Crystalline and liquid Si3N4 characterization by first-principles moleculardynamics simulations

Aurelio Mauri1,a, Massimo Celino2, Niccolo Castellani1, and Davide Erbetta1

1 Numonyx now Micron, via Olivetti 2, Agrate Brianza (MI), Italy2 ENEA, C. R. Casaccia, via Anguillarese 301, 00123 Rome, Italy

Abstract. Silicon nitride (Si3N4) has a wide range of engineering applications where its mechani-cal and electronic properties can be effectively exploited. In particular, in the microelectronics field,the amorphous silicon nitride films are widely used as charge storage layer in metal-alumina-nitride-oxide nonvolatile memory devices. Atomic structure of amorphous silicon nitride is characterized byan high concentration of traps that control the electric behavior of the final device by the trapping-de-trapping mechanism of the electrical charge occurring in its traps. In order to have a deep un-derstanding of the material properties and, in particular, the nature of the electrical active trapsa detailed numerical characterization of the crystalline and liquid phases is mandatory. For thesereasons first-principles molecular dynamics simulations are extensively employed to simulate thecrystalline Si3N4 in its crystalline and liquid phases. Good agreement with experimental results isobtained in terms of density and formation entalpy. Detailed characterization of c-Si3N4 electronicproperties is performed in terms of band structure and band gap. Then constant temperature andconstant volume first-principles molecular dynamics is used to disorder a stoichiometric sample ofSi3N4. Extensive molecular dynamics simulations are performed to obtain a reliable liquid samplewhose atomic structure does not depend on the starting atomic configuration. Detailed characteriza-tion of the atomic structure is achieved in terms of radial distribution functions and total structurefactor.

1 Introduction

In the recent years new non volatile memory deviceshave been introduced to overcome the emerging scal-ing limitation in the stardard floating gate approachdue for example to the statistical charge injection, cellto cell interference and technology complexity. One ofthe most promising advanced memory for replacingthe NVM-NAND architecture is the so called ChargeTrapping Devices [1] based on the discrete trappingof electronic charge in the material defects: in gen-eral an amorphous Si3N4 layer of few nanometer hasbeen employed in the actual memory device prepa-ration. Typically silicon nitride layer is deposited athigh temperature (> 700 oC) by the help of Chemi-cal Vapour Deposition technique with stoichiometricor Si-rich ratio obained by changing reactant gas flowrate. Due to the recent technology approach, i.e. 3Dgeometry shape [2], material intrinsic defects becomemore relevant than the one produced by implanta-tion damage or induced by spourious element suchas Boron or Phosphorus. To explore the formation ofa such defects we use a different approach with re-spect to Ref. [3] based on cluster models taking intoaccount the dynamical evolution at the atomic level of

a e-mail: aurelio.mauri@numonyx.com

defects and their environment. Our approach is similarto that one reported in Ref. [4] where first-principlesmolecular dynamics simulations are used to produce areliable amorphous sample of Si3N4. Our approach al-lows the study of a larger system on longer time scalesfor a full characterization of the Si3N4 system. Aftera detailed analysis of the crystalline phase of Si3N4 asreported in section 2, we report a computational pro-cedure to produce a reliable liquid sample (section 3).The charaterization of the liquid sample is reported insection 4.

2 Si3N4 crystalline α phase

Si3N4 presents two crystalline hexagonal phases: α(shown in Fig. 1) and β belonging to point group c1and c6h, respectively. We present results relatively toboth phases comparing our results with the experi-mental ones reported in Ref. [5] and in Ref.[6]. Weconsider a simulation cell composed by 28 atoms (12Si and 16 N). At the experimental values of the lat-tice parameters (α phase: a=7.753 A, c=5.618 A; βphase: a=7.706 A, c=2.909 A) we compute the elec-tronic band structures in very good agreeement withthe experimental results [6]. In Fig. 2 the EDOS of

EPJ Web of Conferences 15, 02008 (2011) DOI: 10.1051/epjconf/20111502008 © Owned by the authors, published by EDP Sciences, 2011

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Fig. 1. Structure of Si3N4 crystalline α phase

-20

-15

-10

-5

0

5

10

15

Ene

rgy

[eV

]

EV

EC

Γ LH A Γ MK A

Fig. 2. Calculated band for cristalline α phase Si3N4

the crystalline α phase is reported. The band gap isformed between Γ and K points in good agreementwith Ref. [6]. In Fig. 3 we report the calculated totaldensity of electronic states where an HUMO-LUMOband gap of 4.63 eV is found. This value is in goodagreement, within 8% of error, with the experimentalone (4.9-5.1 eV) [6].

3 Simulation modeling approach for liquid

phase generation

To produce a realiable liquid configuration, exstensivefirst-principles Molecular Dynamic simulations havebeen performed by using the standard Car-Parrinellomethod [7]. All calculations are performed at con-stant volume on a system of 223 atoms: Si-N mix-ture with a ratio of r= [N]/[Si]= 1.347 in order toincrease the probability to find point defects. The pe-riodically cubic cell has a size of 13.91 A correspond-ing to the experimental density of amorphous Si3N4

phase (3.1 g/cm) at room temperature. The startingconfiguration has been chosen by randomly generatingthe coordinates of each atom discarding positions with

-20 -15 -10 -5 0 5 10energy (eV)

dens

ity o

f sta

tes

Fig. 3. Calculated DOS for crystalline α phase Si3N4

0 1 2 3 4 5 6r(Å)

0

10

20

30

40

RD

F

N-NSi-NSi-Sitotal

Fig. 4. Radial distribution function for the liquid Si3N4

distance less than 1.74 A from every other atom. Thisprocedure assures a faster and more accurate ther-malization process. Norm conserving pseudopotentialsare used in conjuction with a generalized gradient ap-proximation (GGA) for the exchange and correlationpart of the total energy. The wave functions are ex-panded in plane waves at the γ point of the supercell.A cutoff of 140 Ry yields converged properties for sim-ple molecules (SiSi, NN and SiN dimers) and repro-duce accurately electronic properties of the crystallinephases, as shown in the previous section. A temper-ature control is implemented for both ionic and elec-tronic degrees of freedom by using the Nose-Hooverthermostats. A simulation time of about 5 ps is usedto thermalize the disordered system at high tempera-ture (T= 3200 K) to assure that the system has lostmemory of its initial conditions. Physical quantitiesare then calculated and averaged on a trajectory last-ing about 7 ps at the temperature T= 1800 K.

4 Si3N4 liquid phase characterization

To analyze the short-range order of the obtained liquidphase we have calculated the total radial distribution

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LAM14

0 50 100 150 200θο

0

0.05

0.1

0.15

0.2

0.25

0.3di

strib

utio

n [a

.u.] total

N-N*-SiSi-N*-SiN-N*-NN-Si*-N

Fig. 5. Calculated angular distribution for the liquidSi3N4

function, reported in Fig. 4. The comparison with theexperimental one reported in Ref. [8] confirms the reli-ability of our numerical model. It is interesting to notethat our model well reproduce the very first peak at1.15 A. Partial radial distribution functions reportedin Fig.4 reveal the origin of this first peak in the to-tal one. This peak is not related to the presence ofhydrogen in the sample as explained in Ref. [4] butto the presence of small but not negligible quantity ofN-N bonds. The distance distribution for S-N bond ispicked at 1.80 A, for Si-Si at 2.38 A while in the caseof N-N bond at 1.15 A and 2.73 A.

The angular distribution is shown in Fig. 5. TheN-Si-N distribution has a peak at 106.5◦ very close tothe peculiar value of regular thetraedra. The Si-N-Sihas instead a pick at 115◦ indicating the presence ofplanar NSi3 units. Both Figures 4 and 5 confirm thepicture of a liquid system composed essentially by Siatoms fourfold coordinated and only few threefold andfivefold coordinated. On the contrary, almost all thenitrogen atoms are bound to three silicon atoms. Ho-mopolar bonds are essentially due to nitrogen atoms.Thus the liquid Si3N4 system can not be consideredcompletely chemically ordered. This picture explainsthe great interest of this system for applications inmicroelectronics.

To verify the reliability of our approach also onlong lenght atomic scales, we have computed the struc-ture factor. The calculated structure factor is shownin Fig.6. The agreement is very good over the entirek range with experimental results reported in Ref. [8,4], the position of maxima and minima being accu-rately reproduced. As expected, the shape of the struc-ture factor of our liquid sample is less structured thanthe experimental one obtained on an amorphous sys-tem. In particular the width of the peaks is more pro-nounced and their height significantly lower.

0 2 4 6 8 10 12 14Q(Å

-1)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

neut

ron

stru

ctur

e fa

ctor

Fig. 6. Neutron structure factor for the liquid Si3N4

5 Conclusion and further work

In this paper our first goal has been to achieve a pre-cise characterization of the liquid atomic structure ofthe Si3N4 system. This liquid sample, that we havedemonstrated a reliable rappresentation of the realliquid phase of the Si3N4 system, can be considered agood starting point for the obtention of the amorphousphase. We have shown that our theoretical approachis able to model accurately all the main features of theliquid system both in the short and long range lenghtscales. Moreover we are confident that this procedurecan be applied successfully to produce and charac-terize the amorphous phase. This approach will allowto study accurately the relation between atomic scaleintrinsic defects and the macroscopic structural andelectronic properties of the Si3N4 system.

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