Abstract: As a core concept in semiconductor physics, density of states (DOS) serves as the theoretical foundation for understanding carrier statistics, transport phenomena, and device performance. In order to address three key teaching challenges (including the abstract nature of k-space, complex mathematical derivations, and variations in material band structures), we propose: (1) a “rooms in building analogy method” to visualize quantum states, (2) “ellipsoidal shell/ellipsoid derivation methods” to reveal the physical essence of DOS formulas while simplifying mathematical processes, and (3) illustrate general DOS calculation strategies for common semiconductors using silicon as an example. The investigation aims to establish a structured pedagogical framework to help students overcome conceptual barriers, thereby laying theoretical groundwork for carrier statistics and device performance analysis.

Key words: semiconductor physics, quantum states, density of states, ellipsoid derivation method, DOS calculation strategy