484-brower--prb-1990-3444 - PHYSICAL REVIEW B VOLUME 42,...

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Unformatted text preview: PHYSICAL REVIEW B VOLUME 42, NUMBER 6 Dissociation kinetics of hydrogen-passivated (111) Si-SiOz interface defects K. L. Brower Sandia National Laboratory, P.0. Box 5800, Albuquerque, New Mexico 87185-5800 (Received 23 March 1990) This paper is concerned with the chemical kinetics of the transformation of hydrogen-passivated interface defects (HPb centers) into paramagnetic Pb centers (-Si ESi3) at the (111) Si-SiOZ interface under vacuum thermal annealing. Float-zone (111) silicon substrates were oxidized in dry oxygen at 750°C to a thickness of 500 A, passivated with H2 (D2) at 300°C for 3 h (4 h), and then vacuum thermal annealed at temperatures ranging from 500 to 595°C. The results of this analysis indicate that the kinetic process is described by a first-order rate equation d[HP,,]/dt = -kd[HPb] where kd =kdoexp( —Ed /kT). An activation energy of 2.56i0.06 eV with a preexponential factor kdo of approximately l.2>< 1012 sec’1 was obtained. The reaction rate is reduced if the samples are pas— sivated with deuterium instead of hydrogen. These results suggest that the chemical process is due to the thermal decomposition of the HP], center into Pb centers and atomic hydrogen. Although the activation energy for the diffusion of interstitial oxygen in silicon is also 2.56 eV, a rate-limiting step involving this mechanism is inconsistent with the hydrogen isotope efi‘ect as well as other con- siderations. Comparison of the activation energies for the H2 passivation of the Pb center and disso- ciation of the HPb center are shown to be chemically and energetically equivalent to the dissocia- tion of the H2 molecule as originally indicated by Myers and Richards. Thus, the reverse passiva- tion reaction, H+HPb~+Pb+H2, and the reverse dissociation reaction, H+Pb—>HPb, are exo- thermic reactions that proceed with very little thermal activation in the presence of atomic hydro- 15 AUGUST 1990-11 gen. I. INTRODUCTION An insulating layer (S 1 pm) of Si02 atomically bonded to semiconducting silicon can be made simply by heating silicon in oxygen. Ordinarily, the crystalline silicon atoms at the Si-SiOz interface bond to oxygen atoms of the SiOZ; nevertheless, up to approximately 0.5% of the crystalline interfacial silicon atoms are not bonded to ox— ygen atoms and give rise to a specific dangling bond type of defect, 'SIESI3, called the Pb center. In the neutral charge state this interface defect is observable with elec— tron paramagnetic resonance (EPR). “3 The paramagne- tism of this defect arises from an unpaired electron local- ized in a sp EIIIJ—like hybrid orbital localized on the defect silicon atom.“’ These defects are believed to be the dominant interfa- cial charge traps that make this insulator—semiconductor (IS) system less than ideal in device applications.6'7 In order to minimize the effects of charge trapping at such defects, the defects are exposed to hydrogen, the idea be- ing that the hydrogen will chemically bind to and pas- sivate these defects. The effects of hydrogen on interface states have been observed previously by electrical mea- surementsg‘“ The electrical measurements require a conducting gate on top of the oxide forming a metal- insulator-semiconductor (MIS) structure. For the case of Al-SiOZ-Si device structures, passivation of Si-SiOz inter- face states is achieved simply by heating the device struc— ture to 200 °C independent of the gas ambient.9 Do Thanh and Bauk8 have suggested that in this case pas- sivation occurs as a result of the generation of atomic hy- 42 drogen at the Al-Si02 interface; this source of hydrogen is attributed to prior contamination during device pro- cessing. In this case, a hydrogen atom, or a proton, which might behave like a polaron, diffuses to the Pb center to form a HPb center. (A model illustrating the atomic structure of the passivated Pb center is illustrated in Sec. IV B in Fig. 10.) Reed and Plummer9 have recent— ly characterized the kinetics of this process using capacitance—voltage (C— V) measurements. Since the work function of polysilicon essentially matches that of the sil- icon substrate, polysilicon gates have for the most part supplanted aluminum as a gate material in commercial applications. Fishbein, Watt, and Plummer10 attempted to determine the kinetics of passivation using molecular hydrogen. In their experiments passivation occurred by a mechanism in which H2 entered the oxide primarily at exposed SiOZ edges. Since it was necessary for Hz to difluse laterally distances up to 50 pm, the rate—limiting step observed in their C-V measurements was the diffusion of H2 in the oxide rather than the passivation of the interface states. 10 Recently, we12 determined from EPR measurements the chemical kinetics for the passivation of a specific in- terface defect, namely the Pb center, using molecular hy- drogen. The simplicity in sample preparation and struc- ture needed for EPR measurements avoids many of the complications inherent in preparing device structures for electrical measurements. In our experiments (1101) silicon substrates were oxidized to a thickness of 500 A and ex- posed to H2 under conditions for which the time, temper- ature, and H2 pressure were known. All processing steps Work of the U. S. Government 3444 Not subject to U. S. copyright 42 DISSOCIATION KINETICS OF HYDROGEN-PASSIVATED . . . 3445 were accomplished in situ within a quartz tube to mini- mize any effects due to extraneous hydrogen-related con— tamination. We determined that the rate of passivation was given by the expression d [Pb] , d, =—k}2’[H2][Pb], <1) where kf’ obeys the Arrhenius equation k}2)=k}g’exp<—Ef/kri . (2) The volume concentration of H2 at the interface and within the thermal oxide was assumed to be the same as the physical solubility of molecular hydrogen in bulk vit- reous silica12 as determined theoretically by Shackelford, Studt, and Fulrath13 and empirically by Shelby. 14 Since the equilibrium time for the hydrogen concentration within the thermal oxide was very short (<1 sec) com- pared to the times required for measurable passivation (> 100 min), the rate-limiting step was the passivation re- action itself. From the nature of the kinetic equation [Eq. (1)] and the magnitude of the preexponential constant in Eq. (2), we suggested a physicochemical process by which Pb centers are passivated. According to this model, H2 is physically absorbed into the SiO2 and diffuses as H2 among the accessible interstices of the SiO2 network in- cluding the reaction site at the Pb center. During times that a H2 molecule is adjacent to the Pb center, there is a finite probability that it will react with the Pb center ac- cording to the chemical reaction H2+Pb—>HPb+H, (3) resulting in the passivation of the Pb center and the for- mation of a diamagnetic HPb center. Now, another problem arises and is the focus of study in this paper. Although thermal annealing in H2 results in the disappearance of the Pb resonance, subsequent vac- uum thermal annealing above 500 °C causes the Pb centers to reappear. The purpose of this paper is to determine the physiochemical process by which Pb centers reappear upon subsequent vacuum thermal an- nealing. In this study we are able to show that the Pb centers reappear as a result of thermally activated disso- ciation of HPb centers. Another model involving the reduction of HPb centers by mobil interstitial oxygen from within the silicon is shown to be inconsistent with our experimental results. From this work and one other observation, namely that the sequence of the passivation and dissociation re- actions are equivalent to the dissociation of the H2 mole- cule, emerges a unified model for the hydrogen chemical kinetics of Pb centers. There is reason to believe that the activation energies for the passivation and dissociation reactions are equal or only slightly greater than the ener- gy difference between the respective initial and final con- stituents.‘5"6 Consequently, the reverse passivation and dissociation reactions are predicted to proceed essentially spontaneously in the presence of atomic hydrogen and are expected to be important in a radiation environment. The details of our sample preparation and EPR mea— surements are presented in Sec. II. The results of our EPR measurements are represented phenomenologically in terms of first-order kinetics in Sec. III. Also included in this section are the results of our studies using different hydrogen isotopes. In Sec. IV, two physicochemical models designed to account for the reappearance of the Pb center upon vacuum thermal annealing after H; pas— sivation are examined in terms of our experimental re— sults. In Sec. V the energetics of the passivation and dis- sociation processes, which are sequentially equivalent to the dissociation of the hydrogen molecule, are analyzed and the nature of the energy barriers for the various reac- tions is discussed. Our conclusions derived from this study are presented in Sec. VI. II. EXPERIMENTAL TECHNIQUES A. (001) versus (111) Si-SiOz interface Electron paramagnetic resonance measurements of Phatype defects on the (111) rather than the (001) Si-SiO2 interface are preferred for two reasons. First, the signal- to-noise ratio is greater in the case of the (111) interface because of its greater interface state density. Second, the (111) Si—SiO2 interface has only one type of paramagnetic defect, namely the Pb center, whereas two distinct paramagnetic defects, namely the Pbo and PM centers, are associated with the (001) Si-SiO2 interface. These two de- fects give rise to only two partially overlapping reso- nances providing the applied magnetic field is perpendic- ular to the (001) interface. 17 These complications make it very difficult to measure the intensity of the individual defect spectra associated with the (001) interface. Thus, this kinetic study is limited to the (111) interface. At this time our understanding of the structure of the Pb defect associated with the (111) Si-Si02 is far more advanced than our understanding of the Pbo and Pb1 centers associ- ated with the (001) interface.5 Although the (111) inter- face is ideal in many respects for scientific studies, the (001) interface is the one employed in device structures because of its lower density of interface states, nature of the silicon faceting under etching, slightly different sur- face potential, etc. B. Sample treatment The details of our method of sample preparation and measurement have been discussed previously.12 In this study (111) silicon substrates are thermally oxidized at 750 °C in 760 Torr of dry oxygen for 3l h; 18 this yields an oxide approximately 500 A thick with approximately 3X1012 Pb centers/cm? After the samples have cooled to room temperature in vacuum, they are reheated in situ and annealed in H2 (D2) at 300 °C and 760 Torr for 3 h (4 h); after this treatment, no Pb resonance can be detected in these samples. Finally, after the samples have again cooled to room temperature, the samples are annealed in situ in vacuum (approximately 5 ><10_5 Torr) for a given 3446 time and temperature. This vacuum anneal results in a partial recovery of the Pb signal. Only after this final vacuum anneal are the vacuum-pressure seals broken and the samples removed for EPR measurements. The Pb centers are stable at room temperature with the oxide ex- posed to air. 12 This approach allows us to determine the kinetic parameters that characterize the recovery in the Pb signal. C. Oxidation-annealing system The system used for oxidation, hydrogen, and vacuum annealing consists of a 61-cm—long tubular furnace with a 5.1-cm open bore. A 33—mm-diam, 127—cm-long quartz tube is placed on the axis of the furnace. This tube can be evacuated with a turbomolecular pump or back filled with a gas. The sample holder, shown in Fig. 1, contain- ing our silicon samples to be processed is slipped into this quartz tube. For purposes of quick heating or quenching, the furnace can be repositioned along the length of this sample tube. In the region of the sample holder, a ceram- ic aluminum oxide tube 65 cm long with a 41 mm outside diameter is slipped over the outside of the quartz sample tube. This aluminum oxide tube moderates the thermal radiation from the bare heating coils of the furnace and acts as a blackbody, cylindrical-cavity radiator. “7* Si sample cross sectional ‘ slot view FIG. 1. Schematic of the sample holder in which the silicon samples were thermally oxidized, passivated in H2, and vacuum thermal annealed. The temperature of the silicon holder is mea— sured with the Pt thermocouple. K. L. BROWER 42 The sample holder in which the silicon substrates are oxidized, annealed in hydrogen, and subsequently an- nealed in vacuum is shown in Fig. 1. This sample holder is made of silicon and acquires an oxidized surface. We chose silicon because it is a very clean material. Oxida- tion of the silicon is necessary in order to prevent the reduction of the Pt thermocouple to a platinum silicide. The individual silicon samples are placed in the slots as illustrated. Thus, each silicon sample is contained within a thermal radiation cavity. D. Temperature considerations As indicated in Fig. 1, the temperature of the sample holder is measured using a Pt thermocouple (type S). The first question is how does this temperature relate to the sample temperature, especially in a vacuum environ- ment? Since each sample is contained within a cavity (Fig. 1), each sample necessarily comes to the same tem- perature as the silicon holder by virtue of energy ex- change due to thermal radiation. At 773 K the rate of temperature change for a one-degree-Kelvin temperature difi'erence between sample and holder is approximately 0.9 K/sec; thus, thermal radiation quickly drives these thin, low-mass samples into thermal equilibrium with the silicon sample holder. The second question is since the sample holder in Fig. 1 is heated in vacuum by only thermal radiation, what is the maximum temperature gradient in the silicon sample holder? Our calculations indicate that with the sample holder initially at 300 K and radiated by a blackbody at 873 K, the maximum ra- dial temperature gradient is approximately 0.2 K/ cm. Of course this temperature gradient necessarily decreases as the temperature of the sample holder approaches that of the blackbody radiator. The third question is by how much is the thermocouple junction temperature lowered due to heat conduction loses down the Pt wires? For the case in which our thermocouple is suspended in vacuum, our calculations indicate that the steady—state junction temperature is lowered by approximately 1 K at 873 K due to heat conduction loses down the Pt wires. In order 600 500 400 300 200 100 vacuum anneal temperature (°C) 0 50 100 1 50 200 250 time (min) FIG. 2. Typical time-temperature profile obtained during a vacuum thermal anneal. 42 DISSOCIATION KINETICS OF HYDROGEN—PASSIVATED . . . to minimize this error, the thermocouple junction is placed in thermal contact with the sample holder by plac— ing the tip of the thermal couple in a small hole. Thermal contact is made by packing the hole with Pt wire. In view of these considerations the silicon sample temperature is taken to be the same as that measured by the Pt thermocouple. In the case of the vacuum anneals, it is impossible to impose a rectangular time-temperature profile. A typical time-temperature annealing profile is shown in Fig. 2. To avoid any shortcomings or undue approximations from this limitation, we record the sample temperature as a function of time; the time and temperature are measured every second, digitized, and stored for subsequent analysis (Sec. III). Thus, the measured time-temperature profile is mathematically convolved into our kinetic analysis. E. Thermochemical effects Various chemical effects involving hydrogen and Pb centers as observed by EPR are summarized in Fig. 3. After dry thermal oxidation of (111) silicon at 850 “C, 18 we observe the Pb resonance as illustrated in Fig. 3(a). If in addition to thermal oxidation, the samples are subse— quently reheated and annealed in vacuum for 1 hour at 850 °C, the Pb resonance appears to be unchanged [Fig 3(b)]. Pb centers appear to be stable under thermal an- nealing for temperatures up to at least 850 °C. On the other hand, if after oxidation the samples are annealed in H2 at only 300 “C for 90 min, then the Pb center is just barely detectable [Fig 3(c)]. In this case the loss of signal is attributed to the passivation of Pb centers which renders them diamagnetic. We observe that the effects of passivation can be reversed as evidenced by the reappear- ance of the Pb resonance in Fig. 3(d) by annealing the samples in vacuum at approximately 675 °C; this latter effect is the focus of attention in this paper. III. EXPERIMENTAL RESULTS AND ANALYSIS The results of the analysis presented here are con- sistent with the assumption that the recovery in the Pb signal follows first-order kinetics for which the rate equa- ‘kdof P ,=N 1*e [ blcalc 0[ XP Tprofilc where N0 is the initial concentration of HPb centers, or the maximum concentration of recoverable Pb centers as measured by EPR. Notice that in this solution to the rate equation the time—temperature profile, which is mea- sured experimentally and denoted by the function T(t), is folded into the expression for [Pb Law. In our least-squares—fit analysis to determine Ed and kdo, the calculated values given by Eq. (6) were least- squares fitted to the experimental values, [Pb]exp,, as a function of Ed and kdo. In order to establish the validity exp[~E,,/krm]dz|] , 3447 it (111) Si—Sio2 Pb resonance (b) 850 °c, 1 hr in vacuum Hm WWW??? 7220 7240 7220 7240 7230 7250 7230 7250 B (G) (c) 300 °c, 90 min (a) 300 °c, 90 min in 760 Torr H2 In 760 Torr H2; 615 °c, so min in vacuum (a) unannealed FIG. 3. Thermochemical effects on the Pb resonance at g=2.0016 as indicated by changes in the spectral intensity. (Changes in field position are due only to changes in the reso- nant cavity frequency and are not significant). The vertical sen— sitivity is the same for all four spectra. (a) Pb spectrum as ob- served after dry thermal oxidation of (111) silicon substrates at 850 °C (Ref. 18). (b) Subsequent in situ vacuum thermal anneal- ing at temperatures up to 850 °C have no apparent affect on the Pb centers. (c) Pb centers are passivated by annealing in H2 at 300 “C. (d) All of the Pb centers are recovered upon in situ vac- uum annealing in this case at 675 °C. tion is given by the expression d [P12]. = dt and the rate constant is given by the Arrhenius expres- sion Thus, the calculated concentration of Pb centers, [Pb Lalo reappearing after a vacuum thermal annealing is given by the expression (6) [..____.___________ of the kinetic model, it is necessary to acquire data over as wide a range of temperatures and [Pb]/NO ratios as possible. A range of temperatures is needed in order to determine Ed and kdo; a range of [P,,]/NO ratios is need- ed in order to verify the time dependence implied in the rate equation. Our vacuum thermal anneals ranged from 500 to 595 °C, and the ratio in our measured values of [PH/N0 ranged from 0.2 to nearly 1.0. Although it would be highly desirable to test our kinetic model for ra- tios of [PM/N0 extending over several decades, this has 3448 not been possible due to the limitations in the signal to noise of the Pb resonance. The results of a least-squares fit with respect to Ed and kdo pertaining to the recovery of Pb centers after hydro~ gen passivation are illustrated in Fig. 4 where [Pb ]expt is plotted versus [Pb kale. For these data, which involve passivation with H2, the results of our analysis indicate that this first-order kinetic process proceeds with an ac- tivation energy E, of 2.56 eVi0.06 eV and a preexponen- tial factor kdo, of approximately 1.2)(1012 sec‘l. The standard deviation in [Pb km from [Pb kale is 4.4 which is to be compared with NO having a measured, relative value of 92. A similar plot of [Pb]expt versus [P1,]Ca,c for our deu- terium data is presented in Fig. 5. In this case the tem- perature of our vacuum anneals was restricted to approx- imately 510 “C. A least—squares fit of these data, keeping the activation energy constant and equal to 2.56 eV, gave a preexponential factor kdo, of 9.8)(1011 sec~1 with a standard deviation in [Pb]expt from [P1,]Calc of 3.7. The significance of the deuterium data in comparison with the hydrogen data is discussed in Sec. IV. The correctness in the time dependence implied by the rate equation [Eq. (4)] is demonstrated in Fig. 6 where we have plotted log10( 1 —-[Pb Lynn/NO) versus time t for fixed temperature (approximately 510 °C). In order to also show as distinctly as possible the effects of hydrogen mass on the rate of the dissociation process, we also show in Fig. 6 how the decay rate is affected by the hydrogen iso- tope used in the passivation process. The solid line in Fig. 6 representing the hydrogen data was calculated us- ing the kinetic parameters deduced from the data in Fig. 4, and the dashed line representing the deuterium data was calculated using the kinetic parameters deduced from the data in Fig. 5. A relatively low temperature was 0.0 0.0 0.2 0.4 0.6 0.8 1 .0 [P J /[No] b expt cult: FIG. 4. Plot of the fraction of Pb centers measured experi— mentally after hydrogen passivation and vacuum thermal an— nealing vs the calculated fraction of Pb centers as determined by a least-squares fit with respect to the activation energy E, and the preexponential factor kdo. The vacuum anneal temperatures ranged from 500 to 595 “C. The solid line represents the ideal relationship. K. L. BROWER 42 1.0 deuterium 0.0 0.0 0.2 0.4 0.6 0.8 1.0 [Phlexw /EN°] calc FIG. 5. Plot of the fraction of Pb centers measured experi- mentally after deuterium passivation and vacuum thermal an- nealing at 510.8 °C vs the calculated fraction of Pb centers as determined by a least-squares fit with respect to only the preex- ponential factor kdo; the value for Ed was constant and equal to that deduced from the data in Fig. 4. selected so that the time—temperature profile was essen- tially square to a first approximation, and the experimen- tal data could be plotted as a function of time for essen- tially constant temperature. In order to show the quality of the least-squares fit as a function of temperature, which is essentially an indica- tion of the adequacy of the Arrhenius expression for the temperature dependence in our model, the values for ([PbLXPt—[PbLaIJ/NO pertaining to our hydrogen data in Fig. 4 are plotted as a function of temperature in Fig. 7. fie E. g “In LA I passivation conditions " A 4 h D2 I 3 h H2 O 4 h H2 0 200 400 600 800 t (min) FIG. 6. Semilogarithmic plot of the fraction of HP,J centers (=l—[Pb1mm/No) as a function of annealing times at 510.8 “C assuming a rectangular time-temperature profile. The solid line corresponds to the calculated fraction of HPb centers; the dashed line corresponds to the calculated fraction of DPb centers. 42 DISSOCIATION KINETICS OF HYDROGEN-PASSIVATED . . . 0.4 20 \ 0.2 “a flu A E. o I if g ~02 —o.4 480 520 560 600 T (°C) FIG. 7. Plot showing the distribution of experimental points as a function of the peak annealing temperature. The sensitivity of the hydrogen preexponential factor kdo, to small changes in the activation energy Ed, is shown in Fig. 8. This plot is based on a least-squares fit of the hydrogen data in Fig. 4 as a function Ed for fixed values of kdo indicated in Fig. 8. The optimum values for Ed and kdo cited above are indicated by the square data point in Fig. 8. The standard deviation in [Pb]exp, from [Pb]calc as a function of kdo based on a least—squares fit of the hydro- gen data in Fig. 4 with respect to Ed for fixed kdo is illus- trated in Fig. 9. These data indicate that there is one dis- tinct solution pertaining to the fit of the experimental data to the kinetic equations [Eqs. (4) and (5)]. The square data point corresponds to the optimum value for kdo cited in this paper. 1°14 1°13 1012 -1 kdo(sec ) 1011 10 2.0 2.2 2.4 2.6 2.8 3.0 E(, (eV) 10 FIG. 8. Plot of km as a function of the activation energy Ed, based on a least-squares fit of the data set in Fig. 4 for fixed values of kdo. This plot shows the sensitivity in the value of kdo for small changes in the activation energy. The square data point indicates the optimum values for Ed and km. 3449 a: standard deviation a: 1o‘° 1o11 10‘2 1o13 10“ '1 kdo(sec) FIG. 9. Plot of the standard deviation in [Pb km from [Pb kale resulting from a least-squares fit of the data set in Fig. 4 as function of E, for fixed values of kdo. N0 has a relative value of 92. The data point at the minimum corresponds to the op- timum values for Ed and kdo cited in this paper. IV. CHEMICAL PROCESSES We consider two chemical processes with first—order ki- netics that might conceivably be consistent with the recovery of the Pb signal upon annealing. We will show that the HPb dissociation model is consistent with all the known experimental facts, whereas the oxygen diffusion model is inconsistent with known facts. A. HPb dissociation model Since the annealing is done in vacuum, the most obvi- ous chemical process is simply the dissociation of the HPb center according to the reaction HPb—aPh +H . (7) The rate of dissociation in this case should be sensitive to the isotopic mass of the hydrogen. To a first approxima- tion, the rate constant is given by the expression deVQAS/ke VAH/kT’ where v is an attempt frequency, AS is the change in en- tropy, which for silicon might typically be several Boltzmann factors, and AH is the change in enthalpy. The important point is that in this model the attempt fre- quency arises physically from vibrations involving the hy- drogen, stretching and/or wagging, whose resonant fre- quencies would be affected by the mass of the hydrogen isotope. In the harmonic-oscillator approximation, vibra- tional frequencies are inversely proportional to the square root of the vibrating mass. Also, the entropy factor is ex- pected to be a function of the vibrational frequencies.19 In Fig. 6, log10(1-[P,,]/N0) is plotted versus the an- nealing time in vacuum at constant temperature for sam- ples previously passivated with H2 (square data points) or D2 (triangular data points). These data show that there is 3450 a significant difference depending upon the hydrogen iso- tope. The analysis of our experimental data in Sec. III in- dicates that the preexponential factor [k(H)]d0 for the hy- drogen data is 1.2x 1012 sec‘1 as compared to a value for [k(D)]d0 of 0.98 X 1012 sec—1. Thus, the experimental value for the ratio [k(D)]d0/[k(H)]d0 is 0.82. The change in the frequency factor in Eq. (8) is expected to yield v(D)/v(H) equal to 0.71 in the harmonic-oscillator ap- proximation. Thus, the magnitude of the observed change in the preexponential factor kayo, due to hydrogen isotopic effects is reasonable, and the effect corroborates the HPb dissociation model. B. Oxygen interstitial diffusion model This model suggests itself because the activation ener- gy for the diffusion of bond-centered interstitial oxygen in silicon is 2.54 eV (Refs. 20 and 21) and is very nearly equal to the dissociation energy (2.56i0.06 eV) we have determined for the process involving the reappearance of the Pb center. This model presumes that under vacuum annealing the rate-limiting process is the dilfusion of in- terstitial oxygen in the crystalline silicon from one bond- centered interstitial site to another. We postulate that if an interstitial oxygen atom happens to occupy a site im- mediately adjacent to the defect silicon atom in the HPb center (site “R” in Fig. 10), then it spontaneously in— teracts with the HP}, center to form the Pb center devoid of any neighboring hydrogen as evidenced by the lack of hydrogen hyperfine spectra. The inference is that the OH radical escapes leaving the Pb center. The rate—limiting process in this model is the diffusion of the isolated interstitial oxygen. No experimental evi- dence has been found indicating that hydrogen is a part of the oxygen interstitial or involved in its dilfusion.20’22 Thus, the rate—limiting step involving the diffusion of in- terstitial oxygen is expected to be independent of hydro- gen isotope effects. This clearly contradicts the experi- mental results shown in Fig. 6 and under the known cir- cumstances negates the oxygen interstitial diffusion mod- e1. It is, nevertheless, important to check this conclusion from other viewpoints. Let us consider the kinetics of this model. Infrared measurements of the float-zone sil- icon substrate material used in our experiment indicate an oxygen concentration in the as—received samples of ap- proximately 3.5 X 1015 interstitial oxygen/cm}.23 Since our samples were oxidized at 750° for 31 h, we estimate that the near-surface concentration of oxygen is approxi- mately 5><1016 interstitial oxygen/cm3.24 The rate at which HPb centers are reduced by dilfusing interstitial oxygen atoms in this model is given by the expression lePb] = [0.] dt 2p where [0,] is the equilibrium concentration of interstitial oxygen and p is the concentration of crystalline silicon atoms/cm3. The parameter J is the oxygen interstitial jump rate as deduced from infrared stress-induced di- chroism measurements20 and is given by the expression —J (%+%)[HP,,], (9) K. L. BROWER 42 SlLICON OXYGEN HYDROGEN FIG. 10. Ball-and—stick model of the crystalline silicon envi- ronment around the HPb center at the (111) Si-SiO2 interface. Only the first layer of oxygen atoms of the thermal oxide is shown. The three first nearest-neighbor Si—Si bond-centered in- terstitial sites adjacent to the Si—H bond are denoted as “R.” There are two distinct sets of bond-centered interstitial sites, denoted as “A” and “B,” from which the oxygen interstitial can difl‘use in jumping to the “R” sites. Interstitial oxygen atoms in the “A” sites are considered to have five jump options, one of which is the “R” site. Interstitial oxygen atoms in the “B” sites have six jump options, one of which is the “R” site and two the “ A” sites. J =J0exp( —Edm/kT) , (10) where Edifi is equal to 2.561i0.005 eV and J0 is equal to 5><1015 sec—1.20 The first term on the right side of Eq. (9), namely %, indicates the probability that an oxygen in- terstitial occupying an “A” site jumps to a reaction site “R” in Fig. 10. If the oxygen atom jumps to the reaction site “R” in Fig. 10, then the chemical reaction resulting in the removal of the H atom from the Pb center proceeds spontaneously. The second term on the right-hand side in Eq. (9), namely %, indicates the probability that an oxy- gen interstitial in a “B” site jumps to an “R” site in Fig. 10. The form of Eqs. (9) and (10) indicates that the ac- tivation energy for the diffusion of the oxygen interstitial corresponds to the dissociation energy in Eq. (5) and the preexponential factor kdo, in Eq. (5) corresponds to k _ 17[O,-] J (10— 0 ' The value of kdo as predicted by Eq. (11) is 4.3X109 sec_ 1. This value for kdo is a factor of approximately 300 less than our experimental value of 1.2><1012 sec”1 and does not corroborate this model. (11) 42 DISSOCIATION KINETICS OF HYDROGEN-PASSIVATED . . . 3451 Finally, it does not appear energetically favorable for the oxygen atom to escape from the Pb center with the hydrogen atom as OH; it is energetically more favorable for the oxygen atom to remain bonded with or without the hydrogen to the silicon dangling bond of the Pb center in contradiction with experimental observation. This is based very simply on the relative bonding energies of H—0 (4.44 eV), H—H (4.52 eV), O—Si (8.28 eV), and H—Si (3.09 eV).25 For example, the difference in the binding energies of H—H and H—Si corresponds to 1.43 eV and is close to the experimentally measured value of 1.66 eV for the passivation reaction in Eq. (3) at the Si- SiO2 interface. 15 These binding energies suggest that the Si—O binding will dominate over the 0—H and Si—H binding configurations. Thus, the oxygen interstitial model does not account for either the observed hydrogen isotopic effects, the oxygen-Pb reactivity rate, or the most energetically favor- able chemical process and is therefore rejected. V. ENERGY BARRIERS It is important to note that the two chemical processes involving the passivation of the Pb center, Eq. (3), and the dissociation of the HPb center, Eq. (7), are equivalent to the dissociation of the H2 molecule, H2—>H+H, (12) in the thermal oxide. Thus, the Pb center can be viewed as a catalyst facilitating the dissociation of the H2 mole- cule. The dissociation energy of the H2 molecule in vacu— um is 4.52 eV.25 Although the dissociation energy of the H2 molecule in the interstices of the SiOZ network might be smaller than in vacuum, this energy difference 5 is ex— pected to be small since, for example, the hyperfine split— ting of interstitial atomic H0 in SiO2 is within 1% of the vacuum splitting. Also, SiOz is a rather tightly bound in— sulator with a band gap of approximately 9 eV. By com- paring the energetics associated with the two possible chemical paths by which the H2 molecule is in effect dis- sociated, the internal consistency of our models for the passivation of the Pb center and the dissociation of the HPb center can be demonstrated. This line of reasoning with regard to the hydrogen kinetics of Pb centers has been noted previously. 15’” Let E0, E1, and E2 be the difference in the total ground-state energies between the initial and the final constituents for each of the chemical reactions indicated by Eqs. (12), (3), and (7), respectively. According to the conservation of energy, this implies that for these chemi- cal reactions EO=E1+E2. However, during the course of a chemical reaction, the total energy may have to pass over a maximum energy as indicated by the dashed line in Fig. 11. The measured activation energy corresponds to E0z in Fig. 11 for a given chemical reaction. For the case involving the dissociation of the H2 molecule in vac- uum, it is important to realize that the energy barrier simply increases monotonically as illustrated schemati- cally by the solid line in Fig. 11.26 Furthermore, we sug- gest that the energy barrier for the dissociation of the H2 molecule in the interstices of the SiOz is also monotoni- cally increasing and nearly the same as that in vacuum for reasons mentioned above. Thus, the constraint on the activation energies for the two different chemical paths by which the H2 molecule can be dissociated is S gf—2=ngstf+Ed, (13) where e is expected to be small. Our experimental results indicate that E f +Ed is equal to 4.22 eV as compared to 4.52 eV for The fact that Ef+Ed is only 7% small- er than the dissociation energy of the H2 molecule in vac- uum suggests that the dissociation energy of the H2 mole- cule in the interstices of the SiOz, E 3:32, is approximately 4.22 eV according to Eq. (13). The self-consistency in the values for the activation energies in Eq. (13) also supports the chemical models that we have proposed for the pas- sivation and dissociation processes. Furthermore, in order to keep 6 as small as possible in Eq. (13) and since there already is a 7% deficit, we sug- gest that the activation energies for the passivation and dissociation processes are equal or possibly only slightly greater than the difference in the total energy between the respective initial and final constituents as indicated schematically in Fig. 11. A montonically increasing ener~ gy barrier for the dissociation process appears reasonable since this two-body process is very similar quantum mechanically to the dissociation of the H2 molecule; how— ever, the nature of the energy barrier for the H2 passiva- tion process [Eq. (3)] is less obvious since this is primarily a three-body problem. If in fact there is a slight inter— mediate barrier (dotted line in Fig. 11) to either the pas- sivation or dissociation processes, then this will necessi- tate a corresponding reduction in our estimate of the dis- sociation energy for the H2 molecule in the oxide accord- ing to Eq. (13). Eu initial state H2 —» H + H EH2 H2+Pb—»HPb+H E1 HPb —— Pb + H Ed EH25 Ef+Ed FIG. 11. Unified model for the hydrogen chemistry and ki— netics of Pb centers at the (111) Si-SiO2 interface. The measured values for Ef and E, are (1.66:0.06) and (2.56:0.06) eV, re- spectively. The dissociation energy of the H2 molecule in vacu- um is 4.52 eV; our results suggest that the dissociation energy of the H2 molecule in the thermal oxide is approximately 4.22 eV. 3452 These energy considerations suggest that the reverse passivation reaction, H+HPb—+Pb+H2, (14) and the reverse dissociation reaction, H+Pb—>HP,, , (15) are exothermic chemical reactions that might occur spon- taneously, provided that atomic hydrogen is made avail- able. The availability of atomic hydrogen is the control- ling factor in the occurrence of these reverse reactions. Thus, the rate at which these reverse chemical reactions proceed is predicted to be either source limited, that is, limited by the rate at which atomic H is generated, or diffusion—limited, that is, limited by the rate at which H can reach the Pb center. Defect trapping of the atomic hydrogen may also be an important aspect of any actual problem.15 It has been demonstrated that ionizing radiation re- sults in the release of atomic hydrogen within a typical thermal oxide; thus these exothermic reactions may well occur at relatively low temperatures in a radiation envi- ronment.”28 In the presence of atomic hydrogen the Pb center can be either passivated [Eq. (15)] or the HP,7 center dissociated [Eq. (14)] as suggested by others.8’28 In a radiation environment the competition between these chemical reactions might be a mechanism that in— troduces metastability in the relative number of Pb and HP!7 centers. This metastability may be one of the reasons that account for the difficulty in understanding the effects of radiation on interface states. VI. CONCLUSIONS From this work emerges a unified model for the hydro- gen chemistry and kinetics of (111) Si-Si02 interface de— fects known as Pb centers. The essence of this unified model is summarized in Fig. 11. As indicated in Fig. 11, Pb centers can be passivated with molecular hydrogen to form HPb centers. The activation energy E f, for this re- action is (l.66i0.06) eV.12 Under vacuum thermal an- nealing the studies in this paper indicate that HPb centers dissociate with an activation energy of (2.56i0.06) eV. The Arrhenius preexponential factor for hydrogen is ap- proximately l.2><1012 sec_1 and is smaller by a factor of 0.82 for DPb dissociation. The hydrogen molecule has an activation energy for dissociation of 4.52 eV in vacuum.25 The dissociation en- ergy for H2 might be only slightly reduced in the thermal oxide due to weak interaction with the lattice; therefore it is expected to be thermally stable in the oxide up to at least 600 “C at which temperature chemical absorption K. L. BROWER 42 commences.29 However, the two-step process of passiva- tion and dissociation is equivalent to the dissociation of the H2 molecule and can occur below 600 °C. Because of the equivalence between these two chemical paths, there is a constraint between the activation energies for these chemical reactions as indicated in Fig. 11 [Eq. (13)]. This is a particularly strong constraint since it is well known that the energy barrier for the dissociation of the H2 mol- ecule is monotonically increasing as indicated schemati~ cally by the solid line in Fig. 11. This constraint indi- cates that the maximum total energy of the intermediate reaction configurations in both the passivation and the dissociation reactions is essentially bounded by the initial and final total energies. Although the shape of the ener- gy barrier is not known, a monotonically increasing ener- gy barrier for the passivation and dissociation processes such as illustrated in Fig. 11 is consistent with this con- straint. If in fact the dissociation energy for the H2 mole- cule in the thermal oxide is less, then allowance for (slight) intermediate barriers (dotted line in Fig. 11) in the dissociation-passivation processes may be necessary. These results are consistent with the idea that the dissoci- ation energy of the H2 molecule in the thermal oxide is approximately 4.22 eV. The nature of the energy barriers as shown schemati- cally in Fig. 11 indicates that the reverse reactions occur essentially spontaneously. Obviously, they can only occur in the presence of atomic hydrogen, which ordi- narily is a scarce entity. The reverse passivation reaction [Eq. (14)] generates Pb centers that can be passivated by the reverse dissociation reaction [Eq. (15)] to form HPb centers; hence these reverse reactions appear to be cyclic. Those factors affecting the dominance of either reaction over the other have not yet been determined; however, the work of Reed and Plummer9 suggests that the reverse dissociation reaction [Eq. (15)] dominates over the re- verse passivation reaction [Eq. (14)]. The complexities of radiation effects, which do generate atomic hydrogen27 within the oxide, become self-evident. Under exposure to atomic hydrogen the rate of the reverse passivation— dissociation reactions is expected to be limited primarily by H-diffusion, H-source generation, and/or H-defect trapping. ACKNOWLEDGMENTS Technical assistance for this work was provided by Roger Shrouf. Discussions with S. M. Myers, P. M. Richards, H. J. Stein, and S. K. Estreicher concerning various facets of this work are gratefully acknowledged. This work was performed at Sandia National Labora- tories and supported by the U.S. Department of Energy under Contract No. DE-ACO4—76DPOO789. lY. Nishi, Jpn. J. Appl. Phys. 10, 52 (1971). 2E. H. Poindexter, E. R. Ahlstrom, and P. J. Caplan, in The Physics of SiOz and its Interfaces, edited by S. T. Pantelides (Pergamon, New York, 1978), p. 227. 3P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, J. Appl. Phys. 50, 5847 (1979). 4K. L. Brower, Appl. Phys. Lett. 43, 1111 (1983). 5For a recent review of Si—SiOz defect physics, see the 13 papers 42 DISSOCIATION KINETICS OF HYDROGEN-PASSIVATED . . . in Semicond. Sci. Technol. 4, 961~1126 (1989). 6P. M. Lenahan and P. V. Dressendorfer, App]. Phys. 41, 542 (1982); 44, 96 (1984); J. Appl. Phys. 55, 3495 (1984). 7E. H. Poindexter, G. J. Gerardi, M.-E. Rueckel, P. J. Caplan, N. M. Johnson, and D. K. Biegelsen, J. Appl. Phys. 56, 2844 (1984). 8L. Do Thanh and P. Balk, J. Electrochem. Soc.: Solid-State Sci. Techno]. 135, 1797 (1988). 9M. L. Reed and J. D. Plummer, Appl. Phys. Lett. 51, 514 (1987); J. Appl. Phys. 63, 5776 (1988). 1013. J. Fishbein, J. T. Watt, and J. D. Plummer, J. Electrochem. Soc.: Solid—State Sci. Technol. 134, 674 (1987). 11E. P. Burte and P. Matthies, IEEE Trans. Nucl. Sci. NS-35, 1113 (1988). 12K. L. Brower, Phys. Rev. B 38, 9657 (1988); Appl. Phys. Lett. 53, 508 (1988); in The Physics and Chemistry ofSi02 and the Si—Si02 Interface, edited by C. R. Helms and B. E. Deal (Ple- num, New York, 1988), p. 308. 13]. F. Shackelford, P. L. Studt, and R. M. Fulrath, J. Appl. Phys. 43, 1619 (1972). 14]. E. Shelby, J. Appl. Phys. 48, 3387 (1977). 15S. M. Myers and P. M. Richards, J. Appl. Phys. 67, 4064 (1990). 16K. L. Brower and S. M. Myers, Appl. Phys. Lett. 57, 162 (1990). “K. L. Brower, Semicond. Sci. Technol. 4, 970 (1989). 1E‘lThe “new” silicon substrates used for the most part in this study were from a different manufacturer than the “old” sil- icon substrates used in Ref. 12. The “new” silicon substrates were more lossy in our microwave cavity after thermal oxida- 345 3 tion at 850 “C. This problem was resolved by changing the oxidation temperature to 750 °C. Oxidation of the “old” sil- icon substrates at 750 “C showed no difference in kinetic be- havior from the “new” samples. The data in Fig. 3 happened to have been taken earlier using “old” silicon substrates oxi- dized at 850 °C. 19See, for example, F. Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940), p. 311. 20J. W. Corbett, R. S. McDonald, and G. D. Watkins, J. Phys. Chem. Solids 25, 873 (1964). 21M. Stavola, J. R. Patel, L. C. Kimerling, and P. E. Freeland, Appl. Phys. Lett. 42, 73 (1983). 22H. J. Hrostowski and B. J. Alder, J. Chem. Phys. 33, 980 (1960). 23H. J. Stein (private communication). 24]. C. Mikkelsen, Jr., in Oxygen, Carbon, Hydrogen and Nitro- gen in Crystalline Silicon, Vol. 59 of Materials Research So— ciety Symposium Proceedings, edited by J. C. Mikkelsen, Jr., S. J. Pearton, J. W. Corbett, and S. J. Pennycook (MRS, Pitts- burgh, 1986), p. 19. 25CRC Handbook of Chemistry and Physics, edited by R. C. Weast (CRC, Boca Raton, FL, 1980), p. F—225. 26See, for example, L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics (McGraw—Hill, New York, 1935), Chap. 12. 27K. L. Brower, P. M. Lenahan, and P. V. Dressendorfer, App]. Phys. Lett. 41, 251 (1982). 28D. L. Griscom, J. Appl. Phys. 58, 2524 (1985). 29J. F. Shackelford and J. S. Masaryk, J. Non-Cryst. Solids 21, 55 (1976). SILICON OXYGEN HYDROGEN I I FIG. 10. Ball—and-stick model of the crystalline silicon envi- ronment around the HPb center at the (111) Si-SiOl interface. Only the first layer of oxygen atoms of the thermal oxide is shown. The three first nearest-neighbor Si-Si bond-centered in- terstitial sites adjacent to the Si—H bond are denoted as There are two distinct sets of bond-centered interstitial sites, denoted as “ A” and “B,” from which the oxygen interstitial can difi'use in jumping to the “R” sites. Interstitial oxygen atoms in the "A" sites are considered to have five jump Options, one of which is the “R” site. Interstitial oxygen atoms in the “B” sites have six jump options, one of which is the “R” site and two the “A” sites. ...
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