"tangle of branches" is correct and usable in written English.
You can use it when you need to describe a large cluster of branches, often formed as a result of overgrowth or a storm. For example, "The tree had been knocked over by a gust of wind, leaving behind an impenetrable tangle of branches."
I'm putting the finishing touches to a tangle of branches and leaves jammed between two rocks.
I pushed through the tangle of branches and got inside the clump of low trees.
By the time they were done, the land was a tangle of branches and dead leaves.
But close up, it is a tangle of branches and leaves, nooks and crannies, teeming with habitats for the menagerie of animals calling it home.
We've come up a peaty path winding past oaks, birches and sycamores, though these are sparse and a tangle of branches lie on the ground.
The first speckled egg in the nest was spotted on March 6 by the New York University president, John Sexton, upon whose 12th-floor window ledge the hawks have built their nest, a two-foot-wide tangle of branches.
I began to crawl, dragging my purse, but my heel got caught in a tangle of branch and suddenly I was thrashing about with prickles clutching me like the ghostly fingers of the other children she'd caught.
Architects may also like tree metaphors because a tree's overall structure is regular, while its fine-grained composition, its tangles of branches, are irregular, an arrangement conducive to the kind of design experimentation offered by new digital technologies.
AFTER 10 minutes, though, we were back in wild and magical Kauai, veering onto a narrow fork with a tangle of hau branches crisscrossing overhead.
How the snow creaked underfoot on a very cold clear day, how the low white sun looked through a tangle of black branches.
The 30-year-old cedars and junipers on my new property have a huge tangle of dead branches below the healthy live ones.
