dynamics of localized excitations from energy and time resolved spectroscopy

Dynamics of localized excitations from energy andtime resolved spectroscopy

Nikolaus Schwentner

The electronic structure and the excited state relaxation phenomena in condensed rare gases have been stud-ied by absorption spectroscopy, photoelectron spectroscopy, and time resolved luminescence spectroscopy,all using selective excitation by monochromatized synchrotron radiation. Radiationless and radiative elec-tronic transitions in excited states and the rearrangement of surrounding matrix atoms will be discussed for'excited rare gas atoms in rare gas matrices. Furthermore, experimental results concerning the scatteringof excitons within the free exciton branches, localization of excitons, relaxation within the self-trapped exci-ton states, and energy transfer to guest atoms and boundaries will be presented.

1. Introduction

Excitation of a solid or liquid sample leads to a con-version of the absorbed energy into phonons, photons,and in some cases to the emission of electrons or de-sorption of ions. Upon excitation a nonequilibriumconfiguration of the electronic and nuclear structureoccurs. The new electron distribution at the excitedsite initiates nuclear rearrangements around this site.These structural changes cause nonradiative transitionsto lower lying electronic states. 1 -'3 Therefore structuralchanges and electronic transitions are strongly coupled.During the time elapsing between the fast (101 6-sec)electronic excitation process and the radiative decayprocess that takes place after 10-9 sec or longer for VUVradiation, an interesting cascade of nonradiative elec-tronic transitions and of structural changes takes place.A complete experimental investigation should providethe following information on the cascade:

(1) electronic and geometric structure in the groundstate;

(2) electronic structure in the primary excitedstate;

(3) new nuclear equilibrium configuration for thiselectronic state;

(4) rate constants for the relaxation of this struc-ture;

(5) all intermediate electronic states and all rateconstants for the corresponding radiative and non-radiative transitions in the relaxation cascade to lower,states;

The author is with Universitat Kiel, Institut fur Experimental-physik, 2300 Kiel, Federal Republic of Germany.

Received 6 June 1980.0003-6935/80/234104-11$00.50/0.© 1980 Optical Society of America.

(6) all intermediate nuclear configurations and allrate constants involved in their formation;

(7) electronic states; and(8) equilibrium configurations from which finally

radiative decay to the ground state is observed.Available experiments yield only parts of the whole

cascade. The structural changes in excited states arein general beyond the scope of direct structure investi-gation techniques, such as x-ray diffraction and ex-tended x-ray absorption fine structure analysis(EXAFS).14 The difficulties arise from the short life-times and small densities of the excited states. Toobtain valid information concerning the structure in theexcited states, the development of time resolvedEXAFS1 5 with a time resolution of 10-1 sec will be ofprime importance. Up to now the information con-cerning points (3), (4), (6), and (8) has to be extractedfrom spectroscopic investigations indirectly. More dataare available concerning the electronic states and therate constants involved in electronic transitions. Ab-sorption and photoelectron spectroscopy16 provide re-liable data for point (2), but only some of the interme-diate states [points (5) and (7)] are accessible. Thosestates from which enough light is emitted to be detectedby time resolved luminescence1 7 spectroscopy, or statesthat live long enough to be studied by transient ab-sorption spectroscopy,18 are easily studied. However,many questions remain in the description of even asimple relaxation cascade in electronically excitedstates. From the experimental point of view it seemsworthwhile to search for systems where the centralprocess, i.e., the coupling of electronic excitations withstructural changes, might be accessible, for example,systems where electronic excitation initiates largegeometric rearrangements. Furthermore, there shouldbe an easy way to modify the electronic states and therate constants to allow for a derivation of general trends.

4104 APPLIED OPTICS / Vol. 19, No. 23 / 1 December 1980

Pure and doped condensed rare gases are convenientsystems for these studies 7 for the following reasons:

(1) Electronic excitation breaks up the closed-shellconfiguration. The chemical nature changes from inertto reactive,19 and the excited electron interacts stronglywith its surroundings.

(2) The lattice is very soft,2 0 which allows quite largestructural changes in response to the new electronicconfiguration.

(3) The lattice phonon energies are extremely small 2l(some millielectron volts). The dissipation of electronicenergy in heat needs, in general, the emission of manyphonons. Thus nonradiative electronic relaxationprocesses are slowed down.

(4) The chemical nature is similar in the gas, liquid,and solid phase. Thus relaxation processes and theirdependence on density and on structural order can beinvestigated in all three phases at comparable condi-tions.

(5) Different rare gases and molecular gases can beeasily mixed in the gas phase and codeposited as dopedsamples. 2 2 This allows a systematic variation of elec-tronic and structural parameters at comparable con-ditions.

(6) Rare gases are transparent up to 17-eV photonenergy. Therefore, they are favorable matrices formatrix isolation spectroscopy22 in general.

In the following, some examples of experimentalprogress toward an understanding of the dynamics inelectronically excited states of pure and doped con-densed rare gases will be presented. Reviews have beenprepared by Fitzsimmons,23 Jortner, 7 Zimmerer,2 4

Schwentner,25 Fugol',26 Bondybey and Brus,27 andSchwentner et al.28 In this issue the relevant theory istreated by Toyozawa2 9 and Bassani,3 0 and a discusssionof one- and two-photon absorption results is given bySaile. 31

II. Relaxation Channels in Condensed Rare Gases

For an introduction, some electronic states relevantin the relaxation cascade in liquid He are shown in Fig.1. The scheme describes atomic and molecular statesin the gas phase. The arrows indicate transitions thathave been observed in luminescence emission and intransient absorption experiments in the liquid phase.23

According to these experiments the same electronicstates with only minor changes in the energies appearin liquid and gaseous He. This close correspondenceis due to a rearrangement of the liquid around the ex-cited He atoms. After the rearrangement of the liquidthe centers can be grouped into atomiclike excitedcenters He* and molecularlike centers He*. Bothspecies are surrounded by empty bubbles. The radiusof the bubble exceeds the nearest neighbor separationof 3 A of He atoms in the ground state by far. The ra-dius of the bubble (5-20 A) and its shape, which isnonspherical for states with symmetry unlike s, dependstrongly on the main quantum number and the sym-metry of the specific excited electronic state. Theconfiguration around some of the excited atomiclikestates and its dependence on external pressure has been

calculated.37-41 Also the sizes and the shapes of bubblesaround molecular centers have been estimated fromelectron density calculations in excited states of He2molecules.33 Despite the interesting experimental re-sults concerning the dynamics of these excitedstates,23 36 there exists no consistent description of thevarious relaxation channels, even for a simple systemconsisting of He atoms with only two electrons, neitherfrom a theoretical or an experimental point of view.One main problem is the quite large manifold of chan-nels that are possible due to the formation of two typesof centers. In addition the atomic and molecularlikecenters interact via dissociation and recombinationprocesses.

This example illustrates that in the case of pure liquidand solid rare gases we have to deal with 7 23-28

(1) electronic relaxation of atomiclike states in abubble;

(2) electronic, vibrational, and rotational relaxationof molecularlike states in a bubble;

(3) interaction of these channels by dissociation andrecombination.

In rare gas crystals, excitation creates excitons thatmove free before the deformation of the lattice leads tolocalized centers described above. Therefore, the fateof these free excitons, until they are localized as atomicor molecular centers, has to be analyzed. This in-cludes 3 8

(4) scattering within a free exciton branch;(5) scattering to lower free exciton branches; and(6) localization of excitons.

HZ He*. He Hz

singlet states He"-He triplet states

2e -23

2 *3sl S2,-

22 -s 3

21 i0 1Ei d3ac t

l- 'E9 \ sip0Allu 2 333 2 l 0

ig. .Ptnilcre o e uvshv bee adotedfo

radiative decay to ground statein excited molecular states Cin excited atomic states,

transient absorption f R 3

0 1 2 3 3 2 1 0INTERNUCLEAR DISTANCE (A )

Fig. 1. Potential curves for He. Curves have been adopted fromGinter and Battino,32 except for the singlet states above C 1;g +. 3 3

Arrows indicate observed transitions in liquid He. Transitions to theground state, are from Ref. 34; radiative decay between excited states,

from Ref. 35; transient absorption, from Ref. 36.

1 December 1980 / Vol. 19, No. 23 / APPLIED OPTICS 4105

EMISSIONSPECTRA

EXCITATIONENERGY-.120V 11.54eV-

8 9 10 11

n:1

?) 0.01%/Xe/NeAT T 2 3

11~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3

2e_ v

I ::~~A ": I II/ ~ : ~n12 n=3 n.4 nu2

EXCITATION SPECTRA

9 10 11 12

PHOTON ENERGY [eV]

32

TIME ns)

.2

®_ 09

.4 .6

.

2 4 6

TIME 1rWs

- T 2

2Vl

13

Fig. 2. Excitation spectra (emis-sion intensity vs excitation energy)for Xe in Ne (hatched curves) foreach of the three emission bands I,II, and III. Each emission band isshown without hatching with thecorresponding excitation spectrumand on the same energy scale.Prominent maxima in the excita-tion spectra are marked by a, b, c,d, e. Furthermore, the positionsof excitonic states n = 1, 2, 3, 4 andn = 1', 2', 3', 4' are marked. In-serts at the right-hand side providea survey about the time depen-dence of the intensity in the emis-sion bands at prominent excitationenergies. Left-hand side insertshows the complete emission

spectrum (from Ref. 17).

0z

Fig. 3. Energy level scheme for a solid Ne host and Xe; Kr and Ar 10-guest atom states. Arrows indicate the exciton states n = 1, n = 1,n = 2 of Xe for which the relaxation cascade (Fig. 4) has been

determined.

20-

CONDUCTION BANDS

. . -2 EXCITONS

Xep - GUESTKr 4p STATES

Ar 3p

Ne 2p VALENCE BANDS HOSTTES

Table I. Transition Energies (in Electron Volts) and Lifetimes (in 10-9 sec) of Rare Gas Atoms in a Ne Matrix and of Free Atoms (from Ref. 17)

Exciton Atomic Energy in Ne matrix Energy in Lifetimestate state Absorption'7 Emission'7 Emission52 free atom53 In Ne matrix,"' Of free atom

6s 1S5 8.34; 8.47 8.31n = 1 6s 1S4 9.06 8.61 8.61 8.44 2.4 + 0.2 3.46 i 0.09 (Ref. 54)

Xe/Ne 6s' 1s3 9.45n = 1 6s' 12 10.05 9.80 9.77 9.57 3.5 + 0.2 3.44 + 0.07 (Ref. 54)n = 2 5d 3d2 11.32 10.78 10.40 1.3 + 0.2 1.40 + 0.07 (Ref. 54)

5s 15 10.02 9.91n = 1 5s 14 10.6 10.10 10.16 10.03 2.5 0.2 3.18 + 0.12 (Ref. 54)

Kr/Ne 5s' 1s3 10.51n' = 1 5s' 1s2 11.22 10.78 10.64 3.1 b 0.5 3.11 i 0.12 (Ref. 54)n = 2 4d 3d5 13.35 12.12 12.04 13.0 ± 2 44.5 (Ref. 55)

4s 1s5 11.63 11.54n = 1 4s 14 12.51 11.70 11.71 11.62 5.8 + 0.3 8.4 (Ref. 56)

Ar/Ne 4s 1s3 11.81 11.72n = 1 4s' 12 12.74 11.92 11.92 11.83 1.2 + 0.2 2.0 (Ref. 56)n = 2 3d 3d5 14.82 13.93 13.86 420 + 20


onzz

8

I

- - - -

.2 .4 .6 .2 .4 .6

- is

. I . . . . . . .

ffi ffi i X

nJl

I

O-

In doped samples energy transfer processes becomeimportant. The competition of the processes listedabove with 3 energy transfer by coherent or diffusivemigration of free excitons and energy transfer of local-ized excitons by a Fdrster-Dexter-type interaction 4 2 43

has to be considered.To disentangle all these competing processes, systems

have been analyzed where only a few of these channelsare open. We will start with a discussion of rare gasatoms in rare gas matrices. In the excited states of theguest atoms only the first channel contributes to re-laxation. In this way this channel can be studied sep-arately. Next we turn to the localization processes offree excitons, the branching into the two types of lo-calized states, and to vibrational relaxation within themolecular-type centers. Finally some experiments aredescribed that represent a first attempt to tackle theproblem of relaxation in the free exciton states and oflocalization of free excitons in competition with energytransfer.

Ill. Excited States of Rare Gas Guest Atoms in SolidRare Gas Matrices

After a short characterization of the excited electronicstates of the guest atoms, the rearrangement of thematrix atoms around the excited atoms and the non-radiative and radiative electronic transitions within theguest atom states will be described. The energeticpositions of the occupied valence states of heavy rare gasguest atoms within the band gap of the matrix have beenderived from absorption experiments,444 5 from pho-toelectron yield,4647 and from photoelectron energydistribution measurements.48 49 Absorption44 45 andluminescence excitation spectra'7 (Fig. 2) yield the ex-cited states of the guest atoms within the host band gap.The excited states form, for each kind of guest atoms,two series of excitons that are separated by the spinorbit splitting of the valence states and which will bedenoted by n and n'. A survey of the valence states andthe exciton states for Xe, Kr, and Ar guest atoms in asolid Ne matrix is shown in Fig. 3. The binding energiesof the exciton series, where members up to n = 5 havebeen identified, are determined by the dielectric con-stant of the host and the effective mass of electrons inthe conduction band of the host.17,44-47,50,5' Accordingto the experimental results these states are Wannierexcitons that obey the effective mass approximation.The electron orbit for n 2 2 is large compared with thenearest neighbor separation. For the n = 1 excitonssome corrections have to be included to account for thesmaller electron orbit.45'51 Relative to the corre-sponding Rydberg transitions of the free atom the ab-sorption energies of the excitons in the matrix arestrongly blue shifted by -0.5-1 eV (Table I).

The emission bands were studied first by a-particle7

and x-ray52 excitation. The relaxation channels havebeen investigated by time and energy resolved lumi-nescence spectroscopy using monochromatized syn-chrotron radiation for excitation.'7 The emissionspectrum for excitation of a specific exciton allows anidentification of the corresponding emitting state, and

the energy difference yields the Stokes shift betweenabsorption and emission (Fig. 2). For the guest atomsin Ne, atomic-type emission due to the fine structurecomponents of ns and (n - 1)d states has been ob-served. n is the main quantum number of the lowestexcited state. The emitting states are s4 , 1S2, and 3d5for Ar and Kr and S4, S2, 3d2 for Xe in Ne. Theemission bands are redshifted compared with the ex-citation energies by -0.5-1 eV. Therefore, they are nowclose to the free atomic transitions (Table I). Fur-thermore, the radiative lifetimes in the matrix17 derivedfrom decay curves (Fig. 2) are similar to the free atomicvalues (Table I). From these observations the forma-tion of a bubble around the excited atom has beenpostulated7"17 similar to the case of He. In this bubblethe electronic wave function resembles the free atomiclimit. From the density dependence (Fig. 4) of the n= 1, n' = 1, and n = 2 exciton transition energies, 7 58

an increase by -30-100% of the nearest neighbor sep-aration in the bubble compared with the ground-stateconfiguration has been estimated.17 The large Stokesshifts correspond to very strong differences in the

intensity 3 4 5 6 7nearest neighbour

separation [Al

intensity

Fig. 4. Dependence of the energy position of the lowest states of Xe

atoms on the density of surrounding Ne atoms.5 8 Density is expressedby the mean nearest neighbor separation between a Xe atom andsurrounding Ne atoms. Ne density ranges from 0 through liquid andsolid phase. For solid Ne [density 1.44 (g cm-3) and nearest neighbor

separation = 3.13 A] the maxima of the excitation spectra1 7 (left-hand

side) have been included. Density around relaxed Xe atoms followsfrom a comparison with the emission spectra (right-hand side, hori-

zontal lines) (from Ref. 17).


electron lattice couplings between the ground state andthe excited states. From the Stokes shift Es and in-dependently from the large linewidth H(T) in emis-sion,5 2 a value of S 50 for the Huang Rhys couplingconstant 5 "13 is derived, for example, for the s4 decay ofKr. Again from S an increase in the nearest neighborseparation of AQ 2 A (i.e., 70%) can be predicted. Forthese estimates the following relations have been usedthat are based on the harmonic approximation withlinear coupling and a single characteristic phonon fre-quency hoxp in the strong coupling limit.4-13 M is thereduced mass of the system.

Es = 2Shcp, (1)

H(T = 0) = 2.36 V'hcop, (2)

Shwp= /2Mo.(AQ) 2 . (3)

A similar strong coupling has been derived for the n =1 state of Xe in Ar from the temperature dependenceof the absorption line.7 28 The rise times'7 in the timeresolved emission spectra, which are shorter than 10-1sec, represent an upper limit for the time required forthe rearrangement of the matrix. This upper limit isconsistent with theoretical estimates7 of 10-13 sec.

From the total intensity of individual emission bandsfor excitation of the n = 1, n' = 1, and n = 2 excitonstates, and from the corresponding time dependence ofthe intensity in the emission bands, a quantitativecascade for electronic relaxation has been determined.' 7

The relative intensities of the emission bands for oneexcitation energy yield the branching ratio for radiativeand nonradiative decay to different lower-lying elec-tronic states. The rise and decay times in one emissionband correspond to the times for population (for ex-ample, via relaxation from higher states) and depopu-lation (for example, due to relaxation to lower states).Thus the cascade can be built up consistently in popu-lating first the lowest state and going up stepwise tohigher primary excited states.' 7 Since Ne does not formbound molecular states with Xe, Kr, and Ar atoms, thecomplications due to molecular states, as in the puregases (see He), are absent. Excitation of the n = 1 im-purity state of Xe, Kr, and Ar in solid Ne causes a re-arrangement of the matrix leading to the formation ofthe s4 (3Pl) impurity state. On the basis of the ex-perimental data (Table I) for the radiative decay, it isapparent that the major contribution to the lifetime ofthe s 4 state originates from the radiative decay channelto the ground state. This channel is much faster thanthe two competing radiationless processes (Figs. 5 and6), i.e., radiationless relaxation either to the only lowerlying exited state s5 (3P2) or to the ground state.17Radiationless transition rates Wnr for relaxation be-tween electronic states, which are separated by an en-ergy difference AE of the two minima of the potentialsurfaces, are determined by the coupling constant S. Sdescribes the displacements Q of the equilibriumcoordinates of the two states involved [Eq. (3)] and theorder N = E/hwp. N corresponds to the number ofphonons that are emitted in the dissipation of theelectronic energy difference AE.A 3 For low temper-

atures an exponential decrease of the transition rateswith an increasing energy gap AE or order N is pre-dicted provided that S is not too large:

Wn,(T -°0) = /S exp(- S) exp(-yN),

,y = In(N/S) -1.

(4)

(5)

A contains the electronic matrix element. Accordingto this well-known energy gap law the radiationless re-laxation to the ground state is hindered by the very largeenergy gap. The separation from the s4 to the s5 stateis only 0.1-0.2 eV requiring a radiationless transition ofthe order of N = 10-30. In case the corresponding S isnot too large, the radiationless 14-15 decay will beeffectively blocked by the appreciable energy gap. Theenergy gap law is also manifested in the photoselectionof the n = 1' impurity states of Xe and of Ar in solid Ne.This excitation process, which populates the spin orbitstate of the n = 1 exciton, leads to the formation of themedium relaxed is2 (1P1) state (Figs. 5 and 6). Theexperimental lifetimes (Table I) are again dominatedby the pure radiative decay channel,17 so that radia-tionless electronic relaxation from 1s2 (1P1) to s3(3P),Is4(3P), and s 5 (3P 2 ) is not exhibited on the time scaleof 10-6 sec. The energy gaps of 0.2 eV for Ar and 1.1 eVfor Xe determined by the spin orbit coupling are suffi-ciently large to prohibit electronic relaxation. For Krin solid Ne there is an interesting complication due toimpurity-impurity energy transfer, because in thissystem there is an accidental energetic overlap betweenthe medium relaxed s 2 ('PO) state and the n = 1 (3PJystate. The rise and decay times of the emission bandsof the is 2 and the S4 states after excitation of n' = 1excitons indicate that a resonant dipole-dipole energytransfer42 43 takes place from an excited Kr atom in theis2 state to a nearby Kr atom in the ground state.' 7

The Frster-Dexter radius for this transfer is 21 A.Next we consider the fate of n = 2 guest atom exci-

tations in solid Ne. There are several characteristicdifferences for the n = 2 exciton relaxation cascades forXe, Kr, and Ar guest atoms in a Ne matrix broughtabout by an increasing spread on an energy scale of the(n + )s, the (n - 1)d, the np, and the ns' states in goingfrom Xe to Ar. This spread results in groups of closelying levels, which are separated by increasing gaps(Figs. 5 and 6). Excitation of n = 2 excitons in Xe leadsto a population of the medium relaxed 2s4 and 3d2 states(Fig. 5). The 3d2 state is separated from the next state3dl by a gap of 0.18 eV. It was experimentally estab-lished that the 3d2 state decays radiatively to the groundstate with a time constant of 1.3 X 10-9 sec as well asnonradiatively to 3d'with a time constant of 1.0 X 10-9sec. We note that in this case radiationless processesof the order of N = 30 can have time constants as fastas 10-9 sec. This observation is incompatible with theconsiderations based on the energy gap law and can berationalized in terms of the cancellation effect, whichis exhibited when N S in Eqs. (4) and (5). The energyinterval between the 3d and the 1S2 states is so denselypopulated with other states (Fig. 5) that the radiation-less processes will be extremely fast. Radiative tran-


0

C:1

w

Configuration Coordinate

Q

Fig. 5. (Left): experimental radiative (a) and nonradiative ( 4)

electronic relaxation pathways and time constants in (10-9 sec) for

Xe in Ne in a configuration coordinate diagram. Excitation channels

n = 1, n' = 1, and n = 2 and the matrix relaxation (a) are included.(Right) atomic energy levels (Paschen notation) of Xe with some

lifetimes for radiative transitions to the ground state (-). Long bars

correspond to states with allowed, short bars to forbidden, transitionsto the ground state (from Ref. 17).

20

~~~~~~ 15

0)

t 100

.I

5

5 10 15 20 25 30

3.7ns Temperature( KI\3.7 ns

20ns Fig. 7. Temperature dependence of thetransition rate of Kr n = 1 excitons in an Armatrix. Crosses, experimental points; solid

line, calculated (see text) (from Ref. 59).

')20-7Ons

Alp

2.Ons

X8.4 ns

i 8>l s Fig. 6. Relaxation cascade for Ar in Ne similar to1is the results shown in Fig. 5. Important radiative

transitions between excited atomic transitions areincluded (a) (from Ref. 17).

Table II. Energies and Intensities in Luminescence Bands of Free Excitons a, Atomic Type b, Molecular Type Vibrationally Excited c, and Molecular Type

Vibrationally Relaxed Localized Excitons d

Molecular Atomic

Energy Relative intensity center center

a b c d a b c d hOD 2B ELR Hm ELR Hm

Ne 16.5-17 13-16 1.0 1.0 0.0064 0.4 2.0 0.0003 1.25 0.0008

Ar 12.1 11.64, 11.58 11.37 9.8 1 x0-4 3 X 10-2 5 X 10- 1.0 0.008 0.7 1.86 0.002 1.05 0.001

Kr 10.15 10.05 9.7 8.4 5 X 10-3 5 X 10-3 10-2 1.0 0.0062 0.9 1.38 0.01 0.77 0.01

Xe 8.35 7.6, 7.1 10-3 1.0 0.0055 0.9 0.85 0.02 0.05 5.6

Note: The values have been estimated from experimental data for Ne from Ref. 68, for Ar from Ref. 26, for Kr from Refs. 24 and 71, and

for Xe from Ref. 26. hWD, 2B, ELR, and Hm are the Debye energies, the free exciton bandwidth in k space, the lattice relaxation energy, and

the barrier height for localization, respectively, according to Ref. 26. All energies in electron volts.


sitions, i.e., the dipole-allowed decay from the 3d5 state,are not observed. In the is 2 state the radiationless re-laxation cascade terminates, as has been previouslynoted. No relaxation to 1S3, 1S4, or iss is observed.

The relaxation cascade for the n = 2 excitation of Arin solid Ne (Fig. 6) results in an initial population of themedium relaxed 24 state, which relaxes effectively tothe lowest 3d states (3d5 and 3d6). The gap betweenthe 3d and (4p, 4p') states is sufficiently large to makenonradiative decay rather slow. There is branchingbetween radiative decay of the 3d5 state (420 X 10-9 sec)and slow nonradiative decay to 4p' and 4p states. The(4p', 4p) states are separated by a large energy gap from,the 4s and 4s' levels. Therefore both the 4p' and 4pstates are depopulated radiatively to the 4s as well as4s' state with similar time constants. The intensity isdistributed between radiative channels from the finestructure components of the 4p' (1S2, 1S3) and the 4p(1S4, Is) states with the branching ratios given in Fig.6. The relaxation cascade of Kr in solid Ne is similarto that of the Ar impurity state in the same matrix.' 7

The radiationless relaxation rates are strongly in-fluenced by the matrix and by the temperature. Thetemperature dependence of the lifetime of the Kr1s4 (3 Pl) state in an Ar matrix has been studied as anexample.59 The S4 state is depopulated by radiativedecay to the ground state and by nonradiative decay tothe s 5(3 P2 ) state. Figure 7 shows the temperaturedependence of the decay rate of the 1s4 (3 P1) state, whichexhibits the temperature independent relaxation to Ssat low temperatures and as an activated process athigher temperatures. An analysis of the data with theexpressions given in Ref. 60 can be performed (fit in Fig.7) taking AE = 72 meV and hp = 4 meV, i.e., N = 18.The separation of S4 and ls5 in the Kr matrix of 72meV derived in this way is close to the separation in thefree atom (Table I).

IV. Exciton States of Pure Rare Gas SolidsThe analysis of the dynamics in the excited states of

pure rare gas solids requires the spectrum of excitonstates' 6 as input data.

A. Free and Localized Exciton States

The spectrum of free exciton states with wave vectork = 0 is well known from reflection and absorptionspectroscopy.16 ,61 ,62 It consists of two series of excitonsseparated by the spin orbit splitting of the valencebands. Up to five members of the series have beenidentified. For the n = 1 excitons the energy of thelongitudinal excitons at k = 0 has been determined inaddition to that of the transverse excitons.62 The cal-culations of Knox3 63 show that two additional n =

branches exist that are not accessible by optical ab-sorption. The dispersion of the n = 1 exciton bands vswave vector k has been calculated for Ar.363 Thebandwidth 2B has been estimated also from the widthof the valence bands6 4 for Xe, Kr, Ar, and Ne by Fugol'2 6

(Table II). A schematic illustration for the n = 1 andn' = 1 states in Kr is shown in Fig. 8. In addition tothese bulk excitons surface excitons have also beenobserved.6 2

Three types of localized exciton states have beenobserved in luminescence spectra.7 ,2 4-2 6 ,2 8 They havebeen identified in analogy to emission spectra in thegas phase72628 at high and low pressures. Atomictype localized n = 1 excitons 7 24-2 6

,2 8' 66- 7' are excited

rare gas atoms where a cavity has been formed sim-ilar to those in He and similar to guest atom statesin rare gas matrices. In molecular-type localizedstates7 ,24-26 ,28

,66 -79 a neighboring rare gas atom moves

to the excited atom, and an excimer with a smallerequilibrium separation than the nearest neighbor dis-tance in the undistorted crystal is formed (see He2* inFig. 1). Two species of molecular-type states withdifferent lifetimes24 25 28 ,70 ,71,76-78 in the 10-9 and10- 6-sec regions have been identified. They belong tothe l; and 32u branches of the molecular potentialcurves (Fig. 8). The energy vs the internuclear distancein the molecular-type states is sketched also in Fig. 8.By transient absorption spectroscopy'8 higher atomicstates, i.e., the fine structure components of the 2pstates, have been observed in solid Ne, and higher mo-lecular states have been found in solid Ne, Ar, and Kr.Now we proceed to the dynamics in the excitonstates.

.'

co

zJ

02 3, 4 0

r (A) kT/a

Fig. 8. Scheme for exciton states in solid Kr. (Right) dispersion ofthe n = 1 and n' = 1 excitons vs the wave vector k of the excitons inanalogy to the calculation for Ar.3'6 3 T and L indicate transversaland longitudinal excitons, and the dashed lines correspond to opticalforbidden exciton branches. (Center) exciton series at k = 0 observedin absorption experiments. 6 62 (Left) energy of molecular-type lo-calized excitons vs the internuclear separation r of an excited Kr atomand a neighboring Kr atom in analogy to molecular potential curves

for Xe.65


- a .

B. Self-trapping of Free Excitons and Relaxation inLocalized States

The emission bands and their relative intensities aresummarized in Table II in a tentative way.24 26' 28'68'71a indicates emission from free excitons, b from atomiccenters, c from vibrationally hot molecular centers, andd from vibrationally relaxed molecular centers. It isimmediately apparent from Table II that 99% of theluminescent intensity is emitted from localized statesin all solid rare gases. This implies that the self-trapping process is at least a factor of 100 faster than theradiative decay time of free excitons. Self-trappingoccurs within a time of <10-"1 sec. Self-trapping canbe treated by the theory developed by Toyozawa8 andRashba,1" which is presented also in the paper by Toy-ozawa.2 9 The Lorentzian line shape of the excitons inabsorption 6 2 indicates that initially free excitons arecreated in solid rare gases. The free excitons are stablewhen the lattice relaxation energy ELR is smaller thanthe exciton kinetic energy given by the bandwidth in kspace, i.e., ELR < B or vice versa. Furthermore thiscontinuum theory 8 predicts a barrier of height Hm be-tween the free and localized states, which has to becrossed for localization either by thermal activation orby tunneling. Fugol' and Tarasova 2 6 ,69 derived, in asemiempirical analysis, ELR, Hm, and 2B from spec-troscopic data (see Table II). This analysis explains theexperimental results in a qualitative way. It predictsthe observed stability of the molecular-type centers inNe, Ar, and Kr, and it describes the trend to strongeremission from free excitons in going from Ne to Xe byan increasing barrier Hm. But the predicted instabilityof atomic type centers in Xe and the very large barrierfor formation of molecular-type centers are in dis-agreement with the weak free exciton emission band a(Table II).

This continuum theory8 does not include the micro-scopic structure of the self-trapped centers withoutadditional input data. A microscopic calculation80'8'similar to that for self-trapping of holes in alkali ha-lides8 2 can go further. In the case of rare gas solids, thecalculated molecular potential curves for excim-ers19 3233 83 84 provide information concerning thebranching ratio into atomic and molecular centers. Thepotential curves for He' (see Refs. 19, 32, and 33) andNe* (Ref. 84) show humps -2-4 A, which have to becrossed in the formation of molecular centers. Thesehumps reduce the probability for the molecule forma-tion. They push away neighboring atoms thus favoringatomic centers as observed in solid Ne. Kunsch andColetti85 calculated the local structure around an ex-cited Ne atom from these potential curves. The sepa-ration of the excited atoms from the first shell ofneighboring atoms increases by a factor of 1.37 com-pared with the undistorted lattice. This distortionextends up to the sixteenth shell where it causes de-viations of 1%.

After formation of molecular centers, vibrationalrelaxation in the molecular potential curve will reducethe energy of the centers further.7 Vibrational relax-ation follows an energy gap law similar to Eq. (4). The

rate constant decreases exponentially with the order Ngiven by the ratio of the vibrational spacing and acharacteristic phonon energy. N increases from 4 to 6in going from Xe to Ar, which explains the stronger hotluminescence band c. N jumps to 18 in the case of Ne,thus vibrational relaxation will be incomplete.7 Dueto the anharmonicity in the potential curves of Ne therelaxation is stopped within the fourth or third vibra-tional level.86

C. Exciton Scattering, Self-trapping, and EnergyTransfer

Since strong luminescent emission is observed onlyfrom the lowest localized states, it is necessary to searchfor faster processes than radiative decay to analyze re-laxation processes in free and in higher self-trappedexciton states. Two-photon spectroscopy can providea tool for future investigations as will be discussed bySaile.31 It has been shown that energy transfer pro-cesses are fast enough to compete with localiza-tion4 6-4850 87-89 and free exciton scattering.4 8 89 Twodifferent methods of energy transport by excitons arepossible apart from electromagnetic transport3 :hopping transport of self-trapped excitons via a F6r-ster-Dexter 4 2 43 type of energy transfer, and wave packettransport of free excitons. In the case of wave packettransport, either coherent or diffusive motion willdominate depending on whether the mean free pathbetween scattering events with phonons and latticeimperfections is larger than, or of the order of, the latticeconstant. To distinguish between energy transfer fromlocalized or free excitons, three criteria have been usedin the experimental investigations.

First, the amount of transferred energy per excitonis characteristic of a specific exciton state. For example,the energy of localized excitons is more than 1 eV lowerthan the energy of free excitons. In Ar and Ne matricesthat have been doped with Xe atoms,48 the ionizationenergy of Xe atoms is lower than the energy of the freen = 1 excitons of the matrices (see Fig. 3). Some of thefree electrons produced by ionization of the guest atomsleave the sample and can be detected. The energydistribution of the emitted electrons has been measured.The electrons are ejected either by direct ionization ofthe guest atoms via absorption of the exciting photonsby the guest atoms or via absorption of the light in thematrix and creation of excitons of the matrix and sub-sequent energy transfer from the matrix excitons to theguest atoms. In the second case the energy of theemitted electrons carries the information about thestatus of relaxation of the matrix excitons at the mo-ment of energy transfer. Figure 9 (lowest curves) showsthe energy distribution of the emitted electrons forphoton energies lower than the n = 1 exciton energy ofthe matrix, where all the light is absorbed in the guestatoms that are directly ionized.48 Further results areshown for photon energies corresponding to the n = 1,n' = 1 and n = 2, n' = 2 excitons. In these cases es-sentially all the light is absorbed by matrix excitons, andthe observed electrons stem from energy transfer of thematrix excitons to the Xe guest. The electrons ejected


1 2KMNTIC ENERGWH

3 1 5 6KINETIC ENERGYleVJ

Fig. 9. Electron energy distribution curves (counting rates vs kinetic energy) from films of 1% Xe in Ar and 1% Xe in Ne for several excitationenergies below and within the n = 1, n' = 1 and n = 2, n' = 2 host bands (after Ref. 48). Excitation energies are listed on the horizontal lines.Diagonal bars indicate the highest possible electron energies. Electrons up to this energy are expected when the whole free exciton energy

is transferred. Two maxima are separated by the spin orbit splitting A 0 of Xe (see Fig. 3).

by ionization of 1% Xe in Ar matrix carry the full energyof the free n = 1 and n' = 1 excitons of the Ar matrixwhen these excitons have been excited. Also a con-siderable number of n = 2 and n' = 2 excitons transferthe full free n = 2 (n' = 2) exciton energies. But smallerenergies due to partly relaxed exciton states are alsotransferred. The low-energetic electrons are attributedto transfer from localized n = 2 excitons. For 1'Xe inthe Ne matrix and excitation of the n = 1 and n = 2excitons of the Ne matrix, only the energy of the local-ized atomic Ne centers is transferred to Xe atoms. Thisshows that in the case of n = 2 excitons in Ne, for ex-ample, more than 3 eV of the free exciton energy havebeen dissipated to the Ne lattice, and the exciton hasbeen also localized before energy transfer is completed.From these experiments a time hierarchy for relaxationand energy transfer has been derived.25 48

Second, the range of the energy transfer process istypical for the exciton state involved. Localized exci-tons in solid rare gases are deeply trapped by e- eV, andthermal activation can be excluded. In this case energycan be only transported via pairwise dipole-dipole in-teraction 4 2 43 between the localized exciton and a guestatom or an atom at a boundary. The efficiency of thetransfer process decreases with r 6 or r 3 , when r is thedistance to the acceptor atom or metallic boundary,respectively.4 2 '4 3 '8 9 '9 0 Free excitons are able to migrateto the vicinity of a guest atom or boundary. The rangeof energy transport can depend in this case on the wavevector and electronic state of the free exciton. Fordiffusive motion the range is determined by the diffu-sion length 1, which follows from the diffusion constantD and the lifetime -r of the free exciton state.

= v'-D-,-r . (6)

X is not the radiative lifetime but the self-trapping timeor an even shorter time. When D is dependent on thespecific free exciton state or even on the kinetic energyof the specific exciton, corresponds to the lifetime ofthis state for scattering to lower kinetic energies or tolower exciton states. In solid Xe films deposited ontoan Au substrate, exciton diffusion to the Au substratehas been observed.8 7 At the metal surface electrons areejected due to a Penning-type transfer of the excitonenergy to the metal. Part of the ejected electronspenetrates the solid Xe films, reaches the vacuum in-terface, and can be detected. The energy transfer rangehas been determined from the thickness (100-1000-A)dependence of the number of emitted electrons fordifferent Xe excitons. An average diffusion length of300 A has been obtained.8 7 Similar experiments havebeen performed for Kr overlayers on an Au substrate 89

The efficiency for conversion of excitons to free elec-trons at the Au substrate is 10 times larger than thephotoelectron emission efficiency at the same energy.This proves that the conversion is a true surface processsimilar to electron emission by decay of metastable raregas atoms on metal surfaces.91 Even more interestingthe derived diffusion length is strongly dependent onthe primary excited exciton state. The diffusion lengthincreases monotonicallywith increasing energy of thefree excitons, 8 9 starting with about I = 30 A at the lowenergy tail of the Kr n = 1 exciton and reaching about300 A in the n = 2 exciton (Fig. 10). Figure 10 demon-strates that energy transport is conducted essentiallyby free excitons, because in the transport by localizedexcitons only one type of exciton, independent of theexcitation process, would be involved. Furthermore,transport is faster than relaxation within the free exci-ton states, and it is more efficient for higher excitonstates as is evident from the monotonic increase of


I-

-Jz0U-

IL

1U.U 1.5 11.0PHOTON ENERGY (eV)

11.5

from n = 1 to n' = 1 to n = 2 (Fig. 1(crease of within each exciton bandquestions concerning the relationprobability and kinetic energy of E

cerning the rate constants for thermciton band and energy transfer.

Third, investigation of the time depopulation of the primary excitedthe population of the acceptor stamethod of studying the nature of encesses as has been shown for moleiSuch time resolved luminescent expecarried out for rare gas solids only fbetween Kr atoms in a new matrix.'of time resolved techniques in theusing synchrotron radiation for excitespectroscopy as discussed above, wildiagnostic tool. The investigation outilizes the advantages of a fast procrestrictions due to the limited radiatvolved in luminescence studies.

V. Summary

The dynamics of electronically ex(and matrix isolated systems can novprogress in experimental technique.line shape analysis in absorption anctime and energy resolved luminescspectroscopy, and (3) transient ansorption spectroscopy. These experthe tunability and time structure (

diation.9 5 The advent of structui10-10-sec range will stimulate this f

Fig. 10. (Bottom) diffusion length of Kr excitons vs the excitationenergy of the excitons. Dashed lines indicate the trend. Scatteringof the points corresponds to the uncertainties involved in the evalu-ation of I (from Ref. 89). (Top) absorption coefficient k of Kr(imaginary part of the complex refractive index) vs photon energy(from Ref. 92) used in the evaluation. Maxima correspond to the n

= 1, n' = 1, and n = 2 excitons.

This paper is based on investigations at the syn-chrotron radiation laboratory of DESY in Hamburg incollaboration with several groups. It is a pleasure tothank U. Hahn, E. E. Koch, V. Saile, and G. Zimmererfrom the Lab in Hamburg, H.-W. Rudolf and W.Steinmann from the University of Munich, J. Jortner,Z. Ophir, and B. Raz from the Tel Aviv University, andR. Haensel, M. Skibowski, and H. Wilcke from theUniversity of Kiel for their cooperation.

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/ 030 ~ ~~~/ 0

/ 00

// 0 0

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0 / 0 /

0 // /

0

o- J-

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dynamics of localized excitations from energy and time resolved spectroscopy

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