# 3D drift diffusion and 3D Monte Carlo simulation of on-current variability due to random dopants

Kovac, Urban (2010) 3D drift diffusion and 3D Monte Carlo simulation of on-current variability due to random dopants. PhD thesis, University of Glasgow.

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In this work Random Discrete Dopant induced on-current variations have been studied using the Glasgow 3D atomistic drift/diffusion simulator and Monte Carlo simulations. A methodology for incorporating quantum corrections into self-consistent atomistic Monte Carlo simulations via the density gradient effective potential is presented. Quantum corrections based on the density gradient formalism are used to simultaneously capture quantum confinement effects. The quantum corrections not only capture charge confinement effects, but accurately represent the electron impurity interaction used in previous \textit{ab initio} atomistic MC simulations, showing agreement with bulk mobility simulation. The effect of quantum corrected transport variation in statistical atomistic MC simulation is then investigated using a series of realistic scaled devices nMOSFETs transistors with channel lengths 35 nm, 25 nm, 18nm, 13 nm and 9 nm. Such simulations result in an increased drain current variability when compared with drift diffusion simulation. The comprehensive statistical analysis of drain current variations is presented separately for each scaled transistor. The investigation has shown increased current variation compared with quantum corrected drift diffusion simulation and with previous classical MC results. Furthermore, it has been studied consistently the impact of transport variability due to scattering from random discrete dopants on the on-current variability in realistic nano CMOS transistors. For the first time, a hierarchic simulation strategy to accurately transfer the increased on-current variability obtained from the ‘ab initio’ MC simulations to DD simulations is subsequently presented. The MC corrected DD simulations are used to produce target $I_D-V_G$ characteristics from which statistical compact models are extracted for use in preliminary design kits at the early stage of new technology development. The impact of transport variability on the accuracy of delay simulation are investigated in detail. Accurate compact models extraction methodology transferring results from accurate physical variability simulation into statistical compact models suitable for statistical circuit simulation is presented. In order to examine te size of this effect on circuits Monte Carlo SPICE simulations of inverter were carried out for 100 samples.