Significant <i>k</i> -point selection scheme for computationally efficient band structure based UTB device simulations
Ravi Solanki, Nalin Vilochan Mishra, Aditya Medury
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>s</mml:mi> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>5</mml:mn> </mml:msup> <mml:msup> <mml:mi>s</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.5</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> ) along with significant reduction in computational time.