Key Points
- Solution for electron in a crystal is done using a
periodic set of wells.
- Periodic solution has the form (Bloch) of a free
electron modified by a periodic solution to Sch. Eq.
- This gives rise to a periodic momentum space
description and we only need to use a small finite region of "k" space
-- brillioun zone.
- Periodic "free electrons" give a continuous
multi-valued parabolic E(k) relationship.
- Presence of a periodic barrier forces a decaying
solution between wells which brings about the presence of a band gap.
Questions
- How do we represent an
electron in a crystal?
- Draw the e(k) relationship
for a periodic "free electron"
- How does the presence of a
periodic barrier effect the solution?