Sheet resistance

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The sheet resistance is a measure of resistance of thin films that have a uniform thickness. It is commonly used to evaluate the outcome of semiconductor doping, metal deposition and resistive paste printing. Examples of these processes are: doped semiconductor regions (e.g. silicon or polysilicon), and the resistors which are screen printed onto the substrates of thick film hybrid microcircuits.

The utility of sheet resistance, as opposed to resistance or resistivity, is that it is directly measured using a four-terminal sensing measurement (also known as a four-point probe measurement).

Sheet resistance is measured in ohms/square Failed to parse (Missing texvc executable; please see math/README to configure.): (\Omega/\square) , and is applicable to two-dimensional systems where the thin film is considered to be a two dimensional entity. It is equivalent to resistivity as used in three-dimensional systems. When the term sheet resistance is used, the current must be flowing along the plane of the sheet, not perpendicular to it.

In a regular three-dimensional conductor, the resistance can be written as

Failed to parse (Missing texvc executable; please see math/README to configure.): R=\rho\frac{L}{A} = \rho\frac{L}{W t}

where Failed to parse (Missing texvc executable; please see math/README to configure.): \rho

is the resistivity, Failed to parse (Missing texvc executable; please see math/README to configure.): A
is the cross-sectional area and Failed to parse (Missing texvc executable; please see math/README to configure.): L
is the length.  The cross-sectional area can be split into the width Failed to parse (Missing texvc executable; please see math/README to configure.): W
and the sheet thickness Failed to parse (Missing texvc executable; please see math/README to configure.): t

.

By grouping the resistivity with the thickness, the resistance can then be written as

Failed to parse (Missing texvc executable; please see math/README to configure.): R = \frac{\rho}{t} \frac{L}{W} = R_s \frac{L}{W}

Failed to parse (Missing texvc executable; please see math/README to configure.): R_s

is then the sheet resistance. Because it is multiplied by a dimensionless quantity, the units are ohms. The term ohms/square is used because it gives the resistance in ohms of current passing from one side of a square region to the opposite side, regardless of the size of the square. For a square, Failed to parse (Missing texvc executable; please see math/README to configure.): L = W

. Therefore, Failed to parse (Missing texvc executable; please see math/README to configure.): R = R_s

for any size square.

References

General references

• Van Zant, Peter (2000). Microchip Fabrication. New York: McGraw-Hill, 431-2. ISBN 0-07-135636-3. 

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