  Localized surface plasmons (LSP) in semiconductor particles are expected to
exhibit spatial nonlocal response effects as the geometry enters the nanometer
scale. To investigate these nonlocal effects, we apply the hydrodynamic model
to nanospheres of two different semiconductor materials: intrinsic InSb and
$n$-doped GaAs. Our results show that the semiconductors indeed display
nonlocal effects, and that these effects are even more pronounced than in
metals. In a $150\mathrm{\,nm}$ InSb particle at $300\mathrm{\,K}$, the LSP
frequency is blueshifted 35%, which is orders of magnitude larger than the
blueshift in a metal particle of the same size. This property, together with
their tunability, makes semiconductors a promising platform for experiments in
nonlocal effects.
