  We perform first-principles calculations to investigate the structural and
electronic properties of metal-doped (10, 0) carbon nanotubes (CNTs) on a
single hexagonal boron nitride (hBN) sheet in the presence of an external
electric field. We consider K, Cl and Ni atoms as dopants to study the
dependence of the electronic properties of the CNT on doping polarity and
concentration. The electric field strength is varied from -0.2 V/\AA to +0.2
V/\AA to explore the effects of an external electric field on the electronic
structures. Although the electronic energy bands of the hBN sheet are modified
in accordance with the field strength, its electronic state in the valence or
conduction band does not touch the Fermi level under the field strength
considered. We conclude that the hBN as a substrate does not modify the
electronic structure of the CNT, thereby leading to improvements in the device
performance, compared with that of devices based on conventional substrate
materials such as SiO$_2$.
