Title :
Thin-sample measurements and error analysis of high-temperature coaxial dielectric probes
Author :
Bringhurst, Shane ; Iskander, Magdy F. ; White, Mikel J.
Author_Institution :
Dept. of Electr. Eng., Utah Univ., Salt Lake City, UT, USA
fDate :
12/1/1997 12:00:00 AM
Abstract :
A metallized-ceramic probe has been designed for high-temperature broad-band dielectric properties measurements. The probe has been used to make complex dielectric properties measurements over the complete frequency band from 500 MHz to 3 GHz, and up to temperatures as high as 1000°C. In this paper, we investigate new aspects of the development and utilization of this high-temperature dielectric probe. The first 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 probes. In this case, a two-dimensional (2-D) cylindrical finite-difference time-domain (FDTD) code was developed and used for this analysis. The obtained results were compared and shown to be in good agreement with error-analysis data based on analytical solutions for the special case when an air gap exists between the probe and the material under test. Additional new error-analysis results show that differential thermal expansions and rough surfaces cause considerable errors in these measurements, and the use of probes of small differential thermal expansions, 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 shown that by backing the material under test with a standard material of known dielectric constant, such as air or metal, the complex permittivity of thin samples can be accurately measured. The other new development is related to the use of the developed metallized-ceramic probe to measure the dielectric properties of thin samples at high temperature and over a broad frequency band. With the developed knowledge from the error analysis, and the new FDTD code for thin-sample measurements, the metallized-ceramic probe was used to measure dielectric properties of thin Al2O3 and sapphire samples for temperatures up to 1000°C. This measurement method has important applications in the on-line characterization of semiconductor wafers. Results from the high-temperature thin-sample measurements and the uncertainty analysis are presented
Keywords :
finite difference time-domain analysis; high-temperature techniques; measurement errors; microwave measurement; permittivity measurement; probes; 1000 C; 500 MHz to 3 GHz; Al2O3; FDTD numerical simulation; air gap; broadband nondestructive measurement; complex permittivity; dielectric properties; error analysis; high-temperature coaxial dielectric probe; metallized ceramic probe; on-line measurement; rough surface; semiconductor wafer; thermal expansion; thin sample; two-dimensional cylindrical finite-difference time-domain code; uncertainty analysis; Dielectric measurements; Error analysis; Finite difference methods; Frequency measurement; Metallization; Permittivity measurement; Probes; Temperature; Thermal expansion; Time domain analysis;
Journal_Title :
Microwave Theory and Techniques, IEEE Transactions on