Lightsail

OK, here is my attempt to revive things.
I recently did a simple calculation concerning lightsails and how fast
they could go. I used a graphene film coated with 100 nm of Au as my
sail. I was surprised that no matter how big you make the lightsail,
it cannot exceed solar escape speed using only solar photons. Of
course, the closer you start to the sun the faster you can go but
still cannot exceed suns escape velocity.
I do not have that calc in front of me now but does this seem right to
others? My conclusion is that your lightsail has to be initially
accelerated to escape speed before deploying