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>
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
Ch120a1
Last time
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
2
Examples of
special planes
c
c/l
b/k
b
a a/h
To denote all equivalent
planes we use {h,k,l} so
that
From Wikipedia
{1,0,0} for cubic
includes the 3 cases in
the first row)
A number with a bar
Ch120a-Goddard-L09
indicates
negative
© copyright 2011 William A. Goddard III, all rights reserved
3
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.
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
4
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 acidLewis 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
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© copyright 2011 William A. Goddard III, all rights reserved
5
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
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© copyright 2011 William A. Goddard III, all rights reserved
6
GaAs (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 As
P(1x1)
As
As
As
As
As
As
Ga
Ga
Ga
Ga
Ga
as
as
as
as
as
ga
ga
As
ga
As
As
ga
ga
ga
As
As
As
Ga
Ga
Ga
Ga
Ga
as
as
as
as
as
ga
As
ga
As
Ga
ga
As
Ga
Ch120a-Goddard-L09
ga
As
Ga
ga
As
Ga
ga
As
Ga
© copyright 2011 William A. Goddard III, all rights reserved
7
The
(110) plane (outlined in green, layer 1)
[001]
Cut through cubic unit cell
3
1
[-1,1,0]
1
1
2
02
2
0
0
1c
1
1
surface unit
cell P(1x1)
[010]
1
1
[100]
As atoms
top layer
Ch120a-Goddard-L09
[110]
Ga atoms
top layer
[001]
[-1,1,0]
© copyright 2011 William A. Goddard III, all rights reserved
8
Reconstruction of (110) surface, side view along [-1,1,0]
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
54.7º
54.7º
As
Ga
54.7º
[110]
Si (110)
[001]
Ch120a-Goddard-L09
GaAs (110)
© copyright 2011 William A. Goddard III, all rights reserved
9
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
Ga
As 54.7º
54.7º
Top view
(from [-1,-1,0])
[001]
[-1,1,0]
Ch120a-Goddard-L09
[1,1,0]
side view
[001] (along [-1,1,0])10
© copyright 2011 William A. Goddard III, all rights reserved
Reconstruction of (110) GaAs
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© copyright 2011 William A. Goddard III, all rights reserved
11
III-V reconstruction dominated by local valence
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
12
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
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
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
16
4
Analysis of charges
Bulk structure: each As has 3 covalent bonds and one Donoraccepter 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
0
Ga
3/4
1
5.25e
2.75e
2
As
0
Ga
1
1
3/4
5/4
3/4
3/4
3/4
5/4
a
1
5/4
3/4
5/4
g
5/4
Ch120a-Goddard-L09
1
3/4
5/4
5/4
a
1
Net Q =0
2
As
1
1
5/4
3/4
g
3/4
5/4
0
Ga
1
3/4
5/4
a
1
3/4 III, all rights reserved
© copyright 5/4
2011 William A. Goddard
5/4
3/4
5/4
5/4
2
As
3/4
g
3/4
3/4 17
GaAs (100)
As
As
ga
As
ga
As
ga
As
As
ga
As
As
ga
As
As
As
ga
As
ga
As
Ch120a-Goddard-L09
As
ga
As
ga
As
ga
As
ga
As
ga
As
ga
As
As
ga
As
ga
As
ga
As
ga
As
ga
As
Start with As at
surface, denote
Ga on 2nd layer as
ga.
As
Then top layer is
pure As. Not
stable, get net
negative charge at
surface.
As
If cut off top layer,
get pure Ga on
surface
© copyright 2011 William A. Goddard III, all rights reserved
18
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)
Ch120a-Goddard-L09
1st Layer 
2nd Layer 
3rd Layer 
th Layer 
© copyright 2011 William A. Goddard4III, all
rights reserved
RED
GREEN
ORANGE
WHITE
19
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
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
20
Charges for 2x1 GaAs(100)
2nd layer ga
has 3 e
1
2
1
5/4
2
2nd layer, ga
5/4
3/4
3/4
3/4
3/4
3/4
3/4
3/4
3/4
5/4
2e As-ga
bond
1
2
2e As LP
5/4
3/4
3/4
1st layer As
has 5.5 e
Top layer, As
3/4
Ch120a-Goddard-L09
1
5/4
3rd layer, as
2
5/4
Each surface
As has extra
3/4
0.5 e  dimer
3/4
3/4 has extra 1e
2e As-As
3/4
Not stable 21
© copyright bond
2011 William A. Goddard III, all rights reserved
3/4
Now consider a missing row of As for GaAs(100)
1
5/4
1
Top layer, As
2nd layer, ga
5/4
3/4
3/4
3/4
3/4
3/4
0
ga empty
LP
3/4
0
3rd layer, as
2nd layer ga
has 2.25e
0
3/4
1st layer As
has 5.5 e
3/4
Ch120a-Goddard-L09
Each 2nd layer ga
next to missing
0
As is deficient by
3/4
0.75e extra 0.5 e
3/4
3/4
 4 ga are
3/4
22
missing
© copyright 2011 William A. Goddard III, all rights
reserved 3e
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
Ch120a-Goddard-L09
Extra 1e
Extra 1e
missing 3e
© copyright 2011 William A. Goddard III, all rights reserved
23
Different views of GaAs(100)4x2 reconstruction
-1.0e
Previous page, 3
As dimer rows
then one missing
Ch120a-Goddard-L09
+1.5e
Two missing As row
plus missing Ga row
Exposes 3rd row As
Agrees with experiment
Hashizume
PhysIII,Rev
B 51,
4200
© copyright
2011 Williamet
A.al
Goddard
all rights
reserved
(1995)
24
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
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
25
Start with As at
surface, denote
Ga on 2nd layer as
ga.
GaAs (111)
As
ga
ga
As
ga
As
ga
As
ga
As
As
ga
As
AsThen top
Aslayer is
ga
ga
gaAs. Not
ga
pure
stable, get net
As
As
As
As at
negative
charge
ga
ga
ga
surface.ga
top layer, to
AsCut off As
getga
pure Ga on
ga
ga
ga
ga
ga
surface, but break
As
As
As
3As
bonds. Thus
As
As
As get
ga
ga As at front
ga
ga
ga
ga always
but back slab is
As
As
As
As
As Ga As
ga
ga
ga
ga
ga
ga
ga 26
Ch120a-Goddard-L09
© copyright 2011 William A. Goddard III, all rights reserved
As
As
As
As
Intrinsic semiconductors
+
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Excitation energy
-4.0 eV relative to vacuum=-IP
Energy gap = 1.1 eV
-5.1 eV relative to vacuum = -EA
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© copyright 2010 William A. Goddard III, all rights reserved
28
To be added – band states
Ch120a-Goddard-L09-10
© copyright 2010 William A. Goddard III, all rights reserved
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To be added – band states
Ch120a-Goddard-L09-10
© copyright 2010 William A. Goddard III, all rights reserved
30
Semiconducting properties
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Semiconducting properties
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Ch120a-Goddard-L09-10
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Ch120a-Goddard-L09-10
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35
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
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© copyright 2010 William A. Goddard III, all rights reserved
36
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
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
Ch120a-Goddard-L09-10
© copyright 2010 William A. Goddard III, all rights reserved
38
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
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© copyright 2010 William A. Goddard III, all rights reserved
39
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.
40
Ch120a-Goddard-L09-10
© copyright 2010 William A. Goddard III, all rights reserved
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
Ch120a-Goddard-L09-10
© copyright 2010 William A. Goddard III, all rights reserved
41
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
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© copyright 2010 William A. Goddard III, all rights reserved
42
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Ch120a-Goddard-L09-10
© copyright 2010 William A. Goddard III, all rights reserved
44
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
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© copyright 2010 William A. Goddard III, all rights reserved
45
Substitute As for Se or Ge
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© copyright 2010 William A. Goddard III, all rights reserved
46
Substitute Ga with Zn or Ge
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© copyright 2010 William A. Goddard III, all rights reserved
47
Dopant levels for GaAs
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© copyright 2010 William A. Goddard III, all rights reserved
48
Cohesive energies and Bonds for III-V compounds
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© copyright 2010 William A. Goddard III, all rights reserved
49
Compare IV to III-V same row
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50
n + p materials
n type
p type
CBM
CBM
Efermi
Efermi
VBM
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VBM
© copyright 2010 William A. Goddard III, all rights reserved
51
np junction
p type
n type
Efermi
CBM
CBM
Efermi
VBM
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