Letter pubs.acs.org/NanoLett
Large Anisotropic Conductance and Band Gap Fluctuations in Nearly Round-Shape Bismuth Nanoparticles Debora Marchak,†,§ Denis Glozman,†,§ Yuri Vinshtein,† Sigal Jarby,† Yossi Lereah,‡ Ori Cheshnovsky,*,† and Yoram Selzer*,† †
School of Chemistry, and ‡Wolfson Applied Materials Center, Tel Aviv University, Tel Aviv 69978, Israel S Supporting Information *
ABSTRACT: Unlike their bulk counterpart, nanoparticles often show spontaneous fluctuations in their crystal structure at constant temperature [Iijima, S.; Ichihashi T. Phys. Rev. Lett. 1985, 56, 616; Ajayan, P. M.; Marks L. D. Phys. Rev. Lett. 1988, 60, 585; Ben-David, T.; Lereah, Y.; Deutscher, G.; Penisson, J. M.; Bourret, A.; Korman, R.; Cheyssac, P. Phys. Rev. Lett. 1997, 78, 2585]. This phenomenon takes place whenever the net gain in the surface energy of the particles outweighs the energy cost of internal strain. The configurational space is then densely populated due to shallow free-energy barriers between structural local minima. Here we report that in the case of bismuth (Bi) nanoparticles (BiNPs), given the high anisotropy of the mass tensor of their charge carriers, structural fluctuations result in substantial dynamic changes in their electronic and conductance properties. Transmission electron microscopy is used to probe the stochastic dynamic structural fluctuations of selected BiNPs. The related fluctuations in the electronic band structure and conductance properties are studied by scanning tunneling spectroscopy and are shown to be temperature dependent. Continuous probing of the conductance of individual BiNPs reveals corresponding dynamic fluctuations (as high as 1 eV) in their apparent band gap. At 80 K, upon freezing of structural fluctuations, conductance anisotropy in BiNPs is detected as band gap variations as a function of tip position above individual particles. BiNPs offer a unique system to explore anisotropy in zerodimension conductors as well as the dynamic nature of nanoparticles. KEYWORDS: Bismuth, nanoparticle, STM, anisotropy, conductance
B
ismuth (Bi) has been chosen for this study due to the extreme anisotropy of the mobility tensor of each of the three Dirac valleys in its Fermi surface.1 It has an fcc lattice structure that is rombohedrically distorted along the body diagonal by the Peierls-Jones mechanism2 to result in a long electron Fermi wavelength (∼26 nm), and a particularly anisotropic and small electron effective mass tensor with mbinary = 0.0011me, mbisectrix = 0.26me and mtrigonal = 0.0044me. The anisotropy becomes apparent in galvanomagnetic,3 and de HaasVan Alphen effects,4 in cyclotron resonance5 and Seebeck coefficient6 measurements and recently also in the angleresolved Landau spectrum of this material.7 Indications for anisotropy at the nanoscale can be found in recent thermal conductivity measurements of single crystalline Bismuth nanowires8 which are reported to be highly dependent on the crystal growth direction. In addition, Bi surfaces and thin films9 show striking crystal-dependent differences in their electronic properties relative to the bulk.10,11 Semiquantitative estimation of the expected band structure anisotropy in BiNPs is achieved by a simple particlein-a (cubic) box model using the mass tensor and the nonparabolic dispersion relation at the L-point (see figure 1). While the dispersion relation is parabolic for the T-point holes (eq 1), it is strongly nonparabolic for the L-point electrons and holes and can be described by the Lax © 2012 American Chemical Society
Figure 1. Schematic band structure diagram of bulk Bismuth at the L and T points. At 0 K Δ = −38 meV and the energy band gap between the L-point electrons and holes is Egap = 13.6 meV.
model12 (eq 2).
ℏk y 2 ℏkz 2 ℏkx 2 E T (k ) = + + 2mx 2my 2mz
(1)
Received: December 18, 2011 Revised: January 17, 2012 Published: January 24, 2012 1087
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Figure 2. TEM images of structural changes in a BiNP. Sequences of side (a and b) and top (c and d) view images of two different BiNPs ∼6 nm in diameter revealing structural changes and rotation of the planes in the particles. All snapshots were taken at REST periods.
⎤ Egap ⎡ ⎢ 1 + 4E T − 1⎥ EL(k) = ⎥⎦ 2 ⎢⎣ Egap
separated by abrupt transitions during which surface atomic diffusion is more prominent and full lattice rearrangements can take place giving way to a new stable configuration. During these transitions, the NP is seen as partly or completely blurred, resembling a liquid. This phenomenon can be characterized as quasi-melting. Subsequent REST periods are perceived as ″rotations″ by discrete rotational angles about the central axis, perpendicular to the plane of the TEM grid, similar to previous reports.14−16 The discrete angles have been suggested to originate from a discrete number of dislocations crossing the particles in a plane-by-plane gliding mechanism. The time scale of the transitions and the REST periods are stochastic and observed to be from subseconds (the lowest observation time of the TEM) to several minutes. They are thermally activated, and can be effectively frozen at 80K. The dynamic related changes in the electronic properties of the BiNPs are explored by probing single BiNPs by STM in a double barrier tunnel junction configuration17 (Figure 3) over the temperature range of 80−300 K. In the first set of experiments the temporal fluctuations of tunneling current in individual BiNPs were measured. The STM tip was parked above the center of a selected BiNP using bias and current set point of 1.5 V and 50 pA, respectively. The z distance was fixed, and current measurements (I/t traces) were taken over a period of several seconds. At room temperature I/t traces reveal fast large fluctuations around several defined values of current, as shown in Figure 4a,b, At 80 K the amplitude of fluctuations is reduced to practically the noise of the STM under feedback, and the current is stable at the value of the prefixed current set point (Figure 4c). Given the structural fluctuations observed by the TEM, the current fluctuations can be attributed to several phenomena: different crystallographic orientations with different density of states (DOS) being exposed to the STM tip, structural
(2)
where mx,y,z are the effective mass components,13 kx,y,z are the momentum vectors, and Egap is the direct bulk band gap between the L-point valence and conduction bands (13.6 meV at 0 K). The T-point valence band overlaps with the Lpoint conduction band, making elemental bulk Bismuth a semimetal. This overlap, Δ, is merely 38 meV at temperatures below 80 K. As material dimensions decrease, quantum size effects produce a shift in electronic states that results in an increase in Egap as well as a decrease in the overlap Δ until a semimetal to semiconductor transition becomes appreciable. According to these calculations the band gap of a BiNP with 3 nm is completely dictated by the L-point valence and conduction bands and varies in the range between 0.89 to 1.44 eV depending on the crystallographic direction. We note that the estimated ∼0.5 eV variation is a direct consequence of a structural anisotropy which becomes apparent in a particle consisting of ∼1000 atoms. Such a large variation in the electronic structure is usually induced by structural changes in much smaller entities, i.e., in the HOMO−LUMO gap of molecules comprising of only tens of atoms. Guided by these calculations, Decanethiol protected BiNPs, 3−8 nm in diameter, were prepared using a synthetic procedure that results in single crystal nanoparticles (see supporting material), as verified by high resolution TEM analysis (see figure 2). Prolonged TEM recordings of the free-standing BiNPs (see video in supporting material) show complex dynamics consisting of resting periods (“REST”) where the crystal structure remains relatively stable in time and elements as zone axis, fringes and facets are appreciated. REST periods are 1088
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Figure 3. STM characterization of individual BNPs. (a) The scheme depicts a BiNP in a double barrier tunneling junction. The BiNP is anchored to the Au substrate by thiol groups protruding out of a mixed monolayer of 1:9 nonanedithiol/decanethiol. (b) The topography image shows two BiNPs with diameters of approximately 4 and 6 nm. The inset shows the height cross section through the NPs. (c) The corresponding dI/dV plots, taken at 80 K, reveal apparent size dependent band gap belonging to the bigger NP (C1) and to the smaller (C2).
Figure 4. STM characterization of structural changes in a BiNPs by I/t measurements. Measurements at 300 K reveal two types of I/t fluctuations. (a) Small current fluctuations around the set point. These are attributed to small structural changes taking place around a stable REST configuration. (b) Large current fluctuations attributed to different BiNP orientations facing the tip with significant changes in the local density of states. Inset: I/V sweep revealing large fluctuations and instability of the current once the applied bias is larger than the apparent band gap. (c) At 80 K, no fluctuations above the noise level can be observed in both I/T and I/V measurements (inset).
temperature we can isolate and analyze temperature induced behaviors. In these experiments, the STM tip was parked above the center of a selected BiNP using the same scanning parameters (1.5 V, 50 pA), the z distance was fixed, the feedback turned off, and sequential I/V curves were probed over 63 ms periods (Figure 5). 1000 I/V curves were taken for each BiNP, while resetting the feedback between each I/V curve as described above. The value of Egap, calculated as the difference between the positive and negative bias voltages at which onset of current is observed, was extracted from each curve (e.g., Figure.5, left)
fluctuations affecting the tip-NP distance and quasi-molten periods for which the DOS is higher and can have a significant influence on the tunneling current. The latter effect is a direct result of the fact that Bi expands upon solidification, meaning that the liquid is a denser phase. The DOS of Bi at the liquid phase is higher by a factor of at least 2.5 relative to the solid phase (see ref 10).In order to relate directly to effects on the electronic structure of BiNPs we have undertaken a second set of experiments in which the band gap, Egap, of individual BiNPs was monitored as a function of time and temperature. By decreasing the 1089
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Figure 5. Probing of structural changes in BiNPs by time-resolved STM determination of the band gap. I/V sweeps to extract Egap were carried out at 80, 120, 200, and 300 K (different rows). Left column shows typical I/V sweeps and how Egap is calculated from these curves. The middle column plots traces of Egap as a function of time, revealing both large and small changes in this parameter. The column on the right depicts histograms of Egap at each temperature. These results support larger distribution of the BiNPs over there configurational space with increasing temperature, which is traduced as peak broadening. Peak multiplicities arise from changes in the orientation of the BiNP under the tip.
and the sequence of Egap values was plotted chronologically (Figure 5, center). Finally, histograms of the band gap distribution probed for each series are calculated (Figure 5, right). Measurements were performed at 80, 120, 200, and 300 K. Figure 4 shows that the electronic dynamics as observed by the STM is on a millisecond time scale. In contrast the structural transitions that can be discern by the TEM are limited by the 25 Hz acquisition rate and therefore appear in the subseconds to minutes time scale. We circumvent the extremely difficult task of establishing direct correlation between the two phenomenon by measuring sequential I/(Vs), and observing Egap evolution in time at different temperatures. This allows us to correlate changes in electronic properties that arise from structural instabilities that are temperature activated. Thus, at low tempaeratures where structural fluctuations cease to exist, there are also no conductance fluctuations, while at progressively elevated temperatures both dynamic phenomenon are initiated. At 300 K the fast fluctuations in BiNPs are evident from the I−t measurements. As a result, the electronic structure is very much affected by structural instabilities to allow for dependable systematic band gap measurement. At 200 K the
fluctuations are slower and reliability of the band gap values was substantially better. At 200 K (Figure 5) the histogram peaks are bracketing a region of Egap values between 0.5 and 2.5 eV. We focus our discussion on the result at 120 and 80 K. At 80 K, a NP tends to remain at a certain orientation relative to the STM tip for a longer period of time during which a single Egap value is revealed, as expected for a typical semiconductor quantum dot. The corresponding histogram presents only one narrow peak at the dominant Egap value. Orientational changes, if any, happen very slowly and gradually. Under these conditions, Egap values for different particles vary in the range 1.4− 2.0 eV with a peak width of ∼0.2 eV. At 120 K additional Egap values appear, revealing corresponding peaks in the relevant Egap histograms. This is attributed to the effect of thermal activation of the structural instabilities that allow the BiNPs to fluctuate about a certain orientation giving rise to small changes in DOS. Peak broadening in the histograms around average band gap values arises from increased surface atomic diffusion and transitional quasi-molten events. The unique feature of dramatic band gap variations in single BiNPs arises from a combination of their highly complex and 1090
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Figure 6. Comparison between the conductance properties of a typical BiNP to that of a CdSe/ZnS nanoparticle. The two representative I−V curves taken at two different parking position of the tip above a BiNP show striking difference in the apparent band gap. In contrast, similar measurements with CdSe/ZnS show a constant band gap that does not dependent on tip position. All measurements were taken at 80 K.
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anisotropic electronic structure as well as from their low melting temperature (the melting point of bulk Bi is ∼270 °C and is even lower for NPs18). Given their high surface to volume ratio, the BiNPs present a highly anisotropic electronic system that is continuously searching for its most stable configuration. Higher temperatures activate structural dynamics triggering surface atomic diffusion and lattice rearrangements (annealing dislocations and quasi-melting), which in time allows the BiNPs to change their orientation in the process. Spatial anisotropic conductance can be probed while the BiNPs are frozen at 80 K. I−V curves measured at different parking points over a selected BiNPs reveal Egap values that vary with tip position. In comparison, similar measurements of a CdSe/ZnS nanoparticle of similar size show a uniform (isotropic) band structure (Figure 6). In conclusion, we have assessed the influence of structural dynamics over the transport properties of semiconducting anisotropic nanoparticles. The pronounced “soft matter” nature of BiNPs is evident in their thermally activated structural instabilities and fluctuations. These, in turn, are responsible for the dynamic highly anisotropic conductance these NPs present. The correlation between the two phenomena is established by their simultaneous thermal activation. Work is currently under progress to define correlation by molecular control using different capping ligands to the NPs.
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REFERENCES
(1) Edelman, V. S. Adv. Phys. 1976, 25, 555. (2) Peierls, R. More surprises in theoretical physics; Princeton Univ. Press: Princeton, NJ, 1991. (3) Abeles, B.; Meiboom, S. Phys. Rev. 1956, 101, 544. (4) Shoenberg, D.; Uddin, M. Z. Proc. R. Soc. London Ser. A 1936, 156, 701. (5) Aubrey, J. E. J. Phys. Chem. Solids 1961, 19, 321. (6) Chandrasekhar, B. S. J. Phys. Chem. Solids 1959, 11, 268. (7) Zhu, Z.; Fauque, B.; Fuseya, Y.; Behnia, K. Phys. Rev. B 2011, 84, 115137. (8) Roh, J. W.; Hippalgaonkar, K.; Ham, J. H.; Chen, R.; Li, M. Z.; Ercius, P.; Majumdar, A.; Kim, W.; Lee, W. ACS Nano 2011, 5, 3954. (9) Hofmann, Ph. Prog. Surf. Sci. 2006, 81, 191. (10) Kakizaki, A.; Niwano, M.; Yamakawa, H.; Soda, K.; Suzuki, S.; Sugawara, H.; Kato, H.; Miyahara, T.; Ishii, T. J. Phys. F: Met. Phys. 1988, 18, 2617. (11) Lax, B.; Mavroides, L. G.; Zeiger, H. J.; Keyes, R. J. Phys. Rev. Lett. 1960, 5, 241. (12) Lax, B.; Mavroides, J. G. Solid State Physics; Academic Press: New York, 1960; p 261. (13) Lin, Y. M.; Sun, X.; Dresselhaus, M. S.; Lin, Y. M.; Sun, X.; Dresselhaus, M. S. Phys. Rev. B 2000, 62, 4610. (14) Be’er, A.; Kofman, R.; Fritz, P.; Lereah, Y. Phys. Rev. B 2006, 74, 224111. (15) Be’er, A.; Kofman, R.; Lereah, Y. Cent. Eur. J. Phys. 2010, 8, 1. (16) Wagner, J. B.; Willinger, M. G.; Muller, J. O.; Su, D. S.; Schlogl, R. Small 2006, 2, 230. (17) Banin, U.; Millo, O. Annu. Rev. Phys. Chem. 2003, 54, 465. (18) Olson, E. A.; Efremov, M. Y.; Zhang, M.; Zhang, Z.; Allen, L. H. J. Appl. Phys. 2005, 97, 034304.
ASSOCIATED CONTENT
* Supporting Information S
A description of the synthesis method and an analysis of structural transitions (movie). 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];
[email protected]. Author Contributions §
These authors contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research has been supported by Clal Biotechnology and by the Gordon Center for Energy studies in Tel Aviv University. 1091
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