Calibration Accuracy of a 625 GHz On-wafer Probe Theodore J. Reck, Lihan Chen, Chunhu Zhang, Alex Arsenovic, Arthur Lichtenberger, Robert M. Weikle II and N. Scott Barker Charles L. Brown Department of Electrical Engineering University of Virginia, Charlottesville, VA 22903, U.S.A. Abstract The accuracy of an on-wafer probe system operating at 625 GHz is analyzed. A weighted least squares analysis is applied to the calibration of a one-port measurement system to propagate the non-systematic errors introduced by probe contact and probe placement variation. The worst-case errors of the 625 GHz on-wafer probe system are found and the combined effects of the VNA extender’s power drop-out at the low end of the band with the poor matching of the probe at the high-end results in the 625 GHz probe system being most accurate in the center of the WR-1.5 waveguide band. Between 560 and 625 GHz the worst case error is 0.26 in linear magnitude and 15 ◦ in phase for a 0 dB reflection. I. I NTRODUCTION InP HEMT processes are being developed which produce devices that have f t as high as 550 GHz and f max extrapolated to be 1.44 THz [1][2]. While significant progress has been made in the semiconductor process technology, improvements in the characterization of these devices would greatly accelerate further developments. Direct characterization at the frequency of interest would improve circuit models, decrease circuit development time and provide additional data to inform further process development [3]. Currently, the characteristics of submillimeter and terahertz transistors are measured at lower frequencies and the high frequency behavior is extrapolated [4][5]. Measurements of the devices across the entire operating frequency would reduce the number of approximations and the resulting modeling errors. To address this problem, a micromachining process has been applied to realize an on-wafer probe that operates at 500 to 750 GHz [6][7]. These probes rely on WR-1.5 frequency extenders such as the one developed by Virginia Diodes, Inc. to couple between it and a standard VNA [8]. Since these are some of the first on-wafer measurements at these frequencies, it is important to characterize the errors in the system. At this time, only a one-port system is available at the University of Virginia to characterize these probes, so an offset short calibration is applied to characterize the frequency extenders and 625 GHz on-wafer probes. This paper presents an analysis of the on-wafer probe system accuracy operating at 500 to 750 GHz. This system consists of the micromachined probes, WR-1.5 frequency extenders and a Rohde & Schwarz ZVA 40. Errors due to the probe repeatability and the probe positioning are characterized. These non-systematic errors are propagated through the calibration by using a weighted least squares algorithm developed by Wong [9]. Worst case errors are found and the results show that errors of 0.26 in linear magnitude and 15 ◦ in phase for a 0 dB reflection can be expected. II. ERROR PROPAGATION ALGORITHM Several approaches exist to relate the error in the calibration standards to that of a calibrated network analyzer measurement. Bianco was the first to present an approach that propagated the error through the calibration system and then calculated a quality factor for the calibration based on the errors in the standards [10]. So that redundant standards can be included in the calibration, this work follows the method developed by Wong which propagates the error through a weighted least-squares algorithm to solve for the errors in the calibration. The matrix formulation takes into account the covariances between the error terms, thus avoiding some of the overestimation of error present in Bianco’s analysis. The least squares algorithm still neglects the covariance in the real and imaginary components of the individual measurements, but a monte carlo simulation that captures this effect has shown good agreement with this least-squares algorithm. This results in a slight overestimation of the errors in the system, but is significantly more accurate than the Bianco method. For full details of the error propagation analysis the reader is referred to Wong [9]. 978-1-4244-7449-3/10/$26.00 ©2010 IEEE