Toward a Concept Inventory for Energy Band Theory: Insights from Textbooks and Graduate Exam Syllabi

Energy band theory is a central topic in upper-division solid state physics and plays a foundational role in semiconductors and material science research.However, no validated concept inventory is currently available to measure students' conceptual understandings of this topic.As an initial step toward assessment development, this study reports a content analysis of four widely used textbooks-two in English and two in Chinese-aimed at identifying core concepts in energy band theory across different sources.Results revealed five key concept categories, common across all texts, including foundational approximations, Bloch's theorem, the nearly free electron model, the tight-binding model, and symmetry operators.We validated these concept categories by comparing them against graduate entrance exam syllabi from three major Chinese universities.The convergence between textbook content and national curricular expectations supports these five concept categories as the focus for assessment.This work lays the foundation for future development of a research-based concept inventory, capable of supporting instruction and learning in upper-level solid state physics.