Negative Hall coefficient of ultrathin niobium in Si/Nb/Si trilayers

Structural and transport properties of thin Nb layers in Si/Nb/Si trilayers with Nb layer thickness $d$ from 1.1 nm to 50 nm have been studied. With decreasing thickness, the structure of the Nb layer changes from polycrystalline to amorphous at $d\simeq 3.3$ nm, while the superconducting temperature $T_c$ monotonically decreases. The Hall coefficient varies with $d$ systematically but changes sign into negative in ultrathin films with $d<1.6$ nm. The influence of boundary scattering on the relaxation rate of carriers, and band broadening in the amorphous films, may contribute to this effect.

Figure 1

X-ray diffraction spectra for the $\mathrm{Si}/\mathrm{Nb}\left(d\right)$/Si trilayers with different thickness $d$ indicated in the figure. The consecutive curves are shifted vertically for clarity.

Figure 2

HRTEM images for $\mathrm{Si}/\mathrm{Nb}\left(d\right)$/Si trilayers, with $d$ equal to 11.3 nm (a), 3.3 nm (b), and 1.2 nm (c). The layers in images are (from the top) amorphous Si, niobium, and amorphous Si. The inset at the bottom shows the enlarged Fourier-filtered part of image (a) indicated by the white square.

Figure 3

$R_{sq}$ (a), $T_c$ (b), and $R_H$ at $T=60$ K (c) vs film thickness $d$. In (a) the continuous line shows the fitted dependence $R_{sq}\sim d^{-2}$, and the hatched area indicates the transition region between the polycrystalline and amorphous films. In (b) and (c) the dashed lines are guides to the eye.

Figure 4

Hall resistance $R_{xy}$ versus $B$ at different temperatures for samples with $d=3.9$ nm (a), $d=2$ nm (b), and $d=1.3$ nm (c).

Figure 5

$\Delta R_H/R_H^{300}$ versus $T$ for trilayers with different $d$. The data for $d=1.3$ nm are multiplied by 0.5.

Figure 6

The ratio $T_c/T_{c0}$ versus normal-state sheet resistance $R_{sq}$ for Si/Nb/Si trilayers with different $d$ (full magenta squares) and for several different sets of Nb films prepared by other methods, Ref. [12] (open black squares), Ref. [11] (open blue triangles), Ref. [7] (open green diamonds), and Ref. [8] (full cyan triangle). The dashed magenta line is a guide to the eye. The predictions of the Finkel'stein model are shown by continuous lines, for $\gamma =9$ (black) and $\gamma =15$ (blue).