Modeling, Simulation, and Measurement - Computer Architecture Techniques for Power-Efficiency - page 16

TABLE 2.2: K design parameters for Typical Circuits. Adapted from [ 41 ].

Circuit N K design Notes

D flip flops 22/bit 1.4 Edge-triggered FF

D latch 10/bit 2.0 Transparent latch

+

2-input Mux 2/bit/input 1.9 1.2/input over 2

6T RAM cell 6/bit 1.2 1 RW port

CAM cell 13/bit 1.7 1 RW, 1 CAM port

±

Static logic 2/gate input 11 Depends on speed, load, 3

crafting OS-level management techniques, however, more localized heating information is
almost always necessary.
There are analogies between heat transfer and electrical phenomena upon which we can
build thermal models. Power dissipation results in heat, and this heat flows through regions
based on their thermal resistance ( R ). The amount of heat flow can be analogized to current
( I ), and the heat difference between two regions on a chip is analogous to voltage (V). Because
there are time dependences in both the power dissipation and in its relationship to heat flow
and thermal impedance, a capacitance ( C ) is also modeled. Thus, time-dependent RC models
remain the best way to model localized thermal behavior on chip.
In some early work, TEMPEST modeled temperature based on power dissipation and
density values, but did so only for the chip as a whole, not for individual regions or architectural
units [ 65 ].
Perhaps the most important work on architecture-level thermal modeling thus far been
the HotSpot approach developed by Skadron et al. [ 206 ]. They propose and validate a compact
RC model for localized heating in high-end microprocessors. This model considers both the
lateral relationships between units on chip, as well as the vertical heating/cooling relationships
between the active portion of the silicon die and the attached heat spreader and heat sink layers
that seek to even out temperature and draw heat away from the active silicon.
There are several steps in producing a HotSpot thermal model. First, from a chip floorplan
and other technical details, one needs to deduce the R and C values that comprise the heat flow
network for the RC model. In general, thermal resistance and capacitance relate to the material's
thickness and the surface area of heat flow. In addition, a thermal constant k represents the