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How can I calculate the sheet resistance of a thin film? I have two thin films of 30 and 50 nm, why is the sheet resistance of the 30 nm film is higher than that of 50 nm?

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  • $\begingroup$ The sheet resistance is parallel to the plane so although thick films tend to have a lower SR this is due to compactness of the material. There is not geometrical reason but rather a " different material". In principle thickness and SR are unrelated. What you observe is anyway common for the above reason. Refer to Wikipedia entry Sheet Resistance, it should be enough. $\endgroup$
    – Alchimista
    Commented Feb 13, 2020 at 9:41

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Sheet resistance is inversely proportional to the thickness of a film. Your 30 nm film should have about 5/3 higher sheet resistance than your 50 nm film. With films this thin there may be additional effects that would cause the 30 nm film sheet resistance to be even higher.

The concept of sheet resistance is a convenient way to specify thin films in a semiconductor process (or any process using thin films on an insulating substrate such as PCB or ceramic packages). Layers in the process are designed with a specified thickness that cannot be changed by a device or circuit designer (they are only changed by the semiconductor fab engineers and are eventually "fixed"). The units of sheet resistance, Rs, are ohms/square. Square what?... you may ask. The number of squares is the length to width ratio of the pattern drawn on top of the wafer. So the resistance of any square no matter how large or small is simply $ R_s $. If the pattern has 2 squares end to end then it's 2 squares in series or 2$ R_s $ etc. The choice of the number of square and, in fact, the length and width of the patterned thin film are available to the circuit designer.

If you look at a slab of thin film material of length L, width W and thickness t, then the resistance from end to end is given by the familiar formula

$$ \begin{equation} R = \frac {\rho L}{W t} \end{equation} $$

The two parameters in this equation that are fixed are the resistivity, $ \rho $, and the thickness, t, and so we group them together in a single parameter $ R_s $ such that:

$$ \begin{equation} R_s = \frac {\rho}{t} \implies R = R_s \frac{L}{W} \end{equation} $$

Semiconductor layers also have a well defined sheet resistance even if they may not have a well defined resistivity (the resistivity may be variable with depth in the film). Contactless eddy current probes and 4 point contact probes are used to measure sheet resistance directly. The caveat is that the layer under study should be the only conducting layer on the otherwise insulating substrate.

Sheet resistance is one of the most important concepts for a semiconductor engineer to understand. In meetings in research and industry the question "What is the sheet resistance of this layer?" is one of the most frequently asked questions.

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