1. Miller Indices

2. Equivalent Planes: {h k l}

3. Crystal Directions: [h k l]

4. Bulk Si Growth Pure, single cryst. Si SiO2+2C(coke)→Si+2CO 1800oC
metallurgical grade Si (MGS) (98%)
not single crystal
impurity: several ppm
Si+3HCl (dry)→SiHCl3+H2
Boiling point SiHCl3: 32oC
Fractional distillation → Pure SiHCl3
SiHCl3+H2 →Si+3HCl
Electronic grade Si (EGS)
Impurity: ppb
Poly-cryst
→Single cryst. Si ingot: Czochralski Crystal Growth

5. From Sand to Silicon
(9N: ％)

6. Czochralski Crystal Growth

7. Czochralski Crystal Growth
Crystal Pulling
Requires seed cryst
Melt EGS in quartz-lined graphite crucible

8. Czochralski Crystal Growth

9. Czochralski Crystal Growth
Crystal Pulling
Crystal Ingots

10. Doping
We may add intentional impurity or dopants to Si melt to change its electrical properties.
At the solidifying interface between the melt and the solid, there will be certain distribution of impurities between two phases.
The distribution coefficients Kd is the ratio of the concentration of impurity in the solid Cs to the concentration in the liquid Ls
𝐾 𝑑 = 𝐶𝑠 𝐿𝑠

11. Example:
A Si crystal is to be grown by the Czochralski method, and it is desired that the ingot contain 1016 phosphorous atoms/cm3
(a) What the concentration of phosphorous atoms should the melt contain to give this impurity concentration in the crystal during the initial growth? For P in Si, kd=0.35.
(b) If the Initial load of Si in the crucible is 5kg, how many grams of phosphorous should be added? The atomic weight of phosphorous is 31 gr/mol.

12. Example:

13. Wafer
Ingot: wafer:
Mechanical grinding: cylinder , controlled diameter
Crystal Ingots
Sawing Si ingot to wafers
Mechanical polishing
Front side: CMP: fine SiO2 in NaOH
Shaping and Polishing
wafer

14. Wafer
Ingot: wafer:
Mechanical grinding: cylinder , controlled diameter
Crystal Ingots
Sawing Si ingot to wafers
Mechanical polishing
Front side: CMP: fine SiO2 in NaOH
Shaping and Polishing
wafer

15. Valence bonds

16. Valence bonds

17. Quantum Mechanics Quantum mechanics:
Some experimental observations that led to modern concept of atoms
Photoelectric effect
Atomic Spectrum..
Quantum mechanics:
The electrons in atoms are restricted to certain energy levels by quantum rules
The electronic structure of atoms are determined from these quantum conditions
These quantization defines certain allowable transitions involving absorption and emission of energy by electrons

18. Quantum Mechanics
In 1920 it becomes necessary to develop a new theory to describe phenomena on the atomic scale
Many events involving electrons and atoms did not obey the classical laws of mechanics
A new kind of mechanics to describe the behavior of particles on the small scale
: Quantum mechanics:
Describes atomic phenomena very well
Predicts the way in which electrons behave in solids

19. Photoelectric Effect
Plank: the radiation from a heated sample is emitted in discrete units of energy, called quanta
The energy units: hυ
h=6.63×10-34 J.s
Experiment:
Monochromatic light is incident on the surface of a metal plate in a vacuum
Photoelectric effect: some of the electrons receive enough energy to be ejected from the metal surface into the vacuum

20. Photoelectric Effect
Em=hυ-qΦ
qΦ : Metal work function

21. Atomic Spectra
An electric discharge can be created in gas → the atoms begin to emit light with wavelength characteristics of the gas
Intensity of emitted light vs. wavelength: a series of sharp lines
λ=c/υ
E=hυ=hc/λ

22. Atomic Spectra
The various series in the spectrum follow the certain empirical form:
R: Rydberg constant R= cm-1

23. The Bohr Model

24. Atomic Spectra

25. The Bohr Model

26. Pauli exclusion principle
No more than two electrons in a given system can reside in the same energy state at the same time.

27. Isolated silicon atom

28. Formation of silicon crystal from N isolated silicon atoms

29. Energy Bands
At 0K the electrons will occupy the lowest energy states available to them
For Si crystal: 4N states in the valence band available to the 4N electrons
→ at 0K: every states in the valence band is filled /conduction band: empty

30. Metals, Semiconductors and Insulators
Band structure →electrical characteristics
For electrons to experience acceleration in an applied electric field, they must be able to move into new energy states → there must be empty states available for electrons
Semiconductors at 0K: filled valence, separated from empty conduction band by a band gap

31. Conduction in Metals, Semiconductors, and Insulators

32. Semiconductors and Insulators
An important difference between semiconductor and insulator:
The number of electrons available for conduction can be increased greatly in semiconductors by thermal or optical energy.

33. Metals Metals: bands either overlap or are only partially filled
Electrons and empty states are intermixed within the bands
Electron can move freely under the influence of an electric field → high electrical conductivity

34. The energy momentum diagram
The energy of a free electron is given by:

35. The energy momentum diagram
In a semiconductor crystal, an electron in the conduction band is similar to a free electron in being relatively free to move about in the crystal.
However, because of the periodic potential of the nuclei it is not totally free and effective mass of electron should be used
The electron effective mass depends on the properties of the semiconductor.

36. The energy momentum diagram

37. The energy momentum diagram
mn = 0.19m0
Eg = 1.12eV
mn = 0.063m0
Eg = 1.42 eV

38. Direct and indirect semiconductors
Direct semiconductor does not require a change in momentum for an electron transition from the valence band to the conduction band. (GaAs)
Indirect semiconductor a change of momentum is required in a transition.
Light-emitting diodes and semiconductor lasers use direct semiconductors.

39. Direct and Indirect Semiconductors

40. INTRINSIC CARRIER CONCENTRATION
Thermal equilibrium: The steady-state condition at a given temperature without any external excitations such as light, pressure, or an electric field.
Intrinsic semiconductor: Contains relatively small amounts of impurities compared with the thermally generated electrons and holes.(a perfect semiconductor crystal with no impurities or lattice defects)
EHPs are the only charge carriers in intrinsic material
n=p=ni

41. Carrier Concentrations
Electron in solids obey Fermi-Dirac statistics:
In quantum statistics,  Fermi–Dirac statistics describe a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli exclusion principle.
Distribution of electrons over a range of allowed energy states at thermal equilibrium:
f(E): The Fermi-Dirac distribution function: probability of occupancy of an available state at E
Being filled probability: f(E)
Being empty probability: 1-f(E)

42. The Fermi Level Fermi-Dirac Distribution Function

43. Fermi-Dirac Distribution Function
Probability that a hole occupies a state in valence band

44. Electron Concentration at Equilibrium
If the density of available states in valence and conduction bands are known, f(E) can be used to calculate the concentration of e/h
The concentration of electrons in conduction band:
N(E)dE: density of states(cm-3) in the energy range dE
0: equilibrium condition( like n0, p0)
N(E) α E1/2

45. Density of states
The number of allowed energy states (including electron spin) per unit energy per unit volume(i.e., in the unit of number of states/eV/cm3)
The volume in momentum space for an energy state is h3
p + dp  Volume = 4𝜋 𝑝 2 𝑑𝑝
number of energy states = 2( 4𝜋 𝑝 2 𝑑𝑝 ℎ 3 )

46. Carrier Concentration
p=n=ni intrinsic carrier density

47. Carrier concentration
The concentration of electrons in conduction band

48. Carrier Concentration

49. Carrier Concentration
If we refer to the bottom of the conduction band as Ec instead of E = 0,
Nc is the effective density of states in the conduction band
At room temperature

50. Carrier Concentration
Similarly for hole density
Nv is the effective density of states in the valance band
At room temperature

51. Intrinsic semiconductor

52. Intrinsic semiconductor

53. Intrinsic carrier density vs. Temperature

54. Donors and Acceptors
extrinsic semiconductor: Doping with impurities

55. Donors and Acceptors
The impurity atoms will introduce an energy level or multiple energy levels in the band gap.
Ionization energy for donors
mn : effective electron mass
s : semiconductor permittivity
EH: Hydrogen energy
Ionization energy for donors, measured from the conduction band edge: eV for silicon, eV for GaAs
ionization energy for acceptors, measured from the valence band edge: 0.05 eV for both Si and GaAs

56. Donors and Acceptors
Simple hydrogen atom model cannot account for the details of the ionization energy.

57. Donors and Acceptors

58. Nondegenerate Semiconductor
The electron or hole concentration is much lower than the effective density of states in the conduction band or the valence band.
The Fermi level EF is at least 3kT above EV or 3kT below EC.

59. n-Type semiconductor For complete ionization condition
Electron concentration in conduction band
Fermi level
The higher the donor concentration, the smaller the energy difference (EC – EF);that is, the Fermi level will move closer o the bottom of the conduction band.

60. P-type semiconductors
For complete ionization condition
Hole concentration in valence band
Fermi level
For higher acceptor concentration, the Fermi level will move closer to the top of the valence band.

61. e/h Concentration at Equilibrium
intrinsic
n type
p type

62. Extrinsic carrier concentration in terms of intrinsic carrier concentration
ni : Intrinsic carrier concentration
Ei : Intrinsic fermi level
Ef : extrinsic fermi level

63. Extrinsic carrier concentration in terms of intrinsic carrier concentration
ni : Intrinsic carrier concentration
Ei : Intrinsic fermi level
Ef : extrinsic fermi level

64. Mass action law
under thermal equilibrium conduction

65. Example
A silicon ingot is doped with 1016 arsenic atoms/cm3. Find the carrier concentrations and the Fermi level at room temperature (300 K).

66. Example

67. Both donor and acceptor impurities
The impurity that is present in a greater concentration determines the type of conductivity in the semiconductor.
Charge neutrality
Mass action law
n-type semiconductor

68. Both donor and acceptor impurities
n-type semiconductor
majority carrier is electron
minority carrier is hole
p-type semiconductor
majority carrier is hole
minority carrier is electron

69. Both donor and acceptor impurities
Generally, the magnitude of the net impurity concentration |ND – NA| is greater than the intrinsic carrier concentration ni

70. Fermi level as a function of temperature

71. Fermi level as a function of temperature

72. Electron density as a function of temperature

73. Degenerate Semiconductor
degenerate semiconductor For very heavily doped n-type or p-type semiconductor, EF will be above EC or below EV.
Bandgap-narrowing effect high impurity concentration causes a reduction of the bandgap.
The bandgap reduction for silicon at room temperature: