LÉVY FLIGHT OF HOLES IN InP SEMICONDUCTOR SCINTILLATOR

Abstract

also seem to follow Lévy flights when foraging [11]. Finally, a vast literature is devoted to Lévy flights in finance, "random walk down the Street" [12].Nevertheless, there have been preciously few experimentally available laboratory systems for studying LF transport, ideally with variable parameters. A rather ingenious such system was recently demonstrated by Barthelemy et al. [13], who embedded scattering particles in a glass matrix -together with non-scattering glass microspheres of same refractive index as the matrix. The sole purpose of these spacer spheres was to modify locally the average separation between the scattering particles and thus control the step-length distribution for photon transport. With specially designed, highly non-trivial, distributions of microspheres diameter, the authors were able to observe a Lévy flight of light.Recently, we described [14] a more "natural" lab system exhibiting Lévy flight, namely the direct-gap semiconductor of high radiative efficiency, specifically n-doped InP. The randomly walking particles in this case are minority carriers (holes) and their dominant transport process is photon-assisted hopping. This process, also known as the photon recycling, consists of radiative recombination of a hole at one spot producing a photon, whose subsequent interband absorption leads to the re-emergence of a hole at another spot, possibly far away. The high radiative efficiency and low free-carrier absorption of light in lightly doped InP ensure that photon recycling continues for about 100 times before a hole recombines non-radiatively or a photon is absorbed without leaving a hole behind. The randomness of free flight is set by the emission spectrum in radiative recombination. This spectrum, combined with the interband absorption probability and the probability of photon propagation to a given distance, defines the probability distribution for free flights of photons. Photons generated in the long-wavelength wing of the emission spectrum travel long distances before they get re-absorbed and are responsible for the divergent variance of the distribution and the Lévy-flight nature of the resulting random walk. This process is reviewed in Sect. 2.Manifestations of anomalous transport were found [14] by studying photoluminescence in ndoped InP. The key evidence was derived from the ratio of transmitted and reflected luminescence spectra, measured in samples of the same doping level but very different thicknesses (350 µm vs. 50 µm). The results give a direct experimental proof of the nonexponential decay of the minority-carrier concentration from the surface where the holes were photo-excited initially. The power-law decay of the hole concentration, characteristic of the LF transport, is steep enough at short distances (steeper than an exponent) to fit the data for the thin sample, and at the same time slow enough at large distances (again, compared to an exponent) to account for the data for thick samples. This work is reviewed in Sect. 3. Transport at much larger distances (up to...

Temperature controlled Lévy flights of minority carriers in photoexcited bulk n-InP

“…1 together with the calculated spectrum. Also shown is the luminescence spectrum, observed from the broadside in reflection geometry [8,9]. We note that, compared to the reflection spectrum, the edge-excitation spectrum is noticeably shifted to the red side, indicating substantial filtering [7].…”

“…In the normal transport process, the stationary distribution of minority carriers produced by optical excitation in semiconductors decays exponentially from the excitation area and is characterized by a micron-scale diffusion length l. However, in moderately-doped direct-gap semiconductors with high radiative efficiency, the minoritycarrier transport is strongly modified by the "photon recycling" process (repeated radiative recombination and reabsorption of emerging photons). The distribution of steps in this photon-mediated random walk of minority carriers is defined by the photon reabsorption probability [7] and the single-step probability distribution P(x) can be calculated from the interband absorption and radiative recombination spectra [8].…”

“…The temperature dependent luminescence was studied in the same geometry as earlier [7], using n-InP slab [15] of size 20 mm by 7 mm and thickness d=350 µm, corresponding to x, y, and z directions, respectively. The moderate doping level N D = 3 × 10 17 cm −3 gives optimum radiative efficiency at room temperature [8]. A 808-nm laser beam was focused on the 7-mm edge by a cylindrical lens producing a uniform excitation along the edge.…”

Josephson-based Threshold Detector for Lévy-Distributed Current Fluctuations

“…Still dealing with material issues, also photoluminescence experiments in moderately doped n-InP samples reveal anomalous Lévy-type distribution [12][13][14][15][16][17]. This phenomenon could have a large impact on the design of a number of optoelectronic devices such as multicolored LEDs, opto-thyristors, photovoltaic devices with high efficiency, or semiconductor scintillator for radiation detection [16].…”

Edge excitation geometry for studying intrinsic emission spectra of bulk n-InP

“…Fortunately, in crystals with high quantum efficiency of emission we find a way of avoiding this difficulty, based on the giant spread of the minority carriers in the sample. The minority carrier distribution is strongly modified by the recycling effects (multiple emission-reabsorption events) [18,19,20]. When the losses of carriers (via non-radiative recombination) and photons (via residual free-carrier absorption) are low, the recycling leads to anomalous diffusion and a dramatic increase of the minoritycarrier spread in the sample (up to centimeter-scale distances) [17].…”