Field-enhanced direct tunneling in ultrathin atomic-layer-deposition-grown ${\mathrm{Au}-\mathrm{Al}}_2{\mathrm{O}}_3$-Cr metal-insulator-metal structures

Metal-insulator-metal structures based on ultrathin high-$k$ dielectric films are underpinning a rapidly increasing number of devices and applications. Here, we report detailed electrical characterizations of asymmetric metal-insulator-metal devices featuring atomic layer deposited 2-nm-thick ${\mathrm{Al}}_2{\mathrm{O}}_3$ films. We find a high consistency in the current density as a function of applied electric field between devices with very different surface areas and significant asymmetries in the $\mathit{IV}$ characteristics. We show by TEM that the thickness of the dielectric film and the quality of the metal-insulator interfaces are highly uniform and of high quality, respectively. In addition, we develop a model which accounts for the field enhancement due to the small sharp features on the electrode surface and show that this can very accurately describe the observed asymmetry in the current-voltage characteristic, which cannot be explained by the difference in work function alone.

Figure 1

(a) Schematic of the cross section of a typical MIM structure. (b) SEM image of the 40 $\mu \mathrm{m}$ device, highlighting the measured radii of the bottom (blue) and top (green) electrodes.

Figure 2

Current density ($J$) versus electric field ($E$) curves for devices ${\mathrm{D}}_1$ (40 $\mu \mathrm{m}$ diameter) and ${\mathrm{D}}_2$ (80 $\mu \mathrm{m}$ diameter) at room temperature. The inset shows the $\mathit{IV}$ characteristics of the same devices between $-0.6$ V and 0.6 V.

Figure 3

Large area TEM image showing all compounds of the MIM structure. The uniformity of the ${\mathrm{Al}}_2{\mathrm{O}}_3$ layer and its amorphous structure are clearly visible.

Figure 4

STEM image and corresponding EDX data showing strong and clear signals for Au shown in red, Cr in green, and Al in blue. The oxygen signal is more noisy and is shown in turquoise. The material interfaces appear to be very sharp.

Figure 5

(a) Flat and (b) rough regions highlighted from Fig. 3. The contrast in (b) was enhanced to distinguish the ${\mathrm{Al}}_2{\mathrm{O}}_3$ region shaded by the Cr more clearly. (c) and (d) Energy band diagrams corresponding to the situations shown in panels (a) and (b) with a uniform and distorted potential barrier, respectively. The metal work functions are denoted by ${\mathrm{\Phi }}_{\mathrm{Au},\mathrm{Cr}}$, the insulator electron affinity by ${\chi }_I$, and $U\left(x\right)$ is the potential energy in the insulator.

Figure 6

(a) Geometrical model used to represent a typical peak on the bottom electrode, with the apex radius $r$ (red), the inclination angle of the surface $\theta$ (blue), and the axis of rotational symmetry highlighted (green dashed line). (b) Potential profiles obtained for $r=0.2$ nm as a function of the inclination angle (solid lines). Least-square fits of Eq. (1) to the potentials obtained from finite element modeling are shown as open symbols. (c) Plot showing the voltage dependence of the potential barrier using Eq. (4) and $n=0.63$, which corresponds to $r=0.2$ nm and $\theta ={40}^{\circ }$, in Eq. (1). The dashed lines represent a uniform barrier with the same material parameters. The material parameter ${\chi }_I=1.66$ eV is taken from the fitting results (see below).

Figure 7

Fitting results of the mixed barrier model described by Eq. (7) (solid orange line) and the uniform barrier model where $A_d=0$ in Eq. (7) (dashed blue line), to the experimental data for device $D_1$ (open circles). The inset shows the two contributions to the total current.

Figure 8

(a) Parameter $n$ from Eq. (1) as a function of $r$ and $\theta$ obtained by fitting Eq. (1) to the data obtained via finite element modeling. The dot-dashed lines indicate the projections of the corresponding dotted lines onto the $r-\theta$ plane for selected values of $n$. (b) The same data as in panel (a), but showing $\theta$ as a function of $r$ for a range of fixed $n$ values.

Figure 9

Schematic representations of structures that represent areas that have a higher net field enhancement near the bottom compared to the bottom electrode. The area $A_e$ from Eq. (10) is highlighted in red. The uniform and conformal nature of the deposited film and the roughness smoothing effect are represented but not to scale. (a) Wavelike structure characterized by large values of $n$ with little to no net field enhancement near the bottom electrode. No roughness smoothing occurs in this idealized case. (b) Subnanoscale asymmetric roughness over a large area that, as a result of the density of the sharp peaks, is characterized by a large value of $n$. This is a direct consequence of the roughness smoothing effect [18, 34]. (c) Isolated sharp peak structures characterized by small values of $n$ and small area $A_e$. The roughness smoothing effect occurs at the base of sharp peaks. (d) An isolated, relatively blunt peak with a large area $A_e$ and small value of $n$.