Second-harmonic nonlinearities in RF silicon integrated passive devices

Abstract

High resistivity silicon substrates (HRS) commonly used in RF integrated passive devices (IPDs) require surface treatments to eliminate the parasitic surface conduction effect, which can degrade the quality factor of the components through ohmic losses. High levels of 2nd harmonic distortion have also been reported for unpassivated silicon substrates. The surface treatments that are used to reduce losses also eliminate most of the nonlinearities in these structures. Nonetheless, residual nonlinear behavior is observed even in well-passivated substrates. We report measured 2nd-order harmonic distortion in several different IPD filters for a number of frequency bands and substrate thicknesses. As expected, silicon RF IPDs fabricated on passivated HRS show very low levels of 2nd harmonic generation. However, at signal power levels approaching 1W the 2nd harmonic power in some filters can rise above the -100dBc level, which may cause problems with interference in some multi-band applications. To analyze these results, a simplified analysis of nonlinear substrate coupling in passivated HRS substrates is presented. Measured results show that as in previously reported results for coplanar transmission lines, the mechanisms of filter interaction with the silicon are predominantly tangential to the substrate surface. The response can be modeled by a first-order voltage coefficient of capacitance. The analysis indicates that this coefficient is strongly dependent on several key factors particularly substrate resistivity and frequency. A model of depletion layer depth modulation is presented that matches the observed dependences. Based on this analysis, a simple method for identifying features in the layout that contribute strongly to 2nd harmonic generation in thin-film IPDs is presented.