1. Doping and Crystal Growth Techniques

2. Types of Impurities Substitutional Impurities Substitutional Impurities –Donors and acceptors –Isoelectronic Defects Vacancies Vacancies –Charged Vacancies  Color centers in solids (alkali halides) Interstitial Atoms Interstitial Atoms –Mid Gap Trap Antisite Defects Antisite Defects

3. Back to the Periodic Table

4. Column V Atoms Have 5 outer shell electrons

5. The extra electron on the phosphorous atom is easily removed and becomes a free electron without generating a hole. The phosphorous atom becomes positively charged (ionized).

6. Back to the Periodic Table (again)

7. Column III Atoms Have 3 outer shell electrons

8. The boron atom ‘steals’ an electron from a neighboring Si atom to complete the four bonds with the surrounding Si atoms, generating a hole at the neighboring Si atom. The boron atom becomes negatively charged (ionized).

9. n-type Semiconductors Are doped with donor atoms, which have an extra electron that they donate to the crystal Are doped with donor atoms, which have an extra electron that they donate to the crystal –When the concentration of donor atoms is much greater than the intrinsic carrier concentration, the electron concentration is composed of these donated electrons.

10. p-type Semiconductors Are doped with acceptor atoms, which generate holes in the crystal Are doped with acceptor atoms, which generate holes in the crystal –When the concentration of acceptor atoms is much greater than the intrinsic carrier concentration, the hole concentration is composed of the holes generated by the acceptors.

11. Carrier Concentrations n-type semiconductor p-type semiconductor

12. Bohr model for Hydrogen atom

13. Translation to Donor Atom Include relative dielectric constant Include relative dielectric constant Extra electron has a effective mass equal to the conduction band electrons Extra electron has a effective mass equal to the conduction band electrons

14. Translation to Acceptor Atom Include relative dielectric constant Include relative dielectric constant Missing electron has a effective mass equal to the valence band electrons Missing electron has a effective mass equal to the valence band electrons

15. Heisenberg’s Uncertainty Principle In quantum mechanics, we talk about the probability of finding a particle in a certain place.  x  p ≥ħ/2  t  ≥1/4   t  E ≥ħ/2

16. Impurity Level DeBroglie’s relation The deeper the impurity level from either Ec or Ev, the smaller r n is – i.e, the electron or hole is more tightly bound to the impurity.

17. http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm

18. GaP LEDs have a low concentration of N impurities in them. The impurity energy level has a large k that extends from the X minima to the  minima, allowing the trapped electrons to radiative recombine with holes.

19. Types of Impurities Substitutional Impurities Substitutional Impurities –Donors and acceptors –Isoelectronic Defects Vacancies Vacancies –Charged Vacancies  Color centers in solids (alkali halides) Interstitial Atoms Interstitial Atoms –Mid Gap Trap Antisite Defects Antisite Defects

20. Types of Crystal Growth Product is a boule from which wafers are then cut Product is a boule from which wafers are then cut –Czochralski (CZ) –Float Zone (FZ) –Bridgeman

21. Czochralski http://www.tf.uni- kiel.de/matwis/amat/elmat_ en/kap_6/illustr/i6_1_1.html www.qahill.com/tz/sil icon/silicon.html

23. http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/backbone/r6_1_2.html#_dum_1

24. Impurity Segregation Where Co is the initial concentration of th impurity in the melt

25. Impurity Segregation Atom CuAgAuCGeSnAs koko 4 · 10 –4 10 –6 2.5 · 10 –5 7 · 10 –2 3.3 · 10 –2 1.6 · 10 –2 0.3 Atom OBGaFeCoNiSb koko 0.50.88 · 10 –3 8 · 10 –6 4 · 10 –4 2.3 · 10 –2

26. Float Zone www.tms.org/pubs/journals/JOM/9802/Li/ www.mrsemicon.com /crystalgrowth.htm

27. Impurity Segregation Where C o is the initial concentration of the impurity in the solid and L is the width of the melted region within RF coil

28. Bridgeman Used for some compound semiconductors Used for some compound semiconductors –Particularly those that have a high vapor pressure –Produced “D” shaped boules

29. Crystalline Defects Point Defects Point Defects –Vacancies –Impurities –Antisite Defects Line Defects Line Defects –Dislocations  Edge  Loop Volume Defects Volume Defects –Voids –Screw Dislocations

30. Edge Dislocation http://courses.eas.ualberta.ca/eas421/lecturepages/mylonite.html

31. Screw Dislocation http://focus.aps.org/story/v20/st3

32. Strain induced Dislocations The temperature profile across the diameter of a boule is not constant as the boule cools The temperature profile across the diameter of a boule is not constant as the boule cools –the outer surface of the boule contracts at a different rate than the internal region –Thermal expansion differences produces edge dislocations within the boule  Typical pattern is a “W”

33. Strain due to Impurities An impurity induces strain in the crystal because of differences in An impurity induces strain in the crystal because of differences in –ionic radius as compared to the atom it replaced  Compressive strain if the ionic radius is larger  Tensile strain if the ionic radius is smaller –local distortions because of Coulombic interactions Both cause local modifications to Eg Both cause local modifications to Eg

34. Dislocation Count When you purchase a wafer, one of the specifications is the EPD, Etch Pit Density When you purchase a wafer, one of the specifications is the EPD, Etch Pit Density –Dislocations etch more rapidly in acid than crystalline material –Values for EPD can run from essentially zero (FZ grown under microgravity conditions) to 10 6 cm -2 for some materials that are extremely difficult to grow.  Note that EPD of 10 6 cm -2 means that there is a dislocation approximately every 10  ms.

35. Wafer Manufacturing Boules are polished into cylinders Boules are polished into cylinders Aligned using an x-ray diffraction system Aligned using an x-ray diffraction system Cut into slices using a diamond edged saw Cut into slices using a diamond edged saw –Slices are then polished smooth using a colloidal grit  Mechanical damage from sawing causes point defects that can coalesce into edge dislocations if not removed

36. http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/backbone/r6_1_2.html#_dum_1

37. SCS Manufacturing

38. Carrier Mobility and Velocity Mobility - the ease at which a carrier (electron or hole) moves in a semiconductor Mobility - the ease at which a carrier (electron or hole) moves in a semiconductor –Symbol:  n for electrons and  p for holes Drift velocity – the speed at which a carrier moves in a crystal when an electric field is present Drift velocity – the speed at which a carrier moves in a crystal when an electric field is present –For electrons: v d =  n E –For holes: v d =  p E

39. H L W VaVa VaVa

40. Resistance

41. Resistivity and Conductivity Fundamental material properties Fundamental material properties

42. Current Flow

43. Resistivity n-type semiconductor p-type semiconductor

44. Diffusion When there are changes in the concentration of electrons and/or holes along a piece of semiconductor When there are changes in the concentration of electrons and/or holes along a piece of semiconductor –the Coulombic repulsion of the carriers force the carriers to flow towards the region with a lower concentration.

45. Diffusion Currents

46. Relationship between Diffusivity and Mobility

47. Wafer Characterization X-ray Diffraction X-ray Diffraction –Crystal Orientation Van der Pauw or Hall Measurements Van der Pauw or Hall Measurements –Resistivity –Mobility Four Point Probe Four Point Probe –Resisitivity Hot Point Probe Hot Point Probe –n or p-type material