The compound "染上" is formed through the combination of the verb "染" (rǎn), meaning "to dye," "to catch," or "to acquire," with the directional/resultative complement "上" (shàng), which here indicates a successful attachment or the attainment of a state. Morphologically, it follows a standard verb-complement structure where "上" emphasizes the result of the action "染"—specifically, the idea of something (typically negative, like a habit or illness) taking hold or adhering to a person. Thus, the term semantically evolves from the literal sense of "dye onto" to the metaphorical meaning of "to contract" or "to pick up," as in contracting a disease (染上疾病) or acquiring a bad habit (染上恶习).