Using phonemes to discern the meaning of a written word makes sense in english where written words are just standins for the spoken words. Letters mean nothing by themselves.
In mandarin, the characters can all be broken down into discrete units of meaning, so it makes far more sense to start with morphemes found within the characters. The website Chineasy attempts to breaks down complex characters into their smallest morphemes, what they call “building blocks”. I think the smallest units might be defined at a lower level of abstraction, than Chineasy thinks, but they are still there in the written words.