As operating frequencies on system-level ICs keep climbing, engineers who still have some dim memory of taking an RF class may get a creepy feeling. The specter of microwave design, with its weird, counterintuitive effects, complex device models and intractable analysis tools, keeps flickering in the peripheral vision of designers who find themselves working with 1-GHz clock frequencies, 2.5-GHz RF stages and the like.
And this ghost is no Halloween goblin: It's the real thing. At high frequencies conductors cease to act like wires and begin to act-for better or worse-like waveguides. Mutual inductance creates signal paths where you thought there was only insulation. And then there's skin effect.
Maxwell's Equation insists that as frequency rises, the current in a conductor increasingly crowds to the surface, leaving little or no current density in the interior. This has several profound effects: It increases the apparent proximity of nearby conductors. It decreases the apparent cross-section area of the conductor, causing an observable increase in apparent resistance. And it causes both a substantial increase in maximum current density and a significant field gradient inside the conductor.
So what, you say. We're talking about frequencies we won't reach for a decade, and by that time my company will have gone public and I'll be a VC.
Not so fast. A paper at the recent IEEE SoC conference pointed out that changes in resistance due to skin effect become observable at just above 1 GHz. That's the clock frequency of some new CPUs. Ask the folks who do the clock tree insertion at Intel how insignificant skin effect is. Or those who design high-speed I/O pads.
But the most serious part of the problem right now isn't the fundamental frequency. It's that the actual signals designers are trying to move around are pulse trains-that is, they are rich in odd harmonics. Now, the first major harmonic in a 1-GHz square wave is at 3 GHz-already deep into trouble. And with the edge rates in 130- or 90-nanometer transistors, we are talking about significant energy in those harmonics.
So even if skin effect and mutual inductance don't have much impact on the fundamental frequency, they are going to play havoc with the whole envelope, and with delay calculations. And the amount of energy in the harmonics means that reliability analysis is going to have to look closely at the current densities and field gradients being created, particularly in irregular metal structures with sharp corners. If rules of thumb don't work, the problem may require field solvers on a feature-by-feature level.
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