表 面 物 理 学
江颖
量子材料中心
E. G. Wang
第六课:
表面热力学和动力学
E. G. Wang
本课内容提要：
(一)：表面热力学
表面热力学基本方程
表面张力和表面应力
晶体的表面能和平衡形状
表面的生长模式
(二): 表面动力学
表面生长动力学
表面二维岛的生长
表面二维和三维岛的退化
E. G. Wang
化学中的热力学和动力学
•
将化学反应应用于生产实践主要有两个方
面的问题：
1. 了解反应进行的方向和最大限度以及外界条
件对平衡的影响。
2. 知道反应进行的速率和反映的历程（即机
理）。
•
人们把前者归属于热力学的研究范围，把
后者归属于动力学的研究范围。
E. G. Wang
第一部分： 表面热力学
Josiah Willard Gibbs (1839-1903)
E. G. Wang
前面主要讨论了“静止”表面的结构。这一节
将从宏观角度，运用平衡热力学基本理论研究晶
体表面的各种热现象。
研究宏观热现象的基本方法，是在实验的基
础上，用能量的观点研究温度对表面结构和表面
性质的影响。以平衡态的统计热力学理论为基础，
研究表面热现象及各种特征参数之间的关系，探
讨有关表面热力学、表面物理化学过程的基本规
律。
E. G. Wang
Kinetic Processes and Surface in Equilibrium
Surface is no static system. The characteristic bonding energy of
an atom at a special site and the energy barriers between such sites
determine the probability for adsorption, desorption and diffusion of
atoms at a given temperature.
Fig. 1. Schematic representation of fundamental atomic processes occuring
during epitaxial growth.
E. G. Wang
Principle of detailed balance
In the thermodynamic equilibrium all surface processes proceed in
two opposite directions at equal rates according to the “principle of
detailed balance”. Detailed balance means that the rate constants
for the forward direction, rf, and the backward direction, rb, of a
process satisfy the relation：
rf /rb = exp(-ΔE/kBT),
where ΔE is the energy difference between the initial and final
states. Processes, such as adsorption and desorption, decay and
formation of islands, etc. must obey the detailed balance.
A surface after stopping growth for while at not too high
temperature can be considered to be in thermodynamic equilibrium
with the substrate and the surroundings, e.g., the rest gas.
Crystal growth is clearly related to non-equilibrium kinetic
processes. Yet the “principle of detailed balance” is still fulfilled.
E. G. Wang
Internal energy(内能):
U = U(S,V,N)
dU =(U/ S)V,N dS + ( U/V)S,N dV + ( U/N)S,V dN
dU = T dS – P dV + μ dN
The extensive property of the internal energy:
U(λ S, λ V, λ N) = λ U(S,V,N)
U=TS–PV+μN
S dT – V dP + N d μ = 0 (Gibbs-Duhem 等式)
常用热力学函数:
Enthalpy(焓):
H = U + PV = T S + μ N
Helmholtz free energy (自由能):
F = U - TS = - P V + μ N
Gibbs 函数(Gibbs 自由能) ：
G = F + PV = μ N
Grand potential (巨势，自由能的差) Ω = F - G = - P V
E. G. Wang
1
表面的热力学基本方程
U=TS–PV+μN
For equilibrium system:
T, P, μ are identical in different phases,
S = S1 + S2 + Ss
V = V1 + V2 + Vs
N = N1 + N2 + Ns
U=TS–PV+μN+γA
γ = (U/ A)S,P,N
-surface tension
(表面能也称作表面张力)
Enthalpy(焓):
H = U + PV = T S + μ N + γ A
Helmholtz free energy (自由能):
F = U - TS = - P V + μ N+ γ A
Gibbs 函数(Gibbs 自由能) ：
G = F + PV - γ A = μ N
Grand potential(巨势，自由能的差): Ω = F - G = - P V+ γ A
E. G. Wang
2
吉布斯定义的表面位置:
V = V1 + V2
N = ρ 1V1 + ρ 2V2
In comparison to the total number of
particles we have Ns = 0 & Vs=0
Enthalpy(焓):
H = U + PV = T S + μ N + γ A
Helmholtz free energy (自由能):
F = U - TS = - P V + μ N+ γ A
Gibbs 函数(Gibbs 自由能) ：
G = F + PV - γ A = μ N
Grand potential(巨势，自由能的差): Ω = F - G = - P V+ γ A
Gs = 0
Ω = Ω 1 + Ω 2 + Ω s= - P (V1+V2)+ γ A
Ω s= γ A
E. G. Wang
表面张力 = 表面应力？
Surface tension
Surface stress
液体：Yes！
固体：No！
E. G. Wang
σ
U=TS–PV+μN+γA
γ = (U/ A)S,V,N
dU = A Σij σij dεij
ε
Surface stress
(应力张量)
Linear elasticity theory
Surface strain
(应变张量)
dU = T dS + S dT– P dV – V dP + μ dN + N dμ + γ dA + A d γ
dU = T dS – P dV + μ dN + A Σij σij dεij
S dT– V dP + N d μ + γ dA + A d γ - A Σij σij dεij = 0
dA /A = Σ d εij δij
A d γ + S dT– V dP + N d μ + A Σ ( γij δij - σ ij ) d ε ij = 0
A d γ + (S1+S2 +Ss) dT– (V1 + V2 + Vs)dP + (N1 + N2 + Ns) d μ + A Σ ( γij δij - σ ij ) d ε ij = 0
Si dT – Vi dP + Ni dμ = 0; i=1,2
E. G. Wang
(Gibbs-Duhem 等式)
A d γ + Ss dT– Vs dP + Ns d μ + A Σ ( γij δij - σ ij ) d ε ij = 0
- Gibbs 吸附方程
A d γ + Ss dT– Vs dP + Ns d μ + A Σ ( γ ij δij - σ ij ) d ε ij = 0
- Gibbs 吸附方程
V = V1 + V2
N = ρ 1V1 + ρ 2V2
In comparison to the total number of
particles we have Ns = 0 & Vs=0
E. G. Wang
γ = γ(ε,T)
Ss = -A(γ/T)ε
σij = γδij+ ( γ / εij)T
A special example is liquid surface where the surface
atoms is free to rearrange themselves: σ = γ
若：  γ / ε< 0
E. G. Wang
Equilibrium Shape of Small Crystals
Anisotropy of Surface Energy
The surface free energy per unit area, γ, of a certain crystal
surface varies with its crystallographic orientation
characterized by the surface plane (hkl) or the surface normal
n, i.e., γ=γ (hkl) or γ=γ(n).
晶体达到平衡时，其表面能为各晶面表面能的总和：
∑ γ (hkl) dAhkl
若以θ表示晶面的方向角，则表面能γ随方向角θ的不同而改变。根据表面能
的方向性推测晶体的平衡形状，最成功的方法是Wulff作图法。经过数学上
的严格证明，这一方法得到了公认。
3
E. G. Wang
Fig. 3 shows the orientation dependence. Its nominal (1n) surface (n>>1) represents a vicinal (01)
surface. It consists of a high number of (01) terraces separated by atomic steps of height a. With
θ~1/n as the angle of orientation of [1n] against the [01] orientation, the step density is given as
tan θ/a. If βs is the energy per step and γ(0) is the energy of a (01) face, the surface energy of a (1n)
surface is
γ(θ) = cosθγ(0)+βs(sinθ/a)
The prefactor cosθ guarantees that the relative amount of the (01) terraces to the total surface
area reduces with increasing angle θ. The interaction of steps has been neglected here. The
increase of the angle from θ=0 to large values is accompanied by an increase of the step density.
A proper expression for γ(θ) must hence include the interaction between steps.
Fig. 3 A (1n) surface, which is slightly misoriented from the (01) surface.
E. G. Wang
E. G. Wang
Wulff Construction
Wulff Theorem: The equilibrium crystal shape (ECS) at constant temperature T with
fixed volume V and chemical potential μ is determined by the minimal excess
surface free energy with respect to the surface A
Fs = A(V)γ(n)dA
Subject to the constraint of fixed volume V = V(A)dV.
The theorem states that the ECS is not necessarily that of the minimum surface
area. It may be a complex polyhedron with the lowest total surface energy for a
given volume. In the case of crystals the variation of γ with the normal n will
produce, on each surface element dA, a force proportional to ∂γ/∂n, which will tend
to alter its direction at the same time as γ tends to shrink its area.
A minimal surface only occurs for a perfectly spherical Wulff plot, i.e., an isotropic
excess surface free energy. The corresponding ECS is a sphere.
E. G. Wang
Wulff作图法
表面能是一标量，为了表示其与晶面方向的相关性，引入一矢
量 ,矢量的方向为晶面的法线方向，其长度正比于表面能数值。因
此， (hkl)即为表面能γ (hkl) 的矢径。
E. G. Wang
Fig.9 A polar plot of the
surface free energy for a
2D crystal (solid line) and
the ECS based on the
Wulff construction (dotted
line).
The higher the γ(n), the smaller the corresponding surface. In theoretical (table 2.1),
γ(111)<γ(311)<γ(100)<γ(110), so (110) surface is negligible.
Fig.10 Equilibrium shapes of a Si crystal based on the Wulff construction using (a) exp.
values or (b) theo. values. (100), (311), (110), and (111), from black to white, surface
orientations are considered. (Surface energies from Table 2.1).
E. G. Wang
Surface Energy and Morphology
Facetting and Roughening
The surface buckling happens on a mesoscopic length scale (large than atomic
distances). For a small buckling surface, we have
F’s = A’γ(θ)dA’ = Aγ(θ)dA/cos (θ)
The assumption of a weak variation of γ withθyields an expansion of the integrand
up to second order,
F’s = γ(0)A + Adγ/d θ | θ=0 + ½ A θ 2[γ(0)+ d2γ/d θ 2 | θ=0 ]dA
The first term gives the energy of the flat surface. The second one vanishes for
symmetry reasons. The third term gives the energy due to surface buckling. For γ(0)
+ d2γ/d θ 2 | θ=0 >0, the flat surface is stable (or at least metastable), for its <0, the
buckling surface is more stable.
Fig.11 Small buckling of a
surface.
E. G. Wang
表面上薄膜生长的三种典型模式
层状生长
E. G. Wang
岛状生长
SK 生长
γs -the surface free energy of substrate-vacuum interface
γo - the overlayer-vacuum interface
γs/o - is the substrate-overlayer interface
The equilibrium of the forces holds as
γs = γs/o + γo cosφ
with φ as the angle between the overlayer-vacuum face and the substratevacuum face. Set
Δγ= γs/o + γo – γs
For Frank-van der Merve (2D) mode, we have Δγ  0 with φ = 0;
For Volmer-Weber (3D) mode, we have Δγ > 0 with φ > 0;
For Stranski-Krastanov mode, we have Δγ  0 the first atomic layers (wetting
layer) and Δγ > 0 for the islands.
E. G. Wang
第二部分：表面动力学
E. G. Wang
一般来说，上述表面热力学理论只
能描述处于平衡状态下的表面形貌，
而在实际的薄膜生长过程中，体系往
往是处于非平衡状态，这时候则需要
用非平衡动力学的观点来描述。
E. G. Wang
3D Versus 2D Growth
In thermodynamic equilibrium, there is no net growth. The crystal
growth must be a non-equilibrium kinetic process. The resulting
macroscopic state of the system depends on the reaction paths in
the configuration space. Since the result is kinetically determined,
the obtained state is not necessarily the most stable one.
E. G. Wang
The thermal stability of the Al thin films
Initial surface
2.4ML (300nm x 300nm)
24 hours later( 500nm x 500nm)
Thermally annealed (RT) Al film develops various heights enabling
the comparison of the relative stability of islands with different
heights
E. G. Wang
动力学
• Kinetics is a concept only involved with the
movement of objects.
• Dynamics focuses on the forces and their
effects.
• In certain point of view, we can say kinetics
only deals with the motions of objects, and
dynamics with the reason why and how they
moves.
E. G. Wang
表面动力学
• We can consider the growth on the surface as a
kind of chemical reaction.
• Kinetics: the influence of external macroscopic
variables on the overall reaction rate
(temperature, pressure, relative concentration)
• Dynamics: the detailed atomic motions that
characterize an elementary act of reaction.
• Sometimes these two terms are not
distinguishable.
E. G. Wang
Generic Understanding of Growth
Growth, by definition, is nonequilibrium in nature, and in
many cases is far from equilibrium.
A specific growth mode is selected by the interplay between
thermodynamics and growth kinetics.
Thermodynamics
Kinetics
(various atomic rate processes)
Atom Dynamics
A: formation of a surface vacancyadatom pair,or their recombination.
B: association or dissociation of
adatoms with an atomic cluster &
cluster diffusion.
C: diffusion of a surface
vacancy ,especially toward the lattice
step.
D: falling off a lattice step of an adatom.
E: diffusion of an adatom & its long range interactions with other adatoms.
G: diffusion,dissociation & activation of a ledge atom.
H: dissociation & activation of a kink atom.
• 实验表明，参与表面各种原子过程的原子
扩散能力可以用表面扩散系数来描述。表
面扩散系数与扩散原子的跳跃几率有关,可
以表示为:
• 这里D0 是尝试频率 (1012-1013), Vs 是能量势
垒, kB 是玻耳兹曼常数, T 是温度。
E. G. Wang
表面原子的扩散
-长程跳步 (jump over long distance)
原子每次跳步的距离为晶格常数的整数倍， 即原子每次跳
步的长度大于一个最近邻位。
-交换扩散机制
跳步扩散 (hopping)或替换扩散(exchange)。替换扩散机制产
生的物理原因是由于系统应保持沿扩散路径的断键数目最少。
初态
跳步扩散
替换扩散
过渡态
末态
Philosophy
If we can establish EVERY correspondence between
Atomic Rate Process
Morphological Evolution
then in principle we should be able to select a preferred growth
mode via precise control of the various rate processes.
Two growth models
- Step flow growth
Burton et al, Phil. Trans. R. Soc. London Ser. A 243 299(1951)
台阶指的是两层台面(terrace)之间的边界，沿着晶体某一指数
面切割表面通常都会在表面产生台阶，这种含有台阶的面叫做邻
面(vicinal surface)。由于表面上原子的吸附能力强烈地依赖于吸附
位的最近邻原子数，而位于台阶处的原子比位于表面上的原子具
有更多的配位数，因此沉积原子与台阶的键合更强。这一理论假
定在邻面上，如果沉积原子运动速率较高，在新的沉积原子到来
之前基底上已有的扩散单原子就能够到达台阶处并与之结合。这
样一来，通过沉积原子和台阶的键合使台阶不断前进，从而使生
长连续进行，这种生长叫做模式叫做step flow模式 。较高温度和
较低的沉积速率时更容易造成形成这种生长模式。
(沉积原子运动快)
Two growth models
- 形核和成岛生长模式
一般薄膜的生长温度较低，这样沉积原子在基底上的运动较
慢，在新的沉积原子到来之前基底上的原子不能运动到台阶处。
这些沉积原子就会在表面（台面）上游走，在原子行走过程中，
如果能碰到同类原子，它们便结合在一起，形成原子团。如果这
个原子团满足一定的能量关系，就会增加它们在基底表面上的居
留时间，就有与其它原子集结的更大几率，这就是成核。成核以
后形成的原子团并不是稳定的，还存在原子团的离解过程。只有
在一定条件下满足一定的能量关系，原子团才不再离解，随外来
原子加入或热处理，原子团不断长大。这个一定数量原子构成的
原子团即为前述的临界核。达到临界核以后，若继续入射原子到
达基底表面，那么原子团不断长大成粒子簇，即岛。这样生长就
会通过岛的长大,结合方式进行。
临界尺寸
在经典成核理论中，一个晶核的形成主要取决于Gibbs自由能
的变化量。随着晶核尺寸的增加，会出现一个临界晶核尺寸nc，
使得Gibbs自由能的变化量取极大值。小于这个尺寸的晶核随着粒
子数的增加Gibbs自由能的变化量不断增加，晶核长大的几率比退
化的几率小，是不稳定晶核；相反，大于这个尺寸的晶核，随着
粒子数的增加Gibbs自由能的变化量不断下降，晶核长大的几率比
退化的几率大，是稳定晶核，如图
所示。在数学上，临界晶核尺寸可
以这样确定:
G(n)
0
n nnc
临界尺寸
在二维亚单层生长中，假定已知临界尺寸为i, 由速率方程可
以导出标度关系
这里N是总的岛密度，D是原子在基底表面上的扩散速度，F是沉
积速率，Ei是键能，i是临界尺寸。运用方程， 通过实验测量就可
以推导出微观参数。比如，测量岛密度随沉积流量的变化规律，
可以得到临界尺寸大小i ， 再测量岛密度随温度的变化规律，那
么由已知的i , 就可以得到扩散势垒Ed和前因子D0的大小。Monte
Carlo模拟和实验上都已经证实了标度关系的存在。
休息15分钟
E. G. Wang
亚单层生长时表面上典型的二维岛
当沉积流量F=0.167ML/s,
覆盖率Θ=0.12ML时, 在
Ag/Pt(111)系统中得到的二维
岛STM像。 (a)=110K,
(b)=280K 。
Diffusion-Limited Aggregation
( DLA )
Witten and Sander, Phys. Rev. Lett.47, 1400 (1981)
Citation > 3700
Nucleation without surfactant
Diffusion-Limited-Aggregation (DLA)
Hit and Stick
岛的平均分支宽度 b
(average brach thinkness)
为1个原子宽度 ( b≈1)。
Witten and Sander, Phys. Rev. Lett.47,
1400 (1981)
Nucleation without surfactant
Extended Diffusion Limited Aggregation
Adatoms can relax
along island edges.
这时候沉积原子会沿着岛
边缘扩散，稳定位置是近邻原
子数大于等于2的位置。 在三
角格子上，就会得b为4个原子
宽度的分形岛; 在正方格子上
不存在这个生长区域。
Zhang, Chen, and Lagally, Phys. Rev. Lett.73,
1829 (1994)
Corner Crossing (Irriversible case)
No Corner Crossing
Corner Crossing
Zhong, Zhang, Zhang, Lagally, PRB 63, 113403 (2001)
“Rules of Thumbs”
Based on atomistic mechanisms
Increase of the degree of local
relaxation will lead to a fractal to
compact transition
Either through
Growth temperature
Or
Deposition flux
二维原子岛退化与动力学标度理论
E. G. Wang
Evolution of 2-Dimensional Nanostructures
Power-law Scaling:
A  (t0  t )2 
A: island size
: scaling exponent
t: time
Gibbs-Thomson Formula:

eq
r
  
  exp 

rk
T
 B 
eq

Two limiting cases:
 Diffusion-limited:
 = 1/3
 interface transfer-limited:
 = 1/2
J. G. Mclean, et. al, Phys. Rev. B 55, 1811 (1997).
E. G. Wang
Transition from 1D to 2D Island Decay on
Aniosotropic Surfaces
X , Y  (t0  t ) 
a:  = 0.33 (X direction)
 = 0
(Y direction)
b:  = 0.33 (X direction)
 = 0.33 (Y direction)
Morgenstern等用变温STM细致地研究了二维岛Ag在各向异性表面Ag(110)的退化。他们发现
当温度在175-220K时，观测到准一维的退化行为(a)；而在大约220K左右，体系由准一维退化
转变到二维退化(b)。从图(a) 和图(b) 可以明显地看出在不同温度区域内，岛的退化行为明显
不同。图(c) 显示体系的退化表现出很好的标度行为。根据已有的标度理论的结果，他们用
=0.33的标度率来拟合实验结果。图4.1中的实线为拟合曲线。似乎拟合曲线与实验结果符合
较好，但是事实上在低温区域中，沿x方向盘的退化标度指数不等于0.33，而应该是1/2。
E. G. Wang
Theoretical Model
Island Decay on Anisotropic Surfaces
Dy
Dx
y
Ky
Kx
2Ly
The outer
boundary
x
2Ry
Kox
2Lx
Koy
2Rx
在各向异性表面上二维岛的示意图。下标x和y分别表示不同的方向。  x 和
表示岛的线张力，Kx，Ky是原子在岛边的动能系数，Dx和Dy分别表示沿x和y
方向的扩散常数，Kox和Koy表示原子在外边界的动能系数。
E. G. Wang
y
Scaling Properties of Island Decay
on Anisotropic Surfaces
Low Temperature Regime:
Diffusion Limited
Attachment-Detachment Limited
Lx  (t0  t )
1/ 2
Ly  const.
High Temperature Regime:
Diffusion Limited
Attachment-Detachment Limited
E. G. Wang
Lx  (t0  t )1/ 3
Lx  (t0  t )
1/ 2
Theory contrast Experiments
Theoretical
Scaling exponent
Anisotropic :
1/2
Isotropic :
1/3
E. G. Wang
Quasi-1D and 2D Decay of
Islands on Anisotropic Surfaces
Quasi-1D (Low T regime)
disappear
y
2D (High T regime)
x
E. G. Wang
Scaling Low of 2D Island Decay
X , Y  (t0  t ) 
Symmetry of
Surface
Decay Mode
Diffusion Attachmentlimited
Detachment
limited
Isotropic
2D Decay
1/3
1/2
Anisotropic
Quasi-1D Decay
(low T)
1/2
1/2
1/3
1/2
Anisotropic
E. G. Wang
2D Decay
(high T)
ES势垒对原子扩散的控制及反常ES势垒效应
E. G. Wang
2D ES barrier
Ehrlich & Hudda, J. Chem. Phys. 44, 1039 (1966).
Schwoebel & Shipsey, J. Appl. Phys. 37, 3682 (1966).
E. G. Wang
Ehrlich-Schwoebel (ES) Barrier
ES barrier:
An additional potential
energy barrier against
the descent of atoms at
step edges.
The barrier primarily controls interlayer mass transport.
Low ES barrier results in smooth films, whereas high ES
barrier results in rough films.
E. G. Wang
Islands Decay
Time (s)
Ag/Ag(111)
S. J. Chey, et al.
Surf. Sci. 419, L100
(1998)
E. G. Wang
Time (s)
Time (s)
Cu/Cu(111)
Cu/Cu(100)
M. Giesen, et al.
PRL 80,552(1998)
Maozhi Li, et al.
PRL 86,2345(2001)
Two Categories of Interlayer Mass Transport Mechanisms
Li et al., Phys. Rev. Lett. 86, 2345(2001)
ASD
SSD
Any-Site Descent
Mechanism
Selective-Site Descent
Mechanism
Kinked site
Straight step
E. G. Wang
ASD Mechanism: initially equal terraces
Start:
13,000 atoms in 7 layers
equal terrace widths
#1
#7
Time = 0 s
T2
T4
T6
Time = 120 s
vd = 0.65 eV
vt = 0.35 eV
vs = 0.43 eV
vsk = 0.40 eV
@T=400 K
E. G. Wang
ASD Mechanism: initially unequal terraces
T1
T3
T5
Time = 0 s
T3 T4
T5
T6
Time = 600 s
T3
T4
T5
T6
T=400 K
E. G. Wang
Time = 900 s
SSD Mechanism: initially equal terraces
Start：:
6,000 atoms in 5 layers
equal terrace widths
#1
#5
Time = 0 s
Time = 2.0x104 s
vd = 0.80 eV
vt = 0.43 eV
vs = 0.62 eV
vsk = 0.52 eV
@T=400 K
E. G. Wang
fcc(111) and fcc(100)
Li et al., Phys. Rev. Lett. 86, 2345(2001)
island decay on
fcc(111) surfaces
Small energy
barriers
ASD mechanism
Vs=0.43 eV,Vsk=0.40 eV
constant slope
equal terrace widths
fcc(111)
Slope becomes steeper
fcc(100)
Vs=0.62 eV,Vsk=0.52 eV
island decay on
fcc(100) surfaces
E. G. Wang
large energy
barriers
SSD mechanism
fcc(111) and fcc(100)
Li et al., Phys. Rev. Lett. 86, 2345(2001)
island decay on
fcc(111) surfaces
Small energy
barriers
ASD mechanism
Vs=0.43 eV,Vsk=0.40 eV
constant slope
equal terrace widths
fcc(111)
Slope becomes steeper
fcc(100)
Vs=0.62 eV,Vsk=0.52 eV
island decay on
fcc(100) surfaces
E. G. Wang
large energy
barriers
SSD mechanism
fcc(111) and fcc(100)
Li et al., Phys. Rev. Lett. 86, 2345(2001)
island decay on
fcc(111) surfaces
Small energy
barriers
ASD mechanism
Vs=0.43 eV,Vsk=0.40 eV
constant slope
equal terrace widths
fcc(111)
Slope becomes steeper
fcc(100)
Vs=0.62 eV,Vsk=0.52 eV
island decay on
fcc(100) surfaces
E. G. Wang
large energy
barriers
SSD mechanism
Observed Rapid Decay at T=300 K
“Avalanche Mechanism”
Cu/Cu(111)
Cu/Cu(100)
Site independent
Site dependent
“Robust Model”
(J. F. Wendelken @ ORNL)
E. G. Wang
Concluding Remarks
All adatoms are very busy moving around on
surface in all possible
possibledirections.
directions.
As we learn more and more about the growth
kinetics, we can eventually devise ways to
manipulate atomic motion and dictate on how
they should behave collectively to please us.
Searching for counter-intuitivity ！
E. G. Wang
参考书：
1. F. Bechstedt, Principles of Surface Physics, Springer-Verlag,
2003.
2. M. C. Desjonqùeres and D. Spanjaard, Concepts in Surface
Physics, Springer-Verlag, 1996.
3. Zangwill, Physics at Surfaces, Cambridge, 1998
4. 黄昆，固体物理，高等教育出版社
5. 王恩哥，薄膜生长中的表面动力学（I，II），物理学进展，
Vol.23, 2003
6. 吴自勤、王兵，薄膜生长，科学出版社，2005
E. G. Wang
下一节课
分组讨论：1，2，3，4
每组20分钟，10分钟提问
E. G. Wang
谢谢！
E. G. Wang