Theoretical Study on Material Dependence of Nano-Capacitance


Kazuyuki Uchida, Hiroyuki Kageshima and Hiroshi Inokawa
Physical Science Laboratory

 It is expected that novel physics appear in nano-scale devices, while many studies are needed to clarify such physics. For example, it is not clear what happens on the capacitance characteristics, one of the fundamental characteristics of FETs (field effect transistors), when the device size is decreased in nano-scale. We developed a new method, the EFED (enforced Fermi-energy difference) method, with which we can calculate the capacitance characteristics from first principles if only we provide the atomic distribution and the element type for each atom. We then applied the method for nano-capacitors and discussed physics in the nano-capacitance dependence on the material.
 Since only the most stable electronic states are calculated in usual first-principles methods, electrons distributed extensively in the system to screen the positive charges of the atomic nucleus. To calculate capacitance characteristics, the electrons should be localized. We divided the system’s space into two, and applied external virtual work on the two spaces to redistribute electrons. We minimize the total free energy for the electrons with this additional work and obtained a Schrödinger equation for the electrons to polarize in the system. This is the principle of our EFED method.
 We applied this method on a nano-capacitor and calculated the dependence of the differencial capacitance on the Fermi energy difference. The system consists of repeated-parallel-planes with 3-atomic-layers films of SrTiO3(001). The inverse of the differencial capacitance is shown in the vertical axis of Fig. 2. Classical capacitance of parallel planes is written as C = eS/d, which means that it depends only on the distance of the electrodes, d, and the dielectric constant of the material between the electrodes, e. In nano-structure capacitors, however, the electronic states of each electrode prefer to be discretized because of space quantization and the Coulomb interaction between the electrons. Therefore, the capacitance strongly depends on the difference of the Fermi energies as well as on the distance of the electrodes and the material between the electrodes.

[1] K. Uchida, et al., e-J. Surf. Sci. & Nanotechnol. 3 (2005) 453.

Fig.1 SrTiO3 nano-capacitor.
Fig.2 Capacitance characteristics.

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