Fabrication of Metal-Molecule Contacts

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Group Prof. Dr. E. Scheer Department of Physics University of Konstanz

Fabrication of

Metal-Molecule Contacts

Diploma thesis

by Simon Verleger

29^th June 2006

Konstanzer Online-Publikations-System (KOPS) URL: http://www.ub.uni-konstanz.de/kops/volltexte/2006/1969/

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Gewidmet meinen Eltern, die mich Zeit meines Lebens in Allem unterst¨utzt und mir dieses Studium erm¨oglicht haben.

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List of Figures

1.1 Development of molecular electronics . . . 2

2.1 Sketch of a SAM . . . 4

2.2 Current–length dependency in SAMs . . . 4

2.3 Structure formula of a benzene ring . . . 6

2.4 Illustration of π–bonds . . . 6

2.5 Sketch of molecules with and w/o sidechain . . . 7

2.6 Transmission with and w/o sidechain . . . 7

2.7 Structure of symmetric and asymmetric molecules . . . 8

2.8 IV–data on symmetric and asymmetric molecules . . . 8

2.9 Sketch of a Coulomb blockade system . . . 9

2.10 Coulomb blockade in C10 alkanedithiols . . . 9

2.11 HOMO–LUMO alignment . . . 10

2.12 Simulation of a wire being opened . . . 12

2.13 Typical Al opening curve . . . 13

2.14 Histogram from gold opening curves. . . 13

2.15 Alkanethiols in an MCB . . . 15

2.16 Conductance of thiolated C₆₀ . . . 15

3.1 Principle of the MCB technique . . . 18

3.2 Photographs of the experimental setup . . . 19

3.3 Sketch of the breaking mechanics . . . 20

3.4 Structure formula of polyamide . . . 23

3.5 Structure formula of polyimide. . . 23

3.6 Structure formulas of PMMA and MMA–MAA . . . 23

3.7 Detailed lithographical structure . . . 24

3.8 Sketch of a finished sample . . . 26

3.9 SEM picture of a gold bridge. . . 27

3.10 Detailed photography of the sample holder . . . 29

3.11 General structure of the molecules investigated . . . 30

3.12 Trimer formation process . . . 31

3.13 Dimer formation process . . . 32

3.14 Electronic setup . . . 33

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4.1 Count-distance calibration . . . 37

4.2 Gold opening curve . . . 37

4.3 Closing curves in THF . . . 38

4.4 Sample # SP6: tunneling in air . . . 39

4.5 Sample # SP6: tunneling through decanedithiols . . . 40

4.6 Conductance peak in opening curves . . . 41

4.7 Conductance peak in closing curves . . . 42

4.8 Sample # SP6: opening in decanedithiols . . . 44

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1

Introduction

Electronic transport has been a central issue of physical research during the last century. Tremendous amounts of materials have been investigated, for instance metals, semiconductors and insulating crystals. Research on the electrical properties of metals and semiconductors have led to the development of sophisticated electronic circuits and finally to computer chips. During the ongoing investigation on electronic characteristics, the components have been successively miniaturized.

This process brought forth devices which have become common in daily life, and which are so remarkably small that their chips are hardly visible to the bare eye.

For many years an end has been predicted to the ongoing miniaturization of electrical components due to physical restrictions in the fabrication processes. This end has been successively protracted due to technological advances in the produc- ing industry. Nevertheless, the classic miniaturization methods must finally cease when the size of electrical components reaches a stage in which current quanti- zation effects govern the conductance. This is where molecular electronics takes over.

Molecular electronics takes a different approach than miniaturization: Instead of trying to minimize existing electrical components, one investigates the thinnest wires imaginable: single atoms, chained to one another as a wire. These wires can be designed by chemists in an almost infinite number of shapes, varying in chain length, functional groups, side groups, end groups, etc. A single molecule might possibly act as a wire, diode, or transistor in future electronic devices. Apart from possible applications in industrial devices, research on electronic properties of molecules by itself proves to be an interesting issue of science. Reliably and reproducibly driving a current through a single molecule is a challenging task that scientists have been concerned with for decades.

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1975 1980 1985 1990 1995 2000 year of cited article published

0 25 50 75 100 125

number of citations

Figure 1.1: Increasing interest in molecular electronics indicated by citations of [1].

A. Aviram and M. Ratner discussed for the first time in 1974 that single molecules might be used as electronic components [1]. At that time their ideas were merely theoretical, but today they are considered visionary. The increasing interest and research activities upon molecular electronics may be measured by the number of times their article is cited. Figure1.1 (adopted from [2]) indeed shows a tremendous increase of engagement in this field of research.

The first reliable single-molecule transport measurements were reported in 1997 by Tans et al. [3]. Since then, efforts have been made worldwide to extend knowl- edge about electronic transport through molecules, yet experimental results have shown a large variety. This is caused by one ruling factor: The slightest changes to a molecular device — be it only one single atom which is missing or exchanged

— usually change the overall behavior of the device. This makes investigation of molecules a difficult research topic, because reproducibility on the atomic scale is not easy to achieve for a physicist.

In this thesis, a possibility is presented to measure the electrical conductance of a few or even one single molecule trapped within a mechanically controllable breakjunction. Conjugated carbon bonds are located along the chains of the molecules and they are therefore supposed to exhibit good conductance. The breakjunction technique provides a system of electrodes with fine-tunable tips for trapping the molecules.

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2

Fundamentals and Basic Principles

This chapter provides an overview of basic principles of molecular electronics and current transport through nano-scale wires. Experimental as well as some theoretical fundamentals are presented which are essential for an understanding of the experimental setup and measurements.

2.1 Molecular Electronics

Basic principles of transport through molecules will be addressed in this section, with special regard to the question: What makes a molecule a good conductor, i.e.

what are the governing conductance mechanisms?

2.1.1 Tunneling through Alkanes

Tunneling is not an indication of a good conductor, but on the contrary defines an insulator. Nevertheless, it is mentioned here because many types of molecules exhibit this electrical behavior. Alkanes, the simplest molecular wires, have been a primary subject of intense research. For instance n-alkanethiol CH₃(CH₂)n−1SH has often been investigated, because it can easily be attached to a metal contact due to its thiol (SH) end¹.

Alkanethiols form self-assembled monolayers (SAMs) on gold and other metals.

Investigation of the electrical properties of alkanethiols is a key step in the understanding of electron transport mechanisms in more complex organic molecules²

1Thiol groups have a strong chemical affinity to metals, especially to gold.

2Organic chemistry deals with structures based upon carbon and hydrogen atoms, in contrast toanorganicchemistry.

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12 14 16 18 20 22 24 10^-8

10^-6 10^-4 10^-2 10⁰

0.4V 0.3V 0.2V 0.1V

Jd2 (A)

Jd (A/cm)

Length (Å)

10^-15 10^-13 10^-11 10^-9 1.0V 0.9V 0.8V 0.7V 0.6V 0.5V

C8

C12

C16

Figure 2.1: Schematic of a self- assembled monolayer of alkanethiols sandwiched between two electrodes.

Figure 2.2: Alkanethiols between gold electrodes; log plot of tunneling current densities multiplied by molecular length d at low bias and by d² at high bias vs. molecular lengths with linear fits [4].

that might function as nano-scale electronic components. SAMs have been integrated into electronic circuits via several hybrid interfaces, such as:

metal/molecules/metal [5] or metals/molecules/molecules/metal [6]. Furthermore, metal/molecules/semiconductor [7], [8], and metal/molecules/polymers [9] were used as interfaces.

When investigating the metal/molecules/metal interface, monolayers of alkanethiols are sandwiched between two metal electrodes and a bias voltage is applied to them. Different experimental setups for current-voltage (IV)-measurements on similar SAMs have revealed significant qualitative differences. Alkanethiols were found to exhibit symmetricalIV-characteristics [10], whereas in other experiments asymmetrical characteristics [11], even diodes [8], were observed. These differences presumably result from variations in the measurement procedure, such as different solvents or different metals. During the last few years, it has become obvious that the complexity of molecular electronics had clearly been underestimated in the beginning. Though huge differences in the electrical response of alkanes have been measured as described above, at least one property has remained constant;

comparing alkanethiols of different lengths reveals an exponential dependency of the current density on the chain length [4], [10], [11]. Figure 2.1 shows the con- cept of the experimental setup, while the measured data is presented in figure 2.2.

It shows that the exponential-decay constant depends on the type of molecules investigated, which means that there is some chemical contribution to the current density coming from the monolayer. This is clear evidence that the chains

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2.1 Molecular Electronics

Conduction mechanism Characteristic behavior Direct tunneling J ∼V exp−2d√

2m^∗eΦ/¯h

Thermionic emission J ∼T²exp−eΦ−^qeV /4πd/k_BT Hopping conduction J ∼V exp (−∆E/kBT)/d

Fowler-Nordheim J ∼V²exp−4d√

2m^∗eΦ^3/2/(3¯hV)/d² Table 2.1: Possible tunneling mechanisms, with current density J, bias voltage V, insulator thickness d, effective electron mass m*, elementary charge e, Schottky barrier height (working function) Φ, temperature T, insulator permittivity , and activation energy of electrons ∆E [12].

do not act as pure spacers, but rather that the governing transport mechanism is through-bond tunneling. The current does not flow through the molecules, but rather electrons actually tunnel along the bonds.

Table 2.1 lists some possible tunneling mechanisms that can occur in molecular junctions. Besides the common direct tunneling, there is thermionic emission in semiconductor junctions as well as hopping conductance. In the latter process, thermally excited electrons hop from one isolated state to the next. Fowler- Nordheim tunneling results when the energy of the applied electric field comes in the range of the contact barrier height. There are several other types of tunneling mechanisms, varying with the type of interface and the applied voltage bias.

2.1.2 Saturated versus Conjugated Bonds

A primary classification for molecules is the type of bonds between its atoms.

Simple alkanes as depicted in figure 2.1 only consist of so-called saturated bonds, also known as σ-bonds. This kind of bond is based on binding electrons which are localized between two neighboring atoms.

In contrast to these saturated bonds there are so-called conjugated bonds. The benzene ring in figure2.3consists purely of conjugated bonds. In common chemical writing, these are denoted as alternating double and single bonds, which is a symbolic notation only. Actually, every bond is equivalent to the next one; a continuous chain of delocalized electrons in so-called π-bonds evolves.

Thus, conjugated molecules possess electrons which can move freely along the molecule. These electrons can act as free charge carriers, and the molecule may exhibit conductive behavior. Saturated molecules, on the contrary, possess localized electrons that are strongly coupled to only their origin atoms. Therefore, these molecules show much less conductivity than conjugated ones.

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Figure 2.3: Benzene ring. The alternating double and single bonds symbolize equivalent, delocalized π-bonds. The single hydrogen atoms at every corner are omitted, as usual in chemical structure formulas.

Figure 2.4: The tori illustrate the delocalized π-electrons in a benzene ring.

2.1.3 Influence of Anchor Groups

Molecular devices do not have inherent resistance. Instead, their electronic behavior strongly depends on the interface into which they are coupled, so the nature of the electrodes on each side must be considered. A crucial factor in any molecular device is the atomic coupling to the electrodes. Therefore it is not possible to discuss the electronic properties of a specific molecule, rather only of a complete molecular interface.

A precondition for good conductivity ischemical bonding in contrast tophysical bonding. The latter one (also known as physisorption) means weak coupling due to van der Waals forces or simply polarization, while chemical bonding (also called chemisorption) refers to real covalent bonds. For instance, the conductivity of an alkyl monolayer increases substantially once both ends of the chains are chemically bonded to the contacts [13]. Salomon et al. give a broad overview of measurements on saturated as well as conjugated carbon chains [14]. A fairly comprehensive comparison of different binding mechanisms is offered in that article. Studies so far indicate that the influence of real chemical bonding is less important for conjugated bonds than for saturated ones. This might result from an overlap of the π–orbitals of the conjugated molecules with the spill-over electron density of the metal [14].

Additionally, an anchor group may not just alter, but even govern the conductance of a molecule. If the molecule itself is a good conductor, but the anchor has a large tunneling resistance, then electrons cannot just enter the molecule other than by tunneling or hopping, which drastically reduces the over-all conductance of the device.

A commonly utilized anchor is thiol. Though, the exact binding mechanism of thiols to metals is still being discussed. It is not known if the hydrogen atom is

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released during bond formation, and there is inconsistent opinion about the kind of bond formed. If the thiol integrates its binding electrons into the bonds of the molecule, then it would thereby participate in the formation of a π-bond. A conjugated molecule with thiol ends would therefore be fairly conductive. If, on the other hand, the binding electrons only form a σ-bond, then the charge transfer through the anchor groups would be hindered.

2.1.4 Molecular Geometry and Conductance

Theoretical as well as experimental studies yield evidence that the electronic transport properties of a molecular device are directly related to the geometry of the molecules involved.

this case, !ˆ

L!R"!E" is reduced¹³ to a matrix with a single element. This element is treated as a parameter and we set it equal to!1/2"t, wheret is the hopping matrix element em- ployed in the molecule. The assumptions made above also simplify the calculation of Green’s functions in Eq.!2".Gˆ^a!r"

is obtained from the molecular Hamiltonian with imaginary potentials i!ˆ

R/2 and i!ˆ

L/2 added to it.¹³ This simple approach enables us to describe qualitative features of MEDs.

In particular it helps to establish structure-conductance rela- tionships that might be difficult to identify in more rigorous treatments due to the complexity of theT!E"curves. A second approach to evaluate Eq. !2" is derived from the KS DFT. Again, we only consider the zero-voltage limit. The one-electron picture that we employ^4–6is a combination of the KS method for the molecule plus finite clusters of contact atoms and a self-consistent tight-binding approximation for the remaining contacts. We obtain a Hamiltonian of the entire system that is then used to construct the various quanti- ties needed in Eq.!2".

To completely understand the conductance of a molecule, the wave function"of the MED with a current pass- ing through is needed. Recently, we presented a method^9,14 that permits the calculation of". We enclose the MED in a large but finite box. In such a closed system, the solutions of an independent-particle equation !the orbitals"are real. In- side of the system, where surface effects can be neglected, the wave function # is a combination of forward!#⁺"- and backward !#⁻"-going solution. Note that #^+*=#⁻. The forward-going solution !describing the electron transport from the left to the right contact"is defined such that it has only an outgoing Bloch wave!$⁺"in the right contact and no incoming one. This is the usual Landauer boundary condition.¹¹In the right contact,#is given by

#=#⁺+#⁻=a$⁺+a^*$⁻, !3"

where $⁻ is the backward-going Bloch wave anda is the coefficient of the outgoing Bloch wave. If we calculate the current density of# we obtain

j!r"=##$jˆ!r"$#%=$a$²

!

^#^$⁺$jˆ!r"$$⁺%+#$⁻$jˆ!r"$$⁻%

"

^, ^!4"

wherejˆ!r"=1/2!$r%#r$Pˆ+Pˆ$r%#r$".Pˆ is the momentum op- erator. Note that there are no cross terms contributing to the current density. To eliminate #⁻ from #, we consider a model Hamiltonian that contains a complex one-particle potential %ˆ=&ˆ+i'ˆ,

Hˆ=Tˆ+(ˆ+&ˆ+i'ˆ =Hˆ₀+i'ˆ. !5"

Hˆ₀ is the sum of the kinetic-energy operatorTˆ, the external local potential (ˆ, and the artificial potential &ˆ. For time- independent densities, the continuity equation of Hˆ is reduced to¹⁴

!j!r"= 2

&

^'^ˆ^r!)!r,r!"

'

r=r!, !6"

where) denotes the one-particle density matrix. The diver- gence ofj, i.e., !j, is nonzero, demonstrating that an imaginary potential generates and absorbs current density depend-

ing on the sign of &'ˆ

r!)!r,r!"'r=r!. This property of

imaginary potentials can be exploited^9,14to eliminate the un- desired contribution in Eq.!3".

III. TRANSMISSION THROUGH MOLECULES WITH SIDE CHAINS

Using the Hückel model described above, we consider the butadiene molecule attached to two contacts(Fig. 1!a").

T!E"obtained for this MED is plotted in Fig. 2!blue curve".

As expected, there are four maxima that coincide with orbital energies of the isolated molecule. Note that we only use a single value for the hopping parameter, ignoring the dimer- ization tendency in butadiene and similar systems. Now we attach a hexatriene side chain to the butadiene to obtain the MED sketched in Fig. 1!b". This device yields a dramatic change inT!E" !Fig. 2, black curve". Each energy level of the isolated molecule correlates with a maximum in T!E".

The red dots in Fig. 2 indicate the positions of the energy levels of the molecule. The most remarkable point is, however, that T!E" exhibits strong interference features that manifest themselves at numerous energies of vanishing T.

The energy levels of the isolated hexatriene side chain are marked by black dots above the energy axis. They coincide with the zeros in T!E" of the total system. The observed behavior can be explained with elementary quantum mechanics. We consider the side chain as a one-dimensional object, at the end of which the wave function has to drop to

FIG. 1. Molecular electronic devices containing the butadiene molecule!a"

with a hexatriene!b", two ethene !c", and a styrene side chain !d". The rectangles represent the contacts.

FIG. 2. The transmission probabilityT!E"obtained for the butadiene with

!black curve"and without!blue curve"hexatriene side chain. The red dots

mark the orbital energies of the entire molecule, while the black dots corre- spond to the energy levels of the side chain. The energy is given in units of the hopping parametert. The Fermi energy coincides with the coordinate origin.

134704-2 Ernzerhof, Zhuang, and Rocheleau J. Chem. Phys.123, 134704"2005#

Downloaded 06 May 2006 to 134.34.4.5. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

Figure 2.5: Molecules investigated by Ernzerhof et al.: butadiene molecule (a) with a hexatriene side chain (b). The rectangles represent the contacts [15].

Figure 2.6: Electron transmission probability T vs. electron energy E (arb. units) obtained for butadiene with (black curve) and without (blue curve) hexatriene side chain.

For details, cf. [15].

Ernzerhof et al. performed Kohn-Sham density functional theory and H¨uckel- type calculations on the transmission probabilities of conjugated molecules [15].

These calculations reveal that the addition of side chains to a molecule may re- duce the transmission probability for electrons to zero, depending on its geometry.

Figure 2.5 shows the molecules in question, while figure 2.6 gives the results of the calculations: The transmission probability drops to zero wherever the hopping energy of an electron coincides with an energy level of the side chain. The electron density at the intersection point of side chain and main chain vanishes for electrons with an eigenenergy of the side chain, as described detailed in [15].

Experimental evidence for strong geometrical dependencies of molecular conductance has been presented by J. Reichert et al. [16]. In a mechanically controllable breakjunction, two different types of conjugated molecules were trapped. The first

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S

S S

S

Au Au

NH

O₂N O

V [V]

dI/dU [μA] I [μA]

dI/dV [μS]

Figure 2.7: A spatial symmetric and an asymmetric molecule between two gold leads [16].

Figure 2.8: IV-data (dashed lines) and dI/dV calculations (solid lines) [16]. Blue:

asymmetric molecule, red: symmetric molecule.

type has a completely symmetric structure, whereas the second type has been designed asymmetrically through the addition of two different side chains to the first structure (cf. figure2.7). IV-measurements on the symmetric molecule reveal symmetric curves (red lines in figure 2.8), whereas the asymmetric molecules exhibit asymmetric behavior (blue lines in figure2.8). The difference in shape is presented more obviously by calculation of the numerically differentiated data dI/dV (solid lines).

2.1.5 Coulomb Blockade

Though not solely a phenomenon in molecular electronics, the Coulomb blockade is mentioned in this section particularly because it is a typical effect when investigating organic molecules. Nevertheless, this effect can not be observed in this thesis, because a gate electrode is needed for the Coulomb blockade to occur, as described in this section.

Coulomb blockade appears in mesoscopic and nanoscopic systems when a conductor is coupled between two leads with insulating contacts. Therefore, charge cannot flow, rather it tunnels onto and off of the conductor. This may happen in a molecular device if the linking groups do not conduct well, as described in section 2.1.3. The conductor therefore acts like an island on which charge is stored:

a capacitor with capacitance C. This situation is schematically depicted in figure 2.9: Electrons need an energy of e²/2C above the Fermi level to tunnel onto the island, while holes need the same amount of energy, so the total gap width is

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conductor lead lead

E_F

e²/2C

I [nA]

V [V]

Figure 2.9: Sketch of a Coulomb blockade system. Top: conductor between two leads. Bottom: energy- level spectrum with an energy gap of e²/C.

Figure 2.10: IV-data of C10 alkanedithiols between gold contacts at 4.2 K[17]. The region of constant current supposedly results from Coulomb blockade.

e²/C. This phenomenon can occur only when the energy needed to add an electron to the island far exceeds the energy available from thermal fluctuations, which is hardly obtainable at room temperature.

Once an electron has tunneled onto the island, the electrostatic potential is in- creased bye²/2C. The next electron can only enter if the voltage across the island exceeds a critical value of V > V_c =e/2C [18]. For a voltage in the range V < V_c, the charge transfer is blocked, and one therefore speaks ofCoulomb blockade. Fig- ure2.10displaysIV-curves that supposedly result from this phenomenon: Current flow is blocked for the low voltage range and starts only once a critical voltage bias is reached.

This mechanism might be used to build a single-electron transistor (SET). First, applying a voltage bias to the leads in figure2.9lowers one of the Fermi levels, the right-hand one, without loss of generality. If, in the second step, the potential of the island can be changed in such a way that the free conductor state in figure 2.9 lies between the Fermi levels of the leads, then the charge transfer through the island is possible. If, on the contrary, the free conductor state liesabove or beneath both Fermi levels of the leads, then the charge transfer through the device is not allowed due to insufficient electrical energy. The current flow through the device can therefore be completely controlled by shifting the electrostatic potential of the island. It is therefore necessary to couple the Coulomb island to a gate electrode,

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Figure 2.11: Sketch of the energy level alignment of the HOMO and LUMO of a molecule between the Fermi levels of the metal contacts.

The double arrows each represent a pair of electrons. The Fermi level lies in the HOMO-LUMO gap due to energetic interactions when establishing contact.

LUMO HOMO E_F

Energy

which can raise or lower the electrostatic potential of the island. The different curves in figure 2.10 are obtained from various gate voltages on the island. This measurement demonstrates that it is in principal possible to build a SET.

2.1.6 HOMO and LUMO Shifts

The phenomena described so far are typical for molecules and important in order to understand basic transport mechanisms. However, neither tunneling along saturated bonds nor Coulomb blockade is actually wanted for electronic transport.

This section describes a simple model of current flow through a good molecular conductor.

Unlike metals or semiconductors, there is no electron density of states and no energy band structure in molecules. Rather molecular orbitals provide discrete energy levels, each of which can be occupied by only a few electrons. It is common to use the chemical terms highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). The energy of electrons in the HOMO actually corresponds to the ionization energy of the molecule, which has a typical value of−9 eV (referring to the lowest energy of a free electron in vacuum as zero).

The Fermi levels of noble metal contacts on each side of the molecule have an energy of about −5 eV. When establishing contact, the energy levels of the molecule rearrange due to the influence of the electron densities of the metal until equilibrium is achieved. This is often referred to as the ‘band lineup problem’:

Geometrical reorganization, charge flow and charge rearrangement occur until the potentials of the metal line up with the eigenstates of the isolated molecule. This situation is depicted in figure 2.11. Once the system has reached a stable state, the Fermi level of the metals lies between the HOMO-LUMO gap of the molecule.

If this were any different, charge would flow until this condition resulted.

When a voltage bias is applied to the contacts in figure 2.11, the Fermi level on

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2.2 Transport through Nano–Scale Wires

one side rises whereas it declines on the other side. As soon as the HOMO or the LUMO lies between the Fermi levels, charge can flow freely through the device. The electronic properties of any molecular junction are dependent on the exact relation of the energy levels of the molecule and their alignment with the Fermi levels of the contacts. The calculation of this band lineup problem is a subject of intense theoretical investigation. Recent first-principle calculations yield that the energy offset between the HOMO and the metal Fermi level is rather independent of the isolated molecule’s absolute ionization energy (the HOMO level). But calculations show that, on the contrary, the molecular properties strongly impact the metal work function [19].

Studies of the molecules in figure 2.7, using non-equilibrium Green’s function and density-functional theory, indicate that the influence of the contacts’ electron densities outweighs the effects of any HOMO/LUMO-Fermi alignment [20]. This would mean thatIV-curves did not yield any significant features in the low voltage window. However, experimental studies on the same molecules do show nonlinear properties (cf. figure 2.8). This indicates once more how little is certain about mesoscopic and nanoscopic systems and how much reliable data is required in order to understand transport phenomena on this scale.

2.2 Transport through Nano–Scale Wires

Electronic transport through common macroscopic metal wires can be described in a simplified way by Ohm’s law R=V /I, which can also be written asG=σA/L.

HereGdenotes the conductance, σ stands for the conductivity of the wire,A rep- resents the cross-sectional area of the wire and L the length. When investigating transport properties in nano-scale wires, this law does not hold anymore. The measured conductivities in single-atom contacts are up to two orders of magnitude smaller than Ohm’s law would predict. At the same time, a single-atom contact can sustain a tremendously large current density of 10¹¹ A/cm², which corresponds to 100µA [21]. This stands in contradiction to classic transport laws in macroscopic systems. Transport on the nano-scale must therefore obey other rules than transport in classic systems.

2.2.1 Transport Channels and Landauer Formula

Figure 2.12 shows a simulation of a nano-scale wire being torn apart. During this process, the atoms permanently rearrange their configuration. In such a system, which consists of a narrow wire between two large metal reservoirs, one must consider the possible states for electrons in order to obtain information about the conductance of the device. Unlike in the metal bulk, electrons can occupy only

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Figure 2.12: Simulation of a gold bridge being torn apart [22].

a very restricted number of states in the wire. The limited geometry of the wire confines the possible modes of electrons. Therefore, only charge carriers in a proper mode can enter from the bulk into the wire. These boundary conditions finally lead to an expression for the conductance that shows a step-like dependency on the wire width. This has been validated extensively by experimental data. Figure2.13 shows a so-called opening curve, a plot of the electrical conductance versus the width of the wire.

In a single-atom contact, charge must be carried through the valence orbitals of the central atom. The number of modes that can contribute to charge transport

— also denominated as ‘channels’ — is therefore related to the number of valence electrons of the central atom. The conductance of a device having N conduction channels is summarized in theLandauer formula:

G=G₀

N

X

n=1

t_n; with G₀ = 2e²/h. (2.1) In this equation, t_n is the transmission probability for the nth channel, andG₀ is the conductance quantum withG₀ = (12906 Ω)⁻¹. The name forG₀ is misleading because it is not a quantum in the sense of ‘smallest unit possible’ but rather a typical value of electronic transport in point contacts. Every channelnis weighted with the associated transport coefficientt_n. The total conductance can therefore be smaller than 1G₀, for appropiate values of t_n. The result is that the conductance of a gold point contact equals oneG₀, whereas for an aluminum point contact it is only about 0.8 G₀. Further details about conductance mechanisms in nano-wires may be found in [23], [24].

It is possible to tear apart a wire as in figure 2.12 and close it again repeatedly by themechanically controlled breakjunction technique (MCB) described in detail in chapter3. Hundreds and even thousands of opening curves can thereby be taken from one single sample. Histograms may be obtained from these opening curves

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2.3 Investigation Methods in Molecular Electronics

-0.8 -0.6 -0.4 -0.2 0.0 0.2

0 2 4 6 8

conductance (G/G)0

electrode distance (nm)

0 1 2 3 4 5 6 7 8 9 10

0 200 400 600 800 1000 1200 1400 1600

# Counts

G/G₀

Figure 2.13: Typical opening curve of an aluminum contact, along with an illustration of the electrodes being opened [25].

Figure 2.14: Histogram from 493 opening curves of a gold contact at am- bient conditions [26].

by counting every specific conductance value and by plotting the counts versus the conductance. Figure2.14shows a histogram of almost 500 opening curves of a gold MCB. For higher conductance values, the histogram has a complicated structure.

This is because the atoms arrange slightly differently during every opening process, so the configuration and therefore the number of conductance channels changes with every opening curve. The only configuration that most breaking cycles have in common is the single-atom contact that corresponds to the peak at G₀. Sharp peaks also appear at two and three G₀.

2.3 Investigation Methods in Molecular Electronics

For the characterization of molecules, a variety of experimental setups have been used successfully. This section briefly addresses the advantages and disadvantages of some characterization methods.

Techniques such as nanopore systems [27], nanogaps fabricated by shadow evaporation [28], electromigration [29] or electrochemical methods [30] have been used.

However, these methods involve fixed contact arrangements. Only scanning tunneling microscopy (STM) and mechanically controllable breakjunctions (MCBs) offer a gap which is tunable in real-time during the measurement.

In the STM technique, a number of molecules is deposited onto a conducting surface, which serves as the second electrode in addition to the STM tip that ap- proaches the molecules from above. No chemical bond is usually formed between the molecule and the STM tip, giving rise to the disadvantage of a strongly asym-

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metric configuration of the system [2]. On the positive side, the STM method facilitates high-speed investigation of the diffusion of molecules in real time [31].

A main advantage of the STM is its ability to manipulate the current configuration atom by atom or molecule by molecule [32], and to monitor the configuration with subatomic resolution [33].

The MCB technique provides two electrodes that are separated by the typical size of the molecules (cf. figure 2.12). The electrodes are created by tearing apart a thin metal wire, thus exposing clean fracture surfaces. STM experiments have to be performed in ultra-high vacuum in order to achieve a similar degree of purity. The MCB method allows easy adjustment of the gap size to the length of various types of molecules and also gives control over the mechanical stress of the molecules. Furthermore, by opening and closing the gap repeatedly, many different molecular junctions can be obtained in one experiment. Statistics over multiple measurements are therefore made possible, supported by the good mechanical stability of the system. This stability also allows the investigation of changes caused by external parameters such as magnetic fields or temperature.

An obvious drawback of the MCB technique is the lack of information about the current atomic configuration of the electrodes. Another disadvantage is the fact that the setup is too large to be integrated into future nano-scale electric circuits.

Thus, the MCB method is suitable for characterization of molecules, but hardly for the construction of more complex molecular devices.

A more detailed comparison of investigation techniques may be found in [2].

2.4 Measurements in Liquid Environment

Regarding the phase of molecules, there are two distinct possibilities of investigation. They may either be characterized in a dry phase, or in a liquid environment.

Dry molecules have few degrees of freedom and therefore rapidly assume a fixed configuration. In order to explore the full range of possible chemical reactions, molecules must be dissolved in a liquid solvent. Only within a solvent molecules have sufficient time and spatial freedom to form a monolayer, for instance, or to undergo more complex chemical changes. It must therefore be a primary aim of research in molecular electronics to design experimental configurations which facilitate measurements in liquid environment. Such a setup allows systematic investigation of the effect of different, pure solvents as well as measurements on various kinds of molecules.

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2.4 Measurements in Liquid Environment

(a)

V=0.1V

gap size (arb. units)

I (µA)

0 15 30 45 60 75 90

10^-1

10^-2

10^-3

10^-4

0 30 60 90 120

0.00 0.02 File: 0.04

G/G0

gap size (arb. units)

Figure 2.15: I vs. gap size curves in decanethiol. The solid lines indicate two regions with different tunneling decay constants [34].

Figure 2.16: Conductance vs. gap size curves in thiolated C₆₀ [34].

Measurements in Liquid with an MCB

L. Gr¨uter has constructed the first system that integrates a liquid cell into an MCB setup [34]. During her PhD thesis, measurements on various solvents were performed. By variation of the electrode distance within the solvent, it was found that the solvents differ mainly in their tunneling decay constant.

Monolayers of alkanethiols were assembled on both electrodes of the MCB. The dependency of the current on the gap size was investigated. The measurement revealed two distinct ranges of gap size with different tunneling decay constants (cf. figure 2.15). This behavior is attributed to deformation of the monolayers during reduction of the gap size. When approaching each other, the monolayers may interlock and act as a mechanical resistance opposing further compression [34].

Furthermore, C₆₀ molecules functionalized with one thiol group were investigated. The measurements of solvents mentioned above served as control experiment for the characterization of C₆₀ molecules. It was found that the shape of the conductance curves depends strongly on the solvent used.

The C₆₀molecules are bound by chemisorption of the thiol group to one electrode only. This results in different coupling strengths at each end of the molecule. Plots of the conductance versus the gap size exhibit a local maximum, as presented in figure 2.16. By application of a simple Breit-Wigner tunneling model, it was possible to extract the electronic tunneling rates.

This model for resonant tunneling in a double-barrier junction assumes one specific tunneling constant for each end of the molecule and one discrete molecular energy level between the ends. The thiolated C₆₀ molecule allows for tuning the

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coupling to the electrode, because one tunneling rate is fixed while the other varies exponentially with the gap size. The resonant tunneling model results in a peak in the conductance once the molecular energy level aligns with the Fermi level of the leads.

Measurements in Liquid with an STM

Only a few measurements have been performed with an STM in liquid solution.

B. Xu et al. investigated bipyridine and alkanedithiols of different lengths [35]. The tunneling decay constants of alkanedithiols obtained from these measurements are consistent with values obtained from first-principles calculations. Furthermore, the characterization yields a single-molecule conductance of 2×10⁻⁵G₀ for de- canedithiol and 1.2×10⁻³G₀ for hexanedithiol.

L. Venkataraman et al. characterized amine-terminated molecules in solution between gold contacts [36]. Conductance histograms obtained from this experiment exhibit much sharper peaks than conductance diagrams obtained from dithiol-gold junctions. Therefore, the amine linkage provides well-defined conductance measurements of a single molecule. The tunneling decay constant obtained from these measurements is in good agreement with calculation based on density-functional theory.

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3

Experimental Section

There is still no routine procedure for the investigation of electrical properties of single molecules. Electrodes require small and sharp tips so that a single molecule can be trapped between them. J. v. Ruitenbeek and others have developed one method which suits this task, called mechanically controllable breakjunction technique.

A metal wire only 100 nm in width is produced on a substrate. The gold wire is then carefully stretched by applying mechanical pressure on the substrate, as seen in figure 3.1. Thus, the wire successively narrows until it finally tears apart, thereby providing two atomically sharp electrodes facing each other at the two ends of the metal wire. A detailed sketch of the wire structure may be found on page 24.

In order to trap a single molecule, in the next step, both electrodes are covered with identical monolayers. If the gap measurement between the electrodes equals the total length of two molecules in the monolayer, then one molecule on each electrode may chemically bind to the opposing one and form a dimer¹. The final molecule that links the electrodes is therefore chemically assembled in situ from two identical monolayer molecules. For details, cf. page 32.

Another type of molecule investigated consists of two identical monolayers plus a central linking group which is inserted between the monolayers in situ as well.

The chemical reaction is displayed on page 31.

Provided that the electrode tips are sufficiently sharp, one single molecule will span the gap. For less defined tips, one may expect a few parallel molecules bridging the gap.

1Dimer generally denotes a two-compound structure in chemistry, while trimer accordingly denotes a three-compound structure.

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substrate gold

2!m

L u

t

"u

"x

Figure 3.1: Left: Principle of the mechanically controllable breakjunction technique, with substrate thickness t, distance between counter supports L, free suspended length u, elongation of the free suspended length δu, and movement of the pushing rod δx. Center: Colored scanning electron microscope image of the bridge. Right: Illustration of the central point contact.

This chapter contains a brief description of the breaking mechanism and the setup utilized, followed by an overview of the manufacturing process of the samples.

At the end of the chapter, a description of the molecules investigated is given as well as information about molecule deposition and about the chemical processes involved in the investigation.

3.1 Breaking Mechanics

This section describes the experimental setup. For a picture of the complete installation, cf. figure3.2. The assembly mainly consists of the breaking mechanics, the pipet holder for deposition of molecules and the electrical measurement units (not included in the picture).

The metal bridge does not only need to be opened, but the distance between the bridge ends needs to be adjusted within sub-nanometer range. Astonishingly at first glance, this can be accomplished with a purely mechanical setup as presented in figure 3.2. A sketch of a sample in the center of the breaking mechanism is pictured in figure 3.1. Basically, a centered pushing rod bends the sample, which is held in place by counter supports at the ends. The bending transfers the vertical movement of the pushing rod δx into a lateral stretching of the metal bridge δu according toδu=rδx, where the factor r is given by

r = 6ut

L² . (3.1)

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3.1 Breaking Mechanics

Figure 3.2: Photos of the setup.

Left: 1) pipet holder on xyz-stage, 2) sample holder, 3) motor. Top:

details of the sample holder: a) pipet with PDMS gasket, b) contact clamps (bypassed by a thin, red- coated wire), c) pushing rod.

In this formula (adopted from [37]), u is the free suspended length of the metal bridge, t the substrate thickness, and L equals the distance between the counter supports. Typical values for r range from 10⁻⁴ to 10⁻⁵.

The pushing rod is not moved directly towards the sample in the upper bronze plate (figure 3.3). Instead, it is fixed onto the lower bronze plate. This plate is connected to the upper one by three smooth guiding rods and one differential screw. The lower bronze plate contains a thread nut with a pitch of 0.35 mm, while the thread nut in the upper bronze plate is cut with a pitch of 0.25 mm. The threads of the differential screw are cut accordingly. Rotating the screw by one full turn therefore only raises the lower plate by the difference of the two pitches α= 100µm.

The differential screw is driven by a DC motor using gears with a reduction ratio R_motor = 1 : 5490. The motor is controlled by a computer program and can be positioned at exactly one thousand steps per turn. The continuous elongation δu finally causes the bridge to tear apart, resulting in a gap of width ∆s. The

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sample guiding rod

differential screw

counter bearing pushing rod

Figure 3.3: Sketch of the breaking mechanism showing the differential screw with pitches of 0.25 mm and 0.35 mm, respectively.

relation between the lead distance ∆s and the motor-step count can therefore be finally written as:

∆s=rαR_motorcounts

1000 , (3.2)

with r taken from equation 3.1.

Further details about the breaking mechanics can be found in [23], [38].

3.2 Sample Preparation

3.2.1 Overview

First a short overview of the procedure is provided, supplemented by some information on the materials used (table 3.1). Every step will then be discussed in detail in the following sections.

The starting point of the fabrication is provided by a polished bronze wafer ( ). The wafer is covered with a layer of polyimide ( ), which serves first of all as an electrical insulator and second as a smoothing layer and third as a ‘sacrificial layer’

in the subsequent etching process.

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3.2 Sample Preparation

Electron beam resists: Two layers of resists ( , ) are applied on the polyimide. They differ in resolution and sensitivity when rinsed in proper solvents, which will be crucial during the

‘developing’ step.

Lithography: The scanning electron microscope illuminates those areas on the sample which are to subsequently become the electrodes. The electron beam causes a split-up of chemical bonds in the resists, which can then be affected by certain solvents.

Developing: The exposed structures are washed out by two different solvents. The lower layer is affected by the solvents more than the upper layer. Thus, the profile shows an undercut, which is the decisive factor during the next step.

Evaporation: Metal ( ) is evaporated onto the mask. Due to the metal coming from a well defined direction, the undercut in the profile causes a precise shadow. Thus, the gold on top of the resist has no contact to the gold in the ‘valley’, which will become the electrodes.

Lift-Off: The remaining resists including the metal on top are then completely removed by rins- ing the sample in acetone. Only the metal electrode structure remains, which is insulated from the bronze substrate by the polyimide layer.

Etching: A reactive ion plasma reduces the insulating layer, which is completely removed underneath the central metal wire. Thus, the wire finally becomes a self-supporting bridge.

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Layer Thickness Material

Metal structure 80 nm gold

Resist 160 nm PMMA, cf. section3.2.4

Buffer resist 540 nm MMA-MAA, cf. section 3.2.4 Insulator 1100 nm polyimide ‘Durimide 115 A’

Carrier substrate 200 µm bronze wafer, Ø 60 mm Table 3.1: Details on the different layers.

3.2.2 Polishing the Wafer

A bronze wafer of 200µm in thickness and 60 mm in diameter is chosen as a substrate for the electrode structure. Bronze is an alloy of copper with up to 20 % tin. Its elastic properties allow fot the bending and relaxing of the substrate during the experiment.

The wafer is smoothed by means of a polishing machine, or manually with sand paper and grinding paste, until the surface gleams. Though it is not possible to achieve optimal smoothness on a large scale by this method, roughness at least on a small scale can be avoided. After all, a surface which is smooth within a range of 50µm is sufficient, because this is the critical distance for focusing the electron beam during the lithographical writing process.

Surface profiles of one raw and one polished wafer are depicted in [39]. The pic- tures demonstrate that this polishing method provides an acceptable smoothness.

3.2.3 Insulating Layer

The insulating layer serves three purposes: The layer provides the necessary electrical insulation between the gold electrodes and the bronze substrate. In addition, this layer further smooths the surface, which facilitates the lithography. Further more, this layer is partially removed during the etching process, which makes the metal wire self-supporting. Therefore this layer is also called the ‘sacrificial layer’.

The polyamide ‘Durimide 115 A’ is applied to the bronze wafer and homoge- neously spread out using a spin coater which is located in a flow box that provides a laminar stream of air. Therefore, the area is clean and impurities caused by dust can be prevented. The polyamide is a chain built up periodically by the amides shown in figure3.4.

This polyamide is stabilized in a lab oven. Then, the wafer is put onto a hot plate in a vacuum chamber for a hard bake. During this process, the polyamide changes chemically into the polyimide shown in figure3.5. Water emerges during this process due to chemical internal condensation. Thus, the layer loses about

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OH H

N OH

O O

O

* NH *

Figure 3.4: One monomer of the polyamide ‘Durimide 115 A’.

N O

O

N O

O

* O *

Figure 3.5: Structure of the polyimide after the bake-out.

one third of its initial thickness. The vacuum prevents possible oxidation at high temperatures.

For details on spin coater parameters and baking settings, refer to table 3.3.

3.2.4 Electron–Beam Resists

Two types of resists provide a bilayer which can serve as a mask for the metal structures. The layers utilized undergo a chemical change by being exposed to an electron beam and thereby become soluble by proper solvents. Two different resists are used in order to achieve an undercut in the profile as presented on page 21.

The undercut provides a clean, spatial separation of the gold on top of the bilayer from the gold on the polyimide.

The upper layer is poly(methyl-methacrylate), in short PMMA, and also known as ‘Plexiglas’. The lower layer consists of poly(methyl-methacrylate-co-methacryl- acid), in short MMA-MAA. Figure 3.6 shows the monomers of both chains.

C C CH₃ C

*

O O CH₃

* C C

CH₃ C

*

O O CH₃

* C C C OH

O

*

Figure 3.6: The electron beam resists PMMA and MMA-MAA.

MMA-MAA is applied in an 11 % ethyl lactate solution using the spin coater and is afterwards stabilized by baking the wafer on a hot plate. In the next step, the spin coater is used again to apply the PMMA onto the wafer in a 4 % acetate solution. To finalize the bilayer, the wafer is baked out in the lab oven. Details on the spin coater settings and baking parameters can be found in table 3.3.

Subsequently, the wafer is cut into samples of 19× 4 mm² with the help of a special guillotine. The device allows for cutting with minimal bending of the samples.

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3.2.5 Electron–Beam Lithography

The molecules in the resists can be split up by an energy of about 5 keV [40], which can easily be provided by a scanning electron microscope (SEM). Desired structures can be written into the resists this way.

The SEM is controlled by software. So the structures — once defined within the software — are automatically written with the electron beam. Figure 3.7 shows the complete structure to be written by the SEM. Large pads are visible at both ends, which facilitate the ensuing electrical contact with thin copper wires, which occurs later. The leads narrow towards the center of the structure down to the weak link in the very middle, which measures only 100 nm in width. The two vertical lines are still visible to the bare eye, which allows for centric installation into the breaking mechanics later on.

Writefield 1

320xmagnification 6400x magnification

2,6µm

100 x 200nm² Writefield 1

Writefield 6 Writefield 3 Writefield 2 Writefield 4 Writefield 5

32x magnification

Figure 3.7: Top: The structure as seen with the lithography software of the SEM;

bottom left: The high-resolution 100µm-writefield; bottom right: the metal wire in the center of the 100 µm-writefield.

The SEM’s controlling software is capable of creating writefields of 1000 × 1000µm² at most. The structure design measures more than 4 mm in length.

Thus, it is split into five 1000µm writefields and one 100µm writefield. The small writefield contains the central wire in the highest resolution. In addition to the wire itself, there are several test bridges in the small writefield. They are all written with slightly different write parameters and therefore differ in width and accuracy to the edges. Thereby it is possible to estimate the effect of different

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100 µµm writefield 1000 µµm writefield

Step size 4 nm 61 nm

Write current 5-11 pA 2-3 nA

Exposure time 3-6.5 µs

Dose 280 C/s

Filament current 1.43-1.45 A

Acceleration voltage 30 kV

Table 3.2: Write parameters of the SEM.

exposure parameters. This proves to be convenient, because minor variations in the sample preparation process or in the SEM’s current may demand changes in the exposure parameters.

Details about the lithographical process and the SEM in general are to be found in [40], [39].

3.2.6 Developing

The areas of the resist which have been exposed to the electron beam — the later metal structure — are washed out during this step. The sample is developed immediately after the writing process in order to prevent the split polymers in the resists from re-connecting. The sample is put into a 1:3 solution of methyl isobutyl ketone (MIBK) and isopropanol (IPA) for 20 s, followed by another 120 s in pure IPA. The MIBK-solution provides high-resolution development of the upper PMMA layer. The pure IPA dissolves the lower MMA-MAA layer while hardly touching the PMMA. The IPA also slightly affects areas of the lower layer which have not been directly exposed to the electron beam. This produces the desired undercut in the profile (see sketch on page 21).

3.2.7 Gold Evaporation and Lift–Off

A metal layer must be evaporated onto the sample. This is achieved in the vacuum chamber of an evaporation machine. Within the chamber, there is a small crucible containing gold molten by an electron beam. The heating of the gold is continued until a constant evaporation rate has been established. About 80 nm gold are evaporated at a pressure of about 10⁻⁸ mbar.

Then, the sample is heated in acetone at 60^◦C. The acetone lifts off the remaining resist layers, including the metal covering the layers. Only the desired metal structure remains after this lift-off step, because it was evaporated directly onto the polyimide, which is not affected by acetone. Figure 3.8 shows a sketch of a

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4x magnification Actual size

Figure 3.8: Sketch of a sample after completion of the preparation process; gold structure length in total approx. 4 mm, sample dimensions about 19×4 mm².

sample that has completed the preparation process.

3.2.8 Etching

One final step is needed in order to make the thin wire in the center of the metal structure a self-supporting bridge. In order to achieve this, the sample is put into a vacuum chamber and treated with reactive ion etching. During this process, oxy- gen molecules are split up into free radicals by 50 W-microwave radiation. These radicals greatly affect the insulating polyimide layer by removing about 400 nm of it. The etching is performed isotropically, therefore the polyimide is also affected below the edges of the metal layer. Underneath the central metal wire, the polyimide is hollowed out from both sides, which finally makes the metal bridge self-supporting.

3.2.9 Attaching Wires

Wires must be attached to the big contact pads at the sides of the metal structure shown in figure 3.7 in order to integrate the sample into an electrical circuit.

Kapton-insulated copper wires of 120µm in diameter are used for this purpose.

The Kapton is removed from the end of the wires using sand paper. Then the wires are glued to the contact pads with conductive epoxy glue Epo-Tek H20S, which is unaffected by the solvents utilized in the experiment later on. This is crucial for two reasons: First, solved glue could cause contamination of the molecules.

Furthermore, the wires attached might lose contact if the glue is soaked in the solvent too long.

The epoxy glue must be heated on a hot plate at 60 ^◦C for at least five hours in order to harden. Higher temperatures would accelerate the hardening process, but would at the same time soften the gold bridge, as may be seen in figure 3.9.

During the heating process, the wires must be fixed so they do not slip off the contact pads. Little balls of ‘UHU R tac patafix’ are used, because this material

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Figure 3.9: Colored SEM picture of a gold bridge. Free suspended length of the bridge approx. 2.5 µm, thickness of gold layer approx. 80 nm, height above polyimide approx. 400 nm. Due to accidental overheating on a hot plate, the bridge is hanging down.

— usually used as poster strips — proved to adhere its elasticity at 60^◦C without melting. The sample must be grounded and the wire ends bypassed throughout the contacting process, because the gold bridge reacts highly sensitively to the smallest differences in the electrical potential. It is possible that the etched bridge could melt completely due to a sudden discharge.

27

Fabrication of Metal-Molecule Contacts

Fabrication of

Metal-Molecule Contacts

Diploma thesis

Contents

List of Figures

1

Introduction

2

Fundamentals and Basic Principles

2.1 Molecular Electronics

2.1.1 Tunneling through Alkanes

2.1.2 Saturated versus Conjugated Bonds

2.1.3 Influence of Anchor Groups

2.1.4 Molecular Geometry and Conductance

!

"

&

'

2.1.5 Coulomb Blockade

2.1.6 HOMO and LUMO Shifts

2.2 Transport through Nano–Scale Wires

2.2.1 Transport Channels and Landauer Formula

2.3 Investigation Methods in Molecular Electronics

2.4 Measurements in Liquid Environment

(a)

3

Experimental Section

3.1 Breaking Mechanics

3.2 Sample Preparation

3.2.1 Overview

3.2.2 Polishing the Wafer

3.2.3 Insulating Layer

3.2.4 Electron–Beam Resists

3.2.5 Electron–Beam Lithography

3.2.6 Developing

3.2.7 Gold Evaporation and Lift–Off

3.2.8 Etching

3.2.9 Attaching Wires