You can explain the photoelectric effect with classical light (i.e. as EM waves) as long as you properly quantize the atomic energy levels. This is often called

You can explain the photoelectric effect with classical light (i.e. as EM waves) as long as you properly quantize the atomic energy levels. This is often called s semi-classical model. However, photo-detections with sub-poissonian statistics cannot be explained under this semi-classical model, but it can be explained with properly quantized EM field (i.e. with photons). For reference, see Mandel and Wolf's Quantum Optics textbook.