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

10. primative reciprocal lattice basis vector respectively.
and .

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

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

16. In the coordinate system in which the effective mass tensor is diagonal

17. Acceleration due to an electric filed (F)

18. Effective mass tensor – valid near E(k) minima and maxima only

19. Constant energy surfaces in crystal momentum space cookies

21. Constant energy surfaces near a minimum are ellipsoids

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

23. Acceleration of an electron near an energy minimum in silicon

24. Electron transport effective mass in silicon and germanium

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

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

27. Cyclotron resonance effective mass

28. Cyclotron resonance effective mass –to be shown in the tutorial

29. Cyclotron resonance effective mass –to be shown in the tutorial

30. Density of states effective mass

31. Density of states

32. Example: density of states of hydrogen gas

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

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

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

36. Approximation for the Fermi Dirac distribution for E-Ef>3KT

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

38. Density of states of solids in K space

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

40. Constant energy surfaces in crystal momentum space cookies

41. Volume of an ellipsoid

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

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

44. Conduction band density of states effective mass

45. Valence band density of states effective mass

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

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