Orbital-separation approach for consideration of finite electric bias within density-functional total-energy formalism

Abstract

We present a simple approach for the consideration of bias voltage within the Kohn-Sham formalism of density-functional theory. To be specific, the electronic charging of a metal-insulator-metal capacitor under bias voltage is considered explicitly. This is achieved by separating the Kohn-Sham orbitals around the Fermi level into anode or cathode parts and applying different Fermi levels in the determination of occupation numbers. The formal basis of the present approach is discussed in detail. We test this method against Au-vacuum-Au and Au-MgO-Au capacitors with various dielectric thicknesses. It is shown that the bulk optical and static dielectric constants can be obtained accurately. We also demonstrate that interface effects on capacitance can be investigated straightforwardly. Furthermore, we apply this method to the graphene capacitor and identify the quantum effects in the capacitance, which is well explained by the contribution of the kinetic energy of electrons to the capacitance. The present method can be readily implemented in conventional first-principles codes and provides a unified approach to evaluate capacitance of nanodevices.

First-principles calculation of charged capacitors under open-circuit conditions using the orbital-separation approach

“…We start with a short review of the orbital-separation approach (OSA) of Ref. [13]. In the conventional selfconsistent-field (SCF) KS-DFT scheme, the charge density is constructed in each SCF step from the lowest-energy KS orbitals:…”

“…For example, we may take the zero-bias relaxed capacitor structure as the reference state. The KS orbitals near the Fermi level are separated into each of the electrodes based on their spatial distribution [13], and their energies and occupation are tabulated and saved in an output file. Next, we perform a calculation (which may include structural relaxation or molecular dynamics under bias) using OSA and tabulate the eigenenergies and occupations again.…”

“…Although the original KS formalism was limited to simulation of the electronic ground state, recent advances in simulation methodologies have made possible the simulation of nano structures under electrical bias, which is essential for probing the performance of nanodevices under operating conditions [3][4][5][6][7][8][9][10][11][12]. In this context, we previously proposed the orbital-separation approach (OSA), which is applicable to metal/insulator/metal capacitors of arbitrary geometries as long as there is negligible electronic current between the electrodes [13]. The method is based on the separation of Kohn-Sham eigenstates with energies near the Fermi level into each of the metal electrode parts, then occupying them according to the Fermi levels assigned to each of the electrodes.…”

“…The main merits of this approach are its applicability to arbitrary electrode geometries and freedom of choice in the basis set expansion of the wave functions, as well as simplicity of implementation; a somewhat thorough discussion on the strengths and weaknesses of this approach in comparison with other finite-bias methods has been given in Ref. [13]. Although this made possible closed-circuit, constant-voltage simulations of metal/insulator/metal capacitors, we were unable to calculate the free charge transferred from electrode to electrode.…”

“…This makes energy-based optimization methods for structural relaxation unusable, and we would also lack access to a conserved quantity for evaluation of the accuracy of molecular dynamics simulations (it should be noted, however, that the forces can be obtained without knowledge of the grand potential as shown in Ref. [13]). Another reason is that the ability to evaluate the free charge would make possible open-circuit (constant-charge) simulations, which is particularly useful for examining ferroelectric materials as pointed out in Ref.…”