  It is shown that semiconductor nanoscale resonators with extreme dielectric
confinement accelerate the diffusion of electron-hole pairs excited by
nonlinear absorption. These novel cavity designs may lead to optical switches
with superior modulation speeds compared to conventional geometries. The
response function of the effective carrier density is computed by an efficient
eigenmode expansion technique. A few eigenmodes of the diffusion equation
conveniently capture the long-timescale carrier decay rate, which is
advantageous compared to time-domain simulations. Notably, the eigenmode
approach elucidates the contribution to carrier diffusion of the in-plane and
out-of-plane cavity geometry, which may guide future designs.
