Homogeneous line broadening in individual semiconductor quantum dots by temperature fluctuations

We investigate the effect of temperature fluctuations on the spectral properties of individual semiconductor quantum dots (QD's) used as an active gain medium in laser diodes. On the basis of thermodynamic arguments we show that the QD eigenstates are thermally broadened. Because of the small heat capacity, the temperature of a QD is not well defined, and temperature fluctuations on the order of 3-10 K occur in typical QD structures at room temperature. Due to the temperature dependence of the band-gap energy in semiconductors, the energy band structure and the QD eigenstates become broadened as well. This broadening mechanism puts a lower limit on the minimal homogeneous linewidth and an upper limit on the maximum achievable gain of a QD. Applying the Langevin heat diffusion equation and using time-dependent perturbation theory, we calculate the resulting homogeneous broadening of the optical gain and absorption spectra. An analytical solution in terms of macroscopic thermal material parameters and QD size is derived for a simplified spherical QD structure with a Gaussian-type ground state wave function. We find a strong temperature dependence of the broadening and a change in the line shape function from a Lorentzian at low temperatures to a Gaussian in the high-temperature limit. Owing to the smaller thermal conductivity, ternary/quaternary QD structures exhibit significantly larger broadening than their binary counterparts. In typical In(Ga)As/Ga(Al)As QD's this mechanism broadens the line by about 0.3-1.2 meV at 300 K, and the characteristic temperature T₀ for the peak optical gain is on the order of 100 K.