Scalable HEMT small-signal model extraction based on a hybrid multibias approach

Abstract

A multibias approach for HEMT small-signal model extraction is proposed. The method is based on scaling rules and uses a hybrid direct extraction/particle swarm optimization approach. By the use of a reduced number of S-parameter measurements in the optimization procedure, the computational effort is kept low. The extraction procedure is verified with measurements on metamorphic HEMTs, leading to accurate and scalable models in the millimeter-wave range. Furthermore, the robustness of the proposed method against measurement uncertainties is verified by using PHEMT synthetic data, intentionally affected by errors

Optimization‐based approach for scalable small‐signal and noise model extraction of GaN‐on‐SiC HEMTs

“…The example also includes the extraction of a noise model, by means of a well-known noise-temperature approach. Both the small-signal and noise models agree well with the experimental data.Also these methods rely on a fundamental hypothesis, namely, the validity of a certain set of scaling rules; however, this assumption has been consistently confirmed in practice and is not really a matter of discussion (although slightly different scaling rule sets and even SSEC topologies have been proposed over time) [7,[11][12][13][14][15].The direct-extraction approach and the fit/optimization-based approach are not totally separate; however, in fact, they often present some points of contact. The most important one, probably, is the very fact that optimization typically involves selecting an initial guess of the solution, which in turn calls for the application of a direct-extraction method to start with: this is the case, for instance, for the algorithm described in [11], as well as that presented later in this contribution.…”

“…Both the small-signal and noise models agree well with the experimental data.Also these methods rely on a fundamental hypothesis, namely, the validity of a certain set of scaling rules; however, this assumption has been consistently confirmed in practice and is not really a matter of discussion (although slightly different scaling rule sets and even SSEC topologies have been proposed over time) [7,[11][12][13][14][15].The direct-extraction approach and the fit/optimization-based approach are not totally separate; however, in fact, they often present some points of contact. The most important one, probably, is the very fact that optimization typically involves selecting an initial guess of the solution, which in turn calls for the application of a direct-extraction method to start with: this is the case, for instance, for the algorithm described in [11], as well as that presented later in this contribution. Another possible analogy that can be pointed out between the two approaches is the use of fitting procedures also in some 'standard' methods (where the fitting variable is typically the frequency), aiming at solving problems for which the number of equations would not be otherwise sufficient [3,6,16]; in such cases, it is worth noticing, the fitting does not typically involve iteration or optimization but simple linear regressions, and can therefore viewed as a 'direct' method.…”

“…Another possible analogy that can be pointed out between the two approaches is the use of fitting procedures also in some 'standard' methods (where the fitting variable is typically the frequency), aiming at solving problems for which the number of equations would not be otherwise sufficient [3,6,16]; in such cases, it is worth noticing, the fitting does not typically involve iteration or optimization but simple linear regressions, and can therefore viewed as a 'direct' method. Notice that hybrid approaches can be devised where a part of the extraction is performed through standard techniques, another through optimization: in [17], for instance, the extrinsic capacitances are found via closed formulae, while the remaining elements are optimized; conversely, in [11], for each optimization guess of the extrinsic elements, these are de-embedded and the intrinsic ones are computed via closed formulae.Finally, a third possibility exists, consisting in determining the extrinsic portion of the SSEC through extensive electro-magnetic simulations [18][19][20], complemented by classical or semi-classical approaches [21] for the intrinsic; however, the need for subjecting the device to potentially harmful operating points is typically avoided. The EM-based approach provides much flexibility, and allows to investigate separately the effect of factors, which with the standard approach alone cannot be distinguished from one another.…”

“…Similarly, the effect of each SSEC element in the modeled behavior is considered over the full range of these variables (frequency and bias in particular), rather than mainly under specific conditions purposely aimed at highlighting their contribution. As a side note, this avoids the need for measuring the devices under potentially harmful conditions (cold FET with strong direct current), as required by some early standard approaches [2].Unlike in other methods [11], the optimization involves all SSEC elements (extrinsic and intrinsic ones), so that no painstaking selection of appropriate frequency ranges is required, nor does the risk arise of obtaining, even at intermediate optimizer iterations, unphysical results. Moreover, very complex topologies can be assumed at the only cost of longer computing times, while the corresponding lack of closed-form equations to extract the various SSEC elements has no impact on applicability.…”

“…Of course, in order to obtain sensible, unique solutions, two requirements are necessary: first, that a starting guess be provided sufficiently close to the actual solution, and second, that the SSEC scalable model (topology plus scaling rules) is well suited to the problem and 'well-posed.' In particular, each model element should have a non-negligible effect on at least a portion of the available measurements, and this effect must be distinct from that of the other elements.The details of the proposed method, which in many respects resembles that presented in [11], will be treated in Section 0. Its peculiarities with respect to [11], which also will be discussed in Section 0, 2 of 16 S. COLANGELI ET AL.…”