1. ECE 250 – Electronic Devices 1 ECE 250 Electronic Device Modeling

2. ECE 250 – Electronic Devices 2 Introduction to Semiconductor Physics You should really take a semiconductor device physics course. We can only cover a few basic ideas and some simple calculations.

3. ECE 250 – Electronic Devices 3 Electronic Devices Most electronic devices are made out of semiconductors, insulators, and conductors. Semiconductors –Old Days – Germanium (Ge) –Now – Silicon (Si) –Now – Gallium Arsenide (GaAs) used for high speed and optical devices. –New – Silicon Carbide (SiC) – High voltage Schottky diodes.

4. ECE 250 – Electronic Devices 4 Elements Elements in the periodic table are grouped by the number of electrons in their valence shell (most outer shell). –Conductors – Valence shell is mostly empty (1 electron) –Insulators – Valence shell is mostly full –Semiconductors – Valence shell is half full (Or is it half empty?)

5. ECE 250 – Electronic Devices 5 Semiconductors Silicon and Germanium are group 4 elements – they have 4 electrons in their valence shell. Si Valence Electron

6. ECE 250 – Electronic Devices 6 Silicon When two silicon atoms are placed close to one another, the valence electrons are shared between the two atoms, forming a covalent bond. Si Covalent bond Si

7. ECE 250 – Electronic Devices 7 Silicon Si

8. ECE 250 – Electronic Devices 8 Silicon Si An important property of the 5-atom silicon lattice structure is that valence electrons are available on the outer edge of the silicon crystal so that other silicon atoms can be added to form a large single silicon crystal.

9. ECE 250 – Electronic Devices 9 Si

10. ECE 250 – Electronic Devices 10 Si At 0 º K, each electron is in its lowest energy state so each covalent bond position is filled. If a small electric field is applied to the material, no electrons will move because they are bound to their individual atoms. => At 0 º K, silicon is an insulator.

11. ECE 250 – Electronic Devices 11 Silicon As temperature increases, the valence electrons gain thermal energy. If a valence electron gains enough energy, it may break its covalent bond and and move away from its original position. This electron is free to move within the crystal.

12. ECE 250 – Electronic Devices 12 Si + -

13. ECE 250 – Electronic Devices 13 Si + - Since the net charge of a crystal is zero, if a negatively (-) charged electron breaks its bond and moves away from its original position, a positively charged “empty state” is left in its original position.

14. ECE 250 – Electronic Devices 14 Semiconductors As temperature increases, more bonds are broken creating more negative free electrons and more positively charged empty states. (Number of free electrons is a function of temperature.) To break a covalent bond, a valence electron must gain a minimum energy Eg, called the energy band gap. (Number of free electrons is a function of Eg.)

15. ECE 250 – Electronic Devices 15 Insulators Elements that have a large energy band gap of 3 to 6 eV are insulators because at room temperature, essentially no free electrons exist. Note: an eV is an electron volt. It is the amount of energy an electron will gain if it is accelerated through a 1 volt potential.

16. ECE 250 – Electronic Devices 16 Electron Volt Also, 1 eV = 1.518  10 -22 BTU, but who cares.

17. ECE 250 – Electronic Devices 17 Conductors Elements that have a small energy band gap are conductors. These elements have a large number of free electrons at room temperature because the electrons need very little energy to escape from their covalent bonds.

18. ECE 250 – Electronic Devices 18 Semiconductors Semiconductors have a band gap energy of about 1 eV –Silicon = 1.1 eV –GaAs = 1.4 eV –Ge = 0.66 eV

19. ECE 250 – Electronic Devices 19 Empty States An electron that has sufficient energy and is adjacent to an empty state may move into the empty state, leaving an empty state behind.

20. ECE 250 – Electronic Devices 20 Si + Empty state originally here. This electron can fill the empty state.

21. ECE 250 – Electronic Devices 21 Si + Empty state now here.

22. ECE 250 – Electronic Devices 22 Si +

23. ECE 250 – Electronic Devices 23 Si +

24. ECE 250 – Electronic Devices 24 Empty States Moving empty states can give the appearance that positive charges move through the material. This moving empty state is modeled as a positively charged particle called a hole. In semiconductors, two types of “particles” contribute to the current: positively charged holes and negatively charged electrons.

25. ECE 250 – Electronic Devices 25 Carrier Concentrations The concentrations of holes and free electrons are important quantities in the behavior of semiconductors. Carrier concentration is given as the number of particles per unit volume, or Carrier concentration =

26. ECE 250 – Electronic Devices 26 Intrinsic Semioconductor Definition – An intrinsic semiconductor is a single crystal semiconductor with no other types of atoms in the crystal. –Pure silicon –Pure germanium –Pure gallium arsenide.

27. ECE 250 – Electronic Devices 27 Carrier Concentration In an intrinsic semiconductor, the number of holes and free electrons are the same because they are thermally generated. If an electron breaks its covalent bond we have one free electron and one hole. In an intrinsic semiconductor, the concentration of holes and free electrons are the same.

28. ECE 250 – Electronic Devices 28 Intrinsic Semiconductors = the concentration of free electrons in an intrinsic semiconductor. = the concentration of holes in an intrinsic semiconductor.

29. ECE 250 – Electronic Devices 29 Intrinsic Carrier Concentration B and Eg are determined by the properties of the semiconductor. Eg = band gap energy (eV) B = material constant

30. ECE 250 – Electronic Devices 30 Intrinsic Carrier Concentration T = temperature (ºK) K = Boltzmann’s constant = 86.2×10 -6 eV/ºK

31. ECE 250 – Electronic Devices 31 Material Constants MaterialEg (eV) B Silicon1.12 5.23  10 15 Gallium Arsenide 1.4 2.10  10 14 Germanium0.66 1.66  10 14

32. ECE 250 – Electronic Devices 32 Important Note: Book uses a slightly different Notation!

33. ECE 250 – Electronic Devices 33 Book Material Constants MaterialEg (eV) B Silicon1.12 5.4  10 31

34. ECE 250 – Electronic Devices 34 Example Find the intrinsic carrier concentration of free electrons and holes in a silicon semiconductor at room temperature.

35. ECE 250 – Electronic Devices 35 MathCAD

36. ECE 250 – Electronic Devices 36 MathCAD The concentration of silicon atoms in an intrinsic semiconductor is 5  10 22 atoms/cm 3.

37. ECE 250 – Electronic Devices 37 Extrinsic Semiconductors Since the concentrations of free electrons and holes is small in an intrinsic semiconductor, only small currents are possible. Impurities can be added to the semiconductor to increase the concentration of free electrons and holes.

38. ECE 250 – Electronic Devices 38 Extrinsic Semiconductors An impurity would have one less or one more electron in the valance shell than silicon. Impurities for group 4 type atoms (silicon) would come from group 3 or group 5 elements.

39. ECE 250 – Electronic Devices 39 Extrinsic Semiconductors The most common group 5 elements are phosphorous and arsenic. Group 5 elements have 5 electrons in the valence shell. Four of the electrons fill the covalent bonds in the silicon crystal structure. The 5 th electron is loosely bound to the impurity atom and is a free electron at room temperature.

40. ECE 250 – Electronic Devices 40 Si P -

41. ECE 250 – Electronic Devices 41 Extrinsic Semiconductors The group 5 atom is called a donor impurity since it donates a free electron. The group 5 atom has a net positive charge that is fixed in the crystal lattice and cannot move. With a donor impurity, free electrons are created without adding holes.

42. ECE 250 – Electronic Devices 42 Extrinsic Semiconductors Adding impurities is called doping. A semiconductor doped with donor impurities has excess free electron and is called an n-type semiconductor.

43. ECE 250 – Electronic Devices 43 Extrinsic Semiconductors The most common group 3 impurity is boron which has 3 valence electrons. Since boron has only 3 valence electrons, the boron atom can only bond with three of its neighbors leaving one open bond position.

44. ECE 250 – Electronic Devices 44 Si B

45. ECE 250 – Electronic Devices 45 Extrinsic Semiconductors At room temperature, silicon has free electrons that will fill the open bond position, creating a hole in the silicon atom whence it came. The boron atom has a net negative charge because of the extra electron, but the boron atom cannot move.

46. ECE 250 – Electronic Devices 46 Si B +

47. ECE 250 – Electronic Devices 47 Extrinsic Semiconductors Since boron accepts a valence electron, it is called an acceptor impurity. Acceptor impurities create excess holes but do not create free electrons. A semiconductor doped with an acceptor impurity has extra holes and is called a p-type semiconductor.

48. ECE 250 – Electronic Devices 48 Carrier Concentrations For any semiconductor in thermal equilibrium n o p o =n i 2, where n o = the concentration of free electrons. p o = the concentration of holes. n i = the intrinsic carrier concentration

49. ECE 250 – Electronic Devices 49 Extrinsic Carrier Concentrations For an n-type semiconductor with donor impurities, the concentration of donor impurities is N d with units #/cm 3. If N d >> n i, then the concentration of free electrons in the n-type semiconductor is approximately n o  N d.

50. ECE 250 – Electronic Devices 50 Extrinsic Carrier Concentrations Since n o p o =n i 2 for any semiconductor in thermal equilibrium, and For an n-type semiconductor, n o  N d Where p o is the concentration of holes in the n-type semiconductor.

51. ECE 250 – Electronic Devices 51 Extrinsic Carrier Concentrations For a p-type semiconductor with acceptor impurities, the concentration of acceptor impurities is N a with units #/cm 3. If N a >> n i, then the concentration of holes in the p-type semiconductor is approximately p o  N a.

52. ECE 250 – Electronic Devices 52 Extrinsic Carrier Concentrations Since n o p o =n i 2 for any semiconductor in thermal equilibrium, and For a p-type semiconductor, p o  N a Where n o is the concentration of free electrons in the p-type semiconductor.

53. ECE 250 – Electronic Devices 53 Current in Semiconductors The two processes that cause free electrons and holes to move in a semiconductor are drift and diffusion. Drift – the movement of holes and electrons due to an electric field Diffusion – the movement of holes and electrons due to variations in concentrations.

54. ECE 250 – Electronic Devices 54 Drift Current Assume that an electric field is applied to to a semiconductor. This field acts on holes and electrons.

55. ECE 250 – Electronic Devices 55 Drift Current-Electrons Electrons – The Electric field creates a force in the opposite direction of the electric field – Attractive. v dn is the drift velocity of electrons. J n is the current density due to electrons. n-type

56. ECE 250 – Electronic Devices 56 Drift Current-Electrons The electrons acquire a drift velocity of Where  n is the mobility of electrons with units of cm 2 /(volt-sec). The units of v dn are cm/sec. For low-doped silicon, a typical number is  n =1350 cm 2 /volt-sec.

57. ECE 250 – Electronic Devices 57 Drift Current-Electrons The minus sign (-) indicates that the electrons move in the opposite direction of the applied electric field.

58. ECE 250 – Electronic Devices 58 Drift Current Density-Electrons Current = charge per unit time (coul/sec). Current density = current flowing through a specific area = amps/unit area = coul/(sec- cm 2 )

59. ECE 250 – Electronic Devices 59 Drift Current Density-Electrons e = the charge on an electron = 1.602  10 -19 coulombs. n=concentration of electrons = #/cm 3.  en=charge/cm 3.

60. ECE 250 – Electronic Devices 60 Drift Current - Holes Holes – The Electric field creates a force in the same direction of the electric field. v dp is the drift velocity of holes. J p is the current density due to holes. n-type

61. ECE 250 – Electronic Devices 61 Drift Current-Holes The holes acquire a drift velocity of Where  p is the mobility of holes with units of cm 2 /(volt-sec). The units of v dp are cm/sec. For low-doped silicon, a typical number is  dp =480 cm 2 /volt-sec.

62. ECE 250 – Electronic Devices 62 Mobility - Aside Note that  n >  p. Electrons are faster than holes. P-type and n-type devices operate the same. However, n-type devices are faster.

63. ECE 250 – Electronic Devices 63 Drift Current Density-Holes e = the charge on an electron = 1.602  10 -19 coulombs. p=concentration of holes = #/cm 3.  ep=charge/cm 3.

64. ECE 250 – Electronic Devices 64 Drift Current n-type Drift current due to holes and electrons is in the same direction.

65. ECE 250 – Electronic Devices 65 Total Drift Current Since the hole current and the electron current are in the same direction, the currents add. The total drift current is:

66. ECE 250 – Electronic Devices 66 Ohm’s Law Another form of Ohm’s law is J=  E  is the conductivity of the material. Noting that and

67. ECE 250 – Electronic Devices 67 Conductivity We can find the conductivity of a semiconductor as

68. ECE 250 – Electronic Devices 68 Diffusion Currents (Cover Them)

69. ECE 250 – Electronic Devices 69 Excess Carriers So far we have assumed that the semiconductor is in steady state. Suppose that we shine light on a semiconductor. If the photons have sufficient energy, valence electrons may break their covalent bonds and create pairs of free electrons and holes.

70. ECE 250 – Electronic Devices 70 Excess Carriers These additional holes and electrons are called excess holes (δp) and excess free electrons (δn). When excess holes and free electrons are created, these concentration of holes and free electrons increase above the thermal equilibrium value n = n o + δn p = p o + δp

71. ECE 250 – Electronic Devices 71 Excess Carriers In steady state, the generation of excess carriers will not cause the carrier concentration to increase indefinitely due to a process called recombination. Electron-Hole Recombination – a free electron combines with a hole and both disappear.

72. ECE 250 – Electronic Devices 72 Excess Carriers Generation – Creates free electrons – hole pairs. Recombination – Eliminates free electrons and holes in pairs. Excess Carrier Lifetime – The mean time over which an excess free electron and hole exist before recombination.