An Analytical Scalable Lumped-Element Model for GaN on Si Inductors

In this paper, a wide-band distributed model that can approximate the behaviour of square and octagonal inductors, both with and without tapering, is presented. This paper also presents a novel way of accurately modelling the lateral coupling in the substrate. The presented model can be applied to any foundry process, and its validity has been demonstrated using a novel technology, the D01GH GaN process developed by OMMIC, which has a high resistivity substrate. To do so, seventeen inductors have been designed and manufactured. The proposed model has been verified against EM simulations and measurements of the designed inductors. Comparisons show that the model can correctly estimate the behaviour of the inductor, improving the results of the EM simulations for most cases. The root mean square (RMS) error calculated across the samples when estimating the inductance is 0.0565. The RMS error for the quality factor results (2.2727) is also adequate, although there is more deviation when comparing the results with the measurements.