Radio Frequency Integrated Circuit Design - Webs

The Use and Design of Passive Circuit Elements in IC Technologies
Since most of the applications lie in the 900-MHz to 5-GHz band, it is
easy to see that making lines much thicker than about 4 �m will lead to
diminishing returns. Going any thicker will yield little advantage at the frequencies
of interest, because the center of the conductor will form a dead zone, where
little current will flow anyway.
Example 5.1 Effect of Skin Depth on Resistance
A rectangular aluminum line has a width of 20 �m, a thickness of 3 �m, and
a length of 100 �m. Compute the resistance of the line at dc and at 5 GHz
assuming that all the current flows in an area one skin depth from the surface.
Assume that aluminum has a resistivity of 3 �� �cm. Note that there are
more complex equations that describe the resistance due to skin effects, especially
for circular conductors [1]; however, the simple estimate used here will illustrate
the nature of the skin effect.
Solution
The dc resistance is given by
R = �L
Wt
= 3 ��cm � 100 �m
20 �m � 3 �m
The skin depth at 5 GHz of aluminum is
= 50 m�
�
� = √�f� = √
3 �� �cm
� � 5 GHz � 4� × 10 −7 N
A 2
= 1.23 �m
We now need to modify the original calculation and divide by the useful
cross-sectional area rather than the actual cross-sectional area.
R =
�L
Wt − (W − 2�)(t − 2�)
3 �� �cm � 100 �m
=
20 �m � 2 �m − 17.5 �m � 0.54 �m
= 98.2 m�
This is almost a 100% increase. Thus, while we may be able to count on
process engineers to give us thicker metal, this may not solve all our problems.
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