First-principles study of electronic transport in germanane and hexagonal boron nitride

Abstract

We present a detailed first-principles study on phonon-limited electronic transport in germanane and hexagonal boron nitride (h-BN). We find a high electron mobility of $2380\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ and a low hole mobility of $60\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for germanane. For h-BN, we also find a respectable electron mobility of $118\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ together with a high hole mobility of $444\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. H-BN does not suffer from scattering associated with out-of-plane (flexural) acoustic (ZA) phonons due to its ${\ensuremath{\sigma}}_{h}$ symmetry, but germanane does. Different cutoff wavelengths (${\ensuremath{\lambda}}_{\mathrm{cutoff}}$), ranging from 0.4 to 17.6 nm, are considered to simulate the possible effect of a supporting substrate on the ZA phonons for germanane. Increasing ${\ensuremath{\lambda}}_{\mathrm{cutoff}}$ results in a degradation of the mobility down to $1640\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for electrons and $1\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for holes assuming ${\ensuremath{\lambda}}_{\mathrm{cutoff}}=17.6\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. We also study transport in the presence of a homogeneous electric field $E$. A negative electron differential mobility is observed in germanane for $E>{10}^{4}\mathrm{V}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ due to transfer to the higher effective-mass $M$ valleys. Finally, the calculated mobilities are compared with those obtained for other two-dimensional (2D) materials, showing that germanane has the highest electron mobility, whereas holes in h-BN have the third highest mobility in our list of materials, outperformed only by ${\mathrm{WS}}_{2}$ and ${\mathrm{WSe}}_{2}$. This shows that germanane and h-BN can be considered for future nanoscaled electronic devices. Finally, the high germanane mobility shows that 2D materials can outperform bulk materials if the right material is found and if scattering with acoustic flexural phonons can be suppressed.