Generalized quantum limits of electrical contact resistance and thermal boundary resistance

Abstract

The importance of electrical contact resistance and thermal boundary resistance has increased dramatically as devices are scaled to atomic limits. The use of a rich range of materials with various bandstructures (e.g. parabolic, conical), and in geometries exploiting various dimensionalities (e.g. 1D wires, 2D sheets, and 3D bulk) will increase in the future. Here we derive a single general expression for the quantum limit of electrical contact resistivity for various bandstructures and all dimensions. A corresponding result for the quantum limit of thermal boundary resistance is also derived. These results will be useful to quantitatively co-design, benchmark, and guide the lowering of electrical and thermal boundary resistances for energy efficient devices.

Figures (2)

• Figure 1: Schematic representation of (a) 1D, (b) 2D, and (c) 3D channels with (d) parabolic with $t=2$ and (e) linear with $t=1$ energy bandstructure which is written as $E(k) = [ \sum_{i=1}^{d} (\alpha_i k_i)^2 ]^{\frac{t}{2}}$, where $\alpha_i = \hbar v_{{\rm F}i}$ for linear and $\alpha_{i} = \hbar / \sqrt{2 m_{i}}$ for parabolic bands. The schematic energy band diagram in (f) indicates the current response $J-V$ curve of (g), and results in the contact resistivity in (h).
• Figure 2: The quantum limit of electrical contact resistance for (a) 1D, (b) 2D, and (c) 3D conducting channels. Each of the three plots compare values at $T=$ 300 K for parabolic bandstructure with $m^{\star}=0.2 m_{\rm e}$ shown as thick solid lines, conical bands with Fermi velocity $v_{\rm F}=10^{8}$ cm/s shown a thin solid gray lines, each with spin degeneracy $g_{\rm s}=2$ and valley degeneracy $g_{\rm v} = 1$. The degenerate limit from Equation \ref{['degenerate_limit']} is shown as the dashed line.