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The energy gap of pristine silicon clusters
Journal of Electron Spectroscopy and Related Phenomena 109 (2000) 157–168 www.elsevier.nl / locate / elspec
The energy gap of pristine silicon clusters B. Marsen, M. Lonfat, P. Scheier, K. Sattler* Department of Physics and Astronomy, University of Hawaii, 2505 Correa Road, Honolulu, HI 96822, USA
Abstract Studies of the fundamental energy gap of pristine silicon clusters have been performed using STM and STS. Clusters with ˚ are studied. The size dependence of the gap is determined. For particles below 15 A, ˚ gaps up to sizes between 2.5 and 40 A 450 meV are found. Larger particles exhibit zero gaps. The results are explained in terms of a transformation from diamond ˚ (|44 atoms per cluster). For clusters with diamond structure the surface dangling to compact structure occurring at 15 A bond density is high leading to electronic states filling the energy gap. On the other hand, the compact arrangement of the smaller clusters tends to eliminate dangling bonds. Therefore, finite-gap values are observed for clusters with less than |44 atoms. 2000 Elsevier Science B.V. All rights reserved. Keywords: Silicon clusters; STM; STS; Semiconductors
1. Introduction In recent years extensive work has been performed on semiconductor nanostructures. The most often investigated structures are clusters and nanocrystals [1]. In particular, the electronic band structure of semiconductor quantum dots is of interest [2]. Also the carrier transport and tunneling through dots [3,4], arrays of dots [5], and nanogranular semiconductors [6–8] are important issues. Cluster-assembled materials [9] are new granular materials with quantumconfinement determining their properties. Recently, quantum wires became the focus of increasing interest [10–14]. Both, wires and dots show quantum confinement effects when their diameters are small enough. In addition, the surface of these structures may determine their overall properties. Silicon is at the center of today’s modern elec*Corresponding author. Tel.: 11-808-956-8941; fax: 11-808956-7107. E-mail address: [email protected] (K. Sattler).
tronics consumer industry. From cars to washing machines, almost all consumer goods contain silicon microprocessors in some form. Silicon-based microelectronics is now a more than $100 billion per year industry worldwide, and it is still growing rapidly. Therefore, any new finding about silicon can make a difference in device performance and has the potential to become eventually applied in the semiconductor industry. Microelectronics may eventually go over to nanoelectronics [15–19] and may be the key technology in the 21st century [20,21]. New nanosize-specific functions are expected to exceed those of currently manufactured materials and instruments [7,22]. Nanostructures of silicon are considered to be among the constituents of future electronic devices. Because of the technological importance of Si, there is an enormous volume of published literature on the element. More than 5000 technical and scientific papers are published each year on the subject. How can there still be anything to learn about silicon? One answer is that most studies so far
0368-2048 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 00 )00114-6
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concentrated on bulk silicon. The transfer to the micron size scale does not change the principal properties of the material. Therefore, the physics of silicon in microelectronic units is similar to that of the bulk. In recent years however, microelectronics moved gradually toward nanoelectronics. Structures in electronic devices become significantly smaller and have reached the nanometre size range. Major changes in a material’s properties occur in this range due to quantum confinement [23–25]. Theoretically, small silicon clusters were first proposed to be fragments of the crystalline bulk [26,27]. The clusters were assumed to have diamond structure with non-relaxed surface atoms. Such tetrahedral-bond-network (TBN) clusters have many dangling orbitals and very low average coordination numbers. In further studies crystalline structures were shown either to correspond to high-energy local minima or to be highly unstable [28–32]. Ab initio electronic structure calculations have been used to predict lowest-energy structures for Si clusters in the size range of 2 to 14 atoms [28,29,33–42]. Raghavachari and co-workers [28,37–39] have used (uncorrelated) Hartree–Fock (HF) wave functions to optimize the cluster structures. Tomanek and Schlueter [41,42] used a local-density functional (LDF) method, Pacchioni and Koutecky [29] and Balasubramian [33,34] have performed configuration interaction (CI) calculations, and Ballone et al. [35] have used simulated annealing techniques for geometry optimization. All of these calculations are largely in agreement as to the equilibrium structures for very small silicon clusters. (Si) n with just a few atoms (n,10) were theoretically found to have compact atomic arrangement with cubo-octahedral or icosahedral structure. Theoretical results [42–47] have been confirmed experimentally by Raman spectroscopy [48] and anion photoelectron spectroscopy [49]. The close-packed structure is typical for metallic rather than covalent systems. As bulk silicon is a semiconductor (band gap 1.1 eV), a major change in the electronic properties can therefore be expected with size reduction. The critical size n* for a transition from metallic to covalent bonding was estimated, but with very different values: n* 5 100–1000 [42] and n* 5 50 [43]. Medium-sized silicon clusters, with up to several hundred atoms per cluster, are less well understood.
Various atomic structures have been proposed [43,50–54] and the HOMO–LUMO gap was calculated to depend strongly on the assumed structure [52,55]. Due to the relatively large number of atoms, semiempirical techniques such as the interatomic force field method [56] were used instead of ab initio techniques. In this size range there seems to be a major structural transformation. Jarrold et al. [57] found that clusters up to |27 atoms have a prolate shape while larger clusters have more spherical shapes. Other abrupt changes in properties of medium-sized Si clusters have been observed in photoionization measurements, at n* 5 20–30 [58], and in calculations of the size-dependent frequency shift in Raman spectroscopy (n* | 500) [59]. A structural transformation at n* would imply a concomitant change of the electric polarizabilities of the clusters. In a recent theoretical study of Si n with 10–20 atoms [60] the polarizability is found to be a slowly varying function of n. This indicates that n* is greater than 20. The early work of silicon clusters was inspired by studies of cluster beams. Such clusters are produced under high vacuum conditions and consequently do not have their surface bonds saturated. This situation changed in the early 1990s with a new development for nanostructured silicon. Solid silicon, when electrochemically etched, was made porous and found to show photoluminescence in the visible range [61]. Soon the new effect was attributed to silicon nanowires or particles present in the porous structure. It was supported by the observation that individual silicon particles indeed can show photoluminescence [62–69]. This development led to intense scientific activity to understand both the increase of the band gap (made responsible for the luminescence in the visible range due to interband transitions), and the observed high transition probability. The silicon particles, responsible for the photoluminescence, were considered to have their surface bonds passivated, in accordance with the experimental conditions during the production of porous silicon. Indeed it had been found that unpassivated silicon clusters did not emit any light after UV excitation [69]. Therefore interest in coming years moved away from pristine to passivated silicon clusters. Most of the work concentrated on hydrogen passivated [70– 72] and on oxidized silicon clusters [73–76]. Since the discovery of room-temperature visible
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photoluminescence in silicon nanocrystals [62] and porous silicon [61], the size-dependence of the energy gap of Si nanostructures has been discussed extensively [77–80]. The quantum size effect, resulting in a blue-shift of the energy gap with decreasing size, was widely believed to be at the heart of the novel optical properties [62,81–84]. The energy gap was found to increase significantly with decreasing size, typically between 1.3 and 2.5 eV for particles of 5 to 1 nm in size [84]. The experimental data often were described by the effective mass approximation (EMA). An inverse power law for the band gap behavior as a function of size is predicted by EMA and leads to very large band gaps for particles of small size. Different exponents in the power law have been discussed [23]. Due to the large number of studies it seems that passivated silicon clusters are now well understood. The properties of pristine silicon clusters differ significantly from those of passivated clusters. Early studies in beams [85] and theoretical work showed that the energy gaps of small silicon clusters vary strongly with size [41,42] and structure [55]. Furthermore, the unpassivated silicon clusters are predicted to have energy gaps much smaller than expected from the quantum size effect. For very small Si clusters band gaps below the bulk gap of 1.1 eV [41,42,86,87] and even zero gaps are predicted [50,87]. What a difference the surface passivation makes was illustrated recently in a calculation of pristine silicon clusters and their hydrogenated counterparts [88]. The pristine clusters show a density of states with zero energy gap between HOMO and LUMO. The passivated clusters however show wide band gaps up to 3.4 eV. Obviously, simple models like the effective mass approximation may not be applicable for pristine silicon clusters. EMA is a continuum approach which does not consider the complexity of the atomic structure, the unsaturated surface and the significant changes in hybridization which can occur when the size of pristine silicon particles is reduced. For bulk silicon, the pristine surface contains a high density of dangling bonds. Different facets on a silicon crystal reconstruct in many ways to minimize the surface energy. The 737 reconstruction of the Si(111) surface is the best known example. While reconstruction leads to a reduction of surface dangling bonds it does not eliminate them completely.
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Therefore the reconstructed silicon surface still contains a large amount of dangling bonds and shows strong chemical reactivity. The silicon surface oxidizes rapidly under ambient conditions. The reactivity of silicon clusters is somewhat reduced [89] compared to the bulk but is still very high. Even though some of the dangling bonds disappear by backbonding, relaxation and reconstruction, many are left on the cluster surface. One should note that the smallest clusters consist exclusively of surface atoms. When the surface of such a cluster reconstructs, there is no core-structure left as the whole cluster transforms towards to a more favorable configuration with fewer dangling bonds. In 1989, Kuk et al. [90] published the only paper so far where the band gap of neutral, pristine silicon clusters was determined experimentally. Size-selected Si 10 clusters had been deposited on a Au(001) (5320) surface and imaged by STM in ultrahigh vacuum. Current–voltage curves yielded a band gap of |1 eV. Some of the STM images showed a dark ring around a cluster, apparently due to charge transfer from the surrounding metal substrate to the cluster. A wide variety of cluster sizes was observed even though size-selected clusters were deposited, apparently due to different adsorption sites at the surface and due to the formation of islands. It appears that the deposited Si 10 clusters were strongly affected both by contact among each other (in the islands) and by cluster–substrate interaction. The observed band gap of |1 eV therefore may have shown the combined system of cluster and substrate rather than the individual clusters. The purpose of this work is to determine the energy gap of pristine silicon particles over a size range where major size-dependent changes are expected. Using STM and STS as local probes allows us to study individual clusters. STM is used to image the clusters and the surrounding support and to determine cluster sizes and shapes. STS is used to measure the energy gap.
2. Experimental The clusters were grown on highly oriented pyrolytic graphite (HOPG) upon submonolayer deposition of silicon. Starting from a base pressure of 5310 28 Torr, the deposition was done by DC
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magnetron sputtering of silicon at an argon pressure of 5 to 8 mTorr. In this configuration, it is expected that about 5–10% of the depositing flux of Si is ionized [91]. The silicon target was of 99.999% purity. Before the actual deposition, it was pre-sputtered with the shutter closed, in order to remove a possible oxide layer and surface contaminants. The samples were then exposed to the sputter source for less than 10 s, in order to obtain submonolayer coverage. During the deposition, the discharge current was limited to 50 mA and the voltage was 400 V. At this voltage, silicon atoms are by far the largest fraction of the sputter products [92]. Quite generally, the energy distribution of the sputtered particles has a maximum between half and the full surface binding energy. At high emerging energies the number of sputtered particles mostly decreases inversely proportional to the energy [93]. Once the Si atoms arrive on the HOPG substrate, they are quickly thermalized. The substrates were kept at room temperature during the deposition. With this technique the clusters form after surface diffusion by quasi-free growth on the inert substrate. After the deposition the samples were transferred to the STM chamber (1310 210 Torr). The samples were analyzed by STM at room temperature. Since local STS of clusters is not feasible at room temperature due to the thermal drift, voltage-dependent STM [94] was our STS method of choice. Using this technique, the cluster can be monitored and one can compensate for a small drift. It has been shown that local STS and voltage-dependent STM give comparable results for spectra of an adsorbate [94]. One difference is that the tip distance changes with the bias voltage due to the feedback loop of the STM. The higher the bias voltage, the greater the tip distance will be to keep the tunneling current the same. For the gap determination however, this does not make a difference. Once a Si cluster was selected, a series of STM images at different bias voltages was recorded. If the cluster has a gap and the bias voltage is tuned to be within the gap, there are no states available for tunneling. Accordingly, the cluster is ‘invisible’ until the bias voltage is high enough to allow tunneling into the ‘conduction band’ or out of the ‘valence band’ of the cluster. In constant-current mode this is
reflected by the apparent height Dz of the clusters as it varies with the bias voltage. The equivalent measurement in constant-height mode is the difference DI 5 Icluster 2 Isubstrate , where Isubstrate is the average tunneling current on the substrate and Icluster the current on top of the cluster. Each series of STM images yields a plot of Dz (or DI) as a function of V. To speed up the measurement process, a method was employed which simultaneously recorded images at two different bias voltages, using a multiplexing technique. Even pixels were recorded at bias 1 and odd pixels at bias 2. The preferred setting was to record positive and negative bias at the same time (e. g. 1800 mV and 2800 mV). This technique keeps the z-movement of the tip to a minimum. Clusters in the size range from a few Angstroms to a few nanometres were analyzed on the substrates. The fact that this range of sizes can be found with the same STM tip indicates that it is really the cluster’s and not the tip’s geometry that is being imaged. Still the tip shape may add a little to the apparent lateral size of the clusters. Samples produced at a discharge current of 50 mA or below had well-separated clusters on the smooth HOPG substrate. At higher currents, the coverage was higher and coalescence of clusters was observed. For longer exposure and higher currents we have reported the formation of nanoscale silicon wires [10] on the substrate. The cluster–substrate interaction is an important aspect to consider for the STS studies. A metal surface seems to have an influence on an adsorbed cluster which is too strong for obtaining the properties of the free cluster. On the other hand, for STM and STS studies a conductive substrate is required. The surface of highly-oriented pyrolytic graphite (HOPG) seems to be a reasonably suitable substrate for the investigation of individual clusters by STM and STS. The HOPG surface consists of the perfectly ordered graphene layer with practically no defects (where clusters could be trapped). This can be verified experimentally by STM before the clusters are deposited. The sp 2 nature of the carbon atoms in a graphite layer guarantees that the surface is chemically inert. Any cluster–substrate interaction with the formation of chemical bonds would require a major change in the hybridization locally at the site where the cluster is adsorbed. This would lead to significant
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strain of the cluster and of the graphene layer at the adsorption site. The large strain energy [95] would have to come from the gain in energy due to the bond formation. The well-known nonreactive nature of HOPG and the observed low sticking coefficients for many atoms and molecules (at room temperature) shows that chemisorption is not a process to occur for clusters adsorbed on HOPG. This is supported by studies [96] reporting high scattering yields of Si 1 n and Si n2 (n55–24) impinging on HOPG. Impinging Si clusters have very low sticking probability and are easily re-emitted. If the clusters are formed at the substrate, they are kept on the support by physisorption due to small electrostatic dipole forces.
3. Results and discussion ˚ cluster is shown in Fig. An STM image of a 2.5 A 1. The size of the cluster is determined by taking the full width at half maximum of the intensity distribution. The exact 3-dimensional shape of the clusters cannot be extracted from the STM images. Furthermore, the apparent lateral size of the clusters changes with the bias voltage. At higher bias voltages, there is a regime of saturation for the lateral size. Therefore, an average diameter from several high-bias STM images is used. The uncertainty in this procedure is about 10%.
˚ silicon cluster on HOPG, Fig. 1. STM topograph of a 2.5 A recorded at a bias voltage of 280 mV and a setpoint current of 0.76 nA. The scan size is 3 nm.
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The atomic structure of graphite is visible. No other adsorbed cluster is in the vicinity. Also, the graphite lattice around the cluster is not distorted. It indicates that the interaction between cluster and substrate is small. In fact we were able to move such clusters on the substrate by using the STM tip without changing the cluster’s shape. The atomic structure on top of the cluster is not resolved. The cluster’s imaged topography and shape depends on the tunneling parameters, which are the bias voltage and the setpoint current. Fig. 2 shows a sequence of STM images of the 2.5 ˚ A-cluster. The bias voltage has been varied from 2600 mV to 1600 mV in steps of 25 mV, 50 mV or 100 mV. The apparent height of the cluster stays nearly constant from 2600 mV to 2250 mV. Then, with further increase of the bias voltage, there is a sudden drop. Between 2100 mV and 1100 mV the cluster’s intensity is close to that of the background. Between 100 mV and 200 mV the intensity comes back to the original value. The drop of the apparent height at low bias voltages is illustrated by the section scans in Fig. 3. Between 2100 mV and 1100 mV the apparent height of the cluster is strongly reduced. From such section scans, the DI values are extracted. ˚ The DI(V ) curve for the 2.5 A-cluster is shown in Fig. 4a. The DI values were taken from the sequence of images shown in Fig. 2. DI is a measure for the density of states (DOS) of the cluster. It is not just proportional though, since the transmission coefficient also depends on the tip distance. Still, a reduction of DI means that fewer states are available for electrons to tunnel into or out of the cluster. The value of DI is close to zero in a range from 2100 mV to 1100 mV. This range DV1 5 200 mV and the range DV2 5 350 mV between the first ‘non-zero’ DI values will be used in the determination of the energy gap. In the present case we obtain a gap of Egap 5 1 / 2 e(DV2 2 DV1 ) 5 275 meV. The observed gap is symmetric around zero bias voltage. This shows that there is no charge transfer between cluster and substrate. Charge transfer would lead to a contact potential, which would produce a shift of the energy levels of the cluster relative to those of the substrate. Apart from small variations, the apparent height of the cluster is the same on both sides of the gap. The small variations fall within the error of
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˚ silicon cluster. Voltage-dependent STM was performed at bias voltages in the range of Fig. 2. A series of 20 STM images of the 2.5 A 2600 mV to 1600 mV. The scan size is 3 nm. The setpoint current was kept constant at 0.76 nA. Contrast is enhanced for the images with low bias voltages.
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˚ cluster at bias voltages of 2600 mV, 2200 mV, 2100 mV, 100 mV, 200 mV and 600 mV. The dependence of the apparent Fig. 3. STM images and section scans of the 2.5 A height on the bias is clearly visible.
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Fig. 4. DI(V ) plot for five different clusters. DI is the difference between the tunneling currents measured with the tip located on top of the Si cluster or on the substrate. The points are connected ˚ cluster. Egap 5275 meV. (b) 9 A ˚ cluster. to guide the eye. (a) 2.5 A The STM images were recorded at a setpoint current of 0.76 nA, and at bias voltages between 2500 mV and 11000 mV. Egap 5380 ˚ cluster. The STM images were recorded at a meV. (c) 8.5 A setpoint current of 0.90 nA, and at bias voltages between 2600 ˚ cluster. The STM mV and 1550 mV. Egap 5370 meV. (d) 9 A images were recorded at a setpoint current of 1.00 nA, and at bias voltages between 2700 mV and 1700 mV. Egap550 meV. (e) 16 ˚ cluster. Egap 50 meV. The STM images were recorded at a A setpoint current of 1.00 nA, and at bias voltages between 2500 mV and 1500 mV.
about 5%. The observed DI levels on both sides indicate similar density of states close to the band edges for both occupied and unoccupied energy states. The plot in Fig. 4b shows the DI(V ) distribution ˚ for a 9 A-cluster. Again, there is a range of bias voltages where DI is exactly zero. At the band edges there is a more gradual increase of the intensity. The gap and the slopes of DI are symmetric around zero
bias. The measurements are extended to bias voltages of up to 800 mV. One finds that the conduction band is at least 600 mV broad. ˚ The DI(V ) curve in Fig. 4c is from an 8.5 Acluster. Gap and DI(V ) slopes are again symmetric around zero bias. There is one narrow feature close to the conduction band edge at 1450 meV and another one at 2350 meV in the valence band. There are no cluster states in the gap. ˚ The DI(V ) distribution for a 9 A-cluster is shown in Fig. 4d. The cluster has a very small gap, between 25 and 100 meV wide. The valence band shows two pronounced peaks, at 2550 meV and 2250 meV. In the conduction band there is one pronounced peak at 1350 meV. The observed peaks in the spectrum are ˚ different from those of the 8.5 A-cluster. ˚ cluster is shown. In Fig. 4e the DI(V ) of a 16 A This is one case where DI does not drop to zero — the cluster remains visible throughout the whole range from 2500 mV to 1500 mV. In all cases, the observed features in the bias range 61 V are remarkably different from the featureless bulk DOS at the band edges [97]. In Fig. 5 the energy gap of the analyzed clusters is plotted versus the cluster size. In the range between ˚ and 40 A ˚ only clusters with zero gap are 15 A observed. For smaller clusters, zero gaps are found ˚ as well but non-zero gaps predominate. Below 15 A the gaps tend to increase with decreasing cluster size. The largest gap recorded is 450 meV, for clusters ˚ and 8.5 A. ˚ There is significant scatter of the with 5 A
Fig. 5. Energy gap values as a function of cluster size. For clusters with zero gaps, error bars are omitted for better readability.
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data points in the small size range. Clusters of similar size can have very different energy gaps. For ˚ we find a zero-gap cluster and example at 861 A one with a 250-meV gap. A variety of calculated energy gaps of silicon clusters is shown in Fig. 6. These have been obtained by density functional theory (DFT) [42,50,60,98,99], tight-binding (TB) methods [42,86], or self-consistent-field (SCF) algorithms [86,100,101]. Many results are present for clusters of up to 14 atoms, and there is a large scatter of the gaps between zero and 3.4 eV. Over the whole range from Si 2 to Si 61 , several clusters show zero gaps. We note that clusters with different geometries (isomers) are calculated. The various theoretical approaches can give different gaps for the same geometry [42]. The calculations are performed on the lowest-energy structures or on the structures of isomers low in energy. Fig. 6 illustrates that a spread of gap data can be expected for small silicon clusters. Slightly different size may have a significant effect on the cluster’s structure and electronic properties. We have determined the cluster sizes with an error bar of typically 610%. For a semi-spherical cluster we can relate a given diameter to the number of atoms using the expression n(d) 5 1 / 12 pr d 3 , where r is the number density of Si and n the number of atoms in the
Fig. 6. Calculated energy gaps for silicon clusters. This is an assembly of several studies of silicon clusters using density functional theory (DFT) [42,50,60,98,99], tight-binding (TB) methods [42,86], or self-consistent-field (SCF) algorithms [86,100,101]. For comparison, the present data are included as well.
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cluster. Using the number density of bulk silicon we ˚ 3 . It follows that 13 atoms obtain n(d) 5 0.0131 (d / A) ˚ Si-cluster; 9 A ˚ and 11 A ˚ are in a semi-spherical 10 A Si clusters contain n510 and 17 atoms, respectively. These small-sized clusters are known to have properties depending strongly on their size. One atom more or less may have a pronounced effect on the cluster’s electronic structure. Therefore the energy gap can strongly differ for clusters of similar size. In our experiment we do not determine the number of atoms in a cluster but rather its diameter. In the uncertainty window of 610% there are clusters with slightly different numbers of atoms. Such spread in the number of atoms per cluster explains the observed scatter of gap data. The results are surprising at first. The gaps for ˚ are far below the 1.1 eV clusters smaller than 15 A gap of silicon bulk or the enhanced values due to the quantum size effect. In order to check whether clusters with very large gaps are present we have applied bias voltages up to 62.5 V. Therefore cluster with gaps up to 5 eV could have been detected. Since we do not see anything near the 2 eV to 4 eV gaps reported for surface-passivated clusters (both experimentally [64,68,69,73–76,78,84,102,103] and theoretically [23,70,71,77,80,104–107]) we conclude that the gaps of unpassivated and passivated silicon clusters are entirely different. For unpassivated silicon clusters, dangling bonds may be present at the surface. It is a consequence of the strong directional properties of the sp 3 hybrids and the missing neighbors at the surface. The extended surfaces of bulk silicon show a high density of dangling bonds. Each dangling bond contributes a partially filled surface state. Therefore these states are located in the energy gap around the Fermi level [111–113]. This has been well-demonstrated using a number of methods including tunneling spectroscopy [108–110] and photoemission [115]. On the Si(111) (231) surface for example, STS measurements show the surface state gap of 450 meV [112] rather than the bulk Si gap of 1.1 eV. Since bulk and surface states exhibit different properties, the core and the surface area of a pristine silicon cluster need to be considered separately. In fact, a recent calculation of Si 29 , Si 87 , and Si 357 shows density of states with zero energy gap between HOMO and LUMO [88]. The passivated
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clusters, Si 29 H 36 , Si 87 H 76 , and Si 357 H 204 , however, show the broad band gaps of 3.44 eV, 2.77 eV and 1.99 eV, respectively. Evidently the zero gap of the pristine particles originates from the surface states. In our experiment we observe zero band gaps for ˚ The clusters all clusters with sizes larger than 15 A. appear electrically conductive at all applied bias voltages. We assume that dangling bond states make the surface regions of the clusters conductive. Electrons tunneling between STM tip and sample rather pass through the conducting cluster surface than through the insulating core. Therefore zero band gaps are observed for large silicon clusters. This is independent of the particle diameter within our probed size range. Two transport mechanisms explain the conducting properties of the cluster surface. For high density, the surface states overlap forming a conduction band. The cluster surface then shows the transport properties of a metal. For lower state density, thermally activated hopping between the localized surface states leads to the observed conducting behavior. At present, we cannot decide which of the two transport mechanisms describes our observations. ˚ corresponding to about 44 atoms At about 15 A, per cluster, a major change in the cluster properties occurs. The energy gap opens up and subsequently widens for smaller clusters. Evidently those clusters have no dangling bonds. Hence they must assume a more compact configuration different from the diamond structure. This is in analogy to the extended Si surface facets, which eliminate dangling bonds by reconstruction such as the Si(111) (231) surface [114]. This change to non-zero energy gaps shows a transformation of the electronic structure of the clusters. We associate it with the covalent–metallic transformation suggested previously for silicon clusters by several groups. Accordingly, large silicon clusters are sp 3 hybridized with strong covalent bonds and rigid bond angles giving rise to high surface state density. Around a critical size n* the sp 3 nature of the bonds gradually changes to hybridization other than sp 3 or even to the atomic s and p configurations. In fact, ab initio calculations show that sp 3 is not the favored hybridization for small silicon particles. The change of the electronic structure at the critical size also means a change in the
atomic structure of the clusters. Below n* the clusters are not fragments of the bulk anymore but rather have their cluster-specific structures. These are close-packed structures resembling those of metals. In this sense one may say that at n* a covalent– metallic transition occurs. The use of the term ‘metallic’ may be confusing if small clusters or molecules are considered. It is taken from the bulk solid and is not well defined for nanoclusters. Close-packed crystal structure and zero energy gap between valence and conduction band characterize a metal. A cluster of metal atoms, decreasing in size, may keep the metallic bond character while approaching a nonzero energy gap. Similarly, a small silicon cluster may be closepacked with metallic-type bonding but still exhibiting a non-zero energy gap. Some of the studied silicon clusters exhibit zero˚ as seen in Fig. 8. energy gaps even below 15 A, These clusters have the surface state configurations similar to the larger clusters. It shows that the transition of the electronic properties does not occur for all silicon clusters. Some clusters have sp 3 coordinated bonds even at very small size. They coexist with the compact clusters as structural isomers. This is not surprising because silicon bonds are very strong and many isomers are stable at room temperature. The observation of various band gaps for similarly sized clusters is also a consequence of the analysis of individual clusters using STM and STS. ˚ diameter contains about A silicon cluster of 15 A 44 atoms, with the bulk structure of silicon being assumed for the volume density. This critical size of n* 5 44 can be compared to the widely different theoretical estimates (n* 5 30–4000) [30,41,43,116,117]. A covalent–metallic transition has been postulated but it has not been observed experimentally. Yet there are some indications that such a transition may occur, as a function of cluster size. Chemical reactions of Si 1 show significant n changes in the chemisorption probabilities at n529– 36 (for O 2 adsorption) [89]. The dissociation energy of Si n1 starts to deviate from the smooth size behavior below about n540 [118]. The photoionization threshold exhibits a drop at n | 20–30 [58]. In summary, we have measured the energy gap of pristine silicon clusters with diameters between 2.5
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˚ and 40 A, ˚ using scanning tunneling spectroscopy. A We have observed two size ranges with significantly different electronic properties. Energy gaps up to 450 ˚ or smaller, while all meV exist for clusters of 15 A the larger clusters show zero energy gaps. This observation leads us to conclude that a major transition in the cluster structures occurs at a size of about ˚ that corresponds to about 40–50 atoms per 15 A cluster.
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The energy gap of pristine silicon clusters B. Marsen, M. Lonfat, P. Scheier, K. Sattler* Department of Physics and Astronomy, University of Hawaii, 2505 Correa Road, Honolulu, HI 96822, USA
Abstract Studies of the fundamental energy gap of pristine silicon clusters have been performed using STM and STS. Clusters with ˚ are studied. The size dependence of the gap is determined. For particles below 15 A, ˚ gaps up to sizes between 2.5 and 40 A 450 meV are found. Larger particles exhibit zero gaps. The results are explained in terms of a transformation from diamond ˚ (|44 atoms per cluster). For clusters with diamond structure the surface dangling to compact structure occurring at 15 A bond density is high leading to electronic states filling the energy gap. On the other hand, the compact arrangement of the smaller clusters tends to eliminate dangling bonds. Therefore, finite-gap values are observed for clusters with less than |44 atoms. 2000 Elsevier Science B.V. All rights reserved. Keywords: Silicon clusters; STM; STS; Semiconductors
1. Introduction In recent years extensive work has been performed on semiconductor nanostructures. The most often investigated structures are clusters and nanocrystals [1]. In particular, the electronic band structure of semiconductor quantum dots is of interest [2]. Also the carrier transport and tunneling through dots [3,4], arrays of dots [5], and nanogranular semiconductors [6–8] are important issues. Cluster-assembled materials [9] are new granular materials with quantumconfinement determining their properties. Recently, quantum wires became the focus of increasing interest [10–14]. Both, wires and dots show quantum confinement effects when their diameters are small enough. In addition, the surface of these structures may determine their overall properties. Silicon is at the center of today’s modern elec*Corresponding author. Tel.: 11-808-956-8941; fax: 11-808956-7107. E-mail address: [email protected] (K. Sattler).
tronics consumer industry. From cars to washing machines, almost all consumer goods contain silicon microprocessors in some form. Silicon-based microelectronics is now a more than $100 billion per year industry worldwide, and it is still growing rapidly. Therefore, any new finding about silicon can make a difference in device performance and has the potential to become eventually applied in the semiconductor industry. Microelectronics may eventually go over to nanoelectronics [15–19] and may be the key technology in the 21st century [20,21]. New nanosize-specific functions are expected to exceed those of currently manufactured materials and instruments [7,22]. Nanostructures of silicon are considered to be among the constituents of future electronic devices. Because of the technological importance of Si, there is an enormous volume of published literature on the element. More than 5000 technical and scientific papers are published each year on the subject. How can there still be anything to learn about silicon? One answer is that most studies so far
0368-2048 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 00 )00114-6
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concentrated on bulk silicon. The transfer to the micron size scale does not change the principal properties of the material. Therefore, the physics of silicon in microelectronic units is similar to that of the bulk. In recent years however, microelectronics moved gradually toward nanoelectronics. Structures in electronic devices become significantly smaller and have reached the nanometre size range. Major changes in a material’s properties occur in this range due to quantum confinement [23–25]. Theoretically, small silicon clusters were first proposed to be fragments of the crystalline bulk [26,27]. The clusters were assumed to have diamond structure with non-relaxed surface atoms. Such tetrahedral-bond-network (TBN) clusters have many dangling orbitals and very low average coordination numbers. In further studies crystalline structures were shown either to correspond to high-energy local minima or to be highly unstable [28–32]. Ab initio electronic structure calculations have been used to predict lowest-energy structures for Si clusters in the size range of 2 to 14 atoms [28,29,33–42]. Raghavachari and co-workers [28,37–39] have used (uncorrelated) Hartree–Fock (HF) wave functions to optimize the cluster structures. Tomanek and Schlueter [41,42] used a local-density functional (LDF) method, Pacchioni and Koutecky [29] and Balasubramian [33,34] have performed configuration interaction (CI) calculations, and Ballone et al. [35] have used simulated annealing techniques for geometry optimization. All of these calculations are largely in agreement as to the equilibrium structures for very small silicon clusters. (Si) n with just a few atoms (n,10) were theoretically found to have compact atomic arrangement with cubo-octahedral or icosahedral structure. Theoretical results [42–47] have been confirmed experimentally by Raman spectroscopy [48] and anion photoelectron spectroscopy [49]. The close-packed structure is typical for metallic rather than covalent systems. As bulk silicon is a semiconductor (band gap 1.1 eV), a major change in the electronic properties can therefore be expected with size reduction. The critical size n* for a transition from metallic to covalent bonding was estimated, but with very different values: n* 5 100–1000 [42] and n* 5 50 [43]. Medium-sized silicon clusters, with up to several hundred atoms per cluster, are less well understood.
Various atomic structures have been proposed [43,50–54] and the HOMO–LUMO gap was calculated to depend strongly on the assumed structure [52,55]. Due to the relatively large number of atoms, semiempirical techniques such as the interatomic force field method [56] were used instead of ab initio techniques. In this size range there seems to be a major structural transformation. Jarrold et al. [57] found that clusters up to |27 atoms have a prolate shape while larger clusters have more spherical shapes. Other abrupt changes in properties of medium-sized Si clusters have been observed in photoionization measurements, at n* 5 20–30 [58], and in calculations of the size-dependent frequency shift in Raman spectroscopy (n* | 500) [59]. A structural transformation at n* would imply a concomitant change of the electric polarizabilities of the clusters. In a recent theoretical study of Si n with 10–20 atoms [60] the polarizability is found to be a slowly varying function of n. This indicates that n* is greater than 20. The early work of silicon clusters was inspired by studies of cluster beams. Such clusters are produced under high vacuum conditions and consequently do not have their surface bonds saturated. This situation changed in the early 1990s with a new development for nanostructured silicon. Solid silicon, when electrochemically etched, was made porous and found to show photoluminescence in the visible range [61]. Soon the new effect was attributed to silicon nanowires or particles present in the porous structure. It was supported by the observation that individual silicon particles indeed can show photoluminescence [62–69]. This development led to intense scientific activity to understand both the increase of the band gap (made responsible for the luminescence in the visible range due to interband transitions), and the observed high transition probability. The silicon particles, responsible for the photoluminescence, were considered to have their surface bonds passivated, in accordance with the experimental conditions during the production of porous silicon. Indeed it had been found that unpassivated silicon clusters did not emit any light after UV excitation [69]. Therefore interest in coming years moved away from pristine to passivated silicon clusters. Most of the work concentrated on hydrogen passivated [70– 72] and on oxidized silicon clusters [73–76]. Since the discovery of room-temperature visible
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photoluminescence in silicon nanocrystals [62] and porous silicon [61], the size-dependence of the energy gap of Si nanostructures has been discussed extensively [77–80]. The quantum size effect, resulting in a blue-shift of the energy gap with decreasing size, was widely believed to be at the heart of the novel optical properties [62,81–84]. The energy gap was found to increase significantly with decreasing size, typically between 1.3 and 2.5 eV for particles of 5 to 1 nm in size [84]. The experimental data often were described by the effective mass approximation (EMA). An inverse power law for the band gap behavior as a function of size is predicted by EMA and leads to very large band gaps for particles of small size. Different exponents in the power law have been discussed [23]. Due to the large number of studies it seems that passivated silicon clusters are now well understood. The properties of pristine silicon clusters differ significantly from those of passivated clusters. Early studies in beams [85] and theoretical work showed that the energy gaps of small silicon clusters vary strongly with size [41,42] and structure [55]. Furthermore, the unpassivated silicon clusters are predicted to have energy gaps much smaller than expected from the quantum size effect. For very small Si clusters band gaps below the bulk gap of 1.1 eV [41,42,86,87] and even zero gaps are predicted [50,87]. What a difference the surface passivation makes was illustrated recently in a calculation of pristine silicon clusters and their hydrogenated counterparts [88]. The pristine clusters show a density of states with zero energy gap between HOMO and LUMO. The passivated clusters however show wide band gaps up to 3.4 eV. Obviously, simple models like the effective mass approximation may not be applicable for pristine silicon clusters. EMA is a continuum approach which does not consider the complexity of the atomic structure, the unsaturated surface and the significant changes in hybridization which can occur when the size of pristine silicon particles is reduced. For bulk silicon, the pristine surface contains a high density of dangling bonds. Different facets on a silicon crystal reconstruct in many ways to minimize the surface energy. The 737 reconstruction of the Si(111) surface is the best known example. While reconstruction leads to a reduction of surface dangling bonds it does not eliminate them completely.
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Therefore the reconstructed silicon surface still contains a large amount of dangling bonds and shows strong chemical reactivity. The silicon surface oxidizes rapidly under ambient conditions. The reactivity of silicon clusters is somewhat reduced [89] compared to the bulk but is still very high. Even though some of the dangling bonds disappear by backbonding, relaxation and reconstruction, many are left on the cluster surface. One should note that the smallest clusters consist exclusively of surface atoms. When the surface of such a cluster reconstructs, there is no core-structure left as the whole cluster transforms towards to a more favorable configuration with fewer dangling bonds. In 1989, Kuk et al. [90] published the only paper so far where the band gap of neutral, pristine silicon clusters was determined experimentally. Size-selected Si 10 clusters had been deposited on a Au(001) (5320) surface and imaged by STM in ultrahigh vacuum. Current–voltage curves yielded a band gap of |1 eV. Some of the STM images showed a dark ring around a cluster, apparently due to charge transfer from the surrounding metal substrate to the cluster. A wide variety of cluster sizes was observed even though size-selected clusters were deposited, apparently due to different adsorption sites at the surface and due to the formation of islands. It appears that the deposited Si 10 clusters were strongly affected both by contact among each other (in the islands) and by cluster–substrate interaction. The observed band gap of |1 eV therefore may have shown the combined system of cluster and substrate rather than the individual clusters. The purpose of this work is to determine the energy gap of pristine silicon particles over a size range where major size-dependent changes are expected. Using STM and STS as local probes allows us to study individual clusters. STM is used to image the clusters and the surrounding support and to determine cluster sizes and shapes. STS is used to measure the energy gap.
2. Experimental The clusters were grown on highly oriented pyrolytic graphite (HOPG) upon submonolayer deposition of silicon. Starting from a base pressure of 5310 28 Torr, the deposition was done by DC
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magnetron sputtering of silicon at an argon pressure of 5 to 8 mTorr. In this configuration, it is expected that about 5–10% of the depositing flux of Si is ionized [91]. The silicon target was of 99.999% purity. Before the actual deposition, it was pre-sputtered with the shutter closed, in order to remove a possible oxide layer and surface contaminants. The samples were then exposed to the sputter source for less than 10 s, in order to obtain submonolayer coverage. During the deposition, the discharge current was limited to 50 mA and the voltage was 400 V. At this voltage, silicon atoms are by far the largest fraction of the sputter products [92]. Quite generally, the energy distribution of the sputtered particles has a maximum between half and the full surface binding energy. At high emerging energies the number of sputtered particles mostly decreases inversely proportional to the energy [93]. Once the Si atoms arrive on the HOPG substrate, they are quickly thermalized. The substrates were kept at room temperature during the deposition. With this technique the clusters form after surface diffusion by quasi-free growth on the inert substrate. After the deposition the samples were transferred to the STM chamber (1310 210 Torr). The samples were analyzed by STM at room temperature. Since local STS of clusters is not feasible at room temperature due to the thermal drift, voltage-dependent STM [94] was our STS method of choice. Using this technique, the cluster can be monitored and one can compensate for a small drift. It has been shown that local STS and voltage-dependent STM give comparable results for spectra of an adsorbate [94]. One difference is that the tip distance changes with the bias voltage due to the feedback loop of the STM. The higher the bias voltage, the greater the tip distance will be to keep the tunneling current the same. For the gap determination however, this does not make a difference. Once a Si cluster was selected, a series of STM images at different bias voltages was recorded. If the cluster has a gap and the bias voltage is tuned to be within the gap, there are no states available for tunneling. Accordingly, the cluster is ‘invisible’ until the bias voltage is high enough to allow tunneling into the ‘conduction band’ or out of the ‘valence band’ of the cluster. In constant-current mode this is
reflected by the apparent height Dz of the clusters as it varies with the bias voltage. The equivalent measurement in constant-height mode is the difference DI 5 Icluster 2 Isubstrate , where Isubstrate is the average tunneling current on the substrate and Icluster the current on top of the cluster. Each series of STM images yields a plot of Dz (or DI) as a function of V. To speed up the measurement process, a method was employed which simultaneously recorded images at two different bias voltages, using a multiplexing technique. Even pixels were recorded at bias 1 and odd pixels at bias 2. The preferred setting was to record positive and negative bias at the same time (e. g. 1800 mV and 2800 mV). This technique keeps the z-movement of the tip to a minimum. Clusters in the size range from a few Angstroms to a few nanometres were analyzed on the substrates. The fact that this range of sizes can be found with the same STM tip indicates that it is really the cluster’s and not the tip’s geometry that is being imaged. Still the tip shape may add a little to the apparent lateral size of the clusters. Samples produced at a discharge current of 50 mA or below had well-separated clusters on the smooth HOPG substrate. At higher currents, the coverage was higher and coalescence of clusters was observed. For longer exposure and higher currents we have reported the formation of nanoscale silicon wires [10] on the substrate. The cluster–substrate interaction is an important aspect to consider for the STS studies. A metal surface seems to have an influence on an adsorbed cluster which is too strong for obtaining the properties of the free cluster. On the other hand, for STM and STS studies a conductive substrate is required. The surface of highly-oriented pyrolytic graphite (HOPG) seems to be a reasonably suitable substrate for the investigation of individual clusters by STM and STS. The HOPG surface consists of the perfectly ordered graphene layer with practically no defects (where clusters could be trapped). This can be verified experimentally by STM before the clusters are deposited. The sp 2 nature of the carbon atoms in a graphite layer guarantees that the surface is chemically inert. Any cluster–substrate interaction with the formation of chemical bonds would require a major change in the hybridization locally at the site where the cluster is adsorbed. This would lead to significant
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strain of the cluster and of the graphene layer at the adsorption site. The large strain energy [95] would have to come from the gain in energy due to the bond formation. The well-known nonreactive nature of HOPG and the observed low sticking coefficients for many atoms and molecules (at room temperature) shows that chemisorption is not a process to occur for clusters adsorbed on HOPG. This is supported by studies [96] reporting high scattering yields of Si 1 n and Si n2 (n55–24) impinging on HOPG. Impinging Si clusters have very low sticking probability and are easily re-emitted. If the clusters are formed at the substrate, they are kept on the support by physisorption due to small electrostatic dipole forces.
3. Results and discussion ˚ cluster is shown in Fig. An STM image of a 2.5 A 1. The size of the cluster is determined by taking the full width at half maximum of the intensity distribution. The exact 3-dimensional shape of the clusters cannot be extracted from the STM images. Furthermore, the apparent lateral size of the clusters changes with the bias voltage. At higher bias voltages, there is a regime of saturation for the lateral size. Therefore, an average diameter from several high-bias STM images is used. The uncertainty in this procedure is about 10%.
˚ silicon cluster on HOPG, Fig. 1. STM topograph of a 2.5 A recorded at a bias voltage of 280 mV and a setpoint current of 0.76 nA. The scan size is 3 nm.
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The atomic structure of graphite is visible. No other adsorbed cluster is in the vicinity. Also, the graphite lattice around the cluster is not distorted. It indicates that the interaction between cluster and substrate is small. In fact we were able to move such clusters on the substrate by using the STM tip without changing the cluster’s shape. The atomic structure on top of the cluster is not resolved. The cluster’s imaged topography and shape depends on the tunneling parameters, which are the bias voltage and the setpoint current. Fig. 2 shows a sequence of STM images of the 2.5 ˚ A-cluster. The bias voltage has been varied from 2600 mV to 1600 mV in steps of 25 mV, 50 mV or 100 mV. The apparent height of the cluster stays nearly constant from 2600 mV to 2250 mV. Then, with further increase of the bias voltage, there is a sudden drop. Between 2100 mV and 1100 mV the cluster’s intensity is close to that of the background. Between 100 mV and 200 mV the intensity comes back to the original value. The drop of the apparent height at low bias voltages is illustrated by the section scans in Fig. 3. Between 2100 mV and 1100 mV the apparent height of the cluster is strongly reduced. From such section scans, the DI values are extracted. ˚ The DI(V ) curve for the 2.5 A-cluster is shown in Fig. 4a. The DI values were taken from the sequence of images shown in Fig. 2. DI is a measure for the density of states (DOS) of the cluster. It is not just proportional though, since the transmission coefficient also depends on the tip distance. Still, a reduction of DI means that fewer states are available for electrons to tunnel into or out of the cluster. The value of DI is close to zero in a range from 2100 mV to 1100 mV. This range DV1 5 200 mV and the range DV2 5 350 mV between the first ‘non-zero’ DI values will be used in the determination of the energy gap. In the present case we obtain a gap of Egap 5 1 / 2 e(DV2 2 DV1 ) 5 275 meV. The observed gap is symmetric around zero bias voltage. This shows that there is no charge transfer between cluster and substrate. Charge transfer would lead to a contact potential, which would produce a shift of the energy levels of the cluster relative to those of the substrate. Apart from small variations, the apparent height of the cluster is the same on both sides of the gap. The small variations fall within the error of
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˚ silicon cluster. Voltage-dependent STM was performed at bias voltages in the range of Fig. 2. A series of 20 STM images of the 2.5 A 2600 mV to 1600 mV. The scan size is 3 nm. The setpoint current was kept constant at 0.76 nA. Contrast is enhanced for the images with low bias voltages.
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˚ cluster at bias voltages of 2600 mV, 2200 mV, 2100 mV, 100 mV, 200 mV and 600 mV. The dependence of the apparent Fig. 3. STM images and section scans of the 2.5 A height on the bias is clearly visible.
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Fig. 4. DI(V ) plot for five different clusters. DI is the difference between the tunneling currents measured with the tip located on top of the Si cluster or on the substrate. The points are connected ˚ cluster. Egap 5275 meV. (b) 9 A ˚ cluster. to guide the eye. (a) 2.5 A The STM images were recorded at a setpoint current of 0.76 nA, and at bias voltages between 2500 mV and 11000 mV. Egap 5380 ˚ cluster. The STM images were recorded at a meV. (c) 8.5 A setpoint current of 0.90 nA, and at bias voltages between 2600 ˚ cluster. The STM mV and 1550 mV. Egap 5370 meV. (d) 9 A images were recorded at a setpoint current of 1.00 nA, and at bias voltages between 2700 mV and 1700 mV. Egap550 meV. (e) 16 ˚ cluster. Egap 50 meV. The STM images were recorded at a A setpoint current of 1.00 nA, and at bias voltages between 2500 mV and 1500 mV.
about 5%. The observed DI levels on both sides indicate similar density of states close to the band edges for both occupied and unoccupied energy states. The plot in Fig. 4b shows the DI(V ) distribution ˚ for a 9 A-cluster. Again, there is a range of bias voltages where DI is exactly zero. At the band edges there is a more gradual increase of the intensity. The gap and the slopes of DI are symmetric around zero
bias. The measurements are extended to bias voltages of up to 800 mV. One finds that the conduction band is at least 600 mV broad. ˚ The DI(V ) curve in Fig. 4c is from an 8.5 Acluster. Gap and DI(V ) slopes are again symmetric around zero bias. There is one narrow feature close to the conduction band edge at 1450 meV and another one at 2350 meV in the valence band. There are no cluster states in the gap. ˚ The DI(V ) distribution for a 9 A-cluster is shown in Fig. 4d. The cluster has a very small gap, between 25 and 100 meV wide. The valence band shows two pronounced peaks, at 2550 meV and 2250 meV. In the conduction band there is one pronounced peak at 1350 meV. The observed peaks in the spectrum are ˚ different from those of the 8.5 A-cluster. ˚ cluster is shown. In Fig. 4e the DI(V ) of a 16 A This is one case where DI does not drop to zero — the cluster remains visible throughout the whole range from 2500 mV to 1500 mV. In all cases, the observed features in the bias range 61 V are remarkably different from the featureless bulk DOS at the band edges [97]. In Fig. 5 the energy gap of the analyzed clusters is plotted versus the cluster size. In the range between ˚ and 40 A ˚ only clusters with zero gap are 15 A observed. For smaller clusters, zero gaps are found ˚ as well but non-zero gaps predominate. Below 15 A the gaps tend to increase with decreasing cluster size. The largest gap recorded is 450 meV, for clusters ˚ and 8.5 A. ˚ There is significant scatter of the with 5 A
Fig. 5. Energy gap values as a function of cluster size. For clusters with zero gaps, error bars are omitted for better readability.
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data points in the small size range. Clusters of similar size can have very different energy gaps. For ˚ we find a zero-gap cluster and example at 861 A one with a 250-meV gap. A variety of calculated energy gaps of silicon clusters is shown in Fig. 6. These have been obtained by density functional theory (DFT) [42,50,60,98,99], tight-binding (TB) methods [42,86], or self-consistent-field (SCF) algorithms [86,100,101]. Many results are present for clusters of up to 14 atoms, and there is a large scatter of the gaps between zero and 3.4 eV. Over the whole range from Si 2 to Si 61 , several clusters show zero gaps. We note that clusters with different geometries (isomers) are calculated. The various theoretical approaches can give different gaps for the same geometry [42]. The calculations are performed on the lowest-energy structures or on the structures of isomers low in energy. Fig. 6 illustrates that a spread of gap data can be expected for small silicon clusters. Slightly different size may have a significant effect on the cluster’s structure and electronic properties. We have determined the cluster sizes with an error bar of typically 610%. For a semi-spherical cluster we can relate a given diameter to the number of atoms using the expression n(d) 5 1 / 12 pr d 3 , where r is the number density of Si and n the number of atoms in the
Fig. 6. Calculated energy gaps for silicon clusters. This is an assembly of several studies of silicon clusters using density functional theory (DFT) [42,50,60,98,99], tight-binding (TB) methods [42,86], or self-consistent-field (SCF) algorithms [86,100,101]. For comparison, the present data are included as well.
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cluster. Using the number density of bulk silicon we ˚ 3 . It follows that 13 atoms obtain n(d) 5 0.0131 (d / A) ˚ Si-cluster; 9 A ˚ and 11 A ˚ are in a semi-spherical 10 A Si clusters contain n510 and 17 atoms, respectively. These small-sized clusters are known to have properties depending strongly on their size. One atom more or less may have a pronounced effect on the cluster’s electronic structure. Therefore the energy gap can strongly differ for clusters of similar size. In our experiment we do not determine the number of atoms in a cluster but rather its diameter. In the uncertainty window of 610% there are clusters with slightly different numbers of atoms. Such spread in the number of atoms per cluster explains the observed scatter of gap data. The results are surprising at first. The gaps for ˚ are far below the 1.1 eV clusters smaller than 15 A gap of silicon bulk or the enhanced values due to the quantum size effect. In order to check whether clusters with very large gaps are present we have applied bias voltages up to 62.5 V. Therefore cluster with gaps up to 5 eV could have been detected. Since we do not see anything near the 2 eV to 4 eV gaps reported for surface-passivated clusters (both experimentally [64,68,69,73–76,78,84,102,103] and theoretically [23,70,71,77,80,104–107]) we conclude that the gaps of unpassivated and passivated silicon clusters are entirely different. For unpassivated silicon clusters, dangling bonds may be present at the surface. It is a consequence of the strong directional properties of the sp 3 hybrids and the missing neighbors at the surface. The extended surfaces of bulk silicon show a high density of dangling bonds. Each dangling bond contributes a partially filled surface state. Therefore these states are located in the energy gap around the Fermi level [111–113]. This has been well-demonstrated using a number of methods including tunneling spectroscopy [108–110] and photoemission [115]. On the Si(111) (231) surface for example, STS measurements show the surface state gap of 450 meV [112] rather than the bulk Si gap of 1.1 eV. Since bulk and surface states exhibit different properties, the core and the surface area of a pristine silicon cluster need to be considered separately. In fact, a recent calculation of Si 29 , Si 87 , and Si 357 shows density of states with zero energy gap between HOMO and LUMO [88]. The passivated
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clusters, Si 29 H 36 , Si 87 H 76 , and Si 357 H 204 , however, show the broad band gaps of 3.44 eV, 2.77 eV and 1.99 eV, respectively. Evidently the zero gap of the pristine particles originates from the surface states. In our experiment we observe zero band gaps for ˚ The clusters all clusters with sizes larger than 15 A. appear electrically conductive at all applied bias voltages. We assume that dangling bond states make the surface regions of the clusters conductive. Electrons tunneling between STM tip and sample rather pass through the conducting cluster surface than through the insulating core. Therefore zero band gaps are observed for large silicon clusters. This is independent of the particle diameter within our probed size range. Two transport mechanisms explain the conducting properties of the cluster surface. For high density, the surface states overlap forming a conduction band. The cluster surface then shows the transport properties of a metal. For lower state density, thermally activated hopping between the localized surface states leads to the observed conducting behavior. At present, we cannot decide which of the two transport mechanisms describes our observations. ˚ corresponding to about 44 atoms At about 15 A, per cluster, a major change in the cluster properties occurs. The energy gap opens up and subsequently widens for smaller clusters. Evidently those clusters have no dangling bonds. Hence they must assume a more compact configuration different from the diamond structure. This is in analogy to the extended Si surface facets, which eliminate dangling bonds by reconstruction such as the Si(111) (231) surface [114]. This change to non-zero energy gaps shows a transformation of the electronic structure of the clusters. We associate it with the covalent–metallic transformation suggested previously for silicon clusters by several groups. Accordingly, large silicon clusters are sp 3 hybridized with strong covalent bonds and rigid bond angles giving rise to high surface state density. Around a critical size n* the sp 3 nature of the bonds gradually changes to hybridization other than sp 3 or even to the atomic s and p configurations. In fact, ab initio calculations show that sp 3 is not the favored hybridization for small silicon particles. The change of the electronic structure at the critical size also means a change in the
atomic structure of the clusters. Below n* the clusters are not fragments of the bulk anymore but rather have their cluster-specific structures. These are close-packed structures resembling those of metals. In this sense one may say that at n* a covalent– metallic transition occurs. The use of the term ‘metallic’ may be confusing if small clusters or molecules are considered. It is taken from the bulk solid and is not well defined for nanoclusters. Close-packed crystal structure and zero energy gap between valence and conduction band characterize a metal. A cluster of metal atoms, decreasing in size, may keep the metallic bond character while approaching a nonzero energy gap. Similarly, a small silicon cluster may be closepacked with metallic-type bonding but still exhibiting a non-zero energy gap. Some of the studied silicon clusters exhibit zero˚ as seen in Fig. 8. energy gaps even below 15 A, These clusters have the surface state configurations similar to the larger clusters. It shows that the transition of the electronic properties does not occur for all silicon clusters. Some clusters have sp 3 coordinated bonds even at very small size. They coexist with the compact clusters as structural isomers. This is not surprising because silicon bonds are very strong and many isomers are stable at room temperature. The observation of various band gaps for similarly sized clusters is also a consequence of the analysis of individual clusters using STM and STS. ˚ diameter contains about A silicon cluster of 15 A 44 atoms, with the bulk structure of silicon being assumed for the volume density. This critical size of n* 5 44 can be compared to the widely different theoretical estimates (n* 5 30–4000) [30,41,43,116,117]. A covalent–metallic transition has been postulated but it has not been observed experimentally. Yet there are some indications that such a transition may occur, as a function of cluster size. Chemical reactions of Si 1 show significant n changes in the chemisorption probabilities at n529– 36 (for O 2 adsorption) [89]. The dissociation energy of Si n1 starts to deviate from the smooth size behavior below about n540 [118]. The photoionization threshold exhibits a drop at n | 20–30 [58]. In summary, we have measured the energy gap of pristine silicon clusters with diameters between 2.5
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˚ and 40 A, ˚ using scanning tunneling spectroscopy. A We have observed two size ranges with significantly different electronic properties. Energy gaps up to 450 ˚ or smaller, while all meV exist for clusters of 15 A the larger clusters show zero energy gaps. This observation leads us to conclude that a major transition in the cluster structures occurs at a size of about ˚ that corresponds to about 40–50 atoms per 15 A cluster.
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