  The electric field effect is a useful means of elucidating intrinsic material
properties as well as for designing functional devices. The
electric-double-layer transistor (EDLT) enables the control of carrier density
in a wide range, which is recently proved to be an effective tool for the
investigation of thermoelectric properties. Here, we report the gate-tuning of
thermoelectric power in a black phosphorus (BP) single crystal flake with the
thickness of 40 nm. Using an EDLT configuration, we successfully control the
thermoelectric power (S), and find that the S of ion-gated BP reached +510
$\mu$V/K at 210 K in the hole depleted state, which is much higher than the
reported bulk single crystal value of +340 $\mu$V/K at 300 K. We compared this
experimental data with the first-principles-based calculation and found that
this enhancement is qualitatively explained by the effective thinning of the
conduction channel of the BP flake and non-uniformity of the channel owing to
the gate operation in a depletion mode. Our results provide new opportunities
for further engineering BP as a thermoelectric material in nanoscale.
