ELSEVIER Microelectronic Engineering 40 (1998) 187-194 Parameter extraction for bipolar transistors Fredrik Ingvarson and Kjell O. Jeppson Department of Microelectronics, Solid State Electronics Laboratory Chalmers University of Technology, S-412 96 GSteborg, Sweden Different methods of extracting the DC Gummel-Poon bipolar transistor model parameters are reviewed. First the shortcomings of the classical extraction schemes for the intrinsic model are pre- sented together with some improved procedures. Finally the extraction of the series resistances is addressed. 1. INTRODUCTION Accurate characterization of transistors is extremely important in the semiconductor in- dustry. With CAD tools like SPICE [1] it is possible to simulate circuits containing thou- sands of components. Through simulations it is possible to verify both working circuits and that the circuits perform within specifications. All these simulations rely on both accurate de- vice models and accurate sets of model param- eter values. This implies that all devices must be thoroughly characterized; hence the need for accurate and robust parameter extraction algorithms. The extraction algorithm is to be regarded as an integral part of the transistor model. Further, the extraction algorithm does not only consist of the appropriate manipula- tions of model equations but also instructions on how to dispose the measurement scheme to perform the best characterization using the least measurement effort. Different approaches to extract model pa- rameters exist. Getreu [2] has a complete set of schemes for measuring the model parame- ters for the most common bipolar junction transistor (BJT) models (e.g. Ebers-Moll and Gummel-Poon). Optimization is frequently employed when characterizing transistors [3- 5] often resulting in good agreement between measurements and simulations. However, when using optimization non-uniqueness of the extracted parameter values, trapping in local minima and requirements of substantial computer time are often mentioned as poten- tial problems. The direct extraction approach [6-8] does not exhibit these problems. Here, the extraction is performed using analytical expressions for all model parameters making the extraction fast and well defined. It is pos- sible to reduce the number of measurement points needed to a minimum approaching the number of model parameters to be extracted. However, the sensitivity to noise can then in- crease considerably. By using more measure- ment data than the minimum required and using traditional least square techniques ana- lytical expressions can still be used making this an attractive combination of "pure" direct extraction and optimization. The ability to make fast and accurate ex- tractions is important when large numbers of transistors are to be characterized routinely. This saves both data storage space and compu- ter time. The extraction of the intrinsic model pa- rameters and the series resistances will be dis- cussed in Section 2 and Section 3, respectively. Some experimental results will also be pre- sented showing both measurements and simu- lations. 0167-9317/98/$- see front matter Copyright © 1998 Elsevier Science B.V. All rights reserved. PII: S0167-9317(98)00270-6