Spatial resolution versus data acquisition efficiency in mapping an inhomogeneous system with species diffusion

Abstract

Traditionally, spatially-resolved photoluminescence (PL) has been performed using a point-by-point scan mode with both excitation and detection occurring at the same spatial location. But with the availability of high quality detector arrays like CCDs, an imaging mode has become popular for performing spatially-resolved PL. By illuminating the entire area of interest and collecting the data simultaneously from all spatial locations, the measurement efficiency can be greatly improved. However, this new approach has proceeded under the implicit assumption of comparable spatial resolution. We show here that when carrier diffusion is present, the spatial resolution can actually differ substantially between the two modes, with the less efficient scan mode being far superior. We apply both techniques in investigation of defects in a GaAs epilayer – where isolated singlet and doublet dislocations can be identified. A superposition principle is developed for solving the diffusion equation to extract the intrinsic carrier diffusion length, which can be applied to a system with arbitrarily distributed defects. The understanding derived from this work is significant for a broad range of problems in physics and beyond (for instance biology) – whenever the dynamics of generation, diffusion, and annihilation of species can be probed with either measurement mode.

Optical Imaging of Diffusive Electrons with Different Kinetic Energies in a Semiconductor

“…It is important to make such comparisons under the same laser power because it has been shown in previous work that the diffusion length is sensitive to the excitation power [6,8,9]. Clearly, the three profiles are quite close to each other, which indicates that the diffusion lengths for electrons of different kinetic energies are approximately the same.…”

“…Clearly, the three profiles are quite close to each other, which indicates that the diffusion lengths for electrons of different kinetic energies are approximately the same. The correct function for describing the profile should be a modified Bessel function [4,5,6] but corrected for the final laser spot size, which requires solving the diffusion equation numerically. As an approximation, a simple exponential decay function (e −r/L ) was adopted.…”

“…The semiconductor sample used was a 1 μm thick high-quality GaAs (gallium arsenide) thin-film sandwiched between two GaInP (gallium indium phosphide) layers with a higher bandgap [6,8,9]. GaAs was chosen because of the availability of the high-quality sample as well as its important role in many technology applications, including high efficiency solar cells, semiconductor lasers, and high-speed electronics.…”

“…Because electrons with different kinetic energies emit photons at different wavelengths, the spatial variation of the PL signal for different wavelengths had to be measured and compared to test the hypothesis. In previous studies, both electron and laser beams have been used to generate a local electron population, but the spatial profiles of light emission were typically measured either by including the whole emission spectrum (non-wavelength selective) [5] or by selecting a single narrow band near the bandgap [6,8,9,10]. Thus, the potential wavelength dependence had not been explicitly examined.…”

“…After the PL imaging data is obtained, a computer code, written in Wolfram Mathematica, is used to extract the electron diffusion length. The spatial profile of the PL image is the solution of a diffusion equation including a generation term and a depletion term [4,5,6]. It is usually a decay function of r with a parameter L, where r is the lateral distance measured from the generation site at r = 0; L is the electron diffusion length, assuming that the semiconductor is very thin and diffusion occurs only laterally.…”