\ hoc. IEEE 2004 Inl. Conference on Microelectronic Test StNCluIes, Vol 17, March 2004. 57 3.4 A Novel Method to Obtain 3-port Network Parameters from 2-port Measurements Anuranjan Jha', J. M. Vasi', Subhash C. Rustagi', M. B. Patil' 'Department of Electrical Engineering, IIT Bombay,Powai, Mumhai, India 400076 'Institute of Microelectronics, 11 Science Park Road, Singapore Science Park 11, Singapore 117685 Abstract Two-port description of a four-terminal device like MOS- FET is incomplete. For complete analysis and at higher fre- quencies, four terminal characteristics have to be obtained. We describe a simple and novel measurement technique to obtain the complete description from two-port measure- ments on a single test structure. No extra test structures are needed in this procedure. Such measurements are r e ported for the first time for a MOSFET. Introduction HE continuous downscaling of the MOSFET channel T length has resulted in pushing the cut-off frequency limits of a MOSFET into deep gigahertz regime. Advances in the CMOS technology have enabled fabrication of pas- sive elements like on-chip inductors, MIM capacitors etc. with reasonable quality and their behavior can he accu- rately predicted [l]. MOSFETs, thus, have become serious contenders for use in RF circuits [a]. To predict correct circuit behavior, it is therefore necessary to have accurate MOSFETs model for the complete bias range and for all the frequencies of interest. The works on RF modeling, described in [3]-[7] analyze MOSFET in a two-port form with source tied to the sub- strate. This is an incomplete description. The source and bulk terminals are physically separate and they form the third port. DC bias across them induce charge on rest of the terminals and signals too get coupled at this port. As the frequency of operation increases, the charge associated with the bulk terminal will also effect the device perfor- mance. We, therefore, need to consider MOSFET in its most general form-a four-terminal configuration. Techniques to obtain three-port characteristcs from two- port measurements have been reported in [8]-[IO]. These approaches require three different test structures and/or are very involved in the analysis. Characterization involv- ing different test structures will also introduce devicelevel variations in the measurements. In addition, the terminat- ing impedance interferes with the DC-biasing of the device as has also heen mentioned in [8]. We discuss, in this paper, a new way to obtain all the small signal parameters of a four-terminal MOSFET us- ing a common two-port Network Analyzer and only one simple test structure, We describe the theory behind our measurements and the set-up to achieve that. We present measurement results and ways to verify our procedure. Theory and Measurement Setup Any n-port network is fully characterized by its n-port parameters like s, y, z and h. They are inter-convertible 0-7803-8262-S/04/$I7.0002004 IEEE using simple matrix manipulation [ll]. We seek here any one of these sets of parameters just from two-port measure- ments. At RF and microwave frequencies, sparameters can he easily and accurately measured. In (81, threeport charac- teristics are obtained by assembling two-port sparameters of special test structures. These two-port sparameters di- rectly correspond to the entries of 3x3 sparameter rna- trix as the third port has been terminated using a 50 ohm resistance. This procedure has some inherent drawbacks. At RF regime where deembedding of shunt parasitics is needed, having different device structures can give incor- rect results. Moreover, the 50 ohm termination in series with the intrinsic Drain interferes with the DC-biasing of the device. Using the procedure described below we can get any set of three-port parameters from suitable sets of two-port measurements using a twc-port Network Analyzer. This is a much simpler and cost-effective way as compared to the use of less prevalent multiport network analyzers. A. MOSFET y-paramelers A threeport network description of a MOSFET takes care of any signal coupling with respect to the common bulk terminal. In addition to this, we will see, a three-port description is essential in determining terminal charges in- duced due to DC biases at all the terminals. We intend to analyze yparameters of a MOSFET. They help us to get the complete four-terminal charge description. MOSFET being a four-terminal device has sixteen y- parameters. Y a Ysd Yga 1 i ] - - 1 Ydg Ydd Yda ] [ :I] (1) It is also known that, for any n-terminal device, the nxn y-parameter matrix has the following property [12]: Ysg Yad Ysa Yab Va Ybg Ybd Yba Ybb U5 " " CY1.C = CYjh =o (2) j=1 k=l This means that the sum of row-entries as well as the sum of column-entries in the 4x4 matrix in Eqn. 1 is zero. The problem is thus reduced to finding only 9 out of the 16 yparameters. These nine yparameters then give the complete three-port characterization of the device with one terminal being common to all the ports. With hulk as the common ground, MOSFET has three ports, namely, G a t e to-Bulk, Drain-to-Bulk and Source-to-Bulk. We then need 04CH37S16 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 2, 2008 at 00:34 from IEEE Xplore. Restrictions apply.