ISSN 1063-7826, Semiconductors, 2006, Vol. 40, No. 11, pp. 1338–1345. © Pleiades Publishing, Inc., 2006. Original Russian Text © M.A. Semina, R.A. Sergeev, R.A. Suris, 2006, published in Fizika i Tekhnika Poluprovodnikov, 2006, Vol. 40, No. 11, pp. 1373–1380. 1338 1. INTRODUCTION Low-dimensional semiconductor heterostructures have widespread practical applications, and therefore, the optical properties of such structures are extensively studied theoretically and experimentally. In these stud- ies, of special interest are the bound states of electron– hole complexes (excitons, X + and X – trions, etc.) that define the spectral features of the structures near the fundamental absorption band edge. In narrow quantum wells (QWs), a noticeable effect on such complexes is produced by their localization in the plane of the QW at various structural defects, such as fluctuations of the well width [1–5], compositional inhomogeneities [6–9], fluctuations of the distribution of the built-in charges [10–12], etc. For example, the binding energy of the X trion in deep narrow QWs may be even larger than that in the hypothetical limit of the two-dimensional (2D) structure. As a rule, the binding energy of electron–hole com- plexes is calculated with the use of variational methods. Among these methods, the currently most-used meth- ods are those in which the trial functions involve a large number (on the order of 1000) of adjustable parameters (see, e.g., [13, 14]). Using such methods, it is possible to determine, with a very high accuracy, not only the energy of the complex but also its wave function. How- ever, for the most part, such methods are extremely cumbersome, and the physical interpretation of the results obtained by these methods is often rather diffi- cult. In addition, these methods are most efficient in the calculations for particular structures with fixed param- eters. At the same time, if we need to trace the depen- dence of the energy of the complex on the structural parameters over a wide range of their magnitudes and to clarify the qualitative regular trends, the exactness of these methods becomes unnecessarily high. In this context, it would be important to construct a trial wave function that would allow us to calculate the binding energy of an electron–hole complex localized in the plane of the QW even with a lower accuracy, but in a simple descriptive manner applicable to the most general case. Such an approach would allow us to understand the structure of the complex and to estimate its binding energy for arbitrary parameters of the local- izing potential without cumbersome calculations. 2. CHOICE OF THE TRIAL FUNCTION We are dealing with deep narrow QWs, in which the motion of charge carriers can be considered as 2D motion. We characterize the interaction of electrons and holes with a defect by independent single-particle attractive 2D potentials of arbitrary shape for electrons, U e (r e ), and holes, U h (r h ), where r e and r h are the 2D coordinates of an electron and a hole. In this manner, it is possible to describe, e.g., fluctuations in the QW width [1, 15] or composition [6, 15]. We consider an electron–hole complex that consists of N e electrons and N h holes. For such a system, the Schrödinger equation in the general form is written as (1) where the Hamiltonian is (2) H ˆ Ψ r e 1 … r e N e r h 1 … r h N h , , , , , ( ) = E Ψ r e 1 … r e N e r h 1 … r h N h , , , , , ( ) , H ˆ T ˆ e T ˆ h V ˆ c V ˆ e V ˆ h . + + + + = Localization of Electron–Hole Complexes at Fluctuations of Interfaces of Quantum Dots M. A. Semina^, R. A. Sergeev, and R. A. Suris Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia ^e-mail: msemina@yahoo.com Submitted March 15, 2006; accepted for publication March 31, 2006 Abstract—The localization of two-dimensional electron–hole complexes at the attractive potential of arbitrary shape is treated theoretically. A general method of construction of simple descriptive trial functions is suggested to calculate the binding energy of the ground state of such complexes. The limiting cases corresponding to dif- ferent relations between the characteristic parameters of the system are analyzed. The developed approach is illustrated by particular calculations for the exciton in a two-dimensional quantum well with an additional lat- eral potential. PACS numbers: 73.21.Hb, 71.35.Gg DOI: 10.1134/S1063782606110157 LOW-DIMENSIONAL SYSTEMS