Theoretical analysis of the bias-voltage dependence of the apparent barrier height

We have analyzed the bias voltage dependence of the apparent barrier height (ABH), using a self-consistent calculation within the density functional theory. We have found that the ABH shows the bias polarity dependence in both of the two Al(100) surfaces, the one without reconstruction and the one containing the vacancy cluster in the layer next to the surface. We have also found that the surfaces have opposite bias polarity dependences of the ABH. These results cannot be understood in the light of the formation of the surface dipole layer, but can be understood from two factors: the reduction in the effective potential and the change in the surface electron states by the applied bias voltage.