Putting your phone on silent kills the sound, but the screen can still light up, and the phone is still within reach. Research shows that just having a phone in view measurably reduces attention, even if it's never touched.
That's because the brain tags the phone as a potential source of something, which keeps a small slice of attention occupied in the background.
Instead of silent mode, putting the phone in another room or a drawer entirely works far better. Once it's out of view, that small slice of attention actually gets freed up.