often the spin state of the excited system is an important factor, and the Hartree-Fock approach is employed, possibly with a correction for the correlation effect. Many recent HF simulations on excited systems have concentrated on determining the equilibrium structures. Only a relatively small number of studies have been made so far in the molecular dynamics (MD) simulation of excited systems [4,5], as will be discussed below. This contrasts with the MD studies of the ground state based on the method developed by Car and Parrinello [6] which is based on LDA. In ionic materials, the lattice and electronic polarizations can be important. At the same time, interfacing the central quantum cluster and the surrounding crystal is a complex problem. Various embedding approaches have been proposed in recent works [7,8*,9,10*]. A good review of some of these approaches is given in [l 11. In the following text I present several examples of recent computational simulations of systems in which the excited electron plays a central role. Of necessity, they are based on different methods of varying levels of sophistication. It is significant to find that, where different methods have been applied to the same system, results which are in agreement with each other have been obtained. It is hoped that the review will show the progress which has been made recently in understanding some of the significant processes taking place during electronic excitations and will indicate the similarities, as well as the differences, between various systems. A number of systems which demonstrate unusual properties under excitations as well as important practical applications have yet to be analyzed.
Excited state phenomena Song
Large-scale atomic processes induced by electronic excitations in insulators Localized systems containing either a hole or an excited electron have been studied earlier with various approximate methods [12]. The semi-empirical CNDO method was used for the simulation of halogen desorption with the core or valence excitations [13]. Simpler electron defects have been .studied with the extended-ion method which is an approximation to the one-electron Hartree-Fock approach [14]. The presence of both the hole and excited electron (e.g. the self-trapped exciton: STE), however, in a polarizing medium turned out to be more complex. In many insulating crystals, ionizing radiation produces characteristic fluorescence emission bands with large Stokes shifts, as large as about 75% of the band gap energy. Ionizing radiation creates lattice defects. Some of the extensively studied materials include the ionic halides (bulk, surface and nanocrystallites), quartz, rare gas solids and diamond. The atomistic structure of the STE and its relation to the radiation-induced lattice defects, the Frenkel defect pair (also known as the F-H pair), has become understood only recently [15,16’]. Self-trapped
excitons
835
energy surface [19**,21”]. The effect of configuration interaction is expected to be significant where many excited states are densely distributed, such as in the on-center geometry ]2+]. Different approaches have led to results which are consistent with each other and that have given a good account of the experimental data, showing that the fundamental processes are now well understood. We have reproduced in Figure 1 the adiabatic potential energy surface (APES) calculated by the all-electron HF method for the spin triplet STE in NaE covering the range between the on-center STE and the third nearest neighbor F-H pair (a separation of 8A). Figure 2 presents the spin density of the electron and hole plotted on a plane as the STE undergoes axial relaxation. It clearly shows the excited electron localization around the anion vacancy as the off-center relaxation proceeds.
Fiaure
1
r
I
6.2 r
in ionic halides
It is not surprising that the first simulation of the STE in alkali halides was based on a combination of relatively simple approximations: the excited electron by the extended-ion approximation; the hole by the CNDO code; and the lattice by conventional pair potentials [ 171. The total energy of the system was minimized by optimizing simultaneously the electron wavefunction and the atomic positions of a limited number of atoms in the crystal. The main points of this study are as follows. Firstly, the STE in alkali halides is equivalent to a primitive F-H pair (the excited electron localized on an anion vacancy as an F center, with the hole localized on the molecule ion Xz - occupying an anion site). Secondly, the driving force promoting the process is in the strong excited electron localization at an anion vacancy. Thirdly, the available relaxation energy is between 1eV and ZeV, part of which can be used to induce dynamic creation of lattice defects at low temperatures. Such a strong spontaneous symmetry breaking relaxation with sufficient energy to promote atomic rearrangement was initially surprising. As will be seen in other examples, it is the excited electron which is the prime driver of the atomic rearrangement. In recent years a number of Hartree-Fock many-electron simulations have been made. Both all-electron HF [18,19**] and valence-electron-only HF [20,21**] calculations, with and without the correlation effect included, have been performed on relatively small quantum clusters embedded approximately in the remainder of the ionic lattice. These works confirmed the main points enumerated above. The inclusion of the correlation effect does not alter the overall features, but can have some subtle effect on the adiabatic potential
3.21;.
’ 1
’ 2
’ 3
’ 4
’ 5
’ 6
’ 7
’ 8
’ 9
Adiabatic potential energy surface (APES) of the system STE-Frenkel pair in NaF drawn along the coordinate Qs (the distance between the excited electron and the hole along the [l101 axis). The UHF (unrestricted Hartree-Fock) and MP2 (Moller-Ptesset second order perturbation theory) results are represented by the dashed and continuous lines, respectively. Published with permission from [lQ”I, Fig. 2.
Studies of the STE decay near a surface have also been made for several halide crystals [22,23]. The presence of a surface introduces some unexpected elements. For instance, the relaxation along the close-packed [llO] row is modified near the surface and results in a dynamic desorption perpendicular to the (100) surface. Also, the surface itself directly influences how the exciton localizes. Very close to the surface, it was observed that the excited electron localizes in such a way that the resulting axial relaxation propels the molecule ion Xz- away from the surface towards the bulk, and dynamical desorption is not obtained in the first two layers below the surface. According to a recent simulation, desorption only seems to occur for layers starting with the third below the surface (KS Song, Y Cai, unpublished data).
836
Modelling
Figure
and simulation
of solids
of an F center
2
simulations (a)
[27], there
on the bulk
is a close
similarity
with
the
surface.
In ionic halides of other lattice structures, such as in CaFz and in SrFBr, the absence of a close-packed halogen row has a profound influence on the radiation defect production. Despite the large relaxation energy released in the off-center motion of the STE, no long-range atomic motion leading to well separated F-H centers
500
follows [Z&29]. In these materials, the defects created are mostly of transient species which recombine with short lifetimes. A concurrent excitation into the hole band can lead to the creation of stable, well-separated, defect pairs owing to excitation-induced hole hopping diffusion. Both experimental data and theoretical calculations have contributed to our understanding of these phenomena.
a
k)
5.0 2.5
a3 g
0.0
a -2.3
-s.o -8
-6
-4
-2
0
2
4
6
8
410>(i) ,Spin density of the excited electron and hole obtained for the system STE-Frenkel pair in NaF at three different values of 02. The on-center, geometries.
(a) Q-J=
0, and two off-center, (b) Q2 = 1 .O Reproduced with permission from [24].
A, (c)
1.45
A,
With the recent interest in nanocrystallite materials, a number of simulations have been made on alkali halide nano-clusters [25,26*,27]. The method based on LDA and pseudopotentials is applied to molecular clusters with varying numbers of excess electrons and net charges. Although the method is not designed to study excited states, it is possible to simulate nanoclusters containing a self-trapped hole, X2 -, or an F center, an excess electron localized around the X- vacancy, by studying the ground state of an appropriate cluster [26*]. Regarding the relaxed structure of the excitation near the surface leading to the ejection of an energetic halogen atom and the formation
Processes mediated by excited electrons in silver halides Latent image formation in silver bromide is one of the oldest examples of the processes induced by photo-excited electrons. Many models have been proposed, the most famous being those developed by Gurney and Mott [30]. Recent reviews of experimental works [31-331 suggest the importance of the clusters containing interstitial silver ions with deep-shallow levels. Although the atomistic structure of the steps taken in the nucleation of a latent image is not identified, the models proposed involve bistable (deep-shallow) centers. We are now at the stage where the theoretical simulations can propose a model and compare it with experimental data. Ab initio HF calculations of some of the steps involved are being performed [34]. In this regard it is worth noting that a simpler deep-shallow defect system in CdF&r, Ga [35] offers an interesting analogy. A recent first principles calculation [36’] of the APE!% of the systems involving In, Ga, Y and SC shows that all four trivalent impurities have a shallow donor-like level, accompanied by a large lattice relaxation. Only In and Ga (but also Al, according to a qualitative estimate) also have a deep level. A small potential barrier, of the order of 0.1 eV, separates the two levels. The presence or absence of the deep level is attributed to the difference in the short range potential of the impurity atoms. Self-trapped exciton in quartz SiOz is an important material in optics and electronics. Recent computer simulation studies based on two different methods determined the structure of the STE and its relation to radiation-induced defects. The first one [37,38] was based on the INDO code and studied both a cluster embedded in an ionic lattice and a supercell lattice containing the STE. The second one [39,40] was based on an all-electron HF method applied to a quantum cluster embedded in an array of ions. Remarkably, both simulations gave converging results of the structure of the STE. The main points are the following. In the relaxed exciton, the hole and the excited electron are split in space. The hole is mostly centered on an oxygen atom which moves into an interstitial site, while the
Excited state phenomena Song
excited electron is centered on the oxygen vacancy and on the surrounding Si atoms. Relatively small displacements of atoms and small changes of bonding angle induce substantial changes of the energy of the total system. This reflects the partly covalent nature of SiO2 and contrasts with the situation found in ionic halides. The first work also studied the evolution of the STE into a Frenkel pair and found that they occur on the same energy surface. A fairly large potential barrier (about 1 eV) was obtained, which was attributed to the limited size of the super cell used. It is interesting to compare the STE in quartz and in alkali halides. The hole is not known to self-trap in crystalline quartz, although it does so in the amorphous phase. However, in both types of material the excited electron plays a crucial role by localizing on an attractive site and thereby inducing a stabilizing relaxation with a lowered symmetry, Self-trapping of excitons in diamond Two different methods have been applied to determine the structure of the core-STE in diamond. Mainwood and Stoneham [41] have used the self-consistent MD approach based on the CNDO technique. The core-STE is characterized by a large relaxation of one particular bond along a cl 1 l> direction and results in a large Stokes shift. From the calculated dynamic relaxation, the line-shapes of the X-ray absorption and emission of the core exciton have been obtained, as will be described in the next section. Mauri and Car [4P], on the other hand, have performed a first-principles study of the core exciton in diamond based on the LDA valence electron-only HF calculation. Their result is similar to that obtained in [41], and gives a bond stretching of about 28% between the excited carbon and its partner atom. While the hole is localized on the excited carbon atom, the electron is on the stretched bond. They also report that the bi-exciton (valence) self-traps, while a single valence exciton does not. They speculate that in the sub-picosecond melting experiment excitonic self-trapping could play an important role because of the fast relaxation time and the energy released. Similar speculations which associate the creation of a large number of self-trapped excitons to drastic, or catastrophic, processes have recently been made in other contexts as well [43,44]. localized
exciton in silicon nanocrystallite
We make a brief allusion to recent works on similar systems in covalent materials mainly to point out some similarities between the ionic and covalent materials. One is the exciton self-trapping in the porous Si and the other is the core exciton self-trapping in diamond. Based on an approximate tight-binding approach as well as an ab i&o LDA method, Allan et a/. (3.1 found that an intrinsic localized surface exciton state (STE) exists and is either stable or metastable. A free, delocalized, exciton state is found on the same energy surface as the self-trapped state separated by a small energy barrier. The configuration coordinate is the interatomic distance of a pair of Si atoms
837
which forms a dimer at the surface. In the STE the electron and hole are found split on the weakly interacting Si dangling bonds. It is interesting to note that in the STE the two particles split again in space as in the other cases described above. They attributed the porous Si luminescence to the STE state on the cluster surface, and added that the STE state obtained in Si can be expected in other semiconductors as well.
Transfer of excitation
energies
In a number of examples the electronic excitation energy is transferred from the host system to a guest system with high efficiency. In LiF with a physisorbed layer of carbonyl sulfide, the transfer of the host electronic excitation energy to the adsorbed molecule is so efficient that the ensuing photodissociation yield of the molecule is 103 to 104 times larger than that in the gas phase [4.5]. This is attributed to the transfer of energy from the F center in the bulk to the molecule on the surface. In NaCl with adsorbed layers of CzHz, the host excitation energy is transferred to the molecular excitation accompanied by a complete quenching of the characteristic host fluorescent emission 1461. In CsX (where X is a halogen atom) crystals, the electronic excitation energy of the F center is converted with high efficiency into the vibrational energy of a nearby CN- molecule, while in KC1 the conversion is much weaker [47,48]. Where the transfer is efficient, the F luminescence quenching is strong, and vice versa. The APES of the FH (CN-) center in CsCl:CN- and KCl:CNhave been calculated [49] based on the same approach as in the approximate studies of the STE. Figure 3 shows the APES for the electron in the excited -pY > state (with the y-axis connecting the ‘F center and the CN- molecule) for both CsCl and KCl. While in KCl:CNthe excited and the ground state APESs do not cross, the two APESs strongly interact and cross in CsCl:CN-. This result therefore explains the quenching of the F luminescence in CsCl:CN-. To understand the mechanism of the e-v (electronic to vibrational) energy transfer (e.g. the preferential transfer to the u-4 state), would require a quantitative analysis of the radiationless transition between the excited and ground states. There have been several recent numerical simulations of the radiationless transition. One is the determination of the lineshapes of X-ray absorption and emission bands of the core-exciton in diamond [41]. Mainwood and Stoneham have obtained the time variation of the relaxation energies from an MD simulation based on the CNDO approach. From Fourier analyses of the relaxation curve, the frequencies and the dampings of the modes involved are obtained, which led to the determination of the lineshape function. The Stokes shift and linewidths obtained are in qualitative agreement with experiment. Another example is found in the ab initio prediction of the absolute value of the radiationless transition rate in
838
Modelling
Figure
and simulation
of solids
3
The APES of the system F&N-) in (a) KCI(CN-) and in (b) CsCI(CN-). Cl, and C12 represent, respectively, the bond length of the molecule CN- and the distance between the F center and the mid-point of the molecule. Shown are the excited py state and the Franck-Condon ground state. Reproduced with permission from 1501.
the possible tunable laser material KzNaSc(Ga)Fb:Cr3+ [Sl]. Woods et a/. have performed embedded cluster calculations of APES for the ground and excited states. Vibrational overlap integrals were evaluated between the two states directly by diagonalizing the vibrational Hamiltonian. The lineshape functions were then obtained. The radiationless transition rate was evaluated with no adjustable parameters. By comparing their calculations with the experimental data they concluded that the rate depended on the detailed features of the APES in an extremely sensitive way. There have been extensive studies of the technical aspects associated with radiationless transition rate calculations. The most notable are the new approaches of MD involving electronic transitions between several energy surfaces [SZ]. Such studies are at the stage of theoretical test on simple models and applications to practical systems are for the future.
Conclusions The study of atomistic structure and dynamics of processes induced by electronic excitation is relatively recent. While the study of the ground state based on the LDA has often proven successful, that of the excited state requires different approaches. Approaches based on the HF and beyond are characterised not only by some of the difficulties specific to them (e.g. convergence to the desired state), but also by the steep scaling of computer time with the size of the basis used. Although it is possible to cut the size of the basis by employing pseudopotentials and removing core electrons, sometimes this can present problems. The frequently used pseudopotentials remove
all but the valence shells. This does not allow for the core polarisation which can be important in some systems [ 18,201. Simulations based on the pseudopotentials which include all the outermost occupied electron shells in the HF calculations could remedy the situation. From the examples reviewed above, it appears that for many complex systems a simulation based on some suitable approximate methods is often desirable when such approaches are available. They serve as a valuable prelude to more sophisticated and expensive simulations. A practical ab initio method of implementing an MD simulation of an excited system, similar to that formulated by Car and Parrinello for the ground state, is very desirable. There are a number of interesting processes involving excited electrons in insulators and semiconductors, and many of them are important in the field of materials applications [53]. This field is only in the early stages of its development.
References
and recommended
reading
Papers of particular interest, published within the annual period of review, have been highlighted as:
. ..
of special interest of outstanding interest
1.
Lundqvist S, March NH (Eds): Theory of the Inhomogeneous E/e&on Gas. New York: Plenum Press: 1983.
2.
Delley B: An all-electron numerical method for solving the local density functional for polyatomic molecules. J Chem Phys 1990, 92:508-517.
Excited
3. .
Allan G, Delerue C, Lannoo M: Nature of luminescent surface states of semiconductor nanocrystallites. Phys Rev Lett 1996, 76:2961-2964. On the basis of an approximate tight-binding and ab initio LDA approaches, the authors have found that the exciton self-traps on the surface of the nanocrystallite. The porous Si luminescence is attributed to such STE. An interesting aspect to note is that the ground state and the STE state belong to two different symmetries and are therefore orthogonal to each other. The excited state is therefore another ground state of a different symmetry which the density functional principle can handle. 4.
Cui S, Johnson RE, Cummings PT: Ejection of atoms upon selftrapping of an atomic exciton in solid argon. P@ Rev 8 1989, 39:9580-9583.
5.
Krylov Al, Gerber RB, Gaveau MA, Mestdagh JM, Schilling B, Visticot JP: Spectroscopy, polarisation and nonadiabatic dynamics of electronically excited Ba(Ar), clusters: theory and experiment. J Chem Phys 1996,104:3651-3663.
6.
Car R, Parrinello M: Unified approach for molecular dynamics and density-functional theory. Phys Rev Letr 1985, 66~2471-2474.
9.
Lewandowski AC, Wilson TM: Lattice-embedded multiconfigumtional self-consistent-field calculations.of the Mn-petirbed F-center defect in CaF*:Mn. Phys Rev B 1995, 62:100-l 09.
10. .
Vail JM, Rao BK: Electronic structure of crystals: embedded quantum cluster with overlap. lnt J Quantum Chem 1995, 63~67-76. The consequence of the cluster-embedding orthogonal&y and the associated problems of cluster normalization and total energy evaluation are discussed. 11.
Grimes RW, Catlow CRA, Shluger AL (Eds): Ouantum Mechanical Cluster Calculations in Solid State Studies. Singapore: World Scientific Pub Co: 1992.
12.
Stoneham AM: Theory of Defects in Solids. Odord: Clarendon Press; 1975.
13.
ltoh N, Stoneham AM, Harker AH: A theoretical study of desorption induced by electronic tmnsition in alkali halides. Surf Sci 1989,217:578-589.
14.
Bartram RH, Stoneham AM, Gash P: Ion-sire centers. Phys Rev 1968,176:1014-l 024.
15.
Williams RT, Song KS, Faust W, Leung CH: Off-center selftrapped excitons and creation of lattice defects in alkali halide crystals. Phys Rev B 1986,33:7232-7240.
effects in color
16. .
Song KS, Williams RT: Self-Trapped ficitons. Heidelberg: Springer-Verlag; 1996 (2nd edn). [Gardona M (Series Editor): Springer Series in Sdid-State Science, vol 105.1 This monograph presents an up-todate description of the STE in a variety of insulators. lt also contains a brief introduction to the extended-ion approach based on the use of spherically symmetrical floating Gaussians as the basis. 17..
18.
Song KS, Leung CH, Williams RT: A theoreti=l basis for the Rabin-Klick criterion in terms of off-center self-trapped-exciton relaxation. J Phys-Condens Matter 1989,1:683-687. Song KS, Baetzold RC: Structure of the self-trapped exciton and nascent Fmnkel pair in alkali halides: an 8b initio study. Phys Rev B 1992,46:1960-l 969.
phenomena
Song
839
19. ..
Song KS: Decay of the self-trapped exciton and Frenkelpair formation in NaF: an eb fnftfo study. Phys Rev B 1996, 63:12537-l 2540. In this all-electron HF work which includes the correlation effect by the MP2 method, the range of the electron and hole centers’ separation is extended up to the third nn distance (9 A). No energy barrier larger than about 0.2 eV, is found, suggesting that a dynamic Frenkel pair creation is possible in this alkali halide. 20.
Puchin VE, Shiuger AL, Tanimura K, ltoh N: Model of self-trapped excitons in alkali halides. Phys Rev B 1993, 47:6226-6240.
21. ..
Puchin VE, Shluger AL, ltoh N: Electron correlation in the seiftrapped hole and exciton in the NaCl crystal. Phys Rev B 1995, 52~6254-6264. In this work the authors aoolied the Gaussian92 code to the cluster 0~ (Na),d, in which the cores ‘iare represented by norm-conserving pseudbpby tentials. Electron correlation was included by the MP2 method. As in their earlier works without the correlation effect, the barrier for large separation was still present. The authors found a local energy minimum of the triplet STE at the on-center geometry. They argued that at the on-center geometry the effect of configuration interaction could be important. 22.
Puchin VE, Shluger AL, ltoh N: Theoretlal studies of atomic emission and defect formation by electronic excitation at the (100) surface of NaCl. Phys Rev B 1993,47:10760-l 0768.
23.
Song KS. Chen LF: Excitonic instability and athermal halogen atom desorption from NaBr, KBr and RbBr. Radiat Eff Defect Solid 1994, 128:35-45.
24.
Song KS: Decay.of the self-trapped exciton and large scale atomic motion in the ionic halide crystals J Luminesc 1996, 66-673309-395.
25.
Rajagopal G, Bamett RN, Landman U: Metallization clusters. Phys Rev Lett 1991,67:727-730.
Meng J, Barry Kuru A, Woodward C: Electronic structure and optical properties of the impurity Cu+ in NaF. Phys Rev B 1988, 38:10870-l 0073. Gryk TJ, Bartram RH: Embedded molecular cluster modeling of TIO (1) and Gao (1) centers in potassium chloride. J Phys Chem Solids 1995, 66:863-869. -. .. . Valence-electrons-only KHF calculattons are performed tar the ground and low lying excited states. The chlorine ions surrounding the thalium ion are either included in the SCF calculation or represented by point charges. A simplified single-center (the impurity ion only) model gave excellent results of optical transition energies.
state
of ionic
26. .
Bamett RN, Cheng HP, Hakkinen H, Landrnan U: Studies of excess electrons in sodium chloride clusters and of excess protons.-_ in water. ._- J Phys Chem 1995,99:7731-7753. Based on the LDA-MD approach, the structures of vanous sodium chloride clusters are studied. It is interesting to note that some of the well-known crystal bulk defect species are found in the clusters. For example, Nal &I, 2+ simulates an F center (the excess electron) while (NaGl)2+ simulates a selftrapped hole. 27.
Li X, Beck RD, Whetten RL: Photon-stimulated ejection of atoms from alkali-halide nanocrystals. Phys Rev Left 1992, 60~3420-3423.
28.
Adair M, Leung CH, Song KS: Equilibrium configumtion of the self-trapped exciton in CaF2 and SrF2. J Phys C: Solid State Phys 1985, 18:L909-L913.
29.
Baetzold RC, Song KS: Self-trapped excitons in SrFCl studied by ab initio methods. Phys Rev B 1993,4&l 4907-l 4914.
30.
Gurney RW, Mott NF: The theory of photolysis of silver bromide and the photogmphic latent image. Proc R Sot Lond Ser A 1938,164:151-167.
31.
Hamilton JF: The silver halide photographic 1908, 37:359-441.
32.
Eachus RS, Olm MT: Defect-mediated photochemical processes in the silver halides. J Sot Photogr Sci Technof Japan 1991,54:294-303.
33.
Kanzaki H, Tadakuma Y: Electronic processes in chemicallysensitized emulsion grains of silver bromide. J Phys Chem Solids 1994, 55:631-645.
34.
Baetzold RC, Eachus RS: The stability of a split interstitial silver ion in A&l. J Phys: Condens Matter 1995,7:3991-3999.
35.
Dmochowski JE, Langer JM, Kalinski 2, Jantsch W: CdF+ln - a critical test of the Toyozaws model of impurity self-trapping. Phys Rev Lett 1986,56:1735-l 737.
process. Adv Phys
840
Modelling
and simulation
of solids
44.
Toyozawa Y: Condensation of relaxed excitons in static and dynamic phase transitions. So/id State Commun 1992, 04:255-257.
45.
Leggeti K, Polanyi JC, Young PA: Photochemistry of adsorbed molecules. V. Ultraviolet photodissociation of OCS on LiF(OO1). J Chem Phys 1990, 93:3645-3657.
46.
Dunn SK, Ewing GE: Energy transfer from self-trapped excitons in NaCl to physisorbed C2Hp Chem Phys 1993, 177:571-578.
Shluger AL: The model of a triplet self-trapped exciton in crystalline SiOF J Phys C: So/id State Phys 1988, 21 :L431 -L434.
47.
Yang Y, von Osten W, Luty F: Total transformation of electronic F-center emission into multi-state CN- vibrational emission (4.8 pm) in CsCI. Phys Rev 1985, 32:2724-2726.
Shluger AL, Stefanovich E: Models of the self-trapped exciton and nearest-neighbor defect pair in SiOl. Phys Rev B 1990. 42:9664-9673.
40.
Rong F, Yang Y, Luty F: Coupling and energy transfer between F centers and CN- defects. Cryst Latt Defects Amorph Mat 1989, 18:1-25.
39.
Fisher AJ, Hayes W, Stoneham AM: Structure of the self-trapped exciton in quartz. Phys Rev Left 1990, 64:2667-2670.
49.
40.
Fisher AJ, Hayes W, Stoneham AM: Theory of the selftrapped exciton in quartz J Phys C: Solid State Phys 1990, 2:6707-6720.
Song KS, Chen LF, Tong PQ, Yu HW, Leung CH: A study of the F”(CN) centre in KCI and CsCI: the potential energy surface and eV energy transfer. J Phys: Condens Matter 1994, 6:5657-5666.
50.
Chen LF, Song KS: E-V energy transfer in the F&N) center in KCI and CsCL Radiation Effects and Defects in So/ids 1995, 134:405-409.
51.
Woods AM, Sinkovits RS, Bartram RH: Computer modeling of thermal quenching of chromium photoluminescence in fluoride elpasolites. J Phys Chem So/ids 1994, 55:91-97.
52.
Tully JC: Molecular dynamics with electronic Phys 1990, 93:1061-1071.
53.
Shinozuka Y, Katayama-Yoshida H: Dynamics of non-equilibrium solid by electronic excitetion - towards the creation of new materials science: Solid State Physics 1993; Tokyo, Agne Gijutsu Center [Special issue, in Japanese].
36. .
Cai Y, Song KS: A study of bistable (shallow-deep) defect systems in CdF2 M3+ (M: In, Ga). J Pbys: Condens Matter 1995, 712275-2204. Using the extended-ion approach the detailed structure of the shallow and deep states associated with I++ and Gas+ are obtained. The same method is used to study the structure of Y3+ and Sc3+ centers which show only a shallow level. The difference between the two groups of trivalent ions is in the binding energy of the outermost s-level in the Madelung potential at the cation site. 37.
38.
41.
Mainwood A, Stoneham AM: A comparison of the core exciton and nitrogen donor in diamond. J Phys: Condens Matter 1994, 6:4917-4927. 42. Mauri F, Car R: First-principles study of exciton self-trapping in . diamond. Phys Rev Lett 1995, 75:3166-3169. The APES of the core exciton is obtained based on the LDA approach. The relaxation is similar to that found in [41] and is about 28% of the regular bond length. The electron and hole split in space along the stretched bond. Valence exciton is found to be free, but a biexciton (valence) is found to self-trap. 43.
Faust WL: Explosive molecular 245:37-42.
ionic crystals. Science
1989,
transitions.
J Chem
Excited state phenomena Augustin
KS Song
Recent
in theoretical
induced
progress
by electronic
contributed
excitation
to our understanding
of the exciton
self-trapping,
radiation
defect
between
defects
creation,
simulations
of processes
in insulating
solids
has
of some of the basic
recombination
steps
luminescence,
photo-desorption
and interaction
in various large bandgap
materials.
It is
hoped that these examples will stimulate further progress in other systems, many of which have potential practical applications.
Addresses Department of Physics, University of Ottawa, Ottawa, Ontario, Kl N 6N5, Canada; e-mail:[email protected] Current Opinion in Solid State & Materials l:834-040
Science
1996,
0 Current Chemistry Ltd ISSN 1359-0286 Abbreviations APES adiabatic potential energy surface CNDO complete neglect of differential overlap F-H pair Frenkel defect pair HF Hartree-Fock INDO intermediate neglect of differential overlap LDA local density approximation MD molecular dynamics STE self-trapped exciton
Introduction An electronic excitation has a lifetime which may vary typically between a nanosecond and a millisecond. During this relatively short lifetime, the balance of forces between the atoms in a solid can be broken locally, and as a consequence a number of processes, which are not observed in the ground state, can occur. Recent progress in ultrafast spectroscopic techniques has made it possible to explore many processes which involve the excited states. In this review, I will not cover processes which take place in semiconductors. There are interesting systems, such as the DX centers etc., which offer some similarities to those that will be discussed. The principal feature shared by these centers is the characteristic large lattice distortion. Although allusions will be made, it is felt that semiconductors should be treated separately. I will concentrate on processes induced by electronic excitation in large bandgap materials. In many of the large gap materials, the excitation energy is localized in space either around pre-existing defects and impurities, or, more interestingly, can be localized spontaneously (self-trapped) as a result of strong electron-lattice interaction. An energy package of perhaps several electron-volts can become concentrated within a space of the order of an atomic volume. As this is accompanied by a local breakdown of the balance of forces, a large-scale atomic
rearrangement can follow. The details depend on the nature of the chemical bonding and coordination in the lattice. Examples are found in radiation-induced lattice defect formation and atomic desorption in ionic halide crystals, in quartz and even in rare gas solids. The latent image formation in silver halide crystals, familiar to us for over a century, is also an example of this. In many radiation-related devices, for example X-ray storage phosphors and scintillation detectors, the ionizing radiation creates electron-hole pairs which are trapped at some centers at or below room temperature until they can be released to produce signals at the time of reading. In recent years, in parallel with the progress in the new sophisticated computaexperimental techniques, tional methods have been developed and applied to the atomistic studies of processes taking place in excited insulators. While the studies of the ground state have been extensively based on the density functional approaches [l], in particular on the local density approximation (LDA) [2,3*], the excited state studies rely on other approaches. Often the spin state of the excited system is an important factor, and the Hartree-Fock approach is employed, possibly with a correction for the correlation effect. Many recent HF simulations on excited systems have concentrated on determining the equilibrium structures. Only a relatively small number of studies have been made so far in the molecular dynamics (MD) simulation of excited systems [4,5], as will be discussed below. This contrasts with the MD studies of the ground state based on the method developed by Car and Parrinello [6] which is based on LDA. In ionic materials, the lattice and electronic polarizations can be important. At the same time, interfacing the central quantum cluster and the surrounding crystal is a complex problem. Various embedding approaches have been proposed in recent works [7,8*,9,10*]. A good review of some of these approaches is given in [l 11. In the following text I present several examples of recent computational simulations of systems in which the excited electron plays a central role. Of necessity, they are based on different methods of varying levels of sophistication. It is significant to find that, where different methods have been applied to the same system, results which are in agreement with each other have been obtained. It is hoped that the review will show the progress which has been made recently in understanding some of the significant processes taking place during electronic excitations and will indicate the similarities, as well as the differences, between various systems. A number of systems which demonstrate unusual properties under excitations as well as important practical applications have yet to be analyzed.
Excited state phenomena Song
Large-scale atomic processes induced by electronic excitations in insulators Localized systems containing either a hole or an excited electron have been studied earlier with various approximate methods [12]. The semi-empirical CNDO method was used for the simulation of halogen desorption with the core or valence excitations [13]. Simpler electron defects have been .studied with the extended-ion method which is an approximation to the one-electron Hartree-Fock approach [14]. The presence of both the hole and excited electron (e.g. the self-trapped exciton: STE), however, in a polarizing medium turned out to be more complex. In many insulating crystals, ionizing radiation produces characteristic fluorescence emission bands with large Stokes shifts, as large as about 75% of the band gap energy. Ionizing radiation creates lattice defects. Some of the extensively studied materials include the ionic halides (bulk, surface and nanocrystallites), quartz, rare gas solids and diamond. The atomistic structure of the STE and its relation to the radiation-induced lattice defects, the Frenkel defect pair (also known as the F-H pair), has become understood only recently [15,16’]. Self-trapped
excitons
835
energy surface [19**,21”]. The effect of configuration interaction is expected to be significant where many excited states are densely distributed, such as in the on-center geometry ]2+]. Different approaches have led to results which are consistent with each other and that have given a good account of the experimental data, showing that the fundamental processes are now well understood. We have reproduced in Figure 1 the adiabatic potential energy surface (APES) calculated by the all-electron HF method for the spin triplet STE in NaE covering the range between the on-center STE and the third nearest neighbor F-H pair (a separation of 8A). Figure 2 presents the spin density of the electron and hole plotted on a plane as the STE undergoes axial relaxation. It clearly shows the excited electron localization around the anion vacancy as the off-center relaxation proceeds.
Fiaure
1
r
I
6.2 r
in ionic halides
It is not surprising that the first simulation of the STE in alkali halides was based on a combination of relatively simple approximations: the excited electron by the extended-ion approximation; the hole by the CNDO code; and the lattice by conventional pair potentials [ 171. The total energy of the system was minimized by optimizing simultaneously the electron wavefunction and the atomic positions of a limited number of atoms in the crystal. The main points of this study are as follows. Firstly, the STE in alkali halides is equivalent to a primitive F-H pair (the excited electron localized on an anion vacancy as an F center, with the hole localized on the molecule ion Xz - occupying an anion site). Secondly, the driving force promoting the process is in the strong excited electron localization at an anion vacancy. Thirdly, the available relaxation energy is between 1eV and ZeV, part of which can be used to induce dynamic creation of lattice defects at low temperatures. Such a strong spontaneous symmetry breaking relaxation with sufficient energy to promote atomic rearrangement was initially surprising. As will be seen in other examples, it is the excited electron which is the prime driver of the atomic rearrangement. In recent years a number of Hartree-Fock many-electron simulations have been made. Both all-electron HF [18,19**] and valence-electron-only HF [20,21**] calculations, with and without the correlation effect included, have been performed on relatively small quantum clusters embedded approximately in the remainder of the ionic lattice. These works confirmed the main points enumerated above. The inclusion of the correlation effect does not alter the overall features, but can have some subtle effect on the adiabatic potential
3.21;.
’ 1
’ 2
’ 3
’ 4
’ 5
’ 6
’ 7
’ 8
’ 9
Adiabatic potential energy surface (APES) of the system STE-Frenkel pair in NaF drawn along the coordinate Qs (the distance between the excited electron and the hole along the [l101 axis). The UHF (unrestricted Hartree-Fock) and MP2 (Moller-Ptesset second order perturbation theory) results are represented by the dashed and continuous lines, respectively. Published with permission from [lQ”I, Fig. 2.
Studies of the STE decay near a surface have also been made for several halide crystals [22,23]. The presence of a surface introduces some unexpected elements. For instance, the relaxation along the close-packed [llO] row is modified near the surface and results in a dynamic desorption perpendicular to the (100) surface. Also, the surface itself directly influences how the exciton localizes. Very close to the surface, it was observed that the excited electron localizes in such a way that the resulting axial relaxation propels the molecule ion Xz- away from the surface towards the bulk, and dynamical desorption is not obtained in the first two layers below the surface. According to a recent simulation, desorption only seems to occur for layers starting with the third below the surface (KS Song, Y Cai, unpublished data).
836
Modelling
Figure
and simulation
of solids
of an F center
2
simulations (a)
[27], there
on the bulk
is a close
similarity
with
the
surface.
In ionic halides of other lattice structures, such as in CaFz and in SrFBr, the absence of a close-packed halogen row has a profound influence on the radiation defect production. Despite the large relaxation energy released in the off-center motion of the STE, no long-range atomic motion leading to well separated F-H centers
500
follows [Z&29]. In these materials, the defects created are mostly of transient species which recombine with short lifetimes. A concurrent excitation into the hole band can lead to the creation of stable, well-separated, defect pairs owing to excitation-induced hole hopping diffusion. Both experimental data and theoretical calculations have contributed to our understanding of these phenomena.
a
k)
5.0 2.5
a3 g
0.0
a -2.3
-s.o -8
-6
-4
-2
0
2
4
6
8
410>(i) ,Spin density of the excited electron and hole obtained for the system STE-Frenkel pair in NaF at three different values of 02. The on-center, geometries.
(a) Q-J=
0, and two off-center, (b) Q2 = 1 .O Reproduced with permission from [24].
A, (c)
1.45
A,
With the recent interest in nanocrystallite materials, a number of simulations have been made on alkali halide nano-clusters [25,26*,27]. The method based on LDA and pseudopotentials is applied to molecular clusters with varying numbers of excess electrons and net charges. Although the method is not designed to study excited states, it is possible to simulate nanoclusters containing a self-trapped hole, X2 -, or an F center, an excess electron localized around the X- vacancy, by studying the ground state of an appropriate cluster [26*]. Regarding the relaxed structure of the excitation near the surface leading to the ejection of an energetic halogen atom and the formation
Processes mediated by excited electrons in silver halides Latent image formation in silver bromide is one of the oldest examples of the processes induced by photo-excited electrons. Many models have been proposed, the most famous being those developed by Gurney and Mott [30]. Recent reviews of experimental works [31-331 suggest the importance of the clusters containing interstitial silver ions with deep-shallow levels. Although the atomistic structure of the steps taken in the nucleation of a latent image is not identified, the models proposed involve bistable (deep-shallow) centers. We are now at the stage where the theoretical simulations can propose a model and compare it with experimental data. Ab initio HF calculations of some of the steps involved are being performed [34]. In this regard it is worth noting that a simpler deep-shallow defect system in CdF&r, Ga [35] offers an interesting analogy. A recent first principles calculation [36’] of the APE!% of the systems involving In, Ga, Y and SC shows that all four trivalent impurities have a shallow donor-like level, accompanied by a large lattice relaxation. Only In and Ga (but also Al, according to a qualitative estimate) also have a deep level. A small potential barrier, of the order of 0.1 eV, separates the two levels. The presence or absence of the deep level is attributed to the difference in the short range potential of the impurity atoms. Self-trapped exciton in quartz SiOz is an important material in optics and electronics. Recent computer simulation studies based on two different methods determined the structure of the STE and its relation to radiation-induced defects. The first one [37,38] was based on the INDO code and studied both a cluster embedded in an ionic lattice and a supercell lattice containing the STE. The second one [39,40] was based on an all-electron HF method applied to a quantum cluster embedded in an array of ions. Remarkably, both simulations gave converging results of the structure of the STE. The main points are the following. In the relaxed exciton, the hole and the excited electron are split in space. The hole is mostly centered on an oxygen atom which moves into an interstitial site, while the
Excited state phenomena Song
excited electron is centered on the oxygen vacancy and on the surrounding Si atoms. Relatively small displacements of atoms and small changes of bonding angle induce substantial changes of the energy of the total system. This reflects the partly covalent nature of SiO2 and contrasts with the situation found in ionic halides. The first work also studied the evolution of the STE into a Frenkel pair and found that they occur on the same energy surface. A fairly large potential barrier (about 1 eV) was obtained, which was attributed to the limited size of the super cell used. It is interesting to compare the STE in quartz and in alkali halides. The hole is not known to self-trap in crystalline quartz, although it does so in the amorphous phase. However, in both types of material the excited electron plays a crucial role by localizing on an attractive site and thereby inducing a stabilizing relaxation with a lowered symmetry, Self-trapping of excitons in diamond Two different methods have been applied to determine the structure of the core-STE in diamond. Mainwood and Stoneham [41] have used the self-consistent MD approach based on the CNDO technique. The core-STE is characterized by a large relaxation of one particular bond along a cl 1 l> direction and results in a large Stokes shift. From the calculated dynamic relaxation, the line-shapes of the X-ray absorption and emission of the core exciton have been obtained, as will be described in the next section. Mauri and Car [4P], on the other hand, have performed a first-principles study of the core exciton in diamond based on the LDA valence electron-only HF calculation. Their result is similar to that obtained in [41], and gives a bond stretching of about 28% between the excited carbon and its partner atom. While the hole is localized on the excited carbon atom, the electron is on the stretched bond. They also report that the bi-exciton (valence) self-traps, while a single valence exciton does not. They speculate that in the sub-picosecond melting experiment excitonic self-trapping could play an important role because of the fast relaxation time and the energy released. Similar speculations which associate the creation of a large number of self-trapped excitons to drastic, or catastrophic, processes have recently been made in other contexts as well [43,44]. localized
exciton in silicon nanocrystallite
We make a brief allusion to recent works on similar systems in covalent materials mainly to point out some similarities between the ionic and covalent materials. One is the exciton self-trapping in the porous Si and the other is the core exciton self-trapping in diamond. Based on an approximate tight-binding approach as well as an ab i&o LDA method, Allan et a/. (3.1 found that an intrinsic localized surface exciton state (STE) exists and is either stable or metastable. A free, delocalized, exciton state is found on the same energy surface as the self-trapped state separated by a small energy barrier. The configuration coordinate is the interatomic distance of a pair of Si atoms
837
which forms a dimer at the surface. In the STE the electron and hole are found split on the weakly interacting Si dangling bonds. It is interesting to note that in the STE the two particles split again in space as in the other cases described above. They attributed the porous Si luminescence to the STE state on the cluster surface, and added that the STE state obtained in Si can be expected in other semiconductors as well.
Transfer of excitation
energies
In a number of examples the electronic excitation energy is transferred from the host system to a guest system with high efficiency. In LiF with a physisorbed layer of carbonyl sulfide, the transfer of the host electronic excitation energy to the adsorbed molecule is so efficient that the ensuing photodissociation yield of the molecule is 103 to 104 times larger than that in the gas phase [4.5]. This is attributed to the transfer of energy from the F center in the bulk to the molecule on the surface. In NaCl with adsorbed layers of CzHz, the host excitation energy is transferred to the molecular excitation accompanied by a complete quenching of the characteristic host fluorescent emission 1461. In CsX (where X is a halogen atom) crystals, the electronic excitation energy of the F center is converted with high efficiency into the vibrational energy of a nearby CN- molecule, while in KC1 the conversion is much weaker [47,48]. Where the transfer is efficient, the F luminescence quenching is strong, and vice versa. The APES of the FH (CN-) center in CsCl:CN- and KCl:CNhave been calculated [49] based on the same approach as in the approximate studies of the STE. Figure 3 shows the APES for the electron in the excited -pY > state (with the y-axis connecting the ‘F center and the CN- molecule) for both CsCl and KCl. While in KCl:CNthe excited and the ground state APESs do not cross, the two APESs strongly interact and cross in CsCl:CN-. This result therefore explains the quenching of the F luminescence in CsCl:CN-. To understand the mechanism of the e-v (electronic to vibrational) energy transfer (e.g. the preferential transfer to the u-4 state), would require a quantitative analysis of the radiationless transition between the excited and ground states. There have been several recent numerical simulations of the radiationless transition. One is the determination of the lineshapes of X-ray absorption and emission bands of the core-exciton in diamond [41]. Mainwood and Stoneham have obtained the time variation of the relaxation energies from an MD simulation based on the CNDO approach. From Fourier analyses of the relaxation curve, the frequencies and the dampings of the modes involved are obtained, which led to the determination of the lineshape function. The Stokes shift and linewidths obtained are in qualitative agreement with experiment. Another example is found in the ab initio prediction of the absolute value of the radiationless transition rate in
838
Modelling
Figure
and simulation
of solids
3
The APES of the system F&N-) in (a) KCI(CN-) and in (b) CsCI(CN-). Cl, and C12 represent, respectively, the bond length of the molecule CN- and the distance between the F center and the mid-point of the molecule. Shown are the excited py state and the Franck-Condon ground state. Reproduced with permission from 1501.
the possible tunable laser material KzNaSc(Ga)Fb:Cr3+ [Sl]. Woods et a/. have performed embedded cluster calculations of APES for the ground and excited states. Vibrational overlap integrals were evaluated between the two states directly by diagonalizing the vibrational Hamiltonian. The lineshape functions were then obtained. The radiationless transition rate was evaluated with no adjustable parameters. By comparing their calculations with the experimental data they concluded that the rate depended on the detailed features of the APES in an extremely sensitive way. There have been extensive studies of the technical aspects associated with radiationless transition rate calculations. The most notable are the new approaches of MD involving electronic transitions between several energy surfaces [SZ]. Such studies are at the stage of theoretical test on simple models and applications to practical systems are for the future.
Conclusions The study of atomistic structure and dynamics of processes induced by electronic excitation is relatively recent. While the study of the ground state based on the LDA has often proven successful, that of the excited state requires different approaches. Approaches based on the HF and beyond are characterised not only by some of the difficulties specific to them (e.g. convergence to the desired state), but also by the steep scaling of computer time with the size of the basis used. Although it is possible to cut the size of the basis by employing pseudopotentials and removing core electrons, sometimes this can present problems. The frequently used pseudopotentials remove
all but the valence shells. This does not allow for the core polarisation which can be important in some systems [ 18,201. Simulations based on the pseudopotentials which include all the outermost occupied electron shells in the HF calculations could remedy the situation. From the examples reviewed above, it appears that for many complex systems a simulation based on some suitable approximate methods is often desirable when such approaches are available. They serve as a valuable prelude to more sophisticated and expensive simulations. A practical ab initio method of implementing an MD simulation of an excited system, similar to that formulated by Car and Parrinello for the ground state, is very desirable. There are a number of interesting processes involving excited electrons in insulators and semiconductors, and many of them are important in the field of materials applications [53]. This field is only in the early stages of its development.
References
and recommended
reading
Papers of particular interest, published within the annual period of review, have been highlighted as:
. ..
of special interest of outstanding interest
1.
Lundqvist S, March NH (Eds): Theory of the Inhomogeneous E/e&on Gas. New York: Plenum Press: 1983.
2.
Delley B: An all-electron numerical method for solving the local density functional for polyatomic molecules. J Chem Phys 1990, 92:508-517.
Excited
3. .
Allan G, Delerue C, Lannoo M: Nature of luminescent surface states of semiconductor nanocrystallites. Phys Rev Lett 1996, 76:2961-2964. On the basis of an approximate tight-binding and ab initio LDA approaches, the authors have found that the exciton self-traps on the surface of the nanocrystallite. The porous Si luminescence is attributed to such STE. An interesting aspect to note is that the ground state and the STE state belong to two different symmetries and are therefore orthogonal to each other. The excited state is therefore another ground state of a different symmetry which the density functional principle can handle. 4.
Cui S, Johnson RE, Cummings PT: Ejection of atoms upon selftrapping of an atomic exciton in solid argon. P@ Rev 8 1989, 39:9580-9583.
5.
Krylov Al, Gerber RB, Gaveau MA, Mestdagh JM, Schilling B, Visticot JP: Spectroscopy, polarisation and nonadiabatic dynamics of electronically excited Ba(Ar), clusters: theory and experiment. J Chem Phys 1996,104:3651-3663.
6.
Car R, Parrinello M: Unified approach for molecular dynamics and density-functional theory. Phys Rev Letr 1985, 66~2471-2474.
9.
Lewandowski AC, Wilson TM: Lattice-embedded multiconfigumtional self-consistent-field calculations.of the Mn-petirbed F-center defect in CaF*:Mn. Phys Rev B 1995, 62:100-l 09.
10. .
Vail JM, Rao BK: Electronic structure of crystals: embedded quantum cluster with overlap. lnt J Quantum Chem 1995, 63~67-76. The consequence of the cluster-embedding orthogonal&y and the associated problems of cluster normalization and total energy evaluation are discussed. 11.
Grimes RW, Catlow CRA, Shluger AL (Eds): Ouantum Mechanical Cluster Calculations in Solid State Studies. Singapore: World Scientific Pub Co: 1992.
12.
Stoneham AM: Theory of Defects in Solids. Odord: Clarendon Press; 1975.
13.
ltoh N, Stoneham AM, Harker AH: A theoretical study of desorption induced by electronic tmnsition in alkali halides. Surf Sci 1989,217:578-589.
14.
Bartram RH, Stoneham AM, Gash P: Ion-sire centers. Phys Rev 1968,176:1014-l 024.
15.
Williams RT, Song KS, Faust W, Leung CH: Off-center selftrapped excitons and creation of lattice defects in alkali halide crystals. Phys Rev B 1986,33:7232-7240.
effects in color
16. .
Song KS, Williams RT: Self-Trapped ficitons. Heidelberg: Springer-Verlag; 1996 (2nd edn). [Gardona M (Series Editor): Springer Series in Sdid-State Science, vol 105.1 This monograph presents an up-todate description of the STE in a variety of insulators. lt also contains a brief introduction to the extended-ion approach based on the use of spherically symmetrical floating Gaussians as the basis. 17..
18.
Song KS, Leung CH, Williams RT: A theoreti=l basis for the Rabin-Klick criterion in terms of off-center self-trapped-exciton relaxation. J Phys-Condens Matter 1989,1:683-687. Song KS, Baetzold RC: Structure of the self-trapped exciton and nascent Fmnkel pair in alkali halides: an 8b initio study. Phys Rev B 1992,46:1960-l 969.
phenomena
Song
839
19. ..
Song KS: Decay of the self-trapped exciton and Frenkelpair formation in NaF: an eb fnftfo study. Phys Rev B 1996, 63:12537-l 2540. In this all-electron HF work which includes the correlation effect by the MP2 method, the range of the electron and hole centers’ separation is extended up to the third nn distance (9 A). No energy barrier larger than about 0.2 eV, is found, suggesting that a dynamic Frenkel pair creation is possible in this alkali halide. 20.
Puchin VE, Shiuger AL, Tanimura K, ltoh N: Model of self-trapped excitons in alkali halides. Phys Rev B 1993, 47:6226-6240.
21. ..
Puchin VE, Shluger AL, ltoh N: Electron correlation in the seiftrapped hole and exciton in the NaCl crystal. Phys Rev B 1995, 52~6254-6264. In this work the authors aoolied the Gaussian92 code to the cluster 0~ (Na),d, in which the cores ‘iare represented by norm-conserving pseudbpby tentials. Electron correlation was included by the MP2 method. As in their earlier works without the correlation effect, the barrier for large separation was still present. The authors found a local energy minimum of the triplet STE at the on-center geometry. They argued that at the on-center geometry the effect of configuration interaction could be important. 22.
Puchin VE, Shluger AL, ltoh N: Theoretlal studies of atomic emission and defect formation by electronic excitation at the (100) surface of NaCl. Phys Rev B 1993,47:10760-l 0768.
23.
Song KS. Chen LF: Excitonic instability and athermal halogen atom desorption from NaBr, KBr and RbBr. Radiat Eff Defect Solid 1994, 128:35-45.
24.
Song KS: Decay.of the self-trapped exciton and large scale atomic motion in the ionic halide crystals J Luminesc 1996, 66-673309-395.
25.
Rajagopal G, Bamett RN, Landman U: Metallization clusters. Phys Rev Lett 1991,67:727-730.
Meng J, Barry Kuru A, Woodward C: Electronic structure and optical properties of the impurity Cu+ in NaF. Phys Rev B 1988, 38:10870-l 0073. Gryk TJ, Bartram RH: Embedded molecular cluster modeling of TIO (1) and Gao (1) centers in potassium chloride. J Phys Chem Solids 1995, 66:863-869. -. .. . Valence-electrons-only KHF calculattons are performed tar the ground and low lying excited states. The chlorine ions surrounding the thalium ion are either included in the SCF calculation or represented by point charges. A simplified single-center (the impurity ion only) model gave excellent results of optical transition energies.
state
of ionic
26. .
Bamett RN, Cheng HP, Hakkinen H, Landrnan U: Studies of excess electrons in sodium chloride clusters and of excess protons.-_ in water. ._- J Phys Chem 1995,99:7731-7753. Based on the LDA-MD approach, the structures of vanous sodium chloride clusters are studied. It is interesting to note that some of the well-known crystal bulk defect species are found in the clusters. For example, Nal &I, 2+ simulates an F center (the excess electron) while (NaGl)2+ simulates a selftrapped hole. 27.
Li X, Beck RD, Whetten RL: Photon-stimulated ejection of atoms from alkali-halide nanocrystals. Phys Rev Left 1992, 60~3420-3423.
28.
Adair M, Leung CH, Song KS: Equilibrium configumtion of the self-trapped exciton in CaF2 and SrF2. J Phys C: Solid State Phys 1985, 18:L909-L913.
29.
Baetzold RC, Song KS: Self-trapped excitons in SrFCl studied by ab initio methods. Phys Rev B 1993,4&l 4907-l 4914.
30.
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31.
Hamilton JF: The silver halide photographic 1908, 37:359-441.
32.
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33.
Kanzaki H, Tadakuma Y: Electronic processes in chemicallysensitized emulsion grains of silver bromide. J Phys Chem Solids 1994, 55:631-645.
34.
Baetzold RC, Eachus RS: The stability of a split interstitial silver ion in A&l. J Phys: Condens Matter 1995,7:3991-3999.
35.
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process. Adv Phys
840
Modelling
and simulation
of solids
44.
Toyozawa Y: Condensation of relaxed excitons in static and dynamic phase transitions. So/id State Commun 1992, 04:255-257.
45.
Leggeti K, Polanyi JC, Young PA: Photochemistry of adsorbed molecules. V. Ultraviolet photodissociation of OCS on LiF(OO1). J Chem Phys 1990, 93:3645-3657.
46.
Dunn SK, Ewing GE: Energy transfer from self-trapped excitons in NaCl to physisorbed C2Hp Chem Phys 1993, 177:571-578.
Shluger AL: The model of a triplet self-trapped exciton in crystalline SiOF J Phys C: So/id State Phys 1988, 21 :L431 -L434.
47.
Yang Y, von Osten W, Luty F: Total transformation of electronic F-center emission into multi-state CN- vibrational emission (4.8 pm) in CsCI. Phys Rev 1985, 32:2724-2726.
Shluger AL, Stefanovich E: Models of the self-trapped exciton and nearest-neighbor defect pair in SiOl. Phys Rev B 1990. 42:9664-9673.
40.
Rong F, Yang Y, Luty F: Coupling and energy transfer between F centers and CN- defects. Cryst Latt Defects Amorph Mat 1989, 18:1-25.
39.
Fisher AJ, Hayes W, Stoneham AM: Structure of the self-trapped exciton in quartz. Phys Rev Left 1990, 64:2667-2670.
49.
40.
Fisher AJ, Hayes W, Stoneham AM: Theory of the selftrapped exciton in quartz J Phys C: Solid State Phys 1990, 2:6707-6720.
Song KS, Chen LF, Tong PQ, Yu HW, Leung CH: A study of the F”(CN) centre in KCI and CsCI: the potential energy surface and eV energy transfer. J Phys: Condens Matter 1994, 6:5657-5666.
50.
Chen LF, Song KS: E-V energy transfer in the F&N) center in KCI and CsCL Radiation Effects and Defects in So/ids 1995, 134:405-409.
51.
Woods AM, Sinkovits RS, Bartram RH: Computer modeling of thermal quenching of chromium photoluminescence in fluoride elpasolites. J Phys Chem So/ids 1994, 55:91-97.
52.
Tully JC: Molecular dynamics with electronic Phys 1990, 93:1061-1071.
53.
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36. .
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