This paper proposes a novel method for practical prediction of interconnect conductor surface roughness effect on multi-gigabit digital signals.
Abstract
The high-frequency content of state-of-the-art digital signals acts like a magnifying glass
for microscale PCB effects like glass weave and copper surface roughness. In this paper,
we present an experimental, numerical, and analytical investigation of the important role
that these effects play in defining the characteristic impedance of interconnects, the
associated attenuation and phase constant, as well as the appearance of resonances in the
insertion and return loss. By means of 3D EM simulations, macromodels are developed
and correlated to measurements up to 50 GHz using a test vehicle designed using
different prepregs, laminates and copper foils. As a result, recommendations and
guidelines are provided for proper material selection and trace routing that mitigate such
effects.
Summary: PCB laminates are inhomogeneous structures constructed from multiple
dielectric and metal layers. Thus, the anisotropic nature of PCBs introduces a variation of
the dielectric characteristics of the substrate with position and may also originate
resonances that considerably degrade the performance of interconnects. Despite this, it is
a common practice for design engineers to solely rely on vendor published ε and TanD
parameters obtained by a Bereskin and/or Stripline-resonator technique applied to smooth
resin cast of homogenous material. Similarly, the properties of metal layers are typically
characterized by bulk properties; at best, modified based on the model developed by
Hammerstad and Jensen to account for the increase on the attenuation due to copper
roughness. However, as communication speeds continue to rise, it becomes imperative to
analyze the impact of micro-scale effects not only on the attenuation constant, but also on
the phase constant and the characteristic impedance of the interconnects so that accurate
representations can be achieved for reliable circuit design.
In this paper, we study these micro-scale effects in detail. In particular, we analyze the
dependence of the electrical properties of interconnects with respect to their position on
the weave as well as the effects that result from the periodicity of the fiber glass bundles,
which can give rise to resonances. Furthermore, we discuss the mechanisms that produce
such resonances and propose an analytical equation for their prediction, validated by 3D
electromagnetic simulations and measurements. For this purpose, a 3D fabric weave
model based on actual prepreg layer measurements is created and simulated using an EM
simulator. A PCB test vehicle was fabricated with sets of traces running at various angles.
The predicted, simulated, and measured resonances are shown to be in excellent
agreement.
The focus of our investigation of copper roughness is not only on the additional
attenuation introduced by the roughness, but also on the additional time delay, which can
be directly extracted from our time-domain simulations. The investigation starts with the
common approach where the copper surface bumps are assumed to be periodic. A
parameterized model is developed which takes given surface statistics as input. The
statistical data to generate such models are taken directly from optical profile meter
measurements of copper foils. Bear in mind, however, that the large aspect ratio between
the roughness feature size and the overall interconnect length makes the use of these 3D
models currently unfeasible. For this reason, we propose a computationally inexpensive macromodel based on a frequency-dependent surface impedance model. After the models
are developed, we use them to predict the effects of copper roughness on signal
propagation and to characterize the copper foil by simulation. Our models are then
correlated to existing models and measurements.
For the experimental validation of the modeling results presented in this paper, we
determine the complex propagation constant (γ) and characteristic impedance (Zc) of
various high speed test lines. In our experiments we determine γ and Zc from line-line
measurements, which is desirable for a more accurate and systematic characterization of
the micro-scale effects on high-speed interconnects. Finally, as a result of our micro-scale
investigations of PCBs, we provide guidelines and recommendations for material
selection, stack-up optimization and trace routing not only for taking these effects into
consideration but also for mitigating them as much as possible.