A theory for anomalous spectral behaviors observed in proton-enhanced microstrip inductors on silicon with its brief derivation

The verified applicability of proton-beam treatment (the so-called, "π technology") in both the 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). Potentially, the PBS can end the traditionally laborious mixed-mode product development cycle and eventually become the general SOC integration platform. Recently, however, there are several questions encountered in the proton-enhanced inductors. Among others, there are explosive rise of the inductance near certain frequency in some cases but not in others, and the inductor size effect that dubiously alters the frequency at which the above anomaly takes place. Such difficulties seem to go beyond the current understanding of the microstrip inductors. A new theory is briefly presented here to address the possible cause of such puzzles.