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Excitons are compound particles formed from an electron and a hole insemiconductors. The impact of this substructure on the phonon-excitoninteraction is described by a closed system of microscopic scatteringequations. To calculate the actual excitonic thermalization properties beyondthe pure bosonic picture, this equation is derived directly from anelectron-hole picture within the Heisenberg equation of motion framework. Inaddition to the well-known bosonic character of the compound particles, weidentified processes of a repulsive, fermionic type, as well as attractivecarrier exchange contributing to the scattering process. In this analyticalstudy we give general statements about the thermalization of excitons in twoand three dimensional semiconductors. We give insights on the strong dependenceof the thermalization characteristics of the exciton Bohr radius and thethermalization wavelength. Above all, we analytically provide arguments why abosonic behavior of excitons - such as an enhanced ground state occupation -requires the dominant phonon scattering to be quasielastic. Acoustic phononstend to fulfil this, as each scattering event only takes small amounts ofenergy out of the distribution, while optical phonons tend to preventmacroscopic occupations of the lowest exciton state, since the Pauli repulsionbetween the individual carriers will then dominate the thermalization dynamics.

Fermionic vs. bosonic thermalization in the phonon-driven exciton dynamics: An analytic dimensionality study