Exciton relaxation in bulk wurtzite GaN: the role of piezoelectric interaction

Abstract

A theoretical study on the relaxation of coupled free carriers and excitons after non‐resonant optical excitation in bulk wurtzite GaN is presented. In particular the effect of the acoustic piezoelectric scattering is taken under consideration, and the respective rates have been calculated, including screening effects. Results show that the piezo‐acoustic rates are bigger in the wurtzite phase of GaN with respect to the cubic phase, and they are really sensitive to the background doping of the sample. Simulations of the full dynamics of the system are performed by using an Ensemble Monte Carlo method under which all the relevant scattering mechanisms are included. The set of semiclassical Boltzmann equations for electron and hole populations is complemented by an additional equation for the exciton distribution and is coupled by reaction terms describing phonon‐mediated exciton binding and dissociation. The temporal evolution is studied in the short range time (100 ps) after photo‐excitation. It shows that a high background doping prevents the electrons to relax toward low energy states.

Magneto-Optic Effect in Amorphous Bi3Fe5O12 Waveguides Sputtered at Room Temperature

“…The intrasubband, piezoacoustic transition rates of carriers have already been reported [15] for both wurtzite and cubic symmetry, having in mind an isotropic Bohr radius for the case of excitons. Here we highlight the effect of the anisotropy of the excitonic wave function [18] on the scattering rates according to the variational method [19].…”

“…We calculate the total piezoelectric rate of carriers according to the Fermi golden rule, assuming strict conservation of energy and momentum and considering the real energy of the acoustic phonon in the collision. We also use the squared spherical averages of the piezoelectric constants during the calculation of PE scattering rates [15]. In addition, we calculate the rates in the presence of static screening for a background doping density of 10 17 cm −3 , characteristic of bulk wurtzite GaN samples.…”

“…We can account for these fluctuations to the modified maxima and minima of the exciton form factor with respect to different values of the exciton wave vector K [22]. Nevertheless, despite these differences between the rates for different variational parameters, the PE emission rates will always be greater than the deformation potential scattering rates within a wide temperature range, especially when the impurity concentration is lower than 10 15 cm −3 [15]. The zone-centre GaN POP frequency values are taken from experimental results [23] and the dielectric constants are taken from Lee et al [4].…”

“…Furthermore, free exciton and excitonpolariton photoluminescence studies have taken into account the hexagonal lattice anisotropy only in recent years [13]. On the other hand, ensemble Monte Carlo simulations [14] have successfully described the evolution of free and bound carriers under a variety of scattering mechanisms, including the piezoelectric (PE) scattering in bulk GaN of wurtzite and cubic symmetry [15][16][17]. …”

Intervalley energy of GaN conduction band measured by femtosecond pump-probe spectroscopy

“…For excitation above 1.06 eV, the DT decay time is prolonged by the electron scattering to the L valley and back to the Γ valley. The intervalley scattering takes place primarily with participation of LO phonons, since the electron scattering time by large wave vector LO phonons is much smaller than that for corresponding acoustic phonons [24,25]. At room temperature, the population of LO phonons is small, thus, scattering with a phonon emission is much more likely than with absorption [24].…”