Recent aggressive progress in nano-devices requires the precise understanding on the electric properties of nano-structures. Theoretical studies on the material dependence of such electric properties are mostly limited on the conductance of the nano-structures, while the capacitance is also very important property as seen in the gate of the three terminal devices such as field effect transistors. We have therefore developed so-called enforced Fermi energy difference method for the first-principles calculations [1]. In this method, the induced charges and the free energy can be calculated from first principles for the system consist of two spacially separated electrodes with a fixed chemical potential difference. In this contribution, we applied this method to the capacitor made of the electrodes of silicon (111) nano-slabs with the hydrogen-terminated surfaces. The capacitance is obtained from the differential of the induced charge on the anode by the chemical potential difference between the electrodes.
The calculated results show that the capacitance changes with the chemical potential difference, being contrast to the classical electromagnetics. Such a non-classical change of the capacitance can be explained from the band diagram of the electrodes. When the infinitesimal charges are induced on the electrodes, the Fermi energies of the anode and the cathode should match with the valence band top and the conduction band bottom, respectively. Since the chemical potential difference is the difference of the Fermi energies between the anode and the cathode, it corresponds to the band gap of the electrode nano-slabs. Thus, the capacitance is zero when the chemical potential difference is smaller than the band gap. When the induced charges increase, the Fermi energy of the anode decreases from the valence band top and that of the cathode increases from the conduction band top. Therefore, the density of states of both electrodes should affect the capacitance.
We also studied the electrode spacing dependence and the electrode thickness dependence of the capacitance. All the calculated results show that the capacitance really depends on the material properties of the electrode nano-slabs.
[1] K. Uchida et al, Phys. Rev. B74, 035408 (2006).
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