Ideal Thickness in 2D van der Waals Multilayers with Vertical Double Side Contacts

Two-dimensional (2D) van der Waals (vdW) materials inherently possess interlayer resistance between adjacent layers, significantly influencing their carrier distribution across the material's thickness, particularly in relation to the positioning of metal electrodes. Herein, by taking into account the Thomas-Fermi charge screening theory and a resistive network model, we systematically explore the thickness-dependent effective carrier density profile for bottom contact, top contact, and vertical double-sided contact (VDC), where the top and bottom contact electrodes are connected. VDC provides the least resistive conducting paths for carriers within 2D vdW multilayers by suppressing interlayer resistance effects, resulting in a spatial redistribution of carrier density along the thickness under varying electrostatic vertical and lateral bias conditions and consequently establishing separate bottom and top channels. The highest effective mobility, particularly for VDC, is observed at approximately 10 nm, highlighting the increasingly pivotal role of the bottom channel in the high electron accumulation regime as the thickness increases. To validate our computational results, numerous back-gated n-type WSe₂ transistors with thicknesses ranging from 4 to 244 nm were fabricated. Superior electrical properties, including carrier mobility, conductivity, and a high on/off current ratio, were observed at thicknesses of 8 to 10 nm, in excellent agreement with our numerical calculations. Our findings offer valuable insights for advancing next-generation electronic transistors based on 2D vdW multilayers.