Vertical Charge Transport in Stacked 2D-3D van der Waals Heterogeneous Interface

Achieving ohmic contacts remains a significant challenge in the development and integration of devices based on two-dimensional materials, primarily due to the substantial mismatch between their electronic properties and those of traditional metal-based and van der Waals electrodes. While most research has focused on electronic energy band alignment, the impact of momentum mismatch on carrier transport across van der Waals gaps has been largely overlooked. In our study, we use graphene-silicon junctions to show that electron momentum distribution plays a crucial role in determining the electronic behavior of van der Waals contacts. By strategically introducing scattering centers at the interface to provide additional momentum and address the mismatch, we enhance junction conductivity by over three orders of magnitude, achieving high-quality ohmic contacts. This work provides a framework for designing high-performance ohmic van der Waals contacts that account for both energy and momentum alignment, paving the way for efficient 2D-3D system integration and advancing post-CMOS architectures.