Complex permittivity of gallium arsenide and sapphire to 220 GHz

Abstract

Despite the industrial relevance of sapphire and gallium arsenide (GaAs) for electronic applications, there are few reports on the value of complex permittivity and dielectric loss at frequencies above 110 GHz using integrated circuit topologies such as coplanar waveguides. Available materials characterization reports at microwave frequencies use methods that quantify bulk material properties and may miss the effective material properties present in the substrate structure and most relevant for integrated circuits at the frequencies of interest. Using a wafer-level method to extract the complex permittivity of sapphire and GaAs to 220 GHz, we found that the complex permittivity of intrinsic GaAs (εon−wafer≈13) and the convoluted in-plane and out-of-plane complex permittivity of c-plane sapphire (εon−wafer≈10.5) did not show dispersion up to 100 GHz. This result shows the importance of wafer-level tests for sapphire, where on-wafer permittivity diverges from nominal single-axis values. Above about 100 GHz, different data analysis approaches yielded increasingly different permittivities. This result provides useful data to electronics designers, materials scientists, and physicists while also providing insight into mechanisms that could produce unexpected frequency dependence.