Is the resistivity and square resistance of silicon material the same meaning?

Resistivity is a physical quantity used to express the electrical properties of various substances, and is an intrinsic property of materials. By definition, the resistance of a conductor made of a material with a length of 1 m and a cross-sectional area of 1 m² is numerically equal to the resistivity of the material in Ω・m (Ω・cm, which is commonly used in semiconductors). For semiconductor silicon materials, the resistivity is related to the concentration of electrons and holes inside the silicon, and is not affected by the size and shape of the silicon material. In other words, resistivity reflects the ability of the silicon material itself to block the passage of electric current, and it focuses on the intrinsic electrical properties of the material.

The square resistance, the full name of square resistance, refers to the resistance per unit area of the film, and its value is equal to the resistivity divided by the thickness in Ω/m. Square resistors have the unique property of having the same edge-to-edge resistance for any size of square, regardless of whether the side length is 1m or 1mm. This property gives square resistance a particular advantage in thin-film-related applications.

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In practical application scenarios, the difference between the two is even more significant. For silicon wafers or silicon-on-insulator (SOI), resistivity is often used in the data sheet to characterize its basic electrical parameters. Wafers are generally divided into high-resistance silicon and low-resistance silicon, and the concentration of impurities in high-resistance silicon is very low, usually below 10¹²cm⁻³, which makes the resistivity of high-resistance silicon wafers very high, between 10³ - 10⁶Ω・cm. Because the higher the resistance, the higher the purity requirements for silicon, the manufacturing process of high-resistance silicon is extremely complex, and many nominal high-resistance silicons will have a certain degree of resistivity attenuation after annealing. In such scenarios, the resistivity can intuitively reflect the overall electrical performance of the silicon wafer or SOI, which provides an important basis for subsequent material selection and process design.

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The concept of square resistance was mainly proposed for thin films, and its advent made the electrical design of MEMS devices easier. Imagine that square resistance is like a square block, and when we know the square resistance, we can easily calculate the total resistance by counting the number of squares (the length of the resistance divided by the width). Therefore, the introduction of blocks and square resistors greatly facilitates the communication between design and manufacturing personnel. For polycrystalline silicon or injected monocrystalline silicon, we don't even need to know the injection depth (junction depth) accurately, and we can successfully complete the design of the circuit part just by measuring the square resistance, which greatly improves the design efficiency.
In summary, although the resistivity and square resistance of silicon materials are related to the electrical properties of silicon materials, they have completely different connotations and applications. Resistivity focuses on the intrinsic resistance properties of the material itself, while square resistors focus more on the convenient application of thin-film resistors in practical design and manufacturing. A clear distinction between these two concepts is essential for a better understanding of the electrical properties of silicon materials and their practical applications in the semiconductor field.