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We examine collective effects in an ensemble of close-packed ultrasmall CdSe quantum dots by comparison of optical properties of dense and diluted thin film composites. Studies of absorption spectra, photoluminescence excitation spectra and electroabsorption of diluted and condensed structures along with numerical simulation confirmed that in a dense ensemble extended electron states occur by analogy with Anderson transitions in disordered solids. Therefore evolution from isolated quantum dots to quantum dot solids in case of strong confinement results in a drastic modification of optical and electronic properties. * ) Supported by Volkswagen-Stiftung. phys. stat. sol. (b) 224, No. 2, 393-396 (2001)

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Dedicated to Professor Jozef T. Devreese on the occasion of his 65th anniversary PACS 71.38.-k The polaron energy and the effective mass are calculated for an electron confined in an asymmetrical finite quantum well constructed of Al x l Ga 1Àx l As/GaAs/Al x r Ga 1Àx r As layers. To simplify the study we suggest a model in which parameters of a medium are averaged over the ground-state wave function. Our model reproduces the correct three-dimensional asymptotics at both small and large widths. We obtained a rather monotonous behavior of the polaron energy as a function of the confining potential width and found a peak of the effective mass. A comparison with theoretical results by other authors is made.1 Introduction Choosing the topic of the present paper we have been strongly motivated by the results obtained by Hai, Peeters and Devreese in Refs. [1,2]. They considered a polaron confined to a quasi two-dimensional quantum well constructed of a layer of GaAs in a Al x Ga 1Àx As medium. As is well known, systems of reduced dimensions -quasi-two dimensional (2D) quantum wells, quasi-one dimensional (1D) quantum wires and quasi-zero dimensional (0D) quantum dots -have attracted a lot of attention the last two decades when their practical realization became possible. Now, investigations of semiconductor heterostructures appear much more often than investigations of bulk samples. The opportunity to engineer the electronic properties of a device ''as desired" made these systems advantageous both for basic research and technical applications.The authors of the papers [1,2] solved the problem of a polaron in a 2D symmetrical quantum well in the scope of the second order perturbation theory in powers of the electron-phonon coupling constant a with all phonon modes being incorporated. Peaks of the phonon induced energy shift and the polaron effective mass were found for some values of the confining potential widths. In principle, the same approach can be used while dealing with a quantum well constructed of many layers of different materials. But the problem becomes then too complicated because one has to take into account interface phonon modes at each frontier of different materials as well as quantized phonon modes inside each of the layers [3][4][5][6][7][8][9][10]. The influence of the mentioned modes on polaron properties was studied in Refs. [11][12][13][14]. Here we formulate a simplified model to take these effects into account and to deal with the effective confining potential and only one bulk phonon mode.

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