Progress Report for Subproject 4
Characterization and manipulation of the basic building blocks
of advanced materials
Field-Induced Shifting of Thickness-Dependent Transmission Resonance on
Thin Ag Films
蘇維彬、呂欣明、施華德、蔣季倫、張嘉升、鄭天佐
中文摘要
銀在矽(111)77 表面會形成表面平坦
的單晶薄膜。我們利用掃描穿隧顯微儀在
不同厚度的銀薄膜上作能譜量測。所得能
譜包含兩種量子效應所產生的訊號，分別
是共振穿透以及駐波態。共振穿透會隨銀
薄膜厚度的增加而往低能量移動，呈現厚
度相依的性質。此外，隨著增加穿隧電流，
我們亦觀察到共振穿透會往高能量移動。
也就是改變探針-樣品之間的電場引發共
振穿透移動的現象。
When the thickness of a metal film is
comparable to the electron de Broglie
wavelength, electrons in the film as well as
those transmitting through the film can both
manifest the quantum size effect (QSE). For
the former, electrons are confined in a
quantum well of the metal film to form
quantized standing wave states in the
surface normal. For the latter, the electron
QSE appears above the vacuum level, and
can be explained to be due to an interference
of electron waves that are reflected from the
film surface and the film-substrate interface.
The QSE results in the electron transmission
spectra of the metal film to reveal
resonances [1], i.e., electron can penetrate
the film easily at some specific energy.
Although this transmission resonance is a
phenomenon of free electron scattered by
the quantum well, Kubby et al.’s pioneer
work have demonstrated that it can be
probed by the scanning tunneling
spectroscopy (STS) on the √3Sn/Si(111)
surface [2]. However, according to the
quantum mechanics, the energy level of the
transmission resonance may vary with the
width of the quantum well, which was not
explored in the work of Kubby et al.
It is known that flat silver films with the
(111) face can be grown on Si(111)7×7 at
room temperature[3]. Since the transmission
resonances have been observed in the
Ag/W(110) system [1], it can be expected
that they would also appear in the
Ag/Si(111)7×7 system. We utilize the
scanning tunneling spectroscopy (STS) to
investigate the electronic structure of Ag
film of different thickness at the energy
range of 2~9 eV above the Fermi level. Our
results demonstrate that the transmission
resonance indeed can be observed by STS
關鍵詞：掃描穿隧顯微儀及能譜術、銀薄
膜、共振穿透、駐波態
Abstract
It is known that flat silver crystalline
film can be grown on Si(111)77 surface.
We use scanning tunneling microscopy and
spectroscopy to probe the electronic
structure of the film of different thickness.
Each
spectroscopy
contains
signals
originated from two kinds of quantum
phenomena.
They
are
transmission
resonance, and standing-wave states. In
spectra, the transmission resonance moves
toward the vacuum level with increasing
film thickness, showing thickness-dependent
behavior. In addition, we also have observed
that the transmission resonance may move
toward high energy with increasing
tunneling current. This shifting of
transmission resonance is induced by the
electric field in the tunneling gap.
Keywords: Scanning tunneling microscopy
and spectroscopy, silver film, transmission
resonance, standing-wave state
I. Introduction
1
and its energy level varies with film
thickness, consistent with the quantum
mechanics. Besides the transmission
resonance, however, sharp peak features are
also found in the spectra, which are
quantized states related to reflected electrons
confined in the triangular potential well
between the tip and sample. We term them
standing-wave states (QBS) [4, 5].
1/T=1+V2sin2(kt)/4E(E+V)
(1)
where T is the transmission probability, E is
the energy of incident electrons, V is the
depth of the potential well, t is the width of
the well, and ħ2k2/2m=E+V. It is plausible to
assume that Ag film has a similar square
potential well in the surface normal. Figure
2(b) shows calculated curves of the
transmission probability as a function of
electron energy for 9~11-layer thick films
by using Eq.(1) with the the parameters V is
8 eV [1] and t is equal to layer number ×2.5
Å. Each calculated curve exhibits an
oscillatory aspect, indicating that both
transmission and reflection can occur for
any energy except at certain energy levels
(marked by dash lines) electrons can
penetrate the film totally, which are termed
the transmission resonance. The energy
levels of transmission resonance move
toward the vacuum level with increasing
film thickness. This is consistent with the
bump features shown in Fig. 2(a). The
calculated (Cal.) values of the energy
separation
between
the
first
two
transmission resonances are tabulated in Fig.
2(a). They decreases with increasing film
thickness and agree with the experimental
(Exp.) measurements. Because of these
similarities, we thus conclude that the bump
features are resulted from to the
transmission resonance.
Figure 3(a) shows Z-V spectra acquired
on the 5-layer film at the conditions of
different tunneling current. It is obvious that
the withdrawn distance of the tip decreases
with increasing the tunneling current while
ramps the bias. Therefore, the mean electric
field between tip and sample would increase
with the tunneling current. Since the
standing-wave states are formed in the
potential well between the tip and the
sample, their energy levels may vary with
the tunneling current. Figure 3(b) shows that
standing-wave state 1, 2, 3 all move toward
higher energy with decreasing the
withdrawn distance, i.e. increasing the
electric field. However, it is clear that the
transmission resonance as marked by arrows
in spectra is also shifted with the electric
II. Results and Discussion
Figure 1(a) shows a typical STM
topography image of the Ag film grown at
room temperature. STS is used to take Z-V
spectra (not shown) on films of different
thickness. The black curve in Fig. 1(b)
shows a dZ/dV-V spectrum differentiated
from a Z-V spectrum taken on a film of 9
atomic layers above the silicon substrate.
For comparison, the spectrum is also
acquired on the crystal Ag(111) surface,
drawn as the gray curve in Fig. 1(b). Both
curves are similar and reveal peak features
that were interpreted as the standing-wave
states in the tunneling gap in previous
studies. Besides these peaks, two extra
bumps marked by two black downward
arrows are also observed in the curve of
9-layer thick film. However, they do not
appear in that of crystal Ag, indicating that
the bump feature is specific to the Ag thin
films. These peak and bump features can
also appear in the spectra obtained by
lock-in technique with the feedback kept
active, as shown in Fig. 2(a). There arrows
mark the bump features appearing in the
spectra of 9~11-layer thick film (indicated
by number in the parenthesis). It is obvious
that the energy separation between the bump
features decreases with increasing film
thickness. In addition, the energy levels of
these bump features are all located above the
vacuum level, refering to the work function
of the Ag film on Si(111) being 4.41 eV [6].
These properties guide us to think that the
bump features is due to the QSE above the
vacuum level.
According to quantum mechanics, the
probability for an electron transmitting
through a square potential well obey the
following equation [7]
2
field. Figure 3(c) shows the energy level of
the transmission resonance decreases with
increasing
withdrawn
distance,
i.e.
decreasing the electric field. Since the
potential well between the tip and the
sample for forming standing-wave state 1, 2,
3 can be approximated to a triangular
potential well, we can obtained the electric
field from the energy separation between the
standing-wave states. According to the
calculation, we estimate the electric field
varies from 0.19 V/Å to 0.24 V/Å when the
tunneling current is changed from 0.8 nA to
10 nA. Under this change of the electric
field, the shifting of the transmission
resonance is about 0.29 eV.
(a)
0.8
(b)
0
1
3
2
crystal
9-layer
0.6
0.4
III. Conclusions
0.2
0.0
In summary, we have observed the
transmission resonance of thin Ag films
formed on Si(111)7×7 by STS. According to
the quantum mechanic, this transmission
resonance should change with the film
thickness. We indeed observed this
thickness-dependent behavior. In addition,
the transmission resonance can be shifted by
the tunneling current. This shifting is
induced by the electric field between the tip
and the sample.
1
2
3
4
5
6
7
8
9
10
Sample bias
(c) (V)
standing-wave
state
EF
transmission
tip
V
EF
vacuum
level
Z height
sampl
e
Fig. 1 (a) The growth of flat Ag films on
Si(111)77 surface at room temperature at
the coverage of 3.6 ML. Image size is
150×150 nm2. (b) dZ/dV-V spectra
differentiated directly from Z-V spectra
measured on the 9-layer thick Ag film
(black curve) and crystal Ag(111) surface
(gray curve). (c) Schematic triangular
potential well formed in STM configuration.
Electrons tunneling from the tip are of
probability to be reflected by film surface to
form the standing-wave states (peak 1, 2, 3
in (b)) in the triangular potential well
IV. Reference
[1] B.T. Jonker, N.C. Bartelt, and R.L. Park,
Surf. Sci. 127, 183 (1983).
[2] J. A. Kubby, Y. R. Wang, and W. J.
Greene, Phys. Rev. Lett. 65, 2165
(1990).
[3] P. Sobotík, I. Ošťádal, J. Mysliveček, T.
Jarolímek, and F. Lavický, Surf. Sci.
482-485, 797 (2001).
[4] G. Binnig, K. H. Frank, H. Fuchs, N.
Garcia, B. Reihl, H. Rohrer, F. Salvan,
and A. R. Williams, Phys. Rev. Lett. 55,
991 (1985).
[5] R. S. Becker, J. A. Golovchenko, and B.
S. Swartzentruber, Phys. Rev. Lett. 55,
987 (1985).
[6] A. Thanailakis, J. Phys. C: Solid State
Phys., 8, 655 (1975).
[7] Stephen Gasiorowicz, Quantum Physics,
John Wiley & Sons, 1974.
3
Fig. 3 (a) Z-V spectra acquired on the
5-layer film at the conditions of different
tunneling current. (b) Spectra acquired by
lock-in technique. The standing-wave states
and the transmission resonance move higher
energy with decreasing the withdrawn
distance. (c) The energy level of the
transmission resonance as a function of the
withdrawn distance.
Fig. 2 (a) spectra acquired on 9~11-layer
thick films by lock-in technique with the
feedback kept active. Number in parenthesis
indicates film thickness. (b) Calculation
curves of transmission probability as a
function of electron energy for 9~11-layer
thick films. Dash lines indicate energy
levels of transmission resonance.
4