Device Physics

1. Device Physics 박 기 찬

2. Contents - Energy Band - Carrier Action • p-n Junction • Metal-Semiconductor Contact - Metal-Insulator-Semiconductor Capacitor - MOSFET

3. Energy Band - Atomic bonding and energy band • Fermi level and carrier concentration

4. Atomic Bonding and Energy Band

5. Periodic Table of Elements

6. Electronic Energy Levels in Si Atom

7. sp3 Hybridized Atomic Orbitals s orbital px orbital py orbital pz orbital Tetrahedron sp3 hybrid orbital

8. Crystal Structures

9. Energy Band Split

10. Insulator, Semiconductor, Metal Metal Insulator Semiconductor

11. Electron Energy in Solid Insulator, Semiconductor Metal EVAC electron affinity ionization potential work function work function EC EF Eg EV

12. Energy Band and Bond Model T = 0 K T > 0 K For an intrinsic silicon, n = p = ni = 1010 cm-3 @ 300 K

13. Concept of Hole The movement of a valence electron into the “empty state” is equivalent to the movement of the positively charged “empty state” itself. This is equivalent to a positive charge (“hole”) moving in the valence band.

14. Temp. Dependence of Bandgap Energy bandgap decreases as temperature rises.

15. N-Type Doping T = 0 K A substitutional phosphorous atom (donor) with five valence electrons replaces a silicon atom and a negatively charged electron is donated to the lattice in the conduction band. T > 0 K

16. P-Type Doping T = 0 K A boron atom (acceptor) with three valence electrons substitutes for a silicon atom and an additional electron is accepted to form four covalent bonds around the boron leading to the creation of positively charged hole in the T > 0 K valence band.

17. Donor vs. Acceptor

18. Impurity Levels

19. Fermi Level and Carrier Concentration

20. Fermi Level Electrons in solids obey Fermi-Dirac statistics. The distribution of electrons over a range of allowed energy levels at thermal equilibrium is governed by the equation, F(E) gives the probability that an available energy state at E is occupied by an electron at absolute temperature T. k is Boltzmann’s constant ( k = 8.6210-5 eV/K = 1.3810-23 J/K ). EF is called the Fermi level. For an energy state at E equal to the Fermi level EF, the occupation probability is 1/2.

21. Fermi-Dirac Distribution

22. Carrier Concentration Number of electrons in the conduction band is given by the total number of states multiplied by the occupancy , integrated over the conduction band. > 3 , so Boltzmann statistics apply.

23. Distribution of Electrons and Holes

24. Distribution of Electrons and Holes N-type semiconductor P-type semiconductor

25. Fermi Level Position vs. Doping

26. Carrier Concentration Number of electrons in the conduction band is determined by the position of with respect to .

27. Mass Action Law for nondegenerate semiconductor

28. Intrinsic Carrier Concentration ,

29. Temperature Dependence of ni

30. Donor and Acceptor Level

31. Carrier Conc. vs. Temperature for nondegenerate semiconductor

32. Fermi Level Position vs. Temp.

33. Carrier Action - Drift and diffusion • Recombination and generation

34. Drift and Diffusion

35. Drift of Carriers Vth = 107 cm/s @ 300K Typical random behavior of a hole in a semiconductor (a) without an electric field and (b) with an electric field.

36. Drift Velocity Drift velocity of an electron with an applied electric field.

37. Mobility

38. Temperature Effect on Mobility Mobility decreases as temperature rises.

39. Impurity Effect on Mobility

40. Drift Currents Electrons and hole flow in opposite directions when under the influence of an electric field at different velocities. The drift currents associated with the electrons and holes are in the same direction.

41. Resistivity conductivity

42. Resistivity vs. Dopant Concentration

43. Velocity Saturation in High E-field At low electric fields, . The mobility is independent of the electric field. When the fields are sufficiently large, however, nonlinearities in mobility and, in some cases, saturation of drift velocity are observed. → saturation velocity @ RT:

44. Band Bending • Carrier kinetic energies • Electron potential energy P.E. of charge Q = QV (c) Electrostatic potential (Voltage)

45. Diffusion of Carriers

46. Diffusion of Carriers The flow or flux of carriers proportional to the concentration gradient (Fick’s law). is call the diffusion coefficient. This flux of carriers constitutes a diffusion current, The total conduction current is given by the sum of the drift and diffusion current. Einstein relation

47. Constancy of Fermi Level In Equilibrium, there are no external influences such as electric field and temperature gradient. Accordingly electrons are evenly distributed and do not move macroscopically. Their distribution is determined by their energy and described by This indicates that the Fermi level is constant in equilibrium. Wheat does “evenly distributed” mean? In thermal equilibrium, what is even in a system? → Temperature!! Regarding the distribution of electrons, “evenly distributed” means that the probability of electron occupation for every state at the same energy level is constant. E1/4 E1/2 = EF E3/4

48. Einstein Relation These two equations give the relationship and similarly for p-type semiconductor,

49. Diffusion Length

50. Recombination and Generation