nature of the chemical bond with applications to catalysis, materials science, nanotechnology,...

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L09 Ch120a-Goddard-

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Nature of the Chemical Bond with applications to catalysis, materials

science, nanotechnology, surface science, bioinorganic chemistry, and energy

William A. Goddard, III, [email protected] Beckman Institute, x3093

Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics,

California Institute of Technology

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

Course number: Ch120aHours: 2-3pm Monday, Wednesday, Friday

Teaching Assistants:Sijia Dong <[email protected]>Samantha Johnson <[email protected]>

mailto:[email protected]

mailto:[email protected]

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L09

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© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L09 3

Examples of special planes

a

b

c

b/k

a/h

c/l

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


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.


Bonding in GaAsMaking 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


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


gaas

gaas

gaas as

ga gaas

ga

gaas

gaas

gaas

gaas

ga gaas

GaAs (110)

AsGa

AsGa

AsGa

AsGa

AsGa

As

AsGa

AsGa

AsGa

AsGa

AsGa

As

AsGa

AsGa

AsGa

AsGa

AsGa

As

P(1x1)

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


The (110) plane (outlined in green, layer 1)

As atoms top layer

1

1

c 1

3 1

02

1

2

1

0

11

20

[100]

[010]

[001]

[110]

[-1,1,0]

Ga atoms top layer

surface unit cell P(1x1)

[001]

[-1,1,0]

Cut through cubic unit cell


Reconstruction of (110) surface, side view along [-1,1,0]

[001]

[110]

54.7º54.7º

54.7º

Si (110)

Ga As

GaAs (110)

Si has dangling

bond electron at

each surface atom

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


Reconstruction of GaAs(110) surface

Top view (from [-1,-1,0])

[001]

[-1,1,0] [001]

[1,1,0]

As has 3 covalent bonds, leaving 2 electrons in 3s lone pair, Ga has 3 covalent bonds leaving 0 eletrons in 4th orbital

54.7º54.7ºGa As

side view (along [-1,1,0])


Reconstruction of (110) GaAs


III-V reconstruction dominated by local valence


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


Analysis of chargesBulk 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

As Ga As Ga AsGa

a g a ga g3/4

3/43/4

3/4

3/43/4

3/43/4

3/43/4

3/43/4

5/45/4

5/45/4

5/45/4

5/45/4

5/45/4

5/45/4

3/4 3/43/4 5/45/45/411 11 11 11 11

202020

5.25e 2.75e Net Q =0


GaAs (100)

ga ga

ga ga

ga ga

ga ga

ga ga

ga 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.

If cut off top layer, get pure Ga on surface

AsAs AsAs

AsAs AsAs

AsAs AsAs

AsAs AsAs

AsAs AsAs

AsAs AsAs

AsAs AsAs


The GaAs (100) surface, unreconstructed

1st Layer RED2nd Layer GREEN3rd Layer ORANGE4th Layer WHITE

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)


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

AsGa

AsGa

AsGa

AsGa


Charges for 2x1 GaAs(100)

2 2

2 21 1

1 1

3/4

3/4

3/4

3/4

5/4

5/4

5/43/4

3/4

3/4

3/4

3/4

3/4

3/4

3/4

3/4

3/4

3/4

3/4

5/4

5/4

5/4

Top layer, As

2nd layer, ga

3rd layer, as2e As-ga bond

2e As LP

2e As-As bond

2nd layer ga has 3 e

1st layer As has 5.5 e

Each surface As has extra 0.5 e dimer has extra 1e Not stable


Now consider a missing row of As for GaAs(100)

1 1

3/43/4

3/4

5/4

3/4

3/4

3/43/4

3/4

3/4

3/43/4

3/4

5/4

Top layer, As

2nd layer, ga

3rd layer, asga empty LP

0

2nd layer ga has 2.25e

1st layer As has 5.5 e

Each 2nd layer ga next to missing As is deficient by 0.75e extra 0.5 e 4 ga are missing 3e

0

0 0


Consider 1 missing As row

out of 4Extra 1e

missing 3e

missing 3e

Extra 1e

Extra 1e

Extra 1e

-1-1-1+3=0 net charge

Thus based on electron counting expect simplest surface reconstruction to be 4x2. This is observed


Different views of GaAs(100)4x2 reconstruction

Previous page, 3 As dimer rows

then one missing

Two missing As row plus missing Ga rowExposes 3rd row As

Agrees with experimentHashizume et al Phys Rev B 51, 4200 (1995)

+1.5e-1.0e


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


As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

As AsAsga gaga

ga

Asga

As

ga

GaAs (111) 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

© copyright 2010 William A. Goddard III, all rights reservedCh120a-Goddard-L09-10 27

Intrinsic semiconductors

+ -


Excitation energy

-4.0 eV relative to vacuum=-IP

-5.1 eV relative to vacuum = -EAEnergy gap = 1.1 eV


To be added – band states


Semiconducting properties


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


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


N-type semiconductor

Ionize extra electron get strong bond

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



IP(P)=4.05 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

0.054 eV


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 bondThus 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.


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



EA(Al)=5.033 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

0.067 eV


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 GeWhat happens if we replace Ga with Zn or Ge


Substitute As for Se or Ge


Substitute Ga with Zn or Ge


Dopant levels for GaAs


Cohesive energies and Bonds for III-V compounds


Compare IV to III-V same row

© copyright 2010 William A. Goddard III, all rights reservedCh120a-Goddard-L09-10

np junction

52

CBM

VBM

n type

Efermi

CBM

VBM

p type

Efermi

Get charge flow from n type to p type until Fermi energy (chemical potential) matches

nature of the chemical bond with applications to catalysis, materials science, nanotechnology,...

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