Work Function Reduction for Field Emission

Doping proper amount of properly selected elements lowers the work function ( ) or the threshold (Vj) in cold-cathode field emitters such as diamond, diamond-like carbon (a-C), or carbon nanotubes (CNTs) [4, 9, 63-65]. The Vx of the N-doped 

If the N-induced mid-gap impurity levels (1.7 eV Ec and 1.5 eV E ) are dominant, the carbon co-doped with P and B should perform better than the carbon doped with N, as the P- and B-derived states (0.46 eV Ec and 0.38 eV Ey) are more benehcial to the band structure. Boron is a shallow substitutional acceptor in diamond with a level at 0.38 eV above the valence band edge Ey, and phosphorus can act as a shallow donor with a level 0.46 eV below the conduction band edge Ec [76]. 

The 3B correlation mechanism resolves the discrepancy regarding chemical effect on the work function. The weakly bounded sp orbitals of a P atom are hard to be hybridized compared with the 2sp orbitals of O and N because the 3sp electrons are more mobile than the 2sp electrons of N and O. The delocalized 3sp electrons determine that the P atom acts as a n-type donor that adds simply a DOS feature to a position 0.46 eV below the Ec of a diamond [76]. The fact that P doping gives little reduction in the work function compared to O or N doping [66] means that the impurity gap levels narrow the bandgap but barely reduce the work function. 

Unlike P and B, O and N could expand the bandgap of a semiconductor instead, through compound formation. Therefore, N and O act not as impurity donors or accepters traditionally in semiconductors, as charge transportation and polarization occur during the process of reaction. 

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