Gas-phase synthesis of semiconductor nanoparticles is
often supported
by optical in situ measurements to determine the particle size, phase,
and volume fraction. These attributes are connected to the optical
properties of these particles, which depend strongly on the temperature
and particle size as well as the phase transition near the melting
point. To support such measurements, we derive a Lorentz-oscillator
model for solid silicon and germanium with temperature- and particle-size-dependent
transition energies, line widths, and oscillator strengths. The model
yields the complex dielectric function that is then processed using
Mie theory to calculate size-dependent absorption and scattering cross-sections
for nanoparticles as well as nanoparticle aerosols.