Microscopic quantum theory of spatially resolved photoluminescence in semiconductor quantum structures

Abstract

We present a microscopic analysis of spatially resolved photoluminescence and photoluminescence excitation spectroscopy in semiconductor quantum structures. Such theoretical and numerical framework provides a general basis for the description of spectroscopic imaging in which the excitation and detection energies and spatial positions can all independently be scanned. The numerical results clarify the impact of the near-field optical setup on the obtained images and resolutions. ͓DOI: 10.1063/1.1711184͔In recent years, measurements based on spatially resolved photoluminescence ͑PL͒ provided direct information on the spatial and energy distribution of light emitting nanometric centers of semiconductor quantum structures, thus opening a rich area of physics involving spatially resolved quantum systems in a complex solid state environment. [1][2][3][4][5][6] In particular, near-field optical microscopy and spectroscopy can detect the optical characteristics of individual quantum dots ͑QDs͒ among, e.g., a high-density ensemble of naturally formed QDs, 7 whereas usual far-field methods provide only ensemble-averaged properties. Detailed simulations of Zimmermann, Runge, and Savona 8,9 have clarified many aspects of the intrigued nonequilibrium dynamics giving rise to photoluminescence spectra in these quantum structures. However, theoretical simulations of near-field imaging spectroscopy of semiconductor quantum structures focus on calculations of local absorption. [10][11][12][13] In contrast, as a matter of fact, almost all experimental images are obtained from PL measurements. Here we present a microscopic theory of spatially resolved photoluminescence in quantum structures that includes both light quantization ͑essential to describe radiative recombination͒ and phonon scattering. The theory also includes the description of spatially confined excitation ͑illumination mode͒ and/or detection ͑collection mode͒. It is worth noting that we are faced with a strictly nonequilibrium problem. Nonequilibrium here arising from both radiative recombination ͑preventing full thermalization͒ and from the local nature of the excitation source ͑in the illuminationmode setup͒. We are also faced with the problem of the differences between illumination (I) and collection (C) scanning near-field optical microscopy ͑SNOM͒ instruments. The equivalence between these two working modes has been established on the basis of the reciprocity theorem for electromagnetic fields. 14 However, this theorem holds for linear and passive media. While semiconductor structures, at low excitation densities, show a linear behavior, phonon scattering and radiative recombination prevent them from being passive.The positive frequency components of the operator describing the signal that can be detected by a general nearfield setup can be expressed as 15 Ŝ t ϩ ϭ bg ϩ ϩŜ ϩ , where  bg ϩ is the elastic background signal ͑largely uniform along the x -y plane͒ proportional to the input electric-field operator, and Ŝ ϩ is related to the sample polarization densi...

Dark-State Luminescence of Macroatoms at the Near Field

“…This allows one to break in the near field the usual optical selection rules and to excite dark states whose excitation is forbidden by symmetry in the far field. Spatial maps of dark states in semiconductor nanostructures were simulated for high-resolution SNOM in absorption [14,15] and luminescence [16,17], and were shown to depend sensitively on the spatial near-field resolution. This previous work focused on the analysis of the near-field matrix elements, while assuming for simplicity that dark states couple to their environment in the same manner as bright states do.…”

Near‐field control of the light emission properties of a symmetric semiconductor quantum dot

“…[16], this is a quite reasonable assumption since the photons can be emitted into any solid-angle direction, and the slightly modified photon density of states in the presence of the SNOM tip is not expected to be of great importance. Within these assumptions, recently [8] it has been shown that the nearfield spectrally resolved PL signal collected by the tip can be expressed as…”

“…In addition, we neglect the possible coherent phonon states and the memory effects induced by the photon and phonon fields. The obtained set of kinetic equations is [8,17,19] …”

“…The matrix elements governing the light-matter coupling are a convolution of the quantum states with the exciting electromagnetic field. Succeeding in confining the optical excitation to a very small volume below the diffraction limit, implies the presence of optical fields with high lateral spatial frequencies, determining coupling matrix elements that can differ significantly from far-field ones [8][9][10][11][12][13]. Hence SNOM is more than just a spatial selection of inhomogeneous surface systems.…”

“…The SNOM ability to resolve the individual quantum constituents of semiconductor nanostructures has been widely demonstrated [4][5][6]. If the spatial near-field resolution falls below the extension of confined quantum systems, spatially resolved photoluminescence (PL) maps out the spatial probability distribution of the wave function times the corresponding level occupation [7,8]. The matrix elements governing the light-matter coupling are a convolution of the quantum states with the exciting electromagnetic field.…”