Applicability of Macroscopic Transport Models to Decananometer MOSFETs

Abstract

We perform a comparative study of various macroscopic transport models against multisubband Monte Carlo (MC) device simulations for decananometer MOSFETs in an ultrathin body double-gate realization. The transport parameters of the macroscopic models are taken from homogeneous subband MC simulations, thereby implicitly taking surface roughness and quantization effects into account. Our results demonstrate that the drift-diffusion (DD) model predicts accurate drain currents down to channel lengths of about 40 nm but fails to predict the transit frequency below 80 nm. The energy-transport (ET) model, on the other hand, gives good drain currents and transit frequencies down to 80 nm, whereas below 80 nm, the error rapidly increases. The six moments model follows the results of MC simulations down to 30 nm and outperforms the DD and the ET models

Simplifying Semiclassical Electron Transport in Highly Inhomogeneous Fields

“…The theoretical viewpoint we have described in this section can be used to interpret, for example, the results of Vasicek et al [14,Fig. 6], shown in Fig.…”

“…1.1 is taken, finding the entire I-V curve on an Intel Core i7 CPU 3.4 GHz machine with the drift diffusion, energy transport and six-moment models took ∼ 3, ∼ 5 and ∼ 15 minutes respectively. In contrast finding the current at a single voltage point with the Monte Carlo model they used as the control took to 6-7 hours [14]. While much faster Monte Carlo simulations are possible-Vasicek et al admit in the paper the Monte Carlo simulation they use is not optimized for speed-this illustrates common problem that Monte Carlo models which do not ignore crucial physics have CPU-times that are several orders-of-magnitude greater than macroscopic models.…”

“…Thus it clear that Ĥq car-par is a well-defined operator: Bloch's theorem states that ψ kν = 1 √ N u kν (r)e ik•r where u kν (r) = u kν (r + R) if R is a lattice vector and N is the number of unit cells in the crystal sample. 14 If we examine the integral over the crystal sample, we note that the integral over any unit cell can only differ from the integral over any other unit cell by a phase factor. As such, we can take the integral of the volume occupied by the unit cell at R = 0-which we refer to as Ωand multiply this integral by the sum of all phase factors relative to this unit cell:…”

“…We refer to the quantity I G (kν; k ν ) as the OVERLAP INTEGRAL [43]. This new expression for the matrix element in turn creates a new expression for Fermi's golden rule from that 14 We have normalized u kν (r) over a unit cell of the crystal.…”

“…The models tend to define the impact ionization via an ansatz for the distribution function which requires all the local moments defined by the six moment model [70,71]. Beyond this requirement however, the impact ionization models are still independent of the macroscopic transport model since the ansatz used to define the impact ionization rate typically has no relation to the assumptions used to close the six moment transport model [72,11,14].…”