Observation of explosive spectral behaviors in proton-enhanced high-Q inductors and their explanations

The verified success of proton-beam treatment in both device isolation and inductor Q-improvement on Si substrates is now enticing some big chipmakers into realizing a VLSI back-end facility: the particle-beam stand (PBS). The PBS can potentially end the traditionally laborious mixed-mode product development cycle and eventually become the general system-on-a-chip (SOC) integration platform. However, the observed Q-improvement might in fact fall short of what it should be. Namely, if substrate resistivity is the sole dominant factor deciding the ultimate inductor Q value, then the proton-achieved resistivity does not bring forth the anticipated ideal Q value. Furthermore, there are several puzzles in the observed inductance spectral behaviors. Thus, there is an explosive rise of inductance near certain frequencies in some cases but not in others, and the inductor size effect alters the frequency at which these inductance rises occur. Such difficulties outwit the existing understanding of the microstrip inductors. A new theory is briefly presented here to unravel the cause of such incomplete Q-improvement and hopefully to resolve all related puzzles. It includes identifying the inductor-substrate coupling effect as a result of the proton bombardment, using a special dipole-dominated expansion of the inductor system equations, and further applying the notion of electromagnetic mass of the electron. With such theoretical insight, ideal high-Q passives may be just a few steps away using the so-called "dipole engineering" approach on PBS.