Updated July 9,
here to go to our main page on resistors
This page discusses
of the differences between five categories of materials according
to their conductivities:
This page also explains the concept
of sheet resistance and conductivity.
below are in common usage but may be seen as arbitrary since there
is no industry standard that can be applied here (perhaps IEEE will
someday come up with one). You can also check out our page on conducting
This category is VERY resistive
(duh). Bulk resistivity is within the range of 1010 to
1022 ohm-centimeter to be considered an insulator. Any
"good" dielectric material is an insulator. Insulators
include glass, plastic, rubber, silicon dioxide, and silicon nitride
Insulating materials have tightly bound electrons (usually eight)
in the outer shell that are happy to remain there even in the presence
of high voltage electric fields.
Semi-insulators have bulk resistivities
between 103 to 1010 ohm centimeters. Cut fresh
from the boule, GaAs wafers are said to be semi-insulating.
Semiconductors have bulk resistivity
in the range of 10-4 ohm-cm (heavily doped) to 103
ohm-cm (undoped, or intrinsic). That's seven orders of magnitude!
Semiconducting elements include silicon and germanium, it is no
coincidence they are both from group 4 of the period table. Semiconducting
compounds include gallium arsenide, indium phosphide, and gallium
nitride, from groups 3/5 or 2/6 of the period table.
Semiconductor materials have
4 electrons in their outer shell (it's half filled). When bonded
together in a crystal lattice, atoms share electrons such that they
each have eight electrons in the outer shell. Electrons are somewhat
loosely bound so they can become carriers in the presence of an
To be considered a conductor,
a material must have a bulk resistivity within the range of 10-6
to 10-4 ohm-cm. Conductor materials have loosely
bound electrons (one or two) in the outer (valence) shell that can
move easily under the influence of a voltage to form current. Conductors
include elemental metals such as copper, gold, silver, aluminum.
Heavily-doped semiconductors can also be considered conductors.
Content moved to a new
and sheet conductivity
This concept is further explained
on our page on resistor mathematics.
Bulk resistivity is a the property
which is independent of frequency and geometry. In microwaves, often
we are dealing with thin films of conductors, which have been applied
at a controlled thickness. A more convenient property to deal with
in this case is sheet resistance. The sheet resistance of a metal
film is often expressed in ohms/square. What's a square? Exactly
on first? I Don't Know's on second.
Recall the equation for calculating
resistance from bulk resistivity:
Remember, the resistance
calculated this way does not account for skin
depth effects. It is accurate if your conductor thickness is
small compared to a skin depth.
If you consider
the quantity L/w, it is unitless. It can be considered as a measure
of how many squares of area your conductor or resistor has.
For example, a thin-film resistor with length 30 mils and width
10 mils is three squares. A smaller resistor of 3 microns length
and 1 microns width also has three squares (thanks Jack!)
If they both have the same thickness and bulk resistivity, they
both have the same value in ohms. They will have far different power
ratings, and the smaller resistor will have a higher usable frequency
response. Be careful not to mix up length and width, a resistor
with 10 microns length and 30 microns width measures 1/3 square,
not three squares!
Rsh, is equal to bulk resistivity divided by thickness.
It can be used to conveniently calculate resistance values from
number of squares, as follows:
As in all engineering,
you will need to keep units consistent in order to make the calculation
correctly (if rho is in ohm centimeters, the thickness must also
be in centimeters). One last thing to consider: sheet conductivity
is the inverse of sheet resistivity. When is sheet conductivity
useful? When you have more than one metal layer. The sheet conductivities
of the layers can be added, because the conduction paths are in