Importance of Probe Choice for Extracting Figures of Merit of Advanced mmW Transistors

Abstract

The measurement of the figures of merit (FOMs) of an advanced and miniaturized transistor becomes a challenge when its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}_{\text {MAX}}$ </tex-math></inline-formula> goes above many hundreds of GHz. In fact, the quantities to be measured become smaller and smaller and thus the influence of the measurement environment becomes less and less negligible. Indeed, when measuring the same test structures using two different renowned commercial probes having a different topology, a “signature” of each probe can been observed, in particular, when plotting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sqrt {U} \times \text {freq}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${U}$ </tex-math></inline-formula> is the Mason gain) as a function of frequency, which is usually carried out for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}_{\text {MAX}}$ </tex-math></inline-formula> estimation. For millimeter wave (mmW) technologies, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}_{\text {MAX}}$ </tex-math></inline-formula> is the key FOM for benchmarking technologies, thus it becomes urgent to clarify this measurement. In this work, we give a proof that measurement becomes probe dependent. We constructed an accurate electromagnetic (EM) model of each probe using X-ray tomography and thus simulated the measurement environment at close proximity of the wafer using EM and SPICE simulation. Hence, each signature of the probe is clearly reproduced by the simulation, highlighting that the unexpected result is not due to an inaccuracy done by the user such as probe positioning or to a limitation of the vector network analyzer (VNA) but is the result of the unwanted coupling between the probe and the substrate or between probes and the inability of the short open load thru (SOLT) and on-wafer thru reflect line (TRL) calibration algorithms to completely remove these couplings.