For a diffused layer that forms a pn junction, an average
sheet resistance R_{S} is defined and related to the junction depth x_{j},
the carrier mobility m and
the impurity distribution C(x)by the following description.

_{}

(Units of m are cm^{2}/V.s)

The sheet resistance, R_{s}, of a diffused layer
is the resistance exhibited in a square of diffused material, which has a
thickness of x_{j}(junction depth).

**The average
resistivity of the diffused layer is given by: **

** **

**r**** = R _{S}x_{j}**

** **

Let us first consider the resistance *R* of the rectangular block of uniformly doped material in figure
below.[1]

*R* is given by

**R = ****r****(L/A)**

** **

Where r is the material's resistivity, and L and A represent the
length and cross-sectional area of the block, respectively.

Using *W *as the
width of the sample and *t* as the
thickness of the sample, the resistance may be rewritten as

**R= (****r****/t)(L/W) = R _{S}(L/W)**

Where **R _{S}
= **

·
Given
the sheet resistance R_{S}, a circuit designer need specify only the
length and width of the resistor to define its value.

·
Strictly
speaking, the unit of sheet resistance is the ohm, since the ratio *L/W* is unitless.

* *

·
To
avoid confusion between R and R_{S}, *sheet resistance is given special
descriptive unit of ohms per square.*

* *

·
The
ratio *L/W* can be interpreted as the
number of unit squares of material in the resistor.

Figure below shows top and side views of two typical
dumbbell-shaped resistors with top contact at the ends. The body of each
resistor is seven "squares" long. If the sheet resistance of the
diffusion were 40 ohms per square, each resistor would have a resistance of 280
ohms.

Using

_{}

And r=R_{S}x_{j} design
curves relating to the surface concentration and the average conductivity have
been calculated for simple diffusion profiles, such as exponential, Gaussian or
erfc distributions.

·
Because
both the junction-depth and the sheet-resistance measurements are simple and
give important information about a diffused layer without elaborate profile
measurements. They are routinely used for monitoring diffusion processes.

·
For
ion-implanted samples, sheet-resistance measurement is a simple method used to
check the electrical activity (combined effects of mobilities and carrier
concentrations) after the sample is annealed or diffused.