Electronic Structure Theory and Mechanisms of the Oxide TrappedHole Annealing Process

S. P. Karna,1 A. C. Pineda,2 R. D. Pugh,1 W. M. Shedd,1 and T. R. Oldham3

1Air Force Research Laboratory, Space Vehicles Directorate, 3550 Aberdeen Ave, SE, Kirtland AFB, NM 87117-5776

2Albuquerque High Performance Computing Center, The University of New Mexico, 1601 CentralAve, NE, Albuquerque, NM 87131

3Army Research Laboratory, AMSRL-SE-RL-RL, 2800 Powder Mill Road, Adelphi, MD 20783

Abstract

First principles quantum mechanical calculationson model SiO2 clusters support the Lelis model ofreverse annealing in the oxide and provide the firstelectronic structure explanation of the process,suggesting that delocalized holes (E'δ centers) areannealed out permanently. Localized holes(E'γ centers) form a metastable, dipolar complex,without restoring the Si—Si dimer bond uponelectron trapping. In the presence of an appliednegative field, these charge neutral, dipolarcomplexes, (E'γ+e−), can readily release theweakly bonded electron, exhibiting a reverseannealing process.

I. INTRODUCTION

Metal oxide semiconductor (MOS)devices are known to have a complex time-dependent response to ionizing radiation [see, forexample, references 1-3]. An importantcomponent of this response is the build up andannealing behavior of positively charged hole trapsin the oxide near the Si/SiO2 interface. Ofparticular interest has been the so-called “negativebias reverse annealing” (NBRA) [3-11]. Hightemperature, biased anneal experiments on

irradiated devices indicate that a significantfraction of trapped holes that under positive biasare apparently annealed out via electron capturereappear when the bias is switched to negativepolarity [3-8]. These experiments suggest theexistence of a metastable neutral center where theelectron and hole are associated, but do notrecombine. Several studies have been performedto understand the physics of this center and of thereverse annealing process [3-8]. While someinsights into the reversibility of the positive chargeannealing process have been achieved, leading toa qualitative model that successfully explains themain experimental observations, the mechanismsunderlying the model have not yet been fullyexplained.

This model, originally proposed by Leliset al. [6,7], involves the trapping and detrappingof electrons at positively charged E' centers (alsosometimes called oxygen vacancy defect centers).E' centers involve an unpaired electron located ata three-fold coordinated tetrahedral Si center anda hole trapped at another, spatially separated, Siatom which can be represented as [Si↑ +Si][12,13]. Here the upward arrow represents anunpaired electron. The E' center has beenidentified as a radiation-induced trapped hole[14]. Experimentally, Lelis et al. observed thatsome of the trapped holes near the interface

appeared to anneal out completely by capturingan electron, and in the model, it is suggested thatthis happens because the broken Si-Si bondreforms. It is also proposed in the model, that ifthe two Si atoms relax to positions too far apartfor the bond to reform, then the captured electrongoes to the neutral Si atom, and pairs up with theunpaired electron instead of going to the positiveSi atom [Si↑↓ +Si]. The result is a metastable,electrically neutral, dipolar complex whichreleases the captured electron under negativebias, restoring the E' center. This proposalaccounted very simply for the experimental databy Schwank et al. [4] and by Lelis et al. [6-8],and it was also consistent with the spectroscopicdata available at the time [14].

Even so, the idea of a metastable dipolewas controversial at first. For one thing, coulombrepulsion between the two electrons on thenegative end of the dipole would make the dipoleenergetically unfavorable, everything else beingequal. This objection was raised most forcefullyby Edwards [15]. Lelis et al. speculated that theenergy gained from relaxation of the oxidenetwork might be enough to offset the electron-electron interaction, but lacked the analyticalcapability to calculate any of the energy levelsassociated with the defect. Other authors haveproposed alternative models. Freitag et al.[16,17] proposed that the experimentallyobserved charge switching was due to anotherunknown defect and that E' centers did notaccount for the charge switching. Fleetwood et al.[18] proposed that while the Lelis et al. modelprobably accounted for part of the observedcharge switching, other defects could also play arole. They suggested several other possible defectstructures that could also switch charge.

However, subsequent experiments tendedto provide additional support for the Lelis et al.model, culminating with the work of Conley et al.[11,19]. Conley conducted a series of biasswitching experiments, similar to those performed

by others, except that he monitored the E'signature with an electron spin resonance (ESR)apparatus. The results showed that E' centers doswitch charge, contrary to the conclusions ofEdwards and Freitag et al. Furthermore, theyswitch charge in precisely the manner proposedby Lelis et al., which appeared to rule out thealternative structures proposed by Fleetwood. (Ofcourse, no experiment can ever completely ruleout some other defect-all one can conclude is thatthe effect of the defect is less than theexperimental error bars, which are never zero.)The Conley experiments showed that the defectdescribed by Lelis et al. is the dominant switchingoxide trap, at least for the samples tested. Theseexperiments, and others bearing on the nature ofthe oxide traps, have been reviewed in detail byOldham in a recent monograph [20].

In this study, we present the results of ourfirst principles electronic structure calculations,which, for the first time, provide a consistent andunified quantum mechanical explanation of theoxide trapped hole annealing process. Our resultssuggest that (i) electron trapping at unstrained E'centers, known as the E'δ centers [21-24],restores the Si—Si dimer bond and permanentlyanneals out the trapped holes and (ii) electrontrapping at strained E' centers, known as the E'γcenters [12,13] and having the atomicconfiguration [Si↑ +Si], results in a charge neutraldipolar complex as suggested by Lelis et al. [6,7].The extra electron in the dipolar complex is onlyweakly bonded and can be easily removed.Furthermore, the present results, for the first time,clearly demonstrate that the trapping anddetrapping of holes strongly depend on themicrostructural features of the oxide network, aneffect which has been long suspected by the oxidecommunity [20].

II. CALCULATIONS

We report calculations on model clustersemploying the ab initio Hartree-Fock (HF)method with STO-3G and DZP basis sets. In theHF method, the electronic Schrödinger equation,HelecΨ=EelecΨ, resulting from the Born-Oppenheimer separation of nuclear and electronicmotion is solved using a variational principle. Theelectronic Hamiltonian, Helec, includes the quantummechanical operators describing the electrons inthe system and their interactions with the nucleiand each other. The electronic wavefunctions canthen be used to construct potential energysurfaces for the motion of the nuclei and the mostfavorable arrangement of the atoms can be foundby minimization of the total energy of the system.In the HF method, trial wavefunctions areconstructed as a Slater determinant of oneelectron molecular orbitals (MOs) which are anti-symmetric under the exchange of any pair ofelectrons as required by the Pauli exclusionprinciple. These 1 electron MOs are written aslinear combinations of one electron atomicorbitals, or basis functions, centered on each ofthe atoms of the system. The variational principleresults in a set of one electron equations for thecoefficients of the molecular orbital expansion, theRoothan or more generally the Pople-Nesbetequations, that must be solved self-consistently.The degree of sophistication of an HF calculationis determined by the number of basis functionsused in the MO expansion and by the degree towhich the basis functions approximate the truebehavior of atomic wave functions. A minimalbasis set calculation, such as that using an STO-3G basis set, uses one basis function for eachinner shell and valence shell atomic orbital. Theaccuracy of HF is significantly improved byperforming an extended basis set calculation inwhich additional basis functions are used todescribe each inner shell and valence shell atomicorbitals. The accuracy is also improved by adding

basis functions (called polarization functions) withhigher angular momentum quantum numbers thanthe maximum angular momentum quantumnumbers of the valence shell electrons in theground state atoms. Extended basis setcalculations, such as the double zeta pluspolarization or DZP basis set calculations wereport here, allow the atomic orbitals to change insize, shape, and direction as the atoms interact[25]. To speed the evaluation of the requiredintegrals, each basis function is written as a linearcombination of Gaussian functions,

∑= )()( rgdr jiji

rrχ ,

where )exp()( 2rrg jj α−∝ . The coefficients dij

and exponents αj are determined by variationalcalculations on single atoms. STO-3G calculationsusually give quite good predictions of bond anglesand bond distances, but fair poorly on energies.DZP calculations give better results especially forenergies, but are much more expensive to do asthe computational cost of the calculation rises asthe 4th power of the number of basis functionsused.

Figure 1. Defect-free oxide with no closedrings. The largest atoms are Si, the mid-sizedatoms are O atoms, and the smallest atomsare H atoms. The bridging oxygen isremoved to form a vacancy site.

Three sets of model clusters of increasingcomplexity and differing network features wereemployed. Model clusters representing precursors

and corresponding hole traps consisted of (a) asegment of the oxide without nearby closed ringstructures [Fig. 1], (b) a segment of oxide with 4three-member (six-atom) rings [Fig. 2], and (c) asegment with 4 six-member (twelve-atom) rings[Fig. 3]. A bridging O atom in the clusters,marked by arrows in Figs. 1-3 is taken as the sitefor vacancy generation and hole trapping. Theoxide network is terminated by H atoms.

III. RESULTS

A. Precursor: Equilibrium geometries for themodel precursor clusters were obtained by abinitio Hartree-Fock (HF) energy minimizationusing atomic basis sets of different sizes. The twosmaller clusters were optimized using a doublezeta plus polarization (DZP) basis set. The largestclusters were optimized using a minimal STO-3Gbasis set. Very little change in the geometry wasnoted between different basis sets. The bonddistance and bond angles are in reasonableaccord with the corresponding experimentalvalues and very well represent the amorphousnature of SiO2.

Figure 2. Defect-free oxide with 4 three-membered rings. The largest atoms are Si,the mid-sized atoms are O atoms, and thesmallest atoms are H atoms. The bridgingoxygen is removed to form a vacancy site.

B. Neutral oxygen vacancy (VO0): The VO

0

sites were created by removing one bridgingoxygen atom in each cluster. An equilibriumgeometry in the VO

0 state for each cluster wasobtained by ab initio HF energy minimization.The optimized equilibrium geometry for the VO

0

center obtained from the oxide cluster in Figure 2is shown in Figure 4. The corresponding structureobtained from Figure 1 is not shown as theresulting effects are very similar.

Figure 3. Defect-free oxide with 4 six-membered rings. The largest atoms are Si,the mid-sized atoms are O atoms, and thesmallest atoms are H atoms. The bridgingoxygen is removed to form a vacancy site.

The main effect of this minimization is theformation of a Si—Si dimer bond with a length ofabout 2.351 Å for the smallest cluster derivedfrom Figure 1 and 2.331Å for the cluster shownin Figure 4 at the oxygen vacancy [26]. Thecorresponding Si-Si dimer bond distance for theneutral vacancy derived from Figure 3, shown inFigure 5, is 2.438 Å [26]. These distances aresubstantially smaller by about 0.64 to 0.79 Å thanthat between the two Si atoms prior to the VO

0

formation. A common feature of all three clustersis that the two Si atoms adjoining the vacancymove inward as noted in previous studies

[12,13,24-27]. The rest of the networkexperiences marginal changes upon relaxation.

C. The positively charged oxygen vacancy(VO

++ 1): In the present study, the oxide trappedholes are represented by the VO

+1 centers. TheVO

+1 centers were generated by removing anelectron from the VO

0 centers described above.After the creation of the positive charge, eachmodel cluster was allowed to totally relax to givea minimum energy configuration.

Figure 4. E'δδ: Si-Si dimer bond at thevacancy. VO indicates the location of themissing O atom.

In the case of the cluster shown in Fig. 4,the two Si atoms forming the dimer bond movedslightly away from each other, by 0.32 Å. For thesmallest cluster, not shown, the two Si atomssimilarly moved apart by 0.35 Å. Marginalchanges were noted in the remaining structure ofthese clusters. Even after repeated geometryoptimization, the two central Si atoms in theseclusters (VO

+1) retained their symmetricconfiguration. We have calculated the 29Sihyperfine coupling constants of the two Si atoms.The calculated value ranged from 87 to 99 Gaussin excellent agreement with the correspondingexperimental value (100G) for the E'δ center [21-23], which has been found from quantummechanical calculations [24,27] to be a trapped

hole shared between two Si atoms. It is importantto note here that the E'δ center represented by ahole trapped on the smaller vacancy structures, inwhich the hole and the unpaired electron areequally shared between the two Si atomsadjoining the vacancy, does not represent theprecursor to the dipolar complex of the Lelismodel [6].

Figure 5. Neutral VO cluster created fromFigure 3 by removing the bridging O atomand optimizing the resulting structure.

In contrast to the smaller clusters, thecluster shown in Fig. 5, immediately distortedupon removing an electron. The resulting structureis shown in Fig. 6. One of the Si atoms moved faraway from its original position, by about 1.33 Å,forming a Si—O bond with another O atom in theback ring. The other Si atom experienced a smallrelaxation, but essentially remained in its originalposition. The back-bonded Si—O distance ismuch larger (about 1.76 Å) compared to anormal Si—O bond which has a length ofapproximately 1.62 Å. In this case, the unpairedelectron spin is completely localized on theundisturbed, three-fold coordinated Si atom. Thedistorted, back bonded Si atom has practically nospin density. This model represents the E'γ center[12,13], the precursor [Si↑ +Si] of the Lelismodel.

Figure 6. E'γγ : No Si-Si dimer bond at thevacancy. Si bonded to O across the flexiblering. VO indicates the site of the missing Oatom.

D. Electron trapping by the oxide holecenters (VO

+ 1+ 1 ++ e −−): Next an electron wasadded to the VO

+1 centers at their respectiveoptimized equilibrium geometries, as shown inFigs. 4 and 6, and the resulting neutral systemswere allowed to fully relax to a minimum energystate. The cluster of Fig. 4 representing the E'δcenter reached an equilibrium structure restoringthe Si—Si dimer bond of the neutral oxygenvacancy centers (VO

0). The binding energy of theelectron in Fig. 4 was calculated to beapproximately 8.90 eV. The electron charge, asexpected, is shared nearly equally by the two Sicenters forming the dimer. This sharing of theelectron charge by the two Si centers is easilyseen in the electron charge distribution in thehighest occupied molecular orbital which is shownin Fig. 7. The cluster with no rings near thevacancy displays similar behavior.When an electron was added to the [Si↑ +Si]complex shown in Fig. 6 and a geometryoptimization was performed, a minimum energystructure was reached after about 25 iterations. Inthis structure, however, the Si—Si dimer bond ofthe VO

0 is not fully restored. The back bonded Si

atom is still separated from its dimer counterpartof the VO

0 by about 2.61 Å which is 0.17Å largerthan inVO

0.

Figure 7. Contour plot of the highest occupiedmolecular orbital for the large neutral oxygenvacancy calculated using a DZP basis set.The solid and dashed lines denote the phase(sign) of the molecular orbital (positive andnegative, respectively).

The system (VO+1+e−) in this state is about 1.99

eV higher in energy than VO0. (The latter result

was computed using the DZP basis set, an STO-3G basis set energies are not very meaningful.)This structure thus represents a metastable state of

the charge neutral VO center. In this state, thecalculated binding energy of the electron, withrespect to the equilibrium VO

+1 structure is about7.29 eV (again using the DZP basis set). Also, theelectron charge in the case of Fig. 6 is largelylocalized on the undistorted Si. This readilyapparent in the electronic charge distribution ofthe highest occupied molecular orbital as shown inFigure 8.

Figure 8. Contour plot of the highest occupiedmolecular orbital for the largest positivelycharged oxygen vacancy using a DZP basisset. The phase (sign) of the molecular orbitalis denoted by solid and dashed lines, whichrepresent positive and negative values,respectively. Note that the electron is largelylocalized on the undistorted Si atom.

IV. DISCUSSION

The calculations on neutral VO0 centers

reveal that regardless of the complexity in theoxide network surrounding the vacancy, thenetwork relaxes in such a way that the two Siatoms adjacent to it move toward each otherwhen the vacancy is first formed. However,trapping of a hole leads to different responses inthe network depending upon the atomic structuresaround the vacancy. For an oxygen vacancylocated at a site with no rings or between small(stiff) rings, a trapped hole is shared betweendimer Si atoms. These structures lead to theformation of E'δ species. For an oxygen vacancylocated between large, flexible rings, hole trappingresults in preferential distortion of the SiO2 ringadjacent to the vacancy. In this case, the hole islocalized at a single Si atom, which tends to distortand form a dipolar bond with an O atom in theback of the flexible (six-member) ring. Theelectron is localized on an essentially undisturbedSi atom. This complex represents the E'γ center.

The type of E' center formed is intimatelyrelated to the local structure of VO. Openstructures with no back oxygen available forbonding and small, inflexible rings both lead to asymmetric relaxation following the hole trapping,whereas large ring structures have both a flexiblenetwork and back oxygen atoms available forbonding. Thus, the first two types of localstructures result in the formation of E'δ whilestructures with properties similar to the third resultin the formation of E'γ centers upon hole trapping.

In both the E'δ and E'γ configurations, theone electron energy level corresponding to theorbital in which the unpaired electron is localizedis lower in energy by more than 10 eV than thenext empty orbital. These levels are referred to asthe highest occupied molecular orbital (HOMO)and the lowest unoccupied molecular orbital(LUMO), respectively. The HOMO and LUMO

in the case of isolated clusters as used in this studyloosely correspond to the top of the valence band(VB) and the bottom of the conduction band(CB), respectively, of bulk SiO2. The HOMO-LUMO energy difference for the E'δ and E'γconfigurations shown in Figures 4 and 6 are listedin Table 1. An added electron, when captured bythe VO

+1 center, goes into the previously singlyoccupied, lower energy level, which in this case isthe HOMO. In the case of the E'δ centers, wherethe HOMO wavefunction has equal contributionsfrom the two Si centers (Figure 7), the addedelectron is shared by the two Si atoms andrestores a covalent bond between them.However, in the case of the E'γ centers theHOMO wavefunction is highly localized on asingle Si atom (Figure 8), so the added electron islocalized there. This gives rise to the dipolarcomplex of the Lelis model. In this state, due toincreased Coulomb repulsion between the twoelectrons in a small volume of space and areduced electron-nuclear attraction, the systembecomes metastable. The added electron in themetastable state has considerably smaller bindingenergy than that in a stable, dimer structure.Therefore, by overcoming the smaller bindingenergy, the system can relax by releasing the extraelectron. This results in the regeneration of thetrapped hole (E'γ) center.

It should be noted that further work isneeded to access the relative stability of themetastable configuration, and the degree to whichpolarization of the surrounding oxide, neglected inour cluster approximation, might further stabilizethe metastable configuration.

Defect Center ∆∆ E (HOMO-LUMO)(eV)

E'δδ � 10.88

E'γγ 11.42

Table 1. ∆∆ E (HOMO-LUMO) for model E'δδ

and E'γγ centers obtained with the use of aDZP basis set.

V. CONCLUSIONS

The present calculations have provided adetailed electronic structure explanation of thereverse annealing process of oxide trapped holes.The results demonstrate that upon electroncapture, a hole shared between two Si atoms (E'δ)completely anneals out by restoring a Si—Sidimer bond. However, a localized hole (E'γ) formsa metastable, dipolar complex, without restoringthe Si—Si dimer bond upon electron trapping. Inthe presence of an applied negative field, thesecharge neutral, dipolar complexes, (E'γ+e−), canreadily release the weakly bonded electron,exhibiting a reverse annealing process.

VI. ACKNOWLEDGEMENTS

We would like to thank the University ofNew Mexico (UNM) for access to the resourcesof their Albuquerque High PerformanceComputing Center (AHPCC) and Maui HighPerformance Computing Center (MHPCC). Thecalculations on the small and medium-sizedclusters were performed using IBM SP2 and SGIOrigin 2000 at AHPCC, MHPCC, and theAeronautical Systems Center/Major SharedResource Center (ASC/MSRC). Thecalculations on the largest model clusters wereperformed using the UNM-Alliance RoadrunnerSupercluster located at AHPCC under Grant

Number 1999022 and on the Vista AzulSupercluster granted to AHPCC under an IBMShared University Research (SUR) grant.

VII. REFERENCES

[1] T. P. Ma and P. V. Dressendorfer, Ionizingradiation effects in MOS devices and circuits,Wiley-Interscience, New York, 1989.[2] F. B. McLean and T. R. Oldham, BasicMechanisms of Radiation Effects in ElectronicMaterials and Devices, IEEE NSREC TutorialShort Course, Snow Mass, Colorado, 1987 (alsopublished as Harry Diamond Laboratories Tech.Report HDL-TR-2129, 1987).[3] J. R. Srour, Basic Mechanisms of RadiationEffects on Electronic Materials, Devices andIntegrated Circuits, IEEE NSREC ShortCourse, Gatlinburg, TN, 1983 (also published asDefense Nuclear Agency Tech. Report DNA-TR-82-20, 1982).[4] J. R. Schwank, P. S. Winokur, P. J.McWhorter, F. W. Sexton, P. V. Dressesndorfer,and D. C. Turpin, IEEE Trans. Nuc. Sci. NS-31,1434 (1984).[5] T. R. Oldham, A. J. Lelis, and F. B. McLean,IEEE Trans. Nuc. Sci. NS-33, 1203 (1986).[6] A. J. Lelis, H. E. Boesch, Jr., T. R. Oldham,and F. B. McLean, IEEE Trans. Nuc. Sci. NS-35, 1186 (1988).[7] A. J. Lelis, T. R. Oldham, H. E. Boesch, andF. B. McLean, IEEE Trans. Nuc. Sci. NS-36,1808 (1989).[8] A. J. Lelis and T. R. Oldham, IEEE Trans.Nuc. Sci. 41, 1835-1843 (1994).[9] R. K. Freitag D. B. Brown, and C. M.Dozier, IEEE Trans. Nuc. Sci. NS-40, 1316(1993).[10] D. M. Fleetwood, M. R. Shaneyfelt, L. C.Riewe, P. S. Winokur, and R. A. Reber, Jr.,IEEE Trans. Nuc. Sci. NS-40, 1323 (1993).

[11] J. F. Conley, Jr., P. M. Lenahan, A. J. Lelis,and T. R. Oldham, IEEE Trans. Nuc. Sci. NS-42,1744 (1995).[12] F. J. Fiegel, W. B. Fowler, and K. L. Yip,Solid State Commun. 14, 225 (1974).[13] K. C. Snyder and W. B. Fowler, Phys. Rev.B 48, 13238 (1993).[14] P. M. Lenahan and P. V. Dressendorfer, J.Appl. Phys. 55, 3495-3499 (1984).[15] A. H. Edwards and W. B. Fowler, FinalReport-ONR Contract N00014-92-J-2001,(1995).[16] R. K. Freitag, D. B. Brown, C. M. Dozier,IEEE Trans. Nuc. Sci. 40, 1316-1322 (1993).[17] R. K. Freitag, D. B. Brown, C. M. Dozier,IEEE Trans. Nuc. Sci. 41, 1828-1834 (1994).[18] D. M. Fleetwood, W. L. Warren, J. R.Schwank, P. S. Winokur, M. R. Shaneyfelt, andL. C. Riewe, IEEE Trans. Nucl. Sci., NS-42,1698 (1995).[19] J. F. Conley, P. M. Lenahan, A. J. Lelis, andT. R. Oldham, Appl. Phys. Lett. 67, 2179-2181(1995).[20] T. R. Oldham, Ionizing Radiation Effectsin MOS Oxides, World Scientific Publishing,New Jersey (1999).[21] R. Tohmon, Y. Shimogaichi, Y. Tsuta, S.Munekuni, Y. Ohki, Y. Hama, and K. Nagasawa,Phys. Rev. B 41, 7258 (1990).[22] K. Vanheusden and A. Stesmans, J. Appl.Phys. 74, 275 (1993).[23] J. F. Conley, Jr., and P. M. Lenahan, IEEETrans. Nuc. Sci. NS-42, 1740 (1995).[24] J. R. Chavez, S. P. Karna, K. Vanheusden,C. P. Brothers, R. D. Pugh, B. K. Singaraju, W.L. Warren, and R. A. B. Devine, IEEE Trans.Nuc. Sci. NS-44, 1799 (1997).[25] Some good general references include: I. N.Levine, Quantum Chemistry, 5th Ed., PrenticeHall, Upper Saddle River, NJ, 2000; A. Szaboand N. S. Ostlund, Modern QuantumChemistry: Introduction to Advanced

Electronic Structure Theory, Dover, Mineola,New York, 1989.[26] A. C. Pineda and S. P. Karna, J. Phys.Chem A, 104, 4699 (2000).[27] S. P. Karna, A. C. Pineda, W. M. Shedd,and B. K. Singaraju, in Silicon-on-InsulatorTechnology and Devices IX (ProceedingsVolume 99-3), P.L.F. Hemment, Ed., TheElectrochemical Society, Pennington, NJ, 1999,pp. 161-166.