Compact modeling of interconnect and substrate coupling at GHz frequencies

Interconnect performance can be solved to within arbitrary accuracy by numerical electromagnetic (E/M) simulation, but it is a much more challenging task to translate these results into an accurate, fast and robust lumped element model compatible for circuit simulation. The schematic is first chosen to reflect the physics as much as possible; and this helps to minimize the functional complexity of the lumped element values (parasitics). Nevertheless the parasitics still display frequency-dependences that should not be ignored. The models must be very robust to deal with the extremes of layout variations such as coupling between two metal lines that may be distant or may overlap or cross if they are on different layers. Some of the coupling parasitics can be determined with a 2-dimensional approach; but at the other extreme, substrate coupling requires a full 3-dimensional treatment. Attention must also be given to the circuit configuration of coupled lines: If each line provides the return path for the other, the current density concentrates toward the edge of the lines closest to the opposite line-significantly affecting the resistances and inductances at these frequencies. Finally there are the substrate doping and trench options that are useful depending on the situation, and these should also be modeled. A tool was developed (named HIPER) that calculates the lumped element values. HIPER is also used to calculate interactions with bond-pads (very short and fat lines) and with spiral inductors. Most models for spiral inductors assume a nearby ground, which is the case when they are measured-an assumption that can now be lifted