  Carrier mobility is a crucial character for electronic devices since it
domains power dissipation and switching speed. Materials with certain high
carrier mobility, equally, unveil rich unusual physical phenomena elusive in
their conventional counterparts. As a consequence, the methods to enhance the
carrier mobility of materials receive immense research interests due to their
potential applications in more effective electronic devices and enrichment of
more unusual phenomena. For instance, introducing a flat hexagonal boron
nitride (h-BN) substrate to enhance the carrier mobility has been achieved
experimentally. However, the underlying mechanics is not well understood. In
this study, we estimate the carrier mobility of phosphorene on h-BN substrate
(P/h-BN) within the framework of the phonon-limited scattering model at
first-principles level. %Our results are generic. Besides high-$\kappa$
dielectric property, h-BN also possesses excellent mechanical property of a
high two-dimensional elastic modulus. The P/h-BN heterostructure inherits the
high elastic modulus of h-BN, leading to an enhanced carrier mobility in
phosphorene. Owing to the weak van der Waals interactions between the layers,
the unique electronic properties of phosphorene are almost perfectly preserved
near the Fermi level, guaranteeing the superior electronic transport in P/h-BN.
Our findings offer a new perspective to improve the carrier mobility in
phosphorene as well as other 2D materials based field effect transistors.
