Lecture 8 January 24, 2013 GaAs crystal surfaces, n-p dopants Si

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1 Lecture 8 January 24, 2013 Ga crystal surfaces, n-p dopants Si Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinornic 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 sistants:sijia Dong <sdong@caltech.edu> Samantha Johnson <sjohnson@wag.caltech.edu> Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved Ch120a- 1 Goddard-

3 Examples of special planes c c/l a a/h To denote all equivalent planes we use {h,k,l} so that indicates Ch120a-Goddard-L09 netive b/k b {1,0,0} for cubic includes the 3 cases in the first row) A number with a bar From Wikipedia copyright 2011 William A. Goddard III, all rights reserved 3

4 The zincblende or sphalerite structure Replacing each C atom of the diamond structure alternately with Ga and so that each Ga is bonded to four and each 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) at corners: (0,0,0) 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 and 4 Ga. Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved 4

5 Bonding in Ga Making a covalent bond between to each atoms, one might have expected tetrahedral 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 sp 3 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 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 Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved 5

6 Other compounds Similar zincblende or sphalerite compounds can be formed with Ga replaced by B, Al,In and /or 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 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 Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved 6

7 Ga (110) The surface unit cell, P(1x1) is ½ the crosssection for the (110) plane outlined in the unit cell cube at the right. Note that top surface has equal number of Ga and P(1x1) Ga as Ga as Ga Ga as Ga as Ga Ch120a-Goddard-L09 Ga as Ga as Ga Ga as Ga as Ga Ga as Ga as Ga copyright 2011 William A. Goddard III, all rights reserved 7

1 1 [100] 2 The (110) plane (outlined in green, layer 1) [001] 3 1 1 2 0 2 0 0 1 1c 1 1 [110] [-1,1,0] [010] Cut through cubic unit cell surface

8 1 1 [100] 2 The (110) plane (outlined in green, layer 1) [001] c 1 1 [110] [-1,1,0] [010] Cut through cubic unit cell surface unit cell P(1x1) atoms top layer Ch120a-Goddard-L09 Ga atoms top layer [001] [-1,1,0] copyright 2011 William A. Goddard III, all rights reserved 8

9 Reconstruction of (110) surface, side view along [-1,1,0] Si has dangling bond electron at each surface atom 54.7º 54.7º Surface 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. Ga angle 0º è 26º 54.7º Ga [110] Si (110) Ga (110) [001] Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved 9

10 Top view (from [-1,-1,0]) Reconstruction of Ga(110) surface has 3 covalent bonds, leaving 2 electrons in 3s lone pair, Ga has 3 covalent bonds leaving 0 eletrons in 4 th orbital Ga 54.7º 54.7º [001] [1,1,0] [-1,1,0] Ch120a-Goddard-L09 [001] copyright 2011 William A. Goddard III, all rights reserved side view (along [-1,1,0]) 10

16 Reconstruction of Ga(110) surface, discussion We consider that bulk Ga 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 Ga cleaves very easily compared to Si. No covalent bonds to break. has 3 covalent bonds, leaving 2 electrons in 3s lone pair. H3 has average bond angle of 92º. At the Ga surface 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 Ga surface Ga relaxes downward until has average bond angle of 119º. This changes the surface Ga- bond from 0º (parallel to surface to 26º. Observed in LEED experiments and QM calculations Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved 16

17 Analysis of charges Bulk structure: each has 3 covalent bonds and one Donoraccepter bond(lewis base Lewis acid). This requires 3+2=5 electrons from and 3+0=3 electrons from Ga. We consider that each bulk Ga bond has 5/4 e from and ¾ e form Ga. Each surface has 5/ = 5.25e for a net charge of each surface Ga has ¾+1+1+0= 2.75 e for a net charge of Thus considering both surface Ga and, the (110) is neutral e 2.75e Net Q = Ga Ga Ga 1 1 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/4 a g a g a g 5/4 5/4 5/4 5/4 5/4 17 Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved

18 Ga (100) Start with at surface, denote Ga on 2 nd layer as. Then top layer is pure. Not stable, get net netive charge at surface. If cut off top layer, get pure Ga on surface Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved 18

19 The Ga (100) surface, unreconstructed Every red surface atom is bonded to two green 2 nd 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 H 2 ) Ch120a-Goddard-L09 1 st Layer à RED 2 nd Layer à GREEN 3 rd Layer à ORANGE 4 th Layer à WHITE copyright 2011 William A. Goddard III, all rights reserved 19

20 Ga(100) surface reconstructed (side view) For the perfect surface, in top layer, Ga in 2 nd layer, in 3 rd layer, Ga in 4 th layer etc. For the unreconstructed surface each has two bonds and hence three electrons in two nonbonding orbitals. Expect atoms to dimerize to form a 3 rd bond leaving 2 electrons in nonbonding orbitals. Surface - bonds Ga Ga Ga Ch120a-Goddard-L09 Ga copyright 2011 William A. Goddard III, all rights reserved 20

21 2 nd layer has 3 e 2e - bond 2e LP 1 st layer has 5.5 e Ch120a-Goddard-L09 Charges for 2x1 Ga(100) /4 5/4 5/ /4 5/4 5/4 2e - bond copyright 2011 William A. Goddard III, all rights reserved Top layer, 2 nd layer, 3 rd layer, as Each surface has extra 0.5 e è dimer has extra 1e Not stable 21

Now consider a missing row of for Ga(100) 1 1 Top layer, empty LP 1 st layer has 5.5 e Ch120a-Goddard-L09 5/4 0 0 0 2 nd layer has 2.

22 Now consider a missing row of for Ga(100) 1 1 Top layer, empty LP 1 st layer has 5.5 e Ch120a-Goddard-L09 5/ nd layer has 2.25e 5/4 Each 2 nd layer next to missing is deficient by 0.75e extra 0.5 e è 4 are missing 3e copyright 2011 William A. Goddard III, all rights reserved 0 2 nd layer, 3 rd layer, as 22

Consider 1 missing row out of 4-1-1-1+3=0 net charge Extra 1e missing 3e Extra 1e Thus based on electron counting expect simplest surface

23 Consider 1 missing row out of =0 net charge Extra 1e missing 3e Extra 1e Thus based on electron counting expect simplest surface reconstruction to be 4x2. This is observed Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved Extra 1e Extra 1e missing 3e 23

24 Different views of Ga(100)4x2 reconstruction Ch120a-Goddard-L09-1.0e Previous page, 3 dimer rows then one missing +1.5e Two missing row plus missing Ga row Exposes 3 rd row Agrees with experiment Hashizume et al Phys Rev B 51, 4200 (1995) copyright 2011 William A. Goddard III, all rights reserved 24

25 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 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 Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved 25

26 Ga (111) Ch120a-Goddard-L09 copyright 2011 William A. Goddard III, all rights reserved Start with at surface, denote Ga on 2 nd layer as. Then top layer is pure. Not stable, get net netive charge at surface. Cut off top layer, to get pure Ga on surface, but break 3 bonds. Thus get at front always but back slab is Ga 26

36 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 ps decrease as go down the periodic table Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 36

37 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 Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 37

38 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 4 th 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 =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 Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 38

39 To be added band states IP(P)=4.05 ev ev Remove e from P, add to conduction band = = ev Thus P leads to donor state just 0.045eV below LUMO or CBM Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 39

40 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 4 th 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 =0.067eV. leaving behind an Al making covalent bonds to all four Si neighbors. Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 40

41 Next consider Al substitutional impurity in Si Since the net excitation energy 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 Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 41

42 To be added band states EA(Al)=5.033 ev ev Add e to Al, from valence band = = ev Al leads to acceptor state just 0.067eV above HOMO or VBM Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 42

45 III-V Compounds Energy Gaps for III-V much bigger than for group IV Consider Ga, what happens if we replace with Se or Ge What happens if we replace Ga with Zn or Ge Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 45

52 np junction p type n type CBM E fermi CBM VBM E fermi VBM Get charge flow from n type to p type until Fermi energy (chemical potential) matches Ch120a-Goddard-L09-10 copyright 2010 William A. Goddard III, all rights reserved 52

Lecture 8 January 28, Silicon crystal surfaces

Lecture 8 January 28, Silicon crystal surfaces Lecture 8 January 28, 203 Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy Course number: Ch20a Hours: