The effective mass

# The effective mass

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## The effective mass

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1. The effective mass • Conductivity effective mass – determines mobility. • Density of states effective mass – determines NC • Cyclotron effective mass – can be measured directly

2. Electron in a periodic potential • Why does the semiconductor industry use single crystal material (when possible) ?

3. Electrons are not scattered by a periodic potential – move with a constant velocity as in vacuum !

4. Electron in vacuum

5. Dispersion

6. Electron in vacuum

7. Electron in a periodic potential

8. Electron in a 3D periodic potential

9. Expansion of E(kx,ky,kz) near a minimum value E0= E(kx0,ky0,kz0)

10. Expansion of E(kx,ky,kz) near a minimum value E0= E(kx0,ky0,kz0)

11. Acceleration due to an electric filed (F)

12. Constant energy surfaces in crystal momentum space cookies

13. Constant energy surfaces near a minimum are ellipsoids

14. Constant energy surfaces in Si and Ge near a minimum are ellipsoids of revolution

15. Electron transport effective mass in silicon and germanium

16. Homework competition – find a shorter way to prove this equation for germanium than given in last year’s home exam

17. The spherical case - • Electrons in GaAs • Holes in Si, Ge, GaAs

18. Cyclotron resonance effective mass

19. Density of states effective mass

20. Density of states

21. E g(E) Example: density of states of hydrogen gas

22. E g(E) Density of states of solids

23. E E f g(E) Density of electrons in an energy band

24. E E f g(E) Density of holes in an energy band

25. E E f g(E) Density of electrons in an energy band

26. Density of states of solids in K space

27. The density of states in an energy interval is proportional to the volume in K space between two constant energy surfaces

28. Constant energy surfaces in crystal momentum space cookies

29. Volume of an ellipsoid

30. Volume of a constant energy (E’) ellipsoid

31. Density of states near a conduction band minimum or valence band maximum, and the definition of the density of states effective mass

32. Conduction band density of states effective mass

33. Valence band density of states effective mass

34. Summary • Conductivity effective mass – determines mobility. • Density of states effective mass – determines NC • Cyclotron effective mass – can be measured directly

35. k hh lh E Elective home exercise • Derive conductivity and density of states effective mass for holes.