Simulation of three-dimensional effects in VLSI devices* P. Ciampolini, A. Pierantoni, A. Forghieri and G. Baccarani Dipartimento di Elettronica, Informatica e Sistemistica, Universit~ di Bologna, viale Risorgimento 2, 401 36 Bologna (Italy) Two dimensional (2D) modelling of electron devices is already established as an indispensable tool for VLSI design, and a number of very sophisticated 2D device simulators have been developed. The increasing miniaturization and packing density of VLSI circuits is now boosting research activity towards three-dimensional (3D) device simulation. In this paper we pre- sent some results obtained with our prototype 3D simulator, HFIELDS-3D, and discuss some topics related to the underlying philosophy and to the implementation of a vector code, which we are now exploiting on a CRAY X- MP48 machine. 1. Introduction Numerical simulation of semiconductor devices in two dimensions has become a powerful and reliable tool, with applications ranging from the investigation of new devices" physical behaviour to the characterization of fabrication processes. New VLSI technologies are now utilizing various strategies for increasing chip densities, e.g. by reducing the size of devices and packing them more closely, by means of three dimensional (3D) integration techniques. In so doing, a number of physical and geometrical effects can no longer be approximated by two- dimensional (2D) models, so it is necessary to resort to 3D simulators. Even if the extension of any 2D code to the third dimension should be, in principle, fairly easy, many significant problems arise, related mainly to the management of huge amounts of data and the need to cope with complex geometries. In practice, only a few examples of working 3D simulation codes are known from the literature [1-3], most of them adopting some limiting assumption to the generality of their approaches. In this paper, we present some practical applications of the 3D simulator named HFIELDS-3D, which has been developed at the University of Bologna, from the proven 2D code HFIELDS [4]. In Section 2, the physical model adopted and numerical techniques are briefly reviewed; Section 3 deals more specifically with speed-up strategies while in Section 4 the simulation of a complex realistic structure is presented. Finally, some conclusions are drawn in Section 5. 2. Physical model and discretization strategy Two different classes of method are widely adopted to numerically solve the fun- damental set of semiconductor devices equations: (i) finite difference schemes, • This paper, in an earlier form. was originally prL'sentrd at MIEL-89 Conference. Nit. Yugoslavia. MICROELECTRONICS JOURNAL Vol. 21 No. 6 © 1990 Elsevier Science Publishers Ltd., England 5