Matheus BORDIN GOMES

Integrated passive devices play a major role in the design of RF and millimeter-wave (mm-wave) circuits on silicon: inductors, transformers, transmission lines, couplers, power dividers, baluns, etc., are key components and have a direct impact on circuit performance: gain, noise, bandwidth, phase errors, common-mode rejection, and isolation performance.

Based on electromagnetic (EM) simulations, RF/mm-wave designers can create their own custom devices to achieve optimized performance and form factors and verify their frequency response at the functional level. However, with increasingly stringent RF/mm-wave specifications and considering the improvements in silicon technologies (f_T, f_max, noise factor, linearity, power), the precision and performance of passive components become increasingly critical. Circuit designers then face numerous challenges in simulations and validation (proximity effects, coupling, on-wafer characterization), and uncertainties that can prevent achieving high-performance RF/mm-wave passives. Furthermore, EM simulations do not provide truly transferable information from one design to another, whether it is understanding RF/mm-wave loss mechanisms and their frequency dependencies, parasitic coupling phenomena, etc.

In practice, optimizing the performance of RF passive devices remains tedious for each new design. One might turn to software optimization to reduce design times. However, the complexity of circuits, with increasingly complex Back-End-Of-Line (BEOL), does not currently allow for such an approach because full-wave EM simulations still result in prohibitive simulation times for an optimization-based approach, even with significant computational resources. Moreover, a design approach based solely on circuit optimization does not ultimately allow for progress (or very slow progress) in understanding physical phenomena, and of course, does not enable the creation of innovative circuit topologies from scratch. Therefore, analyzing the state-of-the-art and synthesizing models or charts remains the preferred approach.

The context of millimeter-wave circuit design also raises the question of the approach to be favored according to the frequency, between lumped and distributed circuits. Lumped circuits involve inductors, capacitors, and transformers, while distributed circuits rely on the use of propagation lines. In RF and up to at least 50 GHz, the lumped approach is preferred for two main reasons: (i) the surface area of circuits based on propagation lines (couplers, baluns, power dividers, etc.) is prohibitive in terms of cost, and (ii) the quality factor of lumped elements (MIM or MOM capacitors, spiral inductors) is significantly higher than that of propagation lines (around 15 at 20 GHz for propagation lines, compared to approximately 30 to 50 and 20 for capacitors and inductors, respectively). However, from a certain frequency, probably between 50 GHz and 100 GHz, the interest in designing passive circuits based on propagation lines grows, as the circuit surface area decreases with frequency and the quality factor of propagation lines increases, unlike that of capacitors which decreases, and we begin to see designs mixing lumped and distributed approaches [Zhang 2023a]. Furthermore, designing inductors or transformers becomes very complicated due to parasitic capacitances, whose value, roughly constant regardless of frequency, due to frequency-independent design rules in the first order, becomes critical as frequency increases, with equivalent impedances (1/Cω) approaching 50 Ω. Most mm-wave design teams observe this, and most designs beyond 100 GHz are based on a distributed approach [Rao 2021], [Zhang 2023b]. However, no published study provides an informed comparison between a lumped and a distributed approach, on the same frequency bands, using the same technology, and for the same circuit specifications. This can be explained by several reasons, (i) the design time, silicon surface, and characterization cost incurred by such a comparison, and (ii) the inability to conduct an exhaustive study on several types of circuits (Couplers, Baluns, Power Dividers, Low Noise Amplifier, Power Amplifier, VCO, Phase Shifter, etc.), several frequencies, and several technologies. Each technology offers a different BEOL, which will lead to a more or less pronounced advantage for one of the two approaches, lumped or distributed. For example, a 22 nm CMOS technology has a relatively thin BEOL, leading to propagation lines with much lower performance than the same lines made on a 55 nm BiCMOS BEOL, where the BEOL thickness is much greater, while inductors and capacitors have relatively close performance. Thus, the use of a distributed approach in 22 nm CMOS technology will be more debatable, at least up to a certain frequency.

In conclusion, we have described the context of RF/mm-wave circuit design by highlighting two key aspects for designers, (i) "which design approach to choose between EM simulations and models/charts?" or more precisely "how to best manage these two complementary approaches to understand loss mechanisms, substrate effects, effects related to dummies (tiling) due to metal density rules, parasitic coupling of circuits, and how to correctly characterize them?", which implies having models and/or charts for passive circuit design, and (ii) "how to determine the preferred approach between lumped or distributed circuits?".

The proposed thesis topic for this CIFRE thesis aims to answer these two questions, as described below.