It was shown that elastic tunneling through \;a p-n junction in gapped bilayer graphene can lead to oscillatory transmissi on as a function of bandgap [1]\, where a combination of the semiclassical considerations and numerical calculations were used. In this talk\, I wil l first present how we confirm the numerical results of that work analytic ally by using the method of steepest descents\, where we treat the momentu m as time in Schrö\;dinger'\;s equation in momentum space. In the p resence of phonons\, we then use a similar approach and generalize it to t he phonon-assisted tunneling\, I will discuss how the presence of phonons\ , and the associated inelastic processes\, can contribute to the transport across the p-n junction in gapped bilayer graphene. Near zero temperature \, I will show phonon can enhance the transmission when an electron emits or absorb a phonon and jump from one branch point to another\, and the con ductance will behave like a step function in terms of voltage where the co nductance increases with the square root of voltage firstly and eventually becomes constant.

\n\n[1] R. Na
ndkishore and L. Levitov\, Proceedings of the National Academy of Sciences
**108**\, 14021 (2011)