Transcript Topic 8 - ICQM PKU

硅烯
报告人：戴凝
同组成员：曹传午、骆佳伟、李新棋、牛佳森、苏唐
目录
⦁表面结构
⦁Si-Ag的表面结构（硅烯）
⦁硅烯的能带计算
表面结构
systems presenting a tendency to order
• 形成二维周期性的表面合金
Systems showing a tendency to phase separation
• 形成一层纯溶质层
Systems presenting a tendency
to order
The Si/Cu(110) was the first
prototype of semiconductor on
metallic surfaces
Room temperature (RT) deposition of silicon on Cu(110) surface
Change the thickness of Si :
0.1ML:
160×160 nm 2 STM image of the Cu(110)
surface after deposition of less than 0.1 Si ML at
RT. A step on Cu(110) is seen at the upper part of
the image. Alloy clusters are aligned along ⟨-112⟩
surface direction. The arrow indicates the ⟨-110⟩
surface direction
Room temperature (RT) deposition of silicon on Cu(110) surface
Change the thickness of Si :
0.5ML:
STM image of the Cu(110) surface after
deposition of 0.5 Si ML. Room temperature
(RT) deposition of 0.5 monolayer (ML) of silicon
on a Cu(110) surface leads to the formation of a
c(2 × 2) superstructure
Room temperature (RT) deposition of silicon on Cu(110) surface
Change the thickness of Si :
0.5ML:
Top view
Side view
The c(2 × 2) unit cell is shown in the
figure. Filled and empty circles
represent Si and Cu atoms.
Room temperature (RT) deposition of silicon on Cu(110) surface
Change the thickness of Si :
0.55ML:
0.55 Si ML on Cu(110). (a) A general view of the surface (33×28nm2), (b) Si
chains on c (2×2) surface alloy (15×7.5nm2), (c) individual Si chains (10 × 5
nm2), (d) Profile along the line represented in (c)
Room temperature (RT) deposition of silicon on Cu(110) surface
Change the thickness of Si :
0.8ML:
0.8 Si ML on Cu(110).
and posterior annealing
at 250 °C. (a) overview
of the surface (48×48
nm2), (b) detail of the
linear chains (6.2 × 6.2
nm2), (c) profiles along
the indicated directions
of (b)
Systems with tendency to phase separation
The prototype system for this case is Ge/Ag
presents a strong tendency toward phase
separation and a large germanium surface
segregation
studied by AES , LEED , STM , SXRD , PES
2.2.1 Ge/Ag(100)
The growth of Ge on Ag(100) at RT was found to be
close to the layer by layer mode
俄歇电子能谱
• 测定俄歇电子的能量从而获得固体表面组成等信息的技术。处于激发态的
原子可能发生两类过程。 一类是内壳层空穴被外壳层电子所填充,由此释放
出能量而产生X射线荧光。另一类是电子由外壳层落到内壳层，用所释放出
来的能量打出一个其电离势更低的轨道电子（通常为价电子）。后一个过
程称为俄歇过程,以发现此过程的法国科学家P.-V.俄歇命名，被打出来的电
子称为俄歇电子。用光或电子轰击固体表面，都能产生俄歇效应。
俄歇电子在固体中运行也同样要经历频繁的非弹性散射，能逸出固体
表面的仅仅是表面几层原子所产生的俄歇电子，这些电子的能量大体上处
于 10～500电子伏，它们的平均自由程很短，大约为5～20埃,因此俄歇电子
能谱所考察的只是固体的表面层。俄歇电子能谱通常用电子束作辐射源，
电子束可以聚焦、扫描，因此俄歇电子能谱可以作表面微区分析，并且可
以从荧光屏上直接获得俄歇元素像。它是近代考察固体表面的强有力工
具，广泛用于各种材料分析以及催化、吸附、腐蚀、磨损等方面的研究。
Part I illustrates an example of
the deposition of about one
monolayer of germanium and
Part II is the dissolution kinetics
in the bulk recorded for different
temperatures just after
deposition.
• The variations of Ag and Ge
Auger peak-to-peak
intensity ratio ( I Ge / I Ag )
versus time
• Part I : deposition (1 ML)
• Part II : thermal behavior
just after deposition
• Part II
• Both kinetics that are recorded at 250 and 264 ° C, show that at the
beginning of annealing, a rapid dissolution occurs followed by a blocking
of this dissolution on a plateau whose level depends on temperature.
• At 320 ° C, a rapid dissolution at the beginning of the kinetics is observed
followed by a slower one up to a quasi-complete dissolution
LEED test :
(i) a sharp and well defined p ( 4√2 × 2√2 ) R45 ° LEED pattern after dissolution at
250 ° C,
(ii) a fuzzy ( 1 × 1 ) LEED pattern after dissolution at 264 ° C,
(iii) a sharp ( 1×1 ) LEED pattern after dissolution at 320 ° C in good agreement
with the quasi complete dissolution observed on the kinetics.
0.5 ML
Ge tetramers
(a) Filled-state STM image of a 10 nm × 10 nm
area surface after deposition of 0.5 ML of
germanium at room temperature (the unit cell
is shown as a rectangle),
(b) Atomically resolved STM images.
The dissolution at 250 ° C gives rise to the same structure as
in Fig. 7a indicating the stability of Ge tetramers.
Ge tetramer vacancies
(a) Filled-state STM images of 20 nm × 20 nm
area of the Ag(001) surface recorded at room
temperature after a short annealing of the
sample at 260 ° C for a few
minutes. (b) The same filled-state STM image
for a 10 nm × 10 nm area.
0.5 ML
(a) STM images ( 50 nm × 50 nm ) of the
surface recorded after a further
annealing of the sample for 20 min maintained
at 260 ° C. (b) Magnification of the
figure to reveal the details.
a further 20 min annealing of the sample
maintained
at 260 ° C
Result
• existence of a plateau on a dissolution kinetics recorded by AES corresponds to a
specific surface structure.
• The Ge dissolution proceeds by successive disappearance of Ge tetramers
confirming the large stability of the latter on the Ag(001) surface.
2.2.2. Ge/Ag(110)
After deposition
of 0.5 Ge ML coverage, the LEED pattern
revealed a c ( 4 × 2 )
superstructure.
Empty state STM image (8
× 8 nm2
, V = 40 mV, I = 1 . 76 nA)
showing
the c ( 4 × 2 )
superstructure at atomic
resolution with two
tetramers in the surface
unit cell (rectangle). The
tetramer (circle) is clearly
noticeable.
Based on the STM images and SXRD
measurements, an atomic
model of the surface structure with Ge atoms
forming tetramer
nano-clusters that are perfectly assembled in a
two-dimensional
array over the silver top layer was proposed
2.2.3. Ge/Ag(111)
On the (111) surface, the LEED pattern shows a
(√3 ×√3 ) R30 °after deposition of 1 / 3 ML of Ge
(√3 ×√3 ) R30 ° LEED pattern ( E p
= 52 eV ) left-upper corner. Filledstate STM image (6 . 4 nm×6 . 4
nm, V = −50 mV, I = 2 . 0 nA). A
line scan along the [110]
direction gives the corrugation
shown in the lower-left corner.
a new c (√3 × 7 ) LEED pattern appears and
become sharper at 1 ML of Ge coverage
Filled-state STM images (3 × 3
nm2
, V = −0 . 005 V, I = 5 nA)
showing
the local arrangement within
the c (√3 × 7 ) superstructure
unit cell
four tetramers per c (√3 × 7 ) unit cell
The Ge 3d core levels of the (√3 ×√3 ) R30 °
was analyzed by PES
Using a Doniach–Sunjic line shape,
the Ge 3d spectra have been fitted with
two components (S1)
and (S2) at 28.80 and 29.07 eV binding
energies, respectively (in
the whole coverage range). The (S1)
component of the spectrum
is attributed to the (√3 ×√3 ) R30 °
superstructure. The (S2)
component, which is weak at low
coverage and increases markedly
beyond 1 / 3 ML, is assigned to the
growing second superstructure c (√3 × 7 )
Ge 3d core-level spectra recorded at normal
emission at a photon energy
of 65 eV during the growth
the open structure adopted by the germanium
atomsreveals the delicate balance between
metallic and semiconductorlike interactions.
On each face orientation it results from the
competition between the Ge–Ge interactions,
which tend to favor the most compact
tetramers,
while the Ge–Ag interactions can be
strong enough at the surface to favor the
formation of a surface alloy.
Si-Ag的表面结构（硅烯）
Silicene on Ag(100)
• Stripes
Silicene on Ag(110)
• ribbons
Silicene on Ag(111)
• Sheets
Experiments of silicone on Ag
• Si/Ag system demonstrates phase
separation with very low solubility unlike
Ge/Ag
• Si structure only forms on top of Ag
without diffusion
• Approaches: STM, LEED, SXRD…
1. On Ag(100)
• Growth at RT:
layer by layer, no ordered structure
• Growth (or annealing) at 230C
two ordered structure:
A: from the beginning to 1 mono layer
B : beyond one ML Si coverage
1. On Ag(100)
A
A p(3*3) superstructure
A tetramer composed by
two tilted Si dimers
B
2 superstructures:
P(7*4) & 2 joined
hexagon chains
2. On Ag(110)
Nanowires observed
Deposit Si in
UHV below 1
mono layer
coverage
Height profile asymmetry
misalignment
Deposit Si at RT,
NW length is very disparate
(1.5-30nm)
[-110] Ag direction)
4aAg[100] wide
2aAg[1-10] periodicity along NW
2. On Ag(110)
Annealing at 230C
Significant NWs elongation (>100nm); Width no change
Nanodots disappear for long annealing time
• 1D diffusion results in NW formation
2. On Ag(110)
Si grow at 200 °C, one mono layer
5 × 2 periodicity
2. On Ag(110)
Structural asymmetry
A square and a
parallelogram
side-by-side
2. On Ag(110)
High resolution STM revealing honeycomb arrangement
Silicene NRs
2. On Ag(110)
• ab initio calculations
2. On Ag(110)
NRs arc describes better NWs
Bending by incommensurability
•
•
•
Si NRs involve 30 Si atoms & five layer
thick(4*6)Ag(110)
Bulking : responsible for the asymmetry
Chiral coupling between NRs mediated
by the Ag substrate
This causes the NRs asymmetry
and the Ag substrate dip
Mechanisms? Theory part?
2. On Ag(110)
Normal incidence, 45°emission
EUV(极紫外)
Metallic
DOS increase
Si/Ag
Ag substrate
These states:
A). not Ag surface states ;
B). won’t disperse at normal emission
They are Si NRs surface states !
2. On Ag(110)
605meV
SO split
605meV
Normal emission
SO split
EUV(极紫外)
S2 S1
实际测到的是最上面的黑线，通过理论公式拟合，得到
下面的一系列峰。其中每个颜色是一个电子态，每个电
子态有两个峰，因为有自选轨道劈裂。
S2: 来自NWs底部的Si原子；
S1：来自顶部Si原子；
S3,S4：来自其他NW末端，或
者纳米点上的Si原子。
2. On Ag(110)
• Normal emission; Orthogonal to NWs: No
dispersion !
• Without annealing—no dispersion !
• So they are quantum well levels
• Coexistence of quantum confinement and metallicity
• Electronic states hybridization
• 这几个图就说，室温下生长得到了高长宽比的，原子级完
美的Si纳米线，显示出了很强的金属性。这样的纳米结构，
有很多用处和前景，很promising,
• 比如可以通过掺杂，变成半导体或者绝缘体性质，或者改
变宽度，可以应用在电子学，或者用来对齐大分子等等……
挺唬人的
2. On Ag(110)
oxidation process of the Si NR
3. On Ag(111)
highly ordered honeycomb structure
sheet of silicene epitaxy on silver
Silicence on Ag(111)
综述文章中: 2010年有人在Ag(111)
合成了硅烯,但是支持性的证据仅有STM图像,而且硅原子间距为0.19nm(理
论估算为0.22~0.24之间),所以不被承认.
在综述文章发表一年后,硅烯领域取得重大突破,在银的(111)成功合成的硅
的单原子层(PRL 108,155501).
单原子层有六角蜂窝单层结构.实验组是通过控制沉积时间来控制层数的,
原文并没有对整体的均一性做出展示.
由于硅烯的原子直径大,pi键的相互作用小,所以一般不会形成自然的单层
结构.依赖金属基底,可以沉积硅原子得到单层结构,同时也就无法研究电学
性质.基底的选择既要考虑不能和硅成键,又要考虑晶格形状和硅有一定倍
数关系,形成不是很大的超晶格.
一般硅烯都被吹成新一代半导体器件的候选材料.这一领域的下一个突破
应该是在绝缘基底上生长硅,并且得到均一的薄膜
硅烯的STM图像,蜂窝状结构其实是基底和硅组成的超晶格.通过沉积
时间控制层数.
一般来说,实验组会拿出生长的最漂亮的区域的图像放在paper里.
生长前后的ARPES图,沉积后引入了线性的色散关系
理论计算了STM图像,与观察结果对比
硅烯与基底图
精确哈密顿量与波函数
H=
ℏ2 2
ℏ2 2
𝑄2
𝑄𝑒 𝑒 2
−
𝛻 −
𝛻 +
−
+
2𝑀𝑛 𝑛 2𝑚𝑖 𝑖
𝑅𝑚𝑛 𝑟𝑛𝑖 𝑟𝑖𝑗
总波函数：Ψ 𝑅𝑛 , 𝑟𝑖
波恩-奥本海默近似
电子哈密顿量与波函数
𝐻𝑒 =
ℏ2 2
𝑄𝑒 𝑒 2
−
𝛻 +−
+
2𝑚𝑖 𝑖
𝑟𝑛𝑖 𝑟𝑖𝑗
多电子波函数：Φ𝑒 𝑟𝑖 , 𝑅𝑛
单电子轨道近似
DFT理论
利用变分法求得Kohn-Sham 方程
其中交换关联能形式未知，有各种经验性的近似公式
TB模型
忽略电子相互作用项，或对电子相互作用采取平均场近似
Tight-binding（TB）模型
• 布洛赫定理：𝑇𝑎 𝜓⟩ = 𝑒 𝑖𝑘∙𝑎 𝜓⟩
• 一个能量本征态对应一个k；一个k对应许多个能量本征态，张成
一个波函数k子空间。
• 每一个k子空间都要选取一组正交完备基。用参数A与α标记：
𝑒 𝑖𝑘∙𝑅𝐴 𝑅𝐴 , 𝛼
𝑘, 𝐴, 𝛼 =
𝑅𝐴
TB模型的近似：单电子能级α
• 不考虑内层轨道与外层轨道的耦合，仅取α为最外层电子附近的
能级。
• 考虑轨道杂化，用杂化轨道（π轨道与σ轨道）代替单原子轨道
（如硅的3s轨道与3p轨道）。选取不同的杂化轨道可以得到不同
的TB模型（如sp3模型与sp3s*模型）
TB模型的近似：跃迁能
• 在计算矩阵元 𝑘, 𝐴𝑖 , 𝛼𝑖 𝐻 𝑘, 𝐴𝑗 , 𝛼𝑗 时，会遇到 𝑅𝐴𝑖 , 𝛼𝑖 𝐻 𝑅𝐴𝑗 , 𝛼𝑗 的
计算，通常做如下的近似：
• 若𝑅𝐴𝑖 与𝑅𝐴𝑗 在同一个（或相邻两个）原胞之内，则
𝑅𝐴𝑖 , 𝛼𝑖 𝐻 𝑅𝐴𝑗 , 𝛼𝑗 取值为一个常数，称为跃迁能。这种近似方法
称作近邻近似（或次近邻近似）。
TB模型计算石墨烯
• 在近邻近似下，TB模型可以得
到石墨烯能带的解析解！
• 石墨烯是sp2杂化，α仅取π键
轨道，π键能带如图
• 狄拉克锥
TB模型计算硅烯
• α-硅烯
• 直接将石墨烯TB模型中的C原
子替换为Si原子，改变相应参
数即可
• 不稳定
• β-硅烯
• 稳定结构
• 硅的111面（原胞）卷曲而
成，不是平面结构
TB模型计算结果
• 次近邻近似
• 不同的杂化模型：sp3与
sp3s*
• 不同的硅烯模型：α-硅烯与
β-硅烯
• 都有狄拉克锥！
DFT理论简介
• Kohn-Sham方程：
ℏ2 2
−
𝛻 +𝑉 𝑟 +
2m
𝜌 𝑟′
𝑑 𝑟′ + 𝑉𝑋𝐶 [𝜌 𝑟 ] 𝜓𝑖 𝑟 = 𝜀𝑖 𝜓𝑖 𝑟
𝑟 − 𝑟′
• 对于交换关联能𝑉𝑋𝐶 [𝜌 𝑟 ]，不同的近似公式给出不同的计算方法
（如LDA，GGA等）
• 通过反复迭代K-S方程（𝜌 → 𝜓 → 𝜌 → 𝜓 → ⋯），给出能级的数值
解。
DFT理论的计算结果
• 左右两幅图代表不同的几何构型的硅烯下DFT理论解出的能带
结构。左图为high-buckling结构，右图为low-buckling结构。