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Page 1: Institute for Micromanufacturing - Author Query Formramu/msnt505/lec_notes/Kuila/... · 2004. 4. 21. · In this chapter, the electrostatic surface potential 35 (ESP; due to chemisorbed

Page 1 of 1

Author Query Form Queries and/or remarks

AQ No. Details 1 The Introduction was too long; an 'Overview' heading was inserted after the

first paragraph. Pls. confirm if this is acceptable; otherwise, pls. provide a shorter Introduction (max. 3 paragraphs). Pls. check also if the section levels are correct.

2 Fig. 2: Pls. confirm whether the source here should be added to the reference list.

3 Images of Figs. 3 and 6 have no explicit (a) and (b) parts. Pls. check. Thank you.

4 Unfortunately, our guidelines do not accept annotated references. The annotation was captured as a footnote to the text discussion. Kindly confirm if this is correct. You may also delete the annotation or incorporate the commentary into the text itself.

5 Reference list and their citations were changed to conform with Dekker's reference style. Please check if everything is correct.

6 Pls. provide the publisher location. 7 Please provide the volume number for Refs. [23,37]. The URL in Ref. 37 is

invalid. Pls. check 8 Please update the status. Please note that the figures will appear as black and white (unless specified by

Dekker) in the print version and colored in the web version. The note, "for the color version of the image visit www.dekker.com" was placed because of this.

Article No.: 120013844

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Marcel Dekker, Inc. ARTICLE/CHAPTER INFO SHEET

D/Encyclopedia: E-ENNC/ISSN/ISBN: Print 0-8247-4797-6C/ISSN/ISBN: Web 0-8247-4797-6D/Article ID number: 120013844C/Article title: Nanoscale Charge Transfer in Metal-Molecule HeterostructuresD/Unarticle or Article type:C;A/Key words: Nanostructures, Charge transfer, Electron transfer, Electrostatic surface potential,

AFM, Kelvin force microscopy, Peptides, Self-assembled monolayers, Contact-potential difference, Scanning probe techniques, Reflectance absorption infrared spectroscopy, Ellipsometry, Molecular electronics, Electrostatic force microscopy

D/Copyright holder: MDIC/Author number: 1.00E+00C/Author first name: DebasishC;A/Author middle initial:C:A/Author last name: KuilaA/Suffix to last name:C;A/Degrees:C;A/Author e-mail address: [email protected];A/Author fax:C;A/Author phone:

C;A/TitleC;A/Department Institute for Micromanufacturing and Chemistry ProgramC;A/Institution Louisiana Tech UniversityC;A/Street Address 911 Hergot AvenueC;A/City RustonC;A/State/Province LouisianaC;A/Postal code 71272C;A/Country U.S.A.C;A/TitleC;A/Department Institute for Micromanufacturing and Chemistry ProgramC;A/Institution Louisiana Tech UniversityC;A/Street address 911 Hergot AvenueC;A/City RustonC;A/State/Province LouisianaC;A/Postal code 71272C;A/Country U.S.A.C;A/Department Institute for Micromanufacturing and Chemistry ProgramC;A/Institution/Company Louisiana Tech UniversityC;A/Street address 911 Hergot AvenueC;A/ Office complexC;A/ Suite, floor, room no.C;A/ City RustonC;A/ RegionC;A/ State/Province LouisianaC;A/ Postal code 71272C;A/ Country U.S.A.C/Author number: 1

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C/Author number: 2C/Author first name: DavidC;A/Author middle initial: B.C:A/Author last name: JanesA/Suffix to last name:C;A/Degrees:C;A/Author e-mail address: [email protected];A/Author fax:C;A/Author phone:

C;A/TitleC;A/Department School of Electrical EngineeringC;A/Institution Purdue UniversityC;A/Street AddressC;A/City West LafayetteC;A/State/Province IndianaC;A/Postal code 47907C;A/Country U.S.A.C;A/TitleC;A/Department School of Electrical EngineeringC;A/Institution Purdue UniversityC;A/Street addressC;A/City West LafayetteC;A/State/Province IndianaC;A/Postal code 47907C;A/Country U.S.A.C/Author number: 3C/Author first name: CliffordC;A/Author middle initial: P.C:A/Author last name: KubiakA/Suffix to last name:C;A/Degrees:C;A/Author e-mail address: [email protected];A/Author fax:C;A/Author phone:

C;A/TitleC;A/Department Department of ChemistryC;A/Institution University of California-San DiegoC;A/Street AddressC;A/City La JollaC;A/State/Province CaliforniaC;A/Postal code 92093-0358C;A/Country U.S.A.C;A/TitleC;A/Department Department of ChemistryC;A/Institution University of California-San DiegoC;A/Street addressC;A/City La JollaC;A/State/Province CaliforniaC;A/Postal code 92093-0358

Current affiliation(s): Repeat if same as affiliation at time of authorship

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Page 5: Institute for Micromanufacturing - Author Query Formramu/msnt505/lec_notes/Kuila/... · 2004. 4. 21. · In this chapter, the electrostatic surface potential 35 (ESP; due to chemisorbed

1 Nanoscale Charge Transfer in2 Metal–Molecule Heterostructures

3 Debasish Kuila4 Louisiana Tech University, Ruston, Louisiana, U.S.A.

5 David B. Janes6 Purdue University, West Lafayette, Indiana, U.S.A.

7 Clifford P. Kubiak8 University of California—San Diego, La Jolla, California, U.S.A.

9

10

11 INTRODUCTION

12 What is nanoscale? Albert Einstein’s doctoral research,

13 using experimental data on the diffusion of sugar in water,

14 showed that each single sugar molecule measures about a

15 nanometer in diameter, a billionth of a meter. One nano-

16 meter is the approximate width of 10 hydrogen atoms laid

17 side by side. It is one thousandth the length of a typical

18 bacterium (�1 mm, 10�6 m), one millionth the size of a

19 pin head, one billionth the length of Michael Jordan’s

20 well-muscled legs (�1 m). While the exact definition of

21 ‘‘nanotechnology’’ is somewhat imprecise, the term

22 generally implies devices or structures with at least two

23 characteristic dimensions in the range of 1–100 nm. Along

24 with biomedical research and defense—fighting cancer

25 and building missile shields—nanotechnology has be-

26 come a visible and energized discipline in science and

27 technology. It spans fields from condensed matter physics,

28 engineering, molecular biology to large swath of chem-

29 istry[1,2] (Fig.F1 1). Key themes within this area include

30 1) the ability to understand, and ultimately to control,

31 important properties of materials and structures at the

32 nanometer scale; and 2) improved understanding of how

33 nanostructured elements interact with the external envi-

34 ronment. In this chapter, the electrostatic surface potential

35 (ESP; due to chemisorbed dipoles on a surface) mea-

36 surements and experimental results derived from our

37 collaborative efforts as well as that of other groups are

38 discussed. A brief overview of current theoretical under-

39 standing including our ongoing calculations is included.

AQ1 40 OVERVIEW

41 In contrast to the relatively recent recognition of nano-

42 technology as a field, charge transfer has been known for

43 decades.[3,4] It is a very important process in chemistry,

44 biology, and physics in semiconductor devices and in

45 electronics. Our respiration, photosysnthesis, many bio-

46 logical processes, and thin films of tunnel-diode involve

47 electron or charge transfer, in some cases even at a large

48 distance.[5] In both respiration and photosynthesis, the

49 primary action of the energy source (combustion of sub-

50 strate by oxygen in respiration and absorption of light by

51 chlorophyll or bacteriochlorophyll in photosynthesis) is to

52 move charges or electrons, a long distance, in an electron-

53 transport chain.[6,7] Charge transfer in photosynthetic re-

54 action centers[8] and in protein–protein electron-transfer

55 complexes such as hemoglobin[9] can even occur at liquid

56 helium temperature. The measurement of electrical cur-

57 rents, I, tunneling through insulating layers, as in the in-

58 vention of Esaki tunnel-diode, is a classic example of

59 charge transfer in semiconductor devices.[10]

60 The quest for miniaturization of semiconductor devices

61 has created a tremendous interest in nanomaterials in re-

62 cent years.[11,12] Nanoscale structures have now become

63 essential parts of integrated circuit (IC) technologies for

64 providing faster computer chips. Decades before compu-

65 ters pervaded our workplaces and homes, Gordon Moore,

66 cofounder of Intel Corporation, observed that the number

67 of transistors per unit area in an IC chip was doubling

68 approximately every 18 months. This relationship, widely

69 known as Moore’s Law,[13] has held for over 30 years. It

70 drives much of the technology development and is re-

71 sponsible for the continuous increase in computer speeds,

72 memory capacities, and capabilities of components based

73 on ICs. In the first international conference on nanoma-

74 nufacturing at MIT in April 2003, Intel showed their

75 progress toward 100-nm computer chips. However, there

76 is a limit to the top-down approach, a concern shared by

77 the researchers in semiconductor industry.[14]

78 The gap between the top-down approach and the size of

79 an individual molecule (Fig. 1) may be best realized using

80 a bottom-up approach. Nanotechnology with direct impact

81 on commercial application of nanoscale systems will de-

82 pend on their assembly with predefined geometry either in

Encyclopedia of Nanoscience and Nanotechnology 1

DOI: 10.1081/E-ENN 120013844

Copyright D 2004 by Marcel Dekker, Inc. All rights reserved.

120013844_E-ENN_R1_BATCH10_111403

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83 solution or on a solid support. Interesting new phenomena

84 such as single-electron charging effects[15] and conduc-

85 tance quantization[16] have already been discovered. As

86 decreasing the size of microfabricated components be-

87 comes increasingly difficult, it is possible that molecular

88 electronic approaches can play a significant role in elec-

89 tronics. As molecules with sizes in the range of 1–3 nm

90 have been shown to have interesting functionality when

91 integrated into device structures, this approach should

92 provide inherent scalability to the nanoscale (Fig.F2 2).

93 Aviram and Ratner originally proposed in 1974 that

94 molecules could replace computer-chip components and a

95 single molecule with a donor–spacer–acceptor would be-

96 have as a diode when placed between two electrodes.[17]

97 This has now been extended to electronics using hybrid

98 molecular and monomolecular devices and has been

99 reviewed recently by Aviram and his colleagues at

100 IBM.[18] More significantly in the past 5 years, nanoscale

101 devices ranging from simple switches and wires to more

102 complex transistors and circuits have been unveiled. Let

103 us review briefly what is inside an IC and a few major

104 accomplishments in the past 5 years.

105 An IC chip, the heart of a computer, is made of silicon,

106 a semiconductor material. A stamp-size chip can hold

107 billions of components, primarily the transistors that allow

108 a computer to process instructions, perform calculations,

109 and manage data flow. The transistor is a switch that

110 controls and generates electrical signals using three

111 terminals: the source, gate, and drain. More sophisticated

112 functions can be performed using multiple transistors.[19]

113 In computational circuits such as microprocessors, the

114 transistors are typically interconnected to form logic

115 gates, which represent and manipulate data using a binary

116 system often designated as ‘‘1’’ and ‘‘0.’’ The binary

117 system, or rather the patterns and sequences of 1 (‘‘on’’)

118 or 0 (‘‘off’’) can be interpreted as numbers. Generally, the

119 state (‘‘1’’ or ‘‘0’’) of a given logic gate is determined by

120 the voltage state at the output of that gate. The state of a

121 logic gate switches in a specified response to its inputs,

122 based on the configuration of wires that interconnect the

123 gates within the IC. The switching signals consist of

124 voltages, and associated electronic charge/current, flow-

125 ing through the wires leading into the logic gate. Within

126 an IC, bits of information can also be stored in memory

127 cells, where a bit is typically represented by a quantity of

128 electronic charge or a voltage state.[19]

129 Typically, the wires in ICs are made from metals,

130 which are good electrical conductors. In the past decade,

131 individual molecules have been shown to conduct elec-

132 tricity; the Aviram–Ratner mechanism, slightly modified,

133 has been confirmed both in macroscopic and nanoscopic

134 conductivity measurements.[20] Simulations have shown

135 that gold nanowires can be stretched to one-atom thick-

136 ness. Phaedon Avouris at IBM designed a ‘‘NOT’’ gate

Fig. 1 An overview of micro- and nanoscale.

Fig. 2 a) A schematic representation of a unit cell of metal/molecule/metal device structure. b) Potential AQ2scaleable logic/memory

circuit using unit cell devices. c) Characterization of self-assembled metal/molecule/substrate structure with well-controlled interfaces.

Using a flat Au substrate, this structure provided the first report of the resistance of organic molecules and the first room-temperature

Coulomb staircase in a controlled nanostructure. (Note: for the color version of the image visit www.dekker.com.) (From Andres, R. P.;

Bein, T.; Dorogi, M.; Feng, S.; Henderson, J. I.; Kubiak, C. P.; Mahoney, W.; Osifchin, R. G.; Reifenberger, R. ‘‘Coulomb staircase’’ at

room temperature in a self-assembled molecular nanostructure. Science, 1996, 272 (5266), 1323–1325.) (Go to www.dekker.com to view

this figure in color.)

2 Nanoscale Charge Transfer in Metal–Molecule Heterostructures

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137 (similar to the part of a computer’s logic circuitry) with

138 nanotubes.[21,22] A nanotube covering gold electrodes

139 formed two p-type transistors: one covered with an insu-

140 lator and the other was exposed to chemical processes,

141 converting it to n-type.

142 As with a typical transistor in IC, containing three

143 terminals: the source, gate, and drain, conductive tripod-

144 shaped molecules have been attached to three terminals to

145 form a transistor. Charles Lieber and his group at Harvard

146 University have designed a nanoscale memory device

147 using crisscrossed nanotubes as both wires and, at their

148 junctions, switches.[23,24] The tubes that touch are ‘‘on’’

149 and that do not are ‘‘off’’ and they can hold that state

150 indefinitely. Cees Dekker, of Delft University, unveiled a

151 transistor that worked at room temperature using a semi-

152 conductor carbon nanotube, an electrode, and a sub-

153 strate.[25] In contrast, Mark Reed at Yale and James Tour

154 at Rice have designed organic molecules that serve as

155 conductors. When a voltage is applied and varied to the

156 molecule containing a para-nitro aniline moiety (aromatic

157 species), it functions as a switch.[26]

158 The Yale–Rice team followed the bottom-up approach

159 to assemble the system on a gold surface using chemical

160 self-assembly which relies on ordered and functional

161 structure formed by dipping a Au-substrate into a solution

162 containing the aromatic thiol. This is the basis of a com-

163 mon bottom-up approach for making nanoscale devices

164 based on self-assembled monolayers (SAMs). The SAMs

165 of organic thiols have been widely studied and they have

166 been reviewed in recent literature.[27,28]

167 The current–voltage measurement of SAMs is one of

168 the most active area of research because of its role in

169 molecular electronics and other sensing applications. The

170 resistance or conductance of molecules bonded to an Au

171 electrode has been measured using scanning probe tech-

172 niques by different groups.[29–34] For example, in the case

173 of insulating SAMs of dodecanethiol (DDT), octade-

174 cylthiol (ODT), and resorcinarene C10 tetrasulfide

175 (RC10TS) on Au(111), the electrical conductivity of the

176 monolayers, measured using scanning tunneling micros-

177 copy (STM), is observed to depend both on the monolayer

178 thickness and on the nature of the Au/S bond. Leakage

179 current densities across 1.4-nm DDT and 2.0-nm RC10TS

180 on Au indicate superior insulating properties of the latter

181 at high voltages. The SiO2 layers with comparable leakage

182 current densities were calculated to have a thickness of 1.0

183 and 1.5 nm, respectively. These data strongly suggest that

184 organic SAMs are capable of providing necessary insu-

185 lation for the efficient operation of molecular or nanoscale

186 electronic circuits.[35]

187 A close coupling between theoretical modeling[36] and

188 experimental measurements is necessary to provide useful

189 insights into the conductance spectra of organic molecules

190 interfaced with semiconductor and metal surfaces. This

191 can be exemplified by the work of the teams led by Datta

192 and Reifenberger of Purdue University.[34,37,38] The basic

193 picture for molecular conduction is fairly straightforward

194 in principle. Consider a molecule of phenyl dithiol sand-

195 wiched between two gold electrodes as shown in Fig. F33.

196 The molecular energy levels consist of a set of occupied

197 levels separated by a gap from a set of unoccupied levels

198 (Fig. 3b). At equilibrium, the Fermi energy (Ef) is typi-

199 cally located somewhere in the gap between the highest

200 occupied molecular orbital (HOMO) and the lowest un-

201 occupied molecular orbital (LUMO). When a bias is ap-

202 plied, the Fermi energy in the right contact (m2) floats up

203 by eVd relative to the right contact (m1), i.e., m2�m1 = eVd.

204 The low bias conductance is determined by tunneling near

205 the Fermi energy. The conductance of the molecule

206 increases dramatically when the bias is large enough that

207 one or more of the molecular energy levels lie between

208 m1 and m2. This basic picture has been extended into a

209 quantitative model using the standard methods of

210 quantum chemistry.[38]

Fig. 3 (a) Phenyldithiol (1,4-benzenedithiol) sandwiched between two gold electrodes. (b) Schematic diagram showing AQ3molecular

energy levels and electrochemical potentials of the contacts.

Nanoscale Charge Transfer in Metal–Molecule Heterostructures 3

N

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211 ELECTROSTATIC SURFACE POTENTIAL

212 Although significant progress has been made in different

213 areas of nanotechnology, a proper understanding of charge

214 transfer at the metal–molecule interface is still lacking. In

215 contrast to I–V studies, the electrostatic surface potential

216 of SAMs—due to the presence of dipoles on a surface—

217 has not been explored that much. As shown in Fig.F4 4, ESP

218 arises from the dipoles created by the chemisorbed aro-

219 matic thiol on Au (Fig. 4). Now the question arises, why is

220 this important? First of all, the measurement of ESP gives

221 an insight into the electronic properties of SAMs. Sec-

222 ondly, such measurements provide a diagnostic feature for

223 the molecule and better models for I–V measurements.

224 Furthermore, a knowledge of ESP can help build a po-

225 tential chemical field-effect transistor (FET) for nano-

226 electronic devices. The origin of the measured potential is

227 intimately related to orientation and bonding as well as the

228 molecule itself. Thus ESP measurement is of fundamental

229 interest and has potential applications for chemical and

230 biochemical sensors (Fig. 4AB).

231 What follows next is a description of ESP measurements

232 and experimental results derived from our collaborative

233 efforts as well as that of other groups. A brief overview of

234 current theoretical understanding of ESP measurements

235 including our ongoing calculations is included.

236 ESP Measurements

237 Although several techniques exist for measuring the sur-

238 face potential of monolayers, the most widely used

239 method is the vibrating Kelvin probe developed initially to

240 measure the contact-potential differences (CPDs) between

241 two conducting materials.[37,38] When two metals are

Fig. 4 Top: Self-assembled monolayers of xylyldithiol chemisorbed on gold; the opposite charge dipoles produce electrostatic surface

potential (ESP); bottom, the ESP measured with or without the molecule chemisorbed on the surface using electrostatic force

microscopy (EFM). (AB) A schematic view of potential chemical sensors based on electrostatic surface potential measurements of a

SAM of an organometallic compound before and after it is exposed to a gas. (Go to www.dekker.com to view this figure in color.)

4 Nanoscale Charge Transfer in Metal–Molecule Heterostructures

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242 electrically connected, electrons flow immediately from

243 one metal to the other until an equilibrium is established,

244 i.e., when both metals reach the same electrochemical

245 potential. The potentials outside the metals are no longer

246 strictly constant due to these slight surface charges, cre-

247 ating a potential drop from one metal to another, which is

248 described as the local CPD between these two metals

249 (Fig.F5 5). The CPD for clean metal surfaces is the differ-

250 ence in work functions (defined by removal of an electron

251 from the surface to vacuum) of the two materials. The

252 work function is modified as the surface is coated with

253 SAMs of different dipole moments (Fig. 5). However, as

254 the work function of the tip is the same for both mea-

255 surements, the surface potential of the SAM-coated Au

256 can be referenced to the bare Au substrate (Fig. 4).

257 A commercial AFM can be modified as the Kelvin

258 probe to enable surface potential measurements (Fig. F66).

259 Two conductors are arranged as a parallel plate capacitor

Fig. 6 An electrostatic force microscopy (EFM) set-up using a modified AFM to measure the electrostatic surface potential; (b,

bottom) an expanded view of the AFM tip over the Au substrate. (Go to www.dekker.com to view this figure in color.)

Fig. 5 The contact potential difference (CPD) due to difference in work functions resulting from the AFM tip over metal and the metal

coated with the self-assembled monolayer of a molecule.

Nanoscale Charge Transfer in Metal–Molecule Heterostructures 5

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260 with a small spacing (nanometer scale), and the resultant

261 CPD (as shown above in Fig. 5), in a simple sense, can be

262 defined as VCPD = � (f1� f2)/e, where f1 and f2 are the

263 work functions of the conductors that include the adsorbed

264 layers. A periodic vibration between the two plates at a

265 frequency o gives an alternating current (a.c.) with the

266 same frequency o when the two plates have different

267 work functions.[39]

IðtÞ ¼ ðVbias þ VCPDÞoDC cosot

268269 The zero point of a.c. can be detected when the additional

270 bias voltage is applied between the two plates until the

271 electric field between them disappears, i.e., VCPD=�Vbias.

272 The spatial resolution of CPD in electrostatic force mi-

273 croscopy (EFM) can be improved using a Kelvin probe tip

274 and has been called Kelvin probe force microscope

275 (KFM) by Nonnenmacher and coworkers.[40]

276 The electrostatic surface potential (Vs) measurement is

277 based on the standard noncontact force detection tech-

278 nique described elsewhere.[41,42] In short, the tip is held at

279 a fixed distance of approximately 100 nm above the

280 sample using a noncontact topographic feedback system

281 as shown in Fig. 6. This system controls the separation by

282 monitoring and maintaining a specific mechanical vibra-

283 tion of the cantilever (or) near its resonance frequency.

284 The electrostatic force on a conducting tip held close to

285 a conducting surface is given by F=� (1/2)V s2 (dc/dZ);

286 where Vs or VSAM is ESP.

287 The ESP for a SAM, relative to that of a bare metal

288 surface, is defined as:

VSAM ¼ Nmol

2Ke0

~pn ð1Þ

289290 where Nmol is the local density of molecules in the SAM

291 (assuming uniform coverage), ~p is the dipole moment of

292 the adsorbed molecule, n is a unit vector normal to the

293 surface, K is the relative dielectric constant of the mo-

294 lecular monolayer, and e0 is the permittivity of vacuum.

295 The effective charge distribution of a SAM can be

296 modeled as a sheet dipole per unit area given by the dipole

297 moment per molecule (md, typically expressed in Debye)

298 times the density of molecules on the surface. For a

299 monolayer of molecules having a dipole moment of 1 D

300 [defined as the separation of two electronic charges (+q

301 and �q) over a distance of 0.021 nm within a molecule],

302 Nmol = 4�1018 molecules m�2, a density typical of SAMs

303 with molecules such as the ones studied here, and with

304 K = 2 yields VSAM � 380 mV if a perpendicular orienta-

305 tion of the molecule with respect to the surface is assumed

306 (Fig. F77).

307 Experimental: Characterization of308 Substrate and SAMs

309 In order to remove the background ESP, all measurements

310 were referenced to a clean Au(111) substrate (Fig. 4,

311 bottom), prepared by flame annealing.[41,42] One of the Au

312 substrates is always used as reference while the others are

313 used for SAM preparation. In addition, the surface po-

314 tential measurements were always measured with respect

315 to an oxidized piece of LTG:GaAS (GaAS grown at lower

316 temperature; ��450 mV with respect to LTG:GaAS) as

317 it has always yielded reliable surface potential.

318 The clean flame-annealed gold substrates were then

319 dipped into �1 mM solution of the desired thiol in a

320 suitable solvent such as ethanol or dichloromethane,

Fig. 7 A typical representation of a SAM with respective charges on the Au-substrate. (From Ref. [43].)

6 Nanoscale Charge Transfer in Metal–Molecule Heterostructures

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321 usually for overnight. The SAM-coated Au-substrates

322 were rinsed with the solvents, next day, and dried in air or

323 inside a glove-box with a stream of N2.

324 The SAMs were characterized using two common

325 methods: reflectance absorption IR spectroscopy (RAIRS)

326 and ellipsometry.[41,42] While RAIRS can detect the

327 presence and orientation of thiols bonded to the surface,

328 ellipsometry, another similar optical technique, measures

329 the thickness of a monolayer. A typical RAIR spectrum of

330 an aromatic thiol, with thickness of 0.8 nm, used to form a

331 charge-transfer (CT) complex (see ‘‘Surface Potential

332 Measurements of a CT Complex’’) is shown in Fig.F8 8 (see

333 Ref. [42] for the description of the peaks).

334 Electrostatic Surface Potential Results

335 Evans and Ulman first studied the ESPs of SAMs of

336 alkanethiols on gold surfaces using a macroscopic Kelvin

337 probe.[43] As the probe diameter was on the order of a few

338 millimeters, the surface potential produced by a large

339 number of molecules (�1013) was measured. These

340 measurements indicated a dependence of the ESP on the

341 number of CH2 groups that formed the backbone of the

342 alkanethiols. A change of �10 mV per CH2 group was

343 observed. Thus while the ESP of dodecanethiol (DDT)

344 was �520 mV, that of octadecylthiol (ODT) was mea-

345 sured to be �580 mV.

346 In these studies, Evans and Ulman modeled SAMs as a

347 two-dimensional ensemble of dipoles with length l, where

348 l is approximately the length of the molecule (Fig. 7). A

349 layer of negative charge resides very close to the Au

350 substrate, while the positive charge is thought to lie at

351 the tail of the molecule, approximately a distance l above

352 the gold surface. The orientation of the dipole moment is

353 inferred from the positive slope in the surface potential

354 as the chain length is increased. This suggests that in-

355 crease in ESP is directly related to the change in distance

356 between the two charged sheets. In molecular terms,

357 this implies that the effective R+–S� dipole (where

358 R = CnH2n+ 1) must be larger than the Au+–S� dipole and

359 this is reasonable as the Au+ can be screened within a very

Fig. 8 A reflectance absorption infrared spectrum of tetramethylxylyldithiol chemisorbed on Au.

Fig. 9 The electrostatic surface potentials of dodecanethiol

(DDT) and octadecylthiol (ODT) chemisorbed on Au. (Go to

www.dekker.com to view this figure in color.)

Nanoscale Charge Transfer in Metal–Molecule Heterostructures 7

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360 short distance by the electrons within the metal, whereas

361 this cannot be applicable for the monolayer (see ‘‘Nega-

362 tive Surface Potential’’).

363 Recently, Lu et al. used a KFM to measure the surface

364 potential of alkanethiol SAMs transferred to a gold sub-

365 strate using microcontact printing techniques.[44] The

366 lateral resolution in this case was �50 nm. As in the case

367 of Evans and Ulman, a dependence of surface potential

368 on the chain length is observed (�14 mV per CH2

369 unit). These measurements were made with respect to a

370 –COOH-terminated thiol SAM, making it difficult to

371 estimate the absolute value of the potential produced by

372 the molecules themselves. However, these studies clearly

373 established a strong dependence in the polarity and mag-

374 nitude of the ESP on the number of CH2 groups present

375 in an alkanethiol molecule.

376 The ESP measurements of alkanethiols using a modi-

377 fied AFM or EFM at Purdue have yielded much lower

378 values than that reported by Evans and Ulman. An average

379 surface potential of 100±20 mV for DDT SAMs and

380 230 ± 30 mV for ODT SAMs (Fig.F9 9) are observed. Al-

381 though the ESP measurements of alkanethiols by Evans

382 and Ulman, Lu et al., and that measured by the Purdue

383 group are somewhat different from each other, they may

384 still be compared on a qualitative sense as shown in Fig.F10 10.

385 The large difference between the surface potential

386 measured by the Purdue group and those reported by

387 Evans and Ulman may arise due to different standards. As

388 the electrostatic force is a long-range interaction, the

389 cantilever as well as the tip contributes to the electrostatic

390 force. It is estimated that SAM interrogated by the EFM

391 technique is roughly given by a circular region with a

392 diameter of �40 mM, a dimension determined roughly by

393 the triangular region of the cantilever supporting the tip.

394 Thus due to the uncertainties of the absolute values of the

395 surface potential, it is more relevant to discuss only the

396 relative changes between alkanethiols with different chain

397 lengths. The relative dependence of ESP on chain length is

398 in agreement with that reported by Lu et al.[44]

399 There are other factors that may explain the observed

400 difference in ESP values. Evans and Ulman did reference

401 their measurements to polycrystalline Au.[43] If the S–Au

402 bonding is affected by the orientation of the surface Au

403 atoms, then it is possible that the charge associated with S–

404 Au bond also depends on the orientation of the surface Au

405 atoms. Thus the charge associated with the S–Au bond can

406 cause an offset in the magnitude of the surface potential.

407 Further investigation is necessary to know the effect of the

408 orientation of the Au atoms on surface potential.

409 The ESP measurements are further complicated by

410 contamination of the surface. The preparation of the Au

411 surface can affect the packing density as well as the ori-

412 entation of the molecule. A ‘‘bare’’ Au substrate has been

413 considered as a control sample in our measurements.

414 Zehner et al. have shown in their studies that the ESP

415 value varies with time using hexadecanthiol (HDT) SAM

416 as a reference.[45] In our studies also, we have observed

417 the ESPs of DDT and ODT SAMs decrease slightly with

418 time.[41] This may indicate that SAM organizes further

419 with time and this is consistent with structural changes

420 observed over time by Barrena et al.[46] Similarly, Saito et

421 al. have used a monolayer of octadecyltrimethoxysilane

422 (ODS) and have shown how the electrostatic potential

423 depends on the surface coverage of the monolayer.[47]

Fig. 10 The electrostatic surface potentials of alkanethiols measured at Purdue and elsewhere. (From Ref. [41].) (Go to

www.dekker.com to view this figure in color.)

8 Nanoscale Charge Transfer in Metal–Molecule Heterostructures

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424 Thus how exactly different factors such as the substrate

425 and packing of SAMs affect surface potential may need to

426 be addressed further.

427 Effect of solvent on ESP measurements

428 To our knowledge, this aspect has not been reported in the

429 literature. We have examined the surface potential of

430 SAMs of ODT prepared from different solvents such as

431 ethanol, dichloromethane, and acetonitrile. The solvents

432 used for SAM formation do not form a chemical bond

433 with Au as they are removed by evaporation. Thus it is

434 unlikely that the solvents themselves can form a close-

435 packed monolayer. This is corroborated by IR spectro-

436 scopic investigations of Gericke et al.[48] which provide no

437 evidence of solvent molecules embedded in the mono-

438 layer. Our ESP measurements yield an average surface

439 potential of 200 ± 50 mV for ODT SAMs (prepared from

440 different solvents) with respect to bare Au(111), thus

441 showing no significant effect of solvent on surface po-

442 tential measurements.

443 ESP measurements of symmetric and444 nonsymmetric aromatic thiols

445 The structure of the molecule may play a significant role

446 and we investigated this by ESP studies of symmetric and

447 nonsymmetric aromatic molecules shown in Fig.F11 11. The

448 SAMs of these molecules were characterized using RAIR

449 and ellipsometry[41,42] and the RAIR spectrum of a typical

450 sample such as tetramethyl–xylyldithiol (TMXYL) is

451 shown in Fig. 8 (above). The molecules with a symmetric

452 structure, xylyldithiol (XYL) and TMXYL, show a small

453 surface potential with respect to Au (�+50 and �+16

454 mV). The nonsymmetric molecules show significantly

455 higher potential: benzyl mercaptan, which is equivalent to

456 replacing one of the CH2SH groups of XYL with a hy-

457 drogen atom yields an average surface potential that is

458 >+200 mV with respect to gold. Similarly, the replace-

459 ment of one CH2SH group with –CH3 in PMBM results in

460 a large surface potential with respect to bare Au(111)

461 (Fig. 11) substrate.

462 The difference in surface potential (Fig. 11) may be

463 explained on the basis of the structures considering the

464 absence of symmetry or lower symmetry in benzyl mer-

465 captan (BM) and pentamethylbenzyl mercaptan (PMBM).

466 In both XYL and TMXYL, there is a symmetry present in

467 the structures. So the expected dipole moment of these

468 systems before attachment to the Au surface will be low

469 or negligible. However, it is not obvious what happens to

470 the dipole moment of the system when the hydrogen is

Fig. 11 The electrostatic surface potentials of symmetric and nonsymmetric aromatic thiols chemisorbed on Au. (Go to

www.dekker.com to view this figure in color.)

Fig. 12 The electrostatic surface potentials of mono-, di-, and

tri-phenyl thiols.

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471 replaced by gold and attached to only one side of the

472 molecule. Experimental results seem to suggest that the

473 Au–S and H–S dipoles, in some sense, cancel each other;

474 but preliminary theoretical calculations suggest that this

475 may not be the case; attachment of three, six, and seven

476 Au clusters does produce significant dipole moments for

477 the symmetric molecule as well (see ‘‘Theoretical Mod-

478 eling of the Surface Potential of SAMs’’). Overall, these

479 measurements suggest that the molecular structure plays a

480 significant role in the charge transfer between S and Au.

481 Negative Surface Potential

482 The molecular structure and attachment of sp2-hybridized

483 carbon to sulfur bound to Au can have a profound effect

484 on the charge transfer or on the ESP measurements of the

485 SAMs of phenyl, biphenyl, and triphenyl thiols (Fig.F12 12).

486 The ESP of mono-phenyl thiol becomes negative with

487 respect to bare Au (�0.38 V) and increases further for

488 biphenyl, �0.76 , and levels off for the triphenyl species

489 at �0.72 V (Table T11). The surface potential produced by

490 these thiols can be estimated using the formula described

491 in Eq. 1 (Fig. 7). The angle of inclination can be estimated

492 using the RAIRS data and with respect to normal they are

493 0�, 31.79�, and 36.13�, respectively. Both the calculations

494 from isolated molecule (unpublished) and ESP data show

495 a significant shift in ESP when an additional phenyl ring is

496 attached to phenyl thiol and it levels off with three phenyl

497 rings.[49]

498 It is interesting to compare the observed ESP results of

499 phenylthiols with other aromatic thiols and alkanethiols.

500 From a chemical standpoint, the bonding of sulfur to gold

501 produces polarization: [Au]+�SR. In contrast to the situ-

502 ation in aliphatic thiols or benzyl mercaptan with a CH2

503 group attached to S that is bonded to Au, the negative

504 charge on the sulfur of phenyl thiols becomes relatively

505 large as it can be delocalized through several conjugated

506 structures. Hence a negative surface potential is observed

507 (see below).

508 Negative surface potential has also been measured for

509 SAMs of helix peptides. Miura et al.[50] have prepared

510 SAMs of two peptides with different molecular length,

511 LipoA16B and LipoA24B (Fig. F1313; notice that LipoA24B,

512 figure on the right, is much longer), and observed a

513 few hundred millivolts negative surface potential. These

Table 1 The electrostatic surface

potentials of mono-, di-, and tri-phenyl

thiols (Fig. 12)T1.1

Phenylthiols ESP, VT1.2

Monophenyl thiol �0.38±0.04T1.3Biphenylthiol �0.76±0.04T1.4Triphenylthiol �0.72±0.02T1.5

Fig. 13 The electrostatic surface potentials of N-terminal peptides with different lengths chemisorbed on Au; the one on the right is

longer than that of the left peptide. (From Ref. [50].)

10 Nanoscale Charge Transfer in Metal–Molecule Heterostructures

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514 peptide SAMs with N-terminal attached to sulfur, that is

515 connected to gold, show tilt angles of the helix axis from

516 the surface normal to be 36� and 30�, respectively, by

517 FTIR-RAIR spectroscopy. The large dipole moment of the

518 helices directs toward the surface, with a negatively

519 charged surface of the SAM exposed outside (Fig. 13).

520 The molecular arrangement is important for the evaluation

521 of the effect of the large dipole moment of the helices

522 because the alkyl-thiol SAMs, described above, produce a

523 positive surface potential because of the ionic nature of

524 the Au+–S� bond. Clearly, the large dipole moment of the

525 helices exceeds over the effect of Au+–S� to yield the

526 observed negative surface potential of the peptides. Fur-

527 ther, the surface potential of LipoA24B (tetracosapeptide)

528 is much larger than LipoA16B (hexadecapeptide) and is

529 consistent with the view that it originates from the dipoles

530 aligned toward the surface. The calculated dipole

531 moments, using MOPAC, are 55 D for the hexadecapep-

532 tide and 83 D for the tetracosapeptide and consistent with

533 the observed experimental results. These results further

534 emphasize that for a physically adsorbed species, the ef-

535 fect of individual dipoles on the surface potential is ap-

536 proximately evaluated only by considering the mutual

537 depolarization of a set of dipoles. In contrast, for a che-

538 misorbed adsorbate, the dipole moment or ESP cannot be

539 predicted easily.[51]

540 Surface potential measurements541 of a CT complex

542 The interplay between positive and negative ESP can be

543 controlled by chemistry alone. A CT complex SAM can

544 be formed by reacting a strong electron acceptor such as

545 tetracyanoethylene (TCNE) with a SAM of TMXYL

546 which is an electron donor[42] (Fig. F1414). It has been shown

547 previously that molecular conduction is greatly influenced

548 by the location of the equilibrium Fermi level within the

549 HOMO–LUMO gap (Fig. F1515).[34,37,38] Thus mixing of the

550 orbitals or rather the energy levels can produce a signifi-

551 cant surface potential of the SAM. As shown in Table T22,

552 the surface potential of TMXYL is close to that of bare

Fig. 14 A molecular doping experiment to produce a charge-

transfer complex of tetramethyl–xylyldithiol (TMXYL) and

tetracyanoethylene; orientation of TMXYL changes before and

after its reaction with TCNE and after removal of TCNE from

the complex. (From Ref. [42].)

Fig. 15 The HOMO–LUMO diagram of an isolated metal and an isolated molecule. (Go to www.dekker.com to view this figure

in color.)

Nanoscale Charge Transfer in Metal–Molecule Heterostructures 11

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553 Au(111) because of the molecule’s symmetric structure.

554 However, complexation to yield a CT complex of

555 TMXYL–TCNE produces a negative surface potential

556 which is due to the accumulation of negative charge on the

557 surface of the complex as observed for the peptides above.

558 As TCNE is a strong P-electron acceptor, a significant

559 amount of electron density is withdrawn from TMXYL,

560 the donor molecule, and is redistributed over the complex.

561 This can be confirmed by the removal of TCNE using

562 tetrathifulvelene (a strong donor), which returns the sur-

563 face potential to the value before the reaction of TMXYL

564 with TCNE.

565 Theoretical modeling of the surface566 potential of SAMs

567 Although we have measured the surface potential of

568 several SAMs, there is no quantitative understanding of

569 these measurements at present. As a first step for the

570 SAMs on gold, we have used a quantum chemistry soft-

571 ware, Hyperchem Pro 6 software[41] (parameters for the ab

572 initio calculations; basis set STO-3G, Fletcher–Reeves

573 geometry optimization). These initial calculations deter-

574 mine the dipole moment of alkanethiol molecules without

575 their attachment to the Au(111) atoms. The dipole

576 moments from these calculations for DDT, HDT (hex-

577 adecanethiol, CH3(CH2)15SH), and ODT are 0.67, 0.72,

578 and 0.74 D, respectively (1 D = 3.336�10�30 C m).

579 Now using the Eq. 1 above and typical parameters such

580 as a packing density of 4.46�1018 molecules/m2,[52] and a

581 molecular tilt of 30�,[53] and a dielectric constant of

582 �2.5,[43] the model potentials for DDT, HDT, and ODT

583 are calculated to be +450, +480, and +500 mV, respec-

584 tively (Fig. 10). The magnitude of the calculated poten-

585 tials is close to the data published by Evans and Ulman,[43]

586 which may suggest that EFM measurement is probably an

587 indicator of how well the SAM is organized when it is

588 bound to a metallic surface.

589 It is possible to calculate the dipole moments of DDT

590 and ODT from the surface potentials measured by the

591 Purdue group. Using the same parameters, the dipole

592 moments are estimated to be 0.17 and 0.39 D, respectively.

593 These are smaller than the calculated values. Furthermore,

594 the dependence of the dipole moments on the number of

595 CH2 groups present in the molecule is different by a factor

596 of three between the calculated and measured values.

597 Similar difference between experimental and theoreti-

598 cal results has been observed by Taylor for the surface

599 potential of monolayers both at the air–water interface and

600 deposited onto solid supports.[51] The ESP calculated for

601 an un-ionized stearic acid monolayer, DVHead + DVTail =

602 727 mV, is almost twice the experimental value of

603 390±10 mV. Such a discrepancy, however, is not sur-

604 prising as the model ignored 1) possible hydration effects

605 on the head group; 2) imaging effects in the subphase; and

606 3) reorientation of water molecules. A significant negative

607 contribution from these sources would reduce the dis-

608 crepancy between the experimental and theoretical results.

609 In order to establish the measured surface potential on a

610 firm ground and especially those of the aromatic systems

611 adsorbed on gold, we have done quantum chemistry cal-

612 culations using the supercomputer facilities at La Tech.

613 As a starting point, we have considered benezenethiol and

614 benzenedithiol molecules adsorbed on Au surfaces.a

615 The Eq. 1 for the ESP above indicates that the orien-

616 tation with respect to the surface normal and the dipole

617 moment of the molecule interacting with the surface can

618 be obtained using computational chemistry. First, it is

619 necessary to optimize the geometry of the molecule

620 adsorbed on the metal surface of interest to a reasonable

621 approximation, and then calculate its dipole moment in

622 that configuration. The orientation of the molecule can be

623 experimentally verified using RAIR spectroscopy.

624 The gold surfaces are modeled by a single layer of 3

625 and 6 gold atoms and clusters of 4, 7, 10, and 13 gold

626 atoms, all of which have (111) lattice. Fig. F1616 shows the

627 structure of the benzenedithiol molecule adsorbed on

AQ4

a

Table 2 The electrostatic surface

potentials (vsam) of TMXYL and the

charge-transfer complex TMXYL-TCNE

on Au(111) (Fig. 14)T2.1

Species ESP, mVT2.2

TMXYL (upright) 20±70T2.3TMXYL-TCNE �140±25T2.4TMXYL (flat) 30±60T2.5

aThe quantum chemistry calculations for this work are all done with the

Gaussian98 package of programs, using density functional theory and the

details will be published elsewhere (Ref. [54]). The popular B3LYP

functional is used for all calculations. Different basis sets are used for

different atoms: the LanL2DZ basis set, which consists of a double zeta

basis along with the Los Alamos relativistic effective core potential, is

used for the gold atoms, the 6–31G(d) basis for the carbon and sulfur, and

the 4–31G(d) for the H atoms. Most of the previous studies have used

basis sets such as the LanL2DZ for all the atoms in the system. The use of

the n–31G(d) family of basis sets on the nonmetal atoms yields a much

lower variational energy compared to a calculation in which LanL2DZ is

used for all the atoms. The additional flexibility of the basis set and the

presence of the extra d-functions to describe polarization effects allow

for a more accurate description of the molecular structure, charge density

distribution, and, therefore, of the dipole moment. Our objective has been

to use the largest basis set possible while keeping the calculations to a

manageable size.

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628 typical cluster of gold atoms using a mixed basis set.[54]

629 The smallest unit of the gold surface (111) consists of a

630 cluster of three gold atoms, which can be denoted as Au3

631 hereafter. The preferred bonding site of the S atom in the

632 interaction of thiols with (111) gold surfaces[55] cannot be

633 fully represented by the hexagonal close-packing (hcp)

634 hollow site. It requires the presence of a fourth gold atom

635 below the plane of the triangle, denoted as Au4 in Fig. 16.

636 Larger gold clusters consisting of 6, 7, 10, and 13 gold

637 atoms, denoted as Au6, Au7, Au10, and Au13, respectively,

638 were also considered to determine the influence of addi-

639 tional layers of metal atoms. The Au13 cluster has been

640 designated as a ‘‘magic number’’ cluster by Larsson et al.,

641 where an octahedral cluster has been shown to have the

642 lowest energy from DFT calculations.[56] It should be

643 mentioned, in this context, that recently a 20-atom cluster,

644 Au20, has been found to have exceptional stability and a

645 large band gap,[57] but this cluster lacks the symmetry of

646 the clusters studied here.

647 The results of our ongoing calculations show that both

648 symmetric and asymmetric molecules bonded to Aun

649 clusters have significant dipole moments.[54] In general,

650 the symmetric molecules tend to have smaller dipole

651 moments, which is qualitatively consistent with experi-

652 mental observations. However, the calculations indicate

653 that the origins of these dipole moments may have less to

654 do with the Au–S bonds rather than the charge distribution

655 in the rest of the molecule. A careful analysis of the

656 charges is currently underway. These comments further

657 underscore the fact that a fundamental theoretical under-

658 standing of the mechanisms by which SAMs develop

659 ESPs on gold is still lacking.

660 Organosilane SAMs

661 In contrast to the SAMs on Au, the experimental surface

662 potentials of organosilane SAMs agree very well with the

663 calculated values acquired by KFM. In the ab initio mo-

664 lecular calculations of surface potentials of organosilane

665 SAMs, Saito et al. used H3C(CH2)15CH3 for n-octade-

666 cyltrimethoxysilane (ODS), F3C(CF2)7CH2CH3 for hep-

667 tadecafluoror-1,1,2,2-tetrahydro-decyl-1-trimethoxysilane

668 (FAS), and H2N(CH2)6NH(CH2)2CH3 for n-(6-amino-

669 hexyl)aminopropyltrimethoxyslane (AHAPS) as mod-

670 els.[47] The structures of ODS-, FAS-, and AHAPS mole-

671 cules were gauche and antiforms, respectively. The ODS,

672 FAS, and AHAPS molecules have net dipole moments of

673 0.03, 2.38, and 0.57 D, respectively. If these alkyls stand

674 normal to the substrate, the dipole moment would be zero

675 according to Eq. 1. In reality, these molecules are tilted

676 on the surface and the calculated ESP values match well

677 with the values acquired by KFM. These results perhaps

678 indicate that molecule–semiconductor interface behaves

679 differently from that of metal–molecule heterostructure.

680 CONCLUSION

681 Nanoscale charge transfer studies at the interface of

682 metal–molecule heterostructures are very important to

683 provide a better understanding of useful nanostructures.

684 Research from different laboratories suggests that build-

685 ing SAMs on a surface can bridge the gap between the

686 top-down approach and the size of individual molecules.

687 The electrostatic surface potential studies of SAMs are

688 limited in contrast to their I–V measurements. The Kelvin

689 probe measurements using a modified AFM can produce

690 reliable ESP results. Although the absolute values of ESP

691 may differ because of substrate preparation, contamina-

692 tion, etc., the qualitative values of the alkanethiols com-

693 pare well among different groups; the ESP values

694 increase with the increase in chain length. The solvents

695 used to prepare the SAMs do not appear to have any

696 major effect on the measured values. However, the

697 structure, especially symmetry, plays a significant role on

698 the ESP values of aromatic thiols; while the ESP of

699 xylyldithiol and tetramethyl–xylyldithiol are quite low,

700 their nonsymmetric counterparts such as benzyl mercap-

701 tan and pentamethylbenzylthiol produce a significant

702 positive surface potential. The molecular structure and the

703 attachment of sp2-hybridized carbon of phenyl thiol to

704 Au(111) can have a profound effect on ESP as its sign is

705 reversed and becomes more negative with the addition of

706 the second aromatic ring. This, however, levels off for

707 triphenyl thiols.

Fig. 16 The optimized geometry of a phenyldithiol molecule

attached to four-atom gold cluster. (Go to www.dekker.com to

view this figure in color.)

Nanoscale Charge Transfer in Metal–Molecule Heterostructures 13

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708 A negative surface potential, i.e., nanoscale charge

709 transfer in the opposite direction, has also been observed

710 in helical peptides. Furthermore, chemistry alone through

711 the formation of a CT complex of tetramethyl–xylylthiol

712 (TMXYL) with tetracyano-ethylene (TCNE) can reverse

713 the sign and magnitude of ESP.

714 Theoretical calculations, to understand charge transfer

715 in Au/S heterostructures using Hyperchem Pro 6 and

716 Gaussian 98, seem to predict the trend, but not the mag-

717 nitudes of dipole moments or ESP of the molecules.

718 Further, in contrast to the observed experimental results,

719 our initial calculations show that both symmetric and

720 nonsymmetric molecules bonded to Au clusters have

721 significant dipole moments. Thus the use of 4, 6, or 13

722 gold atoms to represent the gold surface may not be ad-

723 equate to compare the calculated ESPs with the experi-

724 mental results. Although the ab initio calculations of

725 organosilane SAMs by Saito et al. match quite well with

726 the experimental results, extensive theoretical studies will

727 be necessary to have a better understanding of the ESP

728 measurements of organothiol SAMs on gold.

729 ACKNOWLEDGMENTS

730 We thank Professors Ron Reifenberger and Supriyo Datta,

731 and Drs. Steve Howell, Bala Kasibhatla and Helen

732 McNally for experimental results and some of the theo-

733 retical discussions presented here. We are very grateful

734 to Professor B. Ramachandran and Mr. Devendra Patel

735 for the quantum chemistry calculations done using the

736 supercomputing facilities at La tech. We also thank Pro-

737 fessor P. Das, Dr. Avik Ghosh, Dr. Prashant Damle, and

738 Mr. Titas Rakshit for useful discussions. D.K. would like

739 to thank Mr. Patel for his help with the manuscript and

740 Louisiana Tech for its support to write this chapter.

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