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Marcus theory to electron transfer in small-scale electronics,. ¸ = 1/k; k is the .... L. C. L. Hollenberg, G. Klimeck, M. Y. Simmons, Nat. Nanotechnol. 2012, 7, 242. 2.
Received: December 18, 2013 | Accepted: January 8, 2014 | Web Released: January 16, 2014

CL-131185

Insight from Molecular-scale Electron Transfer to Small-scale Electronics Norifusa Satoh Environment and Energy Materials Division, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047 (E-mail: [email protected]) Downscaling to atomic or molecular scale at room-temperature operation of single-electron electronics has been believed to accelerate the operation speed due to the decrease in capacitance. However, the insight based on molecular chemistry indicates a completely opposite direction for atomic- and molecular-scale electronics and gives a description of resistance; thermal fluctuation of the surrounding media induces electron transfer and dielectric surroundings stabilize the chargeseparated states. To achieve a smooth electron transfer with atomic precise device structures resistive to the thermal fluctuation, the paper suggests molecular oxide electronics.

Molecules and atoms have attracted much attention as the ultimate small components in the next-generation electronics,1 because downscaling improves the processing speed as well as the device integration.2 Additionally, Coulomb blockade (CB) on small charging dots has the potential to control single electrons for energy-saving information processing. To maintain quantized levels for CB, the charging energy E needs to have excess thermal energy at least 10 times more: E = e2/2C > 10kBT, where C is the capacitance for a dot with a diameter 2r, given as follows: C = 4³¾0¾r. Besides, the charging time constant ¸ is given by ¸ = RC, where R is the resistance. Then, use of atomic- and molecular-scale dots may result in high-speed single-electron electronics at high temperature, such as room temperature. However, R would increase in downscaling due to localization of charges on the small components as known as CB. Although the other requirement to observe CB is given by R > h =e2 based on the Heisenberg uncertainty principle, R has not been described yet. In this study, we first attempt to apply Marcus theory to electron transfer in small-scale electronics, ¸ = 1/k; k is the electron-transfer rate, then propose a description for R, and discuss the experimental condition to confirm the phenomena. Marcus theory has been widely accepted to explain electron transfer in chemical and biological systems.3 Note that Marcus theory can be applied to solvent-free systems such as electronics, because the theory was originally confirmed in a rigid glass to suppress the diffusion of molecules.3b The main concept is that electron transfer occurs after the formation of activation states in both donors and acceptors through the reorganization of its surrounding media. In brief, dynamics of the surrounding media dominates electron transfer. Thus, electron transfer in molecular scale is completely different with electron tunneling in nanoscale, where the reorganization becomes negligible.3h The following expression is originally given for k:   ðG þ ­ Þ2 k ¼ k0 exp  ð1Þ 4­ kB T where k0 is the rate constant, kB is the Boltzmann constant, T is the absolute temperature, ¹¦G is the free energy for the electron Chem. Lett. 2014, 43, 629–630 | doi:10.1246/cl.131185

transfer, and ­ is the reorganization energy comprising the innershell contribution (­in) and outer-shell contribution (­out): ­ = ­in + ­out. Note that ­in depends on the structural changes in redox molecules during the electron transfer. In a two-sphere system of donor and acceptor molecules, ­out is given by    e2 1 1 1 1 1 ­ out ¼ ð2Þ þ   n2 ¾ 4³¾0 2rD 2rA RDA where ¾0 is the vacuum permittivity, e is elementary charge, rD and rA are radii of donor and acceptor molecules, respectively, RDA is the center­center distance between the donor and acceptor molecules, n is the refractive index of the surrounding media, n2 represents electron polarization as the optical dielectric constant at high frequency, and ¾ is the static dielectric constant of the surrounding media for atomic responses, including dipole polarization and ionic polarization. In a one-sphere system for a molecule on electrode, ­out for solvation is modified as follows:    e2 1 1 1 1 ­ out ¼   ð3Þ 4³¾0 2r 4Relec n2 ¾ where r is the radius of the molecule and Relec is the distance from the center of the molecule to electrode. Assuming ¹¦G = ¹¦G0 = 0, where ¹¦G0 is the standard free energy, eq 1 does not explain the actual electron transfer because it does not count the influence of the surrounding media on ¹¦G (Figure S1).4 In the practical numerical calculation of k to compare with experimental data, Weller equation is adopted to take into account the Born term ¦GS for the solvation energy of ions and the Coulombic term W for the electrostatic work in ¹¦G:3d­3f G ¼ G0 þ GS þ W

ð4Þ

where ¹¦G0 depends on systems such as the standard redox potentials and applied voltage in electrochemical systems and vibrational zero­zero energy and photoexcited energy in photoinduced electron-transfer systems; ¦GS and W are given for the two-sphere system by   e2 1 1 ð5Þ þ GS ¼ 8³¾0 ¾ rD rA e2 4³¾0 ¾RDA and for the one-sphere system by W¼

ð6Þ

e2 ð7Þ 8³¾0 ¾r e2 W¼ ð8Þ 16³¾0 ¾Relec As experimentally confirmed, the combination well describes that high ¾ surrounding media accelerate the charging process on small dots owing to solvation by the surrounding media (Figure 1a). Assuming to embed 1-nm dot into SiO2 (¾ = 3.9, n = 1.52), Al2O3 (¾ = 9, n = 1.72), HfO2 (¾ = 25, n = 1.89), GS ¼

© 2014 The Chemical Society of Japan | 629

(a)

(b)

Figure 1. Simulation of k for electron transfer in various ¾ surrounding media (a) and in various n surrounding media (b) using eqs 1 and 4, assuming ¹¦G0 = 0 and ­in = 0. and TiO2 (¾ = 85, n = 2.50), k/k0 = 3.34 © 10¹7, 8.60 © 10¹4, 1.03 © 10¹2, and 8.88 © 10¹2, respectively. Although it is well known that electron polarization effect is important in ­out (Figure 1b), the solvation and electrostatic work to form charge-separated states also influence k significantly due to the contribution to ¹¦G. Interestingly, these results lead to a totally opposite direction for atomic- and molecular-scale electronics. Based on an assumption of constant R, atomic- and molecular-scale electronics have been demonstrated under a vacuum condition (¾ = 1 in vacuum) to achieve high speed, because C and ¸ decrease with r and ¾. Additionally, the low-temperature operation has advantages to suppress thermal diffusion of small dots on substrate and to prevent quantum information from disordering. The combination of Marcus equation and Weller equation, however, describes molecular-scale electron transfer accelerated in high ¾ surrounding media to stabilize charge-separated states; the actual electron transfer occurs when a charge-separated atomic configuration appears during thermal fluctuation. Meanwhile, considering the fact that the surrounding media decrease attenuation factor ¢ for k0 from around 2­5 in vacuum to 1 or less, where k0 £ exp(¹¢RDA or elec),3c,3g the surrounding media benefit not only the operation speed but also the production reliability. Because the surrounding media buffer the distance dependence, that suppresses the fluctuation in performances caused by the distribution in RDA or elec. Overall, small-scale electronics require high ¾ surrounding media and rigid device structure resistant to thermal fluctuation to achieve smooth electron transfer. Finally, we correlate R with r, ¾, and RDA or elec using ¸ = RC = 1/k as follows:   1 ðG þ ­ Þ2 ð9Þ ¼ 4³¾0 ¾rk0 exp  4­ kB T R

630 | Chem. Lett. 2014, 43, 629–630 | doi:10.1246/cl.131185

Taking into account ¦GS and W, eq 9 explains the increase in R due to CB effect but does not express R constant in nanoelectronics due to the assumption of single electron transfer. Experimentally, molecular oxide electronics would be an ideal candidate because (a) oxide consists of strong ionic covalent bonds, (b) molecular-scale oxide dots can be precisely obtained,5 (c) the oxide dots can be seamlessly surrounded with atomic layer deposition oxide,6 and finally (d) oxide is high ¾ and high n material. In sophisticated chemical and biological systems, ultrafast electron-transfer rate 1011¹1013 s¹1 is observed.3c,7 Hence, THz data processing could be achieved. The high-speed data processing consumes energy and generates heat loss even though decreasing to single-electron level in current; this is another reason why thermal resistive structure is necessary for single-electron electronics. Note that ultrasensitive electrometer,8 parallel circuit of dots, or monitoring other physical parameter changes is necessary to analyze singleelectron movement in devices. In conclusion, we have discussed atomic- and molecularscale electronics from the viewpoint of molecular chemistry suggesting that the knowledge in molecular-scale electron transfer will lead the world of small-scale electronics. This work was supported in part by Grant for Basic Science Research Projects from The Sumitomo Foundation. References and Notes 1 H. Park, J. Park, A. K. L. Lim, E. H. Anderson, A. P. Alivisatos, P. L. McEuen, Nature 2000, 407, 57; J. Park, A. N. Pasupathy, J. I. Goldsmith, C. Chang, Y. Yaish, J. R. Petta, M. Rinkoski, J. P. Sethna, H. D. Abruña, P. L. McEuen, D. C. Ralph, Nature 2002, 417, 722; M. Fuechsle, J. A. Miwa, S. Mahapatra, H. Ryu, S. Lee, O. Warschkow, L. C. L. Hollenberg, G. Klimeck, M. Y. Simmons, Nat. Nanotechnol. 2012, 7, 242. 2 D. J. Frank, R. H. Dennard, E. Nowak, P. M. Solomon, Y. Taur, H.-S. P. Wong, Proc. IEEE 2001, 89, 259. 3 a) R. A. Marcus, Angew. Chem., Int. Ed. Engl. 1993, 32, 1111. b) G. L. Gaines, III, M. P. O’Neil, W. A. Svec, M. P. Niemczyk, M. R. Wasielewski, J. Am. Chem. Soc. 1991, 113, 719. c) C. C. Moser, J. M. Keske, K. Warncke, R. S. Farid, P. L. Dutton, Nature 1992, 355, 796. d) R. M. Williams, J. M. Zwier, J. W. Verhoeven, J. Am. Chem. Soc. 1995, 117, 4093. e) P. A. van Hal, J. Knol, B. M. W. Langeveld-Voss, S. C. J. Meskers, J. C. Hummelen, R. A. J. Janssen, J. Phys. Chem. A 2000, 104, 5974. f) E. E. Neuteboom, S. C. J. Meskers, P. A. van Hal, J. K. J. van Duren, E. W. Meijer, R. A. J. Janssen, H. Dupin, G. Pourtois, J. Cornil, R. Lazzaroni, J.-L. Brédas, D. Beljonne, J. Am. Chem. Soc. 2003, 125, 8625. g) N. Satoh, T. Nakashima, K. Yamamoto, J. Am. Chem. Soc. 2005, 127, 13030. h) N. Satoh, L. Han, Phys. Chem. Chem. Phys. 2012, 14, 16014. 4 Supporting Information is available electronically on the CSJ-Journal Web site, http://www.csj.jp/journals/chem-lett/index.html. 5 N. Satoh, T. Nakashima, K. Kamikura, K. Yamamoto, Nat. Nanotechnol. 2008, 3, 106; N. Satoh, T. Nakashima, K. Yamamoto, Sci. Rep. 2013, 3, 1959. 6 M. Leskelä, M. Ritala, Angew. Chem., Int. Ed. 2003, 42, 5548; H. Kim, J. Vac. Sci. Technol., B 2003, 21, 2231; R. G. Gordon, Polym. Mater.: Sci. Eng. 2004, 90, 726; S. M. George, Chem. Rev. 2010, 110, 111. 7 T. Ito, T. Hamaguchi, H. Nagino, T. Yamaguchi, J. Washington, C. P. Kubiak, Science 1997, 277, 660; G. Benkö, J. Kallioinen, J. E. I. Korppi-Tommola, A. P. Yartsev, V. Sundström, J. Am. Chem. Soc. 2002, 124, 489. 8 R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov, P. Delsing, D. E. Prober, Science 1998, 280, 1238.

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