LabAdviser/314/Microscopy 314-307/SEM/Nova/Micro 4-point probe: Difference between revisions
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[[image:Module schematics.PNG|800x800px|center|thumb|Figure 4: module schematics of the SEM Module system with all its components.]] | [[image:Module schematics.PNG|800x800px|center|thumb|Figure 4: module schematics of the SEM Module system with all its components.]] | ||
The electrical resistivity of metallic bulk and thin-�lm samples is usually | |||
measured by the 4-point probe technique. The classic arrangement, visible | |||
in Fig. 2.15, consists of four needle-like electrodes in a linear arrangement, | |||
with a current injected into the material via the outer two electrodes, while | |||
the resulting di�erence in electric potential is measured via the two inner | |||
electrodes. | |||
By using separate electrodes for the current injection and for the determination | |||
of the electric potential, the contact resistance between the metal | |||
electrodes and the material does not show up in the measured results. Since | |||
the contact resistance can be large and can strongly depend on the condition | |||
and materials of the electrodes, it is easier to interpret the data measured | |||
by the 4-point probe technique than from a 2-point probe system. | |||
If the sample has a �nite size and if the spacing between the probes is | |||
s1= s2 = s3 = s, the resistivity is given by: | |||
� = 2a�s | |||
V | |||
I | |||
where a is the thickness correction factor for thicknesses t equal to or less | |||
than half the probe spacing (t=s < 0:5): | |||
Substituting Eq. 2.9 in Eq. 2.8 we get: | |||
If both sides of Eq. 2.10 are divided by t we get: | |||
which we refer to as sheet resistance. When the thickness t is very small | |||
respect to the spacing s, Rs is the preferred measurement quantity, being | |||
independent of any geometrical dimension and therefore a function of the | |||
material alone. | |||
In this thesis, a variation of the classic 4-point probe method was used, | |||
called micro 4-point probe (�4PP) [17]. This because the electrodes of the 4- | |||
point probe can easily scratch a metallic �lm with thickness in the nm range, | |||
thus reaching the substrate and giving inaccurate electrical measurements | |||
as result. Fig. 2.16a shows a �4PP probe chip. Visible are the ceramic | |||
substrate, the Ag/Pd connector strips and the Si base from which the four | |||
cantilevers extend. For the movements, the probe chip is connected to a | |||
micromanipulator inside a SEM. Aided by SEM imaging, the probe gently | |||
touches the thin-�lm surface in 2-point probe mode without scratching it, | |||
followed by the collection of the data in 4-point probe mode (Fig. 2.16b). | |||