Device modeling challenges in the realm of overlapping physical scales: From atomistic to continuum, from coherent to diffusive transport

Abstract

Device modeling has been essential in discovery of innovative concepts, assessing their value proposition and in guiding the process engineering of devices to continue Moore's Law performance scaling for Metal Oxide Semiconductor Field Effect transistors (MOSFET) [1]. TCAD has traditionally relied on continuum model of transport by solving drift-diffusion (DD) equations and including bandstructures through effective mass descriptions. These approaches break in nanometer scale quantum devices. Higher level models of quantum transport atomistic nonequilibrium Green's function (NEGF) [2] and semiclassical Monte Carlo (MC) [3] simulations are used for assessing new materials and novel concept devices. NEGF device simulations typically do not include realistic structures and assume a simplified form of scattering. Monte-Carlo simulations account for quantum effects, for example, the source-drain tunneling, within effective quantum correction potential approaches. The corrections to the drift-diffusion model through ballistic mobility models [4] [5] and quantum corrections [6] have been used to extend TCAD simulations to scaled devices. In this talk we will use the tool box of these simulation methods to discuss various important aspects of physics in scaled devices and their impact on assessing new materials as alternative channels using TCAD modeling. We will discuss the distribution of resistance at low and high supply voltage in short devices which approach ballistic limit and discuss the implication it has on assessing advantage of Ge vs Si channel on-current performance of PMOSFET. Scaling device crossection size down to a few nanometers brings us to a modeling realm where we can count the number of atoms in a device. In this realm we typically rely on tight-binding atomistic models to capture effects of confinement in devices [2]. We will discuss the dependence of bandgaps on size of the nanowire and ultra-thin body in IIIV, Si and Ge materials. Tight-binding atomistic descriptions meet their set of challenges in modeling ultra-scaled devices where the effects of interfaces and imperfections become critical to account for. We will show that using known bulk tight-binding parameters for each material alone cannot in general describe even ideal interfaces between semiconductors. We will discuss this on the example of InAs hydrostatically strained to Si interface. This brings us to use more advanced Hamiltonians, such as, for example, Extended Huckel Theory (EHT) [7], and have a close coupling between tight-binding models and ab-initio Density Functional Theory (DFT) methods. We will apply the Extended Huckel theory to model the bandstructures of bulk semiconductors and nanowires. We will show that the Huckel method is predictive in modeling the effect of confinement in nanowires. We conclude with a discussion of challenges of bridging the gap between detailed material modeling and characterization and semi-classical device level modeling.