Theory of spontaneous emission of quantum dots in the linear regime

We develop a fully quantum-mechanical theory for the interaction of light and electron–hole excitations in semiconductor quantum dots. Our theoretical analysis results in an expression for the photoluminescence intensity of quantum dots in the linear regime. Taking into account the single-particle Hamiltonian, the free-photon Hamiltonian, the electron–hole interaction Hamiltonian, and the interaction of carriers with light, and applying the Heisenberg equation of motion to the photon number expectation values, to the carrier distribution functions and to the correlation term between the photon generation (destruction) and electron–hole pair, we obtain a set of luminescence equations. Under quasi-equilibrium conditions, these equations become a closed-set of equations. We solve them analytically, in the linear regime, and we find an approximate solution of the incoherent photoluminescence intensity. The validity of the theoretical analysis is tested by investigating the emission spectra in the high-temperature regime, interpreting the experimental findings for the emission spectra of a lens-shaped In_0.5Ga_0.5As self-assembled quantum dot. Our theoretical predictions for the interlevel spacing as well as for the dephasing time caused by electron–longitudinal optical phonon interactions are in good agreement with the experimental results.