NONIDEAL CONDUCTOR MODELS - Advanced Signal Integrity for High-Speed Digital Design - page 236

magnification at a 30 ◦ angle. Figure 5-23 SEM photograph of rough copper at 5000 ×

roughness profile that can be described as spherical particles, joined together in
a network to form a distorted surface, as shown in Figure 5-24. An individual
snowball is located a distance x i below a flat copper surface, has radius a i , and,
when it experiences an external electromagnetic field intensity, as it would in
the region below the copper trace when a signal is propagating on a transmis-
sion line, it will dissipate power similar to the hemisphere described in equation

Electrodeposited
copper spheres

a i

x i

Flat Copper Plane

Figure 5-24 Cross section of a distribution of copper spheres that create a 3D rough
surface in the form of copper “pyramids” on a flat conductor.