RAPID COMMUNICATIONS PHYSICAL REVIEW B 92, 121201(R) (2015) Correct determination of low-temperature free-exciton diffusion proﬁles in GaAs S. Bieker, T. Kiessling, * W. Ossau, and L. W. Molenkamp Physikalisches Institut (EP3) der Universit¨ at W ¨ urzburg, 97074 W¨ urzburg, Germany (Received 23 June 2015; published 2 September 2015) We report on low-temperature spatially resolved photoluminescence (SRPL) experiments to study the diffusion of free excitons in a 1.5-μm-thick layer of high-purity epitaxial GaAs. Extending previous SRPL experiments, we analyze the stationary diffusion proﬁles detected on the second LO-phonon replica of the free exciton. This allows us to circumvent the inherent interpretation ambiguities of the free-exciton zero-phonon line. Moreover, a spatially resolved line shape analysis of the (FX) − 2 LO replica provides direct experimental access to the pump-induced exciton temperature proﬁle. We demonstrate that only resonant optical excitation prevents the buildup of a temperature gradient in the carrier system, which otherwise severely distorts the stationary and time-resolved free-exciton diffusion proﬁles. DOI: 10.1103/PhysRevB.92.121201 PACS number(s): 78.55.Cr, 71.35.−y, 78.20.−e, 66.30.−h Introduction. In spatially resolved photoluminescence ex- periments, the excitation laser beam is tightly focused to a few-micrometer spot size on the sample surface. Electrons, holes, and excitons, which are only created in this relatively small excitation volume, move freely through the crystal until they are eventually captured by impurities or annihilated by radiative or nonradiative decay. In high-purity semiconductors that exhibit low residual impurity concentrations, the charac- teristic length scale of photocarrier migration can signiﬁcantly exceed the spatial extent of the pump spot. Spatially resolved photoluminescence (SRPL) detection schemes monitoring the spatial distribution of the luminescence intensity then provide direct experimental access to photocarrier transport processes. In distinction from traditional transport experiments, spatially resolved optical spectroscopy techniques obviate the applica- tion of electric ﬁelds and are not limited to the investigation of charged particles. SRPL experiments are widely used to investigate the diffu- sion of photoexcited charge carriers and excitons in semicon- ductors and semiconductor nanostructures. Most commonly, above-band-gap illumination is used to excite a localized photocarrier packet. Diffusion coefﬁcients are then derived from comparison of the resulting diffusion proﬁles to solutions of the photocarrier diffusion equation. This approach, however, may face ambiguity problems. In this Rapid Communication, we report on SRPL ex- periments on a nearly defect-free GaAs layer to study the diffusion of free excitons. Our measurements reveal a peculiar dependence of the stationary exciton diffusion proﬁle on the excitation wavelength. We unambiguously demonstrate that only under resonant optical excitation, the experimental diffusion proﬁles are correctly described by the commonly used formulation of the photocarrier diffusion equation, which assumes a spatially nonvarying diffusion coefﬁcient. Because of localized heating in the carrier system, slight off-resonant excitation already results in severe distortions of the exciton diffusion proﬁles. We show that the same difﬁculty applies to time-resolved SRPL experiments that use pulsed optical excitation. * tobias.kiessling@physik.uni-wuerzburg.de Sample and experimental setup. The investigated sample is a nominally undoped, 1.5-μm-thick epilayer of (001)-oriented molecular-beam-epitaxy-grown GaAs. The active layer is enclosed between one 250-period GaAs/Al 0.09 Ga 0.91 As superlattice on the bottom and one 80-period superlattice of identical composition on top to prevent optically excited excitons from diffusing out of the layer and to suppress surface recombination [1]. The low-temperature photoluminescence (PL) spectrum of the sample is displayed in Fig. 1(a). The dominance of the free-exciton recombination line (FX) along with the extremely weak bound exciton luminescence indicates a negligible defect concentration in the active layer. From a comparison with spectra reported in the literature [2,3], we estimate a residual impurity concentration of 1 × 10 12 cm −3 . We use a standard confocal SRPL technique to detect spatially resolved PL proﬁles. The sample is mounted on the cold ﬁnger of an optical liquid-helium-ﬂow cryostat. Tunable optical excitation is provided by a continuous wave (cw) Ti:sapphire laser. The laser beam is focused at normal incidence on the sample surface by an inﬁnity-corrected NA = 0.4 microscope objective to a (1/e) intensity spot diameter of 3.6 μm. Luminescence is collected by the same objective, focused on the entrance slit of a 1 m focal length monochromator equipped with a 1200 mm −1 grating, and detected by a liquid-nitrogen-cooled CCD array. Spatial information on the local PL intensity is contained in the vertical pixel number of the two-dimensional CCD image. The spatial resolution of the detector assembly is 1.0 μm. Results and discussion. The inhomogeneous partial dif- ferential equation describing photocarrier diffusion in bulk semiconductors reads [5] ∂ ∂t n(x,t ) = ∇ · [D∇ n(x,t )] − n(x,t ) τ + g(x,t ), (1) where n(x,t ) is the photocarrier density, D is the diffusion coefﬁcient, τ is the photocarrier ensemble lifetime, and g(x,t ) represents the source term due to the laser excitation spot. To simplify Eq. (1), it is typically assumed that the diffusion coefﬁcient D does not depend on the spatial coordinate x and that the diffusion process is isotropic. The density proﬁle n(x,t ) → n(r,t ) then depends only on the radial distance r with respect to the pump spot and the photocarrier diffusion 1098-0121/2015/92(12)/121201(5) 121201-1 ©2015 American Physical Society