|
|
| Line 57: |
Line 57: |
|
| |
|
| [[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.]] |
|
| |
| = Micro 4-point probe =
| |
|
| |
| 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. 5, 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.
| |
|
| |
| 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 finite 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).
| |
