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Accurate statistical models of FET devices are needed for yield-oriented MMIC design. In particular, currently used linear statistical models are not adequate in applications where bias point variations have a strong impact on overall yield. The paper describes a nonlinear statistical model of MESFET and HEMT devices in which statistical parameters are considered as Gaussian multivariate random variables. An automatic procedure is developed to achieve extraction of the statistical model of a FET device from a database of DC Ids and S-parameter measurements, and it is checked on a GaAs HEMT monolithic process. A statistical model has been extracted for Philips PML-D02AH GaAs HEMT devices and accurate evaluation of the S-parameters covariance matrix has been made. Statistical pair-wise tests on mean values, standard deviations and correlation coefficients show that the proposed methodology has the capability of reproducing statistical population distributions.