  Extensive numerical calculations show that the capacitance of back-gated
nanowires with various degrees of dielectric embeddings is accurately described
with an effective dielectric constant as long as the difference between the
dielectric thickness and the gate-nanowire distance is held constant. This is
valid for dielectrics with permittivities ranging from simple air to water.
However, due to screening the scaling is not valid if the dielectric lies down
well below the nanowire. Moreover, when only the dielectric thickness varies
the capacitance characteristics are S-shaped with three distinct regions, of
which only the first two can be used for dielectric sensing. The first region
is almost linear while the middle region, with a span of two diameters around
the center of the nanowire, is the most sensitive.
