11 September 2000 Ž . Physics Letters A 274 2000 75–83 www.elsevier.nlrlocaterpla Correspondence between quantum and classical motion: comparing Bohmian mechanics with a smoothed effective potential approach L. Shifren ) , R. Akis, D.K. Ferry Center for Solid State Electronics Research, Department of Electrical Engineering, Arizona State UniÕersity, Tempe, AZ 85287-5706, USA Received 4 August 2000; accepted 9 August 2000 Communicated by L.J. Sham Abstract We simulate Bohm and classical trajectories through a constricted quantum wire. Results are obtained with and without self-consistency as well as with an AeffectiveB potential, calculated by smoothing the self-consistent potential. Including this effective potential generates classical trajectories with behavior remarkably similar to that of the actual quantum system. q 2000 Elsevier Science B.V. All rights reserved. PACS: 73.20.Dx; 73.23.Ad; 03.65.-w 1. Introduction Ž . The Semiconductor Industry Association SIA projects that by the end of 2009 devices will employ 0.05 mm gate lengths and have oxide thickness of less than 1.5 nm. Groups from Toshiba and Lucent Bell Labs have already fabricated n-channel MOS- w x FETs with effective gate lengths below 25 nm 1,2 , showing that these feature sizes are feasible. In this sub-micron regime, quantum effects should dominate electron transport. Amongst other complications caused by quantum mechanics, in small structures ) Corresponding author. Tel: q 1-480-965-3452, Fax: q 1-480- 965-8058. Ž . E-mail address: lucian.shifren@asu.edu L. Shifren . one needs to worry about the effective size intro- wx duced by the wavelike nature of the carriers 3. Although several quantum mechanical approaches to simulation of semiconductor devices have been de- Ž wx . veloped see Ref. 4 for a review , most tend to be complicated and computationally intensive. More- over, they tend to be unattractive from an industrial point of view since even the most advanced indus- trial simulation tools currently used are typically still particle based. One way of doing quantum mechan- ics while still retaining the description of the carriers as particles with well defined trajectories is to use w x the Madelung–Bohm approach 5–7 . This approach has been incorporated, though in a rather limited way Ž . it is only applied to part of the device , in a Monte wx Carlo simulation of a resonant tunneling diode 8. Bohm trajectories have also been studied in semicon- 0375-9601r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0375-9601 00 00527-2