Role of Surface Passivation and Doping in Silicon Nanocrystals

Journal of Computational Methods in Sciences and Engineering 7 (2007) 219–232 219IOS Press

Role of surface passivation and doping insilicon nanocrystals

R. Magria,∗, E. Degolib, F. Ioria, E. Luppia, O. Pulcic, S. Ossicinib, G. Canteled, F. Tranid andD. Ninnod

aCNR-INFM-S3-CNISM and Dipartimento di Fisica, Universita di Modena e Reggi Emilia, Via Campi213/A, I-41100 Modena, ItalybCNR-INFM-S3 and Dipartimento di Scienze e Metodi dell’Ingegneria, Universita di Modena e ReggioEmilia, via G. Amendola 2, I-42100 Reggio Emilia, ItalycEuropean Theoretical Spectroscopy Facility(ETSF) and Dipartimento di Fisica – Universita di Roma“Tor Vergata” Via della Ricerca Scientifica 1, I-00133 Roma, ItalydCNR-INFM-Coherentia and Dipartimento di Fisica, Universita di Napoli “Federico II”, ComplessoUniversitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy

Received 14 March 2007

Accepted 8 May 2007

Abstract. The absorption and the emission spectra of undoped and doped silicon nanocrystals of different size and surfaceterminations have been calculated within a first-principles framework. The effects induced by the creation of an electron-hole pairon the atomic structure and on the optical spectra of hydrogenated silicon nanoclusters as a function of dimension are discussedshowing the strong interplay between the structural and optical properties of the system. Starting from the hydrogenated clusters,(i) different Si/O bonding at the cluster surface and (ii) different doping configurations have been considered. We have foundthat the presence of a Si-O-Si bridge bond at the nanocrystal surface gives rise to significant excitonic luminescence features inthe near-visible range that are in fair agreement with photoluminescence (PL) measurements on oxidized and SiO2 embeddednanocrystals. The study of the structural, electronic and optical properties of simultaneouslyn- andp-type doped hydrogenatedsilicon nanocrystals with boron and phosphorous impurities have shown that B-P co-doping is energeticallyfavorable withrespect to single B- or P-doping and that the two impurities tend to occupy nearest neighbors sites. The co-doped nanocrystalspresent band edge states localized on the impurities that are responsible of a red-shifted absorption threshold with respect tothat of pure un-doped nanocrystals in agreement with the experiment.

1. Introduction

The extreme integration levels reached nowadays by Si microelectronics industry have permitted highspeed performance and unprecedented interconnection levels. However, the present interconnectiondegree is sufficient to cause interconnect propagations delays, overheating and information latency.To overcome these problems, photonic materials, in which light can be generated, guided, modulated,amplified and detected, need to be integrated with standard electronics circuits to combine the informationprocessing capabilities of electronic data transfer and the speed of light. In particular, chip to chip or

∗Corresponding author. E-mail: [email protected].

1472-7978/07/$17.00 2007 – IOS Press and the authors. All rights reserved

220 R. Magri et al. / Role of surface passivation and doping in silicon nanocrystals

even intra-chip optical communications all require the development of efficient optical functions andtheir integration with state-of-the-art electronic functions [1]. Silicon is the desired material, becauseSi-based optoelectronics would open the door to faster data transfer and higher integration densities atlow cost.

The main limitation of a silicon based photonics remains the lack of any practical Si-based lightsources. Several attempts have been employed to engineer luminescent transitions in an otherwiseindirect material [1]. Following the discovery of photoluminescence (PL) from porous silicon [2],extensive experimental and theoretical work has been devoted to nanostructured silicon [3], with theaim to get relevant optoelectronic properties from it. Optical gain was then found in Si-nc embedded inSiO2 [4]. It is generally accepted that the quantum confinement (QC), caused by the nanometric size, isessential for obtaining PL emission in Si-nc, but some PL features, such as: (i) the red-shift of the PLpeak with respect to the absorption onset (Stokes Shift); (ii) the substantial redshift (RS) of the PL energywith respect to the theoretical predictions based merely on the QC model and its independence from thesize for small (< 3 nm) crystallites, need still to be explained. Baierle et al. [5] and G. Allan et al. [6]stressed the importance of bond distortion at the Si-nc surface in the excited state (EXC) in creating anintrinsic localized state responsible of the PL emission. Wolkin et al. [7] observed that also oxidationintroduces states in the gap, which pin the transition energies. They and others [8,9] suggested that theformation of a Si=O double bond is responsible of the RS of the optical absorption edge upon oxidation.On the contrary, Vasiliev et al. [10] showed that similar absorption gaps can be obtained also in thecase of the O atom connecting two Si atoms (bridge bond) at the Si-nc surface. Recently TD-ALDAcalculations of Gatti and Onida [11] on six small different prototypical oxidized Si clusters found thatthe RS of the absorption edge is much more pronounced in the case of the double Si= O bond thanfor bridge bonds. Same results were reached also in Ref. [12] where many oxidized configurations forsilicon nanocrystals were considered using a TDDFT-B3LYP approach. Although all these calculationsaddress the absorption, yet the large majority of the experimental results and the most interesting onesare relative to PL measurements, thus are strictly related to the excited state.

Another way to circumvent the indirect gap behavior of bulk Si is given by the introduction in theSi-nc of an isoelectronic impurity or by a simultaneousn- andp-type impurity doping [13]. It hasbeen shown that the PL peak can be tuned also below the bulk Si band gap by properly controlling theimpurities, for example by B and P co-doping [13–15]. Besides, under resonant excitation condition,the co-doped samples did not exhibit structures related to momentum-conserving phonons, suggestingthat in this case the quasidirect optical transitions are predominant. Only few first principles studies ofimpurities in silicon quantum dots are present in the literature, and they are mainly devoted to quantumconfinement effects in singly doped Si-nc [16–18]. The results point out that the ionization energy ofthe singly doped Si-nc is virtually size independent and that the donor and acceptor binding energies aresubstantially enhanced.

In this paper we address the issue of the role played by the excited state in the determination of theStokes Shifts and the PL peak position in undoped and doped small hydrogenated Silicon clusters ofdifferent size and different surface terminations. In Section 2 we will describe the Constrained DensityFunctional Method applied to hydrogenated silicon clusters and report our results for the Stokes Shifts.In Section 3 we will show the absorption and emission spectra calculated for a small hydrogenatedsilicon cluster with an oxygen atom adsorbed on its surface. The optical spectra have been calculatedalso including excitonic effects. Finally, in Section 4 we discuss the effects of boron and phosphorusdoping and co-doping on the impurity formation energies and on the electronic and optical properties ofSi-nc. Some conclusions will be drawn at the end.

R. Magri et al. / Role of surface passivation and doping in silicon nanocrystals 221

2. Ground and excited state of hydrogenated Si nanocrystals

The study of the silicon nanocrystals (Si-nc) has been done within the DFT, using a pseudopotential,planewave approach [19]. The calculations of this section have been performed with the ABINITcode [20]. Norm-conserving, non-local Hamann-type pseudopotentials have been used. The Kohn-Sham wave functions have been expanded in a plane-wave basis set, with an energy cutoff of 32 Ry.Each Si-nc has been embedded within a large cubic supercell, containing sufficient vacuum in order tomake the interactions between nanocrystals negligible. Convergence with respect to both the energycutoff and supercell side has been carefully checked. A gradient corrected Perdew-Burke-Ernzerhof(GGA-PBE) exchange-correlation functional has been used for both structural and electronic propertiescalculations.

In the constrained DFT method, also referred to as the∆SCF approach, the excited state correspondsto the electronic configuration in which the highest occupied single-particle state (HOMO) contains ahole (h), while the lowest unoccupied single-particle state (LUMO) contains the corresponding electron(e). The nanocluster excitations are thought to occur when the atomic positions are fixed in theirground-state equilibrium geometry.E(N) is the N -electron ground-state energy andE(N ; e − h)the total energy of the nanocluster calculated with the electron-hole pair constraint. The differenceεA = E(N ; e − h) − E(N) gives the energy needed for the creation of the pair, and defines theabsorption edge. After the excitation, due to the change in the charge density, atomic relaxation occursuntil the atoms reach a new minimum energy configuration, in the presence of the electron-hole pair.The emission energy is defined asεE = E′(N ; e− h)−E′(N), whereE ′(N ; e− h) andE ′(N) are thetotal energies evaluated in the presence and in the absence of the electron-hole pair, respectively, whenthe atoms occupy the equilibrium positions appropriate to the excited(e − h) state. The absorption andemission processes are represented schematically in Fig. 1.

The difference∆EStokes = εA − εE defines the Stokes shift. Thus, the Stokes shift arises fromatomic relaxation following the excitation process. This model relies on the assumption that the atomicrelaxation under excitation is faster than the radiative electron-hole recombination. Our calculations arenot spin-polarised, however similar computations performed by Franceschetti and Pantelides [21] withinlocal spin-density approximation, showed that the singlet-triplet splitting is significantly smaller than theStokes shift.

Because of the large surface to volume ratio, the presence of an electron-hole pair in the clusters causesa strong structural deformation with respect to the ground-state atomic geometry. The atomic deformationis larger for the smaller systems. As a result, the difference between absorption and HOMO-LUMOground state (GS) gap and between emission and HOMO-LUMO excited state (EXC) gap increaseswith the diminishing of the nanocluster dimension. In particular, the GS HOMO-LUMO gap tends tobe smaller than the absorption energy while the EXC HOMO-LUMO gap tends to be larger than theemission energy, so that trying to deduce the Stokes Shift simply from the HOMO-LUMO gaps leads toerrors especially large for small clusters.

Our results are collected in Table 1. We see that the Stokes shifts diminish with the increase of theH-Si-nc size and are substantially in agreement with those of Puzder et al. [22] and Franceschetti etal. [21] although our values lie between theirs. The discrepancies could be due to the different codesused to perform the calculations.

We have also calculated the optical spectra for some small clusters using: (i) LDA Kohn and Shameigenvalues and eigenvectors in the Random Phase Approximation (RPA-LDA, neglecting Local Fields),(ii) quasi-particle self-energy corrected eigenvalues within the GW method (RPA-GW), (iii) a time de-pendent adiabatic local density approximation (TD-ALDA), and (iv) a many-body perturbation approach


Table 1Stokes Shift values for hydrogenated Si clusters: present work versus theoretical datapresent in literature

H-Si Diameter Theoryclusters (nm) This work Ref. 22 Ref. 21 Ref. 25 Ref. 26Si1H4 0.0 8.38Si5H12 0.45 5.67Si10H16 0.55 4.40 LDA QMCSi29H36 0.9 1.35 0.69 1.0 2.92 0.22 0.70Si35H36 1.1 0.92 0.57 0.8 1.67Si66H64 1.3 0.50Si87H76 1.5 0.22 0.32Si29H24 0.8 0.84 0.34 0.4 1.17

Fig. 1. Schematic representation of the absorption and emission processes assumed in the Constrained Density FunctionalApproach.

through the solution of the Bethe-Salpeter equation (BSE). Both LDA-RPA and GW-RPA are withinthe scheme of the independent particle RPA (IP-RPA). For Si5H12 (see Fig. 2) the RPA-LDA schemeunderestimates the gap with respect to the experimental value (6.5 eV) [23]. The RPA-GW method(which includes the self-energy corrections to the Kohn-Sham eigenvalues) opens the gap. The effects ofthe electron-hole interaction on the optical properties (through BSE) are also quite large, the calculatedexcitonic binding energy being of the order of 3 eV. The optical gap is reduced partially compensating theGW opening. Interestingly, the BSE and TDLDA results are similar for the absorption onset with the firstexcitonic peak around 6.5 eV in agreement with the experimental result. A very accurate calculation ofthe optical gap of Si5H12 using both a TDDFT- B3LYP and a multi-reference second-order perturbationtheory MR-MP2 approach has given the values 6.66 eV and 6.76 eV, respectively, in good agreementwith our theoretical value [24].


Fig. 2. (Color online) Absorption spectra of the Si5H12 cluster calculated using different DFT based methods: LDA-RPA black(black), GW-RPA red (dark gray), BSE violet (light gray), TDLDA blue (light black).

3. Absorption and emission spectra: The role of nanocrystal surface oxidation

The aim of the present section is to investigate the mechanisms involved in the modification of theelectronic and optical properties of Si-nc when they are oxidized. We start from an hydrogenated clustere.g. the Si10H16 nanocrystal, and add an oxygen atom to its ground state atomic structure. This can bemade either without removing H atoms, hence leading to Si10H16O, with an O atom placed on one of the12 equivalent Si-Si bonds, or by replacing a pair of hydrogen atoms with one oxygen (in this case, noSi-Si bond is broken). In the latter case, one is led to one of four different isomers of Si10H14O. In theseisomers, oxygen is covalently bonded to silicon, with either a double bond (“double” isomer, containinga Si= O bond like in the silanone H2SiO structure), or with different bridge-bonds (i.e., Si-O-Si bonds).In particular, oxygen can make a bridge between two “first neighbors” or “second neighbors” Si atoms(called “asym” and “sym” isomers) or it can lay in an “interstitial” position inside the Si10 cage (“interst”isomer). The cluster structures we have considered are reported in Fig. 3.

We have found that the isomer with double Si= O bond (i.e., Si10H14O-double) undergoes smalleratomic relaxations than isomers with bridge bonds: as a consequence the Si10H14O-sym is 1.7 eV morestable than Si10H14O-double. Oxidation induces significant changes in the electronic properties. First,one expects a splitting of the degenerate Kohn-Sham levels of Si10H16, due to the symmetry reduction;second, adding an oxygen atom will introduce electronic states with respect to the non-oxidized cluster,third, the oxygen-related states appear inside the energy region of the Si10H16 HOMO-LUMO gap. It isthen interesting to calculate the absorption and emission optical spectra. For both the ground and excitedstate optimized geometries, the transition energies and the optical response,Im ε(ω) (the imaginarypart of the nanocrystal dielectric function), are evaluated through first-principles calculations beyondthe one-particle approach. We consider Si10H16, Si10H14O-double (Si10H14 = O), and Si10H14O-sym(Si10H14 > O). First, we have calculated the Stokes Shifts as the difference between the band edge statesin absorption and emission. The Stokes-Shifts are calculated using: (1) TDLDA, (2) GW-BSE and (3)the constrained-LDA and are reported in Fig. 4. We can see that the Stokes Shifts calculated using thethree different approaches for the hydrogenated system and for the cluster with the double Si= O bondagree, while for the system with the bridge bond there are relevant differences. In this last case the BSEapproach shows that more than onee− h pair has a substantial contribution to the lower energy exciton.


Fig. 3. (Color online) Structure of Si10H16, Si10H16O and the four isomers of Si10H14O. In the ball and stick representation,Si is light blue (gray), H is gray (light gray), and O is red (dark gray).

Obviously CDFT works best when the excited state is a linear combination ofe− h pairs with only onesingle dominant component (e.g. the transition between the HOMO and LUMO levels). However wenotice that, by performing a CDFT calculation, one allows all the orbitals to relax hence the resultingexcited state, even if represented by one electron-hole pair, is not the same as the unrelaxed state whichenter the linear combination ofe − h pairs building up the excited state in the BSE scheme. Thus someorbital mixing is present even at the CDFT level.

For the absorption and emission spectra we consider the self-energy corrections [27] by means of theGW method and the excitonic effects through the solution of the Bethe-Salpeter equation [28]. Theeffect of local fields is included, to take into account the inhomogeneity of the systems. Actually, wefound that, in the case of finite systems, such as clusters, the effect of the local fields on the opticalspectra (both absorption and emission) is the stronger components, much more relevant than the excitoniceffects. The inclusion of the local fields, even in the simple RPA approach, leads to a blueshift of themain peaks and substantially changes the transition oscillator strengths. In order to perform emissionspectra calculations, we use the excited state atomic geometry together with the ground state electronicconfiguration. Thus, strictly speaking,Im ε(ω) corresponds to an absorption spectrum in the newstructural geometry. In other words, we consider the emission, in first approximation, simply as the timereversal of the absorption [29]. We show the results in Fig. 5. Each panel reports the imaginary partof the dielectric function for absorption (dashed line) and emission (solid line) for the three considered


Fig. 4. (Color online) Calculated Stokes shift for the Si10H16, Si10H14 > O and Si10H14 = O double clusters. The calculationhave been performed using GW+ BSE: left, red (dots), TDLDA: middle, blue (squares), constrained LDA: right, purple(triangles) methods.

clusters. Self-energy, local-fields and excitonic effects (BSE-LF) are taken into account. The absorptionfeatures of the three cases are similar showing an increase of the absorption with the energy. On thecontrary, the emission-related spectra are clearly different. Whereas the fully hydrogenated Si10H16

cluster and the Si10H14 = O cluster show similar emission, in the case of the Si-O-Si bridge bond(bottom panel) an important excitonic peak, separated from the rest of the spectrum, is evident at 1.5 eV.Actually, bound excitons are present also in the fully hydrogenated (at 0.4 eV) and in the Si10H14 = O(at 1.0 eV) clusters, with calculated binding energies even larger than in the case of the Si-O-Si bridgebond (3.4 and 3.6 eV respectively, to be compared with a binding energy of 2.0 eV in the case of thebridge bond cluster). Nevertheless, the related transitions are almost dark and the emission intensity isvery low. Only in the case of the Si-O-Si bridge bond the photoluminescence peak appears thanks to thestrong oscillator strength of the related transition.

The comparison of our results with the experiment suggests that the presence of a Si-O-Si bridge bondat the surface of a Si-nc can explain the nature of luminescence: only in this case the presence of anexcitonic peak in the emission related spectra, red shifted with respect to the absorption onset, providesan explanation for both the observed Stokes Shift and the PL in the near-visible range. It is worth tostress that the role of the interface has been experimentally proven to be important for the PL propertiesof embedded Si-nc in SiO2 and suggested to play a role in the mechanism of population inversion atthe origin of the optical gain [30]; besides, Monte Carlo approaches have demonstrated that Si-O-Sibridge bonds are the main building blocks in the formation of Si-SiO2 flat interfaces [31] and form thelow energy structures at the interface of Si-nc embedded in silicon dioxide [32]. In conclusion, our


Fig. 5. (Color online) Absorption (dashed line, black) and Emission (solid line, red) spectra in the ground state and excited stategeometries, respectively for Si10H16 (top panel), Si10H14 = O (central panel) and Si10H14 > O (bottom panel).

theoretical results, obtained by ab-initio calculations including excitonic effects, suggest that the Si-O-Sibridge bond may be responsible for the observed strong PL peak, and shed some light on the role of theSi-nc-SiO2 interface.

4. Doping silicon nanocrystals

There is experimental evidence that doping control at the nanoscale can add optical properties whichcannot be achieved in pure systems. In the case of silicon nanocrystals it has been shown that the PLpeak can be tuned even below the bulk Si band gap by properly controlling the impurities, for example byB and P co-doping [15]. We have investigated the structural changes of Si-nc after inserting the dopantimpurity as a function of the: (i) nc size; (ii) the impurity position within the nanocluster and (iii) thenumber of doping species. We performed our calculations using a plane-wave, pseudopotential densityfunctional approach. We consider B and P impurities in substitutional sites within spherical Si-nc, withdiameter ranging from 1.04 nm (Si29H36) to 2.24 nm (Si293H172). Full relaxation with respect to theatomic positions is performed for both doped and undoped systems using the ESPRESSO package [33],within the GGA approximation using Vanderbilt ultrasoft [34] pseudopotentials. The Si-nc have beenembedded in large supercells in order to prevent interactions between the periodic replicas.

First, we have studied the change of the structural properties due to the impurity presence. It comesout that the amount of relaxation around the impurity is directly related to the impurity valence. Amore significant distortion is found for the trivalent impurity (boron). In fact, for the B-doped clusters,while the Si-Si bond lengths remain almost unchanged, some relaxation occurs around the impurity. Theoverall structure acquires a C3v symmetry, with the impurity displaced along the<111> direction from


the nanocluster center. Such displacement leads to one longer and three shorter (and equal) Si-impuritydistances. While the longer bond length does not depend much on the nc size, the shorter ones decreasewhen the nc size increases. It is interesting to note that the relaxation of bulk Si containing one Bimpurity leads to an “almost”Td symmetry, in which the four B-Si bonds are practically the same. Fora pentavalent impurity, such as P, the relaxation leads to a nearlyTd symmetry, in which the differencesbetween the four P-Si bonds are negligible, less than 0.7%.

The formation energy (FE) of a neutral X impurity is defined as the energy needed to insert the Xatom with chemical potentialµX within the cluster after removing a Si atom which is transferred to theexternal chemical reservoir, assumed to be bulk Si:

Ef = E (Sin−1XHm) − E (SinHm) + µSi − µX

where E is the total energy of the system,µSi the total energy per atom of bulk Si,µX the total energy peratom of the impurity (the total energy per atom in the tetragonal B50 structure for B, and the orthorhombicblack phosphorus for P). Our calculations show that for smaller Si-nc a larger energy is required to bindthe impurity. For B-doped Si-nc we found a decreasing behavior ofEf vs. 1/R, that can be described bythe linear formula:

Ef = 0.80 + 4.64/R

whereR is expressed in Å andEf in eV, and the valueEf = 0.80 eV corresponds to the B impurity inbulk Si. For P-doped Si-nc the same decreasing behavior ofEf vs. 1/R has been found, with a linearformula:

Ef = 0.21 + 4.98/R

The calculated formation energy is lower for larger Si-nc. This behaviour is in qualitative agreementwith the observed suppression of the PL in doped Si nanocrystals, since doping of the nanocrystal withIII or V group shallow dopants tends to suppress the photoluminescent emission. Fujii et al. [15] haveindeed shown that on increasing the annealing temperature both the Si-nc size increases and a strongerPL suppression is observed. This effect is a signature of an higher impurity concentration, thus showingthat larger Si-nc can more easily sustain the doping.

The formation energy changes also as a function of the impurity site within the Si-nc. It is much lowerwhen the B impurity is located in the sub-surface Si layer. In Fig. 6 we show the formation energy ofa B neutral impurity in the Si146BH100 cluster. The impurity is located in many sites from the clustercenter toward the surface along two paths, as shown in Fig. 6(a). The calculated energies are shown inFig. 6(b). On thex-axis we put the distance from the center of the replaced Si atom in the Si147H100

cluster. The more stable sub-surface sites are explained by considering that atomic relaxation aroundthe impurity is easier in such positions. Thus, as the B atom is moved toward the surface the formationenergy decreases. The local structure around the impurity has aC2v symmetry, with two shorter and twolonger Si-impurity distances (the two bonds with the Si surface atoms). Recently these findings havereceived an experimental support [35].

When the Si nc is doped with both a B and a P atoms (co-doping) the differences among the impurity-Sibond lengths are smaller and an almostTd symmetry is recovered.

This fact is reflected in the formation energy results, which are reported in Fig. 7, for singly B-,P-doped and (B-P)-co-doped Si-nc. In all cases the impurities are located in subsurface positions. In thefigure at the top the neutral impurities are located at the largest possible distances, at the bottom they are


Fig. 6. Formation energies for neutral impurities as a function of the impurity position within the cluster (b). The impurity ismoved along two different paths toward the surface, as shown in (a).

nearest neighbors. Figure 7 shows that the simultaneous (P-B) doping strongly reduces (by about 1 eV)the formation energy with respect to both the two single-doped cases and, in the case the two dopantsare near-neighbours, the co-doped Si-nc is even stable (negative FE). The formation energy reductionis almost independent from the Si-nc size. Thus, Si-nc can be more easily simultaneously doped thansingly doped; this is a consequence of a charge transfer which entails a minor structural deformation.Moreover the formation energy is lower when the impurities are nearest neighbours, thus confirming theimportant role played by the electrostatic attraction.

The dopants insert donor or acceptor states within the Si-nc gap lowering the HOMO-LUMO energygapEG. For single-doped Si-nc the dopant level falling within the gap is strongly localized either onB or P impurity. For example in the case of Si86BH76 nanocrystals the defect level is located abovethe valence band and the energy gap is reduced from 2.59 to 2.31 eV, whereas for the Si86PH76 dopednanocrystals the defect level is located below the conduction band and the energy gap is 2.34 eV. Theelectronic properties of (B-P)-codoped Si-nc are qualitatively and quantitatively different from those ofeither B- or P- doped Si-nc. For the Si85BPH76 nanocrystalsEG is lowered from 2.59 eV (pure Si-nc)to 1.82 eV (co-doped Si-nc). The results for the Si145H100 case are similar:EG is reduced by codopingfrom 2.30 eV (pure Si-nc) to 1.56 eV. In the case of Si-nc larger than those considered here, which havea smallerEG, it would be possible by co-doping to obtain anEG even smaller than that of bulk Si inagreement with the experiment [12,14]. In the co-doped case the HOMO is strongly localized on the Bimpurity and the LUMO on the P impurity.

We have calculated the absorption and emission spectra of co-doped Si-nc, comparing the IP-RPA


Fig. 7. Formation energy of the neutral impurities located at subsurface positions as a function of doping: B (left), P (right) and(B-P) (middle) doped nanoclusters. The lines are a guide for the eyes. Dashed lines (green and blue): the neutral impurities areseparated from each other by the largest possible distance within the Si-nc; solid lines (black and red): the neutral impurities arelocated at nearest neighbor distances in the codoped clusters. Squares (green and black) are related to the Si87H76 nanoclusters,circles (red and blue) to the Si147H100 ones.

spectra with those where the many body effects are included, within a GW-BSE approach. This approachtakes into account the self-energy correction (in the GW approximation), the local fields, and the electron-hole interaction. We analyze separately the role on the optical spectra of: (i) the nanocrystal dimension,(ii) the distance between the B and P impurities and (iii) the many body effects.

We find that the dopant states in the Si-nc gap give rise to new optical transitions below the absorptiononset of the un-doped Si-nc.

In Fig. 8 we report the IP-RPA absorption spectra of the Si145BPH100 cluster. The energy range at theabsorption onset where the optical transitions due to the dopant levels contribute most is shown in detail.The figure shows how the features at the absorption onset change with the distance between the B and Pimpurities. We can see that by increasing the B and P distance the onset shifts to lower energies whilethe dipole oscillator strength of the first transition diminishes. This behavior is due to the reduction ofthe interaction between the acceptor and donor levels, which opens the gap, and the diminishing of theelectron (localized on the P atom) and the hole (localized on the B atom) wave function overlap.

To enlighten the effects of the local fields and of the electron-hole coupling on the optical absorption andemission spectra of the co-doped nanocrystals we have applied the GW-BSE approach to the calculationof the optical spectra of the Si33BPH36 cluster. For the calculation of the emission spectra the clusteratoms are located in the equilibrium positions appropriate to the approximated excited state which hasan electron in the HOMO and a hole in the LUMO. The comparison of the spectra with those obtainedusing the simple IP-RPA approach reveals the presence of sharp excitonic features at the spectrum onsetwhen the many-body effects are taken into account. As in the case of the oxidize clusters, the emissionspectrum is red shifted to lower energies with respect to the absorption spectrum. This energy red-shiftallows us to estimate the Stokes Shift which we compare with that obtained using the simple DFTapproach in Table 2.

As we can see from the table the difference in the estimation of the Stokes Shift provided by the twotheories is only 0.16 eV. In Fig. 9 we show the absorption and emission spectra of Si33BPH36 obtainedincluding the many body effects through the GW+ BSE approach. We can see the strong red-shift ofthe first excitonic peak and the increase in its intensity.


Table 2Absorption gap, emission gap, and StokesShift ∆ calculated as the HOMO-LUMOdifference in DFT and the GW+ BSE ap-proaches

Si33BPH36 DFT GW+ BSE ∆

Abs. (eV) 2.77 3.35 0.58Ems. (eV) 1.78 2.20 0.42∆ (eV) 0.99 1.15 0.16

Fig. 8. Absorption spectra of Si145BPH100 nanocrystal with the B and P impurities located at the largest (10th neighbors,slashed filling) and the shortest (2nd neighbors, dark homogeneous filling) distance.

5. Conclusions

In this paper we have presented the results of first-principles calculations of the structural, electronicand optical properties of hydrogenated silicon-based nanoclusters. We have analysed the effects onthe atomic structure and the optical spectra of: (1) the surface bonding by an oxygen atom; (2) thedoping by B, P and both B and P atoms; (3) the electronic excitation. This last point is essential tocorrectly describe photoemission experiments where the cluster initial state is indeed an excited state.The Si-based nanocrystals have diameters ranging from few angstroms to 2.5 nm. In particular we havefound that:

i) the presence of a single electron-hole pair causes a strong deformation of the structures withrespect to their ground-state configuration, which is more relevant for the smaller systems;

ii) a significant contribution to the Stokes shift arises from structural relaxation after excitation ofthe nanocluster. Thus considering the HOMO-LUMO gaps of the ground and excited state as theproper absorption and emission energies provides a prediction which is worse the smaller is thecluster;


Fig. 9. Absorption (filled region) and emission (empty region) spectra including many body effects of Si33BPH36.

iii) the inclusion of the many-body effects through the BSE or the TDLDA gives results for the absorp-tion spectra that are quite similar regarding the absorption onset and substantially in agreementwith the available experimental data;

iv) the oxidation of a Si-nc induces structural modifications and significant changes in the electronicand optical properties that depend on the type of the Si-O bond;

v) the inclusion of the excitonic effects in the calculation of the emission spectra suggests that theSi-O-Si bridge bond might be responsible for the strong PL peak experimentally observed inoxidized Si-nc;

vi) Si-nc can be more easily simultaneously doped than singly doped;vii) finally, co-doping is a way to engineering the PL properties of Si-nc.

Acknowledgments

The authors thank INFM/CNR/CNISM and CNISM “Progetto Innesco” and the MIUR COFIN-PRIN2005.

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Role of Surface Passivation and Doping in Silicon Nanocrystals

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