Homogeneous line broadening in individual semiconductor quantum dots by temperature fluctuations

We investigate the effect of temperature fluctuations on the spectral prope rties of individual semiconductor quantum dots (QD's) used as an active gai n medium in laser diodes. On the basis of thermodynamic arguments we show t hat the QD eigenstates are thermally broadened. Because of the small heat c apacity, the temperature of a QD is not well defined, and temperature fluct uations on the order of 3-10 K occur in typical QD structures at room tempe rature. Due to the temperature dependence of the band-gap energy in semicon ductors, the energy band structure and the QD eigenstates become broadened as well. This broadening mechanism puts a lower limit on the minimal homoge neous linewidth and an upper limit on the maximum achievable gain of a QD. Applying the Langevin heat diffusion equation and using time-dependent pert urbation theory, we calculate the resulting homogeneous broadening of the o ptical gain and absorption spectra. An analytical solution in terms of macr oscopic 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, ter nary/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 te mperature T-0 for the peak optical gain is on the order of 100 K.