On Schrödinger's equation with a generalized potential Yu A Rozanov (Invited) Merging Technologies: Bipolar and MOS Douglas Ritchie and Shuichi Sato Numerical Investigation on Origin of Microscopic Surface Roughness during Si Etching by Chemically Reactive Plasmas

The carrier effective masses of CaO in the cubic phase are estimated by ab initio calculations, which are used for the simulation of Si/CaO metal-oxide-semiconductor (MOS) devices by solving Schrödinger and Poisson equations self consistently. It is shown that higher switching speed, longer lifetimes, and higher endurance can be obtained replacing SiO2 by CaO as gate dielectric, suggesting promising biomedical applications for Si/CaO-based MOS devices due to the CaO bio-compatibility. Concerns with reliability and gate leakage currents through ultrathin SiO2 dielectrics in metal-oxide-semiconductor field-effect transistors (MOSFET’s) are driving research efforts to find appropriate high dielectric constant (high–κ) materials for SiO2 replacement. CaO may be considered as an interesting candidate for SiO2 replacement as a dielectric gate material. It exhibits high mechanical and radiation resistance, and its wide band gap energy (7.1 eV) combined with a reasonably high dielectric constant (11.8) indicates a typical insulator behavior [1]. Concerning bio-compatibility, CaO incorporation in TiN–based films [2] and diamond-like carbon [3] is improving biological acceptance of these materials for bio-medical applications. The formation of a Ca–O–Si heterobriding bond favors Si–Ca–O interfacing, which points to a feasible development of improved bio-compatible Si-based biosensors through growth of CaO films in silicon surfaces [4]. In this work we perform a first-principles study of the electronic properties of the CaO cubic phase, estimating its band gap energy and carrier effective masses, which are fundamental for device simulation. To demonstrate the possibility of CaO for MOS device applications, we calculate the low frequency capacitance and the electrostatic potential drop within the oxide of both Si/CaO and Si/SiO2 MOS devices, which allows a direct comparison of the role of CaO and SiO2 as gate dielectrics. The calculations were performed with the ABINIT code, which is based on self-consistent plane-wave expansion combined with ultrasoft pseudopotentials [5]. For the sake of comparison, many-body effects were described in the local density approximation (LDA), using the Perdew-Zunger exchange term [6] with the Ceperley-Alder parametrization [7], and in the generalized gradient approximation (GGA), within the framework of the Density Functional Theory (DFT). The 3s2-, 3p6-, and 4s2-Ca; 2s2-, and 2p6-O electron states were treated as part of the valence-band states. In the CaO cubic phase, the cations Ca and anions O are located at IVC-17/ICSS-13 and ICN+T2007 IOP Publishing Journal of Physics: Conference Series 100 (2008) 042006 doi:10.1088/1742-6596/100/4/042006 c © 2008 IOP Publishing Ltd 1 (0,0,0) and (0.5,0.5,0.5), defining a fcc unit cell. Through a total energy minimization process with a cut-off energy of 700 eV, the lattice constants a = 4.712 Å (LDA) and a = 4.819 Å (GGA) were obtained. These values are in very good agreement with the measured value a = 4.81 Å [8]. Figure 1. CaO band structure along high-symmetry axis of the cubic Brillouin zone calculated using both GGA (solid line) and LDA (dashed) approximations. Figure 1 exhibits the calculated band structure of cubic CaO along the main high-symmetry directions in the Brillouin zone (BZ) for both LDA and GGA approximations (relativistic contributions were disregarded). CaO presents an indirect band gap with conduction band minimum located at the X-point. In addition, there is a secondary energy valley at the Γ-point giving rise to a direct band gap. For the indirect band gap, we obtained EG(Γ→X)=3.44 eV (LDA) and EG(Γ→X)=3.67 eV (GGA), while for the direct one we obtained EG(Γ→Γ)=5.07 eV (LDA) and EG(Γ→Γ)=4.79 eV (GGA). All theoretical values for the band gap energy are smaller than the experimental gap of 7.1 eV [1], which is due to the well-known underestimation of the energy values of conduction band states in ab initio calculations within the density functional theory. There are several others first-principles calculations of the CaO electronic properties [9, 10], in which EG(Γ→X) and EG(Γ→Γ) were estimated to be in the 2.91–14.96 eV and 5.02–9.71 eV range, respectively. However, no data concerning the carrier effective masses were published previously. The CaO carriers effective masses for the main directions in the Brillouin zone are shown in Table 1. They were obtained by fitting to a parabola, the curves of energy versus ~k along the Γ−X and Γ− Γ lines. We observe that the carriers effective masses are highly anisotropic in both conduction and valence bands, and that there is a large discrepancy between results obtained with the LDA and GGA approximations. Since experimental results on the effective masses in cubic CaO are still lacking, a direct evaluation of our theoretical estimates is not possible. The primary requirement for a gate dielectric to be used in MOS devices is to efficiently block the charge carriers between the channel and the gate. Thus, energy barriers for both electrons and holes in the semiconductor substrate have to be high enough in order to prevent thermally stimulated injection. Unfortunately, recent results reveal that the energy gap is inversely proportional to the dielectric constant for several candidate oxides [11]. In the case of CaO, its reasonably wide band gap makes it a feasible option for this task. However, the energy barriers are not known because the Si/CaO band offset has not been measured yet. Here, we IVC-17/ICSS-13 and ICN+T2007 IOP Publishing Journal of Physics: Conference Series 100 (2008) 042006 doi:10.1088/1742-6596/100/4/042006