colloidal zn1,-cds: optical saturation of the exciton band and

1630 J. Opt. Soc. Am. B/Vol. 7, No. 8/August 1990

Colloidal Zn1,-CdS: optical saturation of the excitonband and primary photochemistry

studied by subpicosecond laser flash photolysis

N. P. Ernsting and M. Kaschke*

Abteilung Laserphysik, Max-Planck-Institut fur biophysikalische Chemie, Postfach 2481, D-3400 Gttingen, FederalRepublic of Germany

H. Weller and L. Katsikas

Bereich Strahlenchemie, Hahn-Meitner-Institut Berlin, D-1000 Berlin 39, Federal Republic of Germany

Received August 4, 1989; accepted March 6, 1990

Quantum-size crystallites of Zno 95Cdo05S in an aqueous colloidal solution were optically excited using intensesubpicosecond laser pump pulses tuned to the exciton band. Optical probing in the UV registered saturationand the kinetics of ground-state recovery due to carrier recombination, with lifetimes in the 0.8-30-psec range.Optical probing at 616 nm monitored the yield of Auger electron emission. The saturation and yield curves, asa function of pump fluence, are described by a simple kinetic model that involves the exciton lifetime beforetrapping (-30 fsec) and the maximum number of electrons (-16) that can be emitted per particle.

INTRODUCTIONThe nonlinear-optical properties of direct-gap semicon-ductors have been examined intensively over the past fewyears. Here we address those nonlinear properties thatare derived from the absorption of multiple photons andthat are thus caused by a high density of photogeneratedcharge carriers. The material systems that have beenstudied include bulk crystalline semiconductors' and mi-crocrystals that are embedded in a glass host.2 7 Ex-amples of the latter type are the familiar glass color filtersfor the green and red spectral region. They contain crys-tallites of CdS,-.Sex, and their absorption edge is con-trolled by the proper choice of the Se mole fraction x andaverage particle size. A relatively young class of materialsconsists of very small (diameters ranging up to 100 A)crystallites. These microcrystallites are usually preparedby chemical reaction, either in a polymer film89 or as a col-loid from solution.10 '19

The electronic structure of semiconductor crystallitesdepends pn their size. Here it is useful to distinguishcrystallites, which behave as the corresponding bulk semi-conductors do, from microcrystallites, in which an elec-tron and a hole that are created by optical absorption areconfined in close proximity to each other owing to thesmall size of the particle.20 In the first case electron-hole pairs, which are bound by Coulombic interaction, i.e.,bound excitons,2 ' will normally exist only for a brief timebefore the thermal dissociation of the electron and thehole into the conduction and the valence band, respec-tively. Hence, at room temperature the excitonic absorp-tion below the band gap is often diffuse. In the secondcase, which involves quantum-size particles, i.e., with adiameter of the order of the Bohr diameter for a boundexciton in the bulk semiconductor, spatial dissociation

cannot occur. The effect of spatial confinement on elec-tronic structure is threefold. First, there are no valenceor conduction states near the Brillouin zone center, whichrecords long-range crystallinity. 4 Second, spatial con-finement terms are added to the band energies; thereforeoptical absorption at the bulk band gap and that cor-responding to band-band transitions is greatly reduced.Third, the electron and hole wave functions always over-lap appreciably. In this sense, the lowest states of anelectron and hole in a small semiconductor microcrystalmay be called excitonic. 4 The excitonic absorption takesover the integral oscillator strength, which in large crys-tals is carried by band-band transitions near the Brillouinzone center.2 2 Therefore very small particles of ZnS, forexample, show an intense, structured absorption band atthe lowest absorption energies that correspond to the cre-ation of an exciton.14

In large semiconductor particles, the effects of quantumsize are insignificant. The absorption of multiple pho-tons, for example, from the leading part of a short laserpulse, leads to appreciable densities of charge carriers,which in turn modify the crystal band structure and theexcitonic levels below the band gap. There are three basicphotophysical effects: band-gap renormalization, 2" bandfilling,2 4 and screening.2 5 Free charge carriers lowerthe band gap by the exchange-correlation energy of theelectron-hole liquid.2 6 This band-gap renormalizationresults in altered Fermi occupation probabilities forcharge carriers at their respective band edge. Band fill-ing2 4 and concomitant phase-space filling then reduces op-tical absorption for the remaining part of the laser pulse.Free charge carriers also screen the Coulomb interaction,which is responsible for bound excitons,2 527 so that the ex-citonic binding energy decreases. At the Mott density for

0740-3224/90/081630-08$02.00 © 1990 Optical Society of America

Ernsting et al.

Vol. 7, No. 8/August 1990/J. Opt. Soc. Am. B 1631

free carriers, bound excitons are no longer stable, and theexcitonic levels merge into the renormalized band gap.

Crystallites are of intermediate size if their diameter isseveral times the diameter of the bound exciton in the cor-responding bulk material. With increased screeningowing to photogenerated charge carriers, the excitonicdiameter approaches the physical diameter of the crystal.Consequently the exciton energy is raised by confinementterms, which results in a blue shift for the excitonic absorp-tion in the course of excitation.28 In quantum-size micro-crystallites, the electronic wave functions of the lowest,excitonic states encompass the entire crystallite. There-fore screening by photogenerated free or (possibly) bybound charge carriers should be more effective than thatby larger particles; also, the effects should be more pro-nounced because of the increased spectral weight of theexcitonic transitions.2 9 Yet semiconductor-doped glassesthat exhibit the largest quantum confinement have gener-ally shown the smallest absorption bleaching. This hasbeen attributed to a comparatively large electron-holerecombination rate for the quantum-size particles, sothat the (stationary-state) density of photogeneratedcharges that affect the optical properties should be low inthis case.6

Surface chemistry is usually needed in order to stabilizethe colloidal microcrystals in solution against aggregation.As the particle size decreases, the chemical nature of thesurface becomes increasingly important regardless of thehost material. Thus relatively small absorption bleachingin quantum-size semiconductor particles may also belinked to photochemical changes during excitation, whichwill mainly involve traps for electrons and holes, locatedon the crystal surface. In quantum-size CdS, for exam-ple, holes can be trapped at the surface by oxidizing a freevalence of S2 to form a sulfide radical anion, S-.30

In this paper we distinguish experimentally betweenthe original exciton and the trapped electron-hole pairs.We examine quantum-size Znl-,CdxS as a colloid in water.Using subpicosecond pump pulses, the steady-state densityof excitons is monitored indirectly through Auger emissionof electrons on further excitation. The recombination oftrapped electron-hole pairs is indicated by ground-staterecovery. Specifically, we report (i) the kinetics ofground-state recovery at 308 nm, (ii) the saturation char-acteristics for 0.26-psec pump pulses at 308 nm, (iii) therelative yield of photoproducts that absorb at 616 nm(mainly solvated electrons) as a function of pump energydensity.

EXPERIMENTAL

Sample PreparationAqueous stock solutions were prepared of Zn(CI04)2 and ofCd(C104 )2 (both 0.1 M) and of sodium polyphosphate(Riedel-deHaen; 0.1 M, if a molecular weight of 609 is as-sumed). The synthesis was carried out in a 2-L flaskthat was sealed against air and fitted with a septum, a pHelectrode, and a glass frit for bubbling with Ar.

To 352 mL of water in the flask were added 22.80 mL ofthe Zn solution, 1.20 mL of the Cd solution, and 24 mL ofthe polyphosphate solution. The total Zn2+ and Cd2+ con-centration was thus 6 x 10-3 M. The solution was de-

gassed thoroughly for 5 min by bubbling with Ar. Thenthe pH was adjusted to 11.0 by using a 1N NaOH solution,and Ar bubbling was resumed for at least 20 min. Finally,42 mL of gaseous H2S was quickly injected into the volumeabove the solution, and the flask was vigorously shakenfor 15 sec. The resulting ZnO95Cdo.05S colloid was agedovernight, which led to a steepening of the absorptionedge caused by annealing of crystal imperfections andsome reduction in particle size dispersion."' Transmis-sion electron microscopy showed a mean particle diameterof 40 A.

Laser SystemThe subpicosecond laser system is based on a XeCl* ex-cimer laser with two parallel discharge tubes (LambdaPhysik EMG 150). The system provides intense pumppulses at 308 nm with a pulse duration of 0.26 psec, whichis mainly determined by the XeCl* gain bandwidth.

Two different approaches were used to generate subpi-cosecond fundamental red pulses at 616 nm. The firstapproach used a cascade of short-cavity dye lasers3' thatpumped a microscopic distributed feedback dye laser3 2 thatwas tuned to 616 nm. The second approach employed acolliding-pulse-mode laser (FSU Jena Laserinstruments).3 3

In either case the short red pulses were amplified in achain of dye-laser amplifiers that were pumped by the out-put from the first discharge channel of the excimer laser.Part of the amplified red pulse was used for probing (afterappropriate attenuation). The remainder was frequencydoubled to 308 nm. The doubled pulses were then ampli-fied in two passes through the second channel of the ex-cimer laser. Final UV pulse energy was typically 1.5 mJ,of which 5% was contained in a low-intensity, 15-nsec back-ground pulse owing to amplified spontaneous emission.The duration of the short UV pulses was determined froman autocorrelation using two-photon ionization in 1,4-diazabicyclo[2.2.2]octane (DABCO) vapor.

The pump-probe setup for narrow-band probing at 308or 616 nm has been described in Ref. 34.

RESULTSThe absorption spectrum of colloidal Zno95Cdo0 5S in wateris shown in Fig. 1. The corresponding bulk band gap(taken as the appropriate linear combination of the bulkband gaps of wurtzite ZnS and CdS) is also indicated in-the figure. The red-edge absorption of the colloidal soluvtion is clearly shifted to higher energies from the bulkband gap, indicating quantum confinement. Alsofgivenin the figure is the particle diameter as function of thewavelength of the first excitonic transition, according to asimple theory [a H atom in a spherical box, with a finitepotential wall height of 3.8 eV (Ref. 35)]. From this curvewe estimate the mean particle diameter of 40 A, which isin agreement with the transmission electron microscopyinvestigations. The concentration of colloidal particlesshould then be -0.54 x 10-5 mol/L; the absorption crosssection of a particle at 308 nm is inferred to be 25.4 A2.

Figure 2 shows the temporal development of optical den-sity at 308 nm after excitation with a pump pulse of 0.26-psec duration at 308 nm. The kinetic curves wererecorded for various pump energies per area, or pump flu-

Ernsting et al.


energy / eV

1.5

._ 1.0

a)-O

° 0.5. _

0.0

0.0

250 300 350 400

wavelength /nm

Fig. 1. Solid curve: Absorption spectrum of aqueous colloidalZno95Cdoo 5S. Dotted curve: Particle diameter estimated fromthe spectral location of the exciton band.1136

I~~~ Q0.71511ll1l

0.70711'iiii 1>.3 ps 30 ps

0.696

1.3 ps c

0.691 - ,

>1 ~1.3 psdC~~~~~~

-O

.U0.715

0`0.682 .... 1.0 Ps

0.60 I

0.50

I 0 . 1 . I T r T 0 I I I-5 0 5 10

TIME / psecFig. 2. Temporal behavior of optical density at 308 nm for exci-tation with 0.26-psec pulses at 308 nm. Small-signal optical den-sity was 0.715. Fluences (in photons per square angstrom) werea, 0.116; b, 0.289; c, 0.578; d, 1.16; e, 2.89. The data werefit by instant rise and biexponential decay, which was convolutedwith Gaussian pump- and probe-pulse shapes (full width athalf-maximum 0.26 psec); the corresponding lifetimes are alsoindicated.

ences. Measurements are indicated by error bars, andthe solid lines are the result of fits as described below.During the pump pulse, transient bleaching occurredwithin the experimental time resolution. With increasingpump fluence, the decrease in optical density at 308 nmbecame larger, and a fast decay process in the 1-psec timerange became more pronounced. In the measured timerange of 10 psec, the experimental data can be fitted by aninstantaneous rise and a biexponential decay with life-times of 0.8-1.3 and 30 psec, convoluted with Gaussianpump- and probe-pulse shapes. However, nanosecond ex-periments show that the decay of bleaching extends intothe microsecond time range. Therefore these fits mayreflect only characteristic peaks in a wide distribution oflifetimes. Deviations at time t 0 psec for the highestfluence i.e., for curve e in Fig. 2, are due to two-photonabsorption by the solvent water.

Small-signal optical density at 308 nm was 0.715, asmeasured with a conventional spectrophotometer. Themeasured optical densities just before the short pumppulse are seen to be lower than the small-signal value.This is explained as initial bleaching by the preceding am-plified spontaneous emission.

Photochemical changes were monitored by transient ab-sorption at 616 nm. The rise of transient absorption oc-curred within the time resolution of this measurement,0.5 psec (obtained by cross correlation of pulses at 308 and616 nm). No significant absorption decay was observedfor times up to 10 psec after excitation.

Figure 3 shows the maximum changes of optical densityfrom the small-signal values at 308 and 616 nm for 2 mmof the colloidal solution as a function of pump fluence.At the top of the figure the pump fluence has been trans-lated into the number of photons absorbed per particle(see below).

DISCUSSION

The colloidal solution of ZnO.95Cd005S in water shows anexcitonic absorption band centered at 300 nm. The spec-

0.35

0.30

a 0.250C4- 0.200

cu 0.15

ct 0. 1 0

C' 0.05

0.00 0.0

calc. no. of photons absorbed per particle

0 10 20 30 40 50

1.0 2.0 3.0 4.0 5.0fluence / e16 photons cm-2

Fig. 3. Maximum changes of optical density from the small-signal case. Squares: Changes at 308 nm, from fits of Fig. 2.Circles: Changes at 616 nm, measured i psec after excita-tion. Curves are the result of model calculations (see text). Thedashed curve indicates the calculated contribution that is due to616-nm absorption by holes only.

. . . . .

Ernsting et al.


tral shift from the bulk band gap, estimated at 330 nm,indicates confinement in particles with a diameter of ap-proximately 35-40 A." A particle of this size can accom-modate only -420 unit cells of wurtzite ZnS. In bulkZnS, on the other hand, the binding energy Exb for boundexcitons is 80.9 meV.'6 One has

with Al= me* 3' + miV', (1)

where a, denotes the bulk excitonic radius, me* the effec-tive electron mass, and mi the isotropic hole mass.36

Using me* = 0.28mo and mi = 0.54mo (mo is electron restmass),3 7 we estimate the bulk exciton diameter to be 32 A.The microcrystallites in aqueous colloidal solution thusbelong to the regime of strong confinement. In order toget a feeling for the size of the particles, we first estimatethe transit time for a classical electron. The velocity v ofthermal electrons in the crystallite is

v = (3kT/me*) 112 = 1.85 x 107 cm/sec; (2)

hence the transit time through a 40-A microcrystalliteshould be 22 fsec. Now we return to quantum physics.Because of strong confinement, the is electron wave func-tion and the ls hole wave function have appreciable valuesbeneath and near the surface of the microcrystal, whichresults in good overlap with wave functions of localizedsurface states of lower energy. It is therefore reasonableto expect extremely fast trapping of photogenerated chargecarriers by these surface states, on the femtosecondtime scale.

Photochemically, trapping of holes means oxidation ofS2 to produce a sulfur radical anion S- . These show abroad absorption with a maximum of -480 nm that ex-tends far into the red spectral region. The assignment ofthis band to S- could be confirmed by pulse radiolysisexperiments in which surface S -'would be generated in-dependently from the photochemical effects that follow op-tical absorption inside the microcrystal.3 0

Trapping of photogenerated electrons in colloidal CdSprobably takes place at shallow traps associated with sur-face Cd2".

Auger Processes of Aqueous ColloidalZn(Cd)S MicrocrystalsFor colloidal CdS and Cd3 P2, it was reported3 8'3 9 thatnanosecond excitation leads to hydrated electrons, whichmay be detected by their absorbance at 616 nm. By anal-ogy we also attribute the absorbance change at 616 nmunder subpicosecond excitation to the formation of sol-vated electrons. This assumption is corroborated by fem-tosecond experiments with CdS and ZnS in which thespectrum of the hydrated electrons was recorded. Wewill report on these measurements in a forthcomingpaper.4 0 In the experiment discussed here, the highestpump fluence results in the absorption of more than50 photons per particle within 0.26 psec (see Fig. 3) and ina correspondingly large density of photogenerated, trappedand free, charge carriers. At equivalent densities forbound excitons in bulk semiconductors, Auger emission ofan electron, with concomitant exciton-exciton annihila-tion, becomes likely.21'4' From our data we estimate thehighest quantum yield for emitted electrons to be 36%.This has to be compared with a quantum yield of 3% for

nanosecond excitation with comparable fluence (as deter-mined in an independent experiment). Since the absolutenumber of photons absorbed per particle and photolysispulse was the same in the subpicosecond and nanosecondexperiments, the difference lies in the time between suc-cessive absorption of two photons by one particle. It isreasonable to assume that under nanosecond excitationthe originally formed charge carriers are already trappedat the surface before a second photon is absorbed. Augeremission can therefore occur only by the interaction of ei-ther one free and one trapped ej1h+ pair or of two trappedpairs. Because the spatial overlap of trapped ej1h+ pairsis relatively small, the quantum yield of hydrated elec-trons is only a few percent.

Under subpicosecond excitation, however, the meantime between successive absorption of photons by one par-ticle is only several femtoseconds. In this case the proba-bility is large that the e/h+ pair that was formed in thepreceding absorption process should still be free, i.e., inan excitonic state. Since there should be extensive over-lap between two free excitons in the microcrystal, theprobability of Auger recombination of electron and hole,with photoemission of an electron, becomes high. Forevery ejected and solvated electron, the colloidal particleremains with a trapped hole. In nanosecond flash experi-ments it was found that positive holes react with eachother to form sulfur atoms.3 8 We assume that the yield ofthis reaction is negligible on the picosecond time scale.

Assignment of Decay of Bleaching at 308 nm toTrapped-Carrier RecombinationAt low pump fluence the decay of excitonic bleaching at308 nm is well described by a single exponential compo-nent with decay time of 30 psec. No corresponding ki-netic component was found in the temporal developmentof absorption at 616 nm. We assign the decay of bleachingto the recombination of trapped charge carriers. The re-combination should have a wide distribution of rates be-cause of distributions in the tunneling distances betweenthe trapped electrons and the trapped holes and becauseof distributions in trap depths.42 The time range of themeasurements reported here excludes the observation ofdecay components with time constants that are signifi-cantly longer than 30 psec. Hence we conclude that thefastest recombination rate at low flux has a time constantof 30 psec.

At high pump fluence many photons are absorbed perparticle from the pump pulse, which leads to a high con-centration of trapped carriers and to decreased averagetunneling distances for recombination. This is consis-tent with our observations. From Fig. 2 it can be seenqualitatively that increasing pump fluence enhances thekinetic contribution of decay components with lifetimesin the 0.8-1.5-psec range.

Model for Multiphoton Absorption byColloidal ParticlesA model for sequential multiphoton absorption in confinedZn(Cd)S colloidal particles is shown in Fig. 4 (left-handside). Essentially, it is a refinement of a model proposedin Ref. 38. Absorption of a photon, with an absorptioncross section uo, leads to the first exciton state a. This is

Ernsting et al.

a. = h(2AEX)-,


b zeta 1;/ s e -+

esolv°F0 * / k °Si G~& 2k,

: rel Cr ,ke2.

k solv

Fig. 4. Full (left-hand side) and simplified (right-hand side) for-mal rate model for multiphoton absorption by semiconductormicrocrystallites. Singly or doubly excited electronic states ofthe entire crystallite are indicated by one or two +- pairs, re-spectively, included in a shaded circle. Trapped charge carriersare represented by + or - located in a notch on the periphery.

followed by trapping, presumably at the surface, with arate constant kT. Alternatively, the exciton may absorb afurther photon with absorption cross section o(o*. Be-cause of screening, oo* should be less than o0. We setso* = ao with a screening factor a < 1, say a 0.5.Now assume a fluence of 2 photons/A2 , which correspondsto a flux I of 7 photons/A' psec-'. Then pumping withrate constant Ioo* = 90 psec-1 can compete with trappingwith rate constant k, which corresponds to an excitonlifetime of 11 fsec. Thus a doubly excited state b isreached. In the case of negligible confinement, this statewould correspond to the simultaneous existence of two in-dependent excitons in the colloidal particle; the probabil-ity of finding both excitons present would be the productof the probabilities for one exciton only; hence the trap-ping rate constant of the biexciton as a whole should betwice the trapping rate constant for one exciton. For sim-plicity, this relationship is also assumed to hold in thepresent case of strong confinement.

A second decay channel for the doubly excited state b isgiven by emission of an electron, with rate constant kA,which leads to a deexcited modified particle with one ad-ditional excess hole. Hole absorption is low at 616 nmand negligible at 308 nm.30 Therefore the modified par-ticle may be treated as the original one is (but see below).In the scheme of Fig. 4, electron emission is indicated bydotted lines.

An intense subpicosecond pump pulse leads to the ab-sorption of several tens of photons per particle, and eachexcitation adds a trapped hole and either a trapped or anemitted electron. The rate constants krec,i for electron-hole recombination should depend on the number of

trapped charge carrier pairs i. The kinetics of ground-state recovery (Fig. 2) suggests that recombination ratesare slower than our pumping rates, at least for moderatefluences. Therefore, the effect of the intense pump pulsewould be to drive population up the main diagonal in thescheme of Fig. 4. In its course the overall pump absorp-tion changes continuously as absorption cross sections vi(i = 1,2,...), which are reduced from 0o because ofscreening by trapped charge carriers, become effective.

Now imagine a representative particle x(s) that has accu-mulated a mean number (i) of trapped charge carrierpairs. To a first approximation, this number determinesthe optical properties, i.e., cross sections CO and o(i)*. Ab-sorption of one photon leads to the excitonic state a(i). Ifthis is followed by ultrafast (surface) trapping, a particlex(,)+i is created, and so on.

This suggests a simplified model, which is shown on theright-hand side of Fig. 4. The ground state x refers to aparticle that has absorbed an average number nabs of pho-tons and emitted an average number neI of electrons; adenotes the exciton and b the doubly excited state. Pho-ton absorption increases nabs, and electron emissionincreases ne,. Screening by the first exciton is includedthrough

r* = ao,. (3)

Screening by trapped electrons is accounted for by lettingor depend on nabs - net. We set

a. = 0o{o + (1 - 3) exp[-(nb. - nfei)/n]I},

with a < ,( < 1. (4)

Equation (4) describes an exponential decrease of the ab-sorption cross section with an increasing number oftrapped electrons. Its limiting value P0o-a corresponds tounsaturable absorption,8 and n, is a characteristic numberof trapped electrons.

Electron emission should also proceed more slowly aspositive charge accumulates on the particle. For everyemitted electron, the ionization potential is increased byan amount e2/(sR). Eventually the electron affinity ofthe solvent will be exceeded and electron emission mustcease. Therefore, we set

kA = kAo(l - nel/nA)

kA = 0

for nel < nA,

otherwise. (5)

Here, kAo is the initial rate constant for the Auger process,and nA stands for the maximum number of electrons thatcan be emitted per particle.

The rate equations for the simplified model of Fig. 4are then

ii = Iu(1 - na - b) - (Ic* + kT)na + 2 kTnb,

nb = I*na - (2kT + kA)nb,

he1 = kAnb,

nagb = I0(1 - n - nb) + Iu*na.

(6)

(7)

(8)

(9)

Application to Saturation CurvesThe rate equations were integrated numerically using aGaussian pulse shape for the pump flux I(t), with a full

Ernsting et al .


Table 1. Parameters for the Saturation and Yield Curves in Figure 3

Parameter Definition Value

N No. density of particles with 40-A diameter 3.24 x 1015 cm-3

d Optical path length 0.2 cmODo Small-signal optical density at 308 nm 0.715C- Absorption cross section at 308 nm 25.4 x 10-16 cm 2

a Screening factor for screening by untrapped electrons 0.5P Screening factor for screening by trapped electrons 0.7n,,, Characteristic number of trapped electrons for reduction of 5- 5voel Absorption cross section of solvated electrons at 616 nm' 0.572 x 10-16 cm 2

OWhole Absorption cross section of holes at 616 nm 0.013 x 10-16 cm 2

kT Exciton trapping rate constant 35 x 1012 sec-kAo Initial Auger emission rate constant 1015 sec-nA Maximum number of emitted electrons per particle 16

'Ref. 43.

width at half-maximum of 0.3 psec, that is normalizedto the pump fluence and centered at t = 0 psec. Fort = 0.3 psec the following observables were then calcu-lated (N is particle number density, d is path length):The change of optical density at t pump wavelength at308 nm is

AOIDpump = g(e)Nd[o-(1 - na - nb) - CO], (10)

the total optical density at the probe wavelength of616 nm is

ODprobe = g(e)Nd[rejnei + UThole(nab. - nei)], (11)

and the (minor) contribution by hole absorption is

ODhole = g(e)Ndh.l(nb. - el). (12)

This procedure was repeated for various pump fluences,and thus curves like those in Fig. 3 were obtained. Arelatively small value for the hole absorption cross section,o-hole = 0.0127 A2, was transferred from similar measure-ments for colloidal CdS in isopropanol. 40 The curve forprobe absorption at 616 nm therefore reflects the yield ofemitted electrons. Its shape and scale is largely deter-mined by the trapping rate kT, the initial Auger emissionrate kAo, and the maximum number nA of electrons thatcan be emitted. Increasing kT enhances quadratic behav-ior at low fluence and reduces the scale, increasing kAoincreases the scale, and nA controls the absorbance at satu-ration. The parameters for best overall agreement withexperiment are collected in Table 1. In particular, kAo =

1000 psec- , n = 16, and k = 35 psec-1, which corre-sponds to an exciton lifetime of -30 fsec, in agreementwith earlier conjecture.' 3

Assessment of Parameter ValuesThe number of model parameters is rather large in view ofthe small number of data points shown in Fig. 3. Theparameter values given above and the corresponding simu-lations in Fig. 3 should therefore be viewed as a test of theapplicability of the model rather than a determination ofmaterial properties. In the following we discuss brieflythe extent and limits of the determination of modelparameters.

0.35 -

- 0.30-

o 0.25 -

o 0.20 -

bX 0.15

,d 0.10

- 0.05 -

I n non 0.° 1.0 2.0 3.0 4.0 5.0 6.0

fluence / e16 photons cm-Fig. 5. Simulated changes of optical density at 308 and 616 nm,as a function of pump fluence. Here the screening parameter awas varied. Solid curves correspond to the best description ofthe experimental data shown in Fig. 3.

The exciton-trapping rate constant kT is essentially de-termined by measuring the yield of solvated electrons thatare obtained through successive two-step excitation.Therefore the number of created excitons and biexcitonsmust be estimated. This estimate depends critically onthe screening parameters a and , [Eqs. (3) and (4)]. For ademonstration of this sensitivity, Fig. 5 shows simulatedsaturation curves for which a has been varied (while keep-ing kT constant). The large changes in the simulatedcurves are an indication that, conversely, kT can be deter-mined only if a is well known. As a practical consequence,the wavelength of excitation should be tuned to the onsetof the dense spectral region -0.4 eV above the lowest exci-ton state, which should correspond to a = 8 = 1.0.

The high value for the Auger emission rate constant kAis relatively noncritical and merely indicates an initialquantum yield near 1 for the process. For example,changing kAo to 500 psec'1 leads to a small decrease of thecalculated electron yield only at the highest pump fluence.

The maximum number nA of electrons that may beemitted per particle is responsible for the plateau of the616-nm absorbance at high pump fluence. The measuredabsorbance in the visible range also contains a contribu-

Ernsting et al.


tion that is due to trapped holes. Therefore nA may bedetermined quite well if a suitable model colloid can befound that permits a quantitative assessment of the holespectrum.

Practical prerequisites for determining the exciton life-time and other material parameters are crystallites with anarrow size distribution in aqueous solution. Our modelprovides a common basis for the interpretation of satura-tion data from several such colloidal solutions, which mayinclude particles of various diameters. If that interpre-tation fails, the model should be extended to include co-herent two-photon absorption and the dependence ofscreening parameters a and 83 on the number of accumu-lated holes.

CONCLUSIONWe have monitored the yield of solvated electrons fromsubpicosecond excitation of quantum-size Zn0.95Cd005S mi-crocrystallites in an aqueous colloidal solution. The yieldas a function of pump fluence was modeled in a simplekinetic scheme that involves the exciton lifetime beforetrapping and a maximum number of electrons that can beemitted per particle. The data are consistent with an ex-citon lifetime of -30 fsec. Therefore the number densityof particles with a free exciton should be small comparedwith the number density of particles that have a largenumber of trapped electrons and holes, even for pumppulses with 0.26-psec duration. Consequently, any bleach-ing for the pump pulse must be primarily caused byscreening that is due to trapped charge carriers. A shortexcitonic lifetime, in the femtosecond range, combinedwith relatively inefficient screening by trapped chargecarriers at high densities, is thus seen as the reason forthe small nonlinear saturation effect in quantum-sizesemiconductor particles.

ACKNOWLEDGMENTWe are grateful to S. Szatmari for advice on copying hismicroscopic distributed-feedback dye-laser system, toF P. Schiifer and A. Henglein for valuable discussions, tothe Deutsche Forschungsgemeinschaft for supportthrough the Leibniz Prize Program, and to AlexanderMiller for a critical reading of the manuscript.

* On leave from the Zentralinstitut fur Optik und Spek-troskopie, Akademie der Wissenschaften der DDR, 1199Berlin, German Democratic Republic.

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Appl. Phys. B 46, 1-17 (1988).2. J. Warnock and D. D. Awschalom, "Picosecond studies of elec-

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colloidal zn1,-cds: optical saturation of the exciton band and

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