Definition

• Sheet resistance
• Refers to the resistance of a semiconductor film or a metal film per unit area
• Sheet resistance is only related to film thickness and material properties

• R-resistance -Ω, ρ- resistivity Ω.cm, L-length -cm, S- area -cm²
• Rs=ρ/d
• Rs-sheet resistance -Ω/sq, ρ- resistivity -Ω.cm, d- thickness -cm

Linear four probe test principle

• Four probes with equal spacing of S
•  
• The probe applies appropriate pressure and falls vertically on the silicon wafer to form ohmic contact
• A current (I) is applied between the two outer probes (1,4) to form a test loop
• Two intermediate probes (2,3) are connected to a high-impedance precision voltmeter and the potential difference V is measured

When the sample diameter is greater than 40s, the thickness is d>5s, the edge effect correction factor and thickness correction factor are both 1, the resistivity calculation formula:

ρ=2πsV/I

For extremely thin samples, the thickness (W) is much smaller than the probe spacing (s) （w/s<0.5), when the horizontal dimension is infinite:

• In the case of equidistant probe test, the probe spacing is independent of the measured result, and the resistivity is proportional to the thickness (W) of the measured sample
• 4.5324 - often referred to as sheet resistance correction factor

Sheet resistance, a thin layer of semiconductor with a square surface, showing resistance in the direction of current

• Rs=ρ/Xj=4.5324V23/I
• Xj，Junction depth

Advantages and disadvantages of linear four probe method:

Advantages:

• The test theory is simple and mature, and it is reliable after practical test.
• The test accuracy is higher than that of other probe methods under the same conditions.
• There are no strict requirements on the size of the test wafer, and it can be used to test wafers with irregular shapes or thicknesses.

disadvantage

• Contact testing, prone to damage or contaminate the wafer under test.
• The test needs to form a stable ohmic contact, and the test time is long, especially when testing multiple points.
• Contact testing requires higher wafer contact surfaces.

Conversion of doping concentration and resistivity

For P-type silicon

• ρ-resistivity，N-Doping concentration

For N-type silicon