Multiscale Modeling Study of Native Oxide Growthon a Si(100) Surface

L. Cvitkovich1, M. Jech1, D. Waldhor1,2, A.-M. El-Sayed1,3, C. Wilhelmer1 and T. Grasser11Institute for Microelectronics, Technische Universitat Wien,

2Christian Doppler Laboratory for Single-Defect Spectroscopy in Semiconductor Devices,Gußhausstraße 27–29, 1040 Vienna, Austria

3Nanolayers Research Computing, Ltd.,1 Granville Court, Granville Road, London N12 0HL, United Kingdom

E-mail: [cvitkovich | jech | waldhoer | elsayed | wilhelmer | grasser]@iue.tuwien.ac.at

Abstract—Silicon and its native oxide SiO2 are the mostcommonly used materials in semiconductor device technology.After decades of research in this field, details of the initialoxidation and the subsequent O migration and amorphization arestill a subject of interest. In this paper, we present a multiscalemodeling approach to investigate the oxidation process of aSi(100) surface. Starting from the adsorption and dissociationof single O2 molecules, we further extended our investigationstowards the initial oxidation of the first Si layer and subse-quent O migration. Finally, we construct a realistic model of aSi/SiO2 interface consisting of around 5000 atoms. The employedsimulation techniques used in this study range from densityfunctional theory (DFT) to density functional based tight binding(DFTB) to classical molecular dynamics (MD).

I. INTRODUCTION

The thermal oxidation process of silicon has been of generalinterest for researchers in both engineering and scientific fieldsduring the last five decades [1]. The Si/SiO2 interface is unri-valed in terms of quality and usability for nano-technologies.The interplay between Si and O gains even more importancesince oxygen is one of the most common impurities in com-mercially grown single-crystalline silicon [2]. With the contin-uous downscaling trend for smaller devices, understanding theinitial surface oxidation as well as the growth of amorphousSiO2 (a-SiO2) on a Si substrate becomes crucial.

In this work, the oxidation process of a Si(100) surface isstudied using a multiscale simulation approach on various sys-tem sizes. Starting from surface models containing 226 atomsthe adsorption and dissociation of single O2 molecules onto aSi(100) surface is investigated by means of ab initio moleculardynamics (AIMD). As we increase the O surface coverageand study subsequent O migration into Si, we employ densityfunctional based tight binding (DFTB) as the method of choicefor our dynamical simulations. Ultimately, the formation ofa-SiO2 is modeled within classical molecular dynamics sim-ulations (MD) utilizing classical interatomic potentials. Theexperimentally observed layer-by-layer oxidation of Si [3] ismimicked by placing O atoms in the Si bond-center sites [17].By following this simulation technique, we obtained a realisticSi/SiO2 interface model containing 4992 atoms.

II. METHODOLOGY

Depending on the system size and the complexity of thecalculations such as the simulation time, we applied different

techniques. The details of the utilized methods and theirapplications within this work are summarized below.

A. DFT setup

Density functional theory (DFT) calculations are carriedout using the CP2K package [4]. This code uses the mixedGaussian and plane waves approache (GPW) which is usedin combination with a double-ζ Gaussian basis set and theGoedecker-Teter-Hutter (GTH) pseudopotentials [5], [6]. Theplane-wave cutoff is set to 650 Ry. The exchange-correlationenergy is calculated by means of the semilocal generalizedgradient approximation (GGA) functional PBE. The geome-try optimizations is carried out using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [7] with a force con-vergence criterion of 1.54× 10−2 eV/A. Within the AIMDsimulations, the total energy is conserved (microcanonical orNVE ensemble) and the total spin is restricted to S = 0. Calcu-lating the minimal energy barrier between two configurationsis done using the climbing-image nudged-elastic-band (CI-NEB) method [8], [9] with a spring constant of k = 8.2 eV/A.

B. DFTB setup

In order to study oxidation mechanisms beyond the initialsteps of O adsorption and dissociation, further investigationsinevitably have to be carried out on larger model systems.Especially for DFT calculations, the computationally feasiblesystem size is limited to a few hundred atoms. The DFTBmethod uses merely an expansion of the total energy of DFTwith respect to the charge density and operates based on a self-consistent charge (SCC) algorithm [10]. The simulations arecarried out using the DFTB+ package [11], [12]. The Slater-Koster parameter set pbc-0-3 [13], which is suitable for solidsand surfaces of Si-O systems, is used for all DFTB calcula-tions. In our simulations, we employ atomic basis functions upto the p- and d-shells for O and Si, respectively. For geometryoptimizations again a BFGS algorithm implemented in theDFTB+ package is utilized.

C. MD setup

MD simulations are conducted with the software packageLAMMPS [14] using two different force fields. The ReaxFFforce field [15] is used for investigating adsorption paths of O

onto a Si surface as discussed below. Additionally, a modifiedStillinger-Weber (SW) potential parametrized for a-SiO2 [16],[17] is used to create credible Si/SiO2 interfaces. All classicalMD simulations are modeled within a microcanonical ensem-ble imposing gaussian distributed velocities at the beginning.

D. Preparation of atomic structures

The Si surface structure that served as the basis of our inves-tigations consists of a 4×4×12 Si slab. The dangling bonds atthe bottom Si layer are passivated using H. Optimizing the cellwithin DFT results in lattice constants of a = b = 15.523 A.The cell size in the c-direction is set to c = 37.22 A leavinga vaccuum of 20 A above the slab. Reconstruction of thecleaved surface leads to the formation of asymmetrical dimerrows on the surface [18]. The reconstructed surface atomsform alternating rows of tilted dimers. This reconstructionminimizes the number of dangling bonds on the surface bytransferring one electron of the lower Si dimer to the upperone. In the present case eight dimer units are formed within thesimulation cell. Note, however, that the surface reconstructionvanishes for most classical interatomic potentials since theyare not designed to reproduce surface configurations.

III. RESULTS

In order to provide a complete picture of the oxidationand amorphization of Si, we first investigated the adsorptionand dissociation of single O2 molecules onto the Si(100)surface. Subsequently, the preferred oxidation pathways areinvestigated in a statistical manner by analyzing the adsorptionpaths of around 3000 individual O impinging events on a cleanSi surface. Subsequently, we examined the surface structuresforming at higher O coverage and the resulting O migration.We found evidence for a strain-driven diffusion of O in Si,that results in an oxidation front that penetrates into the Sisubstrate as more O is provided at the surface. Finally, thecreation of a Si/SiO2 interface is presented in the last part ofthis section.

A. Surface Dissociation

As a starting point for the AIMD calculation we placed oneO2 molecule 2.5 A above the DFT relaxed p(2 × 2) Si(100)surface. Next we assigned random, normally distributed ve-locities that are scaled to match the specified temperatureT = 600 K. Spin-restricted (S = 0) MD simulations arerun for 700 fs with a step size of 0.5 fs. Snapshots of thesimulation together with the Mulliken charges of the O atomsand their neighboring Si atoms over time are shown in Fig. 1.The O2 molecule rapidly moves towards an upper Si dimeratom that gets charged positively as the O2 molecule comescloser, as indicated by the Mulliken charge analysis. After170 fs, the oxygen molecule is situated right above the Sidimer and the dissociation process starts. This is accompaniedby an increase of charge of the other neighboring non-dimerSi atoms. During the adsorption process, the O2 moleculepicks up an additional charge of roughly −e, indicating anelectron transfer from the Si surface to the O2 molecule. After

about 250 fs the chemisorption process is completed and theO atoms are located at the backbonds of the upper Si atom,see Fig. 1. Similar results have been found in other studiesthat investigated the adsorption of O2 on a Si surface withinthe scope of AIMD, e.g. [19], [20].

0 100 200 300 400 500Time [fs]

0.5

0.0

0.5

Char

ge [e

]

Neighboring SiO atoms

t = 0 fs t = 70 fs t = 170 fs t = 210 fs t = 400 fs DFT relaxed

Fig. 1. The dissociative chemisorption of O2 (red atoms) onto a reconstructedSi(100) surface (yellow atoms). Snapshots of the AIMD simulation are givenin the upper panel. The top right panel shows the geometry optimized structureafter dissociation. The spin density for values 0.002 e/a0 and −0.002 e/a0is depicted by cyan and magenta isosurfaces, respectively. The Mullikencharges of the O2 and the neighboring Si atoms during the first 500 fs of thechemisorption is shown in the lower panel. The raw data of the simulation(transparent lines) is postprocessed for better visualization. Note that at thebeginning a minority of the simulation steps did not converge to the requiredcriteria, see the raw data. However, this can regularly happen in a dynamicsimulation due to the occurrence of rare and complex geometries, but doesnot affect the final simulation result.

Performing a Bader charge analysis [21] indicated thatthe dissociation alters the charge distribution not only inthe immediate vicinity of the dissociation site but also atother Si dimers. Subtracting the electron density of the initialconfiguration from the electron density of the dissociated andsubsequently relaxed configuration allows to visualize thischarge redistribution, as depicted in Fig. 2.

Fig. 2. The difference in the electron density before and after the dissociation.The blue and red isosurfaces represent an increase and decrease of chargedensity, respectively.

B. Surface Coverage

Stable configurations of a fully oxidized Si surface layerwere found in a previous study [22] and are reproduced bymanually placing the oxygen atoms and relaxing the structureby using DFT. As shown in Fig. 3, there are two stable surfaceconfigurations named A and B, which can be distinguished bytheir O ring pattern distribution. The total energy per dimerE′ of configuration B is 0.43 eV larger compared to config-uration A. Other configurations are generated by introducingrandom distortions and subsequent relaxation. In most casesthe structures relaxed back to the initial configuration or toconfigurations with higher energy. However, as is the case forconfiguration C, some O atoms of the initial configurationB migrated deeper into the Si slab and lowered the totalenergy of the system. The diffusion process lowered theenergy of configuration C by 0.19 eV per dimer comparedto configuration B.

Configuration AE’ = 0 eV

Configuration BE’ = + 0.43 eV

Configuration CE’ = + 0.24 eV

Fig. 3. Stable configurations (A and B) of fully oxidized Si surfaces and astructure with lower energy compared to B (C) due to O atoms (red) migratingdeeper into the Si surface (yellow). Side and top views of the structures aredepicted in the upper and lower panel, respectively. E′ denotes the energy perdimer with respect to configuration A. The diffused atoms in C are indicatedby red arrows.

C. Oxygen Migration

We used configurations A and B as a starting point forDFTB-MD simulations at temperatures ranging from 100 K to1500 K and simulation times of 7.5 ps. The results show thatthe structures are dynamically stable at the given temperatures.If additional O2 is supplied to the surface, O atoms in thevicinity of the excess O2 are “pushed” downwards and migratedeeper into the surface. This result shows that the O doesnot diffuse regularly but might be exposed to a rather strain-driven diffusion process. In order to understand why O doesnot migrate spontaneously, we calculated the energy barrier fora typical diffusion trajectory. The preferred location for an Oatom in crystalline Si is at the bond-center sites between twoSi atoms. In order to develop some insight into the diffusionpaths of O, we conducted a NEB calculation in which theinitial and final configurations are DFT-relaxed bond-centerconfigurations, as shown in Fig. 4. An initial trajectory of5 images is obtained by linearly interpolating between theendpoints. The resulting band is optimized using the CI-NEBmethod. The results show that the energy barrier to overcome

is about 1.72 eV. This barrier implies that the thermal diffusionof O is strongly inhibited.

0 1 2 3 4 5 6Configuration coordinate [Å]

0.0

0.5

1.0

1.5

2.0

Ener

gy [e

V]

12

3

4

5

1 2 3 4 5

Fig. 4. Results of the NEB simulation for the migration of O (red) from onebond-center site (1) to an other (5) via the transition state (3). The energybarrier along this trajectory is 1.72 eV.

D. Amorphization

Previous studies have shown that defect-free SiO2 orSi/SiO2 interfaces can be created using the melt and quenchtechnique [23]. The present work follows another approach inwhich the O atoms are placed consecutively. The amorphiza-tion of a 8× 8× 28 Si(100) surface is modeled by placing Oatoms at the Si bond-center sites and then relaxing the structureby using a modified SW potential [17]. A MD calculation isrun for 10000 steps (∆t = 0.2 fs, T = 600 K) each time16 atoms are placed. 3200 O atoms are placed in total untila stoichiometric composition of the SiO2 layer is reached.The O atoms are placed layer by layer, naturally providing aSi/SiO2 interface growing from the top. This modeling methodis based on experiments that show that Si is primarily oxidizedin layers [3]. For the scope of these calculations the bottomlayer is not passivated; however, the position of the atoms inthis layer is fixed, mimicking an ongoing crystalline Si bulk.Snapshots of this simulation and a Si/SiO2 interface structureduring oxidation are shown in Fig. 5.

The resulting SiO2 model is in good agreement with ex-perimental observations [24] and previous studies of inter-faces [23], [25]. The density is 2.51 g/cm3, binding anglesshow an average of 109.12° for O-Si-O and 140.47° for Si-O-Si. The average O-Si distance is 1.645 A. These values arereached after an approximately 5 A thick interfacial transitionregion. Furthermore, the obtained structure shows a ratherlarge portion of 5 % over- and undercoordinated Si atoms. Itremains to be seen if this is an artifact of our current simulationsettings which might not occur during slower simulations athigher temperatures.

IV. CONCLUSIONS

In the present work, we have investigated the oxidation of aSi(100) surface using a multiscale simulation approach rangingfrom DFT to DFTB and finally to classical MD simulationsat the largest scale. First, we investigated the dissociation and

Fig. 5. Upper panel: snapshots of the Si/SiO2 interface growth. Thefinal model consists of 4992 atoms providing a stoichiometric composi-tion of SiO2 (excluding the Si substrate at the bottom). Lower panel: theSi/SiO2 interface after 30% of the O is placed.

subsequent chemisorption of O2 molecules on a Si surfaceby means of ab initio calculations. The results show that theO2 dissociates via an electron donation from the upper Sidimer atom and its nearest neighbors. However, to compensatefor the charge transfer, the charge density is redistributed atdimer sites further away as well, providing a more reactivesurface for further O2 adsorption [19].

Increasing the number of oxygen atoms in our simulations,we have reproduced stable configurations of oxide monolayersthat cover the Si surface. Using MD simulations within theDFTB method, we observed no signs for O migration upto temperatures of 1500 K if no additional O is provided.Simulations that employed classical interatomic potentials arein line with this observation. Hence, we postulate a straindriven, rather than a thermally driven diffusion process. Thisobservation is in accordance with previous studies, focusingon individual aspects of thermal oxidation [3], [17], [20], [22],[26]. This is further supported by a NEB calculation for Omigration in Si bulk between bond center sites, which yieldsa barrier of 1.72 eV which results in a very slow diffusion rateat typical oxidation temperatures.

A large model of a-SiO2 is finally obtained by utilizing amodified SW potential [17]. By placing O at the bond-centersites of neighboring Si atoms, the growth and amorphizationof SiO2 on a Si substrate is simulated. The obtained structureshows values of density and binding angles that agree wellwith experimental values. Furthermore, the results are similarto other studies that employed the melt and quench techniqueto obtain a-SiO2 structures [23], [25], which justifies thismodeling approach.

V. ACKNOWLEDGMENTS

This project has received funding from the European UnionsHorizon 2020 research and innovation programme under grantagreement No. 871813, within the framework of the project

Modeling Unconventional Nanoscaled Device FABrication(MUNDFAB). The authors acknowledge support from theChristian Doppler Laboratory for Single-Defect Spectroscopyin Semiconductor Devices and the Vienna Scientific Cluster(VSC).

REFERENCES

[1] B. E. Deal et al, “General Relationship for the Thermal Oxidation ofSilicon,” J. Appl. Phys., vol. 36, pp. 3770, 1965.

[2] F. Shimura, “Single-Crystal Silicon: Growth and Properties,” SpringerHandbook of Electronic and Photonic Materials, 2017.

[3] H. Watanabe et al, “Kinetics of Initial Layer-by-Layer Oxidation ofSi(001) Surfaces,” Phys. Rev. Lett., vol. 80, 345, 1998.

[4] J. VandeVondele et al, “Quickstep: Fast and accurate density functionalcalculations using a mixed Gaussian and plane waves approach,” Com-put. Phys. Commun., vol. 167, pp. 103-128, 2005.

[5] J. VandeVondele et al, “Gaussian basis sets for accurate calculations onmolecular systems in gas and condensed phases,” J. Chem. Phys., vol.127, 114105, 2007.

[6] S. Goedecker et al, “Separable dual-space Gaussian pseudopotentials,”Phys. Rev. B, vol. 54, 1703, 1996.

[7] C. G. Broyden, “The Convergence of a Class of Double-rank Minimiza-tion Algorithms,” J. Appl. Math., vol. 6, 76, 1970.

[8] R. Elber et al, “A method for determining reaction paths in largemolecules: Application to myoglobin,” Chem. Phys. Lett., vol. 139, 375,1987.

[9] G. Henkelman et al, “A climbing image nudged elastic band method forfinding saddle points and minimum energy paths,” J. Chem. Phys., vol.113, 9901 (2000).

[10] Th. Frauenheim et al, “ Self-Consistent Charge Density-FunctionalBasedTight-Binding Method for Predictive Materials Simulations inPhysics, Chemistry and Biology,” J. Phys. Chem. A, vol. 111, 26, 2007.

[11] B. Aradi et al, “DFTB+, a Sparse Matrix-Based Implementation of theDFTB Method,” J. Chem. Phys., vol. 111, 26, pp. 5678-5684, 2007.

[12] M. Elstner et al, “Self-consistent-charge density-functional tight-bindingmethod for simulations ofcomplex materials properties,” Phys. Rev. B,vol. 58, 7260, 1998.

[13] C. Koehler et al, “Theoretical investigation of carbon defects anddiffusion in α-quartz,” Phys. Rev. B, vol. 64, 085333, 2001.

[14] H. Aktulga et al, “Parallel reactive molecular dynamics: Numericalmethods and algorithmic techniques, ” Parallel Comput., vol. 38, 245,2012.

[15] J. C. Fogarty et al “A reactive molecular dynamics simulation of thesilica-water interface,” J. Chem. Phys., vol. 132, 174704, 2010.

[16] F. H. Stillinger et al, “Computer simulation of local order in condensedphases of silicon,” Phys. Rev. B, vol. 33, 1451, 1986.

[17] T. Watanabe et al “Novel Interatomic Potential Energy Function for Si,O Mixed Systems,” Jpn. J. Appl. Phys., vol. 38, L366, 1999.

[18] A. Ramstad et al “Theoretical study of the Si(100) surface reconstruc-tion,” Phys. Rev. B, vol. 51, 20, 14504, 1995.

[19] L. C. Ciacchi et al, “First-Principles Molecular-Dynamics Study ofNative Oxide Growth on Si(001),” Phys. Rev. Lett., vol. 9, 196101,2005.

[20] H. Kageshima et al, “First-Principles Study of Oxide Growth on Si(100)Surfaces and at SiO2 /Si(100) Interfaces,” Phys. Rev. Lett., vol. 81, 5936,1998.

[21] W. Tang et al “A grid-based Bader analysis algorithm without latticebias,” J. Phys.: Compute Mater., vol. 21, 084204, 2009.

[22] N. Salles et al, “Strain-driven diffusion process during silicon oxida-tion investigated by coupling density functional theory and activationrelaxation technique,”, J. Chem. Phys., vol. 147, 5, pp. 054701, 2017.

[23] M. Jech et al, “Ab initio-treatment of silicon-hydrogen bond rupture atSi/SiO2 interfaces,” Phys. Rev. B, vol. 100, 195302, 2019.

[24] A. C. Diebold et al, “Characterization and production metrology of thintransistor gate oxide films,”, Mater. Sci. Semicond. Process., vol. 2, 103,1999.

[25] A. Bongiorno et al, “O2 oxidation reaction at the Si(100)-SiO2 interface:A first-principles investigation,” J. Mater. Science., vol. 40, pp. 3047–3050, 2005.

[26] K. Shiraishi et al, “Phenomenological Theory on Si Layer-by-LayerOxidation with Small Interfacial Islands,” Jpn. J. Appl. Phys., vol. 39,pp. L1263-1266, 2000.