Right side
矣 supplies the sound (yǐ → āi, an initial-vowel shift) — pure phonetic role, since
矣 itself is just a classical sentence-ending particle with no concrete meaning. Same phonetic in
唉 (āi, sigh) and
挨 (āi, suffer). Today
埃 is mostly seen in
尘埃 (dust) and
埃及 (Egypt, transliteration).