LETTER pubs.acs.org/NanoLett
Emergent Multistability in Assembled Nanostructures Jianshu Yang,† Steven C. Erwin,*,‡ Kiyoshi Kanisawa,§ Christophe Nacci,† and Stefan F€olsch*,† †
Paul-Drude-Institut f€ur Festk€orperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375, United States § NTT Basic Research Laboratories, NTT Corporation, Atsugi, Kanagawa, 243-0198, Japan ‡
bS Supporting Information ABSTRACT: Scanning tunneling microscopy (STM) at 5 K reveals that native atoms in the surface layer of a semiconductor crystal become bistable in vertical height when a nanostructure is assembled nearby. The binary switching of surface atoms, driven by the STM tip, changes their charge state. Coupling is facilitated by assembling adatom chains, allowing us to explore the emergence of complex multiple switching. Density-functional theory calculations rationalize the observations and a lattice-gas model predicts the cooperative behavior from first principles. KEYWORDS: Scanning tunneling microscopy, density-functional theory, semiconductor surfaces, indium arsenide, STM manipulation of single atoms
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any systems in nature adopt multiple stable states in response to an external stimulus. Multistability is a defining aspect of biological systems1,2 and a prerequisite for virtually all digital technologies. The design and operation of macroscopic multistable systems is generally based on locally bistable switching of charge,3,4 optical,5,6 or magnetic7,8 states. Binary and multiple switching in single atoms and molecules adsorbed on a surface can be stimulated and then probed with atomic resolution using scanning tunneling microscopy (STM) at cryogenic temperatures. Examples include the control of vertical9 and lateral10 hopping of adsorbed atoms (adatoms), reversible charging of adatoms,11 and conductance1214 as well as magnetic-state15 switching in molecules. The STM tip can also be used to assemble nanostructures from atoms and molecules16 and then stimulate lateral motion of those constituents.17,18 Here we show that individual atoms within surface-supported nanostructures can become bistable and give rise to physically multistable systems with surprisingly complex behavior. We used STM to assemble nanostructures by atom manipulation16 and observed multistable behavior from the coupled vertical motion of atoms in the surface layer of a IIIV semiconductor crystal. Bistable switching of the atoms changes their charge state. The resulting interactions between switched atoms create new minima in the potential-energy landscape of the nanostructure. To investigate these changes, we assembled a series of atomic chains and stimulated switching with the STM tip. Chains whose length satisfies a simple “magic number” criterion have a single deep energy minimum. All others have multiple minima with nearly equal energies and exhibited rapid, random switching between the different metastable states. We developed a lattice-gas model that explains both types of behavior theoretically from first principles. r 2011 American Chemical Society
Nanoscale assemblies of indium adatoms were constructed on the InAs(111)A surface19 by vertical atom manipulation20 (see Supporting Information, SI). Figure 1a shows an STM image of a pristine In6 chain formed by six In adatoms, Inad, occupying neighboring In vacancy sites. When the STM tip is placed above the chain center and a bias voltage (V = 0.5 V) applied, the two central atoms merge into a single bright protrusion (Figure 1b) to form a state we label “ON”. The transformation can be detected spectroscopically in currentvoltage (IV) curves (Figure 1c) with the tip fixed above the chain center. Starting from the pristine “OFF” state, a discontinuous jump in the current occurs at V = 0.37 V as the bias is ramped up from 0.3 to 0.5 V (Figure 1c, red curve), followed by a narrow region of dynamical switching between ON and OFF states. Reversing the process, by starting from the ON state and ramping down the bias from 0.3 to 0.5 V (blue curve), creates a corresponding drop in current at V = 0.39 V as the state changes to OFF. For voltages between these thresholds both states are robust and stable for hours or longer. For the straight In6 chain, the ON state involves the central atom pair and never occurs at the outermost atoms, suggesting a significant energy cost at the chain ends. To verify this, we created an In6 hexagonal ring with periodic boundary conditions. The STM images in Figure 1di reveal six equivalent ON states associated with the six Inad neighbor pairs within the hexagon. Multiple ON states, and bistable switching between OFF and ON, also occur in two-dimensional (2D) nanostructures such as the In4 rhombus (Figure 1j) and In6 triangle (Figure 1km). More complex 2D structures such as the filled In7 hexagon Received: March 22, 2011 Published: May 17, 2011 2486
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Figure 1. Switching behavior in one- and two-dimensional In nanostructures. (a) STM image of a pristine In6 chain consisting of In adatoms at neighboring In vacancy sites, separated by 8.57 Å, on InAs(111)A. The enhanced gray scale (right) shows the (2 2) Invacancy reconstruction and its hexagonal unit cell. (b) Same as (a) after placing the tip above the chain center and applying a bias of 0.5 V. The two central atoms merge into a single protrusion (referred to as ON versus the pristine OFF state). (c) IV curves acquired with the tip at the chain center at constant height (initial set-point current 0.1 nA) indicating OFF-to-ON switching at 0.37 V when starting at OFF (red curve), and ON-to-OFF return switching at 0.39 V when starting at ON (blue curve). (di) Images of an In6 ring in six equivalent ON states. (jo) Images showing ON states in two-dimensional Inad nanostructures: (j) an In4 rhombus, (km) an In6 triangle, and (n,o) a filled In7 hexagon. (p) Proposed structural model demonstrating that the defect positions coincide with native In surface atoms (blue arrows) between adjacent vacancy sites occupied by Inad atoms (black). Examples include the ON states in (j,m) and (o).
(Figure 1n,o) reveal a still greater variety of multiple-ON (binary and ternary) states. In every case, the merged ON-state protrusion is centered between a pair of neighboring Inad atoms. The proposed structural models in Figure 1p reveal that at each such midpoint on InAs(111)A there is a native surface In atom (Insurf, highlighted by blue arrows). This coincidence suggests that the defect involves the central Insurf atom. Moreover, the bistability implies that this Insurf atom can assume two distinct stable states. DFT calculations21,22 (see Supporting Information for details) confirm this hypothesis. Figure 2a shows the change in total energy of an infinite Inad chain as the height of a single Insurf atom (blue curve, blue arrow in the inset) is varied. Two stable minima are found, one with the Insurf atom coplanar with the surface In layer and one with the Insurf atom in a popped-up position 1.5 Å above the surface, close to the height of the Inad atoms themselves at 1.7 Å. In contrast, an Insurf atom outside the chain (red arrow) shows a single stable height (red curve). By identifying the ON/OFF states with the high/low position of
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Figure 2. Structural bistability and charge state. (a) DFT total energy of an infinite Inad chain (black circles) versus the height of an Insurf atom. Two types of Insurf atoms are considered: the Insurf between two adjacent chain atoms (blue outline) is bistable while the Insurf outside the chain (red outline) is stable only in the surface plane. (b) Electrostatic potential induced by a single Inad measured at 5 to 6 Å tip height (green circles) and corresponding theoretical potential (green curve) of a screened point charge. (c) Potential measured relative to the center of an OFF-state In6 chain (red triangles) and theoretical potential (red curve) for chain atoms with individual charges þ1e. The measured potential in the ON state (blue triangles) is reproduced by the theoretical potential (blue curve) from the superposition of charges þ1e on the four outer atoms and a reduced effective charge, obtained from DFT, of þ0.2e on the complex consisting of the two inner atoms and the popped Insurf between them.
Insurf atoms centered between adjacent Inad atoms, it is now easy to understand not only the bistability of short linear chains (Figure 1a,b) but also the complete manifold of multistable states found in the 2D nanostructures (Figure 1d-o). This physical bistability has consequences for the electronic nature of In nanostructures: a single OFF-ON switching changes the local electronic structure from metallic to insulating, and changes the apparent (experimentally observed) charge state of the nanostructure by ΔQ = 2e. Consider a single Inad on InAs(111)A, which is a surface donor with charge þ1e (ref 23) giving rise to a screened Coulomb potential around itself. At positive sample bias this potential locally increases the number of conduction states available for tunneling, resulting in an increased apparent height2426 and thus a faint halo around Inad atoms at positive bias.20,23 The screened Coulomb potential leads to a bias offset in IV curves measured close to the charged adatom,25 allowing the potential to be mapped as a function of position. Figure 2b shows the measured potential (green symbols) versus distance from a single Inad. The green curve shows the theoretical potential resulting from screening by a 2D electron gas27 (2DEG, see Supporting Information section C). This screening depends only on the magnitude of the charge (þ1e) and the effective mass of the surface-accumulated electrons inherent to the InAs(111)A surface,23,28 m*=0.043me, and provides an excellent parameter-free description of the potential.29 Figure 2c shows the measured and theoretical potential near an In6 chain, recorded along the direction perpendicular to the chain axis (see the dashed line in Figure 1a). In the OFF state, the theoretical potential created by superposition (Figure 2c, red curve) of the single-atom contributions agrees well with the data, establishing that Inad atoms maintain their individual charges when assembled into an In6 chain. In the ON state, however, the measured In6 potential is markedly suppressed (Figure 2c, blue symbols). This suppression 2487
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Figure 3. Stability, statistics, and energetics of multiple states. STM images demonstrating p-fold multiple-ON states in InN chains with (a) (N, p) = (10, 2), (b) (N, p) = (14, 3), and (c) (N, p) = (18, 4). (d) Time sequence of 512 steady-state constant-current height profiles of an In18 chain imaged at 0.2 V revealing a single highly stable multiple-ON state with p = 4. The profile scans were interleaved with excitation scans along the chain at 0.5 V (not shown). (e) Time sequence of an In16 chain revealing strong dynamical fluctuations due to rapid switching between different p = 4 states (from 0 to 200 s) and to a p = 3 state (after 200 s). (f) Statistical probability of finding p popped Insurf atoms (upon excitation at 0.5 V), establishing that the system favors a constant density p/N ≈ 1/4 of popped atoms. (g) Theoretical energies E(N,p) for the lowest-lying configurations of a lattice-gas model based on parameters from DFT. Vertical dashed lines mark the predicted transitions, separated by ΔN ≈ 4, between states with p and p þ 1 popped atoms.
can be understood by counting electrons during a gedanken experiment in which an In2 dimer is first assembled and then switched from OFF to ON. The clean InAs(111)A-(2 2) reconstructed surface is insulating,30 i.e., there are no partially filled dangling bonds left at the surface. When an Inad atom is added, it donates one electron to the 2DEG states,23 rendering the system metallic. Adding a second Inad, to form an In2 dimer in the OFF state, leaves the system metallic with two electrons in extended 2DEG states. To create the ON state, we imagine first removing the central Insurf atom. This removes three electrons from the system and thus creates three holes in the valence band, localized at the three As dangling bonds. Two of these holes can be filled by electrons transferred from the doped 2DEG states. We now return the removed Insurf atom as a popped-up atom sitting above the In vacancy. This popped atom is equivalent to another Inad atom adsorbed at a vacancy and therefore adopts the usual þ1e charge state by giving up one electron. This electron fills the third hole and restores the system to an insulating state. The net result is that the OFF-ON transition changes the system from metallic to insulating. The above reasoning suggests that for In2 the ON state leads to an increased charge (ΔQ = þ1e) in apparent contradiction to the suppression observed for In6. The resolution lies in the different spatial extent of the screening electrons in the two states. In the OFF state of In2, the two donated electrons are in extended 2DEG states, and hence their screening properties are well described by the standard 2DEG expression. In the ON state, the three donated electrons are localized at the As dangling bond orbitals close to the popped Insurf atom, and hence their screening is much shorter ranged. Indeed, for distances beyond several angstroms the potential of an In2 dimer in the ON state is that of a nearly neutral complex (DFT calculations give the effective total charge as þ0.2e). Thus, beyond small distances the ONOFF transition changes the apparent charge state of the In2 dimer by approximately ΔQ = 2e. In this regime, the theoretical potential of an In6 chain in the ON state can then be constructed by assuming normal þ1e charges on the four outer atoms and a nearly zero (þ0.2e) net charge on the inner two atoms. The
result (Figure 2c, blue curve) is in excellent agreement with the measured potential. Longer chains exhibit more complex behavior. Most striking is the emergence of both stable and dynamically unstable states with multiple-ON configurations for InN chains with N > 8. Figure 3ac shows highly stable multiple-ON configurations for certain “magic” chain lengths N* = 10, 14, 18. Other N values show unstable rapid switching; compare Figure 3d,e, showing stable and unstable behavior, respectively. The magic values arise from two effects: a preferred spacing of four sites between popped Insurf atoms, and suppression of popped atoms at the chain ends, leading to the empirical expression N* = 4p þ 2 (p is the number of popped atoms). To analyze this behavior statistically, we scanned many chains, first at positive bias above the OFF-to-ON threshold (exciting dynamical switching) and then at low positive bias below the threshold (probing the steady state). Figure 3d shows the time evolution over several minutes, reconstructed from ∼500 scans, of an In18 chain. The multipleON state with four popped atoms is highly stable and shows only rare fluctuations in the positions of the popped atoms. In contrast, the In16 chain shows significant excursions in the popped-atom positions as well as a competition between p = 3 and p = 4 states (Figure 3e). Using similar data collected for chains with N = 4 to 18 in 2.3 104 individual states, we constructed the probability distribution P(N, p) for ON states of InN chains with p popped atoms (Figure 3f). This distribution is peaked at N = 4p þ 2, indicating a preference for a fixed density 1/4 of popped atoms with uniform spacing. These observations are the outcome of a competition between the energy gained by popping an Insurf atom (65 meV per atom; see Figure 2a) and the energy cost from the Coulomb interaction between popped atoms. Here we construct a lattice-gas model to analyze this competition. The model consists of particles on a one-dimensional lattice of sites representing the Insurf atoms. Let ni denote the occupancy (0 or 1) of site i with 0 denoting an unpopped atom and 1 denoting a popped atom. If there is a particle at a site, it contributes an energy E0 = 65 meV to the total energy. The particles are charged (Q = þ1e) and hence 2488
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increase the total energy through their electrostatic interaction. We assume a screened Coulomb interaction with magnitude J and dimensionless screening length λ. The total energy of the system is therefore E¼
X i
X ei j=λ E0 ni þ J ni nj i j i
