THIN-SAMPLE MEASUREMENTS AND ERROR ANALYSIS OF HIGH-TEMPERATURE COAXIAL DIELECTRIC PROBES

A metallized-ceramic probe has been designed for high-temperature broa d-band dielectric properties measurements, The probe has been used to make complex dielectric properties measurements over the complete freq uency band from 500 MHz to 3 GHz, and up to temperatures; as high as 1 000 degrees C. In this paper, we investigate new aspects of the develo pment and utilization of this high-temperature dielectric probe, The f irst aspect is related to the results of an uncertainty analysis which was performed to quantify the errors due to the differential thermal expansion between the inner and outer conductors of metal coaxial prob es, In this case, a two-dimensional (2-D) cylindrical finite-differenc e time-domain (FDTD) code was developed and used for this analysis, Th e obtained results were compared and shown to be in good agreement wit h error-analysis data based on analytical solutions for the special ca se when an air gap exists between the probe and the material under tes t, Additional new error-analysis results show that differential therma l expansions and rough surfaces cause considerable errors in these mea surements, and the use of probes of small differential thermal expansi ons, such as the developed metallized-ceramic probe, is essential for obtaining accurate results, We also used FDTD numerical simulations to help investigate the use of this probe for the nondestructive complex -permittivity measurements of electrically ''thin'' samples, It is sho wn that by backing the material under test with a standard material of known dielectric constant, such as air or metal, the complex permitti vity of thin samples can be accurately measured, The other new develop ment is related to the use of the developed metallized-ceramic probe t o measure the dielectric properties of thin samples at high temperatur e and over a broad frequency band, With the developed knowledge from t he error analysis, and the new FDTD code for thin-sample measurements, the metallized-ceramic probe was used to measure dielectric propertie s of thin Al2O3 and sapphire samples for temperatures up to 1000 degre es C. This measurement method has important applications in the on-lin e characterization of semiconductor wafers, Results from the high-temp erature thin-sample measurements and the uncertainty analysis are pres ented.