Abstract
We report a new computational model to incorporate carrier heating/cooling
effects for the finite-difference time-domain (FDTD) simulation of
electromagnetic interactions with semiconductor media. The model is
formulated to be computationally efficient enough to be applied to FDTD
simulations of photonic devices of complex structural geometry. The model
developed here is built on top of a previous multi-level multi-electron
(MLME) model we presented and the new model is called MLME-dynamical
temperature (MLMEDT) model. The key developments here include the following.
1) Intraband transition terms with electron and hole temperature parameters
that vary with time and space are introduced. 2) Rate equations for the
explicit update of carrier temperature are formulated. A computationally
efficient method is used to evaluate these carrier temperature rate
equations which circumvent iterative procedures as well as the need to
dynamically compute the chemical potential by presolving the relational
functions required using dimensionless fitting functions. The temporal
update of these fitting functions only needs the total carrier number
densities, which are already obtained in the MLME model computation. 3) The
changes in the total carrier kinetic energy density and carrier number
density due to all interband processes such as stimulated
emission/absorption and intraband processes such as free carrier absorption
are tracked to drive the carrier temperature rate equations. 4) The thermal
relaxation of the electron and hole temperatures to the lattice temperature
and the thermal relaxation between electrons and holes are also included. In
order to validate the approach, simulations of thermalization of
nonequilibrium carrier distributions and nonlinear gain and refractive index
dynamics in semiconductor optical amplifiers (SOA) are presented.
Quantitative agreement with nonlinear gain dynamics experiments of SOA
directly verifies the accuracy of the current approach. Additionally, a 2-D
simulation of a microdisk laser is presented to depict how FDTD can be used
to visualize the spatial profile of carrier temperatures. The computational
time of the MLMEDT model is found to be only ~10% more than that
of the MLME model, thus showing high computational efficiency.
© 2011 IEEE
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