Heating and melting of plasma-bornhydrogenated silicon clusters byreactions with atomic hydrogen

Ha-Linh Thi Le*, Nancy C. Forero-Martinez, and Holger Vach

CNRS-LPICM, Ecole Polytechnique, 91128 Palaiseau, France

Received 3 October 2013, revised 19 November 2013, accepted 20 November 2013Published online 18 December 2013

Keywords clusters, hydrogen, molecular dynamics simulations, phase transitions, silicon, thin films

* Corresponding author: e-mail linh-ha-thi.le@polytechnique.edu, Phone: þ33 169 334 321, Fax: þ33 169 334 333

Ab initiomolecular dynamics simulations have been carried outto investigate quantitatively “realistic” heating and meltingprocesses of plasma-born hydrogenated silicon clusters dueto reactions with atomic hydrogen in a plasma reactor. ForH-exposure processes, we have chosen one hydrogenatedamorphous silicon cluster (Si15H10) and the 1 nm hydrogenatedsilicon nanocrystal Si29H24. Our results indicate that the

average energy resulting from each H-atom reaction is aboutthe same for both the amorphous and the initially crystallineclusters before the clusters start undergoing their structuraltransition from the solid to the liquid state. We show that themelting temperature of the Si29H24 nanocrystal is between 1621and 1668K and that its complete phase transition takes about15 ps after the melting temperature is reached.

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1 Introduction Polymorphous hydrogenated silicon(pm-Si:H) thin films produced by plasma enhanced chemicalvapor deposition (PECVD) largely improve the performanceof solar cells, LEDs, and transistors over those based onamorphous silicon materials. Hydrogenated silicon nano-crystals embedded in an amorphous siliconmatrix are thoughtto be responsible for this improvement [1]. It was shown thatthe synthesis of those silicon nanocrystals/nanoparticles istaking place in the gas phase of the plasma, not on thesubstrate itself [2]; and that their size can be controlled with aquite narrow size dispersion by varying the plasma on-time ofsquare-wave-modulated silane plasmas [3].

The formation processes of these hydrogenated siliconnanoparticles were “visualized” at atomic scale by means ofsemi-empirical molecular dynamics simulations [4, 5]. First,the experimentally employed silane plasma is characterizedby a fluid dynamics model [6, 7]. The fluid modelcalculations provide information about relative densitiesof all plasma species, their temperatures, the energydistribution of the reactive species, mean free path lengthsand time intervals between chemical reactions. For aH2/SiH4 discharge, it is demonstrated that atomic hydrogenand SiH3 radicals are the dominant dissociation products;however, hydrogen and silane molecules are still the major

plasma species. Namely, the density of SiH4 molecules isabout 50 times smaller than that of molecular hydrogen, butabout 1000 times greater than that of SiH3 and 10 timesgreater than that of atomic hydrogen. In addition, all reactivespecies are found to have a room temperature energydistribution. This distribution can be described as aMaxwell–Boltzmann distribution function at room tempera-ture. Based on those results of fluid model, the growthprocess of hydrogenated silicon clusters are hence startedby the reaction between a SiH4 molecule and a SiH3 radical.Thereafter, the continuation of the cluster growth issimulated by the impact with additional SiH4 molecules.All of the formed clusters exhibit amorphous structures, veryrich in hydrogen with the hydrogen atoms always on top ofthe cluster surfaces.

The crystallization of amorphous hydrogenated siliconclusters by the reactions with hydrogen atoms was alsoshown in molecular dynamics simulations [5, 8] and laterconfirmed in experiments [3]. The interaction with atomichydrogen leads to cluster heating while the collision withhydrogen molecules cools the cluster down. The simulationsperformed in Ref. [5] reveal that by changing the impingingH-atom flow rates while keeping the same number ofhydrogen molecules, we can control the structure of the

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growing hydrogenated silicon clusters. The hydrogen-treated clusters can evolve to crystalline structures withrelatively low H impact rates. For very high H impact rates,however, the clusters can melt since the clusters do not havesufficient time to cool down between two subsequentcollisions with hydrogen atoms.

The interaction of the cluster with H-atoms leads tocluster heating that is necessary for the cluster to overcomeenergy barriers to more stable structures. Moreover, depend-ing on the H impact flux rates and cooling down rates ofclusters by the collisions with hydrogen molecules, they canbecome either amorphous or crystalline. The present studyhas been dedicated to investigate quantitatively how atomichydrogen heats up plasma-born hydrogenated silicon nano-particles necessary for their melting and crystallization beforetheir deposition on the silicon substrate.

2 Computational details In our investigation, wehave chosen an amorphous hydrogenated silicon clusterSi15H10 and the 1 nm hydrogenated silicon nanocrystalSi29H24 for the hydrogen exposure processes. The Si15H10

cluster was formed in a cluster growth process under plasmaconditions presented in Ref. [4]. The Si29H24 nanoparticleexperimentally produced from the dispersion of bulk siliconby lateral electrochemical etching exhibits a crystallinestructure and outstanding optical properties [9–13]. Wechose here the Si29H24 nanoparticle as a model for crystallinenanoparticles generated in plasma reactors. These clustersare optimized to their minimum energy structures. Figure 1presents the corresponding configurations. Thereafter, theclusters are heated up to room temperature using a quasi-canonical ensemble process. The clusters are then thermal-ized for 5 ps (for Si15H10) and 15 ps (for Si29H24) in themicrocanonical ensemble.

For the heating process, we consider a pure hydrogenplasma with a high concentration of H-atoms. To this end,hydrogen atoms are sent to the clusters, one after the other,with an impact energy of 0.025 eV (i.e., with a velocityof 2225m s�1) corresponding to a Maxwell–Boltzmanndistribution at room temperature [6]. Each hydrogen-cluster

reaction is calculated in the microcanonical ensemble andfollowed for 10 ps after the reaction took place in the case ofSi15H10 and 30 ps in the case of Si29H24.

All of our calculations have been carried out withthe ab initio molecular dynamics simulations packageVASP [14–16] using density functional theory (DFT) inthe generalized gradient approximation (GGA) and with theprojector-augmented wave (PAW) method [16]. Moleculardynamics simulations are performed using theVerlet algorithmwith a time step of 1.0 fs.

To determine the cluster temperature after each reactionwith atomic hydrogen, we have developed a program toseparate the translational, rotational, and vibrational kineticenergies of a cluster based on the scheme proposed byJellinek and Li [17, 18]. The cluster temperature is calculatedfrom the average vibrational kinetic energy:

T ¼ 2 Evibh i3N � 6ð ÞkB ; ð1Þ

where N is the number of cluster atoms, kB is the Boltzmannconstant.

To analyze the structure characteristics of the clustersduring the hydrogen treatment process, we have calculatedtheir radial distribution functions (RDFs). The RDF gives theprobability of finding a pair of atoms with an interatomicdistance r in comparison with the probability expected fora completely random distribution at the same density. Theexpression to calculate RDF is described as follows [19, 20]:

gðrÞ ¼ nðr;DrÞrNtrun4pr2Dr

; ð2Þ

in which g(r) is the RDF, nðr;DrÞ the average number ofatoms in a shell of width Dr at distance r, r the average atomdensity, N the total number of atoms, and trun is the numberof steps selected to calculate the RDF.

In order to determine phase states of the clusters duringthe H-exposure process, we have also investigated thebehavior of the mean-square displacement (MSD) definedas [21]

MSDðtÞ ¼ 1N

XNi¼1

riðt0 þ tÞ � riðt0Þ½ �2* +

; ð3Þ

where ri(t) denotes the position of atom i at time t, N is thenumber of atoms.

From the slope of the MSD, we can calculate the self-diffusion coefficient [22]:

D ¼ 16ddt

MSDðtÞð Þ: ð4Þ

All of the average values are calculated over the last5ps or 15ps of each trajectory for Si15H10 and for Si29H24,respectively.

Figure 1 The initial configuration of the hydrogenated siliconclusters. The large brown spheres represent silicon atoms while thesmall white ones represent hydrogen atoms.

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3 Results and discussions3.1 Hydrogen-induced heating of hydrogenat-

ed silicon nanoparticles3.1.1 Si15H10þnH Figure 2a shows a heating process

of the Si15H10 cluster while it adsorbs atomic hydrogen. Thecluster is heated rapidly (about 330–400K for each reaction)during the first three reactions with H-atoms. Thereafter, thecluster temperature increases more slowly, namely about190K for the fourth reaction and only about 60K for thefifth H-atom to reach 1704K. Therefore, we suggest thatthe Si15H10 might melt and undergo a phase transition tothe liquid state at a temperature between 1450 and 1704Kbecause most of the energy which the cluster gains fromthe fourth and fifth reactions with H-atoms is probablyemployed to carry out structural changes and only a smallpart of the reaction energies is used to heat up the clusterfurther.

As a result of the H adsorption, there are more and moresilicon hydrides (SiH2 and SiH3) formed on the clustersurface because of hydrogen diffusion. Those siliconhydrides are weakly bound on the cluster surface. In sometrajectories, one SiH4 molecule desorbs from the surface ofSi15H16 cluster typically after the reaction with six H-atoms.

The remaining Si14H12 cluster rearranges its structure andends up with a final temperature of 1903K.

3.1.2 Si29H24þnH During the H-exposure process,the cluster temperature rapidly increases during the first sixH-atom adsorption reactions following a staircase functionwith numbers of reactions with H-atoms (see Fig. 2b for atypical and representative reaction dynamics). In the shownexample, the seventh reaction with a H-atom leads to theetching of one SiH4 molecule from the cluster surface. Asa result, the cluster temperature slightly decreases (from1343 to 1288K). The remaining Si28H27 cluster then adsorbsone H-atom and heats again to 1507K. Thereafter, wehave observed a slowly increasing cluster temperature fromthe eighth to the 12th reaction with H-atoms (from 1507 to1668K). This range of temperature is near the melting pointof bulk silicon. Therefore, we suppose that there is astructural transition from the solid to the liquid state.

We calculated the average cluster temperature increasefor each reaction during the first three H-atom reactions forSi15H10 and during the first six H-atom reactions for Si29H24.Those values are about 375 and 186K for Si15H10 and forSi29H24, respectively. The ratio between those values isinversely proportional to the cluster masses. This implies thatthe average energy resulting from each H-atom reaction isabout the same for both the amorphous and the initiallycrystalline clusters according to thermodynamics before theclusters start undergoing their structural transition from thesolid to the liquid state.

3.2 Melting dynamics The RDFs were investigatedto examine how the atomic hydrogen damages the structureof the clusters. The RDFs of the Si15H10 cluster after eachH-atom reaction (Fig. 3a) show that the second peak is lesspronounced indicating that the structure of the Si15H10

cluster becomes more and more disordered as the clusteris heated up.

The RDFs of Si29H24 cluster show that after tworeactions with H-atoms, the cluster remains in its crystallinestructure because the features of the second and third peakare still clearly distinguishable. After the reaction with thefifth H-atom, however, the second peak entirely disappeared.The peak at 3.85Å becomes broader during the H-inducedcluster heating because of the less well-defined clustergeometry.

From the RDFs, we can observe how the clusterstructures change due to the hydrogen-induced heating.However, to further distinguish between solid and liquidphases of our clusters, we also consulted the MSD of siliconatoms in the clusters at different equilibrated temperaturesafter the H-atom reactions (Fig. 4). The MSD at 722K (afterthe first reaction) exhibits a solid-like behavior. The MSDgraphs for the intermediate temperatures at 1055 and 1450Kmark the onset of the phase transition to the liquid state.After the fourth, fifth, and sixth H-atom reactions, the MSDsclearly indicate a liquid state. The ballistic regimes in theMSD graphs of both the Si15H14 cluster at 1641K and the

Figure 2 Evolution of the instantaneous temperature of clusterswith the number n of reactions with H-atoms: (a) Si15H10;(b) Si29H24.

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Si15H15 cluster at 1704K last about 0.25 ps and are directlyfollowed by diffusive regimes. On the other hand, for theSi14H12 cluster at 1903K, the silicon atoms are in theballistic regime only up to about 0.1 ps suggesting a lessstable cluster configuration.

The MSD graphs for Si29H24 shown in Fig. 5a and bindicate that the Si29H24 cluster clearly remains in the solidstate although it heated up to 1507K due to its reaction witheight H-atoms. Continuing the hydrogen exposure process,we have observed the onset of the structural transition to theliquid state after the reaction with the 11th H-atom yielding a

cluster temperature of about 1621K. The cluster completesits phase transition to the liquid state after the reaction withthe 12th hydrogen atom as can be concluded from the liquid-like behavior shown in theMSD graph; i.e., the silicon atomsin the cluster are in the ballistic regime for about 0.2 ps andenter the diffusive regime of the liquid state thereafter.

Interestingly enough, we have observed a slight decreasein cluster temperature about 15 ps after the Si29H24 clusterreacted with the 12th H-atom. Right after the reaction, thecluster temperature reached 1813K, then it slowly decreasedand finally equilibrated at 1668K. We have investigatedthe MSD graphs of the silicon atoms in the cluster directlyafter it reacted with the 12th H-atom (Fig. 6b) and after itequilibrated (Fig. 6c). TheMSD graph right after the reactionwith the 12th H-atom exhibits the same slope as the one ofthe MSD graph after the 11th H-atom reaction. It means thatthe cluster is still at an intermediate state before the completechange to the liquid-like state is achieved. The MSD graphafter the cluster equilibrated at 1668K, however, clearlyshows a liquid-like behavior. This indicates that the phasetransition is only completed about 15 ps after the Si29H24

cluster reacted with the 12th H-atom. During this process,the cluster gained the reaction energy to make a structural

Figure 3 The RDFs of the clusters during the heating processesinduced by the subsequent reactions with H-atoms: (a) Si15H10; (b)Si29H24; (c) Si28H27.

Figure 4 (a) MSD of silicon atoms in the Si15H10 cluster atdifferent temperatures due to the subsequent reactions withH-atoms; (b) a zoom to show the details of the MSD graphs.

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transition to a less stable state. Therefore, we have seenabove that the temperature decreased slightly.

Figure 7a shows that the self-diffusion coefficients ofsilicon atoms of the Si15H10 cluster increase with tempera-ture. Those coefficients are extracted from the slopes of theMSD graphs in the diffusive regime at different temperaturesof the H-treatment process. There is a slight increase of theself-diffusion coefficients from 1055 to 1450K, while arapid increase is observed between 1450 and 1704K. In fact,the self-diffusion coefficient at 1704K is about six timeslarger than at 1450K. The self-diffusion coefficient is about0.67Å2 ps�1 at 1903K. This value is quite comparable to theone obtained by Zachariah et al. [23] especially consideringthat his 480-silicon atom cluster is much larger than ours andthat his temperature is yet higher than ours. Using classicalmolecular dynamics simulations with the three-bodyStillinger–Weber interatomic potential, they determinedthe self-diffusion coefficient to be 1.05Å2 ps�1 at 2000Kand concluded that their cluster is in the liquid state.Therefore, we suggest that our H-treated Si15H10 cluster at1903K is also in the liquid state and that there is a structuraltransition from the solid to the liquid state in the temperatureregion between 1450 and 1704K. The self-diffusion

coefficients for the Si29H24 cluster at different temperaturesof the H-exposure process exhibit a very rapid increase(by a factor of about 15) from 0.036 to 0.53Å2 ps�1 in a verynarrow temperature region (1621–1668K) suggesting astructure change to the liquid state resulting from the reactionwith the 12th H-atom (see Fig. 7b).

The self-diffusion coefficients of the H-treated Si15H10

and Si29H24 clusters are about 0.17Å2 ps�1 at 1641Kand 0.53Å2 ps�1 at 1668K, respectively. Those values aresmaller than the self-diffusion coefficient of bulk silicon atthe melting point (2.52Å2 ps�1 at 1687K) obtained fromexperiments [24, 25]. This difference is in agreement withprevious studies about the melting characterizations of pureand hydrogenated silicon nanoparticles [23, 26, 27]. Theself-diffusion coefficients for pure and hydrogenated siliconnanoparticles investigated in those references are alwaysconsiderable smaller than that of bulk silicon at comparabletemperatures. Tentatively, we suggest that the observeddifference in self-diffusion coefficients for bulk and nano-crystalline silicon can be traced back to the relative numberof core and surface atoms. While the core silicon atomsbehave fairly like bulk silicon, the surface silicon atomsexhibit different properties. Zachariah et al. [23] had

Figure 5 MSD of silicon atoms in the Si29H24 cluster at differenttemperatures due to the subsequent reactions with H-atoms: (a) firstsix reactions with H-atoms; (b) last six reactions with H-atoms.

Figure 6 (a) Time evolution of the instantaneous temperature ofthe Si29H24 cluster after the reaction with the 12th H-atom for thechosen typical example; (b) the MSD of silicon atoms in the clusterright after the reaction with the 12th H-atom at a temperature of1813K; (c) the MSD of silicon atoms in the cluster after itequilibrated to 1668K.

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examined a 480-silicon atom cluster over the temperaturerange from 600 to 2000K. The authors found that the surfaceatoms are three to four times coordinated over the studiedtemperature range while the coordination number of coreatoms is around 5 at temperatures up to 1600K and 8.49 at2060K. For a given temperature, the mean bond length ofthe cluster increases with coordination number due to partialelectron deficiency. Consequently, core atoms have largermean bond lengths than surface atoms. This indicates thatthe Si–Si bonding in the core is weaker than at the surface,facilitating the diffusion and thus increasing the self-diffusion coefficient. Our Si15H10 cluster has no core siliconatoms and Si29H24 nanocrystal has only one. Therefore,the self-diffusion coefficients of our clusters at a giventemperature are smaller than those of bigger siliconnanoparticles [23, 26, 27] and bulk silicon [28].

Some previous work concerning the melting behavior ofsmall silicon clusters [29, 30] (from 7 to 21 silicon atoms)has investigated the melting temperature as a function ofcluster size. They have found that the melting temperature ofsmall silicon clusters does not exhibit a clear trend with

cluster size; i.e., some sizes (for instance: 7, 12, 15 siliconatoms) are more stable, and exhibit thus higher meltingtemperatures than other sizes. The authors [30] usedcanonical Metropolis Monte Carlo simulations to studythe thermal behavior of silicon clusters and calculated thebond length root-mean-square fluctuation to characterize themelting behavior of those clusters. They have found thatthe melting temperature of a 15-silicon atom cluster with alayered stack structure is about 1350K and that this clusterstarted melting from about 1250K and was fully melted atabout 1500K. In our work, according to the evolution of thecluster temperature and the self-diffusion coefficients withthe number of reactions with H-atoms, we conclude thatthe Si15H10 cluster starts to melt from 1450K (after threereactions with H-atoms) and becomes totally liquid at about1704K (after five reactions with H-atoms). Looking backat Fig. 2a, the Si15H10 cluster temperature significantlyincreases during the first three H-atom reactions. It remainsnearly constant during the fourth and the fifth reactionwhere the cluster undergoes its phase transition. Thereafter,additional reactions with H-atom heat the liquid siliconcluster further.

4 Conclusions In the present work, the hydrogen-induced heating and the phase transition from crystalline toamorphous and solid to liquid states as well as the on-set foretching of plasma-born hydrogenated silicon nanoparticleshave been investigated quantitatively for the first time.Contrary to previous studies concerning the phase transitiondynamics of pure or hydrogenated silicon nanoparticles, weconsidered here cluster heating induced by reactions withH-atoms as in a realistic plasma reactor instead of using“artificial” velocity scaling.

The results indicate that the average energy resultingfrom each H-atom reaction is about the same for both theamorphous and the initially crystalline clusters before theclusters start undergoing their structural transition fromthe solid to the liquid state. The evolution of the clustertemperature as well as the self-diffusion coefficientswith the number of reactions with H-atoms suggest thatthe clusters undergo the solid to liquid phase transition inthe temperature regions from 1450 to 1704K in the case ofSi15H10 and from 1621 to 1668K in the case of Si29H24. Atthose temperature regions, the cluster temperature slowlyincreases while the self-diffusion coefficients significantlyaugment. In a typical example, we have observed the meltingdynamics of the Si29H24 cluster at 1668K after the reactionwith the 12th H-atom, showing that the phase transition froman intermediate to a completely liquid-like state takes about15 ps after the Si29H24 cluster reacted with the 12th H-atom.

All 24 H-atoms are on the surface of the saturatedSi29H24 cluster before the heating with H-atoms. As a result,this cluster is initially less reactive than the Si15H10 clusterand some of the impinging H-atoms do thus not react withthis cluster at all and are reflected. Despite this differencebetween the two investigated clusters, however, the meltingalways occurs once the reactions with incoming H-atoms

Figure 7 Self-diffusion coefficients of silicon atoms in the twoconsidered clusters at different temperatures resulting from thesubsequent hydrogen exposure reactions: (a) Si15H10; (b) Si29H24.

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supplied enough energy for the solid–liquid phase transitionto take place since the particular cluster structure was losta long time before the melting.

Our quantitative analysis of H-induced processesconcerning plasma-born hydrogenated silicon clustersmight help to improve our understanding of dusty plasmadynamics necessary for the optimization of plasma conditionsemployed for pm-Si:H thin film deposition.

Acknowledgments We acknowledge the ‘Institut duDéveloppement et des Ressources en Informatique Scientifique’(IDRIS) for computational resources (Grant i2012090642).

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