  Black phosphorus stands out from the family of two-dimensional materials as a
semiconductor with a direct, layer-dependent bandgap in energy corresponding to
the spectral range from the visible to the mid-infrared (mid-IR), as well as
many other attractive optoelectronic attributes. It is, therefore, a very
promising material for various optoelectronic applications, particularly in the
important mid-IR range. While mid-IR technology has been advancing rapidly,
both photodetection and electro-optic modulation in the mid-IR rely on
narrow-band compound semiconductors, which are difficult and expensive to
integrate with the ubiquitous silicon photonics. For mid-IR photodetection,
black phosphorus has been proven to be a viable alternative. Here, we
demonstrate electro-optic modulation of mid-IR absorption in few-layer black
phosphorus under field applied by an electrostatic gate. Our experimental and
theoretical results find that, within the doping range obtainable in our
samples, the quantum confined Franz-Keldysh effect is the dominant mechanism of
electro-optic modulation. Spectroscopic study on samples with varying thickness
reveals strong layer-dependence in the inter-band transition between different
sub-bands. Our results show black phosphorus is a very promising material to
realizing efficient mid-IR modulators.
