Phonon-induced photoluminescence from a single

quantum dot in the regime vibrational resonance

Anvar S. Baimuratov, Vadim K. Turkov, Mikhail Yu.

Leonov, YuriiK. Gun'ko, Alexander V. Baranov,

Anatoly V. Fedorov Department of Optical Physics and Modern Natural Science

University of lTMO

Saint-Petersburg, Russia

A bstarct-We develop a theory of phonon-induced

photoluminescence from a quantum dot in the regi me of

vibrat ional resonance. Using the generalized model for

renormalization of the quantum dot's energy spectrum and the density matrix formalism, we derive an expression for the

differential cross-sect ion of the phonon-induced

photoluminescence from a quantum dot.

Keywords-quantum dot; ; photoluminescence; vibrational resonance

I. INTRODUCTION

The secondary-emission spectroscopy is the powerful

optical tool for studying both individual quantum dots (QDs) and their ensembles. It enables one to determine the chemical

composition of the QD material measure the mechanical stress inside a QD, investigate the properties of the QD surface and

study various aspects of the electron-phonon interaction inside QDs. Many of the unique physical properties of semiconductor

QDs underlying their applications in photonics were

determined using the experimental methods of the secondary­emission spectroscopy.

Among the most important interactions in semiconductor QDs is the electron-phonon coupling, which enhances the

dephas ing rates of spectroscopic trans itions and reduces the lifetimes of electronic excitations. This interaction also leads to

the formation of hybrid polaron-like states inside QDs with

resonant electron and phonon subsystems causing a significant modification of the QDs' energy spectra [1, 2]. The vibrational

resonance required for the modification to occur is realized, for instance, where the energy of a phonon mode (supported either

by the QD or the host material) coincides with the energy spacing between a pair of the quantum-confined electron states

of the QD [3, 4]. Often, these are the longitudinal optical (LO) phonons and the polar electron-phonon interaction that couple

the states and induce the resonance. The energy splitting of the

resulting polaron-like excitations is typically in the

Ivan D. Rukhlenko Department of Electrical and Computer Systems

Engineering, Monash University,

Clayton, Australia

mill ielectronvolt range and can therefore be experimentally

resolved only at cryogenic temperatures.

n. RESULTS

We have theoretically studied the process of QD photoluminescence involving the emission of the dispers ion less

optical phonons that are confined by the QD and resonant to a pair of its electron states. To describe this process, we had to

abandon the infinite-potential-well model of the QD and assume that its surface is penetrable for the confmed charge

carriers. This assumption allows the polaron-like states arising

from the resonant electron-phonon coupling to decay with the emission of phonons in spherical QDs. Using the density

matrix forma lis m, we then derived an exact expression for the differential cross section of the stationary, low-temperature

photoluminescence. Being applicable to the cases of arbitrarily degenerate electron states and an arbitrary number of phonons,

our expression describes a wide variety of practical situations.

It may prove useful to experimentalists in the analysis of the frequency-resolved photoluminescence spectra and determination of the fundamental parameters of the polaron­like excitations in semiconductor QDs.

REFEREN C ES

[I] I. D. Rukhienko, A. V. Fedorov, A. S. Baymuratov, and M. Prem aratne, "The ory of quasi-elasti c s econdary emission from a quantum dot in th e regime of vibrat ion al resonance" Opt. Express, vol 19, p.15461,20 11.

[2 ] A. V. Fedorov, A V. Baranov, and K Inoue, " Exciton-phonon coupling in s emiconductor quantun dots: Re9Jnant Raman scatt ering" Phys. Rev. B, vol. 5 6, p. 7491, 1997.

[3 ] A. V. Fedorov and A. V. Baranov, "Exciton-vibration al interaction of the Fro hlich type in quasi-zero-size systems" 1. Exp. Theor. Phys., vol. 83, p. 610, 1 996.

[4] T. Ito h, M. Nishijim a , A. I. Ekimov, C . Gourdon , A. L. Efros, and M. Ro s en, "Polaron and exciton-phonon complexes in CuCI nanoaystals" Phys. Rev. Lett, vo1.74, p. 1645,1995.