  The field screening effect on the electronic and field-emission properties of
zigzag graphene nanoribbons (ZGNRs) has been studied using first-principles
calculations. We have systematically investigated the effect of inter-ribbon
distance and ribbon width on the work function, field enhancement factor, band
gap and edge magnetism of zigzag graphene nanoribbons (ZGNRs). It is found that
the work function of ZGNRs increases rapidly as the inter-ribbon distance Dx
increases, which is caused by the positive dipole at the edge of the ribbon.
For a given Dx, the work function of ZGNRs decreases as the ribbon width W
increases. The wider the width of ribbon, the stronger the effect of
inter-ribbon distance on the work function. Using a simple linear interpolation
model, we can obtain the work function of ZGNR of any ribbon-width. For the
case of Dx < W, the field enhancement factor increases rapidly as the
inter-ribbon distance increases. As we further increase Dx, the enhancement
factor increases slowly and then tends toward saturation. The inter-ribbon
distance of ZGNRs can modulate the magnitude of the band gap and edge
magnetism. These observations above can all be explained by the screening
effect.
