Sheet Resistance

In diffused semiconductor layers, resistivity is a strong function of depth. For circuit design, it is often convenient to work with a parameter called the "sheet resistance" (Rs).

Consider the resistance (R) of the rectangular block of uniformly doped material shown in the figure below.

In this sample the resistance is given by: R = Rho * L / A

where Rho is the resistivity of the sample, and L and A are its length and cross-sectional area, respectively. If W is the width of the sample and t is its thickness (i.e. - A = Wt), then the resistance can be written:

R = (Rho/t) (L/W) = Rs (L/W)

where Rs = Rho/t is the sheet resistance of a layer of this material.

Strictly speaking, the unit for sheet resistance is the ohm (since L/W is unitless). To avoid confusion between R and Rs, however, sheet resistance is specified in unit of "ohms per square." The L/W ratio can be thought of as the number of unit squares (of any size) of material in the resistor.

Figure 2 shows the top and side views of two typical resistors with contacts at each end. The body of each resistor is 7 "squares." If the sheet resistance of these diffused resistors were 50 ohms/square, then the body of each (not including the contacts) would have a resistance of 350 ohms.

Sheet resistance is measured by a 4-point probe. A geometric correction factor (CF) is usually required to convert the voltage/current ratio measured by the 4-point probe into sheet resistance. This correction factor accounts for the sample size, shape and probe spacings. The sheet resistance measure by the probe is given by:

Rs = (V/I) * CF

where V is the measured DC voltage across the two voltage probes and I is the DC current passing through the two current probes. The value of CF for samples of various sizes and shapes can usually be found in a reference book.