Fig. 20

The schematic of the RRAM device with a narrow CF and the corresponding energy band diagram of the quantum point contact model. a Schematic structure of the RRAM device with a narrow CF. b The dispersion curves of the first four electronic subbands under the confinement of CF in certain z. c The dependence of the energy level of the bottom of the subbands on z. The transmission probability T(E) of the bottom of ground quantized subband of a parabolic potential barrier is used for the calculation of electrical transport. The shaded regions are the states occupied by electrons. The number of the subbands is N _ch, with each one contributing to a conducting mode. In this figure, four subbands are shown. V is the applied voltage. V ₀ is the voltage dropped on TE and BE, represented by the two blue oblique lines. Since V ₀ is much lower than V, usually it can be neglected in the calculation. β is the fraction of voltage that drops at the BE interface, E _F is the Fermi level, E _F,TE and E _F,BE are the TE and BE quasi-Fermi levels, t _B is the width of the potential barrier at the equilibrium Fermi energy (E = 0), and Φ _B is the height of the potential barrier, i.e., the bottom of the first subband. The barrier height is different between high resistance state and low resistance state, which leads to different current expressions. In the deep OFF-state, the barrier thickness t _B is equal to the gap length t _gap