Permittivity of Oxidized Ultra-Thin Silicon Films From Atomistic Simulations

Abstract

Abstract-We establish the dependence of the permittivity of oxidized ultra-thin silicon films on the film thickness by means of atomistic simulations within the density-functional-based tight-binding theory (DFTB). This is of utmost importance for modeling ultra-and extremely-thin silicon-on-insulator MOSFETs, and for evaluating their scaling potential. We demonstrate that electronic contribution to the dielectric response naturally emerges from the DFTB Hamiltonian when coupled to Poisson equation solved in vacuum, without phenomenological parameters, and obtain good agreement with available experimental data. Comparison to calculations of H-passivated Si films reveals much weaker dependence of permittivity on film thickness for the SiO2-passivated Si, with less than 18% reduction in the case of 0.9 nm silicon-on-insulator. Index Terms-permittivity, atomistic modeling, oxide interface, density-functional tight binding, silicon-on-insulatorIt is well known that the dramatic reduction of the dimensions of the Si channel, e.g. in ultra-thin-body silicon-on-insulators devices, leads to a significant change in the electronic and dielectric properties of Si, particularly at channel thickness below 6 nm [1-3]. A number density-functional theory (DFT) studies applied to hydrogen-passivated Si films suggest that the decrease in permittivity with the decrease of Si-film thickness becomes significant even earlier than the corresponding widening of the fundamental band-gap, and predict 35-45% reduction at around 1 nm [4][5][6]. On the experimental side however, we are aware of only one study of oxidized Si films down to 3.3 nm, and while a qualitative trend is evident, the scatter of the results precludes us from establishing an accurate quantitative picture towards sub-nm Si thickness [7]. We note further that to the best of our knowledge, the permittivity dependence of oxidized Si films has not been modeled ab initio, most likely due to the complexity and cost associated with including the oxide on each side of Si in DFT. However, very recently we A. Pecchia is with University of Rome "Tor Vergata", Rome, Italy. demonstrated that density-functional tight-binding theory (DFTB), with an accurate parameterization, can give us very good description of the electronic properties not only of bulk Si and SiO2, but also of their interface [3], and allows us to explore substantially larger systems, including transport through ETSOI devices [8]. The purpose of this paper is therefore twofold: 1) to evaluate a way of calculating the dielectric constant of thin-films within the framework of DFTB; and 2) to establish the permittivity dependence on the thickness of oxidized ultra-thin Si films.We employ the DFTB+ computer code [9], implementing the self-consistent-charge DFTB, coupled self-consistently to a Poisson solver [10][11][12]. This permits us to apply bias ( ) and find the distribution of potential ( ) and electric field ( ) in the model atomic structures. The atomic models are the SiO2/Si/SiO2/vacuum super-cells with varying ...

Explicit screening full band quantum transport model for semiconductor nanodevices

“…As will be shown in detail in this paper, the standard model fails in various ways, both for conventional as well as for band-to-band tunneling transistors. It turns out -consistent with previous findings in literature 16,17 -that the electrostatic screening of valence band electrons that do not take part in transport is device physics (and not only material) dependent. The charge interpolation schemes required for band-to-band tunneling devices host an arbitrariness that severely limits the reliability of device performance predictions.…”

Curvature Constrained Splines for DFTB Repulsive Potential Parametrization

“…In the literature, the following Slater-Koster tables for Si are available: pbc-0.3, 40 matsci, 41 and siband. 10 , 42 The pbc-0.3 and matsci sets are known to give a poor description of the band structure for Si polymorphs. 9 In contrast, the electronic parameters of the siband set were optimized by Markov et al 10 toward experimental Si and SiO 2 band structure data.…”

“…Having established a scheme for obtaining the optimal R cut value, we move on to discuss the generation of the repulsive potentials for the silicon polymorphs in our training set (see Section 4.1 ). The electronic energies from SCC-DFTB are obtained using the siband Slater-Koster tables of Markov et al 10 The CCS method was used to optimize the repulsive parameters. Two different types of fitting procedures (optimizations) were done, one using the original constraints on the curvature (strictly positive) and one in which the curvature is allowed to change sign once (switch constraint, see Section 2.3.2 ).…”

“…Next, we consider a training set solely comprising of diamond (4C) and simple cubic (6C) E-V scans. We again use the siband Slater-Koster tables of Markov et al 10 for the electronic SCC-DFTB energies. Figure 7 shows a boxplot comparison using all four expressions above for repulsive fitting, with their combinations of ϵ’s and V ’s for the 4C and 6C Si polymorphs.…”

“…The method can also be systematically extended to overcome limitations in DFT, such as the problem with underestimated band gaps. 9 , 10 …”