Shih et al. Nanoscale Research Letters 2011, 6:409 http://www.nanoscalereslett.com/content/6/1/409 shown in Figure 10b, the two emission peaks appeared in the PL spectrum of QD2 were still visible in the cor- responding PLE spectrum with a slightly broadened resonance at approximately 125 meV measured from the WL. However, in contrast to the results from QD2, the emission peak of the first excited state at 115 meV measured from the WL in the PL spectrum of QD1 was missing in the corresponding PLE spectrum and was replaced by a random background, as shown in Figure 10a. The existence of a quasicontinuum of states has been suggested by the background signal observed in PLE and recently reported by different authors [5,15,16]. Recent experiments also revealed an efficient intradot relaxation mechanism which allowed the easy relaxation of the carriers within continuum states, and transition to the ground state by emission of localized phonons [5] or Auger scattering [17]. Quantitative study and analysis of the existence of acoustic phonon sidebands in the emission line of single InAs QDs was reported in Ref. [18]. The cross transitions provide a continuum of final electronic states that plays a role similar to the reservoir of large-wave-vector states for the excitonic ground state broadening in 2D quantum wells [12]. Therefore, the broadening of the excited state spectra lineshape and the interband absorption in QDs were affected by the interplay between cross transitions and LA phonon scattering. The homogeneous linewidth Γ(T) of excitons is usually described as the sum of a static broadening Γ0 including radiative broadening and a temperature- dependent one, which accounts for acoustic and optical phonon broadening [19]. Efficient coupling to acoustic phonons exists not only for QD ground states but also for excited states. For low temperature, in which the interaction with acoustic phonon is dominant, linewidth broadening is written as [12,13]: Γ(T) = Γ0 + aT, where a accounts for the acoustic phonon broadening effi- ciency. The acoustic phonon broadening efficiency ain- creased with the normalized background intensity [12]. To interpret our experimental findings, bound-to- bound transitions and the bound-to-delocalized state transitions were calculated as a function of dot size at constant confinement potentials. A self-consistent itera- tive approach was used to calculate the energy levels of electrons and holes using non-parabolic and parabolic approximation for the conduction and valence bands, respectively. The calculations were done for a single dot in a large numerical box. The simulated dot geometries were determined from AFM measurements of our QD samples. The calculated onset energies of the continuum measured from the WL edge were 106 and 211 meV for QD1 and QD2, respectively, and are indicated with blue arrows, shown in Figure 10. Meanwhile, to compare dif- ferent values of acoustic phonon broadening efficiencies Page 6 of 7 a for QD1 and QD2, the QD-independent values of the PLE background signal needs to be determined. This was achieved by normalizing the PLE spectra with the WL absorption edge [12] at 1.42 eV for both QD1 and QD2, as shown in Figures 11a, b. However, the excited state of QD1 has the highest value in the normalized PLE intensity even though the energies of the excited states of both QD samples were above the onset ener- gies of the continuum. Therefore, the excited state of QD1 had a higher acoustic phonon broadening effi- ciency and suffered more from the LA phonon-assisted scattering effect, which led to a much larger degree of linewidth broadening. Notably, the excited state of the QD2 at the higher energy also has a larger normalized PLE intensity than the excited state at the lower energy, which showed a broader spectral profile due to the higher phonon scattering rate. Conclusions In conclusion, the magnetic field dependence of the PL and PLE spectra were measured for MBE-grown QD nanostructures with different sizes and shapes. The interband optical properties of QDs were affected by the crossed electron-hole levels. Additionally, The broaden- ing of discrete (resonant) interband optical absorption is attributed to the combined effects of the crossed Figure 11 Normalized PLE spectra with the PLE signal at 1.42 eV at 1.4 K.