Three-stroke grass radical on top, the indexing radical. 芯 originally named the inner pith of a rush plant — the soft, spongy core used as lampwick. From that came the modern senses of any inner core: a pencil lead, a microchip die, a candle wick.
Bottom 心 supplies the sound — xīn read straight across. The heart imagery doubles as a near-perfect semantic match: the core of a plant is the plant's heart, just as 心 is the heart of a person. Phonetic and meaning reinforce each other.