A Bottom-Up Approach toward Fabrication of Ultrathin PbS Sheets

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A Bottom-up Approach Towards Fabrication of Ultrathin PbS Sheets Somobrata Acharya, Bidisa Das, Umamahesh Thupakula, Katsuhiko Ariga, Dipankar Das Sarma, Jacob N. Israelachvili, and Yuval Golan Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl303568d • Publication Date (Web): 08 Jan 2013 Downloaded from http://pubs.acs.org on January 9, 2013

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A Bottom-up Approach Towards Fabrication of Ultrathin PbS Sheets

Somobrata Acharya,*,† Bidisa Das,† Umamahesh Thupakula,† Katsuhiko Ariga,§ D. D. Sarma,‡ Jacob Israelachvili,║ and Yuval Golan┴

†

Centre for Advanced Materials, Indian Association for the Cultivation of Science, Kolkata 700032, India

§

World Premier International (WPI) Research Center for Materials Nanoarchitectonics

(MANA), National Institute for Materials Science (NIMS), JST, CREST, 1-1 Namiki, Tsukuba, Ibaraki, 305-0044, Japan ‡

Solid State and Structural Chemistry Unit & Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore 560012, India

║

Department of Chemical Engineering, Materials Department and Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA

┴

Department of Materials Engineering and Ilse Katz Institute of Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

*Corresponding Author E-mail: [email protected]

ABSTRACT: Two-dimensional (2D) sheets are currently in the spotlight of nanotechnology owing to high-performance device fabrication possibilities. Building a free-standing quantum sheet with controlled morphology is challenging when large planar geometry and ultranarrow thickness are simultaneously concerned. Coalescence of nanowires into large single-crystalline sheet is a promising approach leading to large,

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molecularly thick 2D sheets with controlled planar morphology. Here we report on a bottom-up approach to fabricate high quality ultrathin 2D single crystalline sheets with well-defined rectangular morphology via collective coalescence of PbS nanowires. The ultrathin sheets are strictly rectangular with 1.8 nm thickness, 200-250 nm in width and 3-20 μm in length. The sheets show high electrical conductivity at room and cryogenic temperatures upon device fabrication. Density Functional Theory (DFT) calculations reveal that a single row of delocalized orbitals of a nanowire is gradually converted into several parallel conduction channels upon sheet formation, which enable superior inplane carrier conduction.

KEYWORDS: Nanowires, ultrathin sheet, coalescence, activation energy, DFT

calculations, transport

Two-dimensional (2D) sheets are currently in the spotlight of nanotechnology for fast, high-performance and low-power device fabrication possibilities.1-3 A true 2D sheet can be thought as a system where the charge carriers are confined along thickness but allowed to move in a plane at extremely high speeds.4,5 Fabrication of strongly anisotropic semiconductor 2D sheet with well-controlled morphology is in developing stage. A semiconductor 2D sheet is promising for the use in next-generation nanoelectronic devices because, compared to 1D nanorods or nanowires, it is relatively easy to fabricate complex structures owing to the large planar morphology.1 Atomically thin films become thermodynamically unstable below a critical thickness, typically below dozens of atomic layers.5,6 Atomically thin 2D materials were presumed to be believed as an integral part


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of larger 3D structures before the recent breakthrough of graphene.2,6,7 However, pristine graphene does not have a band gap, a property that is essential for manifold electronic applications.1,6 The strategies of 2D sheet fabrication by mechanical exfoliation,2,6 ionexchange8 or chemical approaches9 often results in irregular morphologies and overlapping layers. Oriented attachment of nanocrystals is another technique favorable to grow 1D nanostructures or 2D sheets.10,11 Recent studies demonstrate the self-assembly of nanoparticles into free-floating sheets or highly uniform superlattices and surface pressure induced 2D phase of quantum dots at the air-water interface.12-14 However, achieving single crystalline continuous semiconductor sheet with large surface area, narrow thickness and well-controlled morphologies has remained challenging. Lead chalcogenides are attractive semiconductor materials for optoelectronic applications such as detectors and emitters of infra-red radiation.15,16 Quite considerable deviation from the stoichiometry may occur in lead chalcogenide nanocrystals leading invariably to an excess of one or the other constituent.17 Since excess of lead ions give rise to free electrons (excess of chalcogenide gives free holes), high carrier densities can be achievable in lead chalcogenide systems. Additionally, the impurity levels coalesce with the energy bands in the lead chalcogenide compounds because of very high permittivities (ε~169 at 300 K), leading to high carrier densities over a broad temperature range.17,18 Thus, a flexible and controllable strategy to process ultrathin 2D sheet of lead chalcogenide with finite band gap holds importance in designing planar devices with superior transport functionalities. We have reported earlier on the synthesis of uniform, ultra narrow (1.8 nm) single crystal PbS nanowires, their 2D distribution and polarization properties.19 While defining a common axis for the polarization measurements by


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aligning the nanowires, we observed a spontaneous side-by-side coalescence into nanoribbons. Here we report on the fabrication of ultrathin 2D single crystalline PbS sheets through collective coalescence of PbS nanowires at the air-water interface with the aid of surface pressure at elevated temperature. The ultrathin sheets are of rectangular morphologies with 1.8 nm thickness, 200-250 nm in width and 3-20 μm in length, while the surface pressure allows a controlled packing density of the sheets on top of a variety of planar substrates. The change in dimensionality from nanowires to sheets is reflected in the electronic properties showing strong dependency of band gap on the shape confinement effect. Large lateral dimensions and planar morphology of the sheets readily allow integration of electrodes for device fabrication showing high electrical conductivity at room and cryogenic temperatures. DFT calculations reveal delocalized nature of π-type sheet orbitals with formation of efficient electron conduction channels compared to the nanowires and nanoribbons, which are responsible for enhanced conductance. The ultrathin PbS sheet formed by scaling up individual nanowires to a large quantum sheet offers possibilities for manifold technological applications owing to the engineered bandgap. Our approach for preparing ultrathin PbS sheet starts with the synthesis of parallel 2D supercrystalline PbS nanowires (Figure 1a and Supporting Information).19 The synthesized PbS nanowires are uniform in width with an average diameter of 1.8±0.08 nm and length of 150-200 nm defining an aspect ratio of ~75-100. The as-synthesized nanowires are self-assembled in domains typically consisting of dozens of parallel nanowires. The capping ligand trioctylamine (TOA) plays an important role in determining the nanowire shape, size and typical assembly pitch of 2.7±0.1 nm. The


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ligand TOA binds to the Pb atoms through nitrogen site owing to its nucleophilic nature while the hydrophobic alkyl chains are exposed outwards. The pitch is less than the combined upright alkyl chains of two TOA molecules indicating interdigitation of the TOA chains, which induces the supercrystalline assembly of the nanowires.19,20 The purified and dried PbS nanowires are re-dispersed in chloroform and spread at the airwater interface of a Langmuir trough.21,22 A scheme shows various stages of sheet formation process by coalescence mechanism of PbS nanowires at air-water interface with the aid of surface pressure (Figure S1, Supporting Information). The uniaxial compression at air-water interface irreversibly aligns the nanowires to yield large area ultra high density parallel assembly of nanowires over ca 15 μm2 (Figure S2, Supporting Information). The best alignment is obtained at a surface pressure range of 25-30 mN/m with superior end-to-end and side-by-side registry.19 Holding the monolayer for 60-90 minutes at this condition results in side-by-side coalescence of 4 to 5 nanowires into nanoribbons of 8 nm to 10 nm in diameter.19 A gentle heating to the aligned monolayer at 50°C for 90 minutes results in ultrathin PbS sheets in a single step. The release of surface pressure and re-compression at various stages of surface pressure allows tuning of packing density of the sheets on top of planar substrates (Figure S3, Supporting Information).


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Figure 1. Images, morphology and modelling of ultrathin PbS sheets. (a) HRTEM images of PbS wires self-assembled into 2D supercrystalline arrays, which is used as starting material for designing PbS sheets. (b) AFM image of a single sheet showing uniform width of 200-250 nm along its length. (c) Tapping mode AFM image of PbS sheet deposited on a freshly cleaved mica substrate. The height profile presented in Supporting Information shows a relative height of ≈5 nm, including TOA layers on the top and the bottom surfaces of the PbS sheets. (d) Large scale AFM topographical image of the sheets deposited on a freshly cleaved mica. The image shows that the sheets are about 3 μm in length and arranged in parallel over a large area on mica substrate. (e) Plane-view and cross-section schematic model of a PbS sheet with adsorbed TOA layers on top and bottom surfaces. TOA molecules with different densities at the top and bottom layers are shown. The TOA monolayer Langmuir Blodgett film is on average ~1.5 nm in height corresponding to an average bilayer thickness of 3 nm of at the top and bottom surfaces of a sheet. The actual thickness of the PbS mineral sheet has been determined by subtracting the thickness of the TOA bilayer from the overall thickness obtained from AFM height profile of a sheet.


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Atomic force microscopy (AFM) images (Figure 1b and 1c) reveal flat and rectangular morphology of the sheets. Each sheet has a uniform width in the range of 200 nm to 250 nm along its entire length, while the smallest sheet is at least of 3 μm in length (Figure 1d) defining a minimum planar area as large as 0.6 µm2. Repetitive height measurements using tapping mode AFM reveal an average thickness less than 5 nm including TOA layers on the top and bottom surfaces of the sheets (Figure 1c and Figure S4 in Supporting Information). The sheets are stable at ambient temperature and can be lifted on various planar solid substrates with large surface coverage using Langmuir Blodgett deposition technique (Figure 1d and Figure S5 in Supporting Information). We have estimated the actual thickness of the inorganic PbS sheets from AFM height profiles and accounting the upright lengths of TOA molecules (Figure 1e). The calculated length of an upright TOA molecule is 1.12 nm,19 while control experiments with bare TOA monolayer LB film in AFM estimates an average height of ~1.5 nm (Figure S6, Supporting Information) suggesting an average thickness of ~3 nm of TOA bilayer at the top and bottom surfaces of a sheet. Taken together, we can determine a sheet thickness less than ~2 nm excluding the TOA bilayer on the top and bottom surfaces of a sheet (Figure 1e). The thickness value is interpretable with the observed 1.8 nm diameter of the PbS wires suggesting a direct side-by-side coalescence of the wires into sheets. High resolution TEM image (HRTEM) shows that the PbS sheets are single crystalline with an inter-planar spacing of 0.30±0.05 nm, consistent with the (200) d-spacing of the PbS rock-salt crystal structure (Figure 2a). Energy dispersive spectroscopy (EDS) analysis carried out in the TEM (Figure S7, supporting information) gives a Pb to S molar


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ratio of ~1:1, in line with a stoichiometric crystal. The rocksalt structure of the sheets is further verified by selected area electron diffraction (SAED) and X-ray diffraction (XRD) (Figures S8, supporting information). The Fast Fourier Transformation (FFT) patterns obtained from the PbS sheets (Figure 2a, inset) confirm the single crystalline nature with reflections correspond to the (200) and (311) spacings of rock-salt PbS. Although the sheets appear flat over a large region, wrinkled patterns are also observed occasionally (Figure S9, Supporting Information). A comparison of FFT pattern from flat and wrinkled portion of the sheet also shows reflections corresponding to the (200) and (311) spacings of rocksalt PbS suggesting monocrystallinity of the sheets (Figure S9, Supporting Information). The (200) and (311) reflections indicate a zone axis of [031] for the sheets. This unique orientation was repeatedly observed and represents a tilt of 18.43° from the [010] axis of the rock-salt structure. Recall that the supercrystalline assembly of the PbS nanowires defines a bilayer of “carpet” formed by the ligand TOA at the top and bottom layers along with the interdigitation between the adjacent nanowires. Expectedly, the ligand layers at the bottom of the nanowires will have larger mobility at elevated temperatures owing to the direct contact with the water subphase of the Langmuir trough. Hence, the release and relocation of TOA from the bottom surface (and side walls) of the nanowires is more probable than the top surface retaining the carpet at the top surface in the integral form. Thus a tilt of the nanowire planes is expected during the coalescence process. The partial removal of TOA reduces the repulsive interaction between the nanowires facilitating the coalescence with a tilt of the (100) planes under the applied surface pressure. The relocation of TOA from the bottom surface of the nanowires leads to a lesser density of TOA on the bottom surface of the sheets compared to the top


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surface (Figure 1e). The 2D oriented attachment from wire to sheet is driven with the aid of surface pressure which is of the order of few tens of megapascals within the Langmuir film. In addition, short side-by-side separation (~0.8 nm) between the adjacent nanowires, low melting point of TOA is supportive for the coalescence mechanism. 400

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and 42°C with (d) the slower component at 50°C (e) the faster component at 50°C. Error bars are shown in the Figures. (f) The optimized geometry for the model Pb2S2 dimer and N(CH2CH2CH3)3 adduct used for binding energy calculations. The length of the ligand N(CH2CH2CH3)3 considered in the calculation is one third of the actual length of TOA and the Pb2S2 cluster is the fundamental unit of PbS nanowire.

The uniaxial compression can be viewed as 2D analogue of high-pressure 3D reactions in bulk, especially when the free energy of the reaction and its transition state are pressure dependent.22,23 We have estimated the energy involved in the PbS sheet formation process from the coalescence reaction dynamics rate at different temperature range by measuring the decrease in monolayer area with time at a constant surface pressure (Figure 2b). The area of the monolayer films decreases with time at a rate that increases with subphase temperature. The coalescence involved with a decrease in the total area by 14% to 80% for the subphase temperature range of 12°C to 50°C respectively. A rapid decrease in the monolayer area is observed within the first 30 minutes of heating at elevated temperature of 50°C (Figure 2b). We carried out kinetics analyses from the area versus time decay curves to extract the rate constant k(T) at different temperature range.24 The decay curves follow first-order kinetics with slower component k2(T) of 0.0235±0.0037 min-1, 0.0277±0.0035 min-1, 0.0335±0.0038 min-1, 0.034±0.0032 min-1 and 0.042±0.0034 min-1 at 12ºC, 20ºC, 27 ºC, 35ºC and 42ºC respectively (Figure 2c). A higher-order kinetics is observed at 50ºC with faster component k1(T) of 0.081±0.0039 min-1 for initial 30 minutes followed by a slower component k2(T) of 0.04±0.0034 min-1 for longer annealing time. Since the TOA molecules have to be removed from the surfaces of the PbS nanowires during coalescence into sheets, we have estimated the energy required to remove TOA


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molecules by calculating the activation energy (Ea) using the relation k(T)=χexp(-Ea/kT), with χ being the frequency factor (see Supporting Information).22 An Arrhenius analysis with the rate constants k2(T) in the temperature range of 12 ºC to 42 ºC and slower component at 50 ºC yields an activation energy of 10±0.7 KJ/mole (Figure 2d). The activation energy involving the faster component k1(T) at 50 ºC can be calculated from an exponential fitting of the rate constants, which results in an energy of 53±0.7 KJ/mole (Figure 2e). The resulting release of adsorption enthalpy, combined with the stabilization by inter-TOA van der Waals forces and possible reorganization of PbS wires, obviously overcompensates by the pressure-area work. In order to validate the derived activation energy of coalescence, we have calculated the binding energy of TOA to the nanowire surface using Density Functional Theory (DFT) method (see Supporting Information). The structure of TOA consists of three hydrophobic alkyl chains and a polar nitrogen head group with two loan pair electrons through which TOA binds to the metal terminal of the PbS wires. Hence, the binding energy calculation should count the interaction of nitrogen head group with the metal terminal of PbS wire, while the effect of alkyl chain length is less significant (Figure S10, Supporting Information).25 We calculated the binding energy by choosing N(-CH2CH2CH3)3 amine to a model Pb2S2 cluster which captures the essential chemical interactions (Figure 2f).26 The calculated binding energy ~55 KJ/mol at 298 K is of the same order of activation energy at air-water interface. Interesting question remains, where the hydrophobic TOA released from the nanowire surfaces locate after coalescence. The released TOA from the bottom surface of the nanowires would like to be accumulated at the air-water interface owing to the hydrophobic nature. AFM images reveal formation of interconnected structure of


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released TOA, which remain in the same monolayer at air-water interface along with the sheets, however, are phase segregated from the sheets (Figure S11, Supporting Information). The morphological transformation of 1D PbS wire into a 2D sheet should affect the electronic structure which we probe using DFT calculations (see Supporting Information).25,27,28 To model the transformation from the wire to sheet, we first construct a Pb18S18 nanowire and dimerize these laterally to yield a Pb36S36 nanoribbon. We then construct an infinite 2D PbS sheet along x-y plane using periodic boundary conditions. These three structures are of increasing width, however with identical thickness (Figure 3a). A decrease in the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) is observed for the Pb36S36 nanoribbon (2.63 eV) compared to Pb18S18 nanowire (2.87 eV). A further decrease in the band gap (1.8 eV) is observed for the infinite 2D sheet in comparison to both nanoribbon and nanowire. Increasing the width results in a decrease of resultant band gap, as is expected considering the degree of confinement (1D > 2D) in 1D and 2D systems. We compared the calculated band gaps with the experimental band gaps for nanowires and sheets estimated from the UV-vis absorption spectra (Figure 3b).

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calculated for the nanowires and sheets are 2.03 eV and 1.81 eV respectively. A control experiment performed by transferring the sheets from the solid substrates to chloroform yielded the same band gap suggesting that the morphology of the sheets remained unaltered after transferring them in the solution medium (Figure S12, Supporting Information). Although, measured band gap is somewhat lower than the calculated band


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gap due to smaller dimension chosen for the model nanowire, the calculated band gaps for infinite sheet reveal a same order with the experimental band gaps. The first principle

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Figure 3. Electronic structure, molecular orbitals and energies. (a) Frontier orbitals for the Pb18S18 nanowire and Pb36S36 nanoribbon and PbS 2D sheet. The model structures are built with identical lengths and thickness but with gradual increase in the widths. The sizes of the finite clusters are 0.29×2.37, 0.89×2.37 nm2 respectively. The 2D sheet is 4 atomic layers thick and infinite along x-y plane. The occupied orbitals are separated from the unoccupied orbitals by the HOMO-LUMO energy gap marked by vertical black line. The numbers indicate the energy of the orbitals in eV. (b) UV-vis absorption spectra of PbS nanowires in dichloromethane suspension


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(black curve). In-situ absorption spectrum of PbS sheet (red curve) directly taken on the Langmuir trough with an optical fiber assembly. The absorption spectrum of the sheets is over all red shifted compared to the nanowires. (c) Model Pb2S2 dimer and the frontier orbitals marked with corresponding symmetry. The dimeric Pb2S2 is a closed rectangular structure with D2h symmetry and Pb-S bond-lengths of 0.26 nm. In the HOMO levels, there are contributions from lead s, p orbitals and sulfur p orbitals while mainly lead pz orbitals constitute the LUMO levels. The HOMO-3 (B3u) level shows fully delocalized electron densities above and below the nodal plane of Pb2S2. The grey balls and yellow balls represent Pb and S atoms respectively (inset). The color code (red and cyan) represent the sign of the orbital wave functions. (d) The comparison of electronic DOS of an infinitely long PbS nanowire (cross-section 0.29×0.29 nm2) and an infinite 2D sheet consisting of four atomic layers and bulk PbS. The nanowire structures are formed by applying periodic boundary conditions longitudinally while applying large vacuum along the perpendicular directions. In case of 2D sheet the periodic boundary conditions in the sheet plane (x-y plane). The band gaps are marked by double headed arrows with the energy gap expressed in eV. The band gap calculated from the DOS for the nanowire is 2.14 eV, 2D sheet is 1.8 eV and bulk having 0.5 eV.

DFT calculations25 reveal that first few unoccupied states (LUMO, LUMO+1, LUMO+2 and LUMO+3) are not fully conjugated (connected π-orbitals with extended electronic wave functions) over the entire length of the Pb18S18 nanowire, which renders them inappropriate for conduction (Figure 3a). However, mixing of unoccupied states (e.g., LUMO+1 and LUMO+2) together may form a suitable conjugated conduction pathway. The HOMO (-5.45 eV) and HOMO-1 (-5.63 eV) states are conjugated and fully spread through the nanowire, which may form suitable conduction channels. HOMO-2 (-5.77 eV) and HOMO-3 (-5.86 eV) are not fully conjugated, however, mixing of these orbitals may form fully conjugated conduction channel. Interestingly, such conjugation increases upon increasing the width owing to more overlapping frontier orbitals (Figure 3a). The electronic eigen states are found to be delocalized in the plane of the 2D sheet. The eigen


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states of the 2D sheet show increased degeneracy of the orbitals compared to the Pb36S36 nanoribbon and Pb18S18 nanowire. Comparison of the nature of occupied orbitals of sheets with the nanowire reveal that a single row of delocalized orbital for nanowire is gradually converted to several parallel conduction channels with increasing width which may enable in-plane carrier conduction. For clear understanding of the formation of conduction channels, we have further analyzed the orbitals of model Pb2S2 with D2h symmetry which is the smallest repetitive unit for nanowire and 2D sheet (Figure 3c). The energy gap between the HOMO (B1U, -6.26 eV) and the LUMO (B2G, -3.11 eV) orbitals of Pb2S2 is 3.15 eV and the orbitals are mainly π-type with reasonable electron densities above and below the nodal plane of the dimer (Figure 3c). Especially HOMO-3 (B3u) in Pb2S2 gives rise to fully delocalized electron densities above and below the nodal plane, suggesting such orbitals may allow 2D conduction upon coalescence of the dimers into a continuous sheet. In case of the 2D sheet the p-states of either Pb or S close to the Fermi energy are responsible for the formation of delocalized states in the sheet plane. We have compared the total electronic density of states (DOS) of PbS nanowire and sheet using GGA methods employing PBE functionals and DZP basis set after full relaxation of the geometries (Figure 3d). The sharp lines in the DOS spectra of nanowire and 2D sheet contain clear signatures of electron confinement compared to the bulk DOS (Figure 3d). The degree of confinement affects the DOS and a larger band gap is observed for most confined system, i.e. the nanowire compared to the 2D sheet. The peaks around 12.2 eV are due to sulfur s-states and the peaks just below the Fermi energy is mostly due to sulfur p-states. The p and d states of Pb are placed at positive energies beyond the Fermi energy in the DOS. The DOS calculations confirm that the p-states of either lead or


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sulfur are responsible for the formation of delocalized states in the sheet plane as observed in Figure 3a and 3c. To explore the transport utility of our PbS sheets, we transferred the sheets onto glass substrate in the form of LB film. Silver electrodes were fabricated using electron beam lithography on the top plane of specific sheets to form devices for four probe measurements (Figure S13, Supporting Information). Transport measurements were performed in vacuum (10-5 Torr) at variable temperature range (298 K to 60 K). The current-voltage curve (Figure 4a) resembles semiconductor nature with a finite band gap at room temperature, showing symmetric transports at negative and positive bias yielding current in the mA range. The overall current-voltage curve is highly temperature dependent since the magnitude of current increases rapidly as temperature increases while maintaining the symmetric nature. The resistance measured as a function of temperature is of the order of kΩ upto 150 K (inset, Figure 4a), which increases exponentially at 60 K. Since our PbS sheets result in large current owing to the existence of π-orbitals with reasonable electron densities above and below the nodal plane of the PbS dimer similar to graphene (Figure 3c), we expect ballistic transport mechanism to prevail in analogy with the large current reported from highly conjugated systems like carbon nanotubes or graphene.29-31 We predict that ballistic transport occurs in our system at lower temperatures (0K) where the phonon assisted hopping transport is not considered. However, we anticipate a cross-over from the ballistic to hopping transport at elevated temperature. Evidences of such cross over from ballistic to hopping/thermally assisted transport are reported for graphene and molecular systems.30,32,33 Within this


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1.6

16

a

60K 150K 250K 298K

b

R (KΩ)

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4 0 -4 -8 -12

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Figure 4. Transport and transmission through the PbS sheet. (a) Temperature dependent (298 K to 60 K) current voltage characteristics of PbS sheet measured in a four probe environment. Silver electrodes with 500 nm, 1 µm and 5 µm spacings were fabricated using electron beam lithography on the top plane of specific sheets for repetitive measurements. The inset shows the Arrhenius plot of resistance versus temperature. (b) The electronic transmission spectra of Ag(100)-Pb36S36-Ag(100) set-up for a set of applied bias voltages. For theoretical transmission studies, the model system is placed symmetrically between two 5×3 Ag(100) electrodes in a way that S atom is situated on a four fold symmetric site and Ag-S bond distances are 0.29 nm. Thus, the scattering region includes two Ag(100) electrodes on either sides of the central Pb36S36 sheet. The transmission spectrum using 6×6 k-points are calculated. The energy scale in the transmission spectrum is relative to the average Fermi level of the two-probe system, i.e. (μL +μR)/2, where μL and μR are the electrochemical potentials of the left (L) and right (R) electrodes respectively. Electronic transport occurs along longitudinal direction whereas the periodic boundary conditions are applied in the transverse direction of the sheet. (c) Comparison of experimental (at 60 K, solid squares) and calculated (at 0 K, hollow circles) current versus voltage characteristics. The electronic transport of Ag(100)-Pb36S36-Ag(100) set-up is calculated for a sets of positive and negative applied bias voltages at 0 K. The current versus voltage characteristics are calculated using self-consistent calculations for Ag(100)-Pb36S36-Ag(100) two probe setup at positive bias voltages till ±1.5 V. Since the interfaces of the device are symmetric, the current versus voltage curve is symmetric for positive and negative bias voltages.


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approximation, a means of the observed enhanced current can be accounted from the abinitio electronic transmission spectra (Figure 4b) calculated using the non-equilibrium Green’s function formalism following Landauer’s scattering theory.34 The transmission spectrum is calculated using T ( E , V ) = Tr[ΓL ( E ,V )G ( E , V )ΓR ( E , V )G + ( E ,V )] , where ΓL/R stands for the coupling matrix between two electrodes and the scattering region and G(E,V) is the retarded Green’s function of scattering region.27,28 The electronic eigen states of the sheet within the two-probe environment are denoted as Molecular Projected Self Consistent Hamiltonian (MPSH) states.27 The MPSH states, which can conduct owing to their conjugation and overlapping nature, show peaks in the transmission spectrum. High values of transmission coefficients are observed due to parallel conducting pathways, simultaneously conducting more than one electron per channel through the sheet. In such case, the total transmission probability T(E) can be defined as T ( E ) = ∑ Tn ( E ) where n is the number of eigen channels, which results in the n

transmission value more than unity in the transmission spectrum.35 For example, the transmission spectrum for 0.2 V bias (Figure 4b and Figure S14 in Supporting Information) shows peak at -1.15 eV corresponding to the HOMO state revealing transmission coefficient >2 due to the presence of two simultaneous conduction channels.36 On the other hand, the transmission peak corresponding to an unoccupied state at 0.85 eV corresponds to one conduction channel showing T(E) ~1. Comparison of the transmission spectra from 0.0 V to 1.5 V shows that the energy gap between peaks corresponding to occupied and unoccupied states decrease with the increase in applied voltage (Figure 4b). The transmission peaks corresponding to the unoccupied states extend into the bias-window resulting in a decrease in energy gap with increasing voltage


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causing larger current. The conductance of the model sheet calculated from the zero bias transmission spectrum is 5.6×10-6 S. The current through the device is evaluated from the transmission

probability

using

the

expression,

+∞

I (V ) = G0 ∫ T ( E,Vb )[nF ( E − μ L ) − nF ( E − μ R )]dE, where G0 = 2e2/h is the quantum −∞

conductance, T(E,Vb) is the transmission coefficient at an applied bias Vb, nF (E-μL(R)) are the Fermi Dirac distribution function, μL,(μR) are the electrochemical potentials of the left (L) and right (R) electrodes.28 The theoretical current versus voltage curve (Figure 4c) is non linear and the current increases with applied bias voltage owing to increased transmission coefficients within the bias window. Since there are no sharp peaks in the transmission spectrum for this bias window, the current versus voltage curve is smooth and featureless and the current obtained in the μA range at 0 K, which is in agreement with experimentally measured transport characteristics at 60 K (Figure 4c). The advantage of our bottom-up approach for designing ultrathin PbS sheet relies in the processing flexibility and large surface coverage with a single crystalline material, which are favorable for device applications. Importantly, the sheets can be transferred on a variety of planar substrates such as hydrophilic quartz, glass, silicon, mica and on the hydrophobic gold substrates with a controlled packing density offering possibility for very large scale device fabrication. We expect that the methodology may provide a general approach for the preparation of controlled 2D structures from a variety of existing 1D materials. Furthermore, nanowires of different material combination can be alternatively used for controlling the crystal composition or to introduce well-defined compositional defects with sub-nm dimensions within a 2D crystal. The delocalization of


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π-type orbitals with enhanced electron densities into gradual parallel conduction channels with increasing width enables superior in-plane carrier conduction paving possibilities for advanced transport based devices. The controlled fabrication of 2D sheets therefore represents both challenges and opportunities. For example, development of highperformance gated electronics, quantum Hall effect devices and transistor applications of the ultrathin 2D sheet with finite band gap ultimately may prove to be the most exciting. The PbS sheets could be useful in optoelectronics and energy harvesting applications that require wide surface area for photon absorption.

ASSOCIATED CONTENT Supporting Information

Additional details on the characterization of PbS 2D sheets, computational methods and DFT calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENTS

Financial support under Grant #SR/S5/NM-47/2005, Grant# SR/NM/NS-49/2009 and INT/EC/MONAMI (25/233513)/2008 from DST, India are gratefully acknowledged. SA dedicates the manuscript to late Professor Shlomo Efrima. YG thanks the Israel Science Foundation for financial support under Grant #340/2010. This work was supported by the US-Israel Binational Science Foundation, Grant #2006032 (JI and YG). We thank Dr. Richard Charvett and the MANA foundry, NIMS for the support with the lithography and transport measurements, and Dr. V. Ezevsky (BGU) for useful discussions.


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(17) Moss, T. S.; Burrell, G. J.; Ellis, B. Semiconductor Opto-Electronics. London: Butterworths, pp. 369, 1973. (18) Wang, R. Y.; et al. Nano Lett. 2008, 8, 2283. (19) Patla, I.; et al. Nano Lett. 2007, 7, 1459. (20) Panda, A. B.; Acharya, S.; Efrima, S. Adv. Mater. 2005, 17, 2471. (21) Henrichs, S.; Collier, C. P.; Saykally, R. J.; Shen, Y. R.; Heath, J. R. J. Am. Chem. Soc. 2000, 122, 4077. (22) Acharya, S.; Efrima, S. J. Am. Chem. Soc. 2005, 127, 3486. (23) Acharya, S.; Hill, J. P.; Ariga, K. Adv. Mater. 2009, 21, 2959. (24) [ A(t ;T ) − A(∞;T )] /[ A(0;T ) − A(∞;T )] = k (T ) , A(t;T) is the area of a film kept at a

temperature T measured at time t. A(∞;T) is the value of the area measured at long reaction times (the asymptotic area, presumably the area occupied by the sheets at temperature T). (25) Frisch, M. J.; et al. Gaussian 03, Revision C.02; Gaussian Inc., Wallingford, CT, 2004. (26) Lin, Y. M.; Dresselhaus, M. S. MRS Proceedings 2002, 737, E17.5. (27) Brandbyge, M.; Mozos, J. L.; Ordejon, P.; Taylor, J.; Stokbro, K. Phys. Rev. B 2002, 65, 165401. (28) Soler, J. M.; et al. J. Phys. Cond. Matt. 2002, 14, 2745. (29) Mayorov, A. S.; et al. Nano Lett. 2011, 11, 2396. (30) Du, X.; Skachko, I.; Barker, A.; Andrei, E. Y. Nature Nanotech. 2008, 3, 491. (31) Chen, F.; Tao, N. J. Acc. Chem. Res. 2009, 42, 429. (32) Zhong, Y.; Liu, K.; Luo, H. G. Phys. Rev. B 2012, 85, 075106.


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(33) Sedghi, G.; et al. Nature Nanotech. 2011, 6, 517. (34) Datta, S. Electronic Transport in Mesoscopic System. Cambridge University Press, New York, 1996. (35) Brandbyge, M.; Sørensen, M. R.; Jacobsen, K. W. Phys. Rev. B 1997, 56, 14956. (36) Jippo, H.; Ohfuchi, M.; Kaneta, C. Phys. Rev. B 2011, 84, 075467.

TOC Graphic PbS nanowires

Temperature

AFM image of PbS 2D sheet

Surface Pressure

Surface Pressure

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A Bottom-Up Approach toward Fabrication of Ultrathin PbS Sheets

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