143-gusev-prb-1995-1759 - PHYSICAL REVIEW B VOLUME 52,...

Info iconThis preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHYSICAL REVIEW B VOLUME 52, NUMBER 3 15 JULY 1995-1 Growth mechanism of thin silicon oxide films on Si(100) studied by medium-energy ion scattering E. P. Gusev Department of Chemistry and Laboratory for Surface Modification, Rutgers University, P. 0. Box 939, Piscataway, New Jersey 08855 H. C. Lu and T. Gustafsson Department of Physics and Astronomy and Laboratory for Su tface Modification, Rutgers University, P. O. Box 849, Piscataway, New Jersey 08855 E. Garfunkel Department of Chemistry and Laboratory for Surface Modification, Rutgers University, P. 0. Box 939, Piscataway, New Jersey 08855 (Received 27 December 1994) The growth of ultrathin oxide films by the thermal oxidation of Si(100) at 1020—1170 K and in 10“‘—- 10‘3 Torr 02 pressure has been studied by high-resolution medium-energy ion-scattering spectros- copy (MEIS). To develop a fundamental understanding of very thin oxide film growth, we utilize sequential isotopic exposures (1802 followed by 1602). MEIS readily distinguishes 180 from ‘60 and the depth distribution for both species can be determined quantitatively with high accuracy. Our results Show that the traditional phenomenological models for silicon oxidation cannot be applied to the initial oxidation. For very thin oxide films (15-25 A), we find overlapping isotope depth profiles in the film. For thicker films (> 40 A), we find that several key aspects of the Deal-Grove model (oxygen diffusion to the Si-Si02 interface and oxide formation at and/or near that interface) are consistent with our results. We also observe 180 loss from the surface after reoxidation in 1602. The complex oxidation behavior during the initial oxidation is likely to be a combination of interfacial, near-interfacial, and surface reac— tions. I. INTRODUCTION The oxidation of metals and semiconductors is one of the oldest and most thoroughly studied class of reactions in materials Science‘—15 Most work has concentrated on either the oxide growth mechanism for relatively thick films (100 A—IO ,um)1_3’6’7’11’12 or the oxygen—surface in- teraction in the limit of submonolayer cover- age.4’5’14’:6_18 The oxidation mechanism in the critical 10—100-A range (the initial oxidation) is much less well understood. The purpose of this paper is to examine the microscopic mechanism for oxide film growth on silicon in the range 15~50 Ultrathin-film silicon oxidation is now of particular relevance to the microelectronics industry as the thick- ness of metal-oxide-semiconductor gate oxides drops well below 100 A. However, despite considerable effort, there is no general agreement concerning the growth mecha- nism fora these films.6’“’12'14 Oxidation of relatively thick (>100-A) films is known to be described by the Deal— Grove model.19 According to this “linear-parabolic” model, the oxide grows via molecular oxygen diffusion through the oxide film and molecular oxygen reaction with silicon at the Si/SiOZ interface. In the limit of thick films, the oxide film growth rate is limited by oxygen diffusion through the film resulting in a parabolic depen- dence of oxidation time versus oxide thickness. When the oxide is very thin, oxygen diffusion is fast compared to the interfacial reaction rate, and hence the latter con- trols the oxidation kinetics. Assuming first-order reac- tion kinetics at the interface, Deal and Grove deduced a 0163-1829/95/52(3)/1759(17)/$06.00 52 linear relationship between oxide thickness and oxidation time in this limit.19 It has been shown, however, that the oxidation kinetics for ultrathin films are faster than would be expected from a linear relationship.8’9’“’12’2o Several phenomenological models, such as the parallel oxidation model,21 the block- ing layer model}22 and others, have been proposed to ac- count for this deviation. The experimental support for these models comes mostly from kinetic data. The idea of the reactive layerlz’23 was advanced later as an attempt to integrate the observation of microcrystallinity near the interface,24 a thin transition region of nonstoichiometric oxidelé'25_27 and deviations of the oxygen isotope distri- butions from the Deal-Grove mechanism, as inferred from experiments by hydrofluoric acid (HF) etching in combination with nuclear reaction analysis (NRA) with oxygen isotopes.24 In contrast to the Deal-Grove model, the reactive layer model posits that oxidation takes place at the top (internal) surface of a “reactive layer” between crystalline Si and amorphous SiOZ. The reactive layer was defined as a thin oxide layer (estimated to be ~10—20 A thick) near the interface that is impermeable to interstitial 02 diffusion. In this paper, our results will be mainly compared with the Deal-Grove and reactive layer models, because they represent two qualitatively different views of the oxidation reaction. Most other models attempt to modify either the mechanism of oxy— gen diffusion or the reaction at the interface, and can, therefore, be considered as modifications of the original Deal-Grove idea. Some of the phenomenological models fit the experi- mental data on oxidation kinetics quite satisfactorily with 1759 ©1995 The American Physical Society 1760 a large number of fitting parameters. Unfortunately, most of the models do not have direct experimental sup- port; an analysis of kinetic results alone does not allow one to conclusively distinguish between models. There- fore, additional experiments must be performed in order to shed light on the complex mechanism of the initial stages of silicon oxidation. The Deal-Grove model considers the reaction at the in- terface as a first-order reaction between silicon and molecular oxygen. Other models21 consider, for example, oxygen dissociation at the interface and again a first- order reaction of atomic oxygen with silicon. Such “gas— phase” considerations ignore the spatial (lateral and vert- ical) aspects of the oxidation at the interface between two solids and the role of the substrate silicon atoms. In par- ticular, they imply random reaction of oxygen molecules with silicon substrate atoms at the interface, although this cannot explain the abrupt oxide/ silicon interface after oxidation. There is intense discussion in the litera- turel‘mg’36 on the issue of lateral homogeneity during the initial oxidation: Does the oxide growth proceed uni- formly on the surface in a layer—by-layer fashion, or are 3D islands of silicon oxide formed? Some photoemis- sion28’30’35 and high-resolution transmission electron mi- croscopy (HRTEM) (Refs. 31—34) results were interpret— ed as evidence for layer-by-layer growth. However, three-dimensional (3D) island growth has also been claimed to occur under certain oxidation condi- tions_13,2s,29 It is generally agreed that there is a transition region (of altered structure and stoichiometry) between crystal- line silicon and a—Si02.9’“'14'16’17’25’27’3’7‘40 The thickness of this region has been reported to be from 5 to 30 A, de- pending on oxidation procedures, oxide thickness, and the probing technique. At the atomic scale, some view the transition region as consisting of silicon atoms in in— termediate oxidation (suboxide) states, Si’”r (n=1, 2, 3)),16’17’25 although this interpretation is now under de- bate.“_43 Other models emphasize structural order“45 and stress anomalies‘”46 in the transition region. Further- more, relatively little is known about the role of the tran- sition region in the initial oxidation. According to the reactive layer model,12’23 silicon atoms difl‘use through the thin reactive layer and react with oxygen on top of this layer, forming the Si02 phase. Tiller and others“—49 have suggested that interstitial silicon generation takes place during the oxidation reaction at the interface. These silicon atoms subsequently diffuse into the oxide, where they interact with oxygen leading to oxidation in the near-interfacial region. However, little experimental evidence has been reported to support this idea. Silicon oxide growth is known to be temperature and pressure dependent. In addition to temperature and pres- sure variations in the rate of oxide growth, there is a re- gion in the (P-T) phase diagram, where SiO desorption (surface etching) takes place. The low-temperature high- pressure part of the phase diagram is characteristic of ox— ide growth, while SiO desorption occurs under high- temperature low-pressure conditions.36'50_53 In one case, Tromp and co-workers54 haove shown that high- temperature annealing of a lOO-A oxide under UHV con- E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 ditions results in oxide decomposition and SiO desorp- tion. Little is known concerning the existence of SiO desorption or 02 exchange under oxide growth condi— tions. In this paper, we discuss the microscopic mechanism(s) of very thin oxide growth during thermal “dry” oxida- tion, and go beyond a simple phenomenological kinetic description. Key problems we address are as follows: (i) Where does the oxidation take place? (ii) Does the Deal— Grove model apply to 15—50-A films? (iii) What is the structure and stoichiometry in the transition region and what is its role in the initial oxidation? (iv) Does oxygen leave the oxide during film growth? We use medium-energy ion scattering (MEIS), a low- energy (50—300-keV) high-resolution version of Ruther- ford backscattering spectroscopy (RBS),55_58 to study sil- icon exposed sequentially to 1802 and 1602 isotopes as our main experimental tool. Due to the high-energy resolu- tion of MEIS, we can quantitatively determine the depth distribution of the two isotopes with high accuracy. Our preliminary results have demonstrated the power of this method.59 It should be noted that ion scattering has been successfully used to study clean silicon surfaces60 and rel- atively thick oxide films.38’54’61 For example, Feldman and co-workers showed with RBS that the transition re— gion between crystalline Si(100) or Si(111) and the SiOz layer for thermally grown oxides consisted of about a S-A nonstoichiometric oxide near the interface and one or two reconstructed silicon layers.37’38’61 ‘63 Isotopic substitution has been employed in the past to study the oxidation mechanism in conjunction with secondary ion mass spectrometry, and NRA with HF etch profiling.24'64—71 These studies helped confirm that thick oxide film growth does follow Deal-Grove kinetics. However, the limitations and uncertainties in the depth resolution of these techniques make meaningful analysis in the ultrathin film regime (15—50 A) difficult. This paper is organized as follows. In Sec. II, we de- scribe the experimental setup and discuss the idea of iso- tope depth profiling with MEIS as a method to study ul- trathin oxide growth. We then present experimental results “(Sec III). A key qualitative result for very thin ( <25 A) oxides is that we observe similar distributions for both isotopes after sequential oxidation, directly im- plying non-Deal-Grove behavior. Isotope profiles in the growing oxide films are compared with known phenome- nological models of silicon oxidation (Sec. IV A). We show in this section that neither the Deal-Grove model (and its subsequent variants) nor theoreactive layer model can be applied for very thin ( < 25 A) films, and we dis- cuss (Sec. IV B) other possible mechanisms for oxide growth during the initial oxidation. Some details of the ion-scattering analysis and the procedure for spectral simulation are given in the Appendix. II. EXPERIMENT We have employed the unique strengths of MEIS (mass-sensitivity, high depth resolution, and quantitative analysis) in our experiments. In MEIS [Fig. 1(a)], a monoenergetic beam of charged particles scatter from 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . surface and near surface atoms. The energy spectra of the scattered particles provides a depth and composition profile of the near surface region. To eliminate the back- ground scattering from atoms in the crystalline Si sub- strate, the experiments are usually performed in a chan— neling geometry with the beam aligned along one of the major crystallographic directions or even in a double- aligned geometry (where the detector axis is also aligned with a crystallographic axis, i.e., channeling and block- ing).56 Energy spectra of backseattered particles can be converted into a mass scale through a kinematic factor. The kinematic factor is a function of target atom mass and scattering angle, and can be calculated within a binary collision model (using classical momentum and en- ergy conservation). In our case, a 97.2-keV incident- proton beam was aligned with the [100] direction of sil— icon and the backscattered protons were collected around 125.0° scattering angle in the (110) plane (double align— ment geometry). Our high—resolution toroidal electro— static energy analyzer is equipped with channel plates and a 2D position sensitive detector, and collects data simultaneously over a wide range of energy ( ~ 1.6 keV at ~ 80 keV) and angles ( ~22").72 Since the scattered parti- cles lose energy via inelastic electronic excitations as they travel through the film, species that lie below the surface can be distinguished from the ones at the surface by their relative energy loss. For IOO-keV protons, the energy loss in Si is about 12 eV/A.73 Our detector gives us ~110-eVoresolution for ~ 80-keV protons. This converts to a ~5—A effective depth resolution for thin oxide films under our scattering conditions. It is useful to point out that the efficiency of the chan- nel plates in the detector can be affected by oxygen used in the oxidation cycles. We found changes (sometimes as large as 20%) after exposing the channel plates to oxygen at pressures higher than 10—6 Torr. Fortunately, this problem does not effect the present result, as most of our oxidation is performed in the sample preparation chamber and, in addition, an overall efficiency change can be corrected with the known Si density in the sub- strate or Si02 layer. But any experiment that is based on information concerning absolute coverages or accurate angular spectra need to carefully consider this problem. The principles of our isotopic oxidation experiments are demonstrated in Fig. 1. In the simple case of oxida- tion in the naturally predominant oxygen isotope (1602), only one oxygen peak is seen in the MEIS channeling en- ergy spectrum [Fig 1(a)]. The high-energy (leading) edge of the peak corresponds to the oxygen atoms at the sur- face, and its energy is given by the kinematic factor; at lower energies, we observe ions scattered from oxygen atoms closer to the Si-SiOZ interface. The thicker the film, the more energy the protons lose on their way to and from the interface, and the broader the peak. Under channeling conditions, silicon layers deep in the crystal- line substrate are invisible to the proton beam due to sha- dowing. As a result, the energy spectrum for protons scattered from silicon atoms also consists of a relatively narrow peak. The peak is due to protons scattered from silicon atoms in the amorphous oxide and in a few sub- strate layers near the interface. Some of the substrate sil- 1761 icon atoms near the interface are still visible to the in- cident protons, due to thermal vibrations and possible distortions near the interface caused by the presence of the oxide layer. For this reason, the silicon peak is slight— 1y broader than the oxygen peak, whose width is solely determined by the oxide thickness. The silicon peak has a higher intensity than the oxygen peak, because the scattering cross section for silicon is about three times greater than for oxygen. To illustrate the type of MEIS spectra anticipated after sequential isotopic oxidation, we consider two limiting cases. For a thin film, the MEIS spectrum should show two separate oxygen peaks: ‘80 at higher energies and 16O at lower energies. If the initial oxidation followed the Deal-Grove model, one would expect an Si1802 oxide mainly near the surface (as the 1802 exposure was per- formed first) and an 16O—containing oxide near the inter— face [Fig. 1(b)]. Since 180 is at the surface, its leading edge should match the energy calculated within the binary collision model (indicated by dashed lines). The protons lose energy traveling through the Si1802 layer be— fore (and after) they reach the Si1602 region, resulting in a shift of the leading edge of the 160 peak with respect to Backseattered Energy FIG. 1. Schematic representation of some possible isotopic distributions (left) and MEIS channeling energy spectra (right) corresponding to (a) uniform oxidation in ‘602, (b) the Deal- Grove model, and (c) uniform isotopic mixing. The scattering conditions used in our experiments are shown in (a). The sym- bol “S” denotes the oxide surface, “I” represents the interface(s). 1762 the binary collision model edge. This shift is proportion- al to the thickness of the Si1802 layer. The widths of both peaks are also proportional to the respective layer thicknesses. Very different spectra would be expected if the oxida- tion took place uniformly throughout the growing oxide film, as this would result in a uniform isotopic mixture [Fig. 1(c)]. In this case, both isotopes are on the surface after sequential oxidation. Therefore, the energies of their leading edges would be given by the binary collision model. Both peaks would have the same width because the isotopes have the same depth distributions. Thus, by simply examining the MEIS leading edge positions and the peak widths, one can begin to model the oxide growth mechanism. More detailed information, in particular the depth profiles, can be deduced from modeling, as demon- strated in Sec. IV. The cross section in MEIS is proportional to the second power of the atomic numbers and, therefore, is relatively small for proton-oxygen scattering. Thus, long data acquisition times (or high proton doses) are required to obtain satisfactory statistics. Unfortunately, increas- ing the ion dose may cause beam-induced damage to the film. To minimize the dose, and hence the damage, on each beam spot (1.00X0.07 mm), we scan across the sample by using a stepper-motor-driven manipulator. Only one sample was needed to collect data with good statistics. We also averaged data points in an energy spectrum over six angular channels (~ 1° width) to enhance our signal-to-noise ratio. In this paper, an ener- gy spectrum nominally taken at 115° therefore refers to data collected at Scattering angles from 114. 5° to 115. 5°. We monitored ion-induced damage by measuring, in a separate experiment, the change of the silicon peak area as a function of the proton dose. The increase in the sur— face peak area does not exceed 5% for the dose used (~3 X 1016 protons cm”). This result is consistent with an estimate of the total number of displaced atoms calcu- lated within Kinchin-Pease cascade theory (~5.4% for silicon, and ~ 3. 5% for oxygen)”74 As a complement to MEIS, low-energy ion scattering (LEIS) (He+, 1— 1.5 keV, scattering angle 145°) was used to determined the isotopic composition in the outermost oxide layer. Because of the high neutralization probabili- ty of He+ in this energy range, only helium ions scattered from the first surface layer survive as ions and are detect- ed; this is the reason for the extremely high surface specificity of this method.“76 We have also employed x- ray-photoemission spectroscopy (XPS) with a Mg K a source to provide information on the oxidation states of silicon atoms in the oxide and as an additional tool to measure oxide thickness. All spectra were taken at room temperature in UHV chambers with a base pressure of about 10_10 Torr. Spectroscopic ellipsometry was used to compliment our results on the thickness of the stoichiometric Si02 and the transition region near the in- terface. These measurements were performed using UVISEL ellipsometer (Instruments S.A., Inc.). We used n-type Si(100) samples (~20X8 mm). They were cleaned in methanol, rinsed in water, and then heat- ed by a direct current in UHV. The samples and sample E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 holder were first degassed at 600—800 K for approximate- ly 40—50 h. This was followed by several flashes to ~1250—1350 K for 30—120 sec. The pressure rose dur- ing the high-temperature flashes, but was always less than 2 X 10_9 Torr. This procedure resulted in a clean Si sur- face as determined by low-energy electron diffraction [(2>< 1) pattern], MEIS and XPS. We concentrated our efforts on oxide films grown in situ at temperatures from 1020 to 1170 K, the temperature range of silicon oxide growth for many industrial applications, and oxygen pressures of 10_3—10_1 Torr. The sample temperature was measured by an optical pyrometer calibrated with a thermocouple. The difference between thermocouple and pyrometer readings was less than 5%. gI‘he final thick- ness of the oxides varied from 15 to 50 A, depending on oxidation temperature, pressure, and time. Research grade (99.995% purity) oxygen was used. Samples were first oxidized in 1802 (1802 isotopic concentration ~98.0%) and then reoxidized in natural oxygen (1602 isotopic concentration 99.8%). Both isotopes were ad- mitted into a preparation (oxidation) chamber in which the background vacuum was in the 10_9-Torr range. A liquid-nitrogen trap was used to reduce the water content of the background gas. To minimize tantalum diffusion from the sample holder during high-temperature oxida- tion,77 we put silicon pads (~0.4 mm thick) between the front of sample and the tantalum clips. The tantalum concentration on the surface was near the limit of MEIS detection (for our conditions less than 0.5% of a mono- layer of Ta). A second set of samples, having a uniform SO-A Si‘602 layer, were produced in a commercial fab fa- cility at IBM (1 atm, 1070 K). They oare employed in studying the oxide structure of 50—60—A films. We also use these samples (reoxidized in 1802) to address the growth mechanism for thicker ( > 50 A) films. Results of this study will be published separately.78 III. RESULTS In this section, we show MEIS, LEIS, and XPS results for films sequentially grown in 1802 and 1602. To develop a more complete picture of the oxidation process, we have performed measurements at various points in the complex pressure, temperature, and time phase space. Figure 2(a) is an MEIS spectrum for a thin oxide first grown in 1802 (70 min), then in 1602 (120 min), at 1120 K and 10_3 Torr. (All MEIS spectra in this paper taken under channeling conditions are shown after subtraction of a very low background.) The thickness of the final ox— ide film is about 20 A, as determined by MEIS (Sec. IV) and XPS (see below). Two well-separated peaks corre— sponding to protons scattered from 16O and 18O are seen in the spectrum. The proton energies corresponding to the leading edges of the peaks, 81.3 keV for 16O and 83.0 keV for 18O, are in excellent agreement with binary col- lision model calculations (81.3 and 83.0 keV, respective- ly), which means that both oxygen isotopes are located on the oxide surface. If either isotope was located com- pletely below the surface, the result would be an addition- al energy loss for protons scattered from that isotope and, as a result, the high-energy edge should shift to a lower 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . Intensity Proton Energy (keV) FIG. 2. MEIS energy spectra at a scattering angle of 115°. The oxidation conditions were (a) 70 min in 1802 followed by 120 min in 1602 at 1120 K and ~10—3 Torr; and (b) 100 min in “‘02 at 1080 K and ~ 10’3 Torr followed by 120 min in 1602 at 1120 K and ~10—1 Torr. The dashed lines show the energies for both isotopes calculated within the binary collision model. The incident-proton energy is 97.2 keV. Intensity is plotted in arbitrary units. value [Fig. 1(b)]. We did not observe such a shift for this thin oxide. In addition, the peak widths for both isotopes are fairly similar, indicating that the distribution of the 18O and 160 regions are similar (since the peak widths are mainly determined by the film thickness), despite the fact that the isotopes were exposed sequentially [Fig. 2(a)]. A closer inspection shows that the peak shapes are slightly different. If we compare their full width at half max— imum (FWHM, Al”), the peak corresponding to 180 (A1 /2=0. 63 keV) is slightly broader than the 160 peak (0.50 keV). The difference in width gets even smaller at intensities lower than half maximum. In Fig. 2(b), we present a MEIS spectrum for a thicker film, ~50 A, grown first in 1802 (1080 K 10*3 Torr) for 100 min and then in 1602 (1120 K, ~10—1 Torr) for 120 min. Again, the leading edges of the peaks corresponding to 16o and 180 atoms (81.3 and 83.0 keV, respectively) are those expected from the binary collision model (81.3 and 83.0 keV). Thus, both isotopes are present on the oxide surface, as with the thinner oxide. However, now the peaks have different shapes and widths, implying different depth distributions for the isotopes in the final oxide. The 180 peak FWHM of 0.60 keV is close to that corre- sponding to the ~20-A oxide, whereas the 160 peak has a width of 1.68 keV (~50 A). Therefore the SO—A oxide consists of an overlapped 16O and 18O oxide layer near the oxide-vacuum surface (analogous to that observed above in the 20-13; oxide), and a thicker 16O-containing layer underneath, adjoining the Si/SiO2 interface. The areas under the peaks are proportional to the total 1763 amolmt of the isotopes in the film. For thicker films, the area under the 180 peak is much smaller than for 20-13. oxide [cf. Figs. 2(a) and 2(b)], indicating a smaller amount of this isotope in the thicker film. The fact that both iso- topes are on the oxide surface after sequential oxidation is also confirmed by LEIS (Fig. 3), where both oxygen masses are seen in the spectrum after oxidation. One should keep in mind that peaks in MEIS are al- ways asymmetric and are not analogous to those ob- served in more traditional spectroscopies; actually, the concept of a FWHM is not very meaningful in our appli- cation of MEIS. Instead, we use an energy-spectra simu- lation program (similar to that used in RBS, see the Ap— pendix) to find the isotopic distribution in the film. The Si 2p XPS photoelectron spectra for these 20- and 50-11 films are shown in Fig. 4. Two peaks are seen in the photoelectron spectra. The peak at ~99 eV, the only one seen after sample cleaning, corresponds to substrate sil- icon atoms. The other photoemission peak is shifted by ~4 eV towards higher binding energy, and results from fully oxidized silicon atoms, shill”)16‘18’25—27'29’79’80 The ratio of the intensity from oxidized silicon atoms, 10x, to the intensity from the substrate, I Si, is used to determine the oxide thickness, x, according to the con- ventional formulam17 x=x1n[(Io,/Isi)(10/I,,)+1]. (1) where A is the Si 2p photoelectron escape length in the oxide, 10 and [w are the Si 2p photoemission intensities for bulk silicon oxide and bulk silicon, respectively (IO/Ia, =1.22 for the Mg Ka source”), and the photo- electron takeofl‘ angle is normal to the surface. The prob- lem in using this formula for determining the thickness is that the values of A for the Si 2p state reported for Mg K a radiation differ significantly, ranging from 21 to 35 Intensity J 300 ‘ 350 ‘ 400 450 Energy (eV) FIG. 3. LEIS spectra after (a) IOO-min oxidation in 1"02 at 1080 K and ~ 10‘3 Torr, and (b) reoxidation in 1602 for 120 min at 1120 K and ~10’l Torr. The primary energy of He+ beam was 1.0 keV and the scattering angle 145°. 1764 Intensity‘ 99 162 ‘ 155 108 Binding Energy (EV) FIG. 4. Si 21) photoemission spectra after (a) 100 min oxida- tion in 1802 at 1080 K and ~10“3 Torr, (b) reoxidation in 1601 for 120 min at 1120 K and ~10‘3 Torr, and (c) 120 min reoxi- dation in 1602 at 1120 K and ~ 10—1 Torr. A.81_83 We choose A=30 A, based on a recent study calibrated with ellipsometry and RBS.82 With this choice of A, the Si 2p spectra shown in Fig. 4(b) and 4(0) corre- spond to oxide thicknesses of ~20 and ~51 A, respec- tively. We have also performed experiments at 1020 and 1170 K in order to understand if this overlap in the depth profiles of oxygen isotopes observed for the 20—A oxide at 1120 K and the transition to (near) interface growth for thicker films holds under other oxidation (temperature and pressure) conditions. Figure 5 shows the evolution of MEIS spectra during oxidation at 1170 K and 10‘2 Torr for increasing oxidation time. For all three samples, the oxidation time to 1802 was the same, 4 min. Again, one can see that the leading edge position of the peaks shows that both isotopes are on the surface after oxidation. This is true for all three oxidation events. After 1602 oxi- dation for 1 h [Fig 5(a)], both peaks have similar widths with 180 being somewhat broader [Al/2(160)=0.54 keV, A,/2(’80)=0.73 keV], again indicative of similar depth distributions for both isotopes. Additional 1(’02 oxidation for 4 h [Fig 5(b)] results in both peaks broadening [A1 /2( 160)=0.75 keV and A1/2(130)=O.92 keV]. Both peaks become broader, which suggests that this layer contains a mixture of both isotopes (although not neces— sarily uniform), which we describe by the phrase “isoto— pic mixing.” As the oxidation develops even further [Fig 5(c)], we observe that A1 a for 16O (1.16 keV) becomes greater than for 18O (0.84 keV). The latter is close to the A1 /2(180) value we observe after oxidation for 5 h [Fig. 5(b)]. This implies that we have a transition to a growth mechanism with oxide growth mainly at the interface. It is worthwhile to note that the peak width at the transi- tion point increases with increasing temperature; A1/2(130)~0. 60 keV at 1120 K (Fig. 2) and A1/2(180)~0.92 keV at 1170 K (Fig. 5). This is an indi- cation that the oxide thickness for the isotopically mixed layer increases with temperature. E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 Isotopic mixing is also observed at lower temperatures. MEIS spectra for samples sequentially oxidized at 1020 K and 10‘2 Torr are shown in Fig. 6. The presence of isotopic mixing at this temperature is deduced from the following observations: (i) both isotopes are located on the surface, as seen from the positions their leading edge, (ii) the peak widths are similar, and (iii) both peaks broaden as the oxidation proceeds [Figs. 6(a) and 6(b)]. Similar to the previous samples, A1/2(160) is slightly smaller than A1 /2(130), reflecting nonuniform mixing. The kinetics of silicon oxidation at this temperature and pressure are very slow. For this reason, we have not reached the transition point to nonmixing behavior within the ~44 h of oxidation time shown in Fig. 6(b). Isotope profiles of the samples oxidized at 1020 (Fig. 6), 1120 (Fig. 2), and 1170 K (Fig. 5) are shown in Figs. 7, 8, and 9, respectively. The procedure of energy spectra simulation employed to calculate the profiles is described in the Appendix. The profiles are normalized in such a way that the total oxygen density near the oxide surface equals 1. Several features of these profiles should be pointed out. (i) Our simulation shows that for very thin oxides, both isotopes are distributed throughout the film [Figs. 7(a), 7(b), 8(a), 9(a), and 9(b)]. 1000 800 600 s 400 - 200 - 800- 600- 400. 200. Intensity Proton Energy (keV) FIG. 5. The evolution of the MEIS spectra with reoxidation in 1602 at 1170 K and oxygen pressure of about 10“2 Torr. All three samples were first oxidized in 1{‘02 at 1170 K and 10—2 Torr for 4 min. Subsequent oxidation times in 1602 Were (a) 60 min, (b) 300 min, and (c) 1860 min. Dashed lines indicate the leading edge positions for both isotopes calculated with the binary collision model. 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . 1765 1000 800 600 400 200 » Intensity 800 - Q (bf) (>009 <> 0.6.70.0...opxzqu... .. 95"...“ 600 _ 3 O 400- 200 Proton Energy (keV) FIG. 6. MEIS spectra for Si(100) samples oxidized at 1020 K and 10‘2 Torr. Exposures in 1302 were 10 min for both sam— ples. This first oxidation step is followed by oxidation in “’02 for (a) 165 min and (b) 2640 min. (ii) The isotope depth distributions are not uniform, as a simple visual analysis of the MEIS peak shape of the thinnest films implies. The net concentration of both iso- topes decreases as we approach the interface; this seems to be a characteristic of the transition region discussed in detail below. However, for the cases we present, the 18’0 density first increases just below the surface and later de- 1020K, 10‘2 Torr 1.0 a 0.8 . 10 min (1802)/165 min (1602) 0.6 » .-~ > 0'4 ’ °.\o\ fem 160 '5 v I. 18 g 0.2 o ..... ..u .... .. O 8 0.0 \K a b. g 0‘8‘ ‘10 min (1802)/2640min(1602) ‘23 0.6- 1’ o,..\ 0.4. I \ Depth (A) FIG. 7. Isotopic depth distributions for the sample oxidized at 1020 K. The original MEIS spectra are shown in Fig. 6. Data points (circles for 16O and squares for 13O) are deduced from spectral simulation, as explained in the Appendix. 1120K 1.0 [ 10’3 Torr a 0-8 * 70 min (mop/120 min (1602) 0.6 » 3%.. ,, El“. 04 r 70-160 *4. 18 0.2 ‘K ““ "" " O 0.0 O . 8 7 0‘0‘0 0.677 K 100 min (1802,1080 KR 04- 10‘3 Torr) then \0 0_2_ 120 min (1602, 10‘1 Torr) \Kfl E 1:. ‘CL -ci.. [Jr-El. than” Normalized Density 0.0 . . v 6 10 20 30 40 50 Depth FIG. 8. Isotopic depth distributions for the sample oxidized at 1120 K. The original MEIS spectra are shown in Fig. 2. creases, whereas the 160 concentration decreases steadily from the surface into the film. The location of the max- imum in the 180 concentration depends on the oxidation time in 1602 (or the final oxide thickness): It moves away from the surface and its maximum value decreases as the oxidation develops further [cf. Figs. 7(a) and 7(b); Figs. 1170K, 10‘2 Torr 1.0 a 0'8' k4 min (1809/60 min (1602) 0.6‘ 0.47 V I, 160 0.2. ' a 18o 0.0 ,5 08* T 4 min (mop/300 min (1502) 8 0.44 ., .5 x“ ' “ g 0.2— 2 0,0- . . r r “LEW-“5 I 0.8. TE“. 4 min (“09/ - 16 06V 1860 mln( 02) 0.4. 0.2. \ :tzvnflm'dl‘ iiDV-Juuhui‘o'fi'hbvépb. 10 20 30 40 Depth (A) FIG. 9. Isotopic depth distributions for the sample oxidized at 1170 K. The original MEIS spectra are shown in Fig. 5. 1766 9(a) and 9(b)]. o (iii) For thicker ~40—50-A films [grown by reoxida- tion in 1602 with a 13—15-A starting Si1802 film, see Figs. 8(b) and 8(0)], the 18O is not distributed throughout the film, but is concentrated near the outer surface. This implies that the oxide grows via 160 reaction with Si at or near the interface with an isotopically mixed layer remaining near the surface. The dynamics of this process can be observed on the sample oxidized at 1170 K (Fig. 8), where all three samples were initially prepared under the same oxidation conditions in 1802 and, therefore, have similar thickness after the first oxidation step. After a 60-min reoxidation in 1602, both isotopes have the same thickness (~20 A) [Fig 9(a)]. Additional exposure in oxygen (5 h) results in an oxide thickness of ~34 A, with the thickness of the 12‘0 containing region of about 24 A [Fig 9(b)]. As the total oxide film gets thicker, ~40 A [Fig 9(c)], the thickness of the 180 containing layer grows more slowly, ~28 A. The point where a transition to nonmixing behavior occurs depends on the tempera- ture, with higher values for higher temperatures [Fig 8(b) and Fig. 9(0)]. (iv) Concomitant to the interface reactions, an isotopi- cally mixed region develops at the surface of the thicker oxides, and the overall amount of 18O in the film de- creases with the oxidation time. (A more complete study of the surface “exchange” reactions will be reported else- where.78 In particular, we found that the “exchange” re- action is enhanced by transition-metal impurities on the oxide surface.) Finally, while we present results only for 115’ scatter- ing angle, we have performed this analysis for four different scattering angles (115, 119°, 125°, and 132°). The profiles deduced from difierent angles are very simi- lar. This fact indirectly supports our assumption of oxide film homogeneity. If the oxide thickness variation was significant or if laterally separate SimO2 and Si1602 re- gions were formed, one would expect different profiles for different scattering angles (especially for the variation on the vacuum-SiO2 side of the film, as ions that travel in SiOZ suffer a large inelastic energy loss and those that travel in vacuum do not). However, the limited angular range precludes good quantitative measurements on how flat the Si/SiO2 interface is. High-energy ion beams (especially of heavy ions) at high ion dose may cause ion induced mixing at the inter- face between two materials.84 To make sure that the mix- ing we observe is not caused by the proton beam, we have performed data acquisition on one sample with a very low proton beam exposure ( ~5 X 1015 protons cmiz). According to the estimates in Sec. II, this dose corre- sponds to the displacement of less than 1% of the atoms. The MEIS spectrum taken under this low-dose condition also shows isotopic mixing and is very similar (but with poorer statistics) to those taken at our typical dose of ~3><1016 protons cmiz. This is clear evidence that the depth distributions observed in our experiments are a re- sult of the oxidation reaction rather than of proton-solid interactions. One result is that we also observe oxygen loss during oxide growth at high temperatures. The area under the E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 180 peak is proportional to the integrated amount of this isotope in the film, and becomes smaller with continuing oxidation in ‘602 (Fig. 5). This implies that some of the initially adsorbed 180 leaves the film during subsequent oxidation, and that the loss increases with oxidation time. Another observation illustrating oxygen loss comes from comparing XPS and MEIS data. For the sample used in Fig. 2(b), the oxide thickness was also determined by XPS. After oxidation in 180,, this XPS thickness is 13 A [Fig 4(a)], and after reoxidation in 1602 it is about 50 A [Fig 4(c)]. Therefore, a 0.26:1.0 18O to 160 ratio should have been expected provided that no 180 left the film dur- ing oxidation. However, if we compare peak areas in MEIS [Fig 2(b)], we obtain a ratio of about 0.04:1. Therefore, much of the initially absorbed 180 must be leaving the film under these conditions. An important problem is stoichiometry and concentra- tion gradients in the thin oxide film. Oxygen and silicon backseattering spectra for a 50-A oxide film grown at IBM facilities and corresponding oxygen and silicon profiles are depicted in Figs. 10 and 11, respectively. Our simulation procedure demonstrates an oxygen to silicon ratio of approximately 20:1 in the film (Fig. 11), as ex— pected from the known Si02 stoichiometry. There is, however, a transition region between SiO2 and crystalline silicon where the oxygen concentration (and the O/Si ra- tio) is lower. This transition region is variously ascribed in the literature to compositional changes,16’85’86 interface roughness,87’38 stressed oxide layers9 or other structural inhomogeneities in the near interfacial oxide. The silicon concentration increases in the transition region when 1200— a g 800 Oxygen (I) C J E E 400] Experiment —Simulation 0 "a 85 86 87 88 Energy (keV) 1200- b g 800- Silicon 2 g 0 Experiment ' ’ 400’ “Simulation u r l 0 '.' ’5’“ . 88 89 90 91 92 Energy (keV) FIG. 10. (a) Oxygen and (b) silicon energy spectra for high- quality SO-A oxide grown at 1070 K. The incidence beam was aligned along (TTO) direction. The scattering angle is 80". Open circles are experimental data; solid lines show the best fit with our simulation procedure (see the text and the Appendix). 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . T Oxygen 1 fi—Oa—o-o—o-o—oaogo l 3‘ ’5 C 8 .5 Silicon g 0 5—, «WWWW Tu E g i 0‘0 ‘ 10 2‘0 Depth FIG. 11. Oxygen (shown as circles) and silicon (diamonds) depth distribution as a function of the distance from the oxide- vacuum interface derived from the data in Fig. 10. The densi- ties are normalized with respect to the oxygen density in “bulk” silicon near the oxide surface. Several A of substrate Si is also Visible due to thermal vibration and distortion by the oxide lay- er. compared to the “bulk” SiO2 near the oxide surface. Be- cause the backscattering yield in the channeling geometry used in Fig. 11 may be lower due to shadowing, we have performed measurements on the same sample in a ran— dom incidence geometry [Fig. 12(a)]. The silicon concen- 6000 5000 7 7 _r _ 4000 3' 7: 11:3 3000 5 2000 Experiment 1000 Simulation 0 so 82 8‘4 86 88 ' 9'0 ' 9'2 Energy (keV) > E 1.00 b CD '5 a 0.75 "O a) N a 0.50 E 0 Z 0.25 0'00 20 4o 60 Depth (A) FIG. 12. (a) MEIS spectrum for a 50-11 oxide taken under random scattering conditions, and (b) the corresponding silicon depth distribution up to 70 A. The scattering angle is ~86°. The experimental data are shown by open squares; the solid line shows the result of the silicon depth distribution simulation. The oxygen peak at ~85—86 keV [shown also in Fig. 10(a)] was not considered in the simulation. The silicon density (b) is nor— malized to the value in the crystalline silicon. 1767 tration profile corresponding to this spectrum [Fig. 12(b)] shows that the silicon concentration in the “bulk” oxide is 2. Into. 1 times lower than in crystalline silicon and that the silicon concentration in the transition region gradual- ly increases to the value of crystalline silicon. One should keep in mind that this “transition region” refers to the near-interfacial region with different composition and structural properties from bulk Si or SiOZ, and does not necessarily coincide with the isotopically mixed layer re- sulting from the oxidation, which can become buried in the growing films (see below). The existence of the transi- tion region is also supported by our XPS experiments (Fig. 13), where intermediate oxidation states are seen in the Si 212 photoelectron spectrum between the substrate peak (Sio) and the peak corresponding to Si02 (Si4+). This suggests the presence of some incompletely oxidized Si. From our MEIS experiments (for the given energy loss and straggling parameters, see the Appendix), we esti- mate the thickness of the transition region for this sample to be 15:i:4 A [Fig. 12(b)]. This value is within the range reported in the literature (5—30 ALH’12’14'16'17’37’38'40 The thickness of the transition region depends strongly on the probing techniques; even the definition of the tran- sition region varies from one study to another. For in- stance, from ellipsometry measurements, the transition region is understood as a layer with optical properties different from both bulk oxide and crystalline silicon.”90 Simulation of ellipsometry energy and angular spectra taken on the same sample with the MEIS gives the best fit if the transition region is about 6 11.91 We will discuss reasons for the discrepancy of the determination of the thickness of the transition region and stoichiometric ox- ide film with MEIS, ellipsometry, and XPS elsewhere.91 Photoemission studies consider the transition region as a layer with local electronic configurations different from ideal Si02. The effect of electronic configuration on the 4000 3000 2000 Intensity 1000 0 - " ~ 98 100 102 104 106 108 Binding Energy (eV) FIG. 13. XPS spectrum for the 50-13; oxide. The solid line shows the experimental data; the dashed line represents a fitting using two Gaussian lines corresponding to Si“+ and substrate atoms (Sio). The shadowed area, formed by suboxide states, is still visible in this SO-A film, although it is clearer for thinner films. 1768 MEIS results is negligible. We use the term transition re- gion to mean a layer of different composition from pure Si and SiOz. One should mention that our MEIS estimate of the thickness of the transition region is influenced by the energy loss and straggling parameters. IV. DISCUSSION Before discussing the mechanism(s) of silicon oxide growth during the initial oxidation, we summarize our main experimental observations. (i) For ultrathin films, we observe overlapping depth profiles for both oxygen isotopes during the first 20—25 A of oxide growth, despite the fact that the samples were exposed sequentially to these isotopes. The isotopic mix— ing holds for all temperatures and pressures used in our experiments. (ii) The isotopic mixing behavior changes as a function of thickness. The mixing happens throughout the film for ultrathin film growth. For thicker final oxide films, two isotopically different regions are observed; for thicker initial oxide films,78 the two isotopically mixed regions are separated, one at the surface, another at the interface. (iii) Some of the initial isotope used to oxidize is lost during subsequent oxidation. (iv) There is a thin transition region between crystalline silicon and silicon dioxide. The silicon density in the transition region is higher than in the “bulk” oxide, while the oxygen density is lower. A. Breakdown of the phenomenological models for silicon oxidation in the limit of ultrathin films We now address the isotope profiles in the context of the reactive layer”’23 and Deal-Grove models,19 and ex- amine the applicability of each model during the initial stage of silicon oxidation. The reactive layer model pro— poses two stages for the initial oxidation. In the first stage, a reactive layer is formed with silicon diffusion through the growing layer to the outermost oxide sur- face, followed by reaction with oxygen at the surface. After this layer is formed, a second stage begins in which oxidation occurs on top of this reactive layer with both oxygen and silicon diffusion to the top of the layer (02 through the bulk Si02 and Si through the reactive layer). The thicknesses of our lS—20~A oxides [Figs. 7, 8(a), and 9(a)] are of the same order as the reactive layer proposed in this model.23 Therefore, for these films, the reaction should take place on top of the reactive layer, which in this case is at the oxide surface. Thus after an 1802, then 1602, sequential oxidation we should expect an 18O oxide layer near the interface and an l6O-eontaining oxide on the surface. This behavior is not consistent with our 13—15-A initial oxide results (Figs. 7—9), which show both isotopes distributed throughout the oxide film. If the Deal-Grove model were applicable (Fig. 1), on the other hand, a reverse isotopic ordering (with 18O at the surface and 160 near the interface) would be ob— served. Our data for very thin oxide films [Figs 7, 8(a), and 9(a)] clearly contradict this. The correct model must E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 account for similar deopth distributions for both isotopes for thin films (15—20 A). For the SO—A oxides with a 13-15—A initial SimO2 lay- er, the reactive layer model predicts an oxygen profile that has a different ordering (160 at the surface and 180 near the interface) than our MEIS spectra show [Fig. 8(b)]. The profile characteristic of the Deal-Grove model (with separate 180 and 160 regions) also does not agree with the experimental data [Fig. 8(b)]. However, if we ig— nore the surface exchange reaction, the basic ideas of the Deal—Grove model (oxygen diffusion through the oxide and reaction at or near the interface) are closer to our data than the reactive layer model. The 16O concentra— tion is very high at the interface of our 40—50-A films, as predicted by the Deal—Grove model; one major incon- sistency, however, is that the Deal-Grove model does not predict behavior that could result in isotopic mixing near the oxide surface for 40—50-A oxides. The applicability of the Deal-Grove model to thin films is still under discussion,12’20 as noted above. Several groups have explored oxidation kinetics for thin ( < 100— A) oxide films and found that they differ from Deal- Grove kinetics.6’8’9’“’12’22’24 It has been suggested re- cently that this deviation could be caused by an error in the oxide thickness determination, and it was claimed that the Deal-Grove model was relevant for very thin films as well.”’93 In contrast to these kinetic studies, our experiments show an atomistic “cross section” of the ini- tial oxidation-oxygen isotope distributions in the growing film, which show the location of the reaction and diffusion pathways; they thus provide direct evidence that the Deal—Grove model cannot be used for very thin (~15—25—A) oxides. For the same reason, models22 that explain the fast oxidation kinetics for very thin oxides by modifying the interfacial reaction or oxygen diffusivity, while still working within the Deal-Grove construct, are not consistent with our results. Recent results on the initial oxidation of silicon at room temperature94~97 showed inverse-logarithmic kinet- ics and were interpreted as implying a field-assisted oxi- dation (Cabrera-Mott) mechanism."6 According to this model, usually used to explain the initial oxidation of metals, the oxidation reaction takes place either at the oxide/vacuum or oxide/substrate interface depending on the nature of diffusing species. The reaction is enhanced by an electric field, which is developed through the oxide film during the oxidation. Although our results cannot rule out this mechanism for the growth of the first oxide layers and room—temperature oxidation, the isotope profiles clearly show that the Cabrera-Mott model (with reaction at either of the interfaces) is not responsible for the highztemperature oxidation of the oxide films thicker than 15 A. B. Mechanisms of oxide film growth during the initial oxidation Our data show that sequential isotopic oxygen expo- sures for ultrathinooxide layers results in the formation of a thin (~ 15—20 A) layer in which both isotopes have a similar depth distribution [Fig. 14(3)]. After the forma- 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . tion of this layer, two reaction pathways develop. The first involves oxygen difiusion through the oxide reacting with silicon at and/or near the interface, and is responsi— ble for the film growth, leaving a mixed isotope distribu- tion at the surface of the oxide [Fig. 14(b)]. The second is a reaction at the surface that results in an exchange of one isotope for the other with no net change in Si to O stoichiometry. There are several possibilities to explain the similar depth distributions of the two isotopes for thin oxides: (1) lateral inhomogeneities, such as oxide island growth; and (2) isotopic mixing during the initial oxidation. Iso— topic mixing, in turn, may be caused by several mecha— nisms: (i) Oxygen reaction with incompletely oxidized sil- icon throughout the transition oxide region. (The incom- pletely oxidized silicon in the near interfacial oxide could be silicon suboxides, or silicon interstitials and/or clus— ters in the oxide.) (ii) Atomic oxygen diffusion within the oxide, perhaps via an exchange mechanism. As noted above, growth mode issues (layer vs island growth) are still unresolved. Much of the work on this W Surface oxygen exchange ...................... {93‘3’3’3’33‘1'2’2'3'$3':’:':'3’:€’3‘3€ we...».v.59.»«assayeaz W Near—interface oxidation Interface oxidation Surface oxygen exchange §\\\\\\\\\\\\ ~50A Near-interface oxidation FIG. 14. Schematic model for silicon oxidation. Oxygen atoms may either react at (i) the interface (and possibly provide the interstitial Si atoms/clusters into the transition region), (ii) react with Si in the form of interstitial atoms/clusters or subox- ides in the transition layer (near-interfacial reaction), or (iii) ex- change with other oxygen atoms at/near the oxide surface. (a) At the earliest stage of oxidation (15—25-A oxide), the near- interface transition region starts from the surface, and as a re- sult, the (near-interfaeial reaction and the surface reaction over— lap. (b) For thicker films, oxygen will difi‘use through the comp- leted SiOZ layer and react at the interface or in the near— interface transition region. This will leave behind a mixed layer at the surface in our case. Concurrently, the surface reaction still takes place (see the text). 1769 subject has used photoemission methods.“38‘30'35’98'100 Some experiments reveal a stepwise increase in the thick- ness of the oxide or suboxide states on Si(100).3°’98’99 Similarly, an oscillatory behavior of the Si1+ and Si3+ in- tensities on Si(lll) has been interpreted as evidence for layer-by-layer growth.101 On the other hand, some au- thors also claimed (based on XPS results) that 3D island growth does take place under certain oxidation condi- tions.”’”'101 Engel and co-workers29 have presented re- sults that imply layer-by-layer growth only at tempera- tures less than 900 K; whereas at higher temperatures, the initial oxidation is 3D, involving nucleation and growth of bulklike oxide islands. Contrary to this, other XPS experimentszg’101 were interpreted in terms of nonuniform oxidation (in the vertical direction) at 573 K, and as layer—by-layer growth at higher temperatures, 873— 1073 K. Using HRTEM, Gibson and co-workers”“34 observed that steps on the Si(111) surface were immobile during oxide film growth, indicative of layer-by—layer growth. Cross-sectional HRTEM does not demonstrate oxide film inhomogeneity characteristic of 3D island growth;24’44’ 102 actually the Si/SiOZ interface is observed to be very abrupt.ll These observations argue against the 3D island growth model as the main source of the similar depth dis- tribution of oxygen isotopes observed for very thin films. We also note that in-air atomic force microscopy (AFM) experiments performed in our laboratory and elsewhere on thin oxides do not show high variations in surface morphology, as would be expected for island growth.“”“106 However, the AFM image resolution is limited by tip shape and size effects;107 thus, if the surface islands are smaller than the AFM tip radius (typically several hundreds of A), the real surface morphology may be hidden. If lateral inhomogeneities were to explain the overlap- ping oxygen isotope depth distributions in our MEIS spectra, one would need to assume that a considerable portion of the surface is clean Si (or, at most, very slightly oxidized) after oxidation in 180. Since the average thick- ness of the oxide layer is ~ 10— 15 A at this point, this im- plies that the oxide island or layer thickness was even thicker in some places and close to 0 A in other places during the initial oxidation. This is inconsistent with our results (Sec. III) and most literature results. The broadening of the 180 distribution during reoxidation in the 1602 environment also cannot be explained by lateral inhomogeneities. Therefore, lateral inhomogeneity dur- ing the initial oxidation is unlikely to be the dominant reason for the similar depth profiles observed for the oxy- gen isotopes. We favor a model in which the isotope profile overlap is caused by oxidation of incompletely oxi- dized silicon in the transition region. However, our results determine neither the configuration of the incompletely oxidized silicon nor the mechanism of its formation. Assuming that incompletely oxidized silicon exists in the near—interfacial region, then switching exposures from one isotope to another could easily lead to isotope profile overlap in the suboxide region, as we observe. We thus argue that we have both interfacial (in an analogy to the Deal-Grove model) and near-interfacial reactions 1770 during oxidation of the lS-A initial oxide films. The in- terfacial reaction forms silicon oxide at the interface, and it continuously supplies the near-interfacial region with a substoichiometric oxide, interstitial silicon and/0r silicon clusters. Recent “spectroscopic ellipsometry measure- ments of a IOO-A silicon oxide were interpreted as offering evidence for a thin (~20-A) mixed (Si02 + amorphous silicon) oxide layer near the interface.90 Scanning-transmission electron microscopy—electron- energy-loss spectroscopy experiments also support the idea of silicon clusters in the thin oxide within about 10 A from the interface.85’86 Unoxidized Si atoms were directly observed recently during oxidation of four silicon layers grown by molecular—beam epitaxy on Ge(lOO).108 Moreover, this study shows Ge/Si mixing in the transi- tion region after the oxidation, the mechanism of this mixing may be similar to the mechanism of isotopic mix— ing suggested in our paper. A suboxide is also seen in photoemission. The concen- tration of the suboxide states [~1—2 ML (Refs. 16 and 17)] does not seem to be high enough to give rise to the isotopic mixing in the whole (15—25 A) film. However, if the suboxide states were constantly being regenerated, a 15—25 A isotopically mixed film could result. Further- more, the original classification of the Si" + suboxide states came from photoemission experiments where different chemical shifts were observed in the Si 2p photo— electron spectra; they were attributed to a Si atom with n oxygen bonds in the first coordination sphere.1("17'25 It was shown that Si1+ and Si2+ states are localized within 6—10 A near the interface, while Si3+ suboxide spreads over about 10—30 A from the interface.16'25 However, re— cent experiments showed that the local electronic configuration in the second coordination sphere also con- tributes to the spectra,”109 implying that the “tradition- al” XPS analysis may have some limitations in identify- ing the nature and quantity43’1‘0 of incompletely oxidized silicon. On the other hand, one should also mention that recent first-principle calculations support the original in- terpretation of the Si” + states.111 Provided that the rate of the near—interfacial reaction is proportional to the concentration of the incompletely ox- idized silicon and recognizing that the concentration of suboxide states should be proportional to the amount of silicon over and above the “bulk—”oxide concentration [Fig. 12(b)], we find the reaction rate should increase throughout the transition region from zero in the bulk oxide to its limiting value at the interface. Actually, the reaction rate should be proportional to both the concen- tration of the suboxide and of the dissolved 02 that diffuses in from the surface. These two should have op— posite gradients in the transition region; thus, the reac- tion may take place throughout the transition region. Al- though we cannot define the exact thickness of the near interface region where the oxidation takes place, nor the concentration gradients and relative reaction rates (they probably depend on the oxidation conditions), the general idea of an interface plus near-interface reaction is perhaps the most straightforward way to understand our results (see Fig. 14). Concerning the surface reaction, we observed 180 loss E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 from the surface when reoxidizing in 16O. This suggests a dynamic exchange process occurring close to the oxide- gas interface in which 160 incorporates, while 180 is lost from the surface, either in the form of SilsO or 02. While we do not observe the desorbing species directly, SiO desorption is known to take place at the temperatures ex- plored in our experiments.14’5"5“’“2’113 Mass- spectrometry experiments under UHV conditions show that molecular oxygen does not desorb from a silicon sur- face up to 1400 K,113 although an 02 isotopic exchange surface reaction cannot be ruled out at the high pressures used during the oxidation. The increased concentration of 180 just below the surface with oxide depth, and the in- crease in the depth at which the transition to a negative 180 gradient occurs with increasing oxidation time [Figs. 7, 8(a), 9(a), 9(b)], can also be explained by either 02 ex- change or SilsO desorption from the oxide surface. We believe that an ‘ ‘interfacial + near- interfaciaH—surface reaction” model is more consistent with our experimental results than “simple” interfacial reaction models, such as the Deal-Grove model. A key point of any correct model should be the active role of the transition region in the initial oxidation, particularly in the reoxidation of incompletely oxidized silicon. The reactive layer model also proposes a transition (reactive) layer. In contrast to the reactive layer model where oxi- dation takes place on top of the reactive layer, our results suggest a more homogeneous reaction rate throughout the transition region. It is also possible to explain the seem- ingly contradictory observations of layer-by-layer growth (as seen by others) and isotopic mixing. Within an interface+near interface reaction model, layer—by—layer growth would result from the interfacial reaction, while isotopic mixing would be caused by the near-interfacial reactions. It is unclear if a transition to a pure interfacial reaction takes place with increasing oxide thickness or if the near-interfacial reaction continues for the thicker films. If the second, near-interfacial channel for oxide forma- tion increases relative to the interfacial channel (in rela- tive rates) as the film becomes thinner, then this could ex- plain the faster oxidation kinetics for very thin oxide films, a departure point of phenomenological modifications of the Deal-Grove model for thin films. Our experiments starting with thin (10—15 A) Silgoz films reoxidized in ‘602 show a transition to Deal-Grove— like behavior for 40—50—25. oxides [Figs. 8(b), 9(0)]. This does support the idea that. oxygen diffuses to the interface and that the oxidation reaction does not proceed uni- formly in thicker films. However, it is still possible that the reaction occurs throughout the thin (10— 15 A) tran- sition region near the interface and that the near— interfacial channel continues to be important for the thick films, where the Deal-Grove model is traditionally used to describe the oxidation kinetics. A more speculative problem concerns how the incom- pletely oxidized silicon is generated. It can result from (i) a simple partial oxidation at/near the interface, or (ii) sil- icon generation or injection in the oxide, concepts which have appeared in some of the recent literature.47_"'9’“4’115 The basic idea in the second case is that Si is injected into 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . the oxide (and Si substrate) during the reaction at the in- terface. The rate of Si generation is thought to be about one silicon interstitial formed for each silicon atom oxi- dized.114 Indirect evidence for this comes from stacking faults seen in the substrate Si after oxidation.24’“4’116 Other related evidence comes from HRTEM experiments on Si(lll) (Ref. 31) and STM experiments on Si(100),“7_119 showing that silicon atom generation occurs during oxygen interaction with silicon surfaces at submonolayer coverages and, as a result, silicon clusters appear on the surface. Some authors who have proposed the “interstitial Si generation” model consider the possibility that silicon ox- idation occurs as a reactive transformation from crystal- line silicon to crystalline Si02 (cristobalite) plus intersti— tial silicon at the interface. Tiller47 suggested that there is a thin ordered oxide layer near the SiOz/Si(100) inter- face that plays an important role in oxidation and can help in understanding the nature of electrical defects at the interface and in the near interfacial oxide. Within this model, subsequent oxidation of the interstitials de- stroys this crystalline oxide phase at its junction with amorphous SiOz and generates new vitreous silica, while newly formed crystalline oxide at the interface with the Si—substrate pushes the oxidation further into the bulk. However, the possible existence of a crystalline oxide near the interface is also a matter of intense debate.14'33'88 Several groups have claimed their results showed evi- dence for an ordered oxide near the inter— face,24"“"45’120_122 while other investigators”’88 do not observe a crystalline oxide using the same techniques. The speculation47 about interstitial Si generation (and diffusion into the oxide) to explain the excess Si in the ox- ide is neither experimentally proven nor completely satis— fying. How deep into the oxide are the Si interstitials in- jected? What fraction of the oxide is formed via the in— terfacial channel and what fraction is formed via the oxi- dation of interstitials? Why is the thickness of the isotop- ically mixed layer for some of our samples [e.g., Figs. 7(b), 8(b), and 9(a)] twice that of the oxide thickness after the first step of the oxidation in 1802 ( ~ 13 A)? Even in a marginal case, when all generated silicon atoms diffuse into the oxide, one should expect only 16O-oxide near the interface for these oxides. However, this is not What we observe, implying that other sources may contribute to the isotopic mixing. An additional source of isotopic mixing may involve atomic oxygen exchange diffusion via oxide defects, as suggested by Mott and co-workers.12 An important unresolved issue is to understand how the surface exchange happens (whether through SiO desorption or 02 exchange) and its dependence on T, p, and film thickness. It would be interesting if SiO desorbs on the oxidation part of the (p,T) phase diagram. The traditional viewpoint“"5‘)’51 is that the high-pressure low— temperature part of the (p, T) diagram is characteristic of oxide formation, whereas SiO desorption and surface etching occurs only on the other, low-pressure high- temperature side. SiO desorption during initial oxidation was also observed recently by Ono, Tabe, and Kageshi- ma123 and oxygen loss was found by NRA during initial silicon oxidation.“ SiO desorption may contribute to iso- 1771 topic mixing near the surface. SiO desorption from a stoichiometric SiO2 surface should leave an excess of O at the surface. This could then diffuse below the surface and contribute to isotopic mixing in the near-surface re- gime. On the other hand, 02 dynamic isotope exchange reactions may become important at very high pressures, although they would not be observed in UHV experi- ments. In either case for ultrathin films, the near- interfacial reaction and the near-surface dynamic ex- change would be occurring in the same place, while for thicker films these two processes would be distinct (Fig. 14). An important practical issue concerns the extent that these results and models are relevant for gate oxides grown under realistic processing conditions. RCA clean- ing and its various modifications (wet chemistry methods) are proven to be very effective in contamination removal (metal, hydrocarbons, etc.) and surface smoothing.124_126 For our in situ oxidation, we have used a more traditional surface science approach, i.e., sample degassing and pro- tective oxide desorption under UHV conditions. To avoid contamination, we minimize the chamber pressure; however, we cannot guarantee the absence of impurities in amounts below the MEIS sensitivity. Oxidation in stainless steel UHV chambers is known to introduce more impurities than state—of-the-art quartz furnaces. We also only demonstrate that isotopic mixing holds in the T: 1020—1170-K range for the oxygen pressures in the 10‘1—10_3—T0rr range, several orders of magnitude lower than the ~l atm used in state-of-the-art device manufacturing. However, our results are consistent, in general, with the results of other isotope labeling experi- ments in which the oxidation of thin24 and thick68 films were performed at much higher pressures in quartz fur- naces. V. CONCLUSIONS We have studied the growth mechanism of ultrathin silicon oxide films, using high-resolution ion scattering with 1802/1602 sequential oxidation. We find that neither the Deal-Grove model and its modifications, nor the reac- tive layer model, offer an accurate description of the behavior of very thin ( < 50 A) films. According to our results, oxide films containing a mixture of both oxygen isotopes are formed during the initial stages (<25 A) of thermal oxidation. The mixing is caused by oxygen reac- tion with incompletely oxidized silicon throughout the transition region. This is followed by oxygen diffusion through previously formed oxide layers to the interface and oxide formation at and near the interface. We also observe oxygen loss from the surface, suggesting SiO desorption or an 02 surface exchange reaction. Contrary to the traditional viewpoint, this oxygen loss takes place during oxide film growth, on the “oxidation part” of the (p, T) phase diagram. ACKNOWLEDGMENTS The authors would like to thank Dr. D. Buchanan (IBM) for his advice and for providing a high-quality ox- 1772 ide sample. We would also like to thank Dr. R. A. Bar— tynski, Dr. D. Hensley, Dr. V. A. Yakovlev, Dr. P. Sta- tiris, Dr. Y. Wu, Dr. A. Diebold, and Dr. J. Mayer for their help and comments. This work was supported in part by the National Science Foundation (DMR-9408578) and the Petroleum Research Fund (28788-AC5). E.P.G. acknowledges partial support from the CAST/NAS pro- gram. APPENDIX: HIGH-RESOLUTION DEPTH PROFILING WITH MEIS As mentioned in Secs. II and III, while it is possible to qualitatively distinguish different oxidation modes from a simple examination of the MEIS peak shapes (Fig. l), we can get more detailed information about the isotope con— centration and depth distribution in the film through simulations. To simulate an energy spectrum, we model the sample as a uniform film with a series of thin slabs parallel to the surface. The scattering yield, Yij from the ith element in the jth slab is given by Yij=Tor,(E,M,,Z,~)n,ij , (A1) where a,(E,M,~,Z,~) is the scattering cross section for the ith element in each slab. 0,- depends on the incident ener- gy E, mass (M,), and charge (2,) of that element, nij is the concentration of the ith element in the jth slab, Ax is the slab thickness, and T is a normalization factor (that also includes the proton beam dose). We use cross sec— tions calculated using a Moliere interatomic potential for the proton—target atom interaction.127 Since silicon oxide film grown on silicon substrate is thought to be mostly amorphous and we are mainly concerned with the oxygen yield, channeling, dechanneling, and blocking effects are ignored. Since protons scattered below the surface lose their en- ergy during both the incoming and the outgoing trajec- tories, the energy peaks from each slab are shifted rela— tive to each other proportional to the value of the energy loss per unit path length (the electronic stopping power, dE /dx).55’56’128 We choose each slab thin enough (2 A) to neglect the energy loss changes within the slab, for both the inward and outward paths (the surface energy approximationm). The electronic stopping power in sil- icon oxide is not known and has, therefore, to be calculat- ed. There are several approximations in the literature that give slightly different values.129 In our calculations, we use the Andersen-Ziegler values73 that have proven to give reasonable values for a variety of systems. The elec- tronic stopping power is energy dependent, with a max- imum around 100 keV for protons interacting with oxy- gen and silicon. Thus, our choice of proton energy helps to increase the depth resolution. It is also worthwhile to note that the changes in stopping power with energy near the maximum are relatively small.73 Therefore the elec- tronic energy loss along the inward path, where the pro- ton energy is about 100 keV, is close to the loss along the outward path, where the proton energy is in the 80—90- keV range. The Andersen-Ziegler approximation allows one to determine the electronic stopping power only for elemental targets. In order to consider compositional E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 and density changes for SiOz, we use Bragg’s rule128 dE/dx =2l-(dE/dx )inl- /N; N=2ini. It should be men— tioned that the stopping powers for silicon and oxygen (17.1 eV curl/1015 atoms for 0, and 24.4 ev earl/1015 atoms for Si) (Ref. 73) are close to that of the electronic stopping power for §O—100 keV protons traveling through SiO2 (14.6 eV/A, in turn rather close to the stop- ping power in bulk Si, 12.2 eV/A); therefore, the change in stopping power in the nonstoichiometric transition re- gion should be relatively small. Another important factor that affects the MEIS energy spectra is energy straggling; this reflects the broadening of the proton energy, due to the stochastic nature of ener- gy losses by electronic excitationsfilw“132 The total- energy peak broadening 92=Q%+(Ki0in)2+flgm in- cludes contributions from the instrumental resolution function (00) and the straggling for the incoming and outgoing trajectories (Q,n and flout, respectively; K i is the kinematic factor for the ith element). We include strag- gling in our simulation through a Gaussian energy distri— bution function, F (E), F(E>=(2snz)*”2exp[—(E—(E>12/292], (A2) where (E ) is the mean (depth dependent) energy of the protons. Bohr’s theory is usually used to calculate the straggling parameter, Q, in the limit of high ion ener- gies.133 For example, for oxygen and silicon Bohr’s theory predicts n,( o )=32.3(x)1/2 (eV) and 9,,(Si)=42.7(x)1/2 (eV), where X (A) is the distance traveled in the sample. However, this free electron theory fails for slower ions ( < 1 MeV for proton), in par- ticular, for lOO-keV protons. Therefore, we use the re- duced straggling values given by the Lindhard-Scharfl‘ ap- proximation2130’134’ ‘35 L(y)/2 (y <3), 1 (y>3), (A3) (om/n, )Zz where y =(v/vo)2/Z2, and U0 is the Bohr velocity, v is the proton velocity, and l(y)= 1.36y1/2 —O.Ol6y3/2.13O’134’135 In particular, for 100—keV protons, this approximation results in reduced straggling com- pared to Bohr’s expression with L(y)/2 values of 0.43 and 0.49 for silicon and oxygen, respectively. Finally, we use Bragg’s rule to calculate the energy straggling param- eter for Si02 from the known values for oxygen and sil- icon. The resulting straggling parameter is energy depen- dent, e.g., 20.4(x )”2 eV for IOO-keV protons and 17(x )”2 eV for 80 keV with x (in A) the distance traveled in the sample. We take this energy dependence into con- sideration in our simulations. The final backscattering spectrum is obtained by integrating individual energy spectra from each slab. The only fitting parameters we use are the depth concentration of the oxygen isotopes and of the silicon atoms in the film. In general, the above-mentioned approximations for electronic stopping power and energy straggling, and Bragg’s rule for ion—solid interactions for compound ma- terials, provide reasonable parameters for a wide variety of materialsm’132 To make sure that the parameters are realistic, we cross-correlate MEIS depth profiles with XPS and ellipsometry results on the same sample.91 For 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . 1773 this purpose, we use a high—quality gate oxide thermally grown in natural oxygen on Si(100) at an IBM fabrication facility. Ellipsometry gave a thickness of about 65 A for this film,91 whereas XPS yielded the ratio of x/A=1.07 [see (1)], that corresponded to the oxide thickness of 51 A (for 2:30 A). Ellipsometry is known to overestimate sil- icon oxide thickness in the limit of ultrathin ( < 100 A) films.“93 The MEIS energy spectra for oxygen and sil- icon taken in a channeling geometry are shown in Fig. 10. The dashed line shows the best fit using our stopping power and energy straggling parameters, and the silicon and oxygen depth distributions are shown in Fig. 11. The 1N. Cabrera and N. F. Mott, Rep. Prog. Phys. 12, 148 (1948). 2K. R. Lawless, Rep. Prog. Phys. 37, 231 (1974). 3A. T. Fromhold, Theory of Metal Oxidation. Volume I. Funda- mentals. Defects In Cristalline Solids (North-Holland, Am- sterdam, 1976). 4P. H. Holloway, J. Vac. Sci. Technol. 18, 653 (1981). 5K. Wandelt, Surf. Sci. Rep. 2, 1 (1985). 6A. Atkinson, Rev. Mod. Phys. 57, 437 (1985). 7F. P. Fehlner, Low-Temperature Oxidation. The Role of Vitre- ous Oxides (Wiley, New York, 1986). 8N. F. Mott, Philos. Mag. B 55, 117 (1987). 9E. Irene, CRC Crit. Rev. Solid State Mater. Sci. 14, 175 ( 1988). 10G. Lucovsky, J. F. Fitch, E. Kobeda, and E. Irene, in The Physics and Chemistry of Si02 and the Si-Si02 Interface, edit- ed by C. R. Helms and D. E. Deal (Plenum, New York, 1988), p. 139. 11The Si—S'iOz System, edited by P. Balk (Elsevier, Amsterdam, 1988). 12N. F. Mott, S. Rigo, F. Rochet, and A. M. Stoneham, Philos. Mag. B 60, 189 (1989). 13F. J. Himpsel, D. A. Lapiano-Smith, J. F. Morar, and J. Bevk, in The Physics and Chemistry of S102 and the Si-Si02 Interface, II, edited by C. R. Helms and B. E. Deal (Plenum, New YOrk, 1993), p. 237. 14T. Engel, Surf. Sci. Rep. 18, 91 (1993). 15C. R. Helms, and E. H. Poindexter, Rep. Prog. Phys. 57, 791 (1994). 16F. J. Grunthaner and P. J. Grunthaner, Mater. Sci. Rep. 1, 65 (1986). 17F. J. Himpsel, F. R. McFeely, A. Taleb-Ibrahimi, J. A. Yar- mofi‘, and G. Hollinger, Phys. Rev. B 38, 6084 (1988). 18V. D. Borman, E. P. Gusev, Yu. Yu. Lebedinski, and V. I. Troyan, Phys. Rev. B 49, 5415 (1994). 19B. E. Deal and A. S. Grove, J. Appl. Phys. 36, 3770 (1965). 20J. Blank, Philos. Mag. B 55, 685 (1987). 21J. M. Delarious, C. R. Helms, D. B. Kao, and B. E. Deal, Appl. Surf. Sci. 39, 89 (1989). 22H. Z. Massoud, J. D. Plummet, and E. A. Irene, 1. Electro- chem. Soc. 132, 2693 (1985). 23A. M. Stoneham, C. R. M. Grovenor, and A. Cerezo, Philos. Mag. B 55, 201 (1987). 24F. Rochet, S. Rigo, M. Froment, C. d’Anterroches, C. Mail- lot, H. Roulet, and G. Dufour, Adv. Phys. 35, 339 (1986). 25F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, Phys. Rev. Lett. 43, 1683 (1979). 26G. Hollinger and F. J. Himpsel. Phys. Rev. B 28, 3851 (1983). oxygen layer thickness from Fig. 11 is 59i4 A. The thickness of the silicon layers is about 56 A; this results from the°50 A of silicon atoms in the oxide and an addi- tional 6 A of substrate silicon visible to the proton beam in channeling. The data shown in Fig. 10 correspond to the scattering angle of about 80°. The profiles (Fig. 11) derived from the simulation of this set of data fit the spectra taken for this sample quite well at the scattering angle of 125°. This fact supports the validity of the simu- lation code, and shows that the film is rather uniform (otherwise, we should have observed an angular depen- dence for the energy spectra). 27G. Hollinger, E. Bergignat, H. Chermette, F. Himpsel, D. Lopez, M. Lannoo, and M. Bensoussan, Philos. Mag. B 55, 735 (1987). 28T. Hattori and K. Onishi, in Interface Control of Electrical, Chemical, and Mechanical Properties, edited by S. P. Murat— ka, K. Rose, T. Ohmi, and T. Seidel, MRS Symposia Proceed- ings No. 318 (Materials Research Society, Pittsburgh, 1994), p. 61. 29J. R. Engstrom, D. J. Bonser, and T. Engel, Surf. Sci. 268, 238 (1992). 30V. D. Borman, E. P. Gusev, Yu. Yu. Lebedinski, and V. I. Troyan, Phys. Rev. Lett. 67, 2387 (1991). 31J. M. Gibson and M. Y. Lanzerotti, Nature 340, 128 (1989). 32F. M. Ross and J. M. Gibson, Phys. Rev. Lett. 68, 1782 (1992). 33F. M. Ross, J. M. Gibson, and R. D. Twesten, Surf. Sci. 310, 243 (1994). 34R. D. Twesten, J. M. Gibson, and F. M. Ross, MRS Bull. 29, 38 (1994). 35T. Horie, Y. Takakuwa, and N. Miyamoto, Jpn. J. Appl. Phys. 33, 4684 (1994). 36A. Feltz, U. Memmert, and R. J. Behm, Surf. Sci. 314, 34 (1994). 37L. C. Feldman, P. J. Silverman, J. S. Williams, T. E. Jackman, and I. Stensgaard, Phys. Rev. Lett. 41, 1396 (1978). 38R. Haight and L. C. Feldman, J. Appl. Phys. 53, 4884 (1982). 39Q. Liu, J. F. Wall, and E. A. Irene, J. Vac. Sci. Technol. A 12, 2625 (1994). 40R. H. Doremus and S. C. Kao, in Interface Control of Electri- cal, Chemical, and Mechanical Properties (Ref. 28), p. 53. 4‘P. Morgen, U. Hoffer, W. Wurth, and E. Umbach, Phys. Rev. B 39, 3720 (1989). 42M. M. Banaszak-Holl, S. Lee, and F. R. McFeely, Appl. Phys. Lett. 65, 1097 (1994). 43H. Kageshima and M. Tabe, in Control of Semiconductor In— terfaces, edited by I. Ohdomari, M. Oshima, and A. Hiraki (Elsevier, Amsterdam, 1994), p. 227. 44A. Ourmazd, D. W. Taylor, J. A. Rentscheir, and J. Bevk, Phys. Rev. Lett. 53, 743 (1987). 45F. H. Fouss, H. J. Norton, S. Brennan, and A. Fisher-Colbrie, Phys. Rev. Lett. 60, 600 (1988). 46T. Yamazaki, S. Miyazaki, C. H. Bjorkman, M. Fukuda, and M. Hirose, in Interface Control of Electrical, Chemical, and Mechanical Properties (Ref. 28). 47W. A. Tiller, J. Electrochem. Soc. 128, 689 (1981). 48$. T. Dunham and J. D. Plummer, J. Appl. Phys. 59, 2541 (1986). 49K. Taniguchi, Y. Shibata, and C. Hamaguchi, J. Appl. Phys. 1774 65, 2723 (1989). 50]. J. Lander and J. Morrison, J. Appl. Phys. 33, 2089 (1962). 51F. W. Smith and G. Ghidini, J. Electrochem. Soc. 129, 1300 (1982). 52R. E. Walkup and S. Raider, Appl. Phys. Lett. 53, 888 (1988). 53J. Seiple and J. P. Pclz, Phys. Rev. Lett. 73, 999 (1994). 5“R. Tromp, G. W. Rublofi", P. Balk, F. K. DeGoues, and E. J. van Loenen, Phys. Rev. Lett. 55, 2332 (1985). 55L. C. Feldman, J. W. Mayer, and S. T. Picraux, Materials Analysis by Ian Channeling (Academic, New York, 1982). 56J. F. van der Veen, Surf. Sci. Rep. 5, 199 (1985). 57F. Fenter and T. Gustafsson, Phys. Rev. B 43, 12 195 (1991). 53F. Statiris, H. C. Lu, and T. Gustafsson, Phys. Rev. Lett. 72, 3574 (1994). 59E. P. Gusev, H. C. Lu, T. Gustafsson, and E. Garfunkel, in In- terface Control of Electrical, Chemical, and Mechanical Prop— erties (Ref. 28), p. 69. 60R. M. Tromp and E. J. van Loenen, Surf. Sci. 155, 441 (1985). 61L. C. Feldman, in The Physics and Chemistry ofSi02 and the Si-SiOz Interface (Ref. 10), p. 199. 62L. C. Feldrnan, Surf. Sci. 299/300, 233 (1994). 63N. W. Cheung, L. C. Feldman, P. J. Silverman, and I. Stensgaard, Appl. Phys. Lett. 35, 859 (1979). 64F. C. Stedile, I. J. R. Baumvol, J. J. Ganem, S. Rigo, I. Tri- maille, G. Battistig, W. H. Schulte, and H. W. Becker, Nucl. Instrum. Methods Phys. Res. Sect. B 85, 248 (1994). 65S. S. Crity and J. B. Condon, J. Electrochem. Soc. 128, 2170 (1981). 66F. Rochet, B. Agius, and S. Rigo, J. Electrochem. Soc. 131, 914 (1984). 67J. A. Costello and R. E. Tressler, J. Electrochem. Soc. 131, 1944 (1984). 68C. J. Han and C. R. Helms, J. Electrochem. Soc. 135, 1824 (1988). 69I. Trimaille and s. Rigo, Appl. Surf. Sci. 39, 65 (1989). 70M. P. Murrell, C. J. Sofield, and S. Sugden, Philos. Mag. B 63, 1277 (1991). 71]. J. Ganem, G. Battistig, S. Rigo, and I. Trimaille, Appl. Surf. Sci. 65/66, 647 (1993). 72R. M. Tromp, M. Copel, M. C. Reuter, M. Horn von Hoegen, J. Speidell, and R. Koudijs, Rev. Sci. Instrum. 62, 2679 (1991). 73H. H. Andersen and J. F. Ziegler, The Stopping and Ranges of Ions in Matter (Pergamon, New York, 1977), Vol. 3. 74G. K. Kinchin and R. s. Pease, Rep. Prog. Phys. 18, 1 (1955). 75H. Niehus, W. Heiland, and E. Taglauer, Surf. Sci. Rep. 17, 213 (1992). 76E. Taglauer, Surf. Sci. 299/300, 64 (1994). 77H. Dallaporta, M. Liehr, and J. E. Lewis, Phys. Rev. B 41, 5075 (1990). 73H. C. Lu, T. Gustafsson, E. P. Gusev, and E. Garfunkel (un- published). 79M. Tabe, T. T. Chiang, I. Lindau, and W. E. Spicer, Phys. Rev. B 34, 2706 (1986). 80F. G. Himpsel, Surf. Sci. 299/300, 525 (1994). 31M. F. Hochella and A. H. Carim, Surf. Sci. 197, L260 (1988). 32J. E. Fulghum, R. Stokell, G. McGuire, B. Patnaik, N. Yu, Y. J. Zhao, and N. Parikh, J. Electron. Spectrosc. Relat. Phenom. 60, 117 (1992). 83W. N. Lennard, G. R. Massoumi, I. V. Mitchell, H. T. Tang, and D. F. Mitchell, Nucl. Instrum. Methods Phys. Res. Sect. B 85, 42 (1994). 84C. J. McHargue, D. L. Joslin, and C. M. White, Nucl. In- strum. Methods Phys. Res. Sect. B 91, 549 (1994). E. P. GUSEV, H. C. LU, T. GUSTAFSSON, AND E. GARFUNKEL 52 35F. E. Batson, N. D. Browning, and D. A. Muller, Microsc. Soc. Am. Bull. 24, 371 (1994). 86P. E. Batson, Nature 366, 727 (1993). 87S. M. Goodnick, D. K. Ferry, C. M. Wilmsen, Z. Liliental, D. Fathy, and O. L. Krivanek, Phys. Rev. B 32, 8171 (1985). 88H. Akutsu, Y. Sami, and I. Ohdomari, Phys. Rev. B 44, 1616 (1991). 39V. A. Yakovlev, Q. Liu, and E. Irene, J. Vac. Sci. Technol. B 10, 427 (1992). 90E. Irene, Thin Solid Films 233, 96 (1993). 91E. P. Gusev, H. C. Lu, E. Garfunkel, T. Gustafsson, and V. A. Yakovlev (unpublished). 92T. Dutta and N. M. Ravindra, Phys. Status Solidi 134, 447 (1992). 93S. C. Kao and R. H. Doremus, in The Physics and Chemistry ofSi02 and the Si-SiOZ Interface 11 (Ref. 13), p. 23. 94M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, and K. Suma, Appl. Phys. Lett. 55, 562 (1989). 95A. Stockhausen, T. U. Kampen, and W. Monch, Appl. Surf. Sci. 56-58, 795 (1992). 96J. Westermann, H. Nienhaus, and W. Monch, Surf. Sci. 311, 101 (1994). 97U. Neuwald, U. Memmert, and R. J. Behm, in Proceedings of the 4Ist American Vacuum Society Symposium (American Vacuum Society, Denver, CO, 1994), p. 177. 98M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, and M. Ohwada, J. Appl. Phys. 68, 1272 (1990). 99M. Morita and T. Ohmi, Jpn. J. Appl. Phys. 33, 370 (1994). 100M. Hirose, T. Yasaka, and S. Miyazaki, Semicond. Res. 36, 263 (1991). 101K. Onishi and T. Hattori, Jpn. J. Appl. Phys. 33, L676 (1994). 102N. M. Ravindra, J. Narayan, D. Fathy, J. K. Stivastava, and E. A. Irene, J. Mater. Res. 2, 216 (1987). 103E. P. Gusev and E. Garfunkel (unpublished). 104M. Suzuki, Y. Homma, Y. Kudoh, and N. Yabumoto, Jpn. J. Appl. Phys. 32, 1419 (1993). 105M. Niwa, M. Udagawa, K. Okada, T. Kouzazki, and R. Sin- clair, Appl. Phys. Lett. 63, 675 (1993). 106A. Diebold and B. Doris, Surf. Interface Appl. 20, 127 (1993). 107J. E. Griflith and D. A. Grigg, J. Appl. Phys. 74, R83 (1993). 108s. D. Kosowsky, C. H. Hsu, P. S. Pershan, J. Bevk, and B. S. Freer, Appl. Surf. Sci. 84, 179 (1995). 109M. M. Banaszak-Holl and F. R. McFeely, Phys. Rev. Lett. 71, 2441 (1993). 110Z. H. Lu, M. J. Graham, D. T. Jiang, and K. H. Tan, Appl. Phys. Lett. 63, 2941 (1993). 111A. Pasquarello, M. S. Hybertsen, and R. Car, Phys. Rev. Lett. 74, 1024 (1995). 112]. Seiple, J. Pecquet, Z. Meng, and J. P. Pelz, J. Vac. Sci. Technol. A 11, 1649 (1993). 113M. P. D’Evelyn, M. M. Nelson, and T. Engle, Surf. Sci. 186, 75 (1987). 114B. Leroy, Philos. Mag. B 55, 159 (1987). 115T. Tamura, N. Tanaka, M. Tagawa, N. Ohmae, and M. Umeno, Jpn. J. Appl. Phys. 32, 12 (1993). “65. M. Hu, J. Appl. Phys. 45, 1567 (1974). “7D. G. Cahill and Ph. Avouris, Appl. Phys. Lett. 60, 326 (1992). 118M. Udagawa, M. Niwa, and I. Sumita, Jpn. J. Appl. Phys. 32, 282 (1993). 119K. Wurm, R. Kliese, Y. Hong, B. Rottger, Y. Wei, H. Neddermeyer, and I. S. T. Tsong, Phys. Rev. B 50, 1567 52 GROWTH MECHANISM OF THIN SILICON OXIDE FILMS ON . . . 1775 (1994). 120G. Renaud, P. H. Fouss, A. Ourmazd, J. Bevk, and B. S. Freer, Appl. Phys. Lett. 58, 1044 (1991). 121T. A. Rabedeau, I. M. Tidswell, P. S. Pershan, J. Berk, and B. S. Freer, Appl. Phys. Lett. 59, 3422 (1991). 122G. Lupke, D. J. Bottomley, and H. M. van Driel, Phys. Rev. B 47, 10 389 (1993). 123Y. Ono, M. Tabe, and H. Kageshima, Phys. Rev. B 48, 14 291 (1993). 124R Jakob, Y. J. Chabal, K. Raghavachari, and S. B. Christ- man, Phys. Rev. B 47, 6839 (1993). 1256. S. Higashi and Y. J. Chabal, in Handbook ofSilicon Wafer Cleaning Technology, edited by W. Kern (Noyes, Park Ridge, NJ, 1993), p. 433. 126T. Ohmi, Proc. IEEE 81, 716 (1993). 127G. Moliere, Z. Naturforsch. Teil A 2, 133 (1947). 128High Energy Ion Beam Analysis and Solids, edited by G. Gotz and K. Gartner (Akademie-Verlag, Berlin, 1988). 129R Sigmund, Nucl. Instrum. Methods Phys. Res. Sect. B 85, 541 (1994). 130F. Besenbacher, J. Andersen, and E. Bonderup, Nucl. In- strum. Methods 168, 1 (1980). 1311’. F. A. Alkemade, W. C. Turkenburg, and W. F. van der Weg, Nucl. Instrum. Methods. Phys. Res. Sect. B 28, 161 (1987). 132Y. Kido and T. Koshikawa, Phys. Rev. A 44, 1759 (1991). 133N. Bohr, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 18, 8 (1948). 134]. Lindhard and M. Scharfl', K. Dan. Vidensk. Mat. Fys. Medd. 27, 15 (1953). 135]. Lindhard and M. Scharff, Phys. Rev. 124, 128 (1961). ...
View Full Document

Page1 / 17

143-gusev-prb-1995-1759 - PHYSICAL REVIEW B VOLUME 52,...

This preview shows document pages 1 - 17. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online