One can compute the energy required to let electrons escape, and its the same as the work function phi. Here, heat provides the energy. I guess the answer is sort of both. Or maybe it's neither. But this wasn't yet really in conflict with a wave picture of light.
Waves spread out, like ripples in a pond.
Photons are small, so small they can apparently be absorbed by single electrons. It's an odd mish-mash. Here, we need two different theories to explain light. Let's look at some more experiments that demonstrated the existence of photons - particles of light. We've just seen how photons can transfer energy to electrons.