Help with My Finch House Please

I would like to make a bird house for finches. I am going to make a basic 6"x6" wooden house with one swing-open wall for cleaning, 1 1/2" entrance hole 4 1/2" up from the bottom of the house and an a-frame roof. It would like to nail it to a tree trunk. My question is how much eave do you need on the roof to deter treerats from sitting on top and sticking their scrawning paws into the entrance hole or do you think the treerats will just hang from the roof if there is an eave? There will be no tree branches near it so the treerats would definitely have to jump to the roof. Thanks muchly.