PHYSICS OF THE SOLID STATE VOLUME 41, NUMBER 5 MAY 1999

Excitons in hybrid organic–inorganic nanostructuresF. Bassani, G. C. La Rocca,* ) and D. M. Basko

Scuola Normale Superiore and INFM Piazza dei Cavalieri, I-56126 Pisa, Italy

V. M. Agranovich

Institute of Spectroscopy, Russian Academy of Sciences, 142902 Troitsk, Moscow District, RussiaFiz. Tverd. Tela~St. Petersburg! 41, 778–780~May 1999!

In two-dimensional heterostructures made of semiconductor and organic layers, when resonancebetween the Wannier and Frenkel excitons is realized, the dipole-dipole interaction couplingthem leads to novel effects. First, we discuss the pronounced nonlinear optical properties of thehybrid Frenkel–Wannier excitons appearing when the energy splitting of the excitonicspectrum is large compared to the exciton linewidths~the case of strong resonant coupling!.Next, we consider the case of weak resonant coupling for which the Fo¨rster mechanism of energytransfer from an inorganic quantum well to an organic overlayer is of great interest: theelectrical pumping of excitons in the semiconductor quantum well could be employed to turn onefficiently the organic material luminescence. ©1999 American Institute of Physics.@S1063-7834~99!00605-X#

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In the last few years, much attention was devoted tostudy of organic crystalline layered structures, boexperimental1 and theoretical.2 The substantial improvemenin the technique of organic molecular-beam depositionled to a variety of good quality heterostructures basedmolecular solids as well as on combinations of organic ainorganic semiconductors. The possibility of growing tailomade systems incorporating different organic crystalline mterials with even more flexibility than for multiple quantuwells based on inorganic semiconductors opens up a prising field of research from the point of view of fundamenas well as applied physics.

Such technological progress prompted us to studyerostructures with resonating Frenkel excitons~FEs! in theorganic material and Wannier–Mott excitons~WEs! in theinorganic one.3 For example, the FE energy in anthracene3 eV, in coronene is 2.9 eV, in PTCDA 2.2 eV, in pentace1.5 eV. Semiconductor quantum wells with resonating Wcan be obtained from III–V and II–VI ternary solid solutionsuch as GaAlAs, ZnCdSe, ZnSSe, judiciously choosingalloy composition and well thickness.

Another concern is the width of the exciton lines.good quality inorganic semiconductor quantum wells,WE linewidth is of the order of 1 meV~usually limited byinhomogeneous broadening!. FEs in organic materials typically have a much larger linewidth~often due to strongelectron-phonon coupling!; for instance, about 200 meV inthin films of PTCDA.1 However, it is possible to choosresonating organic materials with sharp FEs, such as cnene ~exciton linewidth .4 meV @Ref. 4#! or the surfaceexciton of anthracene~linewidth of about 1 meV@Ref. 5#!. Itis important to note that the dipole-dipole interaction copling the FEs and WEs at an organic–inorganic heterojution can be of the order of 10 meV~Refs. 3 and 6!. There-fore, the case of strong coupling~Sect. 1!, in which theexciton linewidths are smaller than the anticrossing ene

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splitting and hybrid excitons~HEs! exhibiting pronouncedoptical nonlinearities are formed,3,6 must be distinguishedfrom the case of weak coupling~Sect. 2!, in which the FEsare much broader and the dipole-dipole coupling gives risan irreversible energy transfer from the inorganic to theganic material.7,8

1. STRONG RESONANT COUPLING: HYBRID EXCITONNONLINEARITIES

In covalent semiconductor quantum wells, optical nolinearities dominated by phase-space filling effects haveready attracted much interest.9 The density-dependent susceptibility near the excitonic resonance can be written as

x~v!.x0~v!S 12n

nSD.

F0

e02\vS 12

n

nSD , ~1!

wherex0 is the linear susceptibility,e0 is the resonance energy andF0 represents the oscillator strength of the exciton is the 2D density of excitons andnS — the saturationdensity given roughly bynS'1/ao

2 , ao being the excitonradius. Indicating the light intensity withI P , we recall thatn}F0I P andF0 is, in turn, proportional to 1/ao

2 . Thus, for agiven I P , the ration/nS is approximately independent of thexciton radius. As long as the exciton radius dependencthe oscillator strength and of the saturation density canout, such a figure of merit of the optical nonlinear responcannot be much improved by tailoring the character ofexcitonic resonance with dimensional confinement or eby changing the material class.10

Here, we focus on a novel way of achieving a larnonlinear optical response exploiting the HEs peculiarorganic–inorganic nanostructures for which the situationquite different. The physical system we are referring to coprises two parallel two-dimensional layers separated bdistance of a few nanometers: the first contains tightly bou

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702 Phys. Solid State 41 (5), May 1999 Bassani et al.

FE ~the size of which is of the order of a unit cell! and thesecond, loosely bound WE~with radiusao of about 10 na-nometers!, having energieseF

0 and eW0 , respectively, and a

center of mass momentum\Q along the layer planes~as-sumed to be conserved!. Near resonance (eF

0.eW0 ), they mix

with each other via the dipole-dipole couplinguVWF0 (Q)u.3,6

When the dipole-dipole interaction energy is larger thenexciton linewidths, the true eigenstates of the system arewith wavefunctions of a mixed character and modified dpersion laws,3,6 in particular when the FE and WE are eactly in resonance the HE eigenvalues are a split doubletthe corresponding wavefunctions are superpositions ofand WE wavefunctions with equal weights. Since the Hpossess both the large radius of Wannier excitons andlarge oscillator strength of Frenkel excitons, their saturatdensitynS is still comparable to that in covalent semicondutor quantum wells, but the photogenerated densityn, for agiven I P , is much higher: as a consequence, the ration/nS

for the 2D HE can be two orders of magnitude larger thfor the usual multiple quantum wells.6

The first-order nonlinear corrections can be expresseterms of the total 2D HE densityn6,9: the WE blue shifteW

1 .0.48Ebpao2n (Eb being the WE binding energy!, the

WE Pauli blocking factorBW.120.14pao2n and the correc-

tion VWF1 to the hybridization due to the modification of th

WE wavefunction uVWF0 1VWF

1 u2.(120.12pao2n)uVWF

0 u2.All these effects are typical for Wannier excitons havingsmall saturation densitynS'1/ao

2 , but here they belong tothe hybrid excitons which also have a large oscillastrength characteristic of Frenkel excitons. Using a standmicroscopic approach,9 we can then write the density depedent 2D susceptibility of hybrid excitons as6

xHE~v;Q!.FF

0~eW0 1eW

1 2\v!

~eW0 1eW

1 2\v!~eF02\v!2BWuVWF

0 1VWF1 u2

,

~2!

where only the dominant term proportional toFF0 has been

retained. In the linear regime,n is negligible andeW1 .0,

VWF1 .0 andBW.1; the poles of the linear susceptibility a

just the HE doublet eigenvalues. With increasing excitatintensity, the FEs are not much disturbed due to their lasaturation density, but the WEs start bleaching and thisfects the above HE susceptibility. For realistic parametersQ.107 cm21 we haveuVWF

0 u.5 meV ~Ref. 2! and, includ-ing phenomenological linewidths of a few meV, we obtain2,6

for the fractional nonlinear change in absorption coefficiclose to resonanceuDau/a'10211cm2 n, which for a givennis of the same order as for a covalent semiconductor qutum well. However, for a given pump intensityI P , the 2Ddensity of photogenerated excitonsn is in our case about twoorders of magnitude larger (n}xHE}FF

0), as anticipated. Wewish to stress that the present effect is typical of hybridcitons and would not be effective in the case of two coupquantum wells of the same material.

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2. WEAK RESONANT COUPLING: FO RSTER ENERGYTRANSFER

A large effort has recently been devoted to the studyorganic light-emitting diodes and lasers. Fo¨rster-like energytransfer between different dye molecules in solid solutiohas already been used to achieve light amplification in ocally pumped organic thin films.11 However, optically-activeorganic materials have poor transport properties compareinorganic semiconductors and the efficient electrical puming of such devices is a challenging problem. Promptedthe rapid advances of epitaxial growth techniques for crtalline molecular materials~even on inorganic substrates!,1

we consider here a novel hybrid configuration in which boinorganic semiconductors and organic materials are presthe basic idea is to pump the optically-active organic mecules via electronic energy transfer from the twdimensional Wannier–Mott excitons of a semiconducquantum well.

We consider a symmetric structure consisting of a seconductor QW of thicknessLw between two barriers othicknessLb each (Lb being a few nanometers!, the wholesemiconductor structure being surrounded by semi-infinslabs of an isotropic organic material. We assume that, infrequency region considered here, the semiconductor bground dielectric constanteb is real ~the same for the welland the barrier! and that of the organic materiale is complex~due to a broad absorption band!. The irreversible Fo¨rster-like energy transfer rate due to the dipole-dipole interactcan be calculated simply from the Joule losses in the orgamaterial.7,8 First, we calculate the transfer rate from freexcitons.7,8 We consider two polarizations: one lying in thQW plane alongk (L-exciton!, the other perpendicular to thQW plane (Z-exciton!. In Fig. 1, we plottL andtZ as func-tions of exciton center of mass momentumk for parametersrepresentative of II-VI semiconductor QWs in a realisstructural geometry. It turns out that the lifetime does ndepend drastically on the polarization and the real parts

FIG. 1. FreeL exciton~solid line! andZ exciton~dashed line! lifetime t vsthe center of mass in-plane wave vectork.

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703Phys. Solid State 41 (5), May 1999 Bassani et al.

dielectric constants. The dependence onLw is also weak. Thebarrier widthLb , when grows, gives an exponential facte2kLb. As a function ofk, t exhibits a minimum atkmin

;1/Lb . Typical values ofk for a thermalized exciton distribution with temperature;100 K are;33106 cm21. We seethat the corresponding lifetimes~tens of picoseconds! aremuch less then the exciton recombination rate which is ab1002200 ps in II-VI semiconductor QWs. Thus the dipoldipole transfer mechanism proves to be efficient enoughtransfer a large fraction of the semiconductor excitationergy to the organic medium.

We have also studied the situation when the QW wifluctuations or the alloy disorder localize the wave functiF(r i) of the center-of-mass exciton motion.8 General prop-erties ofF(r i) are: ~i! it is localized within some distancL.Lw , ~ii ! it is smooth and without nodes. Assuming thdisorder to be isotropic in two dimensions, we need to csider two cases of the polarization being parallel and perpdicular to the QW plane, referred to asX andZ polarizations,respectively. It is possible to get some information aboutdecay rate based only on general properties of the wave ftion, mentioned above. We have three length scales inproblem: Lw , Lb and L. First, only L@Lw are physicallymeaningful. If in additionL@Lb , we obtaint}L, while fora thick barrier (L!Lb) we havet}1/L2. Hence,t has aminimum at someL;Lb . For illustrative purposes, wechoose a gaussian wave function of widthL and show in Fig.2 the results of the calculation (t versusL! for realistic pa-rameter values. We also considered the case of a quthermalized plasma of free electrons and holes.8 The dipole-dipole lifetimes obtained turn out to be as long as 300 ps~andlarger! for II–VI-semiconductors.

According to our results, the kinetics of the initial frecarrier population~produced, e.g., by the electrical pumpin!is not significantly changed by the presence of the orgamedium, since the energy transfer from free carriers turnsto be slower than the process of exciton formation~unlessexcitation density and temperature are very high!. On the

FIG. 2. LocalizedX-exciton lifetimet vs the localization length L~solidline! along with the limiting casesL!Lb andL@Lb ~dashed lines!.

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other hand, the subsequent evolution of free or localizedcitons is strongly affected by the presence of the orgamedium. In an isolated QW the effective lifetime of the eciton distribution may be several hundred picoseconds. Hever, excitons coupled to the organic medium a few nanoeters away efficiently transfer their energy to the orgamolecules before they can recombine inside the QW.quantum wells based on II–VI semiconductors and in aalistic configuration, such transfer may occur on time scaof the order of 10 ps and be effective in activating theganic material luminescence.

To summarize, the simple physical pictures presenabove may lead to new concepts for optoelectronic devbased on hybrid organic-inorganic structures, especiallembedded in a suitable microcavity.2,12 More detailed theo-retical calculations would be useful, but probably the crucfactor will be the technological progress in the synthesissuch systems. We believe that this is a very promising fiof research and hope that the experimental efforts to gand investigate these novel systems will be successful.

Partial support from INFM through the project ‘‘Photoactive Organic Materials’’ ~PAIS G! is acknowledged.V.M.A. is thankful to Scuola Normale Superiore~Pisa, Italy!for hospitality and support.

He also acknowledges partial support through Grant0334049 of the Russian Foundation of Basic ResearcGrant from ‘‘Physics of Nanostructures,’’ the Russian Miistry of Science and Technology and INTAS Grant 93-46

* !E-mail: larocca@ella.sns.it

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7V. M. Agranovich, G. C. La Rocca, and F. Bassani, JETP Lett.66, 748~1997!.

8D. M. Basko, G. C. La Rocca, F. Bassani, and V. M. Agranovich, smitted to European Phys. Journal B.

9S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Adv. Phys.38, 89~1989!; H. Haug and S. W. Koch,Quantum Theory of the Optical andElectronic Properties of Semiconductors, 3rd ed. ~World Scientific,Singapore, 1994!, Ch. 16.

10B. I. Green, J. Orenstein, and S. Schmitt-Rink, Science247, 679 ~1990!.11M. Berggren, A. Dodabalapur, R. E. Slusher, and Z. Bao, Nature~London!

389, 466 ~1997!.12V. Agranovich, H. Benisty, and C. Weisbuch, Solid State Commun.102,

631 ~1997!; V. Agranovich, G. C. La Rocca, and F. Bassani, Pure ApOpt. 7, 119 ~1998!.

Published in English in the original Russian journal. Reproduced herestylistic changes by the Translation Editor.