Linear Combination of Bulk Bands-Method and Atomistic Tight-Binding Descrip- tion of Strained Silicon and Germanium Layers D. Rideau, C. Tavernier, and H. Jaouen STMicroelectronics 850 rue Jean Monnet 38926 Crolles Cedex, France 1. Introduction During the last decade, silicon band structure engineer- ing by means of channel rotation, mechanical strain and quantum confinement has been a very efficient way to im- prove Si and Ge-based MOSFETs. With a view of calcu- lating the transport properties in such systems, the electron community has developed a large variety of computational full band methods, among which the Linear Combination of Bulk Bands-method (LCBB) [1,2] and the atomistic Tight Binding (TB) method [3,4] are now widely used. A recent comparison between LCBB and TB simula- tions in strained Si 2D systems has put forth that the latter method can suffer from inaccurate parameters and fails to describe the modification of the band-structure with strain as well as the warping of the conduction band (CB) in Γ [2]. In this paper, we have revisited these conclusions using a different first-principle based TB parameterization [5] and providing a direct comparing between methods in various confined and strained Si and Ge layers. 2. Bulk Silicon and Germanium The band-structure parameters for the empirical pseudo potential method used in the LCBB and the sp3d5s* model can be found in [5,6]. These parameters have been opti- mized in order to closely match first-principle simulations of relaxed but also strained Si and Ge. Figure 1: Dispersion relation along the Γ-X direction in a 5 nm silicon well calculated with a tight binding model with hybridized orbitals and with Hydrogen passived surfaces. Comparison with LCBB model using various barrier potential heights. For each plot, the tight bind- ing results span on the right part, and the LCBB ones on the left. 3. Two-Dimensional Sub-Band Structure We first consider the case of carrier confinement in the channel of FD-SOI Si-based MOSFEFs. In such devices, the semiconductor channel is embedded in SiO 2 , which forms a [0 0 1]-oriented quantum well. Accurate simulations require in principle an accurate description of both the semiconducting channel and the surrounding oxide layers. Within the framework of the LCBB the confinement in the semiconductor layer can be obtained using an additional positive (negative) potential for the CBs (and the VBs) at the Si/SiO 2 interfaces. There is no simple way to do so with a tight binding model. For that reason, in the tight binding community it is a common practice to simulate MOSFETs devices [3,4] without the SiO 2 regions and to use a ‘standard’ surface state amorphi- zation technique such as raising the energy of a hy- bridized orbital [7] or connecting the surface atoms to monovalent atoms [8]. However, with these two tech- niques different results can be found, as depicted in Figure 1 in case of a 5nm Si well. These results can be compared to the LCBB ones simulated with realistic Si/SiO 2 band offsets (φ BC =3.2 eV for electrons and φ BV =4eV for holes), but also with lower band offsets. As can be seen, the VBs sub-band structure is rela- tively different, but surprisingly, the CBs match rela- tively well. Figure2: Sub-band structure as a function of in-plane wave vectors components for a 2.26 nm germanium quantum well ‘embedded’ in SiO2. Dashed lines: LCBB and Solid lines: tight-binding. Moreover, and in contrast with the results shown in [2], the warping of the CBs in Γ is well aligned between the two models as shown in Figure 2. Figure 3 shows that the relatively good matching holds for the [111]-quantization direction. 4. Wave Functions penetration in the Oxide region Including the oxide regions in a tight binding simula- tion is still in progress. Since oxide is an amorphous material the exact nature of which is not know, sev- eral research groups have proposed to introduced a X X 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 LCBB <-- WAVE VECTOR (a.u.) --> Tight binding Γ ENERGY (eV) Φ CB =1 eV V sp =20eV Hydrogen Φ CB =3.2 eV X/3 X/3 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 LCBB <-- WAVE VECTOR (a.u.) --> Tight binding Γ ENERGY (eV) Φ CB =1.25 eV Φ CB =4 eV Hydrogen V sp =20eV (a) Conduction bands (b) Valence bands WAVE VECTOR k x [2π/a] WAVE VECTOR k y [2π/a] 0.05 0.05 0.1 0.1 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.35 0.35 0.35 0.35 0.4 0.4 0.45 0.45 0.5 0.5 0 0.05 0.1 0.15 0 0.05 0.1 WAVE VECTOR k x [2π/a] WAVE VECTOR k y [2π/a] -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 (a) Zoom of the lowest energy sub-band in the near Γ-region. The equi-energy contour plots from the bottom of the sub-band are spaced by 50 meV. (b) Lowest energy sub-band as a function of in-plane vectors. The limits of the 2D Brillouin zone are shown with solid lines. Dashed lines show the zoomed region in (a). -80- Extended Abstracts of the 2011 International Conference on Solid State Devices and Materials, Nagoya, 2011, pp80-81 P-2-17