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R
G
The conversion factor between resistivity in circular mil-ohms per
foot and ohm-centimeters is the following:
For example, for copper, r � 10.37 CM⋅�/ft:
r (�⋅cm) � 1.662 � 10 �7 (10.37 CM⋅�/ft)
� 1.723 � 10 �6 �⋅cm
as indicated in Table 3.3.
The resistivity in IC design is typically in ohm-centimeter units,
although tables often provide r in ohm-meters or microhm-centimeters.
Using the conversion technique of Chapter 1, we find that the conversion
factor between ohm-centimeters and ohm-meters is the following:
1.723 � 10 �6 �⋅cm � [1.723 � 10 � � �6 1 m 1
� � ] �⋅m
100 cm 100
or the value in ohm-meters is 1/100 the value in ohm-centimeters, and
Similarly:
r (�⋅cm) � (1.662 � 10 �7 ) � (value in CM⋅�/ft)
1
r (�⋅m) �� �
100
�� � (value in �⋅cm)
r (m�⋅cm) � (10 6 ) � (value in �⋅cm)
For comparison purposes, typical values of r in ohm-centimeters for
conductors, semiconductors, and insulators are provided in Table 3.4.
TABLE 3.4
Comparing levels of r in �⋅cm.
Conductor Semiconductor Insulator
Copper 1.723 � 10 �6
Ge 50 In general: 10 15
Si 200 � 10 3
GaAs 70 � 10 6
In particular, note the power-of-ten difference between conductors
and insulators (10 21 )—a difference of huge proportions. There is a significant
difference in levels of r for the list of semiconductors, but the
power-of-ten difference between the conductor and insulator levels is at
least 10 6 for each of the semiconductors listed.
3.5 TEMPERATURE EFFECTS
Temperature has a significant effect on the resistance of conductors,
semiconductors, and insulators.
Conductors
Conductors have a generous number of free electrons, and any introduction
of thermal energy will have little impact on the total number of
TEMPERATURE EFFECTS ⏐⏐⏐ 67