Single-Molecule Devices: Materials, Structures and Characteristics

Biswanath Mukherjee and Asim K. Ray

Centre for Materials Research, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

A. K. Sharma and Danhong Huang

Air Force Research Laboratory, Space Vehicles Directorate, 3550 Aberdeen Avenue SE, Kirtland Air Force Base,NM 87117, USA

(Dated: May 10, 2016)

This review article provides a brief survey of materials, structures and current state-of-the-art techniques usedto measure the charge conduction characteristics of single molecules. Single molecules have been found toexhibit several unique functionalities including rectification, negative differential resistance and electrical bistableswitching, all which are necessary building blocks for the development and configuration of molecular devicesinto circuits. Conjugated organic molecules have received considerable interest for their low fabrication cost,three dimensional stacking and mechanical flexibility. Furthermore, the ability of molecules to self-assemble intowell-defined structures is imperative for the fabrication of molecular based circuits. The experimental current-voltage results are discussed using basic principles of carrier transport mechanisms.

PACS numbers: 87.15.hj

Contents

I. Introduction 1

II. Background 2

III. Charge Transport and Tunneling in Single Molecule Devices 2

IV. Single Electron Transistor Characteristics 3A. Coulomb Blockade Effects 3B. Ballistic Transport 5C. Surface-Plasmon Coupling 6

V. Effect of External Parameters 8A. Mechanical Force 8B. Environment Effect 8C. Local-Heating (Joule) Effects 8D. Energy Level Alignment of Molecule 9E. Mechanically Controllable Break Junction (MCBJ) 9

VI. Preparation of Self-Assembled Monolayers (SAM) 9

VII. Molecular Imaging Methods 11A. Scanning Probe Microscope (SPM) 11B. Scanning Tunneling Microscope (STM) 11C. Atomic Force Microscope (AFM) 11D. Conducting Atomic Force Microscope (C-AFM) 12

VIII. Nanopores 12

IX. Mercury (Hg) Drop Method 12

X. Summary 13

Acknowledgments 13

References 13

I. INTRODUCTION

The study of single molecule devices is of great interest tothe scientific community at large. In the past two decades nu-merous advancements in manufacturing nanoscale materials

with atomic precision have enabled the synthesis/fabricationof true molecular size devices. The ability to fabricate singlemolecule size devices has opened the door to a wide range ofpotential applications in diversified fields of modern quantumelectronics (1; 2).

The charge conduction process in a single molecule is notmerely a function of the intrinsic properties of a molecule, butit is coupled with the type of metal contacts that is made tothat molecule. Therefore, the over-all charge transport mech-anism is a complex function of the molecule, metal-molecule-metal contact bond type, affinities, work function differences,and the local environment. To explore a single molecules elec-tronic functionality, a number of sophisticated tools have beendeveloped in the recent years that can make repeatable and re-liable contacts with single molecules, under a variety of metal-molecule-metal configurations.

In order to illustrate the impact of the electronic chargestates in the nanoscale regime, lets for example consider aconventional planar metal-oxide-semiconductor (MOS) fieldeffect transistor with a gate oxide thickness of 5nm. If thistransistors gate has both width and length of 100nm, andwe apply a 1V on the gate, about 300 electrons would re-side in the channel. A fluctuation of only 30 electrons wouldgive rise to voltage fluctuations of 0.1V . Now if we extendthis example, to the molecular regime, by considering a sin-gle molecule device that is only a few nanometers in length(smaller than the mean free path of an electronic charge) itscorresponding electronic spectrum would be quantized to afew eV . Therefore, the key requirement towards develop-ing single molecule electronic devices is greatly dependenton ones ability to precisely fabricate them with atomic scaleprecision and be able to measure the exact amount of chargefluctuations. Furthermore, in order to accurately model themechanism of the charge transport process, the theoreticalmodels need to include all sources of electric and magnetic

2

Figure 1. Energy band diagram of a D--A molecular junction. (a) under no bias condition and (b) under positive bias. Arrows in part (b) represent the electron transfer. (c) STM measurement of current-voltage characteristics (multiple scans) of a thin film of D-A supramolecule (D = CuPc, A = Rose Bengal).

FIG. 1 (Color online) Energy band diagram of a D--A molecularjunction. (a) under no bias condition and (b) under positive bias.Arrows in part (b) represent the electron transfer. (c) STM measure-ment of current-voltage characteristics (multiple scans) of a thin filmof D-A supramolecule (D = CuPc, A = Rose Bengal).

fields that the molecule is subjected to, which may be part ofa chemical or biological system (1). Additionally, the study ofsingle molecule conductance enables one to extract informa-tion about the chemical and electronic states of a molecule.This information would be useful for further configuring thesingle molecule into for chemical or biosensor device appli-cations (2; 3). This article provides a survey of the materi-als, structures and experimental techniques required to mea-sure the current-voltage characteristics of a single molecule.The experimental carrier conduction results are then presentedbased on basic principles of carrier transport mechanisms.

II. BACKGROUND

Since Aviram and Ratner (4) predicted that theoreticallyindividual molecules could function as electronic devices,tremendous research efforts have been put to investigate theelectrical conductivity of molecules connected with metallicelectrode contacts in the nanoscale regime (58). It was pos-tulated by Aviram and Ratner that a molecule with D--Astructure (D = donor, =sigma bridge, A = Acceptor) con-fined between two metallic electrode contacts could act as anrectifier provided the donor moiety has low ionization poten-tial (I.P.) and the acceptor moiety has an high electron affinity(E.A.) However, the first experimentally measured molecularrectifier was found to have D--A structure (9) instead of a D--A configuration. The rectification properties can be easilyexplained in terms of the energy band diagram of Figure 1.

Figure 1(a) depicts the thermal equilibrium Fermi level ofa molecular system with electrode contracts having energylevels E1 and E2 respectively on each side. In this thermalequilibrium (V = 0V ) the large energy barrier between themolecule and metal contracts impedes electron transfer. How-ever, under positive bias (V > 0V ), the energy level of con-tact E2 can be raised to the acceptors Lowest UnoccupiedMolecular Orbital (LUMO) level. In this biased state, an elec-tron from E2 (Figure 1(b), step 1) can now easily occupy theLUMO level. Consequently, in order to conserve the chargeneutrality of the system, another electron would be kicked-out the donors Highest Occupied Molecular Orbital (HOMO)level to the opposite polarity electrode E1 (step 2). This wouldyield a D+--A configuration which is unstable. Therefore,the molecule would need to relax to the ground state by trans-ferring an electron through the bridge from acceptor LUMO

to donor HOMO (step 3). In the opposite direction (reversebias condition) the whole charge conduction process would belimited by the energy barrier configuration of the system, thusresulting in a diode like behavior. Figure 1(c) shows the Scan-ning Tunneling Microscope (STM) induced current-voltage(I-V) characteristics of a monolayer of a donor (D) and accep-tor (A) molecular thin film having a thickness of 5 6nm.

D-A supramolecule devices been fabricated on silicon (Si)substrates via layer-by-layer (LbL) electrostatic assembly of amonolayer of a donor, viz, Copper (II) phthalocyanine (CuPc),and a monolayer of an acceptor, viz, fluorine dye (Rose Ben-gal) in sequence (10). Because the LbL deposition relies onthe surface charge reversal during the electrostatic adsorptionof each layer, the deposition of one molecular layer or mono-layer is also assured. Electron flow is favorable in one biasdirection while it is limited in the reverse direction in both D-A and A-D assemblies. The rectification ratio (RR) obtainedin the CuPc-Rose Bengal molecular assembly at a bias of 1Vis about 7 and this result has been highly reproducible. The I-V characteristics of the Si-substrate with Pr/Ir Scanning Tun-neling Microscope (STM) tip was found to be symmetrical,which eliminates the possibility of any Si-substrates parasiticeffects influencing the rectification process. It is also notedthat in case of A-D assembly, higher current is obtained ina direction opposite to the D-A assembly when the polarityof the electrodes is kept the same. The experimental resultsfully support a true molecular property of the supramolecule,intrinsic to the asymmetry of D-A or A-D assemblies.

Some other interesting properties that are exhibited by sin-gle molecules are reversible redox switching (11), molecu-lar switching (12), negative differential resistance (NDR) (13),and single molecular electronic circuits (14). Also, the detec-tion and manipulation of electronic spin in molecules haveyielded many novel applications in the newly growing field,popularly known as molecular spintronics, where the mag-netic state of the molecule can be translated into an electricaleffect (1517). There are many properties of single moleculedevices that yet remain to be explored, such as what hap-pens when relatively large voltage biases are applied to singlemolecules, capable of causing significant deformation to theirmolecular structure.

III. CHARGE TRANSPORT AND TUNNELING IN SINGLEMOLECULE DEVICES

As the size of a molecular junction becomes smaller thanthe mean free path of the electronic charged carrier, that iscomparable to the de Broglie wavelength, the carrier trans-port process becomes ballistic and cannot be easily explainedusing Ohms law. Since a molecule has large charge additionenergy and a quantized excitation spectrum, when a micro-scale electrode is contacted with this molecule, it will have astrong effect on the overall conductance process of this molec-ular nanoscale junction. The observation of Coulomb block-ade at low temperature in most single molecules corresponds

3

Figure 2. Energy level diagram of a single molecule device. Discrete lines denote the empty energy levels of the molecule, while the solid lines (below S and D) indicate levels occupied by an electron. S and D represent respectively the Fermi levels of source and drain.

FIG. 2 (Color online) Energy level diagram of a single molecule de-vice. Discrete lines denote the empty energy levels of the molecule,while the solid lines (below S and D) indicate levels occupied byan electron. S and D represent respectively the Fermi levels ofsource and drain.

to quantum excitations of the molecule and charge quantiza-tion. This also has the implications that the thermal energy ofthe electrons is significantly smaller than the Coulomb energye2/2C, where C is the total capacitance of the gate capac-itor and the tunneling junctions. The junction conductanceis much less than the quantum conductance 2e2/h, where, his the Plancks constant. Thus, the quantum mechanical tun-neling effect itself is considered to be weak enough to preventthe charge delocalization of the tunneling electrons. When thewidth of the molecular junction is less than the electrons meanfree path, the resistance of the conducting channel, which isdetermined purely by quantum mechanical effects, is given interms of Landauer resistance (18) R = (h/2e2)(1 T )/T ,where, T is the transmission coefficient. For 100% transmis-sion for all-metal nanogap (T = 1), and the resistance is foundto be quantized in units of h/2e2. (19; 20)

The tunneling effect is observed when the insulating bar-rier is 1nm thick, i.e., a few atoms apart, and the transferof charge follows the sequential tunneling process. Figure 2shows the energy level diagram of a single molecule devicewith S (source) and D (drain) being the Fermi levels of thetwo electrodes and V the applied bias between the two elec-trodes satisfies the relation, i.e., S D = eV . The discretelines above S and D reflect the empty energy levels of themolecule, while the solid lines below S and D are occu-pied by one electron. The molecule-metal electrode contactis assumed to be opaque enough to serve as a tunnel barrier.For sequential tunneling to take place, there must be a stateavailable between S and D, via which tunneling can occur.This results in large current flow through the junction (on-state). On the other hand, unavailability of electronic statesbetween S and D, leads to blocking of charges with only asmall current flow by direct tunneling process (off-state). Thequantized electronic structure of a molecule causing on- andoff-state, can be attributed to the charge addition energy andthe electronic excitation spectrum.

IV. SINGLE ELECTRON TRANSISTORCHARACTERISTICS

In order to explain the electron transport in a singlemolecule device let us use the Single Electron Transistor(SET) theory proposed initially by Kouwenhoven et al (21)and was described in detail by J. Park (22). Figure 3(a) showsthe schematic representation of a SET device, where a quan-tum dot is coupled to all three electrodes capacitively. Al-though the tunnel barrier exists between the dot and all threeelectrodes, the electron tunneling is allowed only between thedot and source/drain electrodes. This also implies that an elec-tron is either on the dot or one of the electrodes i.e. the numberof electrodes on the dot is well defined.

If doped molecules on a chain are coupled strongly, elec-trons in this system can drift through a band-transport mech-anism. However, the randomly-distributed impurities and lat-tice vibrations are still expected to introduce significant scat-tering on their way. If the length of a molecular chain be-comes shorter than the mean-free-path of electrons, on theother hand, the electron motion can be ballistic with a quan-tized conductance.

A. Coulomb Blockade Effects

Figure 3(b) shows a family of I-V characteristics of a sin-gle electron transistor device fabricated from C140 moleculeat different gate voltages (VG). The results were obtained byJ. Park (22). At low bias voltages, flow of electrons is lim-ited/blocked (Coulomb Blockade) because of unavailability ofsufficient energy of electrons to overcome the barrier energyin order to tunnel through the C140 molecule. An estimationof the source-drain voltage (VDS) required to enable tunnel-ing via the lowest-energy state of the molecule can be donefrom the two-dimensional plots of differential conductance(dI/dV ) as a function of VDS and VG. However, an electroncan tunnel through the barrier at very low source-drain bias,near VDS = 0 for a specific value of gate voltage, VG = VC ,where the charge states are degenerate (Coulomb Oscillation).This value of VG is different for different devices/moleculesbecause of differences in the local electrostatic environment.Therefore, we can make sure that as long as the measurementsare performed sufficiently close to VG = VC , current flowsonly through a single molecule.

The electrostatic potential N+1 of the dot [refer to Figure3(a)] is given by N+1 = U(N + 1) U(N), where U(N)and U(N + 1) denote, respectively, the total energy for a dothaving N and N + 1 electrons. Therefore,

N+1 =N+1i=1

Ei +(N + 1)2e2

2C

Ni=1

Ei N2e2

2C

= EN+1 +(N + 1/2)e2

C, (1)

4

Figure 3. (a) Schematic of a single electron transistor device with Allowed tunnel barrier between the small dot and source/drain electrodes. (b) I-V characteristics from a C140 single electron transistor. VG increases in steps of 0.04 V from gray (0.23V) to blue curve. Inset: the Coulomb oscillation curve from the same device. (Adapted from reference 79).

FIG. 3 (Color online) (a) Schematic of a single electron transis-tor device with allowed tunnel barrier between the small dot andsource/drain electrodes. (b) I-V characteristics from a C140 sin-gle electron transistor. VG increases in steps of 0.04V from gray(0.23V ) to blue curve. Inset: the Coulomb oscillation curve fromthe same device. (Adapted from Ref. 23).

where Ei is the kinetic energy of the ith electron in the dot,C denotes the total capacitance of the gate capacitor and thetunneling junction, and (Ne)2/2C = Q2/2C with Q = Nebeing the total charge in the dot. Since N+1 is the minimumenergy required for adding the N th electron, it will be addedto the dot as long as N+1 is below both S and D. In asimilar way, addition of one extra electron to a dot having Nelectrons is possible whenever the electrochemical potentialsatisfies N+1 = N + e2/C + E, where E = EN+1 EN is lower than both S and D. Thus, the N + 1 electronshould have energy larger than the one for N th electron bye2/C + E. The first term e2/C = Ec, representing theenergy required to overcome the Coulomb repulsion amongdifferent electrons, is called charging energy and the secondterm E is the result of quantized electron energy levels ofthe dot.

For the case with N+1 > S , D > N (case 1), allthe levels below N represent filled levels, while those aboveN+1 are empty. The lowest unoccupied level N+1 cannotbe occupied by electrons since it is above the Fermi levels ofboth electrodes. Therefore the current is blocked due to thecharge addition energy and the dot is stable with N electrons.In another case with D > N+1 > S (case 2), the N + 1thelectron can be added from the drain and then it can flow tothe source electrode, thus allowing electric current to flow byconstantly switching the charge state of the dot between Nand N + 1. As the gate voltage VG is increased, the elec-trochemical potential of the dot changes linearly with VG andthis allows one to change the number of electrons on the dot.The conductance (G) as a function of VG at low bias is illus-trated in Figure 4 and shows a series of peak (on-state) as wellas valleys of low conductance (off-state). In the valleys, thenumber of electronics on the dot is fixed (N, N + 1, N + 2and so on) and the current is blocked by the charge additionenergy e2/C + E (case 1). The peaks in the conductancecurve (case 2), known as Coulomb oscillations, indicate thatthe dot carrying current by oscillating between two adjacentcharge states. However, the thermal energy should be ensuredsmall enough to produce Coulomb oscillations, i.e.,

e2/C + E kBT . (2)

For large thermal fluctuations, the Coulomb oscillations will

disappear. Secondly, the contact resistance between the dotand two leads need to be larger than the resistance of a singleconductance channel, that is,

Rcontact h/e2 25.81 k . (3)

Many different systems exhibit single electron transport be-havior, which include metallic nanoparticles (24), single-molecule transistors incorporating trimetal molecules (25),carbon nanotubes (26; 27), semiconducting nanocrystals (28)and single molecules (29; 30).

By including the coupling c of a quantum dot to two elec-trodes, Eq. (1) is modified to (31)

N+1 = EN+1 +(N + 1/2)e2

C+ c L , (4)

where L is the average linear electron density of one-dimensional electrodes. Here, the resonant levels {N+1}will depend on the electrode chemical potential 0 onlythrough the linear electron density L. Therefore,, we get

N+1(0)

0= c

L(0)

0 c g1D(0) . (5)

By choosing the bottom of the electronic energy dispersionas the energy reference point, then the gate potential eVg canbe regarded as the difference 0 between the fixed chemi-cal potential of the conductive substrate and 0. Therefore,we can set 0 = e Vg , where < 1 is a ratio parameterdetermined by the self-consistent calculation.

Let N be the value of the electrode chemical potentialwhich is in resonance with the level N of the quantum dot.Then we obtain the self-consistent equation N = N (N ),and the period of VG (or 0) in the conductance oscillationswill be given by

0 = N+1 N = E +e2

C+ c [L(N+1)

L(N )] = E +e2

C+ c g1D(0)0 , (6)

or equivalently by

0 =E + e2/C

1 c g1D(0) E + e

2/C

K(0)= e VG (7)

with K(0) = 1 c g1D(0) being the screening factor tothe charge addition energy by coupling with one-dimensionalelectron gases. Here, the coupling constant c of the quantumdot can be estimated by

c e2

40effL0

[3

2+ ln

(L0W0

)] e

2

C0, (8)

5

where L0 and W0 are associated with the gate length and thechain width, respectively, and eff is the effective dielectricconstant of the quantum dot. From this we know that C0 isjust the bare dot capacitance and roughly proportional to L0and weakly depends on the chain width as is expected.

For a non-interacting one-dimensional electron gas, thedensity of states per unit length can be calculated as

g1D(0) =

2m

~

occupiedj=1

10 j

, (9)

where m is the effective mass of the electrons, and j isthe bottom of the jth subband. Since g1D(0)/g1D(0) =VG/[2(VG Vth)], we can approximate g1D(0) as a con-stant in a range much smaller than VG Vth, where Vth isthe threshold gate voltage, related to the bottom of the lowestsubband energy dispersion. Furthermore, from Eqs. (5) and(7) we can get

N+1(0)

0= c g1D(0) = 1K(0) . (10)

Finally, for finite temperatures T > 0, by assuming that theobserved conductance peaks can be attributed to the many-body resonant tunneling mechanism (32) through the resonantlevels {N}, we can write down the conductance G with thehelp of Landauer-type formula (33)

G(0, T ) =e2

h

N

AN (0, T )

cosh2(N 0

2kBT

), (11)

where AN (0, T ), which is proportional to c, represents theeffective transmission coefficient through the N th resonantlevel, and we have assumed a Fermi-Dirac distribution for theone-dimensional electron gas, the assumption also used forfitting experimental data in Ref. [34].

B. Ballistic Transport

Whenever the mean-free-path of electrons becomes shorterthan the reduced molecular-chain length, they will enter into aquantum-ballistic regime. In this case, the ballistic heat (Q(1))and charge (Q(0)) currents are given by (35)

Q(`) = 2(e)1`n,k

vnkL

(nk )`[(vnk)f (0)nk,R

(1 f (0)nk,L) + (vnk)f(0)nk,L(1 f

(0)nk,R)] , (12)

Figure 4. Conductance (G) versus gate bias (VG) curves displaying Coulomb oscillation. The numbers (N-1, N, N+1, etc) in each conductance valley represents number of electrons on the dot.

FIG. 4 (Color online) Conductance (G) versus gate bias (VG) curvesdisplaying Coulomb oscillation. The numbers (N 1, N, N +1, , etc) in each conductance valley represents number of elec-trons on the dot.

where ` = 0, 1, L is the channel length, is the chemicalpotential in the channel, and (x) is the unit step function. InEq. (12), n is the sublevel index, k is the wave number of aband, nk = (n+ 1/2)~x + ~2k2/2m represents the nthenergy band, x = (2x +

2c )

1/2, ~x is the sublevel sepa-ration in a harmonic-potential model. c = eB/m, m =m/[1(c/x)2],m is the effective mass,B is the appliedmagnetic field perpendicular to the chain, vnk = nk/~kis the group velocity, and f (0)nk, is the Fermi-Dirac distribu-tion function for the two-dimensional electrodes on the left( = L) and the right ( = R) side, with the chemical po-tential . The physical meaning of Eq. (12) is self-evident.Equation (12) can be simplified, in view of vn,k = vnk(symmetric band), as

Q(`) =2(e)1`

n

0

dk |vnk|(nk )`(f (0)nk,L f(0)nk,R) . (13)

Using L + eV = R , f (0)nk,L f(0)nk,R = eV f

(0)

nk , and = L = R in the limit V 0, where V is theinfinitesimal voltage difference between the left and the rightelectrodes, we find

Q(`) =2eV (e)1`

n

(

n,k1n,k=0

+

n,k2n,k1

+ + n,k

)

sign(vnk)(nk )`[f

(0)nk

nk

]dnk , (14)

where the lower limit equals the energy n,k=0 at k = 0. InEq. (14), the energy integration over the range 0 < k < is chopped into the sum of the integrations between the suc-cessive extremum points n,km , where n,k is assumed to be a

6

monotonic function of k and n,k is the last extremum (min-imum) point. Each integration can be carried out analyticallyfor both ` = 0, 1, yielding the thermoelectric power (TEP) S,given by

S =Q(1)

TQ(0)= kB

eF

n

Cn, [(n, )

f (0)(n,) + ln(e(n,) + 1)], (15)

where = 1/kBT and

F =n

Cn,f(0)(n,) . (16)

Here, -summation indicates summing over all the energy-extremum points on each curve n ( < k < ). Thequantity n, is the extremum energy. For a given curve n,Cn, = 1 for a local energy minimum point and Cn, = 1for a local energy maximum point. The quantity F equals thenumber of the pairs of the Fermi points at T = 0 and is relatedto the conductance G by G = 2e2F/h.

The TEP is quantized at T = 0 K as S =(kB/e) ln 2/[G/(2e2/h)] in general at the energy-extremum points = n, in Eq. (27), whereG = (2e2/h)(i + 1/2) is the zero-temperature quantizedballistic conductance with i = 1, 2, .

We note that m becomes heavier as B increases, leadingto a large density of states. As a result, the sublevels becomedepopulated successively for increasing B. Figure 5 shows Gand S of a conducting molecular chain obtained from Eq. (27)for two temperatures as a function of B when several levelsare occupied at B = 0. The parameter ~x and the electrondensity n1D are given in the inset. The TEP is very smallwhen lies away from the edges of the sublevels because thecontributions to the heat current Q(1) in Eq. (14) from above (nk > ) cancels those from below (nk < ). Thiscancellation does not occur when is within the thermal en-ergy kBT of the sublevel edges, yielding spikes for the TEPjust before a level is depopulated at the knees of the quantumsteps of G. These spikes broaden as T is raised. This behav-ior is similar to the density dependence of the field-free TEPstudied earlier (36).

C. Surface-Plasmon Coupling

For photo-excited spin-degenerated electrons in a quan-tum dot, the semiconductor Bloch equations (37) with ` =1, 2, are given by

dne`dt

=2

~j

Im[(Y j`

) (Meh`,j Y

j` V

eh`,j;j,`

)]

0

1

2

3

4

5

(a)

n1D

= 1.5 x 106 cm-1

x

= 1 meVCon

duct

ance

G(

2e2 /

h)

kBT /

x=0.02

kBT /

x=0.07

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.1

0.2

0.3

0.4

0.5

kBT /

x=0.02

kBT /

x=0.07

The

rmoe

lect

ricP

ower

S(

-kB

/e)

Magnetic Field ( T )

(b)n

1D= 1.5 x 106 cm-1

x

= 1 meV

FIG. 5 Ballistic (a) G and (b) S for two temperatures in a singlechain with four sublevels occupied initially at B = 0. Here, we setm = 0.067me with free-electron mass me. Other parameters aredirectly given in the figure.

+ne`t

rel

`,1Rsp ne1 nh1 , (17)

whereRsp is the spontaneous emission rate and ne` representsthe electron level population. In Eq. (17), the term markedrel is the non-radiative energy relaxation (38) for ne`, and theY j` , Meh`,j , and V eh`,j;j,` terms are given later in this subsec-tion. Similarly, for spin-degenerate holes in a quantum dot,the semiconductor Bloch equations with j = 1, 2, arefound to be

dnhjdt

=2

~`

Im[(Y j`

) (Meh`,j Y

j` V

eh`,j;j,`

)]

+nhjt

rel

j,1Rsp ne1 nh1 , (18)

where nhj stands for the hole energy level population. Again,the non-radiative energy relaxation for nhj is incorporated inEq. (18). Finally, for spin-averaged e-h plasmas, the inducedinterband optical coherence, which is introduced in Eqs. (17)and (18), with j = 1, 2, and ` = 1, 2, satisfies thefollowing equations,

i~d

dtY j` =

[e`() +

hj () ~( + i0)

]Y j`

7

+(1 ne` nhj

) (Meh`,j Y

j` V

eh`,j;j,`

)+ Y j`

j1

nhj1

(V hhj,j1;j1,j V

hhj,j1;j,j1

)`1

ne`1 Veh`1,j;j,`1

]+Y j`

[`1

ne`1

(V ee`,`1;`1,` V

ee`,`1;`,`1

)j1

nhj1 Veh`,j1;j1,`

, (19)where ~0 = ~eh + ~ext is the total energy-level broad-ening due to both the finite carrier lifetime and the loss of anexternal evanescent field, is the frequency of the externalfield, and e`() and

hj () are the kinetic energies of dressed

single electrons and holes, respectively. (37) In Eq. (19), thediagonal dephasing (0) of Y

j` , the renormalization of inter-

band Rabi coupling (Y j` Veh`,j;j,`), the renormalization of elec-

tron and hole energies (third and fourth terms on the right-hand side), as well as the exciton binding energy, are all takeninto consideration.

The steady-state solution to Eq. (19), i.e. under the condi-tion of dY j` /dt = 0, is found to be

Y j` (t|) =

[1 ne`(t) nhj (t)

~( + i0) ~eh

`,j(|t)

]Meh`,j(t) , (20)

where the photon and Coulomb renormalized interbandenergy-level separation ~eh`,j(|t) is given by

~eh`,j(|t) = e`(|t) + hj (|t) V eh`,j;j,`

+`1

ne`1(t)(V ee`,`1;`1,` V

ee`,`1;`,`1

)

+j1

nhj1(t)(V hhj,j1;j1,j V

hhj,j1;j,j1

)

`1 6=`

ne`1(t)Veh`1,j;j,`1

j1 6=j

nhj1(t)Veh`,j1;j1,` . (21)

The Coulomb interaction matrix elements introduced inEqs.(17), (18) and (19) are calculated as

V ee`1,`2;`3,`4 = V0

d2q

qFe`1,`4(q)F

e`2,`3(q) , (22)

V hhj1,j2;j3,j4 = V0

d2q

qFhj1,j4(q)F

hj2,j3(q) , (23)

V eh`,j;j,` = V0

d2q

qFe`,`(q)Fhj,j(q) , (24)

where V0 = e2/820b, the two dimensionless form factors,Fe`,`(q) and Fhj,j(q), are introduced in Eqs. (22)-(24) forelectrons and holes due to quantum confinement by a disk-like quantum dot. In addition, the matrix elements employedin Eqs. (17), (18) and (19) for the Rabi coupling betweenphoto-excited carriers and an evanescent electromagnetic fieldE(r; t) = (t)E(r; ) eit are given by

Meh`,j(t) = `,1 j,1 (t)[Eeh`,j() dc,v

], (25)

where (x) is a unit step function, dc,v is static interbanddipole moment, and the effective electric field coupled to thequantum dot is

Eeh`,j() =

d3r [e`(r)]

E(r; )

[hj (r)

]. (26)

with e`(r) and hj (r) being the electron and hole wave func-

tions, respectively, in the quantum dot.

Using the Greens function (39) G(r, r; ), we can con-vert the Maxwell equation into a three-dimensional integralequation for , = 1, 2, 3

E(r; ) = E(0) (r; )

2

0c2

d3r G(r, r; )P loc (r; ) , (27)

where E(0) (r; ) is an incident surface-plasmon (SP) field.The photo-induced interband optical polarization P loc(r; ),which is related to the induced interband optical coherence,by dressed electrons in the quantum dot is given by (40)

P loc(r; ) = 2 |(r)|2 dc,v{

d3r e1(r)h1 (r

)

}

1~

limt

[1 ne1(t) nh1(t) + i0

eh

1,1(|t)

]Meh1,1(t) , (28)

where ed is the unit vector of the dipole moment and the pro-file function |(r)|2 comes from the confinement of a quantumdot.

Figure 6 presents the quantum dot absorption coefficient0(sp) for a surface-plasmon field, the scattered field |EtotEsp| of the SP field, and the energy-level occupations for elec-trons n`,e and holes nj,h with `, j = 1, 2 as functions offrequency detuning ~sp ~sp (EG + 1,e + 1,h).

8

A dip is observed at resonance ~sp = 0 in the upper-left panel, which appears to become deeper with decreasingamplitude Esp of the SP field in the strong-coupling regimedue to a decrease in the saturated absorption. However, thisdip completely disappears when Esp drops to 25 kV/cm in theweak-coupling regime due to the suppression of the photon-dressing effect, which is accompanied by an order of mag-nitude increase in the absorption-peak strength. The dip inthe upper-left panel corresponds to a peak in the scatteredfield, as can be seen from the upper-right panel of Fig. 6.The scattered field increases with frequency detuning awayfrom resonance, corresponding to the decreasing absorption.As a result, a minimum appears on each side of the reso-nance in the scattered field in the strong-coupling regime. TheMaxwell-Bloch equations couple the field dynamics outsideof a quantum dot with the electron dynamics inside the dot.At Esp = 125 kV/cm in the lower-right panel, we find peaksin the energy-level occupations at resonance, which are broad-ened by the finite carrier lifetime as well as the optical powerof the SP field. Moreover, jumps in the energy-level occu-pations can be seen at resonance due to Rabi splitting of theenergy levels in the dressed electron states. The effect of res-onant phonon absorption also plays a significant role in thefinite value of n2,e with energy-level separations 2,e 1,eapproximately equals to the optical phonon energy. However,as Esp decreases to 25 kV/cm in the lower-left panel, peaks inthe energy-level occupations are greatly sharpened and nega-tively shifted due to the suppression of the broadening fromthe optical power and the excitonic effect, respectively. Ad-ditionally, jumps in the energy-level occupations become in-visible because the Rabi-split energy gap in this case is muchsmaller than the energy-level broadening from the finite life-time of electrons (i.e. severely damped Rabi oscillations be-tween the first electron and hole levels).

V. EFFECT OF EXTERNAL PARAMETERS

The conductance of a single molecule is affected signif-icantly by several external parameters which may cause achange in the local charge distribution, distortion in molec-ular structure or the electronic states of the molecule produc-ing difference in the molecular conductance. A few of theseexternal parameters are listed below.

A. Mechanical Force

The force applied in a molecular junction may distort themolecular structure and hence change the electronic states ofthe molecule producing a difference in the conductivity levels.The effect is more pronounced for softer molecules like olig-othiophenes, since the strong coupling between the electronicstates and the molecular structures causes a large change inthe conductance (41). Secondly, during the breakdown of themolecular junctions the conductance traces although seemedflat, careful examination shows a finite decrease (10-20% de-crease for alkanedithiols) in the conductance upon stretch-

)

160

200 x0.1

25 125

T=300K0=3meV

Lx=210Az0=610A(c

m-1)

10

12

14

16 25 125 175

T=300K0=3meV

Lx=210Az =610A4 k

V /

cm

80

120 175z0 610A

d=12

0(sp

)(

3

4

8z0 610A

d=12

sp|

(10

-4

-30 -20 -10 0 10 20 300

40

- (E + + ) (meV)-30 -20 -10 0 10 20 30

1

2

|Eto

t - E

(E + + ) (meV)sp - (EG+ 1,e+ 1,h) (meV) sp - (EG+ 1,e+ 1,h) (meV)0.5 0.6

0 3

0.4

0.5

Esp=25kV/cm

n1,h

n1,e

n j,h

0 4

0.5

0.6Esp=125kV/cm

n

n1,e

n j,h

0 1

0.2

0.3

n2 e

n2,h

,

n j,e ,

n

0 2

0.3

0.4

n2,h

n1,h

n j,e ,

n

-30 -20 -10 0 10 20 300.0

0.1 2,e

- (E + + ) (meV)-30 -20 -10 0 10 20 30

0.1

0.2 n2,e

- (E + + ) (meV)sp (EG+ 1,e+ 1,h) (meV) sp (EG+ 1,e+ 1,h) (meV)

FIG. 6 Optical absorption coefficients 0(sp) (upper-left panel)and scattering field |Etot Esp| at the quantum dot (upper-rightpanel), as well as the energy-level occupations for electrons n`,e andholes nj,h (lower panels) with `, j = 1, 2, as functions of the fre-quency detuning ~sp ~sp (EG + 1,e + 1,h). Here, theresults for various amplitudes Esp of an SP field with frequency spare presented in the upper panels, along with a comparison of theenergy-level occupations for Esp = 25 and 125 kV/cm in the lowerpanels. The label0.1 in the upper-left panel indicates that the resultis multiplied by a factor of 0.1.

ing (41). Thirdly, a small molecule cannot be stretched with-out tearing to that limit which a molecular junction can with-stand (several angstroms).

B. Environment Effect

The molecular conductance is also a function of the localenvironment, such as, metal ions, solvent molecules, and so-lution pH . The presence of metal ions in solution producestrong binding of the ions to the molecule inducing confor-mational changes of the molecule and hence change in theconductance of the molecule (2). Even the solution pH canchange the electronic states of a molecule resulting significantdecrease in the conductance of the molecule with increase insolution pH (42).

C. Local-Heating (Joule) Effects

In ultra-small scale electronic devices, local heating effectdue to current flow and heat dissipation is a crucial factor.Large current density in the junction can produce substantialheat. During inelastic electron transport in nanoscale junc-tion, although a small amount of electron energy contributesto emission of phonons (43; 44), it may still induce appre-ciable local heating effect (45). An increase in temperatureby 25K above room temperature was observed for oc-tanedithiol at bias of 1V .

9

D. Energy Level Alignment of Molecule

The alignment of the molecular energy levels, i.e., high-est occupied molecular orbital (HOMO) and the lowest unoc-cupied molecular orbital (LUMO), with the Fermi levels ofthe metal contacts determine the conductance of a molecule.A molecule exhibits very low conductance if it has a largeHOMO-LUMO gap ( 5 eV ) in the neutral state. Because,in that case, the Fermi level of the electrode will most likelybe positioned within the gap and thee will not be any trans-fer of electrons from the electrode to the molecule. On theother hand, spontaneous oxidation/reduction of the moleculesand the easy transfer of electrons from one electrode to othertakes place if HOMO/LUMO level is aligned with the metalFermi level leading to high conductance. It is often very diffi-cult to determine the interactions between the molecules andthe electrode, although, STM tunneling spectroscopy has beenused to study the electronic states of molecules absorbed onthe surfaces to resolve different molecular energy levels andtheir relative positions to the Au Fermi level (46; 47). Theelectrochemical gate control of the conductance of several sin-gle redox molecules has also been observed (48; 49).

E. Mechanically Controllable Break Junction (MCBJ)

As shown in Figure 7, the distance between two atomi-cally sharp metallic nanocontacts is easily adjusted by me-chanically breaking a metal wire. The electrical conductanceof self-assembled molecular (SAM) monolayers bridging thejunction (50; 51) is measured by bringing the tips close to eachother with a voltage bias between them while slowly breadingthe contacts. The molecular conductance varies as a result ofvariation of the electrode gap due to the bending of a commonbendable substrate mounting the two wire ends, and the junc-tion becomes insensitive to the external vibrations. A stressedor deformed junction results in different configurations andhence different electronic properties of the molecular species.Due to the high stability of MCBJ, the same junction can beinvestigated repeatedly to obtain a large amount of informa-tion on a molecule with the systematic variation of control pa-rameters such as temperature and magnetic field. Althoughboth electrodes are made of the same metal, and one can-not assume these are truly symmetric junctions. The reasonfor that is because of dimensional control at the atomic level.Random variation is geometrical structural shapes is the ob-vious drawback of existing techniques. Also, the differencesin the sharpness of the broken tips may cause large variationin the electric filed around the broken ends of the wires aswell as heat may be generated from the undesirable motionof the mechanical drive used in this technique. The MCBJtechnique is not found to be suitable for the measurement onhighly integrated molecular electronic devices. However, thelithographically patterned MCBJs have been very useful forthe investigation of molecular conductance of such systemsand do not require ultra-high vacuum and highly cleaned con-ducting substrates.

Figure 5. Schematics of MCBJ. The molecular monolayer is connected with the two Au electrodes via a chemical bond through thiol end groups.

FIG. 7 (Color online) Schematics of MCBJ. The molecular mono-layer is connected with the two Au electrodes via a chemical bondthrough thiol end groups.

VI. PREPARATION OF SELF-ASSEMBLED MONOLAYERS(SAM)

For fabrication of molecular junction, the break junction issubmerged in the solution of the molecule with desired con-centration for an extended amount of time; and the moleculesare then self-assembled onto both of the metallic tips becauseof functionalization of the molecules at both ends bindingwith the metal. The residual molecules which are not in-volved in chemical bonds with the tips may be washed awaywith distilled water. The nanolayers of organic molecules areuniformly chemisorbed over the metal contacts though slowevaporation of solvents. The presence of deformities in thelayer, such as separation of molecules due to excessive tilt orholes in the layer, may cause undesirable electrical short be-tween the electrodes. Alkanethiols on atomically cleaned andpolished gold substrate was commonly used as SAM (52; 53)because of easy formation of stable monolayers as well as hav-ing varieties of potential applications such as sensors, corro-sion inhibition, wetting control and molecular electronic de-vices (54; 55). The nanogap formed as a result of breaking inan MCBJ, is spanned by one or few molecules during SAMpreparation, thus allowing one to measure single molecularconductance. Schematic representation of a self-assembledmonolayer on Au substrate is shown in the inset of Figure8(a).

Typical current-voltage (I-V ) characteristics of the SAMlayer on gold (Au) substrate of a dithiol NOPE molecule com-prised of the same NO2 functionalized OPE oligo (phenylene-ethynylene) NOPE molecules are shown in Figure 8(a) atthree different temperatures of 100K, 200K and 300K. Themolecule showed stable and reproducible I-V characteristicsallowing multiple scans. The differential conductance of themolecule, calculated from the I-V curves with a resistance of2.1/1M being measured at 300K for the voltage scan of1V through 0V , was found to be asymmetric and is shownin Figure 8(b). This observation may be attributed to unevenstrength in electrically coupling between the metal tips (56).It is clear from the figure that the high conductance regionmoves to higher voltage when the temperature is decreased.This implies that a thermal mechanism may be responsiblefor the sudden increase in current (57).

1, 4 Benzene-dithiol (BDT) SAM in gold break junc-tion (51) displayed nearly symmetric differential conductancea limited asymmetry at room temperature for relatively highbias within the bias range 4V . Theoretical studies ofthe BDT/Au break-junction have yielded almost similar re-

10

Figure 6. (a) I-V characteristics of dithiol NOPE molecule measured in the break junction set-up at different temperatures. Inset: schematic representation of a self-assembled monolayer on Au substrate. (b) Differential conductance of the same molecule calculated from data (a).

FIG. 8 (Color online) (a) I-V characteristics of dithiol NOPEmolecule measured in the break junction set-up at different tempera-tures. Inset: schematic representation of a self-assembled monolayeron Au substrate. (b) Differential conductance of the same moleculecalculated from data (a).

sults (58; 59) with symmetric conductance curves. Signif-icant enhancement in differential conductance of the junc-tion was found to increase strongly from low to high volt-age regimes. This behavior was ascribed to the fact that theFermi level of Au contacts fall within the HOMO-LUMO gapof the molecule at low bias. However, transport through res-onant states of the molecular hybridized with the metal tipsincreased conductance at higher biases. However, experimen-tally measured current values disagree with that of theoreticalcalculation (58; 59).

The conductance of quantum point contact (a single metalatom or a row of atoms of the same metal as of the elec-trodes) (60; 61) is usually expressed in units of G0 = 2e2/h(e = electronic charge, h = Planck constant) as at higherbiases, a measure of the transmission of electrons throughthe point contact. The contact size of the order of electronFermi wavelength for electrons in Au is only a few A (forAu, G0 = 77.4S), the appearance of conductance quan-tization (62) indicates the formation of an atomic-scale con-tact between the tip and the substrate with lowest step corre-sponds to a single molecule bridging the two electrodes. Inan earlier experiment based on MCBJ at low temperatures,the conductance is found to be quantized in units of G0 asa function of contact elongation (elongation speed being inthe range of 1-10 pm/s) for four different materials (Al, Au,Pb and Nb) (63). The average conductance as a measure byMCBJ method for 1, 4 benzene-dithiol (BDT) molecule was0.0099G0 in case of dithiol NOPE molecule. A summaryof the present study including the chemical structures of themolecule is presented in Table 1.

VII. MOLECULAR IMAGING METHODS

A. Scanning Probe Microscope (SPM)

Since the scanning tip remain at a distance from the surfaceunder investigation, no chemical bond is formed between thetip and the surface giving rise to a strongly asymmetric con-figuration of the electrochemical potentials of the system. Thetechnique has often been used to directly visualize electro-chemical processes in-situ at the molecular levels for organicmonolayers (64; 65). In order to determine single molecular

Table 1: Summary of Molecules

Molecule Average

Conductance

Technique

used

Chemical Structure Application

[Reference]

1,4 benzene-

dithiol (BDT)

0.0099 G0 (at RT)

[G0 = 2e2/h]

(MCBJ) Molecular

wire

[18, 25]

dithiol NOPE

molecule

0.0007 G0

(at RT)

(MCBJ)

Single

molecule

device

[23, 24]

Copper (II)

phthalocyanine

0.00146 G0

(at RT)

STM Molecular

rectifier

[9]

Fluorone dye

(Rose Bengal)

0.00161 G0

(at RT)

STM Molecular

rectifier

[9]

Pentacene N.A. AFM

Fullerenol (C60) 0.00142 G0

(at RT)

Hg blob Molecular

memory

[10]

C140 0.2 S

(measured at

1.5 K)

STM Single

electron

transistor

[79]

double stranded -

DNA

10-5

10-6

G0 STM break

junction

Molecular

conduction

[2]

C-8 dithiol SAM

C-8 monothiol

SAM

9.3 1.8 10-4

A/cm2 (at 1 V)

3.1 1 10-4

A/cm2 (at 1 V)

Inelastic

electron

tunnelling

spectroscopy

Molecular

electronic

device

[8]

C16H33Q-3CNQ 0.266 S Metal-film-

metal

sandwich

structure

Molecular

diode

[9]

divanadium

molecule

[(N,N,N-

trimethyl-1,4,7-

triazacyclononan

e)2V2(CN)4(-

C4N4)]

N.A. STM

Single

molecule

magnet

[16]

La0.7Sr0.3MnO3/

Alq3/Co

junction

N.A. Nanoscale

cross junction

Organic spin

valve/molecu

lar magnet

[17]

-DNA (as test

structure) N.A. Solid state

nanopore

Single

molecule

biosensor

[22]

FcC11S-SAM

On Au substrate

N.A. STM Negative

differential

resistance

[50]

DNA N.A. AFM Self-

assembled

periodic

nanostructure

[48]

Oligothiophenes 7.5 10-5

G0 (for 4T)

2.8 10-5

G0 (for 3T)

c-AFM

Molecular

switch

[54]

Metalloprotein

(azurin)

N.A. Electrochemic

ally gated

transistor

Bio-

electronics

[94]

11

conductance by SPM technique, the molecule is covalentlybonded to the two probing electrodes and the measurement isperformed under ultra-clean and ultra-high vacuum environ-ment.

B. Scanning Tunneling Microscope (STM)

STM provides a three-dimensional profile of the investigat-ing surface for quantitative determination of surface rough-ness, surface defects, the size and conformation of moleculesand molecular aggregates with atomic precision or even insubatomic resolution (66). When a sharp tip of an atomic di-mension in practice is brought sufficiently close to a substrateadsorbing the molecule, a strong interaction is established be-tween the electron clouds of the surface and tip atoms pro-motes tunnelling of electrons under a small bias. The expo-nential variation of current with tip-sample distance leads tomapping the surface image sample with an atomic resolutionwhen scanned over the two-dimensional surface. The basicset up a STM is shown in Figure 9(a) with two piezo-electricscanners to control the position of the tip over the surface. Theconstant density of states contours is mapped in constant cur-rent mode, by adjusting the tip-sample distance with the use ofa feedback loop. Alternatively, the vertical position of the tip(z-coordinate) can be held constant to record tunnelling cur-rent for mapping the actual density of states. The typical ar-rangements of the Si atoms can clearly be seen from the ultra-high vacuum STM image of a Si (111) 77 reconstructed sur-face in Figure 9(b). In this method, the tip-molecule contactis often less well defined than the molecule-substrate contactpreventing one from determining the absolute conductance ofthe molecule. Figure 9(c) illustrates an alternative methodin which the molecule is adsorbed onto one end of the sub-strate and an organic surfactant coated Au nanoparticles arecovalently bonded to its other end (67). Electron tunnellingfrom tip to the substrate exhibits the Coulomb blockade ef-fect due to the presence of the nanoparticles as Coulomb is-lands (45). Measured I-V curves are interpreted in terms ofthe Coulomb blockade model to determine the conductanceof the molecule (68; 69).

This method has been successfully exploited for the charac-terization of organic monolayers, polypeptides, biomoleculeslike DNA, biological tissues and metallic-protein. There havebeen several reports of STM imaging of DNA molecules em-bedded in metal films (70), protein characterization by electro-chemical techniques (71), studying and investigations of elec-tron transfer in metallic-proteins (72; 73). The conductivitymeasurement of DNA by STM has been employed to examinethe electrical behaviour of DNA as insulators (74), conduc-tors (75), semiconductors (76) and superconductor (77). Ad-ditionally, the study of electron transport through DNA (78),DNA array detection may be accomplished using site specificnanoparticles probes (79), self-assembly of two-dimensionalDNA crystal (? ), controlled manipulation of atoms on givensurfaces for application as electronic ink (64) and the possi-bility of designing the catalysis process at the single moleculelevel and control of the constituents at the molecular lev-

Figure 7. (a) Schematic of STM arrangement with a sharp tip mounted on 3 piezo crystals. X- and y-piezo allow the tip to scan the 2-dimensional surface in xy plane while z piezo controls the tip-sample separation. (b) STM image of a Si (111) 77 surface. Scan area of the image is 1515 m2. (c) STM measurement of molecular conductance. One end of the molecule/SAM is attached to the substrate and the other end is bounded to a Au nanoparticle (Au NP).

FIG. 9 (Color online) (a) Schematic of STM arrangement with asharp tip mounted on 3 piezo crystals. x- and y-piezo allow the tip toscan the two-dimensional surface in xy plane while z-piezo controlsthe tip-sample separation. (b) STM image of a Si (111) 77 surface.Scan area of the image is 15 15m2. (c) STM measurement ofmolecular conductance. One end of the molecule/SAM is attached tothe substrate and the other end is bounded to a Au nanoparticle (AuNP).

Figure 8. (a) Schematic representation of AFM set up. (b) Tapping mode AFM image of a 2 nm pentacene film grown over a polymer coated glass substrate.

FIG. 10 (Color online) (a) Schematic representation of AFM set up.(b) Tapping mode AFM image of a 2nm pentacene film grown overa polymer coated glass substrate.

els (81). These include non-linear current-voltage character-istics with NDR behaviour on redox-active molecular mono-layers (82) and study of field effects on electron transport inmolecules (83). Spectra of a single molecule namely inelasticElectron Tunneling Spectroscopy (IETS) has also be investi-gated with a cryogenic STM (84).

C. Atomic Force Microscope (AFM)

A schematic of the AFM set-up is shown in Figure 10(a).The laser light reflected from the back of the cantilever entersa photodiode/photodetector device. AFM is generally used intapping mode with the cantilever vibrating above the samplesurface and the tip in intermittent contact with the surface.Figure 10(b) shows the tapping mode AFM image of vac-uum deposited pentacene film (2nm) on poly (4-vinyl phe-nol) (PVP) coated glass substrate. The individual grains ofpentacene molecules are seen. Contact mode AFM, where thetip is in contact with the surface continuously, is only used forspecific applications, such as force curve measurements. Themovement of the tip governed by the tip-surface interactions ismeasured by detecting the position of a reflected laser beam,focussed onto the back of the cantilever.

AFM can be used to measure different mechanical proper-ties including adhesion strength and magnetic forces and witha conducting tip used in either contact or non-contact mode

12

of operation (85; 86). This technique offers typically a lowerresolution than STM. However, the capability of imaging bothconducting and non-conducting surfaces in sub-nanometrelevel without the need for any additional sample preparationhas made AFM more powerful tool than STM for in-situ mea-surements and real time imaging of biological and chemicalprocesses (87; 88).

D. Conducting Atomic Force Microscope (C-AFM)

In this mode, a platinum or platinum/iridium coated AFMtip is employed for contact to the molecular monolayer with aview to measuring in-situ the current-voltage characteristics.Topographic images may also be recorded using the Pico scancontroller in another channel. An external bias to the tip isapplied to induce an attractive electrostatic force in additionto the adhesion force, controlling the pressure with which theconductive probe pushes into the sample surface. However,accurate measurement of the molecular conductance requiresthe pressure to be maintained constant [79]. The bimolecu-lar interaction and bond strength have been measured (89) byrecording the force by the biomolecule-functionalized AFMtip when brought in contact with another biological surface,via, protein, cell, tissue. Force-distance curves have beenused for multiparametric imaging of native proteins and pro-tein complexes in the native unperturbed state and to simul-taneous mapping their biophysical and biochemical proper-ties at atomic resolution (90). The variation in tip pressuresmay modify the overlapping of electronic wave functions andhence the injection barrier, affecting charge carriers injec-tion from electrode to the molecule and a dramatic changein the conductive properties of the sample. Carbon nanotube(CNT) AFM probes are found to be more durable and offerthe improved spatial and lateral resolution of the imaging (91).These probes have been used to extract structural informationof tissues (92), multiplexed detection of polymorphic sites anddetection of haplotypes in DNA fragments and positions of thetagged sequences (? ). C-AFM has been used to record Con-ductance switching behaviour and data storage ability of smallmolecules have been studied using the C-AFM technique (94).

VIII. NANOPORES

A nanopore is basically a tiny hole of molecular dimensionbetween two metal electrodes providing stable and well de-fined contacts to the molecular monolayer. A nanopore junc-tion is fabricated by growing a low conductivity silicon ni-tride (SiN) film is on a Si wafer. Selected areas of the waferare then etched away so as to leave free standing SiN films.A pore having diameter 10-50nm is then etched throughthese films (Figure 11). Thin gold film (Au) is evaporated onthe bottom of the wafer over which the SAM of molecule ofinterest is assembled from the other side of the membrane.A top metal contact is then deposited onto the monolayer torecord the I-V characteristics of the sandwich device (95).

Figure 9. Schematics of nanopore in both (a) side view and (b) top view.

FIG. 11 (Color online) Schematics of nanopore in both (a) side viewand (b) top view.

The solid-state nanopore proves to be a versatile single-molecule tool for biophysics and biotechnology applica-tions (96). Ion currents and forces are monitored in nanoporebased sensors involving DNA (97), RNA (98; 99) and pro-teins (100; 101) molecular resolution. Nanopore junction withthioacetatebiphenyl SAM exhibited diode like characteris-tics (95), while NDR and non-volatile memory switching wasobserved in nitro-amino benzenethiolate SAM (102).

IX. MERCURY (HG) DROP METHOD

For ultra-thin organic film or organic monolayer, the depo-sition of a top electrode by thermal evaporation may lead topenetration of highly energetic metallic particles through thefilm and damage it. Hence, for electrical characterization ofSAM of alkanethiol and other molecules Hg-drop method wasdeveloped (103). The SAM was either sandwiched betweentwo mercury drops (104) or assembled on a solid substrate,in which case an Hg drop is used as the top electrode (105).Figure 12(a) shows the schematic representation of a sim-ple experimental arrangement where the Hg drop was usedas the top electrode. Annealed films were kept in a vacuumchamber (103 Torr) at room temperature with the film fac-ing downward. A syringe with a mercury (Hg) drop on its tipwas raised from outside the chamber slowly by a micrometrescrew till the blob just touched the film. The diameter of theblob was below 0.5mm. The contact between the film and theblob was monitored through a microscope. The bias was ap-plied with respect to the Hg electrode and I-V characteristicswere recorded in voltage loops. We have electrically char-acterized monolayer of a typical D-A system, namely CuPc-fullerenol layer-by-layer electrostatically self-assembled filmon Si substrate with Hg blob as the top electrode. Seven con-secutive loops are shown in the Figure 12(b). The monolayerwas initially in the low-conducting off-state which switched tothe high conducting on-state at reverse bias. At any voltage,the current remains at least four orders in magnitude higheras compared to that in the initial scan. The higher level ofcurrent is retained even when the bias is scanned in subse-quent loops. The switching phenomenon in the monolayer ofCuPc:fullerenol is also irreversible in nature making it suitablefor WORM memory applications (10). The method is advan-

13

Figure 10. (a) A schematic diagram of the Hg-blob set up for monolayer characterization. (b) I-V characteristics of CuPc:fellerenol monolayer on Si with Hg blob as the top electrode under multiple voltage loops. First loop is shown with filled symbol and the subsequent loops are shown with open symbols. Arrows indicate the direction of voltage sweep.

FIG. 12 (Color online) (a) A schematic diagram of the Hg-blobset up for monolayer characterization. (b) I-V characteristics ofCuPc:fellerenol monolayer on Si with Hg blob as the top electrodeunder multiple voltage loops. First loop is shown with filled sym-bol and the subsequent loops are shown with open symbols. Arrowsindicate the direction of voltage sweep.

tageous because of its simple design and quick two terminalcharacterization of SAMs. However, the Hg contacts area isquite large making it difficult to probe single molecular con-ductance.

X. SUMMARY

The conductance of a single molecule as the conductancedepends not only on the intrinsic properties of the molecule,but also on the probing electrodes, electrode-molecule interac-tion, and its local environment. For unambiguous determina-tion of the molecular conductance, it is essential to fabricate amolecular junction with well-defined contacts at the atomicscale and to carry out the measurement in controlled envi-ronment. Despite the challenges, tremendous developmentshave been made in fabricating different break junction, SPMtechniques and nanopore methods. Although, the contact ge-ometries in break junction methods are only little known withinsufficient atomic scale structural information, a large num-ber of molecular junctions with different contact geometriescan be created allowing one to determine average molecularconductance from the statistical analysis. STM has been effi-ciently used to create a well-defined metal-molecule-moleculejunction with more limited contact areas and to measure theconductance of single molecule. In addition to the singlemolecule conductance spectra, STM and AFM imaging ofsingle molecule or molecular assemblies and manipulation ofatoms by STM have proved SPM a powerful and versatile toolto probe molecules in atomic and even subatomic resolution.

Acknowledgments

This work is sponsored by the Air Force Office of ScientificResearch, Air Force Material Command, USAF, under grantnumber FA 9550-15-1-0123.

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