HEMT Parameter Extraction Combining Optimization and Direct Parasitic Extraction S. Vandenberghe, 1 D. Schreurs, 1 K. Van der Zanden, 2 G. Carchon, 1 B. Nauwelaers, 1 W. De Raedt 2 1 K.U. Leuven, ESAT-TELEMIC, Kardinaal Mercierlaan 94, B-3001 Heverlee, Belgium; e-mail: Servaas.Vandenberghe@esat.kuleuven.ac.be 2 IMEC, MAP, Kapeldreef 75, B-3001 Heverlee, Belgium Received 23 March 1999 ABSTRACT: A new technique for high electron mobility transistor (HEMT) equivalent cir- cuit identification is presented. The optimization problem is reformulated as an overdeter- mined set of equations. Thus, equations used in direct parasitic extraction can be added in a straightforward way and a measure for error propagation is available. The method is used to identify a 17-element small-signal equivalent circuit. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 81–90, 2000. Keywords: equivalent circuit modelling; parameter estimation; bidirectional search 1. INTRODUCTION The first step in the construction of a nonlinear semi-empirical model is the extraction of a bias dependent linear model from measurements. The identification of the 17-element equivalent circuit is known to be a hard problem, especially if the measured S-parameters are well below the transit frequency of the device. Optimizer based extraction techniques are of- ten used, but do not guarantee a unique solution. Analytical direct extraction methods, as in [1] for cold HEMT models, have the advantage that a so- lution is always found. However, they contain as- sumptions based on the topology of the circuit and device physics that are not always visible or valid. These analytical extraction methods are an ex- ample of a backward, reverse, search. The circuit Correspondence to: S. Vandenberghe Contract grant sponsor: Institute for the Promotion of In- novation by Science and Technology in Flanders (IWT). Contract grant sponsor: Fund for Scientific Research (FWO). Contract grant sponsor: European Space Agency. is solved element per element from selected mea- surements. This is in contrast with measurement- fitting optimization that searches for all unknowns at the same time. The latter is referred to as a forward search. Some techniques combine optimization and ex- traction. The bidirectional search [2] method cal- culates the intrinsic elements for known extrinsic elements using a most likelihood approach. Only the extrinsic elements are optimized for a best fit with the measured S-parameters. Thus, more bias points can be included in the search without in- creasing the search space. An alternative [3] is to optimize the extrinsic elements for a minimum variance on the extracted intrinsic elements. This paper takes the idea a step further. It was noted that, for small changes in the extrinsic el- ements, the error on the extracted intrinsic ele- ments increases linear with frequency. The slope of this error is a measure for the choice of the extrinsic elements. Solving for zero slope refor- mulates the optimization problem as a zero find- ing problem, and equations from direct extraction methods can be added in a straightforward way. 81 © 2000 John Wiley & Sons, Inc. CCC 1096-4290/00/010081-10