Hopping process of bound excitons under an energy gradient

Abstract

We report on the mechanism of hopping for bound excitons under an energy gradient. By means of a Monte-Carlo simulation, we show that this mechanism explains the movement of bound excitons observed experimentally. We show that the speed of the excitons decreases quickly with temperature. Thanks to an effective medium approximation, we deduce an analytical model to estimate the average speed at T ¼ 0 K. Finally, we compare our simulations results to the speed observed in bent ZnO wires and find a good agreement between theory and experiments. V C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4863319] The ability to tune the strain in different structures is interesting for many applications such as the enhancement of the mobility in transistors 1 or the engineering of the optical polarization properties of heterostructures.2,3 Recently, it has been shown that it is possible to design nano/microstructures to obtain a strain gradient and control the motion of excitons. 4,5 In particular, bent nanowires have gained considerable attention because of the possibility to tune the bandgap without plastic relaxation.6-8 For instance, it has been recently demonstrated that excitons can move because of the strain gradient induced by the bending of a wire. However, at T ¼ 10 K at which the experiments are performed, the photoluminescence of ZnO wires is dominated by the emission coming from the donor bound exciton (D X). Thus, experimental evidence indicates that donor bound excitons are drifted by the strain gradient, against simple views implied by their name: "donor bound exciton."The motion of bound excitons has already been observed in inhomogeneous materials such as GaAsP:N, 10,11 InGaN, 12 and MgZnO alloys. 13 In these random alloys, the transfer of such excitons from one donor to another is driven by the tunneling of exciton to lower states. The same mechanism has been observed and successfully described by a stochastic model of exciton transfer in homogeneous GaP with well-defined impurities levels.14 However, in such samples, the random distribution of lowest states makes it difficult to obtain an accurate estimation of the characteristic time for the exciton to jump from one donor to the other.The strain-induced energy gradient in bent micro/nanowires directly builds a "donor ladder" as observed in the scheme of Figure 1. Indeed, because of the continuous change of bandgap energy, the relative positions of donors are sorted by energy along the strain gradient. This arrangement of donors gives the possibility to get an accurate estimation of the hopping rate of excitons, unlike in the case of inhomogeneous materials.In this Letter, we propose a model for the hopping process of donor bound excitons in the presence of an energy gradient. We compute the exciton dynamics by means of Monte-Carlo (MC) simulations taking into account the probability for the transfer of an exciton from a donor to another. We compare the case of zero temperature to the case of a nonzero temperature and show that the mean speed shoul...

Exciton dynamics at a single dislocation in GaN probed by picosecond time-resolved cathodoluminescence

“…As shown in Figs. 3(c) and 3(d), the good agreement between our experimental results and the fits (blue lines) allows us to clearly identify the effective radius of dislocation 14,21 Note that the CL intensity at initial delay is defined as I CL ðr 0 ; t ¼ 0Þ / n 0 N =s r . Considering that no diffusion happens at this moment, the decrease of I CL ðr 0 ; t ¼ 0Þ near the dislocation can be due to either the increase of s r or the reduction of n 0 .…”

Exciton hopping probed by picosecond time-resolved cathodoluminescence

“…However, when raising the temperature, the backward motion of excitons activated by thermal energy affects dramatically the average speed of excitons along the strain gradient. The average speed of D X A s predicted to decrease by almost a factor of 10, when raising the temperature from 0 K to 30 K. 8 Therefore, this model predicts two main features for the hopping process of excitons: (i) the independence of the exciton speed from the energy gradient value at low temperature and (ii) a strong thermal quenching of the exciton speed.…”

“…Since the exciton hopping rate is independent of the energy gradient, 8 instead of the drift-diffusion model applied in Ref. 7, Equation (2) has been solved by finite difference methods to estimate the exciton speed from our measurements.…”

“…8 This model is based on the Miller-Abrahams formalism for the jump rate of excitons in disordered semiconductors. 9 The hopping rate v ij from one donor i at an energy E i to another donor j at an energy E j is given by…”

Strain Gradient Modulated Exciton Evolution and Emission in ZnO Fibers

“…Subsequently, several studies reported the effects of different deformation potentials on the NBE band shift of ZnO nanowires and microwires2930313233. Recently, it was found that the neutral-donor-bound excitons of bent ZnO microwires drifted towards and emitted photons at the tensile side through a hopping process at liquid helium temperature343536. In addition, it was reported that a transverse piezoelectric field could produce separated electrons and holes that drifted to the tensile and compressive sides, respectively, which led to a net redshift of free-exciton PL emission in the bent ZnO nanowire37.…”