1

Single-Molecule AFM Cantilever for THz Force Detection

Fahad Mahmood

Manoharan Lab, Department of Physics, Stanford University

Increasing the resonance frequency of an Atomic Force Microscope (AFM) cantilever is

necessary to effectively probe short-range chemical forces. Current AFM cantilevers

have frequencies of about 100 − 200 kHz, limiting the minimum force-gradient that can

be measured to the order of 10 pN/nm. This study demonstrates the ability of Inelastic

Tunneling Spectroscopy (IETS) to probe THz vibrational modes of a single CO molecule

attached to the tip of a low-temperature Scanning Tunneling Microscope (STM). Using

molecular manipulation, a CO molecule is transferred to the end of the STM tip and lock-

in techniques are used to measure 𝑑2𝐼/𝑑𝑉2 tunneling spectra. Shifts in the frequency of

specific vibrational modes of the CO molecule are analyzed as a function of the tip-to-

sample distance. This shows that a single molecule can be used as an AFM cantilever for

force spectroscopy with the ability to measure small force-gradients to the order of

10−6 pN/nm. IETS with a CO terminated STM tip is also performed over adsorbed CO

molecules on a Cu(111) surface revealing a novel vibrational mode due to coupling

between the two CO molecules. In future, the small force-gradients detected by STM-

IETS can be used to resolve single atoms within a molecule to reveal additional

molecular structure.

1. Introduction

Over the past 20 years, great strides have been made in nano-probe technology, giving us the

ability to not only see matter at the nano-scale but to manipulate it as well [1, 2]. Two such

probes are the Atomic Force Microscope (AFM) and the Scanning Tunneling Microscope (STM).

While both involve moving an atomically sharp tip across a surface, they use fundamentally

different physical phenomena. An AFM uses the changing force between the tip and the surface

to change the resonant frequency of the AFM cantilever. The resulting frequency shift can be

measured to give an image of the surface topography. On the other hand, an STM uses quantum

tunneling of electrons across a potential barrier to image surfaces. Both the AFM and the STM

are capable of resolving individual surface atoms with the STM having the added capability to

study electron density of states and the AFM having the capability to study both short-range and

long-range forces between molecules (force spectroscopy).

While STM imaging can study electron density of states, it is not able to resolve individual

atoms within adsorbed molecules. Unlike the AFM, an STM cannot detect short-range chemical

2

forces between the tip and the sample and thus is only able to image a molecule as a single blob.

Moreover, the shape of the imaged molecule depends on adsorption site on the surface [3].In

theory, if made sensitive enough, an AFM is able to study short-range chemical forces that can

resolve atoms within a molecule [4]. Overall, the sensitivity of an AFM depends on the size of its

cantilever. The smaller the cantilever, the greater its resonant frequency and the smaller the

minimum force-gradient that can be resolved by the AFM [5]. Recently, there has been a strong

interest in developing “nano-cantilevers” which have dimensions on the nano-scale and have

frequencies in the MHz range [6]. The challenge with reducing the size of an AFM cantilever is

to find ways to couple it with the experimental setup to measure its resonant frequency.

This thesis presents STM inelastic tunneling spectroscopy (IETS) as an effective way to

probe the vibrational frequency of a single molecule attached to the STM tip thereby using a

single molecule as an AFM cantilever. A single molecule represents the ultimate limit for the

miniaturization of devices. Thus, a single molecule AFM cantilever is the ultimate limit for

minimizing the size of the cantilever and therefore maximizing its resonant frequency. It is well

known [7] that a CO molecule adsorbed on a Cu(111) surface has THz vibrational modes that

can be measured and studied using STM IETS. By functionalizing an STM tip with a CO

molecule and tracking the molecule’s vibrational modes as a function of tip-sample distance, a

hybrid AFM/STM system can be developed which uses both tunneling and short-range forces to

image surfaces. The THz vibrational modes can allow force spectroscopy with a minimum force-

gradient several orders of magnitude less than the current minimum of typical AFM cantilevers.

The studies presented in this thesis provide a proof-of-principle of using a single-molecule as

an AFM cantilever in a hybrid AFM/STM system. This thesis will first introduce the basic

concepts behind non-contact AFM and STM operation. It will then discuss tunneling theory in

detail to describe inelastic tunneling spectroscopy, the primary measurement technique used for

this thesis. The CO and Cu(111) system will be discussed and measurements made in the

Manoharan lab on the vibrational modes of CO will be presented. The core of this thesis is

based around investigating the vibrational properties of a single CO molecule transferred from

the Cu(111) surface to the end of the STM tip. The results highlight THz vibrational modes

whose frequencies depend on the tip-sample distance. Lastly, IETS with a CO STM tip is

performed over a CO molecule on Cu(111) to reveal a novel vibrational mode due to coupling

between the two CO molecules.

3

2. Non-Contact Atomic Force Microscopy

The original AFM was developed in 1986 by Bining, Quate and Gerber [8]. Developed after

the STM, the AFM provided an experimental technique that could image both conducting and

insulating materials. The AFM consists of a probing tip which is attached to a cantilever. As the

tip moves over a sample, tip-surface forces change the deflection of the cantilever which can be

measured to give an image of the surface.

In the non-contact (NC) mode (Figure 1), the tip-cantilever system, with spring constant 𝑘,

oscillates at an unperturbed resonant frequency (𝑓𝑜 ). As the surface topography changes, the

height between the tip and the sample (𝑧) changes. This in turn changes the tip-sample force,

changing the oscillation frequency of the tip-cantilever system. The resulting frequency shift (∆𝑓)

can be measured to give a map of the surface topography. In most setups, a feedback loop adjusts

the tip-sample height so as to maintain constant ∆𝑓 and constant oscillation amplitude. The

resulting change in the tip-sample height then maps the surface topography.

The tip-sample force consists of both short-range chemical bonding forces (such as covalent

bonds with a range in fractions of nm) and long-range forces (such as van der Waals and

electrostatic forces with a range of up to nm) [1]. As the tip-sample force plays a fundamental

role in the operation of NC-AFM, it is important to understand its relationship with the

oscillation frequency shift (∆𝑓). A simplistic derivation of this relationship is given in [9]. In

general the potential energy between the tip and sample 𝑉𝑡𝑠 causes a 𝑧 component in the tip-

Figure 1: Fundamentals of the Atomic Force Microscope. The AFM consists of a sharp tip attached to an oscillating cantilever. The cantilever oscillates at an unperturbed resonant frequency 𝑓𝑜 . As the tip moves across the surface the tip-surface force changes with the changing surface topography. This in turn changes the frequency of the oscillating cantilever. The resulting frequency shift ∆𝑓 can be measured to give a map of the surface topgography.

Am

plit

ud

e

Tip

Sample

Oscillating Cantilever at 𝒇𝒐 z

4

sample force 𝐹𝑡𝑠 = −𝜕𝑉𝑡𝑠

𝜕𝑧 and a tip-sample spring constant 𝑘𝑡𝑠 related to the force gradient as

𝑘𝑡𝑠 = −𝜕𝐹𝑡𝑠

𝜕𝑧. The cantilever can be approximated as a harmonic oscillator with effective spring

constant 𝑘∗ = 𝑘 + 𝑘𝑡𝑠 . The frequency (𝑓 = 𝑓𝑜 + ∆𝑓) of the oscillator is then given by 𝑓 =

1

2𝜋

𝑘∗

𝑚, where 𝑚 is the mass of the tip-cantilever system. If 𝑘𝑡𝑠 ≪ 𝑘, the expression for 𝑓 can be

expanded as a Taylor series to give an approximate expression for the force-gradient in terms of

the frequency shift:

𝜕𝐹𝑡𝑠

𝜕𝑧= −2𝑘

∆𝑓

𝑓𝑜 (1)

The key part of this equation is that the force gradient goes as 1/𝑓𝑜 : the larger the resonant

frequency, the smaller the force gradient measured by the AFM. Thus, in order to increase the

sensitivity in the measurement of short-range forces, it is necessary to increase the resonant

frequency of the AFM cantilever. As 𝑓𝑜 ∝ 1/ 𝑚, there has been a consistent effort towards the

miniaturization of an AFM cantilever to increase its resonant frequency [6]. Currently, most

AFM cantilevers usually oscillate at a frequency (𝑓𝑜 ) of about 100 − 200 kHz [9]. As the

stiffness is to the order of 1 kN/m [9], this allows AFM’s to probe force gradients to the order of

10 pn/nm. Current techniques for miniaturization of an AFM cantilever include MEMS

fabrication which can make cantilevers with resonant frequencies as high as 100 MHz [10].

Though this is much higher than cantilever frequencies in the kHz regime, it is still well below

frequencies in the THz regime.

3. Scanning Tunneling Microscopy

Developed in 1981 by Gerd Binnig and Heinrich Roher [11], the Scanning Tunneling

Microscope (STM) is a versatile tool primarily used to image surfaces with sub-nanometer

resolution. Apart from topographic imaging, the STM can also be used to carry out spectroscopy

in which measurements are made at a fixed location, recording the current (or derivatives of the

current) as a function of voltage between the STM tip and the sample. Spectroscopic

measurements are used to determine local electronic properties of a sample and can also be used

to probe vibrational modes of single molecules. Finally, the STM allows manipulation of matter

at the atomic scale, providing the unique ability to build nanostructures one molecule at a time.

The experiments in this thesis use atomic manipulation to functionalize the tip with a single

molecule and use spectroscopic techniques to probe its vibrational modes. The experimental

5

work was done in a low temperature (4.2 K) STM that was designed and built in the Manoharan

lab at Stanford. In order to understand the results in this thesis, it is important to review the basic

concepts behind STM operation.

3.1. A Simple Model for the STM

The STM consists of an atomically sharp metal tip positioned above a conducting surface (Figure

2a). The tip and sample are surrounded by vacuum and have a voltage 𝑉 applied across them.

Classically, electron transport between the tip and the sample is forbidden unless 𝑉 exceeds the

work function of the metals. However, electrons can still quantum mechanically tunnel through

the barrier between the tip and the sample. The resulting current can be measured if the tip-

sample distance is extremely small – less than a nanometer. A simple model for this system is a

one-dimensional square barrier (Figure 2b) with a height equal to Φ, the average work function

of the tip and the sample.

An electron can tunnel through this barrier with a probability that is exponentially sensitive to

the distance between the tip and the sample (𝑕). The measured current is then given by:

𝐼 ∝ 𝑒−2𝛼𝑕 (2)

𝛼 is given by:

𝛼 = 2𝑚(Φ − 𝐸)

ħ (3)

where 𝑚 is the mass of the electron and 𝐸 is its energy with respect to the Fermi level.

Figure 2: Fundamentals of the Scanning Tunneling Microscope. (a) The STM consists of an atomically sharp tip positioned above a conductive sample. A bias 𝑉 is applied between the tip can the sample. The potential barrier between the tip and the sample can be modeled as a one-dimensional square barrier (b). If the tip height (𝑕) is sufficiently small, a measurable quantum mechanical tunneling current may flow between the tip and the sample. This current is exponentially sensitive to height giving the STM the ability to image surface topography.

h

V

I

Tip

Sample

z

U

z

Φ

h

V

a)

.

b)

.

6

In its most basic configuration, the STM tip is scanned across the surface with a feedback loop

that keeps the current between the tip and the sample constant. The tip then follows the

topography of the underlying surface. By measuring the amount the tip is displaced in order to

keep the current constant, the surface topography can be constructed. The exponential

dependence of the current to the height of the tip above the sample enables the sub-nanoscale

resolution of images obtained by an STM.

3.2. Tunneling Theory

While the one-dimensional square barrier model for the STM does explain topographic

imaging, it is overly simplified. It is important to apply a rigorous theory of tunneling developed

by Bardeen, Tersoff and Hamaan [12, 13] to understand elastic and inelastic tunneling

spectroscopy. In this theory, the tip and the sample are treated as two separate systems with

eigenfunctions 𝜓𝑡𝑖𝑝 and 𝜓𝑠𝑎𝑚𝑝𝑙𝑒 . When the tip height is sufficiently small, 𝜓𝑡𝑖𝑝 and 𝜓𝑠𝑎𝑚𝑝𝑙𝑒 can

overlap allowing electrons to transition from filled states in one system to empty states in the

other system. The transition rate for electrons to go from an initial state 𝑖 to a final state 𝑓 is

given by Fermi’s golden rule

𝑇𝑖→𝑓 =2𝜋

ħ 𝑀𝑖𝑓

2 (4)

where 𝑀𝑖𝑓 is the matrix element that couples the two states.

Using Fermi’s golden rule, it can be shown [14] that the total tunneling current is given by:

𝐼 =4𝜋𝑒

ħ 𝑀 2𝜌𝑡𝑖𝑝 𝜖 + 𝑒𝑉 𝜌𝑠𝑎𝑚𝑝𝑙𝑒 𝜖 [𝑓 𝜖 + 𝑒𝑉 − 𝑓(

∞

−∞

𝜖)]𝑑𝜖 (5)

where 𝜌 is the density of states, 𝑉 is the sample bias with respect to the tip and 𝑓 is the Fermi-

Dirac distribution function. A number of assumptions can be made to simplify the above

expression.

Firstly, the matrix elements 𝑀 can be modeled by a transmission factor (𝑇) that depends on

the energy, the applied bias, the work functions of the tip and sample and the tip height. Since

the applied bias (for tunneling) is much less than the work functions of either the tip or sample,

the energy and voltage dependence of the transmission can be neglected and it can be shown that

the 𝑇 depends exponentially on the distance between the tip and the sample:

𝑇 ∝ 𝑒−𝛼𝑕 (6)

where,

7

𝛼 = 4𝑚(Φtip + Φsample )

ħ (7)

Secondly, since all the measurements made in this thesis were at 4.2 K, the integral for the

tunneling current can be simplified by taking the zero-temperature limit for the Fermi-Dirac

distribution which becomes a downward step function at the Fermi-energy (𝐸𝐹):

With this distribution, it can be assumed that all states in both the tip and sample are filled below

𝐸𝐹 and all are empty above 𝐸𝐹 + 𝑒𝑉. The integral above can then be simplified to give:

𝐼 ∝ 𝑒−𝛼𝑕 𝜌𝑡𝑖𝑝 𝜖 + 𝑒𝑉 𝜌𝑠𝑎𝑚𝑝𝑙𝑒 𝜖 𝐸𝐹+𝑒𝑉

𝐸𝐹

𝑑𝜖 (8)

Thirdly, since the tip is usually well-defined it can be assumed that 𝜌𝑡𝑖𝑝 is constant over the

required energy range. Since the energy is usually written with respect to the Fermi energy (𝐸𝐹) ,

the final expression for the tunneling current is given by:

𝐼 ∝ 𝑒−𝛼𝑕 𝜌𝑠𝑎𝑚𝑝𝑙𝑒 𝜖 eV

0

𝑑𝜖 (9)

Therefore, the current reflects the integrated sample density of states from 𝐸𝐹 to 𝐸𝐹 + 𝑒𝑉 and

changes exponentially with tip height. The measured current is due to a combination of both

structural and electronic effects. Since the current depends on the sample density of states, the

STM can be used to carry out local spectroscopic measurements.

3.3. STM Spectroscopy

In addition to high spatial resolution, the STM can also provide high energy resolution

though tunneling spectroscopy. This allows the measurement of the local density of states

(LDOS) as a function of energy. To acquire the spectrum at a given point, the STM tip is first

moved to that point and a set-point voltage 𝑉𝑜 and current 𝐼𝑜 are established. The feedback loop

is then opened and both 𝑑𝐼/𝑑𝑉 and 𝑑2𝐼/𝑑𝑉2 are measured using lock-in techniques. Opening

f(E)

E

1

𝑬𝑭

8

the feedback loop allows the tip to remain at a fixed height as the sample bias is varied from

𝑉𝑚𝑖𝑛 to 𝑉𝑚𝑎𝑥 .

The lock-in technique for spectroscopic measurements works by adding a small AC-voltage

modulation ∆𝑉𝑏𝑖𝑎𝑠 = 𝑉𝑚𝑜𝑑 cos(𝜔𝑡) directly to the DC bias voltage 𝑉𝑑𝑐 where 𝑉𝑚𝑜𝑑 ≪ 𝑉𝑏𝑖𝑎𝑠 .

The resulting modulation current can be measured using a lock-in amplifier. To understand how

this relates to 𝑑𝐼/𝑑𝑉 and 𝑑2𝐼/𝑑𝑉2, the tunneling current is written as a Taylor series expansion

around the bias voltage 𝑉𝑏𝑖𝑎𝑠 such that:

𝐼 𝑉𝑑𝑐 + ∆𝑉𝑏𝑖𝑎𝑠 = 𝐼 𝑉𝑑𝑐 + 𝑑𝐼

𝑑𝑉 𝑉𝑑𝑐

𝑉𝑚𝑜𝑑 cos 𝜔𝑡 +1

2 𝑑

2𝐼

𝑑𝑉2 𝑉𝑑𝑐

𝑉2𝑚𝑜𝑑 cos2 𝜔𝑡 + ⋯ (10)

Note that the term in cos 𝜔𝑡 is directly proportional to 𝑑𝐼/𝑑𝑉at the given 𝑉𝑏𝑖𝑎𝑠 whereas the

term in cos2 𝜔𝑡 is directly proportional to 𝑑2𝐼/𝑑𝑉2 at the given 𝑉𝑏𝑖𝑎𝑠 . If the lock-in amplifier

is set to measure the current signal at a frequency of 𝜔 then the voltage measured is directly

proportional to 𝑑𝐼/𝑑𝑉at the given 𝑉𝑏𝑖𝑎𝑠 . Similarly, since cos2 𝜔𝑡 ≡ 1 + cos(2𝜔𝑡), if the lock-

in amplifier is set to measure the current signal at a frequency of 2𝜔 then the voltage measured is

directly proportional to 𝑑2𝐼/𝑑𝑉2 at the given 𝑉𝑏𝑖𝑎𝑠 . By varying 𝑉𝑏𝑖𝑎𝑠 from some given 𝑉𝑚𝑖𝑛 to

some given 𝑉𝑚𝑎𝑥 , both the 𝑑𝐼/𝑑𝑉 and 𝑑2𝐼/𝑑𝑉2 spectrum can thus be obtained by using two

lock-in amplifiers (Figure 3).

Figure 3: Lock-in Techniques for Spectroscopy. A small modulating voltage is added to the DC bias. The resulting tip-sample current is amplified using a pre-amp. A lock-in amplifier measures the signal at the first harmonic 𝜔 to determine 𝑑𝐼/𝑑𝑉. A second amplifier measures the signal at the second harmonic 2𝜔 to determine 𝑑2𝐼/𝑑𝑉2.

3.4. Inelastic Tunneling Spectroscopy

In general there are two types of tunneling spectroscopies: elastic tunneling and inelastic

tunneling (IETS). IETS is the basis for measurements in this thesis and will be described in detail.

During elastic tunneling, an electron that tunnels from the tip to the sample (or vice versa)

9

preserves its energy. The inelastic case involves the tunneling electron losing its energy as it

moves across the tunneling barrier [15].

Earlier it was shown that at a given height the tunneling current represents the integrated

Local Density Of States (LDOS) from 𝐸𝐹 to 𝐸𝐹 + 𝑒𝑉. This is best understood in the electron-

energy diagram illustrating elastic tunneling in Figure 4. The figure shows electrons tunneling

from an Iridium tip to the Cu(111) surface without a molecule present. This electron-energy

diagram has been simplified by showing a constant LDOS. If the spectroscopic measurements

are taken at a constant height (i.e. open loop spectroscopy), then the current (𝐼) changes linearly

with the tip-sample bias (𝑉) giving a constant 𝑑𝐼/𝑑𝑉 and a zero 𝑑2𝐼/𝑑𝑉2 (Figure 5):

𝐼 ∝ 𝜌 𝐸 𝑑𝐸𝐸𝐹+𝑒𝑉

𝐸𝐹

→ 𝐼 ∝ 𝜌𝑒𝑉 (𝑔𝑖𝑣𝑒𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝜌) (11)

Figure 4: Elastic Tunneling Energy Diagram. STM tunneling is often understood by diagrams such as these which show the tip and sample density of states as a function of energy. At 4.2 K, it can be assumed that the states are all filled below the Fermi-energy (𝐸𝐹) and all are empty above it. When a positive bias (𝑉) is applied to the sample with respect to the tip, the energy of the electrons in the tip is raised by 𝑒𝑉. Electrons in the tip with energies above 𝐸𝐹 but below 𝐸𝐹 + 𝑒𝑉 can then tunnel into empty sample states. The total tunneling current thus reflects the integrated sample density of states (shaded orange). In elastic tunneling, there is no loss in the energy of the tunneling electrons and if the sample density of states is constant (as shown), then the tunneling current is directly proportional to the sample bias (Figure 5).

𝑰

𝑬𝑭

𝑬𝑭 + 𝒆𝑽

𝑬𝑭 + 𝒆𝑽

+ 𝜱

Elec

tro

n E

ner

gy

Tip

Sample

Empty States

Filled States

Tip

Sample

V

e-

10

The above described 𝐼-𝑉 measurements are significantly different during inelastic tunneling.

If a molecule is placed between the tip and the sample, then it is quite likely that the tunneling

electron will absorb or emit a vibrational quantum as it interacts with the molecule [7, 16, 17]. In

order for the electron to gain energy, the molecule must relax from an excited vibrational state to

a lower excited state (or to the ground state). This requires that the molecule was already excited

by thermal or other means. However, since the measurements are taken with a low-temperature

(4.2 K) STM, it is unlikely that the molecule is thermally excited. Therefore, the dominant

inelastic tunneling process is one in which an electron loses energy.

This is illustrated in the electron-energy diagram in Figure 6. As the electron tunnels from the

tip into the sample, it interacts with the molecule in between, exciting the molecule from its

ground state to an excited vibrational state with frequency 𝑓. Thus, the electron loses a quantum

of energy (𝑕𝑓). The presence of a molecule between the tip and the sample opens up another

tunneling channel increasing the probability that an electron will be able to go from the tip to the

sample [18].

Therefore, whenever a vibrational mode is excited (electron energy, 𝑒𝑉 > vibrational energy

𝑒𝑉𝑣𝑖𝑏 ), the current increases, producing a kink in the 𝐼-𝑉 graph (Figure 7). This causes a

significant change in the first and second derivatives of current when compared with the case of

elastic tunneling (Figure 5). In particular, the 𝑑𝐼/𝑑𝑉 graph shows a step at 𝑉𝑣𝑖𝑏 indicating the

increase in conductance when the molecule is excited and another tunneling channel is opened.

This leads to sharp peaks in the 𝑑2𝐼/𝑑𝑉2 plot at the vibrational mode energy (Figure 7c). Thus,

precise 𝑑2𝐼/𝑑𝑉2 measurements can be used to track any changes in the vibrational mode

energies of a molecule. These measurements form the basis of this thesis. It is important to note

that fig.6 shows sharp steps in the 𝑑𝐼/𝑑𝑉 plot and sharp peaks in the 𝑑2𝐼/𝑑𝑉2 plot by assuming

Figure 5: 𝑰 − 𝑽 Characteristics for Elastic Tunneling. a) For a constant sample density of states, the 𝐼 − 𝑉 graph is a straight line through the origin. b) The corresponding 𝑑𝐼/𝑑𝑉 graph is a constant. c) The corresponding 𝑑2𝐼/𝑑𝑉2 is zero.

𝑰

𝑽

𝒅𝑰

𝒅𝑽

𝑽

𝒅𝟐𝑰

𝒅𝑽𝟐

𝑽

a)

.

b)

.

c)

11

a zero-temperature limit. Since the STM measurements are taken at about 𝑇 = 4.2 K, thermal

effects lead to a broadening in the measured 𝑑2𝐼/𝑑𝑉2 plots [14].

4. The CO and Cu(111) System

Carbon monoxide molecules on a copper surface have been studied extensively using atomic

probes [19-21]. Many of the properties of CO on a Cu(111) surface are well known, including

vibrational modes of a single CO molecule . However, this system has not been studied with a

CO terminated STM tip. This thesis will use the CO terminated STM tip to study the CO and

Figure 7: 𝑰 − 𝑽 Characteristics for Inelastic Tunneling. a) Kinks are produced in the 𝐼 − 𝑉 graph whenever a vibrational mode is excited at the sample bias 𝑉𝑣𝑖𝑏 . b) The corresponding 𝑑𝐼/𝑑𝑉 graph is shows a downward step at −𝑉𝑣𝑖𝑏 and an upward step at 𝑉𝑣𝑖𝑏 . c) The corresponding 𝑑2𝐼/𝑑𝑉2 shows sharp peaks at both −𝑉𝑣𝑖𝑏 and 𝑉𝑣𝑖𝑏

Figure 6: Inelastic Tunneling Energy Diagram. The overall energies of the electrons in the tip and the sample are the same as that in fig.3. As an electron tunnels from tip to the sample, it interacts with the molecule in between by giving of a quantum of energy that excites a vibrational mode of the molecule. The elastic tunneling channel is shown by the orange arrows whereas the inelastic tunneling channel is shown by the blue arrows.

𝑰

𝑬𝑭

𝑬𝑭 + 𝒆𝑽

𝑬𝑭 + 𝒆𝑽

+ 𝜱

Elec

tro

n E

ne

rgy

Tip

Sample

Empty States

Filled States

𝑕𝑓 Tip

Sample

V

e-

𝒅𝟐𝑰

𝒅𝑽𝟐

𝑽 𝑽𝒗𝒊𝒃 𝑽

𝑰

𝑽𝒗𝒊𝒃

𝒅𝑰

𝒅𝑽

𝑽 𝑽𝒗𝒊𝒃

a)

.

b)

.

c)

12

Cu(111) system. This system is ideal for such a study as it allows CO molecules to be positioned

anywhere on the Cu(111) lattice with atomic manipulation leading to constructed structures

(dimmers etc.) which can then be imaged using the CO terminated STM tip.

Copper has an FCC crystal structure with a lattice constant of 𝑎𝑜 = 3.60 Å at 4.2 K. The

Cu(111) surface is a hexagonal array with an inter-atomic spacing of 𝑎 = 𝑎𝑜/ 2 = 2.55 Å. The

copper sample used in the experiments in this thesis is an atomically flat surface prepared by

repeated cycles of annealing and ion-sputtering. CO molecules are then deposited onto the

surface by exposing the sample to 1 μTorr of CO gas at 20 K. Carbon monoxide is a simple

molecule with a triple bond between carbon and the oxygen atoms (Figure 8). The carbon atom

gives two electrons to the triple bond while oxygen gives four, forming a dative covalent bond.

The molecular orbitals of CO are strongly polarized towards the carbon atoms [22, 23] making

the carbon end more likely to accept electrons. This explains why all bonding to the CO occurs

towards the carbon end of the molecule.

An illustration of CO molecules on the Cu(111) surface is shown in Figure 9a. A CO

molecule bonds on top of a Cu atom with the carbon atom bonded to the Cu atom and the oxygen

atom sticking out perpendicular to the surface [23]. An STM topograph of a CO molecule on

Cu(111) is shown in Figure 9. As seen, the CO molecule is imaged as a depression in the surface

despite sticking out. A CO molecule on Cu(111) reduces the Cu electron density in its vicinity

[14] which reduces the tunneling current and causes the tip to move closer to the surface in

close-loop topography, imaging an isolated CO molecule as a depression.

Figure 8: The Carbon monoxide molecule

𝐂 ≡ 𝐎••

••

13

5. Vibrational Properties of CO on Cu(111)

A CO molecule bound to the Cu(111) surface has 4 vibrational modes: Frustrated Translation

(FT), Frustrated Rotation (FR), CO-Cu Stretch and C-O Stretch [7]. From quantum mechanics, it

is expected that each of these modes will have a discrete energy which can be provided by the

energy of the tunneling electrons. Therefore, if the energy of the tunneling electrons (𝑒𝑉)

exceeds the energy level of a vibrational mode, that vibrational mode can be excited and

observed by the STM.

Experimentally, it is known that only the FT and the FR modes are observed by the STM

[18]. Diagrams showing the motion of the molecules in these modes are shown in Figure 10. The

energy of the FT mode is about 4 meV which corresponds to a vibrational frequency1 of ~1 THz

while the energy of the FR mode is about 35 meV (~8.5 THz). Both these THz modes have been

observed by the Manoharan lab using 𝑑2𝐼/𝑑𝑉2 spectroscopy (Figure 11). It is important to note

that at a temperature of 4.2 K, the thermal energy (𝑘𝐵𝑇) is quite low (0.36 meV) to excite either

of the two modes.

1 For vibrational modes of a molecule confined in a harmonic potential, 𝐸 = 𝑕𝑓

Figure 9: Adsorbed CO molecule on the Cu(111) surface. a) The CO molecule bonds to the Cu(111) surface with the carbon end bonding to a copper atom and the oxygen end sticking out perpendicular to the surface. b) Two CO molecules imaged under closed-loop conditions. The molecules are imaged as a dip as the tip moves into the sample to maintain a constant current. The dip can be clearly seen in the rendered topograph in c).

Carbon

Cu(111) Surface

Oxygen

a)

.

b)

.

c)

Å

10Å

14

Figure 10: Vibrational modes of a CO molecule on Cu(111). a) The Frustrated Translation (FT) mode has an energy of 4 meV. The center of mass of the CO molecule moves as both the oxygen and carbon atom move in phase. b) The Frustrated Rotation (FR) mode has an energy of 35 meV. The carbon and oxygen atoms rotate around the center of mass of the CO molecule. Both atoms move out of phase with each other keeping the center of mass fixed.

b) Frustrated Rotation ~𝟑𝟓 𝐦𝐞𝐕 a) Frustrated Translation ~𝟒 𝐦𝐞𝐕

15

Measurements made in the Manoharan Lab have not only observed these modes but have

also quantified the change in the vibrational mode frequency with distance between the tip and

the sample. To quantify this change, the STM tip was positioned directly above an isolated CO

molecule on Cu(111) at a set-point tunneling current and hence at a set-point height above the

CO molecule. The tip then moves towards the CO molecule with known steps in height (∆𝑧) and

at each ∆𝑧, the 𝑑2𝐼/𝑑𝑉2 spectrum is measured. Gaussian profiles are fitted to the peaks at

±4 meV and at ±35 meV and the change in the center of the peak (the vibrational mode

frequency) is analyzed as a function of the height between the tip and the CO molecule on the

surface. The results are presented in Figure 12. As seen in the figure, the frequency of the FT

mode first increases and then decreases showing a surprising non-monotonic shift in the

frequency. However, the frequency of the FR mode decreases monotonically, showing a change

of about 100 GHz over the 1 Å distance moved by the tip towards the adsorbed CO molecule.

The change in vibrational frequency can be explained by the change in the confining

potential of the molecule. As the tip is brought closer to the molecule the force between the tip

Figure 11: 𝒅𝟐𝑰/𝒅𝑽𝟐 spectrum of a CO molecule with a metal STM tip. Both the FT and the FR mode are observed. Thermal and instrumental effects lead to a broadening in the idealized behavior of the peaks, as shown in Figure 7. The FT mode peak has its center at 4 mV corresponding to a frequency of ~1 THz while the FR mode peak has its center at 35 mV corresponding to a frequency of ~8.5 THz.

Sample Bias (mV)

𝑑2𝐼/

𝑑𝑉

2(a

.u.)

12𝑇𝐻𝑧 12𝑇𝐻𝑧 0

Vibrational Mode Frequency

~4 mV

~35 mV

16

and the molecule changes. This changes the confining potential of the molecule which changes

the spacing between the quantized vibrational energy levels of the molecule (Figure 13). Thus,

by tracking the change in the frequency of the vibrational modes, the change in force between

the tip and adsorbed molecule can be tracked for THz force spectroscopy.

Figure 12: Analysis of the CO on Cu(111) Vibrational Modes as a Function of Tip-Sample Distance. a) The 𝑑2𝐼/𝑑𝑉2 spectra at different tip-sample heights are stacked up together and the peak centers (red crosses) are tracked by fitting Gaussians to the individual peaks. b) The vibrational mode frequency as a function of height for the 4 meV (1 THz) mode. As the tip moves inwards, the frequency shows a surprising non-monotonic shift. c) The vibrational mode frequency as a function of height for the 35 meV (8.5 THz) mode. The frequency decrease monotonically showing a

change of ~100 GHz over the 1 Å distance moved by the tip towards the adsorbed CO molecule.

Sample Bias (mV)

𝑑2𝐼/

𝑑𝑉

2(a

.u.)

Track modes Moving into

sample

Vibrational Mode Frequency (THz) Vibrational Mode Frequency (THz)

Dis

tan

ce t

ow

ard

s m

ole

cule

(Å

)

Dis

tan

ce t

ow

ard

s m

ole

cule

(Å

)

a)

.

b)

.

c)

1.1 Å

0 Å

17

From these observations, it can be proposed that a CO molecule attached to the end of a

metal tip will have similar vibrational modes that can be observed using IETS. Moreover, the

frequency of any given vibrational mode will depend on the interacting force between the CO

molecule attached to the tip and the sample. Therefore, IETS can be used to probe the small-

range forces between the molecule on the tip and a molecule on the surface.

6. A CO Terminated STM tip

A unique capability of the STM is to manipulate a single atom or molecule to engineer matter

at the nano-scale. This is achieved by deliberately bringing the tip close to the sample such as to

exert forces on any atoms and molecules on the surface to move them. Atomic manipulation

using an STM was first demonstrated by Eigler et.al [24] at IBM and has played a central role in

studies in the Manoharan lab [14, 18]. It has also been observed that during the scanning of a

field of CO molecules, a molecule may spontaneously jump from the surface and bond to the

STM tip, producing strikingly different images [25].

With most STM measurements, it is assumed that the STM tip is a metal atom. However, as

described above, it is possible for CO molecule to bond to the end of the tip. This can also be

achieved deliberately as was first shown by Bartels et.al [25]. The process (Figure 14) used in

this thesis to obtain a CO terminated tip is derived from the process used by Hahn et. al [26] and

involves using a high voltage bias as the tip is moved inwards towards the CO molecule:

1. Initial tip-sample bias: 𝑉 = −50 mV, Initial tunneling current: 𝐼 = 1 nA

2. Center tip over CO molecule and change tip-sample bias to 𝑉 = −2.5 V

3. Move tip inwards by 0.5 Å

Figure 13: Confining Potential of an Adsorbed Molecule. The confining potential is approximated as a simple harmonic potential with quantized energy levels (𝑕𝑓). One scenario for the change in frequency is shown above. As the tip moves inwards, the confining potential for the 35 meV changes from the green plot to the blue plot, thereby decreasing the vibrational frequency.

Energy

q

Decreasing 𝑓

18

4. Move tip outwards by 1.0 Å

5. Return to initial conditions of 𝑉 and 𝐼

If the CO molecule has been picked up by the tip, then a rescan of the area will not show the

CO molecule. Moreover, a CO molecule images quite differently with a CO terminated tip than

with a metal tip. As shown before, a metal tip images a CO molecule as a roughly Gaussian dip.

However, with a CO terminated tip, CO molecules appear as “fringed whorls” [14]. This can be

seen in Figure 15. As discussed earlier, the CO molecule bonds to Cu(111) with the carbon end

attached to a Cu atom. Therefore, the CO molecule rotates by 180° as it is picked by the STM tip.

It is interesting to note that the exact structure of a CO molecule imaged by a CO terminated tip

depends on the tip-sample bias. This indicates that above certain biases, tunneling between the

tip and the sample may be exciting vibrational modes of the CO molecule on the tip.

Figure 15: CO on Cu(111) imaged with a CO tip. Instead of imaging as a depression, the CO molecule appears as a “fringed whorl”.

Å

5Å

Figure 14: Functionalizing an STM tip with a CO molecule. There are four basic steps to attach a CO molecule to the STM tip. a) The tip is first centered over the adsorbed molecule and the

tip-sample bias is changed to −2.5 V. b) The tip is then moved inwards by 0.5 Å. c) A sudden change in current is observed as the tip picks up the CO molecule. d) The tip is moved outwards

by 1 Å and a rescan of the area is taken to confirm the molecule has been picked up

a) b) c) d)

19

7. Vibrational Properties of a CO-Terminated Tip

As noted earlier, it is expected that the CO molecule attached at the end of an STM tip will

have vibrational modes similar to the vibrational modes of a CO molecule on Cu(111). These

modes can be excited by IETS between the CO-terminated tip and a Cu(111) surface. First, the

STM Ir tip is functionalized with a CO molecule as described in Section 6. Then both the 𝑑𝐼/𝑑𝑉

and the 𝑑2𝐼/𝑑𝑉2 spectra are measured over a bare Cu(111) surface. These are shown in Figure

16. Both the spectra show vibrational modes at around ±2 meV (~0.5 THz) and around

±31 meV (~7.5 THz). These correspond to the FT and FR modes of CO on Cu(111)

respectively. Note that the energies of these two modes are slightly different than those for CO

on Cu(111). Since the CO molecule is bonded to an Ir atom at the end of a conically shaped tip

instead of being bonded to a Cu atom on atomically flat Cu(111), the confining potential is

different from before.

8. The CO tip as an AFM Cantilever

As discussed in Section 2, changing the height between an AFM cantilever and the sample

surface changes the force between the tip and the sample which in turn changes the vibrational

Figure 16: 𝒅𝟐𝑰/𝒅𝑽𝟐 spectrum of a CO molecule on the STM tip over bare Cu(111). Similar to Figure 11, both the FT and the FR mode are observed. The FT mode has a peak center at 2 mV (~0.5 THz) while the FR mode has a peak center at 31 mV (~7.5 THz).

Sample Bias (mV)

12𝑇𝐻𝑧 12𝑇𝐻𝑧 0 Vibrational Mode

Frequency

~2mV

~31mV 𝑑2𝐼/

𝑑𝑉

2(a

.u.)

20

frequency of the cantilever. The resulting frequency shift can be measured and is used to image

the underlying substrate. As shown before (Section 5), experiments in the Manoharan lab reveal

that the vibrational frequency of a CO molecule on Cu(111) depends on the height of the tip

above the CO molecule. Thus, the LT-STM in the Manoharan lab is able to observe frequency

shifts in the THz vibrational modes of CO on Cu(111). It is hypothesized that the frequency of

the THz vibrational modes of a CO molecule on the tip will also depend on the height between

the tip and the sample. If the resulting frequency shifts can be measured for small changes in the

tip height, then the CO terminated tip can effectively be used as an AFM cantilever to probe

short-range chemical forces that excite vibrational modes in the THz regime rather than in the

kHz regime. This can allow the hybrid AFM/STM system to measure force gradients several

orders of magnitude lower than what is possible using current AFM systems.

To test this hypothesis, the CO-terminated STM tip is positioned above a bare, atomically flat

Cu(111) surface. The 𝑑2𝐼/𝑑𝑉2 spectrum is measured at a setpoint current and voltage. The tip is

then moved inwards with known steps in height (∆𝑧) and at each ∆𝑧, the 𝑑2𝐼/𝑑𝑉2 spectrum is

measured. The centers of the peaks at ±4 meV and at ±35 meV are determined by fitting

Gaussian profiles to the spectra. The vibrational mode energies/frequencies are then analyzed as

a function of height. The results are presented in Figure 17. As seen in the figure, the frequency

of the FT mode decreases by about 0.3 THz as the tip moves towards the sample by 1 Å. On the

other hand the frequency of the frequency of the FR mode first decreases and then increases

showing a maximum change of 0.6 THz.

As discussed in Section 2, the minimum force gradient measured by an AFM goes as 1/𝑓𝑜 .

Since current AFM cantilevers operate in the KHz regime, the ability to probe changes in the

THz vibrational modes of a single molecule opens up the possibility of measuring extremely

short-range forces. As shown before, the minimum force gradient resolved by current AFM’s is

to the order of 10 pn/nm. The results in this section prove that STM IETS provides a useful

technique to use a single molecule as an AFM cantilever to probe force gradients several orders

of magnitude smaller (~10−6 pn/nm) than what is currently possible.

21

9. CO-STM Tip Line Scan over a CO Molecule

So far, the work in this thesis has studied the vibrational frequency of a CO functionalized

STM tip with the tip being positioned over an atomically flat bare Cu(111) surface. For a Cu(111)

surface, it is hard to image individual atoms within the metal lattice; making it difficult to

position the tip directly above a single atom. Also, since the Cu(111) was flat, the STM tip had to

Figure 17: Analysis of the Vibrational Modes of a CO-terminated STM tip as a function of the Tip-Sample Distance. a) The 𝑑2𝐼/𝑑𝑉2 spectra at different tip-sample heights are stacked up together and the peak centers (red crosses) are tracked by fitting Gaussians to the individual peaks. b) The vibrational mode frequency as a function of height for the 2 meV (0.5 THz)

mode. As the tip moves inwards, the frequency decreases by about 0.3 THz over the 1 Å distance moved by the tip towards the CO molecule. c) The vibrational mode frequency as a function of height for the 31 meV (7.5 THz) mode. The frequency

first decreases and then increases showing a maximum change of ~0.6 THz over the 1 Å distance moved by the tip.

Vibrational Mode Frequency (THz) Vibrational Mode Frequency (THz)

Dis

tan

ce t

ow

ard

s m

ole

cule

(Å

)

Dis

tan

ce t

ow

ard

s m

ole

cule

(Å

)

Sample Bias (mV)

𝑑2𝐼/

𝑑𝑉

2(a

.u.)

Track modes Moving into sample

a)

.

b)

. c)

1 Å

0 Å

22

be brought inwards to the sample with known step sizes in order to study the frequency shift with

height. During this process, the STM tip was above the same point on the Cu(111) surface.

Ideally, the CO functionalized tip should be able to scan across a surface and be able to detect

the change in surface topography by changing the vibrational frequency of the CO molecule on

the tip. Notice that similar to AFM imaging, as the surface topography changes, the force

between the CO functionalized tip and the sample changes which in turn changes the vibrational

frequency of the CO molecule on the tip. In this way, the CO molecule at the end of an STM tip

can be made to behave as an AFM cantilever with a mass of the simplest organic molecule and a

vibrational frequency in the THz regime.

To achieve this, the STM tip is functionalized with a CO molecule and an “open loop line cut”

is taken over an adsorbed CO molecule on Cu(111). For the “open loop line cut”, the CO

functionalized tip is first positioned over the center of an adsorbed CO molecule on Cu(111)

using atom locking techniques2. The 𝑑2𝐼/𝑑𝑉2 spectrum is obtained at the center. With an open

feedback loop3, the tip is then moved radially outwards from the center in steps of 𝑑𝑟 with the

𝑑2𝐼/𝑑𝑉2 spectrum taken at each step. In this way the evolution of the 𝑑2𝐼/𝑑𝑉2 spectra can be

traced as a function of 𝑟, the radial distance from the center of the adsorbed CO molecule (Figure

18).

The most interesting observation in Figure 18 is a peak at a sample bias of ~10 mV. This

mode has not been observed before and corresponds to a vibrational frequency of ~2.4 THz. As

seen in the figure, the peak center (i.e. the frequency) of the novel mode decreases as the tip

moves outwards from the center of the molecule and eventually the mode disappears completely.

The novel mode can be clearly seen in the 𝑑2𝐼/𝑑𝑉2 spectrum taken over the center of the CO

molecule (Figure 19a). In contrast, the novel mode is missing for the spectrum taken at a point at

the edge of the adsorbed CO molecule. (Figure 19b). This suggests that the novel mode is most

likely due to coupling between the CO molecule on the tip and the CO molecule on the surface.

This novel mode could be due to a specific interaction between two CO molecules and warrants

more theoretical work.

2 This consists of finding the local minimum in the value of the tunneling current in a small region surrounding the

rough center of the CO molecule. Since the CO molecule is imaged as a dip, the local minimum. 3 An open feedback loop moves the STM tip radially outwards at a constant tip-sample height.

23

Figure 19: 𝒅𝟐𝑰/𝒅𝑽𝟐 spectrum of a CO molecule on Cu(111) with a CO STM Tip. a) Spectrum taken at the center of the CO molecule (marked by the red cross in inset figure). The spectrum shows a three vibrational modes, the FT mode, the FR mode and a novel vibrational mode at 10 mV. b) Spectrum taken at the edge of the CO molecule (red cross in inset). Spectrum shows only the FT and the FR mode. This suggests that the novel 10 meV mode is likely due to a coupling between the two CO molecules.

Sample Bias (mV) Sample Bias (mV)

𝑑2𝐼/

𝑑𝑉

2(a

.u.)

𝑑2𝐼/

𝑑𝑉

2(a

.u.)

~2mV

~34mV ~10mV

~3mV

~32mV

b)

.

a)

.

Figure 18: Evolution of the 𝒅𝟐𝑰/𝒅𝑽𝟐 spectra of a CO molecule with a CO STM Tip. The tip is positioned above the center of a CO molecule (inset) and moved radially outwards at a constant tip-sample height in steps of 𝑑𝑟 =

0.25 Å for a total distance of 5 Å. At each step the 𝑑2𝐼/𝑑𝑉2 spectrum is obtained. The spectra at each 𝑟 are plotted on the color plot in which the red/yellow shades correspond to a vibrational mode. The frequency of the 31 mV mode decreases as the tip is moved outwards. A novel mode is observed at 10 mV which transitions into the 4 mV mode as the tip moves away from the center of the CO molecule.

5Å

Sample Bias (mV)

𝑑2𝐼/

𝑑𝑉

2(a

.u.)

𝒓

Moving away from center

0 Å

5 Å

24

As seen in the Figure 18, the peak center (i.e. the frequency) of the FR mode decreases as the

tip moves outwards. To quantify this change, Gaussian curves are fitted to the peaks at

~ ± 33 mV and the shift in vibrational mode frequency is plotted as a function of 𝑟 (Figure 20).

As the tip moves outwards, the distance between the tip and the sample increases, decreasing the

vibrational frequency. This behavior is different from the one observed in Figure 17c. For the

spectrum over bare Cu(111), the vibrational frequency of the CO molecule on the tip for the FR

mode first decreased and then increased as the tip moved inwards to the sample. However, for

the spectrum over bare Cu(111), the vibrational frequency decreases as the tip moves radially

outwards.

10. Conclusion

In summary, the experiments in this thesis have, first, mapped out shifts in the THz

vibrational modes of a single CO molecule on Cu(111) demonstrating the ability of the STM to

measure changes in vibrational frequency. Second, the experiments have tracked shifts in the

THz vibrational modes of a single CO molecule attached to the end of the STM tip showing the

possibility of using this CO-STM tip as an AFM cantilever with THz frequency. Third, the line

scan over an adsorbed CO molecule reveals a novel 10 meV mode which is likely due to a

specific interaction between two CO molecules and warrants theoretical study. Lastly, the line

Figure 20: Vibrational Frequency of the FR Mode as a function of 𝒓 for CO-CO Interaction. The vibrational frequency decreases by about 0.5 THz as the tip moves radially outwards from the center of the CO molecule at a constant tip-sample height

Vib

rati

on

al M

od

e Fr

equ

ency

(T

Hz)

Radial distance from the center, 𝑟 (Å)

𝒓

25

scan shows the ability of the STM to track the vibrational frequencies of a CO molecule on STM

tip as it moves across a surface.

Overall the results serve as a proof-of principle of realizing a hybrid AFM/STM system in

which a single molecule acts as an AFM cantilever with THz vibration and STM inelastic

spectroscopy is used to detect changes in vibrational frequency.

11. Future Work & Challenges

In the short-run, the most useful approach would be to apply Density Functional Theory

(DFT) to inelastic-tunneling between a CO-STM tip and the Cu(111) surface. DFT calculations

can already accurately predict the vibrational frequencies of a CO molecule on the Cu(111)

surface with STM in-elastic tunneling. This calculation needs to be reversed with the CO

molecule on the STM tip and the frequencies calculated as a function of the tip-sample distance.

Moreover, DFT calculations should also be applied to study the novel 10 meV mode observed

with tunneling from a CO-STM tip to an adsorbed CO molecule. However, there are known

issues with DFT describing Van der Waal and molecular interactions [27], limiting an accurate

theoretical description of the novel 10 meV mode.

Another short-term goal should be to accurately predict the tip-sample force from these

frequency shifts. An approach that has been considered is to treat the CO molecule on the STM

tip as a classical harmonic oscillator similar to an AFM cantilever. Then the force as a function

of 𝑧 can be found by integrating the force gradient (eq.1) over the range the tip moves inwards to

the sample in the experiment described in section 8. The main difficulty is finding 𝑘, the

effective spring constant of the CO molecule. As 𝑘 is given by 𝑚𝑒𝑓𝑓 𝜔𝑜2, an approximate

expression for force is:

𝐹(𝑧) = −4𝜋𝑓𝑜 𝑚𝑒𝑓𝑓 ∆𝑓(𝑧′)𝑑𝑧′𝑧

𝑧𝑜

(12)

Here 𝑚𝑒𝑓𝑓 is the effective mass of the molecule due to the confining potential. Since the

confining potential for the CO molecule on the tip has not been studied theoretically, it is

difficult to solve for 𝑘. However, it is known that 𝑚𝑒𝑓𝑓 will be different for each of the two

vibrational modes (FT and FR) and in general will be smaller than the mass of a free CO

molecule (28𝑢). Thus, eq.11 is used along with the data in fig.17 to calculate an approximate

upper limit on the force function. This gives a force change of about 0.18pN over the 1 Å

distance moved by the tip towards the sample. While this is a rough calculation, it is much less

26

than the force required to move a CO molecule on a Cu(111) surface using the STM tip

(~160 pN) as measured by Ternes M. et al. in [21]. Since the force between the CO-STM tip and

a Cu(111) surface should be substantially less than the force required to move an atom on the

surface, even this rough estimation indicates that the CO-STM tip can be capable of resolving

extremely small forces.

Another goal of the CO-STM tip is to image complex structures. Experiments in section 9

described the ability of the CO-STM tip to measure the 𝑑2𝐼/𝑑𝑉2 spectrum as the tip is moved

radially outwards during “open loop spectroscopy”. For the CO-STM tip to image structures

similar to an AFM cantilever, this process must be carried out over a 2D surface in an “open loop

spectral map”. The peak centers are then determined to find the frequency of the CO molecule at

each point (𝑥, 𝑦) on the surface. The resulting frequency shifts ∆𝑓(𝑥, 𝑦) give a map of the surface

topography. However, since the spectral map takes a substantial amount of time, a major

challenge is controlling the drift of the STM tip. During “open loop spectroscopy’, since the

feedback loop is open, the STM does not adjust the tip-sample distance to keep the tip within the

tunneling regime. This can cause the tip to either crash into the sample or move away from

tunneling in addition to preventing a constant tip-sample distance. The time for the spectral map

depends on the number of points (𝑥, 𝑦) at which the spectrum is measured, averaging during each

spectrum measurement and the lock-in time constant. As a start, to avoid drift a “closed loop

spectral map” was taken using a CO-STM tip over adsorbed CO molecules. Because of problems

with the lock-in amplifier the results have not been discussed before. However, a brief analysis is

presented in Appendix 1 to help future measurements.

Once the measurement settings for the spectral map have been optimized, an ideal system to

study would be CO dimmers and trimers on Cu(111). In general CO molecules do not bond to

one another. When two CO molecules are placed on neighboring sites on the Cu(111) lattice, the

STM images a raised bump between the two CO “dips”. This is called a CO dimer. A similar

behavior is observed at the center of three CO molecules on nearest neighboring sites on the

triangular Cu(111) lattice (CO trimer). Since the “bump” observed is due to the STM imaging

electron density of states, by using a CO-STM tip additional structure for a CO dimer or trimer

may be revealed. Another long term goal is to take a 4D data set over constructed structures such

as dimmers or trimers in which the frequency shift map is measured at different tip-sample

heights. In this way ∆𝑓 can be obtained as a function of (𝑥, 𝑦, 𝑧). By connecting points of

27

constant ∆𝑓, 3D objects can be constructed revealing structures localized around the relevant

bonds between the tip and the sample. In this way, STM measurements can be extended into the

third dimension. Lastly, this measurement technique can also be used to image complex

adsorbed molecules (such as pentacene) to reveal the molecule’s chemical structure.

Appendix 1: CO-STM Tip Spectral Map over Adsorbed CO Molecules.

In order to help with future measurements, the results for a “closed loop spectral map” are

presented below. The CO-STM tip is used to take a spectral map over a (30 Å x 30 Å) region on

a Cu(111) surface with adsorbed CO molecules. The topograph before the measurement is shown

in Figure 21a. The region contains roughly three CO molecules and they are imaged as a

corrugation using the CO-STM tip. The CO-STM tip is then moved across the topograph line by

line taking the 𝑑2𝐼/𝑑𝑉2 spectrum at each point with the feedback loop closed. To save time, the

spectrum is only taken around the FR mode (𝑉 is varied from 25 mV to 40 mV). Overall, the

𝑑2𝐼/𝑑𝑉2 spectrum is measured at 51 x 51 points. Each spectrum (with averaging) takes about

20 s, giving a total run time of about 14 hrs. The lock-in measuring 𝑑2𝐼/𝑑𝑉2 had a sensitivity

of 3 mV and a time-constant of 30 ms.

Figure 21b shows the simultaneous topograph of the region as the spectral map is being taken.

Since this is a “closed loop spectral map”, the change in the tip-sample distance (𝑧) is also

measured as the spectral map is taken. This gives a simultaneous topograph of the region. As

seen in the figure, the z-values are clearly not calibrated properly. Moreover, the simultaneous

topograph shows that one of the CO molecules moved during the measurement making it

difficult to properly image it.

Once the spectral map is obtained, Gaussian peaks are fitted to the spectra and the peak

centers are determined to obtain the vibrational frequencies for the FR mode. The frequency

shifts are then plotted at each (𝑥, 𝑦) to obtain a map of the surface (Figure 21c). As seen, the

frequency map corresponds quite well to the both the topographs, confirming the possibility of

using frequency shifts in the CO-STM tip to image surfaces.

28

Acknowledgments

I would first like to thank Professor Manoharan for his tremendous support and guidance

throughout my undergraduate career. Secondly, I thank Professor Moler for making Quantum

Mechanics understandable! I also owe a lot to Warren Mar who inspired the ideas behind this

project and helped me to understand the workings of the LT-STM (Mota). Wonhee Ko helped

me throughout the summer as we worked on the room-temperature STM “mini-mota”. That

project gave me the necessary background to work on this thesis. I would also like to thank

Kenjiro Gomes for teaching me a number of tricks in MATLAB.

Å Å

GHz

b) Simultaneous Topograph a) Topograph after Spectral Map

c) Image using Frequency Shifts

CO moved during scan

30 Å

Figure 21: CO-STM Tip Spectral Map over Adsorbed Molecules. a) STM topograph of the region with the CO molecule on tip. This is taken after the spectral map. b) Simultaneous topograph of the region using the z-position of the tip during “closed loop spectroscopy”. c) Image of the region by plotting ∆𝑓 at each (𝑥, 𝑦).

29

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