Modeling of Anomalous CV curves in TSVs after wafer thinning

In this work measured anomalous TSV capacitance behavior is modeled and explained. The measurements showed that when the silicon surface around the TSV is in inversion, the TSV to substrate capacitance held a value of _ all the way up to a few hundred kHz. This observation is unusual because a TSV to substrate contact structure is analogous to a classical MOS capacitor, which should only present a value of C_ox up to the minority carrier relaxation frequency, _, which is only in the order of a few Hertz for typical substrates. Below this frequency minority carrier generation and recombination in the depletion region is capable of following the AC signal applied to the structure. However above this frequency majority carrier movement at the depletion layer edge is required to balance the charge equation and the depletion capacitance is seen as a series capacitance with the TSV oxide, and so the measured TSV capacitance is expected to be (_//_ ). Through the work presented here, this frequency shift in the capacitance behavior was successfully understood as being due to an extension of the depletion layer capacitance along the back side of the thinned wafer due to the presence of an inversion layer caused by fixed charges in the back side passivation layer. Furthermore a small signal equivalent circuit model was proposed in order to model this effect and was validated against the results of a commercially available finite element semiconductor simulation tool, namely Silvaco Atlas