  The performance of electronic and spintronic devices based on two-dimensional
semiconductors (2D SC) is largely dependent on the quality and resistance of
the metal/SC electrical contacts, as well as preservation of the intrinsic
properties of the SC channel. Direct Metal/SC interaction results in highly
resistive contacts due to formation of large Schottky barriers and considerably
affects the properties of the 2D SC. In this work, we address these two
important issues in monolayer $\mathrm{MoSe_2}$ Field-Effect transistors
(FETs). We encapsulate the $\mathrm{MoSe_2}$ channel with hexagonal Boron
Nitride (h-BN), using bilayer h-BN at the metal/SC interface. The bilayer h-BN
eliminates the metal/$\mathrm{MoSe_2}$ chemical interactions, preserves the
electrical properties of $\mathrm{MoSe_2}$ and reduces the contact resistances
by prevention of Fermi-level pinning. We investigate electrical transport in
the monolayer $\mathrm{MoSe_2}$ FETs that yields close to intrinsic electron
mobilities ($\approx 26\ \mathrm{cm^2 V^{-1} s^{-1}}$) even at room
temperature. Moreover, we experimentally study the charge transport through
Metal/h-BN/$\mathrm{MoSe_2}$ tunnel contacts and we explicitly show that the
dielectric bilayer of h-BN provides highly efficient gating (tuning the Fermi
energy) of the $\mathrm{MoSe_2}$ channel at the contact regions even with small
biases. Also we provide a theoretical model that allows to understand and
reproduce the experimental $I-V$ characteristics of the contacts. These
observations give an insight into the electrical behavior of the metal/h-BN/2D
SC heterostructure and introduce bilayer h-BN as a suitable choice for high
quality tunneling contacts that allows for low energy charge and spin
transport.
