  Atomically thin black phosphorus (BP) is a promising two-dimensional material
for fabricating electronic and optoelectronic nano-devices with high mobility
and tunable bandgap structures. However, the charge-carrier mobility in
few-layer phosphorene (monolayer BP) is mainly limited by the presence of
impurity and disorders. In this study, we demonstrate that vertical BP
heterostructure devices offer great advantages in probing the electron states
of monolayer and few-layer phosphorene at temperatures down to 2 K through
capacitance spectroscopy. Electronic states in the conduction and valence bands
of phosphorene are accessible over a wide range of temperature and frequency.
Exponential band tails have been determined to be related to disorders. Unusual
phenomena such as the large temperature-dependence of the electron state
population in few-layer phosphorene have been observed and systematically
studied. By combining the first-principles calculation, we identified that the
thermal excitation of charge trap states and oxidation-induced defect states
were the main reasons for this large temperature dependence of the electron
state population and degradation of the on-off ratio in phosphorene
field-effect transistors.
