Significant k-point selection scheme for computationally efficient band structure based UTB device simulations

Abstract

The accurate calculation of channel electrostatics parameters in ultra-thin body devices requires self-consistent solution of the Poisson's equation and the full-band structure of the thin channel. For silicon channel, the full-band structure is obtained using the semi-empirical sp 3 d 5 s * tight-binding model. To make this approach computationally tractable for a wide range of channel thicknesses, in terms of time and resource, only significant k-points in the irreducible Brillouin zone need to be considered. In this work, we present a scheme for precisely identifying the significant k-points based on Fermi-Dirac probability and show that the band-structure approach using those significant k-points can be applied over a wide range of channel thicknesses, oxide thicknesses, device temperatures and different channel orientations. The benchmarking of the obtained channel electrostatics parameters is performed with the results from accurate full-band structure simulations showing excellent agreement (maximum error within 0.5%) along with significant reduction in computational time.

Temperature Dependent Band Gap Correction Model Using Tight-Binding Approach for UTB Device Simulations

“…Given that the Full-Band structure simulation requires that the TB Hamiltonian be assembled at each k-point, this approach becomes computationally cumbersome to simulate the electrostatics of UTB MOS devices, particularly for thicker channels. Therefore, more efficient simulation of the channel electrostatics over a wide range of channel thicknesses is possible through the selection of significant k-points as proposed by Solanki et al [12] and is utilised. Further, through the incorporation of a temperature dependent band gap correction term into the TB Hamiltonian, as shown in the algorithm in Fig.…”

“…By showing that the band gap is the critical parameter which affects the channel electrostatics, TB parameters defined at 0 K along with a temperature dependent correction to the band gap will enable the TB approach to be used to simulate the device electrostatics at any other temperature between 0 K and 300 K. One of the important manifestations of structural confinement of the channel material, seen in UTB devices, is the increase in band gap compared to its bulk value, which is quantified by using TB simulation parameters at 0 K. This quantum confinement based correction along with the temperature dependent band gap correction term is used to suitably modify the temperature dependent band gap model defined for bulk semiconductors [11], thus incorporating the effect of channel thickness and temperature on the band gap. By incorporating the temperature dependent band gap variation for a particular channel thickness into the band structure calculation using the significant k-point selection scheme [12], a computationally efficient approach to simulate the electrostatics of UTB devices over a wide range of channel thicknesses and temperature variations, is proposed in this work.…”

Band-structure based electrostatics model for ultra-thin-body double-gate silicon-on-insulator MOS devices

“…In this section, we present an approach to simulate the electrostatics of UTB DG MOS devices, over a wide range of device temperatures (15 K to 300 K), as shown in supplement S1. By including a temperature dependent band-gap correction term (see supplement S2) and by using the significant k-points identification algorithm reported by Solanki et al [44] (see supplement S3), the semi-empirical TBM is used to simulate the band-structure, which through a self-consistent solution with the 1-D Poisson's equation enables the determination of the electrostatics of UTB double-gate (DG) silicon-oninsulator (SOI) MOS Device, over a wide range of device temperatures ranging from T = 15 K to 300 K (see supplement S4, for further details).…”

“…Having mentioned the challenges associated with the existing models, the sp 3 d 5 s * tight-binding (TB) Method [31][32][33][34][35], while being computationally inefficient [36,37] compared to effective mass approximation (EMA) based approaches [38][39][40][41][42], is found to be more accurate in terms of considering effect of confinement [43] and hence the electrostatics parameters such as potential and electron carrier concentration obtained from utilizing the band-structure calculated from TB method (TBM) are more accurate than the parameters obtained from EMA based approaches. Furthermore, with a view to maintaining the accuracy as well as reducing the computational cost of calculating the band-structure of ultra-thin-body (UTB) devices from TBM, a significant k-point based approach is recently reported by Solanki et al [44], where identification of significant k-points around the band-minima, enables accurate determination of the electrostatics for DG-SOI MOS devices. Additionally, through the inclusion of a band gap correction term, this significant k-point based approach has been extended from low device temperature to room temperature [45].…”

“…We then present a model for the electrostatic potential and the electron carrier concentration, in nanoscale double-gate SOI MOS devices, taking the wave nature of the conduction electron into account. This model is extensively benchmarked with the computationally efficient band-structure based electrostatics simulation results [44,45] and shown to be in very good agreement over a wide range of channel thicknesses, device temperatures and gate voltages. From this model, we further show a simplified approach to obtain the channel charge density demonstrating that the channel charge may be modeled as a diffusion layer of uniform potential (along the depth) whose thickness and potential varies with Channel thickness and gate voltage variations.…”