Electrons and Holes in Solid-State Systems: An ECM Interpretation of Dynamic Mass.

May 16, 2025

This work explores the dynamic interplay of electrons and holes in solid-state systems through the framework of Extended Classical Mechanics (ECM), which introduces the concept of negative apparent mass (−Mᵃᵖᵖ) as a counterpart to active motion. Within semiconductors, electrons serve as mobile negative charge carriers, while holes represent the absence of electrons and behave as positively charged quasi-particles. ECM reinterprets this duality by modelling the hole as a virtual kinetic-energy carrier with −Mᵃᵖᵖ, emerging from the motion of electrons. The analogy mₑ − mₑ = −mₕ illustrates this dynamic symmetry: the motion of an electron (mass mₑ) implies a reciprocal emergence of a hole (−mₕ), not as nothingness but as a reactive, directional mass component. This perspective extends naturally to charge flow in piezoelectric systems, where surface-bound electrons and emergent holes interact dynamically with lattice stress and field-induced polarization. Further, the shared characteristics between holes and photons—both arising from electron transitions and both exhibiting negative apparent mass—are examined, suggesting a unified interpretation of energy, charge, and mass duality under ECM. These insights pave the way for a redefinition of current, charge separation, and electromagnetic emission in both classical and quantum regimes.