表面重构课_薛其坤

4.1 Metal Surface
Although most metal surfaces are relaxed instead of recosntruction, some noble and near-noble fcc metals, Au, Ir, Pt and bcc transition metals, W and Mo, display recosntructions.
Trimer
2.3 Adatoms
[111]
[112]
often on (111) surfaces
[110]
[112]
4. Typical reconstruction surfaces
4.1 Metal Surfaces 4.2 Insulator Surfaces 4.3 Semiconductor Surfaces
Why 原子间的键合
（1）Surface: heterogeneous at microscopic scale （2）Surface processes: adsorption/desorption,
diffusion, reaction……
外来原子与表面原子的相互作用/键合
金属键 共价键（Si，Ge，GaAs/InAs/AlAs, GaN, ZnO…） 离子键（MgO, Al2O3, NaCl…)
Principle 2. A surface tends to compensate charges.
Vacancy reconstruction on GaAs(111)2x2
Principle 3. A semiconductor surface tends to be insulating (or semiconducting).
chains
[110]
(111) surfaces of diamond, Si, Ge
have this kind of chains.
[112]
[111]
[112]
(111)-2x1
Band structure of -bonded chain model
Using NN approximation of TBA, considering the DB interaction
Atomic orbitals along the bonding direction
sp3杂化 sp2杂化 sp杂化
(1)同原子内轨道相互作用
A 1
sp3
(1B)
2A
(2B)
^4
a
h
A
5
b
6
Hirabayashi, J. Phys. Soc.
Charles B. Duke
STM on III-V (100) Surface Reconstructions Xue et al.,
Progress in Surface Science 56, p001-p131(1997)
Element semiconductor surface
Si(100) industry Si(111) cleaved Ge(111) Ge(100)
a
i
a
(x–Ri
)
( )( ) H11 –
H12 – S12
H*11 – S*12 H22 –
1 2
=0
LiH
s(H)
s(Li)
Atomic Orbitals and Their Interaction
AN B8-N
三个假定：
（1） s, Px , Py and Pz
（2） Sab(Ri –Rj )=abij
孤立分子中原子间的成键 固体中原子间的成键
化学键
a p
h
s
b
局域化学键的角度去理解晶体中原子的键合
Orbitals and Bonding
One-Electron Picture
1023-body problem
两个轨道间的成键 双原子分子（H2或者LiH）

(x)
=
a,i
（3） 最近邻和次近邻相互作用 ，
且 Hab(Ri, Rj )= Hab(Ri–Rj )
d=Ri–Rj
n n
p
n d
Löwdin Theorem：Sab(Ri –Rj )=abij
Interatomic Matrix Elements
Vss
Vsp
Vpp
Vpp
Vabk=
abk
Si(111)-2x1 → 7x7 by annealing Ge(111)-2x1 → c(2x8) by annealing
Both of the above are stable upon subsequent cooling indicate that the first 2x1 structure obtained by low-temperature cleavage is only a local stable structure, but not the lowest freeenergy structure which is obtained for both surfaces by annealing and subsequent cooling. In the two processes, high temperature is necessary to overcome the energy barrier between different structure and to generate the adatoms in the lowest free-energy structure.

(k)
1 2
(1

2
)

[
1 4
(1
2 )2

~
V
2
21
S(k) ]2
V~ =H12(d1)+H12(d2)
S(k) =i eikdi
two surface bands
( H11 – H*12
)( ) H12
H22 –
1 2
=0
LöwdinTheorem：Sab(Ri –Rj )=abij
Hebenstreit et al.,Phys. Rev. Lett. 85, 5376(2000)
C(100)-2x1
Bobrov et al., Natrue 413, 616(2001)
4.3 Semiconductor Surfaces
Chem. Rev. 96, 1237-1259 (1996)
表面重构
清华大学物理系 薛其坤
Outline
1. Brief introduction
Bonding at a surface
2. Principle of Surface Reconstruction
3. Reconstruction Elements
3.1 Chains 3.2 Dimers (trimers) 3.3 Adatoms
4. Typical reconstruction surfaces
4.1 Metal Surface 4.2 Insulator Surface 4.3 Semiconductor Surface
5. Summary
1. Brief introduction
Two types of atomic rearrangements
Relaxation Reconstruction
Wood：A(hkl)-nm--B
Examples
1. Si(111)-p2x2 2. Si(111)-3x3-30º-Ga 3. Si(100)-c(2x2)-O
常用的研究手段： LEED, RHEED, STM, 琼角XRD等
Bonding at a surface
K.Oura, V.G.Lifshits et al. <Surface Science-An Introduction>
4.2 Insulator Surfaces
NaCl (111)-1x1
(a) 50nm x 50 nm, 21.2 V, 0.06 nA.
(b) NaCl(111) island with atomic
(c) Structure model of an
resolution (7nm x 7 nm, 21.2 V, 0.3 nA). NaCl(111) island.
Reconstruction tend either to saturate surface dangling bonds via rehybridization or convert them into non-bonding electronic states which may be filled by a lone pair of electrons or be completely empty. Ge(111)c(2x8), C(100)2x1
Jpn. 27. 1475(1969)
Dangling Bonds
= cost 3
B
Si(111)
DB
A
问题：切断一个公价键时， 两个电子如何分配？
B
对电子态的影响
J K J’
2D wave vector
对电子态的影响
br=sp3 – 2 DB=sp3 + 2
(110)
Tilting of the dimers on Si(100) and Ge(100)
Electron Counting Model
费米能级以下的表面态必须全部占据
Bonding and non-bonding surface states
费米能级以上的表面态必须全部空着
non-bonding and antibonding states
2.2 Dimers
Tight-binding Hamiltonian:

~

H *

(k)


(
d

2 cos(k
a2 )V

e V i k dd

e i k ddV
)

~
d 2 cos(k a2 )V

a2 a0 2(0,1,0) dd dd (1, 0, 0)
J K J’
2D wave vector
2. Principle of Reconstruction
Basic Principle：
The surface structure observed will be the lowest free-energy structure kinetically accessible under the preparation conditions.
h2
md2
ss = 1.32 sp = 1.42 pp = 2.22
pp= 0.63
Slater and Koster, Phys. Rev. 94. 1498(1954)
Bonding Hybrids
Electrons are localized between atoms along the bonding direction
Three main principles
Principle 1. A surface tends to minimize the number of dangling bonds by the formation of new bonds. The remaining dangling bonds tend to be saturated.
Wöll et al. Phys. Rev. B 39, 7988-7991(1989)
Pt(110), Au(110)
1x2 missing-row reduces the surface energy.
T. R. Linderoth, S. Horch, E. Læ gsgaard, I. Stensgaard, and F. Besenbacher, PRL,78,4978
3. Reconstruction Elements
3.1 Chains 3.2 Dimers (trimers) 3.3 Adatoms
2.1 Chains
Zig-zag chains
Binary IV-IV(SiC),III-V and II-VI compound semiconductors have planar zig-zag chains of alternating cations and anions along a <-110> direction in their {110} surfaces