Comprehensive Study of Cross-Section Dependent Effective Masses for Silicon Based Gate-All-Around Transistors

Abstract

The use of bulk effective masses in simulations of the modern-day ultra-scaled transistor is erroneous due to the strong dependence of the band structure on the cross-section dimensions and shape. This has to be accounted for in transport simulations due to the significant impact of the effective masses on quantum confinement effects and mobility. In this article, we present a methodology for the extraction of the electron effective masses, in both confinement and the transport directions, from the simulated electronic band structure of the nanowire channel. This methodology has been implemented in our in-house three-dimensional (3D) simulation engine, NESS (Nano-Electronic Simulation Software). We provide comprehensive data for the effective masses of the silicon-based nanowire transistors (NWTs) with technologically relevant cross-sectional area and transport orientations. We demonstrate the importance of the correct effective masses by showing its impact on mobility and transfer characteristics.

Simulation and Modeling of Novel Electronic Device Architectures with NESS (Nano-Electronic Simulation Software): A Modular Nano TCAD Simulation Framework

“…Secondly, as the effective masses strongly depend on the characteristic dimension and the confinement orientation of the nanostructures, an automated module to extract the effective mass from first principle simulations has been implemented in NESS [25]. It can calculate the correct electron confinement and transport effective masses from atomistic simulations (such as density functional theory (DFT)) or semi-empirical models (such as tight-binding (TB)) of the electronic band structure of NWTs with the technologically relevant cross-sectional area, shape, and transport orientations.…”

“…It can calculate the correct electron confinement and transport effective masses from atomistic simulations (such as density functional theory (DFT)) or semi-empirical models (such as tight-binding (TB)) of the electronic band structure of NWTs with the technologically relevant cross-sectional area, shape, and transport orientations. The capabilities of this module have been already demonstrated in accurately computing the effective masses of Si [25] and Si x Ge 1−x [23] NWTs considering different dimensions and shapes.…”

“…Figure 5. 3D profile of electron density in a slice located at the center of the transport direction (X) for n-type (a) square, (b) circular, and (c) elliptic 5 nm × 5 nm NWTs assuming Si 20 Ge 80 fraction and ballistic NEGF transport simulations with L G = 10 nm,[100] transport orientation, V DS = 0.6 V, and V GS = 0.4 V. The effective masses have been computed making use of the effective mass extractor of NESS[25].…”

Enhanced Capabilities of the Nano-Electronic Simulation Software (NESS)

“…First, the structure generator allows the creation and configuration of the 3D device structures [6], [7], including the following main variability sources: random discrete dopant (RDD), line edge roughness (LER), and metal gate granularity (MGG). Second, the effective mass extractor [8] can calculate the correct electron effective masses, in both confinement and transport directions, from the first principle simulations of the electronic bandstructure of nanowire transistors (NWTs) with technologically relevant cross-sectional area, shape, and transport orientations. Third, the material database provides the relevant material parameters for each solver, such as the work-function, affinity, or scattering parameters.…”

Mobility of Circular and Elliptical Si Nanowire Transistors Using a Multi-Subband 1D Formalism

“…The rest of the technological parameters remains identical: the gate oxide has an equivalent oxide thickness (EOT) of 0.8 nm, the metal gate work function is set to 4.35eV, and room temperature (300K) is assumed. In order to accurately reproduce the quantum behavior for diameters smaller than 8 nm, we have extracted [19] the transport and the confinement effective masses from an empirical sp 3 d 5 s * tight-binding simulations with the Boykin's parameter set [20] implemented in QuantumATK from Synopsys [21]. Furthermore, as the surface roughness scattering mechanism dominates the mobility for very high sheet concentrations, all the mobility results are reported at the medium carrier concentration 2.8 × 10 12 cm −2 [16], [17], [22].…”