I am little confused between the built in potential that is built up in the diode depletion region and the barrier voltage that needs to be applied across the PN junction to start conducting. My thoughts say that barrier potential must overcome the built in potential for the diode to start conducting through depletion region but I am not sure if am all correct. If that is the case, does barrier voltage equal or little greater than the built in voltage of diode?
I think, there is a small confusion on your side regarding the meaning of "barrier voltage".
Caused by a diffusion process across the pn-junction there is a "barrier" consisting of a potential difference (called voltage). This "built-in voltage" causes the diffusion to stop at a certain equlibrium. Hence, "barrier voltage" and "built-in voltage" are two different expressions for the same quantity.
For a current to exist through the device there must be an external voltage which is able to reduce this barrier. Thus, this voltage further supports the diffusion process and allows a exponentially rising current. This effect is visible already at an external forward voltage of app. 0.1 Volt).