Screening effects on the field enhancement factor of zigzag graphene nanoribbon arrays: a first-principles study

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 effects 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 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 ZGNRs of any ribbon-width. In 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 can all be explained by the screening effect.