Chapter 5 Acoustic and optical phonon assisted formation of biexcitons
5.3 Photoluminescence spectra analysis
In order to further understand the characteristic of the BX line, the PL-integrated intensities of the BX line as a function of excitation power at various temperatures are depicted in Fig. 5-5. Other than at 80 K as discussed above, IBX is proportional to Iexα with α ~ 1.86 but not an ideal exponent of 2. Its possible causes had been proposed to explain this observation: Phillips et al. [21] demonstrated that the reduction in the exponent α is induced in part by the short lifetimes of excitons and biexcitons in direct-band-gap materials. Yamada et al. [22]reported the radiative lifetime of biexcitons is shorter than that of excitons, leading to the absence of any quadratic dependence of biexciton density as a function of exciton density.
4 16 64
Iex1.86 Iex0.53 Iex0.32
10K 40K 80K
Excitation Power (mW)
Integrated Intensity (a.u.)
Fig. 5-5 Integrated emission intensity of biexciton as a function of excitation power under various temperatures. The corresponding power dependencies IBX ∝ Iexα are also labeled.
However, the key issue is why the exponent α decreases to less than unity (α ~ 0.32 and 0.53) and the integrated intensity exhibits quenching at high excitation power at 10 and 40 K. These phenomena to our best knowledge have not yet been
reported, although similar quenching effect had appeared in Fig. 4 of Ref. [23] for GaN/AlN quantum dots. We will discuss shortly that the scattering of acoustic and optical phonons could be responsible for different degrees of reducing α at different measuring temperature, other than the proposed scattered and annihilated by excitons, other biexcitons, and bound excitons [9,12].
As the excitons having kinetic energy less than those of the optical phonons, the only remaining relaxation process, which lowers the kinetic energy of the excitonic gas, is the emission of acoustic phonons.[24] Due to the small energy quanta of the acoustic phonons, the dissipation of the kinetic energy in the excitonic system is rather slow and requires many scattering events before quasi-equilibrium is reached.
By elevating the temperature so that the kinetic energy of excitons reaches the energy of the lowest optical phonon, the optical phonon scattering will participate in the exciton relaxation.
We utilized the analysis about emission shift of the free exciton with temperature variation [25]: ( )E T =E(0)−λ/[exp(=ϖ /k TB e) 1]− to evaluate the effective exciton temperature. By fitting the experimental data (open circles) at bath temperature (Tb) of 40 - 100 K for excitation power of 2 mW as the solid line in Fig.
5-6, we obtained the fitting parameters: E(0) = 3.379 eV represents the free exciton emission at T = 0 K (c.f. the reported E(0) = 3.379 eV at T = 5 K [26]), λ = 24.3 meV is a proportional coefficient, and = = 16.1 meV is the effective phonon energy, ϖ which is close to the lowest optical phonon of 12 meV. The inset of Fig. 5-6 depicts the estimated effective exciton temperature (Te) as a function of excitation power at various T . Notice that the power dependent energy shift corresponds to Tb e = 32 to 80 K and 40 to 85 K at Tb = 10 and 40 K. Under these conditions, the exciton kinetic energy or Te is inefficient to couple with optical phonons but lowering the
kinetic energy of the excitonic gas by emitting acoustic phonons, and the stochastic approach to the population distribution of the excitons in energy space is justified as in the case of Brownian motion. Estimated Temperature (Te)
Peak Energy (eV)
1/kBT (meV)-1
Fig. 5-6 Experimental (open dots) and calculated (solid lines) exciton energies plotted against inverse temperature. The inset shows the dependence of estimated temperatures (Te) on the excitation power under various bath temperatures (Tb).
Consequently, the decrease in α results from the insufficient cooling of excitons by acoustic phonon scattering for bounding exciton pairs to form biexcitons. On the other hand, due to the laser heating, Te was elevated above Tb from 80 to 114 K at Tb = 80 K. When the elevated temperature so as the kinetic energy of excitons approaches to the energy of the lowest optical phonon, near 12 meV in this case, the optical phonon will participate in the exciton relaxation process. The inelastic scattering between excitons with assistance of optical phonons ionizes one of the scattered excitons to n = ∞ state rather than n = 2 state and efficiently cools the other
exciton to the lower polariton branch so that high P emission was observed for T∞ b = 80 K, as shown in Fig. 5-3. Contrarily, without assistance of optical phonon, high P2
emission was found at T ≤ 40 K. b
5.4 Summary
We therefore conclude that high exciton density does not guarantee bounding exciton pairs to form biexcitons, the acoustic phonon scattering is responsible for exciton relaxation at low temperature while optical phonon scattering will participate in at high temperature. The efficient cooling of exciton with assistance of optical phonon scattering allows effectively bounding exciton pairs to form biexcitons;
contrarily, the exciton relaxation only via multiple acoustic phonon scattering may not efficiently enough to dissipate the excess kinetic energy of excitons to form biexcitons in turn to reduce the exponent of excitation. Furthermore, multi-exciton scattering via colliding with high density of excitons would result in quenching biexciton luminescence under very high excitation power.
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