How To Measure Sheet Resistance of Silicon Substrate？
Sheet resistance refers to the resistance per unit area of a thin film, equal to the resistivity divided by the thickness, measured in Ω/□. Sheet resistance has a characteristic that the resistance from edge to edge of any size square is the same, regardless of whether the side length is 1m or 1mm.
1. When to Use Sheet Resistance for Silicon Wafer?
The concept of sheet resistance is mainly proposed for thin films, which makes the electrical design of MEMS devices more convenient. It is like a square block building block. Once we know the sheet resistance value, as long as count the number of blocks (the length of the resistance divided by the width), it is easy to calculate the total resistance. So, the introduction of blocks and sheet resistance greatly facilitates communication between design and manufacturing personnel. For polycrystalline silicon or implanted monocrystalline silicon, it is not necessary to know the implantation depth (junction depth) that circuit design can be easily completed once know the sheet resistance value.
2. How to Measure the Sheet Resistance of Silicon?
The four probe method is a commonly used method for testing the resistivity and sheet resistance of semiconductor materials. Its basic principle is to place four probes on the sample, and by measuring the current and voltage relationship between the probes, the resistivity and sheet resistance parameters of the sample can be calculated. The four probe method is commonly used to measure the sheet resistance of thin layer materials because it can eliminate the influence of contact resistance and has high measurement accuracy.
Fig. 1 Resistivity measured by four probe method
Four probes with a spacing of s; apply appropriate pressure to the probes and place them vertically on the silicon wafer to form an ohmic contact; Apply current I14 between two outer probes (1,4) to form a test circuit; Two intermediate probes (2, 3) are connected to a high impedance precision voltmeter, and the potential difference V23 is measured; The formula for calculating sheet resistance is:
R=（π/In2) * V23/I14
From the formula, the four probe method is independent of the thickness and shape of the thin film, making it convenient for testing and reading. There is no need to measure the film thickness or junction depth thickness to infer the resistivity.
If the resistivity of silicon wafers with a thickness greater than 0.1mm and a diameter of 2 inches or more needs to be measured, the calculation formula is:
ρ=2πs*V23/I14
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