Underfill materials are used in a packaging of millimeter wave IC. However, there are few reports for dielectric properties of underfill materials in millimeter wave region. A cut-off circular waveguide method is one of a powerful technique to evaluate precisely complex permittivity in millimeter wave region. This method may be useful not only for low-loss materials, but also for mid-loss ones with loss tangent of 10$^{-2}$ order. In this paper, an evaluation technique based on the cut-off circular waveguide method is presented to measure mid-loss underfill materials. As a result, the relative permittivity $arepsilon_{r}$ and the loss tangent tan$delta$ are in the range of 2.8$sim $3.4 and (1.0$sim$1.6)$ imes10^{-2}$, respectively. Also, the measurement precision is 2.3% for $arepsilon_{r} approx 3$ and 40% for tan$delta approx 10^{-2}$.

A 100 GHz grooved circular empty cavity is proposed for the low loss dielectric substrate measurements by the cut-off circular waveguide method in W band. The influence of the excitation holes for the coaxial cable with a small loop are revealed by an FEM based 3D electromagnetic simulator. And also, the diameter of the excitation hole is determined based on the calculated results and the manufacturing accuracy. Then, two kinds of four 100 GHz grooved circular empty cavities are fabricated. Comparative experiments of the cavities with the different excitation holes validate the simulated results. Moreover, the complex permittivity of a PTFE plate is measured using the fabricated four cavities by the cut-off circular waveguide method around 84 GHz. The measured results agree within measurement error about 0.5% for εr and 5% for tanδ. Also, these results accord with results measured by the Whispering-Gallery mode resonator method in 85–110 GHz band. It verifies that the proposed 100 GHz cavity for the cut-off waveguide method is useful for the complex permittivity measurement of low loss dielectric substrates in W band.

The Waveguide-Penetration method is a permittivity measurement technique where a columnar object pierces a rectangular waveguide through a pair of holes at the center of its broad walls. The permittivity of the object is estimated from measured S-parameters . This paper demonstrates a scheme for analyzing permittivity measurement errors in the Waveguide-Penetration method. The sources of errors are categorized into systematic and random error sources. Systematic errors in the values of the sample and waveguide holes diameters, the effect of sample's length, and the influence of ambient temperature are investigated and corrected for. Potential random error sources such as imperfect TRL calibration elements, VNA thermal noise, sample loading, and test-port cable flexure are analyzed and their contribution to random errors are estimated.

A novel resonator structure for the cut-off circular waveguide method is proposed to suppress the unwanted TE modes in the axial direction and TM modes in the radial direction. In this method, a dielectric plate sample is placed between two copper circular cylinders and clamped by two clips. The cylinder regions constitute the TE0m mode cut-off waveguides. The measurement principle is based on a rigorous analysis by the Ritz-Galerkin method. Many resonance modes observed in the measurement can be identified effectively by mode charts. In order to verify the validity of the novel structure for this method, the temperature dependences for three low-loss organic material plates were measured in the frequency range 40 to 50 GHz. It is found that modified polyolefin plates have comparable electric characteristics and low price, compared with PTFE plates. Moreover, it is verified that the novel resonator structure is effective in improvement of accuracy and stability in measurement. The measurement precisions are estimated within 1 percent for εr and within 15 percent for tan δ.

A grooved circular cavity is designed for the millimeter wave measurements of dielectric substrates. The grooves are introduced to separate the degenerate TE01p and TM11p modes in circular cavities. A rigorous mode-matching method is used to investigate the influence of grooves on both the TE01p and TM11p modes. The dimensions of the grooves are determined from the numerical results. Comparative experiments of circular cavities with and without grooves validate the design method.