Analytical model for quantization on strained and unstrained bulk nMOSFET and its impact on quasi-ballistic current M. Ferrier a,b, * , R. Clerc a , G. Ghibaudo a , F. Boeuf b , T. Skotnicki b a IMEP-CNRS, ENSERG, 23 rue des martyrs, 38000 Grenoble, France b STMicroelectronics, 850 rue Jean Monnet, 38926 Crolles, France Received 15 August 2005; received in revised form 10 October 2005; accepted 10 October 2005 The review of this paper was arranged by Enrico Sangiorgi and Claudio Fiegna Abstract This work presents a fully analytical model for the evaluation of quasi-ballistic transport in advanced bulk nMOS devices. Starting from the Lundstrom approach, an original analytical evaluation of energy levels advantageously replaces numerical time-consuming Poisson–Schro ¨ dinger simulations or usual analytical single subband approximations. This model allows an accurate estimation of quan- tum mechanical effects and their impact on quasi-ballistic performances. Based on an improved Airy method, it accounts for the non-linearity of the depletion potential, the wave function oxide penetration and a generalized concept of effective field. As it relies on subband structure, it can easily be extended to biaxially strained devices provided that the band modifications are known. Interest of strained channels is confirmed even on the base of ballistic or quasi-ballistic hypothesis. This model has been used for the evaluation of the ‘‘ballisticity’’ along the ITRS roadmap, showing for next generation devices a quasi-ballistic current slightly higher than that pre- dicted with the usual drift diffusion and saturation velocity equations. However, as already reported, MOS devices still operate far from their ballistic limit down to HP45 nm node. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Bulk nMOSFET; Strained; Analytical model; Quantization; Ballistic; Quasi-ballistic 1. Introduction In spite of difficulties to keep under control short chan- nel effects and to maintain at the same time an accept- able level of performance, advanced bulk MOSFETs still appear as the most probable candidates for CMOS devices integration until, at least, the node 45 nm (L ch = 18 nm) [1]. However, a reliable and physically based model of their electrical performances is still missing. Indeed, currently available compact models (such as MM11 [2], MASTAR [1], BSIM4 [3]) rely on the usual concept of drift diffusion and saturation velocity, implicitly assuming the occurrence of a large number of scattering events in carrier transport from source to drain. However, as the carrier mean free path, of a few decananometers, becomes comparable with the channel length, this assumption may no longer be valid for end-of-roadmap devices, which may operate close to their ballistic limit. In such a regime, as pointed out first by Natori [4] and then by Lundstrom [5], performances are no longer limited by transport mechanisms along the channel but rather by the carrier injection mechanism and scattering processes occurring close to the source end. These phenomena are strongly influenced by the prop- erties of the inversion layer in this area, and in particular by its quantum 2D carrier gas nature [6], especially in highly scaled bulk devices with high channel doping and thin gate oxide. Consequently, quantization must be carefully taken into account in an improved approach for quasi-ballistic 0038-1101/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2005.10.044 * Corresponding author. Address: IMEP-CNRS, ENSERG, 23 rue des martyrs, 38000 Grenoble, France. E-mail address: ferrier@enserg.fr (M. Ferrier). www.elsevier.com/locate/sse Solid-State Electronics 50 (2006) 69–77