To explore the scope of applying single level tunneling models, we first studied I-V characteristics under different coupling and energy offset conditions (figure ) using the three methods, as summarized in figure . We can see the I-V characteristics by the three modeling methods are significantly dependent on coupling and energy offset. First, when coupling is relatively strong, ~100meV, Eq 1 and Eq 2 agree with each other very well, while Eq 3 does not work for small energy offset as low as 0.1 eV. When barrier increases to 0.5 eV, Eq 3 gradually conform and works only under low bias i.e. far from resonance. As the energy offset increase to 1 eV, Eq 3 fully worked at this energy offset at all provided bias range (Figure ). Clearly, the working bias range of Eq 3 depends on the barrier height, the larger energy offset is, the larger bias range that Eq 3 can works. When coupling strength decrease to 10 meV and 5 meV (mild coupling strength, Figure D-F and G-I), Eq 2 starts to deviate from Eq 1. This is because the broadening of Fermi distribution under room temperature (~25 meV) become comparable to the coupling strength, so that the step function condition for Eq 2 will incur more and more error. Eq 3 failed to work again at low barrier and partially work at the mild barrier height (0.5 eV). At a very weak coupling strength (1 meV), again Eq 1 can reasonably describes the tunneling process while Eq 2 and Eq 3 continue to work effectively at high barrier. In this situation, the Fermi distribution cannot be reduced to a step function as the precondition for Eq 2. Therefore, neither the conditions of Eq 2 nor Eq 3 can be satisfied (as seen in figure J and K). On contrary, the validity of these two analytical expressions at high barrier is contingent to a very small integration step size (≤ 0.2 𝑚𝑒𝑉) of Eq 1 that should be smaller than the width of the transmission peak (figure ).