Interdisciplinary research is increasingly recognized as the solution to today's challenging scientific and societal problems, but the relationship between interdisciplinary research and scientific impact is still unclear. This paper studies the relationship between interdisciplinarity and citations at the paper level. Different from previous literature compositing various aspects of interdisciplinarity into a single indicator, this paper uses factor analysis to uncover distinct aspects of interdisciplinarity and investigates their independent dynamics with scientific impact. Three uncovered factors correspond to variety, balance, and disparity. Subsequently, we estimate Poisson models with journal fixed effects and robust standard errors to investigate the relationship between these three factor and citations. We find that the number of citations (1) increase at an increasing rate with variety, (2) decrease with balance, and (3) increase at a decreasing rate with disparity. These findings have important implications for interdisciplinarity research and science policy.