High Speed/mm-wave Measurement-Based Model Development: Uncertainties and Model Sensitivities
(Room 203)
18 Oct 18
3:20 PM
-
3:50 PM
Tracks:
Test & Measurement
Device models must increasingly cover performance well above 100 GHz and often measurements form a part of that modeling process. Model extraction processes interact with mm-wave measurement uncertainties in sometimes surprising ways that can lead to unexpected model results. This paper explores the uncertainties of broadband S-parameter measurements (noise mechanisms and their distributions, on-wafer calibration characteristics, instrument linearity, etc.) and quasi-linear measurements such as AM/AM and AM/PM (affected by instrument linearity, power accuracy vagaries, nonlinear match oddities, etc.) as well as common model extraction techniques for both passive (primarily isolated and coupled inductors and capacitors) and active devices (primarily transistors). There are cases in the parameter space when uncertainty increases in the former and sensitivity increases in the latter can overlap, making for a worst-case scenario. For relatively high reflection and transmission levels, noise in S-parameter measurements is largely multiplicative (i.e., not noise floor-based but scales, in absolute terms, with the reflection or transmission wave amplitude) but usually linear and increasing monotonically with frequency. On-wafer calibration characteristics can vary wildly and popular techniques (line-reflect match and its derivatives) are dependent on both line quality and on certain characteristics of the match standard behavior. Further complicating the picture, particularly above 100 GHz, are increases in probe-to-probe coupling and the possibility of extraneous modes propagating on either the calibration standard substrate or on the DUT wafer. The outcome is an extra-linear increase in uncertainties at high frequencies with particular strength at low transmission and reflection levels. Instrument linearity effects can also vary wildly (from >30 dBm third order intercept products to ~<10 dBm at 110 GHz depending on the structure) which can be important in active device characterization. For quasi-linear measurements, the receiver linearity (including match linearity) is obviously even more important. The RF power level is often critical for model development and the accuracy of this can be impacted by fundamental vs. integrated power differences particularly at higher mm-wave frequencies. On the model extraction front, many processes are nonlinear with respect to S-parameters with great sensitivity increases as full reflection or full transmission is approached. This can create interesting situations since the noise of the measurements is locally maximizing in that area so modifying the measurement setup might help. A number of extracted parameters (e.g., inductor Q, gate-drain capacitance, etc.) rely on multiple S-parameters so it can make a difference if the uncertainty in those S-parameters is correlated or uncorrelated. Understanding those relationships might allow one to alter the setup to minimize correlated uncertainty increases. Further, extrapolation is frequently employed and works from some of the higher frequency measurement data where uncertainties may be increasing. Modifying what portions of the data set are most heavily weighted in the extrapolation may be advised. This paper explores these measurement-based extraction relationships through an analysis of measurement hardware (from kHz range to over 200 GHz), actual measurement/extractions examples and Monte Carlo simulations. The objective is to outline steps that can be taken to minimize unfortunate uncertainty/sensitivity collisions and hopefully improve the resulting extractions.