Current distribution in metallic multilayers from resistance measurements

The in-plane current profile within multilayers of the generic structure Ta/Pt/(CoNi)/Pt/Ta is investigated. A large set of samples where the thickness of each layer was systematically varied was grown, followed by the measurement of the sheet resistance of each sample. The data are analyzed by a series of increasingly elaborate models, from a macroscopic engineering approach to mesoscopic transport theory. Non-negligible variations of the estimated repartition of current between the layers are found. The importance of having additional structural data is highlighted.

Figure 1

Measured sheet conductances (dots) vs thickness of each layer [panels (a)–(e)], followed by the thickness-resolved conductivity plot for the reference sample as derived from the models (f). The fit of each thickness series by a linear law (model 1) is represented by solid lines, whereas the global fit according to Eq. (1) (model 2) is drawn with dashed lines. No structural information is taken into account here, so that the models used are called 1a and 2a. The global rms error is 0.493 mS.sq when fitting each series independently, increasing to 1.621 mS.sq for the global fit. In order to compare the slopes, panels (a)–(e) have the same scales.

Figure 2

Scheme of the sample structure with the various parameters of the Fuchs-Sondheimer model applied to analyze the conductivity data.

Figure 3

Fuchs-Sondheimer fit of all the data, with assumptions described in the text, and without any input from the structural characterization. The resulting rms error is 0.978 mS.sq (model 3a).

Figure 4

High-magnification cross-sectional TEM image of the reference sample.

Figure 5

Fuchs-Sondheimer fit of all the data, taking into account a 2.0-nm oxidized Ta cap thickness. The corresponding rms error is 0.829 mS.sq (model 3b).

Figure 6

Dark-field TEM plane view of the reference sample, obtained by filtering out the (220) diffraction for Pt, Co, and Ni (see diffraction pattern in inset).

Figure 7

Mayadas-Shatzkes fit, with assumptions described in the text, taking into account that 2.0 nm of the Ta cap were oxidized, the grain size varying in proportion to the Pt underlayer thickness (model 4b). The resulting rms error is 0.705 mS.sq. The curve downwards bends at low platinum thickness in panel (b) directly depicts the assumption of model 4; it is absent in the other variant (model 4*, not shown).