Power P-I-N Diode zyxw Modeling Using SPICE Armando Araiijo, Adriano Carvalho, J. L. Martins de Carvalho Faculty of Engineering University of Porto Rua dos Bragas 4099 Porto Codex Portugal zyxwv Abstract-A physics based model for the power p- i-n diode is implemented into the general circuit simulation package SPICE. This model based ort a variational formu:lationand finite element solu tion of the semiconductor equations accurately describes the forwisrd and reverse recovery zyxwv as; well as the conduction behavior. The proce- dure used to implement the resulting model into SPICE is describedL. The simulations are finally compared with known experiments for demon- stration of its effectiveness. I. NOMENCLATURE A, Element Area (cm2) zyxwvuts Cao, C,,, C,, zyxwvutsr , C,, Elementar capacitance (F) D,, D, Electron, hole diffusivity (cm2/s) E Dielectric constant of silicon (Flcm) Id Diode current (A) I,, zyxwvutsrqpo Ip Electron, hole current (A) J,, Jp Electron, hole current densities (A/cm2) L f Circuit leakage inductance (H) LE, Width of the element e , U , pp Electron, hole mobility (cm2/Vs) zyxwv NB Base doping concentration (~m-~) n, Intrinsic carrier concentration (MZ-~) p, n Hole/electron concentration (cmV3) q Electronic charge (C) Rb Base resistance (0) R,,, R,,, R,, , R,, Elementar resistance (0) T Base lifetime (s) Ul, U,. Left, right junctions voltage drops (V) U,.,, Resistive voltage drop in the base (V) U,, Space charge voltage drop (V) Vcc Circuit voltage VT Thermal voltage (V) X1, X,. Left, right boundaries of the base (cm) W Width of diode base (cm) W, = zyxwvut Xr - Xl Instantaneous width of the base (cm) 11. INTRODUCTION The purpose of this paper is to describe the implemen- tation of the physics based power p-i-n diode model de- veloped by the authors [l], [2], into the commercially available circuit simulator SPICE. The model is based on solving the ADE via a variational formulation [3] with posterior solution using one dimensional simplex finite elements. This results in a set of ODEs whose solution gives the time/space hole/electron distribution, as well as the moving boundary abscissas Xl and Xr during re- verse recovery. With the knowledge of p(~, t), n(z, t) and the instantaneous base width, Wb, the diode cur- rent and voltage are determined. The implementation of the obtained model, in a general circuit simulator, is made by means of an electrical analogy with the result- ing system of ODEs. In fact the solution of this system is equivalent to the solution of a circuit made by a set of RC nets and current sources. As the Simulation Program with Integrated Circuit Emphasis (SPICE) is used worldwide we have chosen it for the circuit implementation. The paper is organized as follows. In section 111. the fundaments of the model are summarized and the model equations presented. In section zyx IV. the equivalent circuit representation is deduced, and in section V. the needed sub circuits are constructed. Finally in section VI. the authors present the comparison between simulation and experimental results. 111. MODEL FUNDAMENTALS Considering a p-i-n diode for power applications, assum- ing high level injection and unidimensionality the hole/ electron concentration is given by the well known ADE: subjected to the boundary conditions: First we obtain the variational formulation of (1) sub- jected to the boundary conditions (2) and (3), namely: IEEE zyxwvutsrqpo Catalog Number: 97TH8280 - 211 - ISIE’97 - Gu~”&?s, Portugal