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Physical review. B, Condensed matter

Optical dephasing and excitation transfer of an impurity-bound exciton in a semiconductor: Photon-echo experiments on GaP:N

Laurens W. Molenkamp, Douwe A. Wiersma

Published Dec 15, 1985• 16 citations
Publisher

Abstract

We report low-temperature results of accumulated and two-pulse picosecond photon-echo experiments on the optical transition of the nitrogen-bound exciton in GaP:N. The observed temperature dependence of the dephasing of the so-called A line at 534.95 nm can be explained in terms of (stimulated) phonon processes involving the lower B state and, at higher temperatures, the free-exciton band. The low-temperature-echo decay time of 25.5\ifmmode\pm\else\textpm\fi{}0.5 ps is shown to be determined by the lifetime of a A state. Analysis of the factors governing the intensity of the accumulated photon echo as a function of temperature leads to the conclusion that in the B state temperature-independent excitation transfer occurs. The rate constant of this phenomenon, which we ascribe to excitation tunneling, is ${10}^{7}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$.

DOI
10.1103/physrevb.32.8108

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Journal of the Physical Society of Japan•Aug 15, 1982•12 citations
We report low-temperature results of accumulated and two-pulse picosecond photon-echo experiments on the optical transition of the nitrogen-bound exciton in GaP:N. The observed temperature dependence of the dephasing of the so-called A line at 534.95 nm can be explained in terms of (stimulated) phonon processes involving the lower B state and, at higher temperatures, the free-exciton band. The low-temperature-echo decay time of 25.5\ifmmode\pm\else\textpm\fi{}0.5 ps is shown to be determined by the lifetime of a A state. Analysis of the factors governing the intensity of the accumulated photon echo as a function of temperature leads to the conclusion that in the B state temperature-independent excitation transfer occurs. The rate constant of this phenomenon, which we ascribe to excitation tunneling, is 107{10}^{7}107 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1.
The coherent optical response from 140 nm and 65 nm thick ZnO epitaxial layers is studied using four-wave-mixing spectroscopy with picosecond temporal resolution. Resonant excitation of neutral donor-bound excitons results in two-pulse and three-pulse photon echoes. For the donor-bound A exciton (D0XA{\mathrm{D}}^{0}{\mathrm{X}}_{\text{A}}D0XA​) at temperature of 1.8 K we evaluate optical coherence times T2=33−−50{T}_{2}=33--50T2​=33−−50 ps corresponding to homogeneous line widths of $13--19\phantom{\rule{0.222222em}{0ex}}\ensuremath{\mu}\mathrm{eV}$, about two orders of magnitude smaller as compared with the inhomogeneous broadening of the optical transitions. The coherent dynamics is determined mainly by the population decay with time T1=30−−40{T}_{1}=30--40T1​=30−−40 ps, while pure dephasing is negligible. Temperature increase leads to a significant shortening of T2{T}_{2}T2​ due to interaction with acoustic phonons. In contrast, the loss of coherence of the donor-bound B exciton (D0XB{\mathrm{D}}^{0}{\mathrm{X}}_{\text{B}}D0XB​) is significantly faster (T2=3.6ps{T}_{2}=3.6\phantom{\rule{0.16em}{0ex}}\mathrm{ps}T2​=3.6ps) and governed by pure dephasing processes.
The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.
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Using a stochastic model, we calculate the temperature dependence of the homogeneous linewidth and the two-pulse photon-echo decay rate of optically active impurities in glasses. The theory applies to the low-temperature regime T\ensuremath{\lesssim}10 K, where it is assumed that the dephasing arises from an elastic dipole interaction of the impurity with an array of thermally excited tunneling systems. Averaging over the tunneling parameters and using relaxation rates appropriate to vitreous silica, we find that the photon-echo decay rate varies as T1.1{T}^{1.1}T1.1 and the homogeneous linewidth as T1.2{T}^{1.2}T1.2 for 0.1\ensuremath{\le}T\ensuremath{\le}1 K, assuming a constant density of states for the tunneling systems. Both the photon-echo amplitude and the optical dipole-moment correlation function decay exponentially in time. The rates, however, are different, with a ratio of photon-echo dephasing time to optical-absorption dephasing time of 6.9 at T=1 K, assuming a constant density of states. The relation of our results to various experimental studies is discussed.
We have observed spontaneous photon echoes from acceptor bound excitons in CdSe. The I1{\mathit{I}}_{1}I1​ line is inhomogeneously broadened to about 1 meV. The homogeneous linewidth is, at low temperature and low excitation density, found to be extremely small and is determined by the recombination lifetime ${\mathrm{\ensuremath{\tau}}}_{\mathit{R}}$=500 ps. The bound excitons have negligible interaction with phonons and interact only weakly with free excitons with a collision cross section \ensuremath{\sigma}=5.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ cm2{\mathrm{cm}}^{2}cm2. With increasing temperature, the dephasing of the bound excitons is determined by thermal release from the impurity bound state.
Optical dephasing due to intermolecular interaction is studied for pentacence molecules introduced in naphthalene and p -terphenyl crystals by measuring the ordinary photon echo and the accumulated three-pulse echo. It is found that the reciprocal of pure dephasing time increases linearly with the guest molecule concentration at low temperature where pure dephasing is known to be temperature-independent. A new model based on virtual transfer of excitation energy, i.e. energy transfer without phonon asistance, between guest molecules is presented to interpret this dephasing process. It is shown that observed linear dependence of the line width representing pure dephasing is well interpreted by this model, and that the calculated relationship between the line width and concentration agrees with the experimental one within a factor of about two.