Imaging spectroscopy of quantum wells with interfacial fluctuations: A theoretical description

Abstract

We present a theoretical approach for the simulation of scanning local optical spectroscopy in disordered quantum wells ͑QWs͒. After a single realization of the disorder potential, we calculate spectra on a mesh of points on the QW plane, thus obtaining a three-dimensional matrix of data from which we construct two-dimensional spectroscopic images of excitons laterally localized at interface fluctuations. Our simulations are in close agreement with the experimental findings, and contribute to the interpretation of spatially resolved spectra in QWs. ͓S0003-6951͑00͒04044-4͔Optoelectronics based on very thin active layers of semiconductor, such as quantum wells ͑QWs͒ are now currently used for many commercial applications. The performance of such devices is influenced by interface roughness, impurity concentration, and alloy homogeneity of the QW. Optical spectra of QWs yield valuable information on the quality of the interfaces and the growth process. 1,2 Disorder in a QW results in an effective two dimensional ͑2D͒ potential spatially correlated which tend to localize the center of mass of the exciton. This image was put forth on the basis of detailed theoretical simulations 3-5 and of observed homogeneous and inhomogeneous linewidths. 1 Macroscopic optical probes 1,2 have proven to be powerful techniques for probing localized excitons and hence interface fluctuations of quantum structures, however they perform a spatial averaging of the spectral signal, providing information at best on an inhomogeneous ensemble of quasi-0D ͑zero-dimensional͒ localized exciton states. Recently, techniques of very high spatial resolution optical spectroscopy allowed several groups to study the individual exciton eigenstates laterally localized at interface fluctuations. [6][7][8][9][10][11] Stimulated by the relevance of the experimental results cited above, theoretical approaches modeling the interaction of quantum structures with highly inhomogeneous light fields have been recently presented. 5,[12][13][14][15][16] In this letter, we present theoretical results for scanning local optical spectroscopy in QWs obtained after the simulation of a disorder potential with prescribed statistical properties. We will consider an input light field with a given profile g centered around the beam position R. In experiments done by both illuminating and collecting with the same tip ͑reflec-tion mode͒, the relevant optical signal that can be detected by a general near-field setup is proportional to 17 S ϭ͐dz drP*(r,z)•E(r,z), where P(r,z, ) is the macroscopic polarization of the sample induced by the electromagnetic field E(r,z, ). We have indicated with rϵ(x,y) the projection of the position vector on the plane of the QW and with z the coordinate along the growth direction. Via interferometric techniques it is possible in principle to measure both the phase and the amplitude of S, thus obtaining information on the local complex susceptibility of a sample. 18 Following the general linear response theory, the linear macroscopic polarization P(r...

Is the spatially averaged spectrum equal to the global spectrum?

“…Our analysis is performed on quantum wells (QWs). Interface fluctuations in QWs result in an effective 2D (two-dimensional) spatially correlated random potential that tends to localize the center of mass (COM) motion of excitons [9,10] and produces an inhomogeneous Gaussian-like absorption line [11,12]. Inhomogeneities and disorder effects give rise to surface quantum states, eventually localized, with mixed in-plane k-vectors (the in-plane k-vector is no more a good quantum number).…”

“…We perform specific calculations for the total absorption under sample illumination, considering both global s ¼ 1 ð Þ and local absorption spectra for different spatial resolutions. Calculations are carried out in real space, mapping on a fine mesh of points the Hamiltonian, which is then tridiagonalized by using the Lanczos algorithm [10,13]. We adopt an exciton kinetic mass of m ¼ 0:25m 0 typical for GaAs=AlGaAs quantum wells.…”

Spatially resolved spectra in semiconductor quantum structures: Spatially averaged spectra compared to far-field spectra

“…In particular we study the local optical absorption of semiconductor quantum wells ͑QW's͒ including the effects of interface fluctuations. Interface fluctuations in QW's result in an effective twodimensional ͑2D͒ spatially correlated random potential that tends to localize the center of mass ͑c.m.͒ motion of excitons 8,10 and produces an inhomogeneous Gaussian-like absorption line.…”

“…To what extent these spectral changes are detectable in real systems affected by disorder and imperfections? Does near-field microscopy provide just a spatial selection of inhomogeneous surface systems 8,9 or, in addition, does it enable the optical detection of states not accessible by far-field optical probes? These addressed questions are directly related to the following question: are spatially averaged near-field spectra equal to far-field spectra?…”

Microscopic quantum theory of spatially resolved photoluminescence in semiconductor 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.…”