We propose a new quantum cross structure (QCS) device as a candidate beyond CMOS. The QCS consists of two metal nano-ribbons having edge-to-edge configuration like crossed fins.The QCS has potential application in both switching devices and high-density memories by sandwiching a few molecules and atoms. The QCS can also have electrodes with different dimensional electron systems because we can change the widths, the lengths, and the heights of two metal nano-ribbons, respectively. Changing the dimensions of electron systems in both electrodes, we have calculated the current-voltage characteristics depending on the coupling constants between a molecule and the electrode. We find that the conductance peak is much sharper in case of weak coupling regardless of dimensions of electron systems in electrodes, compared to strong coupling case. We also find that the conductance peak of QCS having electrodes with two-dimensional electron systems (2DES) is much sharper than that of QCS having electrodes with three-dimensional electron systems (3DES) in case of strong coupling because of quantum size effect of 2DES. These results imply that the QCS with the very sharp conductance peak can serve as the devices to switch on and off by very small voltage change.