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Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinor

Lecture 8 January 24, 2013 GaAs crystal surfaces, n-p dopants Si. Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy. Course number: Ch120a Hours: 2-3pm Monday, Wednesday, Friday.

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Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinor

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  1. Ch120a-Goddard-L01 Lecture 8 January 24, 2013 GaAs crystal surfaces, n-p dopants Si Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy Course number: Ch120a Hours: 2-3pm Monday, Wednesday, Friday William A. Goddard, III, wag@wag.caltech.edu 316 Beckman Institute, x3093 Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Teaching Assistants:Sijia Dong <sdong@caltech.edu> Samantha Johnson <sjohnson@wag.caltech.edu>

  2. Last time

  3. Examples of special planes c c/l b/k b a/h a To denote all equivalent planes we use {h,k,l} so that {1,0,0} for cubic includes the 3 cases in the first row) A number with a bar indicates negative From Wikipedia

  4. The zincblende or sphalerite structure Replacing each C atom of the diamond structure alternately with Ga and As so that each Ga is bonded to four As and each As is bonded to four Ga leads to the zincblende or sphalerite structure (actually zincblende is the cubic form of ZnS and the mineral sphalerite is cubic ZnS with some Fe) • As at corners: (0,0,0) • As at face centers: (a/2,a/2,0), (a/2,0,a/2), (0,a/2,a/2) • Ga 4 internal sites: (a/4,a/4,a/4), (3a/4,3a/4,a/4), (a/4,3a/4,3a/4), (3a/4,a/4,3a/4), • Thus each cube has 4 As and 4 Ga.

  5. Bonding in GaAs Making a covalent bond between to each atoms, one might have expected tetrahedral As to make 3 bonds with a left over lone pair pointing away from the 3 bonds, while Ga might be expected to make 3 covalent bonds, with an empty sp3 orbital point away from the 3 bonds, as indicated here, where the 3 covalent bonds are shown with lines, and the donor acceptor (DA) or Lewis acid-Lewis base bond as an As lone pair coordinated with and empty orbital on Ga Of course the four bonds to each atom will adjust to be equivalent, but we can still think of the bond as an average of ¾ covalent and ¼ DA

  6. Other compounds Similar zincblende or sphalerite compounds can be formed with Ga replaced by B, Al,In and /or As replaced by N, P, Sb, or Bi. They are call III-V compounds from the older names of the columns of the periodic table (new UIPAC name 13-15 compounds). In addition a hexagonal crystal, called Wurtzite, also with tetrahedral bonding (but with some eclipsed bonds) is exhibited by most of these compounds. In addition there are a variety of similar II-VI systems, ZnS, ZnSe, CdTe, HgTe, etc

  7. GaAs (110) The surface unit cell, P(1x1) is ½ the cross-section for the (110) plane outlined in the unit cell cube at the right. Note that top surface has equal number of Ga and As P(1x1) As As As As As As Ga Ga Ga Ga Ga as as as as as ga ga ga ga ga ga As As As As As As Ga Ga Ga Ga Ga as as as as as ga ga ga ga ga ga As As As As As As Ga Ga Ga Ga Ga

  8. 3 1 The (110) plane (outlined in green, layer 1) 1 1 2 0 2 2 0 0 1 1 c 1 1 1 [001] Cut through cubic unit cell [-1,1,0] surface unit cell P(1x1) [010] [110] [100] Ga atoms top layer [001] As atoms top layer [-1,1,0]

  9. Reconstruction of (110) surface, side view along [-1,1,0] Surface As has 3 covalent bonds to Ga, with 2 e in 3s lone pair, relaxes upward until average bond angle is 95º Surface Ga has 3 covalent bonds leaving 0 e in 4th orbital, relaxes downward until average bond angle is 119º. GaAs angle 0º 26º Si has dangling bond electron at each surface atom 54.7º 54.7º As Ga 54.7º [110] Si (110) GaAs (110) [001]

  10. Reconstruction of GaAs(110) surface As has 3 covalent bonds, leaving 2 electrons in 3s lone pair, Ga has 3 covalent bonds leaving 0 eletrons in 4th orbital 54.7º Ga As 54.7º Top view (from [-1,-1,0]) [001] [1,1,0] side view (along [-1,1,0]) [-1,1,0] [001]

  11. Reconstruction of (110) GaAs

  12. III-V reconstruction dominated by local valence

  13. Reconstruction of GaAs(110) surface, discussion We consider that bulk GaAs has an average of 3 covalent bonds and one donor acceptor (DA) bond. But at the surface can only make 3 bonds so the weaker DA bond is the one broken to form the surface. The result is that GaAs cleaves very easily compared to Si. No covalent bonds to break. As has 3 covalent bonds, leaving 2 electrons in 3s lone pair. AsH3 has average bond angle of 92º. At the GaAs surface As relaxes upward until has average bond angle of 95º Ga has 3 covalent bonds leaving 0 eletrons in 4th orbital. GaH3 has average bond angle of 120º. At the GaAs surface Ga relaxes downward until has average bond angle of 119º. This changes the surface Ga-As bond from 0º (parallel to surface to 26º. Observed in LEED experiments and QM calculations

  14. Analysis of charges Ga As Ga As Ga As Bulk structure: each As has 3 covalent bonds and one Donor-accepter bond(Lewis base – Lewis acid). This requires 3+2=5 electrons from As and 3+0=3 electrons from Ga. We consider that each bulk GaAs bond has 5/4 e from As and ¾ e form Ga. Each surface As has 5/4+1+1+2 = 5.25e for a net charge of -0.25 each surface Ga has ¾+1+1+0= 2.75 e for a net charge of +0.25 Thus considering both surface Ga and As, the (110) is neutral 5.25e 2.75e Net Q =0 0 2 0 2 0 2 1 1 1 1 1 1 1 1 1 1 5/4 3/4 3/4 3/4 5/4 5/4 5/4 3/4 3/4 5/4 5/4 3/4 5/4 3/4 3/4 5/4 5/4 3/4 a g a g a g 5/4 3/4 3/4 5/4 5/4 3/4 5/4 3/4 3/4 5/4 5/4 3/4

  15. GaAs (100) As As As As As As As As As As As As As As As As As As As As As As As As As As As As Start with As at surface, denote Ga on 2nd layer as ga. Then top layer is pure As. Not stable, get net negative charge at surface. If cut off top layer, get pure Ga on surface ga ga ga ga ga ga ga ga ga ga ga ga ga ga ga ga ga ga

  16. The GaAs (100) surface, unreconstructed Every red surface atom is As bonded to two green 2nd layer Ga atoms, but the other two bonds were to two Ga that are now removed. This leaves three non bonding electrons to distribute among the two dangling bond orbitals sticking out of plane (like AsH2) 1st Layer  RED 2nd Layer  GREEN 3rd Layer  ORANGE 4th Layer  WHITE

  17. GaAs(100) surface reconstructed (side view) For the perfect surface, As in top layer, Ga in 2nd layer, As in 3rd layer, Ga in 4th layer etc. For the unreconstructed surface each As has two bonds and hence three electrons in two nonbonding orbitals. Expect As atoms to dimerize to form a 3rd bond leaving 2 electrons in nonbonding orbitals. Surface As-As bonds As Ga As Ga As Ga As Ga

  18. Charges for 2x1 GaAs(100) 2 2 2 2 2nd layer ga has 3 e 1 1 Top layer, As 2nd layer, ga 5/4 5/4 3/4 3/4 3/4 3/4 3/4 3/4 3/4 3/4 5/4 2e As-ga bond 5/4 3rd layer, as 1 1 2e As LP 5/4 5/4 Each surface As has extra 0.5 e  dimer has extra 1e Not stable 3/4 3/4 3/4 3/4 3/4 1st layer As has 5.5 e 3/4 3/4 2e As-As bond 3/4

  19. Now consider a missing row of As for GaAs(100) 0 0 0 0 1 1 Top layer, As 2nd layer, ga 5/4 5/4 3/4 3/4 3/4 3/4 3/4 3/4 ga empty LP 3rd layer, as 2nd layer ga has 2.25e Each 2nd layer ga next to missing As is deficient by 0.75e extra 0.5 e  4 ga are missing 3e 3/4 3/4 3/4 1st layer As has 5.5 e 3/4 3/4 3/4

  20. Consider 1 missing As row out of 4 Extra 1e missing 3e -1-1-1+3=0 net charge Extra 1e Thus based on electron counting expect simplest surface reconstruction to be 4x2. This is observed Extra 1e Extra 1e missing 3e

  21. Different views of GaAs(100)4x2 reconstruction -1.0e +1.5e Two missing As row plus missing Ga row Exposes 3rd row As Agrees with experiment Previous page, 3 As dimer rows then one missing Hashizume et al Phys Rev B 51, 4200 (1995)

  22. summary • Postulate of surface electro-neutrality • Terminating the bulk charges onto the surface layer and considering the lone pairs and broken bonds on the surface should lead to: • the atomic valence configuration on each surface atom. For example As with 3 covalent bonds and a lone pair and Ga with 3 covalent bonds and an empty fourth orbital • A neutral surface • This leads to the permissible surface reconstructions

  23. GaAs (111) As As As As As As ga ga ga ga ga ga ga As As As As As As As ga ga ga ga ga ga ga As As As As As As ga ga ga ga ga ga As As As As As As As ga ga ga ga ga ga As As As As As As ga ga ga ga ga ga ga Start with As at surface, denote Ga on 2nd layer as ga. Then top layer is pure As. Not stable, get net negative charge at surface. Cut off top layer, to get pure Ga on surface, but break 3 bonds. Thus get As at front always but back slab is Ga

  24. Intrinsic semiconductors + -

  25. Excitation energy -4.0 eV relative to vacuum=-IP Energy gap = 1.1 eV -5.1 eV relative to vacuum = -EA

  26. To be added – band states

  27. To be added – band states

  28. Semiconducting properties

  29. Semiconducting properties

  30. Trends: overlaps between bonded atoms decrease from 2p to 3p to 4p etc Thus bonds are weaker, but antibonds are not as band Thus cohesive energy and band gaps decrease as go down the periodic table

  31. Add substitutional impurity, P, to Si Consider the case in which one Si atom of Si crystal is replace by a P atom (substitutional impurity) Main effect is that P has one more electron than Si Neutral has extra electron in one bond

  32. N-type semiconductor The substituted P can make covalent bonds to 3 of Si neighbors but the extra electron is in the way of making the 4th bond. Thus it is very easy to ionize this extra electron (IP=4.05 eV) donating it to the conduction band (EA=4.0 eV) leaving behind a P making covalent bonds to all four Si neighbors. The net excitation energy is just 4.05-4.00=0.05 eV. Thus as room temperature lots of electrons in conduction band. Get n type semiconductor and P is called an n-type dopant Ionize extra electron get strong bond

  33. To be added – band states IP(P)=4.05 eV 0.054 eV Remove e from P, add to conduction band = 4.045-4.0 = 0.045 eV Thus P leads to donor state just 0.045eV below LUMO or CBM

  34. Al substitutional impurity in Si Consider the case in which one Si atom of Si crystal is replace by a Al atom (substitutional impurity) Main effect is that Al has one less electron than Si The substituted Al can make covalent bonds to 3 of the Si neighbors but it lacks the electron to make a 4th bond 2-e bond Thus the EA of add an electron to make the 2 electron bond is EA=5.033 eV, which is nearly as great as the IP=5.1 eV. Thus removing an electron from the valence band and adding it to the Al-Si bond costs only 5.1-5.033=0.067eV. leaving behind an Al making covalent bonds to all four Si neighbors.

  35. Next consider Al substitutional impurity in Si Since the net excitation energy 0.067 eV there are lots of holes in the valence band at room temperature. Get p type semiconductor and Al is called a p-type or acceptor dopant

  36. To be added – band states EA(Al)=5.033 eV 0.067 eV Add e to Al, from valence band = 5.1 -5.033 = 0.067 eV Al leads to acceptor state just 0.067eV above HOMO or VBM

  37. III-V Compounds Energy Gaps for III-V much bigger than for group IV Consider GaAs, what happens if we replace As with Se or Ge What happens if we replace Ga with Zn or Ge

  38. Substitute As for Se or Ge

  39. Substitute Ga with Zn or Ge

  40. Dopant levels for GaAs

  41. Cohesive energies and Bonds for III-V compounds

  42. Compare IV to III-V same row

  43. n + p materials n type p type CBM CBM Efermi Efermi VBM VBM

  44. np junction p type n type CBM CBM Efermi Efermi VBM VBM Get charge flow from n type to p type until Fermi energy (chemical potential) matches

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