Conformational Electroresistance and Hysteresis in Nanoclusters

Jul 2, 2014 - The predicted hysteretic Coulomb blockade staircase in the current−voltage curve adds another dimension to the rich phenomena of tunne...
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Letter pubs.acs.org/NanoLett

Conformational Electroresistance and Hysteresis in Nanoclusters Xiang-Guo Li,† X.-G. Zhang,‡ and Hai-Ping Cheng*,† †

Department of Physics and Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States

‡

S Supporting Information *

ABSTRACT: The existence of multiple thermodynamically stable isomer states is one of the most fundamental properties of small clusters. This work shows that the conformational dependence of the Coulomb charging energy of a nanocluster leads to a giant electroresistance, where charging induced conformational distortion changes the blockade voltage. The intricate interplay between charging and conformation change is demonstrated in a nanocluster Zn3O4 by combining a first-principles calculation with a temperature-dependent transport model. The predicted hysteretic Coulomb blockade staircase in the current−voltage curve adds another dimension to the rich phenomena of tunneling electroresistance. The new mechanism provides a better controlled and repeatable platform to study conformational electroresistance. KEYWORDS: Conformational electroresistance, self-capacitance, nanoclusters, hysteresis

T

junction formed by a nanocluster one applies a voltage between the Coulomb blockade voltages of two different geometries of the cluster, so that one geometry is in the conduction state while the other geometry is in the blockade state, then a large contrast in resistance is achieved. On the basis of this idea, we can construct a configuration as illustrated in Figure 1, which shows a model system of zinc oxide cluster, Zn3O4. We exploit the two conformational states (i.e., two geometries), which in the case of Zn3O4 are a ringshaped planar geometry, denoted as Geo1, and a chain geometry, denoted as Geo2, for this configuration. The two geometries have different charged states with different conformational energies. The ring geometry has lower energy when the cluster is neutral, but the chain geometry has lower energy when it is negatively charged,13 as confirmed by our own total energy calculations. We will first show through total energy calculations that the self-capacitance and the electronic charging energy of a Zn3O4 cluster depend on its structure, and reciprocally, charging the cluster can cause its structure to change. Consequently the Coulomb blockade voltage of a tunnel junction formed by the electrode−Zn3O4−electrode configuration depends on the charged state of the cluster due to the conformational changes during charging and discharging. We will then use an electron tunneling model to demonstrate that in a simulated measurement of the I−V characteristic of such a tunnel junction a pronounced hysteretic behavior emerges, as shown in Figure 1, resulting from the competition between conformational transitions and the charging and discharging processes. Finally we will investigate the substrate effect by placing a Zn3O4 cluster on an h-BN sheet (see Figure

he tunneling electroresistance (TER) effect, while promising great technological potential in nonvolatile random access memory, also presents a great challenge for physicists and materials scientists due to its wide spectrum of possible mechanisms.1−10 Many have been proposed or observed, including ferroelectric polarization,1 asymmetric metal electrode screening,2 carrier trapping/detrapping,3,5 dipole−electric field interaction,8 conducting filament creation/destruction,4,7 and conformation changes.6 Most of these mechanisms are dominated by electronic effects, but the last two in the list rely on structural changes in the material in response to the current to cause a change in the resistance. In addition, structural change can cause dramatic changes in electronic properties, leading to multiple ways in which conduction paths can be opened and closed, not limited to filament movement4,7 or variations in molecular conductance.6 Yet, effects involving structural changes are more challenging to study not only because of their more complex nature, but also because the structural changes if too small are not sufficient to induce a large electroresistance; however, larger changes are harder to control and repeat experimentally compared to purely electronic changes such as the reversal of polarization. An unexplored territory for electroresistance, which is normally a mesoscale effect, remains in the area of nanoscale clusters, despite a wealth of knowledge accumulated since early 1980s on their size-dependent physical properties and the triumph of nanoscience during the last 15 years.11 Bridging the nano- and mesoscales requires the reexamination of properties of nano building blocks in the context of transport measurements. For ultrasmall systems such as nanoclusters and molecules, the electronic effect of a structural change can be greatly magnified through the Coulomb blockade effect.12 This is because any change in the molecular shape can lead to a sizable change in its self capacitance, which determines the Coulomb blockade voltage. If in the configuration of a tunnel © XXXX American Chemical Society

Received: April 18, 2014 Revised: June 9, 2014

A

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differently charged ground state structures by the Kohn−Sham density functional theory (DFT)17 using the spin-polarized Perdew−Burke−Ernzerhof (PBE) exchange correlation functional in the PAW18,19 pseudopotential formalism implemented in the plane-wave based VASP20,21 package. A 35 Å × 35 Å × 35 Å supercell box is used for isolated Zn3O4 cluster to minimize the interaction between supercells, while in the h-BN substrate system, a 42.21 Å × 42.21 Å × 35 Å × hexagonal supercell is used. The optB86b functional for van der Waals (vdW)22 is used to describe the interaction between clusters and substrate. The h-BN substrate is modeled by a single layer 12 × 12 two-dimensional BN unit cell in our supercell system with four edges terminated by hydrogen atoms and a 10 Å vacuum in both directions of the surface to minimize the interaction between sheets. A single k point, the Γ point, is used for the Brillouin zone integration. The plane-wave cutoff is 500 eV, and the thresholds for self-consistency and structure relaxation are set as 10−5 eV and 0.015 eV/Å, respectively. For the neutral cluster, Geo1 is more stable as its conformational energy is 0.866 eV lower than Geo2. For the charged Zn3O4− cluster, Geo2 is 1.340 eV lower in energy. Table 1 summarizes

Figure 1. Ensemble averaged I−V characteristic for the two-geometry transport model. Each geometry i (i = 1,2) has a neutral state with conformational energy E0i and a charged state with energy E−i , calculated from first-principles. Other parameters are Γ = 0.05 eV, T = 200 K, Δ− = 0.6 eV, Δ0 = 1.0 eV, and a bias sweeping rate v = 0.3 × 1012 AV. The conformation transition processes (circled numbers) are indicated for each bias range. The blockade voltages for both geometries, Vc1 and Vc2, are calculated from the charging energy in eq 1 and indicated on the x-axis. I, II, and III indicate the order of the voltage sweeping sequence. Arrows indicate sweeping directions.

Table 1. Ionization Potential (IP), Electron Affinity (EA), Capacitance (C), and Charging Energy (Ec) of Geo1 and Geo2 for Isolated and h-BN Supported Zn3O4

2b), which enhances the conformational dependence of the Coulomb blockade voltage. The conformation dependence of the Coulomb blockade voltage is calculated from the self-capacitance of the cluster. For an N-electron system, its self-capacitance, C(N), is defined in terms of the single-electron charging energy Ec, which is the difference between the ionization potential (IP) and the electron affinity (EA),14−16 Ec =

e2 = IP(N ) − EA(N ) C(N )

Geo1 vertical

(1)

The total energy, both vertical (no geometry relaxation) and relaxed IP, EA of the Zn3O4 clusters are calculated for two

IP (eV) EA (eV) C (10−20 F) Ec (eV)

8.460 1.418 2.275 7.042

IP (eV) EA (eV) C (10−20 F) Ec (eV)

6.159 1.376 3.349 4.783

relaxed

Geo2 vertical

Isolated Cluster 8.115 8.942 1.574 3.729 2.449 3.073 6.541 5.213 h-BN Supported 6.120 6.086 1.537 3.600 3.496 6.444 4.583 2.486

2(Geo1−Geo2)/(Geo1 + Geo2)

relaxed

vertical

relaxed

8.843 3.780 3.164 5.063

−6% −90% −30% 30%

−9% −82% −25% 25%

6.085 3.740 6.832 2.345

1% −89% −63% 63%

1% −83% −65% 65%

Figure 2. Structure and charge difference of isolated and h-BN supported Zn3O4. (a) Isosurfaces of charge difference (at 0.02 e/Å3) between charged and neutral Zn3O4 for Geo1 (top row) and Geo2 (bottom row). Charge differences between anion and neutral (left column) and between cation and neutral (right column) are shown. Yellow and blue colors indicate positive and negative charge differences. (b) Relaxed structures of Zn3O4 on h-BN sheet for Geo1 (top) and Geo2 (bottom). Left and right columns show top and side views, respectively. Geometrical relaxation yields a nonplanar structure because of the interaction with h-BN substrate. The distance from the cluster (O atom) to the h-BN surface is 2.77 Å for Geo1 and 2.44 Å for Geo2, respectively. B

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where ΓL,R are the imaginary parts of the self-energies due to the two leads and Ec = eVc is the charging energy for injecting an electron. Taking ΓL = ΓR = Γ = constant, the current is,

calculated IP, EA, charging energy (Ec), self-capacitance (C), and percentage change in C for an isolated cluster as well as a cluster on an h-BN sheet. The h-BN supported cluster shows a greater change in the capacitance between the two structures. Calculations for both vertical and relaxed EA, IP show the same trend. Therefore, a wider voltage range for observing the electroresistance can likely be achieved by placing the cluster on a substrate. The I−V curves are calculated from the ensemble average of all possible configurations, which depends on the probabilities, p1(t) and p2(t), of the cluster being in the Geo1 and Geo2 states, respectively, with p1(t) + p2(t) = 1. Both probabilities are functions of time within each charging and discharging process. More specifically, the neutral or charged states of Geo1 and Geo2 have probabilities p01, p−1 and p02, p−2 , where subscripts indicate the geometry and superscripts the charge state, with p01 + p−1 + p02 + p−2 = p1 + p2 = 1. Noting that we can estimate the time scale of charging or discharging processes tc as tc ∼ ℏ/Γ ∼ 10−14 s, where Γ is the imaginary part of the self-energy due to the leads and we use 0.05 eV in our model as shown in Figure 1. Because tc is much faster than the conformation change between two geometries, for the purpose of calculating the transition rates between geometries we can safely assume that for each geometry either p0i = 0 or p−i = 0, so that only the two probabilities p1 and p2, are needed. Using T12 and T21 to denote the transition rates from Geo1 to Geo2 and the reverse process, respectively, and assuming that the transition between the geometries are thermally activated, we can write, T12/T21 = p2/ p1 = exp[(E1 − E2)/kBT]. Within the above constraint, at temperature T, the transition rates take the form, 1 Tij = A exp{[ (Ei − Ej) − Δ]/kBT } 2

I=

Ii =

(E − Ec) + (ΓL + ΓR )2

T (E ) d E =

E ⎞ e ⎛ −1 eV − Ec Γ⎜tan + tan−1 c ⎟ ⎝ 2h 2Γ 2Γ ⎠

eV ⎞ e ⎛ −1 eV − eVci Γ⎜tan + tan−1 ci ⎟ ⎝ 2h 2Γ 2Γ ⎠

(6)

where Vci is the Coulomb blockade voltage for geometry i. These equations yield the hysteretic I−V curves in Figure 1. The conformational dependence of the charging energy arises from the different spatial charge distributions of the neutral and the charged states for the two geometries. Note that, according to eq 1, the charging energy for injecting an electron depends on the total energies of three different charged states, anion, neutral, and cation. In Figure 2a, we plot the charge difference between anion and neutral states (left column) and between cation and neutral states (right column) for both geometries. The largest difference between the two geometries is that the anion state of Geo1 (top left) the top Zn atom gains a significant amount of charge, while in Geo2 almost all change in the charge is on the O atoms. This leads to a large difference in EA (2.206 eV) between the two geometries. The difference for the cation state is more similar, where most of the change in the charge is concentrated on the oxygen sites for both geometries, which explains the relatively small difference in IP (0.728 eV). The presence of the h-BN sheet provides a dielectric response (not shown) to any charge redistribution in the cluster, which almost always enhances the conformational dependence of the charging energy. In Figure 3 we show the density of states (DOS) for h-BN supported Zn3O4 for the ring-shaped geometry. The three rows

(2)

Figure 3. Calculated spin-resolved PDOS for anion, neutral, and cation states of ring-shaped Zn3O4 clusters. Blue and red lines represent the Zn3O4 cluster and h-BN PDOS, respectively. Spin up and down states are plotted above and below the thin horizontal zero line. HOMOs and LUMOs of the neutral state are marked as states H and L, respectively. A smearing parameter σ = 0.001 eV is used.

(3)

are the projected density of states (PDOS) for anion, neutral, and cation states, respectively. The PDOS of the neutral state show that both the highest occupied molecular orbital (HOMO), marked by H, and the lowest unoccupied molecular orbital (LUMO), marked by L, are orbitals on the cluster (blue). Therefore, an electron added to form the anion state should stay on the cluster. When a spin-up electron is added, the state L splits. The spin-up state L shifts below the Fermi energy and becomes the de facto HOMO (but we continue to

ΓLΓR 2

eV

Therefore, the tunneling current for each state is

The ensemble averaged current evolves with time as Itot(t) = p1(t)I1 + p2(t)I2. So in addition to the transition probabilities, we also need the tunneling currents I1 and I2 through the electrode−Zn3O4−electrode junction. We modify the model by Zhang et al.24 for the case of electron injection only. The transmission probability as a function of the electron energy is, T (E ) =

∫0

(5)

where Ei is the conformational energy for geometry i, Δ = Δ0 (neutral geometries) or Δ− (charged geometries) is the barrier height for the conformation change, and A is the attempt frequency, which is typically the order of 1012Hz. The barrier heights are calculated using the climbing image nudged elastic band method,23 which yields Δ0 = 1.0 eV and Δ− = 0.6 eV. This Δ− is measured from a previously unknown intermediate charged state with conformational energy 1.09 eV lower than Geo1 and 0.25 eV higher than Geo2. A further discussion of the effect of the barrier heights is provided in the Supporting Information. The probabilities, pi(t), obey the rate equation, dpi(t)/dt = −pi(t)Tij + pj(t)Tji, for i ≠ j, which has the solution for a given set of initial conditions, pi(t0) where i = 1,2, ⎡ Tji ⎤ ⎥exp[−(Tij + Tji)(t − t0)] pi (t ) = ⎢pi (t0) − Tij + Tji ⎥⎦ ⎢⎣ Tji + Tij + Tji

e h

(4) C

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(6) Donhauser, Z. J.; Mantooth, B. A.; Kelly, K. F.; Bumm, L. A.; Monnell, J. D.; Stapleton, J. J.; Price, D. W.; Rawlett, A. M.; Allara, D. L.; Tour, J. M.; Weiss, P. S. Science 2001, 292, 2303−2307. (7) Lau, C. N.; Stewart, D. R.; Williams, R. S.; Bockrath, M. Nano Lett. 2004, 4, 569−572. (8) Yasutake, Y.; Shi, Z.; Okazaki, T.; Shinohara, H.; Majima, Y. Nano Lett. 2005, 5, 1057−1060. (9) Li, Y.; Sinitskii, A.; Tour, J. M. Nat. Mater. 2008, 7, 966. (10) He, C. L.; Zhuge, F.; Zhou, X. F.; Li, M.; Zhou, G. C.; Liu, Y. W.; Wang, J. Z.; Chen, B.; Su, W. J.; Liu, Z. P.; Wu, Y. H.; Cui, P.; Li, R.-W. Appl. Phys. Lett. 2009, 95, 232101. (11) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. Rev. 2008, 108, 845−910. (12) Altshuler, B.; Lee, P. A.; Webb, R. A. Mesoscopic phenomena in solids; Elsevier: New York, 1991. (13) Gunaratne, K. D. D.; Berkdemir, C.; Harmon, C. L.; Castleman, A. W. J. Phys. Chem. A 2012, 116, 12429−12437. (14) Iafrate, G. J.; Hess, K.; Krieger, J. B.; Macucci, M. Phys. Rev. B 1995, 52, 10737−10739. (15) Shorokhov, V.; Soldatov, E.; Gubin, S. J. Commun. Technol. Electron. 2011, 56, 326−341. (16) Wu, Y.-N.; Zhang, X.-G.; Cheng, H.-P. Phys. Rev. Lett. 2013, 110, 217205. (17) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133−A1138. (18) Blöchl, P. E.; Jepsen, O.; Andersen, O. K. Phys. Rev. B 1994, 49, 16223−16233. (19) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758−1775. (20) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169−11186. (21) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15−50. (22) Klimes, J.; Bowler, D. R.; Michaelides, A. Phys. Rev. B 2011, 83, 195131. (23) Henkelman, G.; Uberuaga, B. P.; Jnsson, H. J. Chem. Phys. 2000, 113, 9901−9904. (24) Zhang, X.-G.; Xiang, T. Int. J. Quantum Chem. 2012, 112, 28− 32. (25) Lu, P.; Kuang, X.-Y.; Mao, A.-J.; Wang, Z.-H.; Zhao, Y.-R. Mol. Phys. 2011, 109, 2057−2068. (26) Weis, P.; Bierweiler, T.; Gilb, S.; Kappes, M. M. Chem. Phys. Lett. 2002, 355, 355−364. (27) Wu, Y.-N.; Schmidt, M.; Leygnier, J.; Cheng, H.-P.; Masson, A.; Bréchignac, C. J. Chem. Phys. 2012, 136, 024314. (28) Khare, N.; Lovelace, D. M.; Eggleston, C. M.; Swenson, M.; Magnuson, T. S. Geochim. Cosmochim. Acta 2006, 70, 4332−4342. (29) Rackovsky, S.; Goldstein, D. A. Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 5901−5905.

label it with L in order to compare to the neutral state). Similarly, if a spin-down electron is removed, then the state H splits, and the spin-down state H shifts above the Fermi energy. In this case, however, the unoccupied H state is almost at the same energy level as the top of the valence band of h-BN. This is probably an artifact of the DFT which tends to underestimate the band gap of an insulator. Conformation dependence of Coulomb charging energy is a general concept that can be applicable to a broad spectrum of nanoclusters and small molecules. Our work here uses a small oxide cluster, Zn3O4, to demonstrate the basic principle. More oxides and other types of clusters should be explored for further understanding of the phenomenon and to find practical applications for this effect. Examples can be found in noble metal clusters25−27 for which multiple isomer structures can coexist, accompanied by a 2D−3D structural transition at a certain cluster size that is sensitive to the charge state of a cluster. Some organic molecules exhibit similar fascinating behavior, such as cytochrome-c, an important biomolecule wellstudied for its charge storage/transfer function, that undergoes conformational change upon charge transfer at interfaces.28,29 We suggest future charge injection experiments to explore and control such structural changes. Calculational examples are included in the Supporting Information.

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ASSOCIATED CONTENT

S Supporting Information *

A discussion about the barrier height as well as the hysteresis of I−V curve near zero bias; two more systems including a gold cluster and an organic molecule are presented to illustrate the generality of the proposed mechanism. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]fl.edu. Phone: (+1)352-392-6256. Fax: (+1)352-392-8722. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES), under Contract No. DE-FG02-02ER45995. A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities (X.-G.Z.). The computation was done using the utilities of the National Energy Research Scientific Computing Center (NERSC).

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