Phys. Status Solidi A, 1–4 (2012) / DOI 10.1002/pssa.201200149 p s sa

statu

s

soli

di

www.pss-a.comph

ysi

ca

ical Section onPhotovoltaics

Part of TopAdvanced Silicon Materials for Electronics and

applications and materials science

P-doping of Si nanoparticles:The effect of oxidation

Alexandra Carvalho*,1, Sven Oberg2, Manuel Barroso1, Mark J. Rayson2, and Patrick Briddon3

1 Department of Physics, I3N, University of Aveiro, Campus Santiago, 3810-193 Aveiro, Portugal2 Department of Engineering Sciences and Mathematics, Lulea University of Technology, 97187 Lulea, Sweden3 Electrical, Electronic and Computer Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK

Received 4 May 2012, revised 28 May 2012, accepted 31 May 2012

Published online 30 July 2012

Keywords doping, nanoparticles, phosphorus, segregation, silicon, theory

* Corresponding author: e-mail aicarvalho@ua.pt, Phone: þ351 234 370 356, Fax: þ351 234 378 197

The radial dependence of the formation energy of substitutional

phosphorus in silicon nanoparticles covered by an amorphous

oxide shell is analysed using local density functional theory

calculations. It is found that Pþ is more stable at the silicon core.

This explains the experimental observation of segregation of

phosphorus to the Si-rich regions in a material consisting of

Si nanocrystals embedded in a SiO2 matrix [Perego et al.,

Nanotechnology 21, 025602 (2010)].

Formation energy of positively charged substitutional phos-

phorus in a 1.5 nm diameter Si nanoparticle covered by a

�2 nm-thick amorphous SiO2 shell, as a function of its distance

to the centre.

� 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction The interaction of silicon nanostruc-tures with the atmosphere or biological environments leadsto the formation of a passivating oxide layer. Owing to thedifferent electronegativities of Si and O, the bonds inthe silica layer are strongly ionic, and the permittivity islower than in the silicon core. This marked differencebetween the core and shell environments bears an influenceon the distribution of charged species, in particular onthe distribution of dopant atoms.

Theoretical studies agree that in stand-alone Si nano-crystals with H-terminated surfaces B and P segregate tothe surface, both to relieve the size-mismatch strain andto saturate Si dangling bonds [1–3]. At the surface, P and Bmay assume threefold coordination, inhibiting the dopantactivity. If the nanocrystals are covered by an oxide layer, asmuch as 95% can be located there, presumable because P

atoms segregate to the surface during growth, becomingincorporated in the oxide during the subsequent surfaceoxidation process [4].

We have shown that in silicon nanocrystals with H- andOH-terminated surface the dopant migration responsiblefor segregation should occur during growth, since theactivation energy, in the absence of mediating defects, is3–4 eV. However, if further oxidation releases silicon self-interstitials, as happens in Si [5], the migration of B and Pwill be enhanced [6].

In this paper we suggest that a re-distribution ofphosphorus during or after the growth of an oxide layercontributes to the incorporation of P in the silicon core of thenanoparticles. This follows from the analysis of the energeticsof charged P atoms in SiO2-covered silicon nanoparticles usingfirst-principles local density functional theory.

� 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

2 A. Carvalho et al.: P-doping of oxidised Si nanoparticlesp

hys

ica ssp st

atu

s

solid

i a

Figure 1 (online color at: www.pss-a.com) Structure of theundoped nanoparticle, obtained from molecular dynamicssimulations.

2 Calculation details2.1 Building the nanoparticle model The model

for the oxidised silicon nanoparticles was built from anapproximately spherical crystalline Si core of 1.5 nmdiameter, surrounded by a spherical shell of b-cristobalitewith about 2 nm outer diameter. The nanoparticle had 161silicon atoms and 196 oxygen atoms. In order to generate arealistic amorphous SiO2 layer and SiO2–Si interfacestructure, the nanoparticle was submitted to an anneal at1800 K using molecular dynamics (MD) simulations.

The molecular dynamics simulations were carried outusing the SIESTA code [7, 8]. The forces are calculated usingthe local density approximation (LDA) of density functionaltheory (DFT). The inner electrons were represented bypseudopotentials of the Troullier–Martins scheme [9]. Thebasis sets for the Kohn–Sham states are linear combinations ofnumerical atomic orbitals [10, 11]. These are single zeta basissets for Si and double zeta polarised basis sets for O. Thecharge density is projected on a real-space grid withan equivalent cutoff energy of 100 Ry to calculate theexchange-correlation and Hartree potentials. The simulationcell was cubic with 35 A side length, and periodic boundaryconditions. The G-point was used for Brillouin zone sampling.

The dynamical equations were integrated using thevelocity Verlet algorithm with a time step of 1 fs. During thefirst 280 fs the system was brought to the target temperatureby velocity rescaling. Then, the system was kept at 1800 Kusing a Nose–Hover thermostat. The inner three shells wereconstrained to the initial positions during the calculation.The total annealing length was 4 ps. Snapshots were taken at2 ps and subsequently at 0.3 ps interval, for comparison.

The structures obtained from the MD simulation wereprepared to serve as input for the static calculations of thedopant formation energies. The structure snapshots were firstfully relaxed at 0 K, then passivated with hydrogen atoms(59) and fully relaxed again at 0 K. The model used in thisstudy was obtained for t¼ 2 ps of MD simulation.

2.2 Electronic structure calculations The geome-try optimisations and electronic structure calculations at 0 Kwere carried out using the Aimpro code (see Refs. [12–14]for more details). The dual space separable pseudopotentialsby Hartwigssen, Goedecker and Hutter were adopted [15].Valence states were expanded over a set of atom-centredCartesian-Gaussian functions [16]. These consisted of 44G�

basis centered on Si, O and H, optimised for silicon, silicaand silane, as described in Ref. [16], and an uncontractedddpp basis set for P. Periodic boundary conditions were onlyused for the models of defects in bulk Si and in bulk SiO2.In those cases, the charge density was expanded in a planewave basis set with a cutoff energy of 200 Ha. Thenanoparticle models had no periodic boundary conditionsimposed (Fig. 1).

3 Energetics of P in Si nanocrystals The depen-dence of the formation energy of substitutional phosphoruson its position in the nanocrystal was analysed by calculating

� 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

the total energy (E) of the 161 doped nanocrystals(Si160O196H59Pþ) obtained by replacing Pþ for each of theSi atoms.

We have considered the positive charge state (Pþ)because this is the most relevant from a technological pointof view. It is the equilibrium charge state of the dopant bothin Si and SiO2 [17]. Similarly, in successfully P-dopednanocrystals [4], the donor state of P-doped nanocrystals canbe thermally activated, transferring its electron to theunoccupied states of the undoped nanocrystals. The P-dopednanocrystal thus becomes positively charged. In ourcalculations, we assume that the positively charged nano-crystals (Si160O196H59Pþ) are isolated from other nanocrys-tals (i.e. are surrounded by vacuum).

The formation energy (Ef) was calculated using asstandard state subsitutional phosphorus in bulk Si, calculatedin a 512 atom supercell:

Eif � EF ¼ E½NCi : Pþ� � E½NC�

� fE½Si511P0� � E½Si512�g

Here, the nanocrystal with P at the ith Si site is noted‘NCi:P’, whereas the nanocrystal without P is noted ‘NC’. EF

is the Fermi level position, measured relative to the vacuumlevel.

The formation energy is lowest at the silicon core, andhighest at the oxide shell (Fig. 2). At the surface, the averageformation energy is slightly lower. This contrasts with the OH-terminated Si nanocrystal, where Pþ prefers to sit close to thesurface, although not directly bonded to the oxygen atoms [3].

4 Geometry The preference for the Si core resultsfrom a balance of different factors. The most importantare mismatch strain and chemical bonding effects. Theformation energy of both neutral and positively charged Ps isabout 5 eV higher in SiO2 than in Si. Further, both strain and

www.pss-a.com

Phys. Status Solidi A (2012) 3

Original

Paper

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

0.0 2.0 4.0 6.0 8.0 10.0 12.0 0

20

40

60

80

100

120

Ef(N

C:P

+ )+E

F (e

V)

Oxy

gen

coun

t

r (Ang.)

Figure 2 (online color at: www.pss-a.com) Formation energy ofPþ in the SiO2-covered nanoparticle (full squares) as a functionof the distance of Pþ to the geometrical centre of the nanocrystal (r).The points correspond to average formation energies for distancesbetween r� 2 and rþ 2 A. The error bars represent the statisticstandard deviation of the samples. On the right-hand axis is repre-sented the oxygen count for the undoped nanocrystal (open squares).The oxygen count corresponds to the number of oxygen atomsbetween r� 2 and rþ 2 A.

0

5

10

15

20

25

30

35

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Cou

nt

Ef(P+)-<Ef(P

+)>

Coord. 4Coord. 5Coord. 3Other

Figure 3 (online color at: www.pss-a.com) Energy versus coordi-nation number. The formation energy is given relative to the averageof the samples hEfi. The histogram is stacked.

Figure 4 (online color at: www.pss-a.com) Types of localenvironment of substitutional Pþ, classed according to the

bonding are affected by the presence of lattice imperfectionsat the interface. Different from the crystalline nanoparticle,in the partially amorphised nanoparticle there are coordina-tion defects and P can associate with lattice imperfections,assuming different coordination numbers. In some cases, theimperfections may help to release strain. In the following, weanalyse separately the correlation of the formation energy ofPþ to its coordination number, and then to the type of bondsformed.

First, we analyse the influence of the coordinationnumber of Pþ (m). For effect of counting the number ofbonds, we use a geometrical criteria: if the distance betweentwo atoms exceeds the sum of their Van der Waals radii byless than 0.5 A, we consider the two atoms bonded. 1 Figure 3shows a histogram for the relative energy for different m. Thedistribution is bimodal. The lowest energy peak is centred atabout 2 eV below the average formation energy hEfi, whilst thehigher energy peak is about 1 eV above it. The lowest energypeak is dominated by m¼ 4. Naturally, Pþ has four valenceelectrons and therefore favours fourfold coordination. Thereare also some samples with m¼ 3, corresponding to caseswhere a lattice defect has given an electron to phosphorus. Thehighest energy peak is also dominated by m¼ 4, but has areasonable share of overcoordinated Pþ. Clearly, though, thecoordination number is not the only parameter determining thephosphorus preference for the Si core.

Thus, we now analyse the influence of the bondinggeometry. Based on a tight-binding picture, we can classify

species it forms bonds to. The figure depicts (a) (nSi, nO, nH)¼(4, 0, 0), (b) (nSi, nO, nH)¼ (3, 1, 0), (c) (nSi, nO, nH)¼(2, 2, 0), (d) (nSi, nO, nH)¼ (1, 3, 0), (e) (nSi, nO, nH)¼ (0, 4, 0),(f) (nSi, nO, nH)¼ (0, 3, 0).

1 A more physical criteria should be based on an analysis of the overlap

population, but this would be prohibitive for the number of bonds and

samples considered here.

www.pss-a.com � 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

4 A. Carvalho et al.: P-doping of oxidised Si nanoparticlesp

hys

ica ssp st

atu

s

solid

i a

0

5

10

15

20

25

30

35

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Cou

nt

Ef(P+)-<Ef(P

+)>

Struc. AStruc. B,C,DStruc. EStruc. FOther

Figure 5 (online color at: www.pss-a.com) Energy versus type oflocal environment of Pþ. The formation energy is given relative tothe average of the samples hEfi. The histogram is stacked.

the local environment of Pþ according to the number ofnearest Si, O and H nearest neighbours (nSi, nO, nH), asdepicted in Fig. 4. The histogram of Fig. 5 shows that type Astructures have the lowest energy, followed by the structureswhere Pþ is bonded to both O and Si. The samples wherePþ has four oxygen neighbours are the highest in energyamongst fourfold coordinated structures. Hence, the pre-ference of phosphorus for the Si core is driven by the lowerenergy necessary to form a Pþ–Si bond at the expense of aSi–Si bond, as compared to the energy necessary to form aPþ–O bond at the expense of a Si–O bond.

This result contrasts with the behaviour of Pþ incrystalline nanocrystals with OH-terminated surface, whichwe reported in a previous article [3]. In that case, Pþ prefersto sit at the sub-surface region, where it forms bonds only toSi, since at the surface the lattice is more flexible toaccommodate the size-mismatched Pþ ion. In the SiO2-covered nanoparticle considered here, the lattice defects atthe interface help to release the strain in the Si core.Therefore, chemical bonding effects predominate, exceptpossibly for the outermost SiO2 layers.

5 Summary The analysis of the formation energy ofsubstitutional Pþ as a function of the dopant location in asilicon nanocrystal covered by a SiO2 shell has revealed thatPþ is more stable in the silicon core than in the SiO2 shell.The preference of Pþ for the Si core is mainly driven by itspreference to form bonds with Si.

Assuming that oxidation leads to the ejection of Si self-interstitials, which can serve as mediators for the diffusion ofP, we suggest that upon annealing phosphorus can be made to

� 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

migrate to the silicon core, where it is more stable. This is inagreement with the observation of phosphorus segregation tothe Si-rich regions in a material consisting of Si nanocrystalsembedded in a SiO2 matrix [18].

Acknowledgements The computations were performed onresources provided by the Swedish National Infrastructure forComputing (SNIC), at KTH (Lindgren), Umea University (Akka),University of Aveiro (Blafis) and Milipeia. The work was funded bythe Calouste Gulbenkian Foundation, the Marie Curie ProgramREG/REA.P1(2010)D/22847 (SiNanoTune) and FCT Portugal(SFRH/BPD/66258/2009 and PTDC/FIS/112885/2009).

References

[1] X. D. Pi, R. Gresback, R. W. Liptak, S. A. Campbell, andU. Kortshagen, Appl. Phys. Lett. 92, 123102 (2008).

[2] G. Cantele, E. Degoli, E. Luppi, R. Magri, D. Ninno,G. Iadonisi, and S. Ossicini, Phys. Rev. B 72, 113303 (2005).

[3] A. Carvalho, M. J. Rayson, and P. R. Briddon, J. Phys. Chem.CQ3 116, 8243 (2012).

[4] A. R. Stegner, R. N. Pereira, R. Lechner, K. Klein,H. Wiggers, M. Stutzmann, and M. S. Brandt, Phys. Rev.B 80, 165326 (2009).

[5] R. C. Newman, in: Early Stages of Oxygen Precipitation inSilicon, in: NATO ASI series, edited by R. Jones (KluwerAcademic Publishers, Dordrecht, 1996), p. 19

[6] H. Bracht, H. H. Silvestri, I. D. Sharp, and E. E. Haller, Phys.Rev. B 75, 035211 (2007).

[7] D. Sanchez-Portal, P. Ordejon, E. Artacho, and J. M. Soler,Int. J. Quantum Chem. 65, 453 (1997).

[8] E. Artacho, D. Sanchez-Portal, P. Ordejon, A. Garcıa, andJ. M. Soler, Phys. Status Solidi B 215, 809 (1999).

[9] N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993(1991).

[10] O. F. Sankey and D. J. Niklewski, Phys. Rev. B 40, 3979(1989).

[11] O. F. Sankey, D. J. Niklewski, D. A. Drabold, and J. D. Dow,Phys. Rev. B 41, 12750 (1990).

[12] P. Briddon and R. Jones, Phys. Status Solidi B 217, 131(2000).

[13] M. J. Rayson and P. R. Briddon, Comput. Phys. Commun.178, 128 (2008).

[14] M. J. Rayson and P. R. Briddon, Phys. Rev. B 80, 205104(2009).

[15] C. Hartwigsen, S. Goedecker, and J. Hutter, Phys. Rev. B 58,3641 (1998).

[16] J. P. Goss, M. J. Shaw, and P. R. Briddon, in: Theoryof Defects in Semiconductors, Topics in Applied PhysicsVol. 104, edited by D. A. Drabold and S. K. Estreicher(Springer, Berlin, 2007), p. 69

[17] J. Lægsgaard and K. Stokbro, Phys. Rev. B 61, 12590 (2000).[18] M. Perego, C. Bonafos, and M. Fanciulli, Nanotechnology

21, 025602. (2010).

www.pss-a.com