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The Dielectric Response of a Semiconductor Quantum Dot: Application to Determine the Photoluminescence of the Dot
Author(s) -
RodríguezCoppola H.,
TutorSánchez J.,
GarcíaMoliner F.
Publication year - 2002
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200207)232:1<89::aid-pssb89>3.0.co;2-3
Subject(s) - quantum dot , physics , excited state , polarizability , curse of dimensionality , quantum mechanics , excitation , basis function , coulomb , condensed matter physics , electron , mathematics , statistics , molecule
Abstract The dielectric function of a quantum dot of arbitrary shape is given in a multilevel extension of the Hubbard approximation which includes exchange in the dynamical response. The analysis is an application of the general formulation for the confined electron gas given by the authors for arbitrary dimensionality. This is formulated in terms of a dual basis of short and long‐range functions, which correspond to all possible interlevel single particle excitations. The internal products of these two types of functions give the matrix elements of the Coulomb interaction for the different allowed transitions. While, strictly speaking, the monoelectronic energy spectrum of the system is infinite, the formal analysis shows that the dual basis of the short and long‐range functions can be truncated while generating convergent approximations to the exact answer. The multilevel nature of the spectrum of confined states is thus included explicitly, while keeping approximations which are both formally valid and controlled to manageable proportions. Numerical results are given for the real and imaginary parts of the polarizability of a typical transition between states of a cubic quantum dot as a function of the excitation energy. This magnitude is not macroscopically measurable because it corresponds to a single transition, and when an external agent perturbs the system, all possible transitions are excited and mutual influences among them are included in the macroscopic response. Thus, a particular transition with given excitation energy may contribute to a plasmon at another, different energy. The polarisability element has a pole for excitation energies equal to the energy difference between the two monoelectronic states involved in the excitation, and the results do not show any significant difference between the random‐phase approximation (RPA) and the Hubbard approximations. A calculation which models the photoluminescence spectrum of the quantum dot is given and compared to results found in the literature.