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Electronic Size Effects in Three-Dimensional Nanostructures Pawel Kowalczyk, Ojas Mahapatra, Simon Brown, Guang Bian, Xiao-Xiong Wang, and Tai-chang Chiang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl3033119 • Publication Date (Web): 30 Nov 2012 Downloaded from http://pubs.acs.org on December 5, 2012

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Electronic Size Effects in Three-Dimensional Nanostructures P.J. Kowalczyk,∗,†,‡ O. Mahapatra,† S.A. Brown,∗,† G. Bian,¶ X. Wang,¶,§ and T.-C. Chiang¶ The MacDiarmid Institute for Advanced Materials and Nanotechnology, Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand, Department of Solid State Physics, Faculty of Physics and Applied Informatics, University of Lodz, 90-236 Lodz, Pomorska 149/153, Poland, and Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA E-mail: [email protected]; [email protected]

November 26, 2012

∗ To

whom correspondence should be addressed MacDiarmid Institute for Advanced Materials and Nanotechnology, Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand ‡ Department of Solid State Physics, Faculty of Physics and Applied Informatics, University of Lodz, 90-236 Lodz, Pomorska 149/153, Poland ¶ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA § College of Science, Nanjing University of Science and Technology, Nanjing 210094, China † The

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Abstract We show that Bismuth nanostructures form three-dimensional patterns governed by twodimensional electronic effects. Scanning tunneling microscopy reveals that both the vertical and lateral dimensions of the structures strongly favor certain values, and that the preferred widths are substantially different for each preferred height. First-principles calculations demonstrate that this vertical-lateral correlation is governed by the Fermi surface topology and that this is itself sensitively dependent on the dimensions of the structure.


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Ultrathin films of materials deposited on surfaces can self-organize into intriguing patterns, a phenomenon central to the design and development of functionality at the nanoscale. 1,2 The underlying mechanisms of pattern formation are an important theme for nanoscale research, and development of new tools for control of nanoscale structure is critical. Electronic effects have been well established as determining the sizes of free clusters (radius quantization) 3 and thickness of flat islands, 4–6 but there has so far been no demonstration of control of the lateral dimensions of nanostructures, except dynamically during coarsening. 7 We have identified Bi as an ideal material for the demonstration of such effects. Bismuth exhibits strong quantum effects because of its small Fermi surface features 8 in reciprocal space, and we show here that these give rise to longwavelength structural modulations in real space. The observation of these quantum size effects is made possible by the high mobility of Bi atoms on highly oriented pyrolytic graphite (HOPG), which facilitates self-assembly and hence allows the structures formed to reflect the energetics of the system. A similar level of control of nanostructure dimensions should be achievable in other systems in which the substrate-adatom interaction is sufficiently weak and could have an important impact on the realisation of, for example, novel spintronic devices and nanoscale topological insulators. 9–12 In this work we investigate Bi(110) nanostructures grown on HOPG using STM, scanning tunneling spectroscopy (STS) and density functional theory (DFT). These nanostructures typically ¯ consist of well-defined islands with a preferred elongation direction along h110i and the (110) plane parallel to the substrate surface (the rhombohedral indexing system is used here). 13,14 The islands (see inset in Figure 1 (a)) have flat bases with narrow stripes on them so that they have rectangular ’wedding cake’ profiles comprising 2, 4, 6 ML thick layers on a 1 ML thick wetting or ’dead’ layer 14 (see further discussion below); for clarity we refer to the island thicknesses as ’2+1’ ML, ’4+1’ ML etc. We show here that the widths of bases and stripes (measured along h112i∗ (where the asterisk indicates that indices are rounded 14 )) are restricted to certain welldefined values due to lateral quantum size effects (QSEs), while electronic effects also stabilise the preferred thicknesses.


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Samples were prepared by evaporation of Bi onto cleaved HOPG in Ultra High Vacuum (∼ 10−10 torr) prior to transfer (without breaking the vacuum) into an Omicron variable temperature STM / AFM system. Details are given elsewhere; 13,14 typical scanning voltages and setpoint currents were -0.8 V and 50 pA respectively. STS measurements (±2.0 V, 1 nA setpoint current, 128 points per curve) were done in current imaging tunneling spectroscopy mode (CITS, 128 × 128 pts2 ) at ∼50 K and the distribution of STS peaks analyzed using a method described in Ref. 15 Electronic structures were obtained from first-principles calculations using HGH-type pseudopotentials and a plane-wave basis set. 16 The main program employed was developed by the ABINIT group; spin-orbit coupling was included using the relativistic LDA approximation and densities of states were calculated by integrating over the entire Brillouin zone. The surfaces were relaxed for all film thicknesses resulting in subtle but important differences in atomic arrangement to those in Ref. 17 We focus here on analysis of STM images (inset in Figure 1 (a)) from samples grown on specially selected substrates where a high density of defects results in a high island density and smaller lateral dimensions compared to our previous work. 13,14 The widths of over 1000 bases and stripes were measured and are recorded in histograms shown in Figure 1. Each measured width (count) has an uncertainty that depends on the resolution (scan size) and so we have accounted for the different uncertainties by substituting each single count by a normalized Gaussian distribution with variance σ 2 = s/r where s is the scan width measured in nm and r is the number of raster points per scan line. The black lines in Figure 1 are the sum of Gaussian distributions obtained in this way. It is readily apparent that 6+1 ML high stripes have very similar widths, as demonstrated by the histogram shown in Figure 1 (a). Two distinct maxima can be seen, centered roughly at 4 nm and 8 nm, as well as a series of weak shoulders at 12, 16 and 20 nm. These features are regularly spaced, i.e. occuring every ∼4 nm. This is a first indication that growth of these islands is governed by QSEs, 4–6 in which case the island width (w) follows the rule: w = nλF6ML /2 where n is a natural number, and the Fermi wavelength can be estimated to be λF6ML = 8 nm.


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Similar periodic peaks are observed in histograms of the widths of 4+1 ML high stripes (Figure 1 (b)). This again is an indication of growth governed by QSE. Based on these width measurements a Fermi wavelength λF4ML = 12 nm can be extracted. The 2+1 ML high bases that support the stripes are much less regular in shape and it is not immediately obvious that they have similar widths. However, the observations above motivated us to perform a similar analysis of the widths of the 2+1 ML high bases. 18 We also find that the histograms of the base widths (Figure 1 (c)) exhibit periodic features, and we are able to estimate a Fermi wavelength λF2ML = 30 nm. 19 In order to confirm that there are preferred widths governing growth (or decay) of Bismuth islands we have also explored mechanically mediated coarsening of the islands. 20 In this technique a scanning probe interacts gently with deposited islands, providing energy in a way that is analogous to thermal annealing, and resulting in morphological changes. In this case it is possible to perform STM imaging and at the same time slowly modify the island’s morphology - results of a typical experiment are shown in Figure 2. The initial situation is that there are large 2+1 ML thick bases (Figure 2 (a)) surrounding 4+1 ML regions. During scanning these bases decrease in area and the 4+1 ML high regions grow (not shown in Figure 2 (a)). Remarkably, the width of the 2+1 ML regions remains nearly constant (see arrows in Figure 2 (a)-(c)), while their length decreases. By analyzing 7 different bases recorded (for over 6 hours) in a set of 34 images (∼150 separate width readings) we were able to create a histogram of the widths as shown in Figure 2 (d). Two distinct maxima are observed, the location of which corresponds perfectly with the above estimate of λF2ML ∼ 30 nm. This clearly indicates the influence of QSE on the observed decay. STS provides a direct probe of the electronic Density of States (DOS) and hence provides insight into the bandstructure of the islands that can then be compared with calculations (see below). STS measurements were performed on many structures of all observed thicknesses and typical spectra are shown in Figure 3 (a). Each spectrum is characterized by a series of peaks that largely reflect formation of quantum well states (QWSs) because of vertical confinement of electrons. Such states were previously observed using ARPES on thicker Bi(110) 16 and Bi(111) 16,21 films


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deposited on Si (there are no previous reports of STS data on ultra-thin Bi films). The structures of ultra-thin Bi(110) films are still uncertain 22 and so comparison of calculated DOS and STS data provides an important check that calculated structures reflect the real structure in the experiments. To compare with the STS data, and - more importantly - to examine the origin of the QSE, we have performed calculations for infinite 2D Bi(110) slabs using DFT. After examining many structures, with, for example, different surface relaxations, 17 and with H-termination to simulate the effect of the substrate, and with thickesses in the range 1-10 ML, we found reasonable agreement of the number and position of the peaks in the calculated DOS (see dotted lines in Figure 3 (a)) and our STS measurements only for freestanding slabs with relaxed surfaces. This is consistent with previous evidence 13,14,21–24 that the wetting layer effectively isolates the Bi islands from the substrate. Figure 3 (c) shows the calculated atomic structure for a 6 ML thick Bi(110) layer. The key features in 4 ML and 2 ML thick slabs are very similar i.e. the bulk-like interior and the Black Phosphorous (BP)-like 22,23 paired-layers at the surface. Figure 3 (c) also shows the corresponding charge densities, which allow an understanding of the strength of the bonds between atoms. Interestingly, the calculations indicate formation of hypervalent bonds in the BP-like paired layers near the surfaces. The absence of dangling bonds at the surface of such a structure also explains the low surface reactivity of Bi(110) films observed in previous experiments. 22 The calculated band structures and Fermi surfaces corresponding to these structures are shown in Figure 4. Having established that the calculations provide a satisfactory description of the DOS in the Bi nanostructures, we now demonstrate that they also explain the observed lateral QSE. The QSE results from the Fermi surface dimensions in the h112i∗ direction (kF vector parallel to ΓX 2 and X 1 M). The calculated Fermi wavelengths for the electron pockets located between Γ and X 1 match the experimental widths for all thicknesses if a small shift of the Fermi level is allowed. Such shifts correspond to charge transfer from HOPG to the Bi islands (n-type doping of islands). 25 Angle resolved photoelectron spectra for ≥6ML films of Bi on HOPG 26 and Bi on Si 16 are also consistent with n-type doping. To get agreement with the experimentally estimated λF (8, 12 and


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30 nm) shifts of 145, 120 and 35 meV are required for the 6, 4 and 2 ML calculations respectively (shifted Fermi level shown by red lines in Figure 4 (a)-(c)). We expect that the wetting layer will have a stronger effect for smaller film thicknesses and this is reflected in the required shifts; alternatively these small shifts (∼0.1eV) may simply reflect uncertainties in the calculated band energies. It is well known 27–29 that Bi(110) surface states are strongly spin polarised, and so we now consider the nature of the electron states (labelled A in Figure 4 (a)) that are responsible for the lateral QSE. Our calculations show that all bands (Figure 4 (a)-(c)) and corresponding Fermi surfaces (Figure 4 (d)-(f)) are doubly degenerate due to coupling of the two film surfaces. 11,21 Hence the strong spin polarisation observed on the surface of bulk Bi(110) 27–29 is supressed. In fact the electron wavefunctions responsible for the lateral QSE have ’bulk’ character (see calculation of the plane averaged charge density in Figure 4 (g)) i.e. the wavefunctions associated with the QSE penetrate the whole of the slab. Incidentally, these wavefunctions make it clear that electrons in these states will be confined by the boundaries between parts of the structure with different thicknesses (Figure 3 (d)). We now return to the question of the origin of the paired layers in the Bi(110) structure. Our calculations (Figure 4 (g); see also 23 ) show clear minima in surface energy for even layer thicknesses which are consistent with the sequence of experimentally observed thicknesses (paired layers on a 1 ML thick wetting layer). Hence it is clear that electronic effects are involved in stabilising the film structure in the vertical direction as well as the lateral direction. The complex interplay between structural and electronic effects merits further investigation, but we believe the present observation that electronic effects control structure in two orthogonal directions is unique. The nature of the wetting layer in the Bi/HOPG system is an intriguing unresolved problem. Wetting layers are observed for Bi on semiconductors 23 and quasi-crystals, 24 but the wetting layer on HOPG 22 is not directly accessible as it is always ’hidden’ beneath an island (even at low surface coverages). In each of these cases 22–24 the Bi wetting layer manifests as a ‘dead’ layer 23 that makes a negligible contribution to the electronic structure of the islands. 21 The present work reinforces


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the view that the wetting layer must be disordered and weakly coupled to the overlayers as it clearly does not contribute to the DOS. In contrast, the wetting layer in the Pb/Si(111) system 30 forms part of a (vertical) quantum well structure, and so it appears that the nature of the wetting layer is determined by system-specific interfacial structure and coupling. Finally, we envisage that electronic effects can be used to control the lateral dimensions of nanostructures in other systems in which the interaction with the substrate is weak enough to allow the influence of oscillations in the electronic energy 6 to be expressed. For many metals λF is comparable to atomic dimensions, and so we expect that these effects will be most accessible in systems with low electron densities (and hence longer λF ). Three particular nanoscale systems that should be investigated with high priority are (i) spintronic Bi-based materials, 11 (ii) topological insulators based on Bi2 Se3 , Bi2 Te3 , Bi1−x Sbx or Bi(111), 9,10,12 and (iii) semiconductor quantum dots in which doping alters the Fermi level (and Fermi wavelength) and hence could control the size of the structure.

Notes The authors declare that they have no competing financial interests.

Acknowledgement This work was supported by the MacDiarmid Institute for Advanced Materials and Nanotechnology (P.J.K., O.M. and S.A.B.), the U.S. Department of Energy (Grant DE-FG02-07ER46383 for T.-C.C.), and the China Scholarship Council and the Young Scholar Plan of NJUST (X.W.).


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References (1) Brune, H.; Giovannini, M.; Bromann, K.; Kern, K. Nature 1998, 394, 451–453. (2) Barth, J. V.; Costantini, G.; Kern, K. Nature 2005, 437, 671–679. (3) Knight, W. D.; Clemenger, K.; de Heer, W. A.; Saunders, W. A.; Chou, M. Y.; Cohen, M. L. Phys. Rev. Lett. 1984, 52, 2141–2143. (4) Zhang, Z.; Niu, Q.; Shih, C.-K. Phys. Rev. Lett. 1998, 80, 5381. (5) Tringides, M. C.; Jalochowski, M.; Bauer, E. Phys. Today 2007, 60, 50 – 54. (6) Miller, T.; Chou, M. Y.; Chiang, T.-C. Phys. Rev. Lett. 2009, 102, 236803. (7) Morgenstern, K.; Lægsgaard, E.; Besenbacher, F. Phys. Rev. Lett. 2005, 94, 166104. (8) Gonze, X.; Michenaud, J.-P.; Vigneron, J.-P. Phys. Rev. B 1990, 41, 11827. (9) Moore, J. E. Nature 2010, 464, 194–198. (10) Hirahara, T.; Bihlmayer, G.; Sakamoto, Y.; Yamada, M.; Miyazaki, H.; Kimura, S.-i.; Blügel, S.; Hasegawa, S. Phys. Rev. Lett. 2011, 107, 166801. (11) Takayama, A.; Sato, T.; Souma, S.; Oguchi, T.; Takahashi, T. Nano Lett. 2012, 12, 1776– 1779. (12) Cho, S.; Kim, D.; Syers, P.; Butch, N. P.; Paglione, J.; Fuhrer, M. S. Nano Lett. 2012, 12, 469–472. (13) McCarthy, D. N.; Robertson, D.; Kowalczyk, P. J.; Brown, S. A. Surf. Sci. 2010, 604, 1273– 1282. (14) Kowalczyk, P.; Mahapatra, O.; McCarthy, D.; Kozlowski, W.; Klusek, Z.; Brown, S. Surf. Sci. 2011, 605, 659 – 667.


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(15) Kowalczyk, P. Surf. Sci. 2009, 603, 747 – 751. (16) Bian, G.; Miller, T.; Chiang, T.-C. Phys. Rev. B 2009, 80, 245407. (17) Koroteev, Y. M.; Bihlmayer, G.; Chulkov, E. V.; Blügel, S. Phys. Rev. B 2008, 77, 045428. (18) The width of the 2+1 ML high bases is defined to be the distance between the edge of the stripe that is typically found in the centre of each island and the furthest point in the base (perpendicular to the stripe, along h112i∗ ). (19) We have ignored the first peak in the histogram (at widths ∼8.3 nm) since in data for wider bases the observed period is ∼15 nm). (20) Blunt, M. O.; Martin, C. P.; Ahola-Tuomi, M.; Pauliac-Vaujour, E.; Sharp, P.; Nativo, P.; Brust, M.; Moriarty, P. Nature Nano. 2007, 2, 167–170. (21) Hirahara, T.; Nagao, T.; Matsuda, I.; Bihlmayer, G.; Chulkov, E. V.; Koroteev, Y. M.; Echenique, P. M.; Saito, M.; Hasegawa, S. Phys. Rev. Lett. 2006, 97, 146803. (22) Kowalczyk, P. J.; Belic, D.; Mahapatra, O.; Brown, S. A.; Kadantsev, E. S.; Woo, T. K.; Ingham, B.; Kozlowski, W. Appl. Phys. Lett. 2012, 100, 151904. (23) Nagao, T.; Sadowski, J. T.; Saito, M.; Yaginuma, S.; Fujikawa, Y.; Kogure, T.; Ohno, T.; Hasegawa, Y.; Hasegawa, S.; Sakurai, T. Phys. Rev. Lett. 2004, 93, 105501. (24) Sharma, H. R.; Fournée, V.; Shimoda, M.; Ross, A. R.; Lograsso, T. A.; Gille, P.; Tsai, A. P. Phys. Rev. B 2008, 78, 155416. (25) Gierz, I.; Riedl, C.; Starke, U.; Ast, C. R.; Kern, K. Nano Lett. 2008, 8, 4603–4607. (26) Bian, G.; Chiang, T.-C. unpublished 2012. (27) Pascual, J. I.; Bihlmayer, G.; Koroteev, Y. M.; Rust, H.-P.; Ceballos, G.; Hansmann, M.; Horn, K.; Chulkov, E. V.; Blügel, S.; Echenique, P. M.; Hofmann, P. Phys. Rev. Lett. 2004, 93, 196802. 10 ACS Paragon Plus Environment

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(28) Hofmann, P. Prog. Surf. Sci. 2006, 81, 191 – 245. (29) Stróz˙ ecka, A.; Eiguren, A.; Pascual, J. I. Phys. Rev. Lett. 2011, 107, 186805. (30) Feng, R.; Conrad, E. H.; Tringides, M. C.; Kim, C.; Miceli, P. F. Appl. Phys. Lett. 2004, 85, 3866.


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STM image of three dimensional Bismuth nanostructures, illustrating the different prefered widths for structures with different thicknesses.


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Is la n d W id th ( n m ) Figure 1: Histograms of widths of (a) 6+1 ML, (b) 4+1 ML and (c) 2+1 ML thick islands obtained from ∼1500 measurements of ∼400 islands. Gray bars are histograms of raw data while the broadening in the black curves accounts for the uncertainty inherent in the experimental measurements (see text for description). For all island thicknesses a regular sequence of peaks is visible in the histograms i.e. there are preferred island widths due to a quantum size effect. Vertical solid and dotted lines indicate multiples of the Fermi wavelength λF and λF /2 respectively. Measured λF are 8 nm, 12 nm and 30 nm for 6+1, 4+1 and 2+1 ML thick islands respectively. Inset in (a) shows typical island morphologies: flat, broad 2+1ML bases with thicker rods and stripes near their centres. The widths recorded in the histograms are the widths of the individual bases, rods and stripes.


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Figure 3: (a) Normalized tunneling spectra (solid lines) for 6+1, 4+1 and 2+1 ML thick islands. Histograms below each spectrum indicate the observed energy range for each peak; 15 scale on the right is in thousands of counts. Dotted lines are calculated DOS for 6, 4, 2 ML thick films. (b) Surface unit cell of Bi(110). (c) Calculated charge density for a {011} plane (see dotted line in (b)) of calculated 6 ML structure showing hypervalent bonds for every second atom in the second layer from top and bottom, together with a ’ball and stick model’ showing the BP-like surface reconstruction. First and second layers are shown using darker and lighter tones respectively. Atoms with out of plane bonds along h110i are indicated with dots. (d) Schematic side view along ¯ h110i of a 2 ML high stripe on top of a 4 ML thick layer. Dashed lines delimit boundaries between regions of different thickness.


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Figure 4: (a)-(c) Calculated dispersion relations for 6, 4 and 2 ML films respectively. Horizontal gray lines indicate the as-calculated location of the Fermi level for each film while red lines indicate the Fermi level after optimised (see text) charge transfer from the substrate to the film. (d)-(f) Calculated Fermi surfaces for 6, 4, 2 ML films respectively with electron and hole pockets indicated using reddish and blueish colors respectively. Different color tones show Fermi surfaces after different shifts of the Fermi energy (due to charge transfer from the substrate). (g) Calculated plane-averaged electronic charge densities within the 6 ML film (the vertical dashed lines separate the atomic layers) for the states labelled A in (a) together with plot of surface energy as a function of thickness of the structure.


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fre q u e n c y

(b )

1 5 1 0

ACS Paragon Plus 5 Environment 0

m

0

1 5

3 0

4 5

6 0

Is la n d W id th ( n m )

7 5

6+1 ML (b) Nano Letters

(a) 19 of 21 Page

0,0

1

freq.

4+1 ML

0

2+1 ML

1

freq.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

freq.

(dI/dV)/(I/V) (arb. units)

0,3

(c)

_ *

(d)

_

6 ML

4 ML

ACS Paragon Plus Environment 0

-1

0

1

Energy (eV)

2

1

X2

M

X1

Γ

(a)

Charge Density (arb. units)

X1

6 ML (d)

M 6 ML

Page 20 of 21

6ML

2kF A 145 meV 90 meV 0 meV

_ X2

_ Γ 0 meV 90 meV 145 meV

4 ML

Energy (eV)

1 2 3 0 4 5 6 -1 7 8 9 1 (b) 10 11 12 0 13 14 15 16-1 17 18 (c) 191 20 21 220 23 24 25 26-1 27 _ 28 Γ 29 30 (g) 31 32 33 34 35 A 36 37 38

M

Nano Letters

(e)

4 ML 4ML

2kF

_ X2

_ Γ

2 ML

0 meV 120 meV

(f)

_ X2 1

_ M 2

3

_ X1

_ Γ

4

5

2ML

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_ M 6

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Surface Energy (eV/unit cell)

Γ

2 ML

_ X2

_ Γ 0 meV 35 meV

ACS Paragon Plus Environment

Layers (ML)

_ X1

_ M

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Nano Letters

ACS Paragon Plus Environment

Electronic Size Effects in Three-Dimensional ... - ACS Publications

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