Ab initio energetics of boron-interstitial clusters in crystalline SiThomas J. Lenosky, Babak Sadigh, Silva K. Theiss, Maria-Jose Caturla, and Tomas Diaz de la Rubia Citation: Applied Physics Letters 77, 1834 (2000); doi: 10.1063/1.1310627 View online: http://dx.doi.org/10.1063/1.1310627 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/77/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Interactions of B dopant atoms and Si interstitials with SiO 2 films during annealing for ultra-shallow junctionformation J. Appl. Phys. 97, 073520 (2005); 10.1063/1.1884246 Electrical activation of B in the presence of boron-interstitials clusters Appl. Phys. Lett. 79, 3764 (2001); 10.1063/1.1423775 Erratum: “Ab initio modeling of boron clustering in silicon” [Appl. Phys. Lett. 77, 2018 (2000)] Appl. Phys. Lett. 77, 4064 (2000); 10.1063/1.1332097 Boron-interstitial silicon clusters and their effects on transient enhanced diffusion of boron in silicon J. Appl. Phys. 88, 4547 (2000); 10.1063/1.1311826 Ab initio modeling of boron clustering in silicon Appl. Phys. Lett. 77, 2018 (2000); 10.1063/1.1313253

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Ab initio energetics of boron-interstitial clusters in crystalline SiThomas J. Lenosky, Babak Sadigh, Silva K. Theiss, Maria-Jose Caturla,and Tomas Diaz de la Rubiaa)

University of California, Lawrence Livermore National Laboratory, Livermore, California 94551

~Received 1 May 2000; accepted for publication 18 July 2000!

We have performed an extensive first-principles study of the energetics of boron clustering in siliconin the presence of excess self-interstitial atoms~SIAs!. We consider complexes with up to four Batoms and two SIAs. We have conducted an extensive search for the ground-state configurations andcharge states of these clusters. We find the cluster containing three B atoms and one SIA~B3I) to beremarkably stable, while all our clusters with more than 80% boron content are unstable. Hence, wepropose B3I to be a stable nucleus that can grow to larger clusters. The energetics presented here canbe used as input to large-scale predictive models for B diffusion and activation during ionimplantation and thermal annealing. ©2000 American Institute of Physics.@S0003-6951~00!00538-6#

Boron is the most widely usedp-type dopant of siliconin modern electronic devices. It is usually ion implanted intoSi, followed by a high temperature anneal which electricallyactivates the B and removes implant damage. As technologygenerations advance and devices become smaller, it is nec-essary to create sharp, ultrashallow profiles with high con-centrations of electrically active B. Two related processeslimit the realization of this goal:~i! the diffusion of the Bduring the high-temperature anneal, and~ii ! the formation ofelectrically inactive B clusters. In order to predict the distri-bution and nonequilibrium solubility of B under implant con-ditions, it is necessary to understand the energetics of both Bdiffusion and cluster formation. These energies can then beused to model the distribution of cluster species within actualdevices, and thus provide the physical foundation for predic-tive process simulators.

Both diffusion and clustering of B occur mainly due tothe presence of excess self-interstitial atoms~SIAs!, createdby ion implantation. These are highly mobile species and arethought to diffuse in a singly positive charge state.1 They areattracted to the negatively charged immobile B atoms (B2),present at the substitutional sites in the diamond lattice. Theysubsequently form a mobile complex (BI1) with a bindingenergy of 0.9 eV. The diffusion of the latter, with an activa-tion energy of 0.6 eV, is responsible for the unwanted spreadof the dopants in Si, as well as the nucleation and growth ofthe immobile B–Si clusters. The latter takes place when BI1

or SIA is captured by a B2 or by a cluster.The mechanism of the B diffusion outlined above has

recently been studied extensively from first principles byseveral groups.2,3 These investigations have explained ex-perimental observations on a quantitative level, which hasencouraged us to embark on a more complicated problem,i.e., the energetics of B clustering in the presence of highsupersaturation of silicon SIAs.

In this work we report the ground state energies andcharge states of small B-SIA clusters, calculated from firstprinciples using density functional theory~DFT! within the

local-density approximation~LDA !. In spite of their rel-evance for silicon processing technology, ours is the firstattempt to determine these energies from first principles. Toour knowledge, the most sophisticated prior treatment of thisproblem was made using semiempirical tight-binding poten-tials ~Cornell model!.4 However, this method can be quiteinaccurate for obtaining subtle energy differences, and as weshall see below most of these results are invalidated by ourcalculations. Other studies of B clustering have been phe-nomenological in nature and have relied on fitting the param-eters of a kinetic Monte Carlo model to the experimentaldiffusion data obtained during high temperature annealing ofion implanted silicon.5 However, given the complexity of thediffusion kinetics associated with these experiments, it is dif-ficult to envision how a model fit to the data can result in aunique solution for the binding energies of the B clusters.Furthermore, this methodology does not provide any infor-mation regarding the charge state of the B clusters, a keyissue for determining electrical activity.

The DFT calculations in this study are performed withthe Viennaab initio simulation package~VASP! plane-wavepseudopotential code,6 with Vanderbilt ultrasoftpseudopotentials,7 supplied by Kresse and Hafner.8 All theclusters are represented by 64 atom supercells and the calcu-lations were performed with a 23232 uniform grid of kpoints. We find the lowest energy Si SIA to be the doublepositively charged tetrahedral SIA Si~T!11 with a formationenergy of 3.23 eV calculated in a large 256 atom cell. Notethat the energetics presented in this letter are true LDA val-ues and contain no adjustable parameters~e.g., the band gap!that are fitted to the experiment.

We have studied clusters containing up to four B atomsand two SIAs, with the exception of B4, which we expect tobe highly unfavorable energetically. For each cluster we tryto find the ground-state structure by relaxing many indepen-dent geometries. Each starting configuration is generated byplacing BI1, Si~T!11, or a hexagonal B interstitial on a siteneighboring a smaller cluster in its ground-state structure.For the small clusters the ground-state configurations aresimple. BI1 consists of a substitutional B2 adjacent to aa!Electronic mail: delarubia@llnl.gov

APPLIED PHYSICS LETTERS VOLUME 77, NUMBER 12 18 SEPTEMBER 2000

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Si~T!11. The B2I cluster contains two boron atoms sharing asingle lattice site oriented along the~100! direction as previ-ously reported by Zhuet al.9 The B3I

2 cluster has a bondcentered boron atom bonded to two substitutional boron at-oms.

However, the larger clusters BnI2 are much harder todescribe and visualize. In general they lack symmetry, andbecause B is a small atom they are quite compact. For theseclusters, the large number of degrees of freedom makes acomplete global minimum energy search computationallyimpossible. In order to gain confidence in our results, weadditionally performed molecular dynamics annealing for afew larger clusters by evolving each of them for about 1 ps at1200 K, and subsequently relaxing to a local minimum. Intwo out of ten cases this procedure led to a slightly lowertotal energy.

Each cluster is also considered in different charge states.However, we find that this often does not affect the finalground-state geometry appreciably. The charge of a cluster isimportant because it is responsible for~i! the dependence ofits energy on the Fermi level,~ii ! its contribution to the ac-tive dopant fraction, and~iii ! its ability to attract or repel amobile SIA. The binding energies for all the clusters aresummarized in Table I. All energies are calculated with re-spect to isolated B2 and Si~T!11. The energy of a complexwith chargeZ varies with the Fermi level (EF) as EF3Z.The energies for the charged species in Table I are givenwith the Fermi level at midgap. The dependence of theground-state energy on the Fermi level for several of theclusters is shown in Fig. 1.

The binding energies in Table I are crucial for predictingthe formation of small B-SIA clusters in silicon in the pres-ence of excess SIAs. Figure 2 shows a reaction diagramwhich displays the relative stability of different clusters bydepicting the energy required to release an Si~T!11 or a BI1

by each cluster. This data can be used as input to predictivemodels for boron diffusion and clustering during thermal an-nealing of ion-implanted silicon.

Figure 2 provides a description of the possible kineticpaths that boron clustering and precipitation in the presenceof excess SIAs may take. We find the B3I complex to beremarkably stable, which indicates that this is a stablenucleus that can grow to larger clusters. It has been argued

before based on kinetic Monte Carlo models of experimentaldata with arbitrary parameters that an SIA rich path is theonly allowed kinetic pathway for boron clustering with theBI2 complex playing a key role in the nucleation of largeinactive boron clusters.5 Our results are consistent with thispicture in so far as the reaction diagram in Fig. 2 shows aplausible path for the formation of BI2 complexes during theearly stages of annealing when the SIA concentration is high.However, our results also show that because of its high bind-ing energy, the B3I complex plays a crucial role in the evo-lution of the active B concentration with annealing time andtemperature.

In order to further test the validity of our LDA calcula-tions, we have additionally performed three calculations us-ing a generalized gradient approximation~GGA! functional.We find the binding energy for BI1, B2I, and B3I

2 to be0.95, 2.23, and 3.24 eV, respectively. These values differ byonly 27%,15%, and15% from the respective LDA values,and we thus conclude that the difference between the twoapproaches is not significant. It is important to note that ourresults contradict the Cornell model, mentioned earlier, inmany important respects. In general, the geometries, chargestates, and energies we find for BnIm clusters do not agreewith their results. Furthermore, this model predicts all boronrich clusters to be stable. However, in Fig. 2 we find that allour only-boronclusters~e.g., B3! are unbound. Furthermore,we find that B4I

5 is unstable with respect to formation ofB3I

2. Hence, our calculations indicate that clusters too richin boron tend to become unstable. This is an important resultfor building Si processing models.

TABLE I. LDA energies for BnIm clusters, containingn boron atoms andmexcess Si interstitial atoms. All values are relative to isolated substitutionalB2 and Si~T!11 interstitials, with the Fermi level at midgap. Energies are inelectron volts, andQ is the charge of each cluster. For each cluster theenergy of the most stable charge state is in bold type.

Q 11 0 21 22 23

B 0B2 1.38 0.96 0.93B3 1.54 1.03 0.89 1.14BI À1.02 20.79B2I 21.43 À2.12 21.60B3I 21.95 22.72 À3.09B4I 21.00 21.85 22.32 À2.40BI2 À2.35 22.24 21.89B2I2 23.22 À3.24 22.79B3I2 23.87 À4.41 23.57B4I2 24.20 À4.80 24.73

FIG. 1. Fermi level dependence of the ground-state energy of three typicalclusters. The Fermi energy is given relative to midgap.

FIG. 2. Boron-interstitial clusters with lowest-energy charge states, showingthe binding energies for release of Si~T!11 and BI1.

1835Appl. Phys. Lett., Vol. 77, No. 12, 18 September 2000 Lenosky et al.

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Greene and co-workers have recently investigated theincorporation of electrically active B in silicon during epi-taxial film growth. Based on their results, it was concludedthat excess boron accumulates at the outer surface and isincorporated as B2I pairs.10 This possible interpretation wasbased on previousab initio calculations9 of B2I which areconsistent with our results, indicating that B2I is electricallyneutral and inactive.

In summary, we have presented the first comprehensiveab initio calculations for the ground-state energies andcharge states of small B-SIA clusters in crystalline Si. Ourcalculations are relevant to device-scale kinetics simulationsfor predicting the distribution and electrical activity of Bduring ion implantation and thermal annealing. For the clus-ters considered, we find the ones with B content higher than80% to be unbound. The remainder of the clusters arestrongly bound, with each added SIA or BI1 typically low-ering the energy by 1 eV. The B3I

2 cluster is unusuallystable, which implies that it plays a prominent role in theevolution of the active B concentration with annealing timeand temperature.

The work at Lawrence Livermore National Laboratorywas performed under the auspices of the U.S. Department of

Energy~US DOE! under Contract No. W-7405-Eng-48; andwith support from the US DOE Office of Basic Energy Sci-ences.

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1836 Appl. Phys. Lett., Vol. 77, No. 12, 18 September 2000 Lenosky et al.

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