Modeling the capacitive nonlinearity in thin-film BST varactors

A simple closed-form expression for the dielectric nonlinearity in thin-film high-permittivity barium strontium titanate (BST) devices is obtained from a third-order power-series expansion for the field-polarization relation. The expression is parameterized in terms of easily measurable quantities of zero-field capacitance and tuning ratio, and compares favorably with data on several representative BST compositions and device sizes. The temperature dependence of the capacitors is treated using a simple linear temperature coefficient in the zero-field capacitance that also compares favorably with experimental data on BST capacitors. The influence of interfacial ("dead" layer), fringing, and parasitic shunt capacitance on the experimental C-V curves is discussed. The results are potentially useful for circuit and electromagnetic simulation.