0741-3106 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LED.2020.2967782, IEEE Electron Device Letters 1 Compact Model for Geometry Dependent Mobility in Nanosheet FETs Avirup Dasgupta, Member, IEEE, Shivendra Singh Parihar, Graduate Student Member, IEEE, Harshit Agarwal, Member, IEEE, Pragya Kushwaha, Member, IEEE, Yogesh Singh Chauhan Senior Member, IEEE and Chenming Hu, Life Fellow, IEEE Abstract—We propose an updated compact model for mobility in Nanosheet FETs. This is necessary since Nanosheet FETs exhibit significant mobility degradation with thickness and width scaling caused by centroid shift, changing effective mass due to quantum confinement as well as various crystal orientations of the various conduction planes. The model takes all of these effects into account. It has been implemented in Verilog-A and validated with experimental data. To the best of our knowledge, this is the first compact model capturing the effect of nanosheet scaling on mobility. Index Terms—Nanosheet, Gate-all-around, mobility, quantum, centroid, mobility degradation, compact model. I. I NTRODUCTION Stacked gate-all-around Nanosheet FETs are the logical successors to FinFETs, offering excellent gate control and increased effective channel width per footprint[1–7]. Physical simulations as well as experimental results show a decrease in the mobility with nanosheet scaling[1], [8–13]. Not only does the nanosheet thickness (T SHEET ) need to be reduced in tan- dem with gate-length (L g ) scaling to maintain proper electro- statics, but continuously variable nanosheet width (W SHEET ) has also been proposed for optimal circuit design [1]. There- fore, it is essential to analyze and model the dependence of mobility on W SHEET and T SHEET scaling for accurate SPICE simulation. In this paper, we discuss and model the various causes that contribute to mobility scaling in sections II and present the final mobility model in section III, followed by the conclusion in section IV. II. MODEL DESCRIPTION The experimental data [1] for the variation of mobility with inversion charge density for different thicknesses is shown in Fig. 1. The tried and tested model for field dependent mobility (μ) is given as [14–16] μ = μ 0 1+ αE β eff (1) A. Dasgupta, P. Kushwaha and C. Hu are with the Department of Electri- cal Engineering and Computer Sciences, University of California Berkeley, Berkeley, CA 94720-2284, USA. Email: avirup@berkeley.edu. S. S. Parihar and Y. S. Chauhan are with the Department of Electrical Engineering, Indian Institute of Technology Kanpur, UP 208016, India. H. Agarwal is with the Department of Electrical Engineering, Indian Institute of Technology Jodhpur, Jodhpur, RJ 342037,India. This work was supported by the Berkeley Device Modeling Center and the Department of Science and Technology, Govt. of India. Fig. 1: Variation of mobility with charge density for different nanosheet thicknesses. The data is for p-type nanosheet FETs [1] with 20nm sheet width and a gate length of 100nm. As can be seen, not only does the field dependence change with changing thickness, but the peak mobility also decreases drastically. The presented model (solid line) matches the experimental data (symbols) with high accuracy. where μ 0 is mobility at low transverse field , α and β are parameters and E eff is the effective transverse electric field. In the following sub-sections we investigate the validity of this model and propose updates to capture the various factors affecting mobility in nanosheet FETs. From a compact modeling point of view, the effect of confinement on the overall mobility can be broadly classified into two parts: (i) the effect on mobility at low transverse field and (ii) the effect on the field-dependence of mobility i.e. the change in the variation of mobility with varying transverse field. The former is taken care of through the concept of effective mass, as discussed in sub-section A, and captures effects of band-structure change as well as relative contributions of different scatterings at low transverse field. The latter, discussed in sub-section B, is taken care of by the field dependent term in the denominator of (1) and captures effects of various field dependent scatterings like phonon-scattering and surface-roughness-scattering. With the gate-all-around structure of nanosheets, another interesting effect that comes up in the mobility at low transverse field is the relative contribution of the various crystal-orientations of the planes of current flow. This has been discussed in sub- section C. A. Effective mass change: The most noticeable effect in Fig. 1 is the drastic decrease in the peak mobility with reduction in nanosheet thickness. This is primarily due to the increased quantum confinement which in turn increases the effective mass (m * ). Since, the