Radio Frequency Integrated Circuit Design - Webs

The Use and Design of Passive Circuit Elements in IC Technologies
Example 5.2 Calculation of Capacitance
Calculate bottom plate capacitance and fringing capacitance for a 1 poly, 4
metal process with distances to substrate and conductor thickness as given in
the first two rows of Table 5.3. Calculate for metal widths of 1 �m and
50 �m.
Solution
Bottom plate capacitance can be estimated from (5.5), which is equivalent to
the first term in (5.6). Total capacitance can be calculated from (5.6) and the
difference attributed to fringing capacitance. Results are shown for the 1- and
50-�m lines in Table 5.3. It can be seen that bottom plate capacitance is a
very poor estimate of total capacitance for a 1-�m line. When calculated for
a 50-�m width, the bottom plate capacitance and the total capacitance are in
much closer agreement. This example clearly shows the inaccuracies inherent
in a simple calculation of capacitance. Obviously, it is essential that layout tools
have the ability to determine parasitic capacitance accurately.
5.5 Parasitic Inductance
In addition to capacitance to the substrate, metal lines in ICs have inductance.
The current flowing in the line will generate magnetic field lines as shown in
Figure 5.4. Note that the Xs indicate current flow into the page.
For a flat trace of width w and a distance h above a ground plane, an
estimate for inductance in nanohenry per millimeter is [3]
L ≈ 1.6
K f
� h
w
Table 5.3
Capacitance for a Line with Width of 1 � m and 50 � m
101
(5.7)
Poly Metal 1 Metal 2 Metal 3 Metal 4
Height above substrate h
(�m) 0.4 1.0 2.5 4.0 5.0
Conductor thickness t
(�m) 0.4 0.4 0.5 0.6 0.8
Bottom-plate capacitance
(aF/�m 2 ) 86.3 34.5 13.8 8.6 6.9
Total capacitance
(aF/�m 2 ) (1-�m line) 195.5 120.8 85.8 75.2 72.6
Total capacitance
(aF/�m 2 ) (50-�m line) 90.0 37.5 16.2 10.8 9.0