Problems for Chapter 2 (15 points) 1. (15 points) i) If the energy dispersion of electrons in a crystal is given by E(k) = En _ Ew cos( ka) 2 2 show that the electron group velocity, vg, is proportional to the wavenumber, k, just like a free particle with an effective mass 2 2 Ewa ii) What is Ew? Based on the tight binding model or the Kronig-Penney model, please discuss the relation between the bandgap and Ew. iii) Discuss the trend of electron effective masses in GaAs, InP, InAs, and InSb and their bandgaps. Can you explain this trend qualitatively? Semiconductors Effective masses (mo) Bandgaps (eV) GaAs 0.067 1.424 InP 0.077 1.344 InAs 0.022 0.354 InSb 0.015 0.18