COMPLEX PERMITTIVITY IN THE AlN–SiC COMPOSITE IN THE MICROWAVE FREQUENCY RANGE 1–100 GHz

Abstract

The dependences of the real and imaginary parts of the complex permittivity in AlN–SiC composites with a silicon carbide content of 20 to 50% over a frequency range of 1–100 GHz for SiC particle average sizes of 0.8 and 2.3 μm are presented. When frequency increases from 1 to 100 GHz, the general pattern is a constant decrease in the real part ε¢ in inverse proportion to the frequency to the 1/5 power. The imaginary part ε² first increases proportionally to the frequency to the 1/2 power when the frequency raises from 1 to 3 GHz, reaches its maximum value in the frequency range 6–8 GHz, and then monotonically decreases in inverse proportio to the frequency to the 1/5 power at frequencies greater than 8 GHz. In the entire frequency range, the values of ε¢ and ε² are found to be frequency-dependent. However, at frequencies above 8 GHz, their ratio ε² / ε¢ = tgδ remains constant and does not depend on the frequency. Analytical expressions for ε¢ and ε² are proposed for these dependencies, allowing their values to be calculated at any frequencies within this range. To construct such dependencies, at least one experimental data point with reliable ε¢ and ε² values should be obtained, preferably in the range from 2 to 5 GHz. This is particularly true to the imaginary part ε² since the nature of changes in its values at frequencies of 1–10 GHz has unique characteristics. To specify the ε¢¢ values at frequencies lower than 8 GHz, two methods are proposed. The first method relies on the geometric construction of the inscribed circle for ε² as a function of frequency, facilitating rapid determination of the ε² value in the frequency range 4–8 GHz for AlN–SiC composites with 20 to 50% SiC. The maximum deviation from the true values of ε² does not exceed 3%. The second method involves the use of calculated parabolas, also inscribed in the dependence of ε² on the frequency. In the range 6–8 GHz, for SiC content lower than 40%, the deviation of ε² does not exceed 3%.