Formation of fluorine-containing defects and nanocrystals in SiO 2

ISSN 1063-7834, Physics of the Solid State, 2015, Vol. 57, No. 11, pp. 2164–2169. © Pleiades Publishing, Ltd., 2015. Original Russian Text © O.P. Gus’kova, V.M. Vorotyntsev, N.D. Abrosimova, A.N. Mikhaylov, D.I. Tetelbaum, E.L. Shobolov, 2015, published in Fizika Tverdogo Tela, 2015, Vol. 57, No. 11, pp. 2106–2111.

SEMICONDUCTORS

Formation of Fluorine-Containing Defects and Nanocrystals in SiO2 upon Implantation with Fluorine, Silicon, and Germanium Ions: Numerical Simulation and Photoluminescence Spectroscopy O. P. Gus’kovaa, b, V. M. Vorotyntseva*, N. D. Abrosimovab, A. N. Mikhaylovc, D. I. Tetelbaumc, and E. L. Shobolovb a Nizhny

Novgorod State Technical University named after R. E. Alekseev, ul. Minina 24, Nizhny Novgorod, 603950 Russia b Sedakov Research Institute of Measuring Systems, ul. Tropinina 47, Nizhny Novgorod, 603137 Russia c Lobachevsky State University of Nizhny Novgorod, pr. Gagarina 23, Nizhny Novgorod, 603950 Russia * e-mail: [email protected], [email protected] Received April 28, 2015

Abstract—The incorporation of fluorine atoms into the silicon dioxide lattice upon F+ ion implantation and the formation of silicon (germanium) nanocrystals in SiO2 upon Si+ (Ge+) ion implantation have been numerically simulated. The calculations for F have been performed by the density functional theory (DFT) method; the calculations for Si and Ge have been carried out by combining the DFT (in the cluster approximation) and Monte Carlo methods. The energy gain of the fluorine atom attachment to one of silicon atoms with the formation of a nonbridging oxygen hole center (NBOHC) and an energy level appearing in the band gap has been demonstrated. In the case of ion implantation, the simulation at a dissolved Si (Ge) atom concentration of ~2 at % has revealed the formation of nanocrystals (NCs) with an average size of ~1 nm. DOI: 10.1134/S106378341511013X

1. INTRODUCTION Silicon dioxide SiO2 films are important components of many electronic devices. The defect composition and density distribution in SiO2 sometimes play a crucial role in the operation of devices and in their behavior under external influences. For example, the sensitivity of parameters of integrated circuits based on MOS transistors (including those fabricated based on silicon-on-insulator structures) to ionizing radiation (IR) is associated with the presence of trap centers for holes in SiO2 [1, 2]. The other structures for which the state of a system of defects and the effect of radiation on it play the key role are resistive memory elements, i.e., a new class of electronic devices (memristors) [3]. One of efficient methods for controlling the state of a system of defects in silicon dioxide is ion implantation. It was found that F+, Si+, Ge+, N+ ion implantation into SiO2 MOS transistor layers allows introduction of electron traps into insulators, which compensate the hole trapping under IR, thus lowers the parameter sensitivity to irradiation [4, 5]. In view of the above, the knowledge of microscopic (atomic) mechanisms of the effect of ion implantation on defect and electronic systems in SiO2 becomes

increasingly relevant. Meanwhile, the atomic structure, energetics of its formation, and electronic properties of defect centers resulting from ion implantation have not been studied in sufficient detail. The objective of the present study is to clarify the mechanisms of the effect of F+, Si+, Ge+ ion implantation into SiO2 layers on the sensitivity to IR. To this end, the most energetically favorable position of the fluorine atom embedded in SiO2 was determined and the corresponding electron energy spectrum was calculated using numerical simulation and quantum chemistry methods. Combining the quantum chemistry (DFT) and Monte Carlo methods, we simulated the incorporation of Si and Ge atoms, which are excessive with respect to stoichiometric SiO2, into silicon–oxygen tetrahedra and the subsequent formation of silicon (germanium) nanoclusters, i.e., electron trapping centers (ETCs). The defect structure of SiO2/Si films subjected to F+, Si+, Ge+ ion implantation was studied by photoluminescence (PL) spectroscopy. The formation of defects such as nonbridging oxygen hole centers (which are also ETCs) in SiO2 upon fluorine ion implantation is confirmed. (Preliminary simulation

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FORMATION OF FLUORINE-CONTAINING DEFECTS Table 1. Total energy of the cells according to the calculations in the DFT approximation Empirical formula

Energy, eV

Si8O16F

−8451.290

Si8O15F

−8018.202 −427.061

O

results for the case of fluorine implantation were previously described in [6, 7].) 2. NUMERICAL SIMULATION The algorithms used in numerical simulation of processes in SiO2 when introducing additional impurity atoms are based on the calculation of the energy gain of this or that atomic configuration (short-range order) and (in the case of F+ implantations) the calculation of the electron energy spectrum for the most energetically favorable configuration. Such an approach does not pretend for strictness, but allows adequate interpretation of available experimental data. Although SiO2 films used in microelectronics are typically amorphous, in numerical calculations, we proceed from the lattice of the crystalline modification of silicon dioxide, i.e., β-cristobalite [8]. This is justified by the fact that the silicon dioxide energetics is mainly controlled by the short-range order of amorphous silicon dioxide, which is almost identical to that in β-cristobalite: in both cases, the structure represents a system of Si–O4 tetrahedra connected by vertices.

DOS, arb. units

Electron trapping center

−25

−20

−15

−10

−5 E, eV

0

5

10

15

Fig. 1. Total electron density of states, calculated for the fluorine-containing cell of β-cristobalite Si8O16F. The energy E is measured from the top of the valence band. PHYSICS OF THE SOLID STATE

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We now turn to the presentation of the method and results of calculations for the case of fluorine introduction. The total energies of defect-free and fluorine-containing cells were calculated by the density functional theory (DFT) method [9] within the generalized gradient approximation (GGA) using the ultrasoft pseudopotential and Perdew–Wang parametrization [10] (the cutoff energy was 20 Ry). Atomic sites in the unit cell were relaxed: positions of all atoms were varied until the forces acting on each atom decreased to 10–2 eV/Å. The Monkhorst–Pack grid (2 × 2 × 2) was used; to calculate the total electron density, integration over the first zone was performed taking into account the weighting factors of k-points. Simulation was performed using the software package described in [11]. The β-cristobalite unit cell contains eight SiO2 formula units, hence, its defect-free cell formula is Si8O16. Two cases of fluorine atom incorporation into the lattice are possible: it either substitutes one of oxygen atoms in the cell (then the cell formula is written as Si8O15F) or is attached to one of silicon atoms with the formation of a defect such as the nonbridging oxygen hole center (NBOHC); in this case, the formula is written as Si8O16F. The corresponding energy difference (ΔE) of the SiO2 : F system per cell is given by

Δ E = E 2 − E1 − E 0,

(1)

where E1 and E2 are the energies of Si8O15F and Si8O16F cells, respectively, E0 is the energy of the isolated oxygen atom. The calculated values of these energies are given in Table 1; we can see that ΔE is negative. From this it follows that the second mechanism of fluorine incorporation is energetically more favorable, and its implementation upon F+ ion implantation is more probable in comparison with the first mechanism. The calculated energy spectrum of outer electrons for Si8O16F is shown in Fig. 1. The electron energy is measured from the top of the valence band. The most important simulation result is the formation of additional energy levels in the band gap (near the top of the valence band). In the case of the generation of electron‒hole pairs by IR, these levels are electron trapping centers (traps) which compensate the hole trapping centers associated with initial defect states in SiO2 and provide a decrease in the sensitivity to IR of structures implanted by fluorine. Figure 2 shows the calculated distribution of the electron density on states of the Si8O16F cell with one trapped electron. It follows from Fig. 2 that the electron charge in this case is localized mostly on the silicon–oxygen tetrahedron containing a one-coordinated oxygen atom. Let us now consider the case of Si+ and Ge+ ion implantation. There are publications, e.g., [12, 13], suggesting that implantation of these ions followed by annealing results in a decrease in the sensitivity of MOS/SOI structures to IR. In [12], it was concluded

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that in the case of Si+ implantation, this is caused by the formation of Si nanocrystals which are electron trapping centers. In [13], it was shown that a significant decrease in the sensitivity to IR is observed even at the Si+ dose corresponding to the average concentration of excess Si atoms, which is equal to 2 at % in the interface Si/SiO2 region of MOS transistors. However, it remained unclear whether the formation of Si nanocrystals is possible at such low concentrations of excess silicon. To clarify this question, we performed simulation described below. In the case of Ge+ ion implantation, calculations were carried out similarly and yielded qualitatively the same results as for Si+ implantation. Let us assume that introduced (excess with respect to stoichiometric SiO2) silicon atoms substitute oxygen atoms before annealing, forming oxygen-deficient tetrahedra. Annealing causes random walk (diffusion) of Si and/or O atoms over the “lattice,” which results in local aggregates of excess Si atoms, which in turn form silicon nanocrystals in the SiO2 matrix, i.e., phase separation (decomposition) of non-stoichiometric oxide SiOx into stoichiometric SiO2 and elemental silicon occurs. This process was simulated by the Monte Carlo method using an algorithm simulating a sequence of elementary events of changes in the concentration of excess silicon atoms in each unit cell of silicon dioxide. The probabilities of these events (in this or that direction) are defined by the difference of cell energies before and after their fulfillment [14]. In this case, the excess Si atom can be incorporated only into cells in which other excess atoms are already present or absent. To simulate using this method, it is first necessary to calculate cell energy changes for corresponding events. As before in the case of fluorine, instead of the random network of amorphous SiO2, we will consider the lattice of the crystalline phase, i.e., β-cristobalite. In stoichiometric SiO2, the central silicon atom in each tetrahedron composing the lattice has four neighboring oxygen atoms. In this case, it is generally accepted that the oxidation state is n = 4. If the tetrahedron contains one excess Si atom, n = 3 and so on; for elemental silicon, n = 0. To calculate the sign and magnitude of the cell energy change by the DFT method with varying number n, we took a representative cluster consisting of two joined tetrahedra. The calculations were performed using the software package [15]. The dangling bonds formed by cluster edge atoms were passivated by attaching SiH3 groups or H to them [16]. The energy changes were calculated by the method described in [17, 18]. The energy differences of the system consisting of a cluster and an isolated oxygen atom (the state before O atom incorporation) and the cluster containing an incorporated O atom were determined. (For convenience, in this scheme it

Electron density localization Oxygen atom Silicon atom Fluorine atom O

Fig. 2. Spatial distribution of the negative electron charge in the silicon dioxide cell containing a fluorine atom.

is accepted that the change in n is caused exactly by incorporation of oxygen atoms; however, the final result is independent of whether oxygen or silicon incorporation is considered.) In calculating the transition probabilities with changes in n, the relative, rather than absolute, energy changes upon incorporation are important. We determined the differences in the cluster energy changes for the transitions (n = 0) → (n = 1) and n → (n + 1) with n > 0. The obtained values of ΔE are given in Table 2. It follows from Table 2 that an increase in the number of excess Si atoms in the tetrahedron is energetically favorable if this tetrahedron already contains 2 or 3 excess silicon atoms. From this circumstance it could be expected that SiOx decomposition into SiO2 and Si is favorable. To test this at low excess silicon concentrations, the next stage of Monte Carlo calculations was performed. A quasi-two-dimensional crystal consisting of 60 × 60 β-cristobalite cells was considered. Addresses of those cells were simulated, in which excess silicon atoms are primarily contained at a given average concentration of these atoms (we took 2 at %) and their random distribution. Then, events of increasing and decreasing oxidation states were simulated for each cell. The probabilities of these events P(+) and P(–), respectively, were determined using the relations

P (+) = 1/[1 + exp(−Δ E n,n+1)/ kT ],

(2)

P (−) = 1/[1 + exp(Δ E n,n+1)/ kT ].

(3)

Table 2. Total energies of representative silicon–oxygen clusters n

En, eV

En+1, eV

0 1 2 3

−62561.659 −66597.731 −70 634.347 −74671.806

−64579.491 −68616.270 −72653.648 −76691.053

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The similar conclusion is valid for the case of germanium ion implantation into SiO2.

60 50

3. PHOTOLUMINESCENCE SPECTROSCOPY OF SiO2 LAYERS SUBJECTED TO ION IMPLANTATION

40 30 20 10

0

10

20

30

40

50

60

Fig. 3. Graphical representation of the steady-state distribution of excess silicon atoms at a concentration of ~2 at %. Bright and black cells correspond to oxidation states of +4 and 0, respectively.

Here T is the absolute temperature and k is the Boltzmann constant. These relations are derived from the Monte Carlo method theory in statistical physics [19]. The simulation result is the new distribution of excess Si atoms over cells. The calculation was multiply repeated until reaching the quasi-steady spatial distribution (Fig. 3). We can see the presence of single cells and their clusters with n = 0. Such a distribution means that SiOx decomposed and elemental silicon nanoclusters were formed. The nanocluster (nanocrystal) volume in the spherical approximation corresponds to the average diameter d ≈ 1 nm. We note that the used approach differs from the approach in which trajectories of diffusing atoms are traced by the Monte Carlo method [20, 21]. A feature of this approach is that it does not require knowledge of energy barriers for elementary atomic jumps and energies of Si nanocrystal–matrix interfaces, i.e., the introduction of the critical nucleus concept. In fact, phase equilibrium rather than process kinetics is simulated. The used algorithm predicts only the final system state upon long enough annealing, but does not answer the question what temperatures and annealing times are required to achieve such a state. It is known from the published data (see, e.g., [22]) that the SiOx decomposition requires about several minutes at an annealing temperature of 1100°C. Thus, our calculation confirms the assumption that the formation of silicon nanocrystals is energetically favorable even at an excess Si concentration of 2 at %. PHYSICS OF THE SOLID STATE

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To experimentally study the defect structure of SiO2 layers before and after F+, Si+, and Ge+ ion implantation, the PL spectroscopy method was used. SiO2 films 300 nm thick grown on silicon by thermal oxidation at a temperature of 1100°C were irradiated with F+ ions (60 keV) with doses of 5 × 1014 and 1016 cm–2, Si+ ions (60 keV) with doses of 5 × 1013 and 1016 cm–2, and Ge+ ions (80 keV) with doses of 5 × 1013 and 1016 cm–2. PL measurements were performed in the wavelength range of 350–900 nm before annealing and after exposure to IR, upon excitation by a pulsed nitrogen laser at a wavelength of 337 nm. The optical scheme included a long-focus lens focusing the laser beam on the sample (the light spot diameter is ~1 mm), a condenser collecting PL emission on a monochromator entrance slit, and a photomultiplier with optimum sensitivity in the wavelength range of 350–870 nm. In front of the monochromator entrance slit, a glass filter was placed, which did not transmit light with wavelengths shorter than 360 nm to reject scattered laser emission. A diffraction grating with 600 gr/mm and an effective wavelength range of 350– 900 nm was used in the monochromator. Among the primary defects emitting in the spectral region under study are neutral oxygen divacancies (NODs) with a PL intensity maximum at ~400 nm, neutral oxygen monovacancies (NOVs) with a maximum in the range of 450–550 nm, and nonbridging oxygen hole centers (NBOHCs) (~650 nm) [23]. As seen in Fig. 4, silicon dioxide modification by implantation of fluorine ions with a dose of 5 × 1014 cm–2 even without annealing leads to the appearance of a wide PL peak in the region of 550–750 nm, whose position is close to the NBOHC peak. This is consistent with the above calculation data according to which a fluorine impurity leads to NBOHC formation (Fig. 2). The fact that the distinct peak caused by NBOHCs appears only for fluorine among three impurities without annealing counts in favor of the “chemical” effect of implanted fluorine on the formation of this peak and confirms the above calculation model. SiO2 films implanted by Si+ and Ge+ ions with a dose of 5 × 1013 cm–2 exhibit PL bands which can be attributed to NOV and NOD emission (Figs. 4b and 4c). The peak in the region of 800 nm characteristic of Si nanocrystals is absent [24]. This is not surprising, since nanocrystal formation requires high-temperature annealing. Such annealing is not required for forming point defects such as NOD, NOV, and

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5

(a) NBOHC λexc = 337 nm 300 K

PL intensity, arb. units

NOV


NOD

1 × 1016 cm−2

5 × 1014 cm−2 Reference 400

NOD

1 2

2 1

400

450

500 550 600 Wavelength, nm

650

700

Fig. 5. Comparison of PL spectra of silicon dioxide irradiated with Si+ ions with a dose of 1 × 1016 cm–2 (1) before and (2) after exposure to ionizing radiation.

NBOHC λexc = 337 nm 300 K


3

0

450 500 550 600 650 700 750 800 Wavelength, nm (b) NOV

4

λexc = 337 nm 300 Κ

1 × 1016 cm−2

An interesting result obtained by the PL method for silicon dioxide layers subjected to Si+ or F+ ion implantation after exposure to IR is modification of PL defect centers (Fig. 5). The samples modified by Ge+ ions appeared to be less susceptible to changes in PL spectra.

5 × 1013 cm−2

Reference 400


NOD

450 500 550 600 650 700 750 800 Wavelength, nm (c) NOV

NBOHC λexc = 337 nm 300 K 1 × 1016 cm−2

5 × 1013 cm−2

Reference 400

450 500 550 600 650 700 750 Wavelength, nm

800

Fig. 4. PL spectra of the initial SiO2 film sample and SiO2 films irradiated with (a) F+, (b) Si+, (c) Ge+ ions in different modes.

NBOHC. As the implantation dose increases, PL peaks are weakened or disappear at all due to the competing effect of radiation defects, i.e., nonradiative recombination centers.

4. CONCLUSIONS The DFT calculations predict that the formation of defects which can be electron trapping centers is possible upon fluorine ion implantation into SiO2. This is confirmed by PL data. Using quantum chemical and Monte Carlo simulation, the possibility of the formation of Si and Ge nanoclusters in SiO2 was analyzed and their average size was estimated at excess atom concentrations previously determined in ionimplanted structures by the secondary ion mass spectrometry method [7]. It was found that nanoinclusions ~1 nm in size can be formed in the SiO2 layer due to the spatial redistribution of excess Si and Ge atoms (with a concentration of ~2 at %). These nanoinclusions can be electron trapping centers upon exposure to IR. Results of photoluminescence measurements showed that the peak, i.e., the emission band whose position is close to the band associated with nonbridging oxygen hole centers, appears upon fluorine ion implantation into SiO2 films even without annealing. This result confirms the data of quantum chemical simulation. The higher sensitivity of PL spectra of SiO2/Si structures with an insulator modified by F+ implantation to IR can be explained by a lower diffusion activation energy of F in SiO2 (in comparison with Si and Ge), which leads to radiative rearrangement of NBOHC-type defect centers.


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The results presented make it possible to judge the mechanisms of increased stability of SiO2 layers subjected to F+, Si+, Ge+ implantation to IR. ACKNOWLEDGMENTS This study was supported by the Ministry of Education and Science of the Russian Federation (state assignment order no. 3.285.2014/K) and within the project part of the state assignment in the field of scientific activity (project no. 10.695.2014/K). REFERENCES 1. V. S. Pershenkov, V. D. Popov, and A. V. Shal’nov, Surface Radiation Effects in Integrated Microcircuits (Energoatomizdat, Moscow, 1988) [in Russian]. 2. D. V. Nikolaev, I. V. Antonova, O. V. Naumova, V. P. Popov, and S. A. Smagulova, Semiconductors 37 (4), 426 (2003). 3. J. J. Yang, M. D. Picket, X. Li, D. R. Steward, and R. S. Williams, Nat. Nanotechnol. 3, 429 (2008). 4. D. I. Tetelbaum, N. D. Abrosimova, A. N. Mikhaylov, and O. P. Smelova, in Abstracts of the VII International Conference “Silicon-2010,” Nizhny Novgorod, July 6–9, 2010, p. 109. 5. C. M. S. Rauthan, G. S. Virdi, B. C. Pathak, and A. J. Karthigeyan, Appl. Phys. 83, 3668 (1998). 6. O. P. Gus’kova, V. M. Vorotyntsev, M. A. Faddeev, and N. D. Abrosimova, Vestn. Nizhegorodsk. Gos. Univ. 1, 43 (2013). 7. E. L. Pankratov, O. P. Gus’kova, M. N. Drozdov, N. D. Abrosimova, and V. M. Vorotyntsev, Semiconductors 48 (5), 612 (2014). 8. E. V. Chuprunov, A. F. Khokhlov, and M. A. Faddeev, Crystallography (IFML, Moscow, 2000) [in Russian]. 9. W. Kohn, Nobel Lecture (The Nobel Foundation, Stockholm, 1999). 10. J. P. Perdew and Y. Wang, Phys. Rev. B: Condens. Matter 45, 13244 (1992).


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Translated by A. Kazantsev