Quantum limits of ballistic electrical and thermal resistances of semiconductors

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 and 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.