Why electric field inside the depletion reigon of a diode not able to push electrons from p to n side under no bias?( There is a small leakage current under reverse bias)

 

Because two effects are in equilibrium. Remember, when you first abut the p-type material to the n-type material there is no electric field because there is not separation of charge. The carriers from both sides diffuse into the other side owing to the density gradient. As electrons move from the n-type to the p-type (and fill "holes") the n-type becomes positively charged and the p-type becomes negatively charged. But now you have a separation of charge resulting in an electric field going from the n-type to the p-type materials. This field wants to pull electrons back from the p-type into the n-type. But, if that happens, then the charge separation is reduced and the electric field is reduced and so the charges want to rediffuse. At some point an equilibrium is reached in which the charge separation from diffusion is just sufficient to create an electric field that prevents further diffusion.