Transverse momentum conservation in 3D-2D electron tunneling in a Cr-Cr₂O₃ (3D-2D) system at room temperature

A quantum well (QW) is an essential component in many electronic and optical devices. For a QW to function as designed, it is typically presumed that the QW layer needs to be made as atomically flat as possible, which usually requires sophisticated techniques such as molecular beam epitaxy (MBE) to grow a thin pristine layer. Here we present a study in which a thin Cr₂O₃ layer (1.5 nm – 2.0 nm) was investigated as a QW, where the Cr₂O₃ layer was formed by a common electron beam deposition of metal Cr and its spontaneous oxidation. We investigated electron tunneling from a bulk Cr (3D) to the Cr₂O₃ QW layer (2D) using a device comprising Cr (source), Cr₂O₃ (QW), SiO₂ (tunneling barrier), and Si (drain). From current-voltage (I-V) measurements at room temperature, we find that the electron tunneling from the Cr to the Cr₂O₃ layer (3D-2D tunneling) faithfully follows both energy and transverse momentum conservation rules, indicating that the obtained Cr₂O₃ layer provides the functionality of an ideal atomically flat QW. We find that the electron tunneling is blocked below a critical voltage V_crit (~2.0 V) as there is no available tunneling path that satisfies the transverse momentum conservation. The 3D-2D tunneling was also numerically investigated by solving Poisson equation and Schrödinger equation, whose outcomes well agree with the experimental findings.