Theoretical studies of the effect of surface passivation on structural, electronic,and optical properties of zinc selenide clusters

Biplab Goswami, Sougata Pal, and Pranab Sarkar*Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India

�Received 19 October 2006; revised manuscript received 11 June 2007; published 20 July 2007�

We present results of our theoretical study of the effect of surface passivation on structural, electronic, andoptical properties of stoichiometric ZnnSen clusters. The effects of -H and -OH passivation on the electronicand optical properties of the clusters are calculated and are compared to that of ZnnSen clusters with truncatedsurfaces. The effects of surface passivation are seen to have a major influence on the band edge electronic andoptical properties.

DOI: 10.1103/PhysRevB.76.045323 PACS number�s�: 73.22.Dj, 61.46.�w, 36.40.�c, 78.67.Bf

I. INTRODUCTION

The electronic and optical properties of semiconductornanocrystals or quantum dots �QDs� have generated wide-spread interest in recent years.1–3 These nanocrystals or QDsrepresent a general class of materials that span the physicaldomain between the bulk materials and a molecule. Whenthe sizes of the nanocrystals become comparable to orsmaller than the bulk exciton Bohr radius, the electronic andoptical properties of these nanocrystals show a spectacularchange from their corresponding bulk properties. These re-sults from the spatial confinement of the nanocrystallites andare referred to as quantum size effects. One such effect is thequantization of the bulk valence and conduction bands,which results in discrete atomiclike transitions that shift tohigher energies as the size of the nanocrystallite decreases.Because of their unique size-dependent optical and electronicproperties, semiconductor nanocrystals are likely to play akey role in the emerging new field of nanotechnology, theapplication of which ranges from optoelectronic devices tobiological fluorescence marking.4–6

Although the real world application of semiconductornanocrystals requires extensive experimental research, theo-retical investigations are of crucial importance since theseallow both to investigate fundamental physics and to opti-mize nanostructured devices. However, theoretical studies ofsemiconductor nanocrystals composed of large number ofatoms are very demanding and one has to restore variousapproximations either in the theoretical method or moreor less realistic assumptions on the structure. Over the pastfew years, there are extensive theoretical studies on thesize evolution of electronic structure of semiconductornanocrystals.7–20 In experimental realizations, nanocrystalsare formed by kinetically controlled precipitation and areterminated with capping ligands, which provide stabilizationof the otherwise reactive dangling orbitals of surface atoms.In experimental studies, the band edge luminescence ofsemiconductor nanocrystal displays a prominent, size-dependent, redshift from the peak of the band edgeabsorption.21,22 This band edge luminescence has often beenattributed to the recombination of surface localized carriers.The role of surface-related states is a likely possibility sincea large number of atoms composing the nanocrystallite resideon the surface. Thus, the molecular nature of the surface

plays an important role in determining the electronic andoptical properties of semiconductor nanocrystals. In view ofthis, the theoretical studies of the role of surface on the elec-tronic properties of semiconductor nanocrystals have becomethe subject of extensive investigation. Thus, Wang andZunger23 and Rabani et al.24 studied the structural and elec-tronic properties of CdSe QDs by using an empirical ligandpotential. Melinon et al. have shown the significant effect ofthe surfactants on the band gap of Si clusters that essentiallychanges from 0 to 3.4 eV.25 Drager et al. have shown thatnot only the number but also the type of the ligands may alsoheavily influence optical properties of the nanoparticles.26,27

Pokrant and Whaley studied the effects of surface structureon electronic properties of CdSe clusters by using the tight-binding model.28 Huang et al. have recently studied the pas-sivated GaAs QDs by using fictitious hydrogen like pseudoa-toms as passivating agents.29 Very recently, Roy andSpringborg have studied the effects of ligands on structuraland electronic properties of InP clusters.30

Recently, we studied the structural, electronic, and opticalproperties of ZnmSen clusters with truncated surfaces.19 Weconsidered both stoichiometric �m=n� and nonstoichiometric�m�n� ZnmSen clusters that were derived from either zinc-blende or wurtzite crystal structures by cutting out a spheri-cal part and subsequently relaxing it to the closest total-energy minimum. ZnSe is a direct band gap semiconductorwith room temperature band gap energy and an emission at2.8 eV, which suggests that ZnSe is a potentially good ma-terial for short-wavelength lasers and other photoelectronicdevices. In addition, ZnSe is of special interest as it exhibits,via quantum confinement effects, tunable blue-ultraviolet�UV� luminescence. The UV range is practically unobtain-able for cadmium-based systems such as CdSe. ZnSe is oneof the promising material for fabrication of light-emittingdevices, such as blue-green laser diodes, and tunable mid-IRlaser sources for remote sensing applications.31–34 Althoughthere are quite a number of experimental studies on the sur-face passivated ZnSe nanocrystals in the literature,35–39 the-oretical studies addressing this issue are scarce and are there-fore highly desirable. In this paper, we propose to study thestructural, electronic, and optical properties of surface passi-vated ZnnSen clusters. In experimental studies, one oftenuses large organic molecules such as cystine or trioctylphos-phineoxide �TOPO�, but for computational reason we have

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chosen to work with smaller ones. In this work, we consid-ered -H and -OH atoms as the passivating agents. Our em-phasis will be on how the presence of surface passivationmodifies the structural, electronic, and optical properties ofZnSe clusters compared to clusters with truncated surfaces.By considering two different passivating agents, we wouldlike to study the dependence of electronic and optical prop-erties of the clusters on the nature of the passivating agents.The passivation with -OH atoms may mimic the passivationwith TOPO since it is the oxygen atom of TOPO that bindswith the metal atom of the semiconductor clusters. Now, oneof the major problems in the theoretical calculation of passi-vated clusters is the site selection, i.e., the site to which thepassivating agents are to be attached. Eichkorn and Ahlrichsstudied passivated CdSe clusters by adding ligands to theclusters so that all Cd and Se atoms were fourfoldcoordinated.40 Roy and Springborg have chosen the single-bonded surface atoms in their study with InP clusters.30 Fromour work on unpassivated ZnSe clusters,19 we have seen thatthe single-bonded atoms are those surface atoms that giverise to orbitals in the vicinity of Fermi level and the clusterswith single-bonded atoms have smaller band gap comparedto other clusters where there were no single-bonded atoms.Therefore, we have chosen to passivate only the single-bonded surface atoms.

This paper is organized as follows. In Sec. II, we brieflymention the density-functional method as used in the presentwork. We devote Sec. III to present and discuss the results ofour calculation on various finite clusters. Section IV containsa brief summary of our findings.

II. THEORETICAL METHOD

The calculational electronic-structure method used in thisstudy, the density-functional tight-binding method �DFTB�,has been described in detail elsewhere.41,42 The density-functional tight-binding method has been used by severalauthors for the structural optimization of the clusters.14–20

The DFTB method is a parametrized DFT scheme based onexpanding the solutions to the Kohn-Sham �KS� equations ina basis set of linear combination of atomic orbitals �LCAO�.The LCAOs were obtained from self-consistent, local-density-approximation calculations on the isolated, neutralatoms using a large set of Slater-type orbitals. For the systemof interest, the effective one electron potential in the KSHamiltonian is approximated by a superposition of theatomic potentials of the corresponding neutral, noninteract-ing atoms. Furthermore, only two-center Hamiltonian matrixelements are considered. The total energy is written as thesum of all occupied Kohn-Sham energies which representsthe “band-structure” energy and the repulsive two-centerterms between the atoms located at Rj and Rk as follows:

E = �i

occ

�i +1

2�j

�k�j

Ujk��R� j − R� k�� . �1�

The pair potentials Ujk are determined so that the total-energy curves of the diatomics are well reproduced. We havetested its transferability by performing calculations on infi-

nite periodic crystalline structures. For the calculations pre-sented here, only 4s and 3d electrons of zinc, the 4s and 4pelectrons of selenium, 2s and 2p electrons of oxygen, and 1selectron of hydrogen atoms were explicitly included. Wehave shown the optimized geometries of some representativeclusters �unpassivated and passivated with either -H or -OH�for both zinc blende and wurtzite types so obtained in Figs.1�a�–1�f�. Furthermore, we used an extension performingwithin the time-dependent density-functional response theory�TD-DFRT�43 for the calculation of the excitation spectra.The calculations performed by this program package is re-ferred to as TD-DFRT-TB. It was previously used for thecalculation of optical properties of CdS and ZnSeclusters.19,20

III. RESULTS AND DISCUSSIONS

In order to analyze different properties, we first define thecenter of the ZnmSen cluster through

R� 0 =1

n + m�j=1

n+m

R� j , �2�

where the summation goes over all the atoms of the cluster.Subsequently, the radial distance for the jth atom is definedas

FIG. 1. �Color online� Optimized structure of �a� unpassivated,�b� -H passivated, and �c� -OH passivated zinc-blende Zn16Se16

clusters and ��d�–�f�� that of wurtzite Zn26Se26 cluster.

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rj = �R� j − R� 0�, j = 1,2, . . . ,n + m . �3�

We show in Fig. 2 the radial distributions of eight differ-ent stoichiometric clusters with either zinc-blende �left col-umn� or wurtzite structure �right column� with or withoutsurface passivation. For the unpassivated clusters, wefound19 that the structural relaxations are almost throughoutthe whole region of the clusters with a somewhat larger re-laxation in the outer region. In this region, some atoms moveaway from the center of the cluster, whereas others approachthe center. Inspecting the radial distribution of the zinc andselenium atoms separately �not shown�, it is found that, inthe outer parts, only selenium atoms move outward, whereasthe zinc atoms move inward. Zinc, being a typical metalatom, prefers a high coordination, whereas the seleniumatom prefers a low coordination. In the presence of surfacepassivation, the general feature that the Zn atoms move in-ward while the Se atoms move outward remains the same.However, in the presence of surface passivation, the atomsare spatially less extended compared to unpassivated clustersas it is evident from the figure. This spatial quenching is

because of the bonding of the surface atoms with the passi-vating atoms, which restricts the outward movement of Seatoms. So our study suggests that passivation essentially re-duces the nanocrystal size and this observation is in goodagreement with recent experimental results of Sarigiannidiset al.39 They showed that organic ligand capped ZnSe nano-crystals have smaller size compared to ligand-free nanocrys-tals.

In Fig. 3, we have shown the Mulliken gross populationsfor the individual atoms as a function of their radial distanceof Eq. �3� for stoichiometric zinc-blende ZnSe clusters. Ineach figure, the left panel is for ligand-free clusters, themiddle panel for -H passivated clusters, and the right panelfor -OH passivated clusters. Only the valence electrons areincluded, i.e., for the neutral atoms these numbers would be12 for Zn and 6 for Se, and we would like to mention that theanalysis based on the Mulliken population is very muchqualitative in nature. From the figure, it is evident that theoutermost atoms in the clusters are Se atoms, while Zn atomsare lying relatively in the inner part of the clusters. This isbecause of the different types of hybridizations of Zn and Seatoms in the clusters. The figure shows that the gross popu-lations are markedly different from that of neutral atoms inthe surface region of the clusters. In this region, the chargeshifts to the Se sites and as a result charge is more localizedon Se sites. The other interesting feature which is clear fromthe figure is that compared to ligand-free clusters, the chargetransfer in -H passivated and in -OH passivated clusters areless in the surface region. The effect of the surface passiva-tion is therefore to reduce the charge transfer in the surfaceregion and the atoms with which the hydrogen atoms or -OHgroups are bonded experience the largest reductions. This isbecause the passivating atoms that are bonded with the Znatoms extract charge from the Zn atom and result in a chargelocalized toward the passivating atom sites. The other passi-vating atoms bonded with the Se atoms shows a differentfeature; the charge is located somewhere near the midpointbetween Se and passivating atoms. This feature, i.e., reduc-tion of charge transfer because of the surface passivation, hasfar reaching consequence in determining the optoelectronicproperties of the surface passivated nanocrystal, which wewill discuss in the subsequent section. We have not shownthe same results for wurtzite-derived clusters because thegeneral features differ only marginally from those of zinc-blende-derived clusters.

In Fig. 4, we have shown the total density of states ob-tained by broadening the individual electronic states slightlywith Gaussian for few representative clusters of both zinc-blende and wurtzite-derived clusters and with or without sur-face passivation. The general features are more or less thesame for all clusters. The bands corresponding to Se 4s func-tions lie in the range between −17.0 and −18.0 eV, the onecorresponding to Zn 3d in the range of −11 to −10 eV, andthe uppermost occupied band between −9.0 and −5.5 eV isformed mainly due to the Se 4p and partly by Zn 4s func-tions. In addition to these bands, both hydrogen passivatedand -OH passivated clusters have some bands in between−17.0 and −12.0 eV. These bands arise from bonds betweenthe surface atoms and the passivating atoms and have nocontribution from the interior of the cluster. These bands,

FIG. 2. Radial distribution of zinc and selenium atoms for zinc-blende- �left column� and wurtzite-derived clusters �right column�of different sizes and with two different types of passivation: �a�Zn16Se16�6�, �b� Zn37Se37�6�, �c� Zn58Se58�6�, �d� Zn83Se83�6�, �e�Zn26Se26�6�, �f� Zn45Se45�2�, �g� Zn58Se58�2�, and �h� Zn69Se69�14��The number within the parentheses denotes the number of passi-vated atoms�. In each panel, the curve pointing downward gives thedistribution of the unrelaxed cluster, whereas the curves pointingupward give the distribution for �from below� the unpassivated re-laxed cluster, the relaxed clusters passivated with -OH groups, andthe relaxed clusters passivated with hydrogen atoms.

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however, are predominant only for small clusters. Anotherimportant observation is that surface passivation removes theenergy band from the band gap region and in effect the high-est occupied molecular orbital–lowest unoccupied molecularorbital �HOMO-LUMO� gap for both hydrogen passivatedand -OH passivated clusters increases significantly comparedto ligand-free clusters. So our study confirms the fact that theenergy bands in the band gap region which were responsiblefor the low band gap for unpassivated clusters are because ofthe single-bonded atoms on the surface.

The optoelectronic properties and the reactivities of semi-conductor nanoparticles are largely controlled by the orbitalsclosest to the gap, i.e., the HOMO and the LUMO. So it isimportant to know the spatial distribution of HOMO andLUMO in the clusters. In order to arrive at a qualitativedescription of the distribution of the various orbitals, we de-fine a radial density as follows. With Nij being the Mullikengross population for the jth atom and ith orbital, we definethe following density:

�i�r�� = �j

Nij�2�3/2

��exp�− ��r� − R� j�2� , �4�

with � being a chosen, fixed constant. However, in reality,there are a number of degenerate or very nearby states closeto the gap, which also play crucial role in optoelectronicproperties. So we have calculated the spherical average ofthe radial density taking into account of all degenerate �ornearby� states, which is the one shown in Fig. 5 for fewrepresentative ligand-free and passivated �both -H and -OHpassivations� ZnSe clusters. The dotted, thin, and thick linesrepresent unpassivated, -H passivated, and -OH passivated

clusters, respectively. From the figure, it is very clear that inmost cases the passivation does affect the orbitals signifi-cantly and the effect of -H passivation and of -OH passiva-tions are quite different. The surface passivated clusters donot follow any general size-dependent trend in the spatialdistribution of HOMO and LUMO. For example, a carefulanalysis of contribution of different atoms to HOMO andLUMO shows that for some hydrogen atom passivated clus-ters �Zn16Se16 and Zn58Se58�, the main contributions toHOMO are from those Zn atoms to which hydrogen atomsare attached. For all other cases, the HOMO and LUMOhave very small contributions from those atoms which arepassivated. From this, we may infer that the HOMO andLUMO states are mostly located within the interior of thecluster with negligible surface overlap. The occupied surfacestates are removed from the gap to deep below the Fermilevel. The empty surface states are also removed from thegap region and displaced to higher energies. A detailedanalysis of the orbital population suggests that HOMO hasthe major contributions from Se atoms and that of LUMOfrom Zn atoms. This observation is in contrast to that ofGaAs dots,44 where both HOMO and LUMO seem to havecontributions from As anions.

Figure 6 shows the variation of the HOMO-LUMO en-ergy gap as a function of the size of the clusters for unpas-sivated, -H passivated, and -OH passivated clusters. Fromthe figure, it is seen that the band gaps are always higher forpassivated clusters compared to unpassivated clusters. Theunpassivated clusters have the lower band gap values, in ac-cordance with the fact that the frontier orbitals are localizedon those atoms which contain dangling bonds; hence, satu-rating those should lead to the increase in the band gap.

FIG. 3. Radial distribution ofMulliken gross populations for thevalence electrons of Zn and Se at-oms for zinc-blende clusters ofdifferent sizes ��a�, �e�, and �i��Zn16Se16, ��b�, �f�, and �j��Zn37Se37, ��c�, �g�, and �k��Zn58Se58, and ��d�, �f�, and �l��Zn83Se83. The left panel is for un-passivated clusters, the middlepanel for -H passivated clusters,and the right panel for -OH passi-vated clusters. The horizontaldashed lines mark the values forthe neutral atoms, i.e., 12 for Znand 6 for Se.

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However, the extent of the increase in band gap because ofsurface passivation depends on whether the clusters are pas-sivated by hydrogen atoms or -OH groups. A careful analysisof the Mulliken population of passivated Zn and Se atomsand those of passivating atoms �i.e., H or O� reveals a closecorrelation on the dependence of band gap on the nature ofsurface passivation. Our general observation is that thehigher the charge transfer from Zn to Se, the larger is theband gap. For -OH passivated clusters where the Zn atomsare bonded to O atom, less charge is available for transfer tothe Se atom since O atoms abstract some charge from Znatoms. However, for -H passivated clusters, there is rela-tively larger charge transfer from Zn to Se and accordingly-H passivated clusters have higher band gap compared to

-OH passivated clusters. As an illustrative example, we con-sider the magnitudes of charge transfer from Zn to Se forboth -H passivated and -OH passivated Zn58Se58 clusters.The values of charge transfer from Zn to Se for -OH passi-vated cluster is 0.233e, whereas that for -H passivated clusteris 0.432e. Pokrant and Whaley28 studied the passivated CdSenanocrystal and have observed a smaller increase in bandgap when passivated with oxygen containing ligands. Thepassivation with oxygen containing ligands very effectivelyremoved Zn dangling orbitals from the band gap region butis relatively ineffective at removing Se dangling orbitals. Thelack of passivation of surface Se atoms when such oxygencoordinating ligands are used was confirmed by experimentalstudies of the surface structure for related CdSe nanocrystalspassivated with ligands such as TOPO.45,46 Oxygen contain-

FIG. 4. Density of states �DOS� for different zinc-blende- �leftcolumn� and wurtzite-derived �right column� clusters of differentsizes as in Fig. 1. In each panel, the bottom, middle, and top curvesshow results for unpassivated, -OH passivated, and -H passivatedclusters, respectively. The vertical dashed lines mark the Fermienergy.

FIG. 5. The schematic representation of the radial distribution ofthe HOMO and the LUMO for zinc-blende- �left column� andwurtzite-derived clusters �right column� of different sizes as inFig. 1. The dotted, thin, and thick curves are for unpassivated, -Hpassivated, and -OH passivated clusters, respectively.

FIG. 6. HOMO-LUMO gap asa function of number of ZnSe pairfor �left� zinc-blende- and �right�wurtzite-derived clusters. The dot-ted, thin, and thick curves repre-sent the gap for unpassivated, -OHpassivated, and -H passivatedclusters, respectively.

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ing ligands are the most commonly used capping species,and therefore this result is of relevance to experimentallystudied ZnSe nanocrystals. The fact that the surface passiva-tion increases the band gap of ZnSe nanocrystal is in agree-ment with the recent experimental observations.37–39 Thus,Geng et al.37 showed that photoluminescence spectra of pas-sivated ZnSe nanocrystal are blueshifted compared to nakedZnSe nanocrystals. Karanikolos et al.38 have shown that thephotoluminescence spectra of passivated ZnSe quantum dotsare blueshifted compared to bulk ZnSe as the particle sizedecreases. In a very recent paper, Sarigiannidis et al.39 havestudied the vapor phase synthesis of passivated ZnSe nano-crystals and their luminescent properties. They have alsoshown that photoluminescence spectra of passivated ZnSenanocrystal show blueshift compared to the naked ZnSe. Oneimportant and interesting feature that emerges from Fig. 5�a�is that -H passivated zinc-blende ZnSe clusters with oddnumber of ZnSe pair �e.g., Zn23Se23, Zn37Se37, etc., with ex-ception Zn83Se83� have smaller band gap compared to clus-ters with even number of ZnSe pair �e.g., Zn28Se28, Zn58Se58,etc.�. For clusters with odd number of ZnSe pair, few atomshave different kinds of coordination from the rest, while forclusters with even number of ZnSe pair, all atoms have thesame kind of coordination. This different kind of coordina-tion for few surface atoms leads to differences in the magni-tude of charge transfer from Zn to Se. As we have alreadyseen that the values of the band gap depend on the magnitudeof the charge transfer from Zn to Se, it may be one of thereason behind the low values of the band gap for clusterswith odd number of ZnSe pair. In our earlier study19 withunpassivated II-VI semiconductor clusters, we observed amarked correlation between the energy gap and the total en-ergy; low total energy �higher stability� correlates with largeHOMO-LUMO gap. This finding may actually be consideredrelated to the hard and soft acid and base principle;47 systemsare particularly inert �stable� if their hardnesses are particu-larly large. As a first approximation, the hardness is simplythe HOMO-LUMO energy gap. This correlation remainspartly true for the passivated clusters, too. So the increase inband gap because of surface passivation may be interpretedas an indication of greater stability of the clusters. Thegreater stability of the passivated ZnSe nanocrystals is con-sistent with the experimental observation38 that the passi-vated ZnSe nanocrystals exhibit a smaller decrease in lumi-nescence intensity compared to unpassivated nanocrystals.

Finally, in Fig. 7, electronic excitations as computed withTD-DFRT43 are shown for different clusters �both passivatedand unpassivated�. The interesting feature of the figure is thevariation of the lowest excitation energies with the size of theclusters and also with the nature of surface passivation. Thelowest excitation energy shows a clear blueshift for passi-vated clusters �both zinc blende and wurtzite� compared tounpassivated clusters. For a particular size, the lowest exci-tation energy depends very much on whether the cluster is ofzinc blende or wurtzite type. This is true for both unpassi-vated and passivated clusters. Therefore, the main crystalstructure as well as surface passivation has strong influenceon the absorption spectrum of a cluster, particularly on themagnitude of the HOMO-LUMO gap.

IV. CONCLUSIONS

While bare semiconductor clusters may be studied in iso-lation in cluster molecular beams, application of clusters�e.g., in optical and electronic devices� requires the forma-tion of arrays of clusters deposited in a matrix or on a sub-strate surface. In order to manipulate clusters into bulk-phasematerials, one must first find methods to stabilize �or passi-vate� the clusters so that they can be brought into close prox-imity without coalescence. In the present paper, we havecalculated the electronic structure as a function of the nanoc-rystallite size for passivated ZnnSen semiconductor clustersby using the DFTB method. The motivation was to studyhow the surface passivation affects the structural, electronic,and optical properties of ZnnSen clusters compared to unpas-sivated clusters. We found that the surface passivation essen-tially reduces the size of the nanocrystal and largely sup-presses the Zn-to-Se charge transfer in the surface region ofthe clusters, which was found for unpassivated clusters. Thesurface passivation has strong influence on the orbital popu-lation of HOMO and LUMO. A detailed analysis of the or-bital population of HOMO and LUMO suggests that HOMOhas the major contribution from the Se atoms, whereas theLUMO has the major contributions from the Zn atoms. How-ever, these atoms are not necessarily those to which the pas-sivated atoms are attached, as it was expected. The surface

FIG. 7. TD-DFRT-TB spectra of zinc-blende- �left column� andwurtzite-derived �right column� ZnSe clusters of different sizes asin Fig. 1. Here, only the results for unpassivated �dotted line� andhydrogen passivated clusters �solid line� are shown. �All y axeshave the same scale, and all curves are broadened with Gaussians,0.27 eV.�

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passivation greatly enhances the HOMO-LUMO gap com-pared to unpassivated clusters and the increase is muchhigher for -H passivated clusters than -OH passivated clus-ters. The dependence of the HOMO-LUMO gap on the na-ture of surface passivation is closely correlated with the mag-nitude of the charge transfer from Zn to Se in the cluster.Hydrogen passivated zinc-blende ZnSe clusters with oddnumber of ZnSe pair have smaller band gap compared toclusters with even number of ZnSe pair. The increase in theHOMO-LUMO gap as a result of surface passivation may beinterpreted as greater stability of the clusters and is in agree-ment with the recent experimental observation. By using

time-dependent density-functional response theory withtight-binding approximation, we have calculated electronicexcitation energies for different size clusters. The lowest ex-citation energies show a clear blueshift for passivated clus-ters compared to unpassivated clusters.

ACKNOWLEDGMENTS

The financial support from CSIR, Government of India�01�1908�-EMR-II/2003�, and DST, Government of India,through research grants is gratefully acknowledged.

*Corresponding author; pranab�69@yahoo.co.in1 C. N. R. Rao, G. U. Kulkarni, P. J. Thomas, and P. P. Edwards,

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