Sensitivity-based optimization and statistical analysis of microwave semiconductor devices through multidimensional physical simulation (invited article)

Physics-based large-signal sensitivity analysis of microwave circuits using technological parametric sensitivity from multidimensional semiconductor device models

“…The evaluation of the dc and small-signal ac sensitivities through a physics-based multidimensional model is discussed in detail in [9]; here, only a few conclusions will be provided, relevant to the ensuing treatment of LS sensitivities. As shown in [9], the dc and small-signal ac sensitivities can be derived by linear perturbation of the device model around a nominal dc working point.…”

“…As shown in [9], the dc and small-signal ac sensitivities can be derived by linear perturbation of the device model around a nominal dc working point. Assume that in (1), the electrical source term includes a dc bias superimposed to small-amplitude timevarying ac generators , i.e., ; suppose now that the parameter set undergoes a small time-independent variation with respect to its nominal value , so that .…”

“…This process has to be repeated times; with being the number of parameters involved. A more efficient approach is discussed in [6], [9], where the explicit solution of the perturbed systems is avoided and only one small-signal analysis on the adjoint system [6] or on a properly transposed system [9] are needed. Basically, both techniques exploit the fact that only the perturbation response at the device terminals (not throughout the device volume) is needed for a full small-change sensitivity characterization; the idea is similar altogether to the network sensitivity analysis method in [5].…”

“…Nevertheless, while the variation of the dc response is caused by a perturbation source term depending on the dc analysis with nominal parameters alone, for the ac sensitivity analysis one must evaluate the response to an ac source term which depends on the sensitivities of the internal potential and mobile charge distributions. Such sensitivities cannot be evaluated as in [6], [9], but require the direct solution of the system (3) for each of the parameters involved. It can, therefore, be concluded that while the dc sensitivity analysis can be carried out (through the methods in [6], [9]) and with negligible overhead with respect to the dc analysis alone, the ac small-signal sensitivity analysis intrinsically requires a fairly greater computational effort.…”

“…To allow for the extension of the method to bipolar and nonstationary transport models, some of the present-day authors proposed a generalization of the adjoint approach, whose idea is derived from Branin's method for the sensitivity analysis of electrical networks [7]. The technique, first proposed with application to the multidimensional noise modeling of semiconductor devices [8], was then recently extended to the dc and ac small-signal sensitivity analysis and exploited for the optimization and statistical analysis of high-frequency (HF) devices [9] within the framework of a bipolar drift-diffusion model.…”