Band gap engineering by functionalization of BN sheet

From first principles calculations, we investigate the stability and physical properties of single-layer $h$-BN sheet chemically functionalized by various groups, viz. H, F, OH, CH${}_{3}$, CHO, CN, NH${}_{2}$, etc. We find that full functionalization of $h$-BN sheet with these groups leads to decrease in its electronic band gap, albeit to different magnitudes varying from 0.3 eV to 3.1 eV, depending upon the dopant group. Functionalization by a CHO group in particular leads to a sharp decrease in the electronic band gap of the pristine BN sheet to \ensuremath{\sim}0.3 eV, which is congenial for its usage in transistor-based devices. For the optimized structure of the sheet, the calculated phonon frequencies corresponding to all the vibrational modes turn out to be real (positive), thereby suggesting their inherent stability. The chemisorption energies of these groups with the B and N atoms of the sheet are found to lie in the range of 1.5--6 eV. The optical absorption and conductivity of these functionalized sheets under polarized light are found to be much higher than that of the native BN sheet.