LabAdviser/314/Microscopy 314-307/SEM/Nova/Micro 4-point probe: Difference between revisions
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= | = 4-point probe theory = | ||
The electrical resistivity of metallic bulk and thin-film samples is usually measured by the 4-point probe technique. The classic arrangement, visible in Fig. 1, 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 difference in electric potential is measured via the two inner electrodes. | The electrical resistivity of metallic bulk and thin-film samples is usually measured by the 4-point probe technique. The classic arrangement, visible in Fig. 1, 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 difference in electric potential is measured via the two inner electrodes. | ||
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s1= s2 = s3 = s, the resistivity is given by: | s1= s2 = s3 = s, the resistivity is given by: | ||
ρ = 2aπsV/I | ρ = 2aπsV/I Eq.1 | ||
where a is the thickness correction factor for thicknesses t equal to or less than half the probe spacing (t/s < 0.5): | where a is the thickness correction factor for thicknesses t equal to or less than half the probe spacing (t/s < 0.5): | ||
a = 0.72t/s | a = 0.72t/s Eq.2 | ||
Substituting Eq. 2 | Substituting Eq. 2 in Eq. 1 we get: | ||
ρ = 2aπsV/I = 4.53V/I Eq.3 | |||
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 ( | If both sides of Eq. 3 are divided by t we get: | ||
Rs = ρ/t = 4.53V/I | |||
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. | |||
== Micro 4-point probe == | |||
In this thesis, a variation of the classic 4-point probe method was used, called micro 4-point probe (μ4PP). This because the electrodes of the 4-point probe can easily scratch a metallic film with thickness in the nm range, thus reaching the substrate and giving inaccurate electrical measurements as result. Fig. 2a shows a μ4PP 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-film surface in 2-point probe mode without scratching it, followed by the collection of the data in 4-point probe mode (Fig. 2b). | |||
= Kleindiek micromanipulator = | = Kleindiek micromanipulator = | ||