First, we discuss the pronounced nonlinear optical properties of the hybrid Frenkel–Wannier excitons appearing when the energy splitting of the excitonic spectrum 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 Frster mechanism of energy transfer from an inorganic quantum well to an organic overlayer is of great interest: the electrical pumping of excitons in the semiconductor quantum well could be employed to efficiently turn on the organic material luminescence.
In the last few years, much attention was devoted to the 1. Strong Resonant Coupling:
study of organic crystalline layered structures, both experiHybrid Exciton Nonlinearities mental  and theoretical . The substantial improvement in the technique of organic molecular beam deposition has In covalent semiconductor quantum wells, optical nonled to a variety of good quality heterostructures based on linearities dominated by phase space filling effects have molecular solids as well as on combinations of organic already attracted much interest . The density-dependent and inorganic semiconductors. The possibility of growing susceptibility near the excitonic resonance can be written as tailor-made systems incorporating different organic crystalline materials with even more flexibility than for multiple n F0 n () 0() 1 - 1 -, (1) quantum wells based on inorganic semiconductors opens nS - nS up a promising field of research from the point of view of fundamental as well as applied physics.
where 0 is the linear susceptibility, is the resonance Such technological progress prompted us to study hetenergy and F0 represents the oscillator strength of the erostructures with resonating Frenkel excitons (FEs) in the exciton, n is the 2D density of excitons and nS — the organic material and Wannier–Mott excitons (WEs) in the saturation density given roughly by nS 1/a2, ao being the o inorganic one . For example, the FE energy in anthracene exciton radius. Indicating the light intensity with IP, we recall is 3 eV, in coronene is 2.9 eV, in PTCDA 2.2 eV, in pentacene that n F0IP and F0 is, in turn, proportional to 1/a2. Thus, o 1.5 eV. Semiconductor quantum wells with resonating WEs for a given IP, the ratio n/nS is approximately independent of can be obtained from III–V and II–VI ternary solid solutions the exciton radius. As long as the exciton radius dependence such as GaAlAs, ZnCdSe, ZnSSe, judiciously choosing the of the oscillator strength and of the saturation density cancel alloy composition and well thickness.
out, such a figure of merit of the optical nonlinear response Another concern is the width of the exciton lines. In cannot be much improved by tayloring the character of the good quality inorganic semiconductor quantum wells, the excitonic resonance with dimensional confinement or even WE linewidth is of the order of 1 meV (usually limited by changing material class .
by inhomogeneous broadening). FEs in organic materials Here, we focus on a novel way of achieving a large typically have a much larger linewidth (often due to strong nonlinear optical response exploiting the HEs peculiar to electron-phonon coupling); for instance, about 200 meV organic-inorganic nanostructures for which the situation is in thin films of PTCDA . However, it is possible to quite different. The physical system we are referring to, choose resonating organic materials with sharp FEs, such comprises two parallel two-dimensional layers separated by as coronene (exciton linewidth 4meV ) or the surface a distance of a few nanometers: the first sustains tight bound exciton of anthracene (linewidth of about 1 meV ). It is FE (the size of which is of the order of a unit cell) and important to note that the dipole-dipole interaction coupling the second, loosely bound WE (with radius ao of about the FEs and WEs at an organic-inorganic heterojunction can 0 10 nanometers), having energies and, respectively, be of the order of 10 meV [3,6]. Therefore, the case of F W and a center of mass momentum Q along the layer planes strong coupling (Sect. 1), in which the exciton linewidths are 0 (assumed to be conserved). Near resonance ( ), smaller than the anticrossing energy splitting and hybrid exF W they mix with each other via the dipole-dipole coupling citons (HEs) exhibiting pronounced optical nonlinearities are |VWF(Q)| [3,6]. When the dipole-dipole interaction energy formed [3,6], must be distinguished from the case of weak is larger then the exciton linewidths, the true eigenstates of coupling (Sect. 2), in which the FEs are much broader and the dipole-dipole coupling gives rise to an irreversible energy the system are HEs with wavefunctions of a mixed character transfer from the inorganic to the organic material [7,8]. and modified dispersion laws [3,6], in particular when the Excitons in Hybrid Organic-Inorganic Nanostructures FE and WE are exactly in resonance the HE eigenvalues properties compared to inorganic semiconductors and the are a split doublet and the corresponding wavefunctions efficient electrical pumping of such devices is a challenging are superpositions of FE and WE wavefunctions with equal problem. Prompted by the rapid advances of epitaxial weights. Since the HEs possess both the large radius of growth techniques for crystalline molecular materials (even Wannier excitons and the large oscillator strength of Frenkel on inorganic substrates) , we consider here a novel hybrid configuration in which both inorganic semiconductors and excitons, their saturation density nS is still comparable to organic materials are present: the basic idea is to pump that in covalent semiconductor quantum wells, but the the optically active organic molecules via electronic energy photogenerated density n, for a given IP, is much higher:
transfer from the two-dimensional Wannier–Mott excitons as a consequence, the ratio n/nS for the 2D HE can be of a semiconductor quantum well.
two orders of magnitude larger than for the usual multiple We consider a symmetric structure consisting of a semiquantum wells .
conductor QW of thickness Lw between two barriers of The first order nonlinear corrections can be expressed in thickness Lb each (Lb being a few nanometers), the whole terms of the total 2D HE density n [6,9]: the WE blue shift semiconductor structure being surrounded by semi-infinite 0.48Eba2n (Eb being the WE binding energy), the W o slabs of an isotropic organic material. We assume that in WE Pauli blocking factor BW 1 - 0.14a2n and the coro the frequency region considered here the semiconductor rection VWF to the hybridization due to the modification of 0 1 background dielectric constant is real (the same for the b the WE wavefunction |VWF +VWF|2 (1-0.12a2n)|VWF|2.
o well and the barrier), and that of the organic material is All these effects are typical for Wannier excitons having a complex (due to a broad absorption band). The irreversible small saturation density nS 1/a2, but here they belong o Frster-like energy transfer rate due to the dipole-dipole to the hybrid excitons which also have a large oscillator interaction can be calculated simply from the Joule losses strength characteristic of Frenkel excitons. Using a standard in the organic material [7,8]. First, we calculate the transfer microscopic approach , we can then write the density rate from free excitons [7,8]. We consider two polarizations:
dependent 2D susceptibility of hybrid excitons as  one lying in the QW plane along k (L-exciton), the other HE(; Q) perpendicular to the QW plane (Z-exciton). In Fig.1, we plot L and Z as functions of exciton center of mass momentum k 0 0 FF ( + - ) for parameters representative of II-VI semiconductor QWs W W, (2) 0 1 0 0 1 in a realistic structural geometry. It turns out that the ( + - )( - ) - BW VWF +VWF W W F lifetime does not depend drastically on the polarization and the real parts of dielectric constants. The dependence on where only the dominant term proportional to FF has been Lw is also weak. The barrier width Lb, when grows, gives retained. In the linear regime, n is negligible and 0, W an exponential factor e2kLb. As a function of k, exhibits VWF 0 and BW 1; the poles of the linear susceptibility a minimum at kmin 1/Lb. Typical values of k for a are just the HE doublet eigenvalues. With increasing excitathermalized exciton distribution with temperature 100 K tion intensity, the FEs are not much disturbed due to their are 3 · 106 cm-1. We see that the corresponding lifetimes large saturation density, but the WEs start bleaching and this (tens of picoseconds) are much less then the exciton affects the above HE susceptibility. For realistic parameters, at Q 107 cm-1 we have |VWF| 5 meV and, including phenomenological linewidths of a few meV, we obtain [2,6] for the fractional nonlinear change in absorption coefficient close to resonance ||/ 10-11cm2 n, which for a given n is of the same order as for a covalent semiconductor quantum well. However, for a given pump intensity IP, the 2D density of photogenerated excitons n is in our case about two orders of magnitude larger (n HE FF ), as anticipated. We wish to stress that the present effect is typical of hybrid excitons and would not be effective in the case of two coupled quantum wells of the same material.
2. Weak Resonant Coupling:
Frster Energy Transfer A large effort has recently been devoted to the study of organic light emitting diodes and lasers. Frster-like energy transfer between different dye molecules in solid solutions has already been used to achieve light amplification in optically pumped organic thin films . Howe- Figure 1. Free L-exciton (solid line) and Z-exciton (dashed line) ver, optically active organic materials have poor transport lifetime versus the center of mass in-plane wave vector k.
Физика твердого тела, 1999, том 41, вып. 780 F. Bassani, G.C. La Rocca, D.M. Basko, V.M. Agranovich recombination rate which is about 100-200 ps in II-VI semi- organic molecules before they can recombine inside the QW.
conductor QWs. Thus the dipole-dipole transfer mechanism For quantum wells based on the II–VI semiconductors and proves to be efficient enough to transfer a large fraction of in a realistic configuration, such transfer may occur at time the semiconductor excitation energy to the organic medium. scales of the order of 10 ps and be effective in activating the We have also studied the situation when the QW width organic material luminescence.
fluctuations or the alloy disorder localize the wave function To summarize, the simple physical pictures presented (r ) of the center-of-mass exciton motion . General above may lead to new concepts for optoelectronic devices properties of (r ) are: (i) it is localized within some based on hybrid organic-inorganic structures, especially if distance L > Lw, (ii) it is smooth and without nodes.
embedded in a suitable microcavity [2,12]. More detailed Assuming the disorder to be isotropic in two dimensions, theoretical calculations will be useful, but probably the we need to consider two cases of the polarization being crucial factor will be the technological progress in the parallel and perpendicular to the QW plane, referred to synthesis of such systems. We believe that this is a very as X and Z polarizations, respectively. It is possible to promising field of research and hope that the experimental get some information about the decay rate based only on efforts to grow and investigate these novel systems will be general properties of the wave function, mentioned above.
We have three length scales in our problem: Lw, Lb and Partial support from INFM through the project ”PhotoacL. First, only L Lw are physically meaningful. If in tive Organic Materials” (PAIS G) is acknowledged. V.M.A.
addition L Lb, we obtain L, while for a thick barrier is thankful to Scuola Normale Superiore (Pisa, Italy) for (L Lb) we have 1/L2. Hence, has a minimum at hospitality and support.
some L Lb. For illustrative purposes, we choose a gaussian He also acknowledges partial support through Grant 96wave function of width L and show in Fig.2 the results of 0334049 of the Russian Foundation of Basic Researches, the calculation ( versus L) for realistic parameter values.
Grant from ”Physics of Nanostructures”, the Russian MinWe also considered the case of a quasi-thermalized plasma istry of Science and Technology and INTAS Grant 93-461.
of free electrons and holes . The dipole-dipole lifetimes obtained turn out to be as long as 300 ps (and larger) for II–VI-semiconductors.
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