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Unformatted text preview: PHYSICAL REVIEW B VOLUME 48, NUMBER 7 15 AUGUST 1993-I Surface silicon-deuterium bond energy from gas-phase equilibration W. R. Wampler, S. M. Myers, and D. M. Follstaedt Sandia National Laboratories, Albuquerque, New Mexico 8 7185-5800 (Received 11 January 1993; revised manuscript received 7 May 1993) The bond strength of deuterium (D) to the surface of silicon was determined to be 2.67:0.1 eV from measurements of the amount of D on the surface in equilibrium with D2 gas at various pressures. This was done by measuring the amount of D on surfaces of closed internal microcavities using nuclear reac- tion analysis. The binding of D to a silicon surface is significantly weaker than the Si-H bond in silane which has been assumed in the past to indicate the strength of the surface Si—H bond. The fact that the Si-D bond strength is comparable to the activation energy for thermal desorption of H from Si suggests a possible reaction path for desorption in which the first and rate-determining step is the dissociation of a Si-H bond followed by the exothermic reaction between the released H atom and a second Si-H to form a H2 molecule and two Si- dangling bonds. Our result also gives a value of 1.8 eV for the activation energy for dissociative adsorption of D2 on silicon. The number of bond sites is comparable to the number of Si atoms on the cavity surfaces calculated from the total cavity surface area determined by TEM. I. INTRODUCTION Many of the processes used in silicon semiconductor device production, such as etching with wet chemistry1 or plasmas,2 and growth of epitaxial layers by chemical vapor deposition,3 cause the silicon dangling bonds on the surface to be terminated with hydrogen. The hydro- gen termination may have beneficial effects, such as pro- tecting the surface from oxidation,4 or detrimental effects such as inhibiting epitaxial growth.3'5 A key parameter in understanding such effects is the strength of the Si-H surface bond which until very recently had not been mea— sured. The Si-H bond strength has been discussed previ- ously in the context of thermal desorption of hydrogen from silicon surfaces.“7 However, the strength of the Si-H bond cannot be determined unambiguously from thermal desorption measurements since thermal desorp- tion involves not only the breaking of Si-H bonds but also the formation of H2 molecules. The activation barriers for adsorption and desorption of hydrogen depend on the reaction path between 2(Si-H)=ZSi-+H2, and the reac- tion paths have been uncertain. Here Si- denotes a sur- face silicon atom with one dangling bond. In the absence of direct measurements, the Si—H surface bond strength has often been assumed to be comparable to that of the H3Si-H bond in silane of about 3.9 eV. 7 Recently we reported a measurement of the Si-H sur- face bond energy using a technique which circumvents the indeterminacy inherent in thermal desorption stud- ies.8 Those experiments examined the release of H from the surfaces of internal microcavities in silicon rather than from external surfaces. For this configuration the rate-controlling processes in the release are promotion of H from Si-H on the cavity surface into solid solution, and diffusion through the lattice to the external surface. The release rate thus depends on the Si-H bond strength, the energy of solution, and the diffusion activation energy. Since the latter two quantities are known, we were able to determine a value for the Si—H surface bond strength of 0163-1829/93/48(7)/4492(6)/$06.00 48 EB =2. 5i0.2 eV, which is considerably smaller than pre- vious widely accepted values. A more direct method of measuring the bond strength is to measure the population of Si-H surface bond states in equilibrium with a state of known free energy such as H2 gas. This method of gas-phase equilibrium is a stan- dard technique widely used to study chemisorption of hy— drogen on metal surfaces.9 However, a large activation barrier for the dissociative chemisorption of hydrogen on silicon surfaces has prevented the use of gas-phase equi- librium to determine the Si-H surface bond strength. Due to the large activation barrier, high temperatures are required to reach equilibrium between the gas and sur- face states. Furthermore, at the temperatures where equilibrium can be achieved, high gas pressures are re- quired to populate a significant fraction of the surface states due to the meager energy difference between the gas phase and surface states. Difliculties with maintain- ing clean surfaces and measuring H surface coverage in the presence of high H2 pressures have precluded the use of this method for study of Si-H bonds on external sur- faces. In the experiment described here we use gas-phase equilibration to measure the bond strength of deuterium (D) to the surface of internal microcavities in silicon. Previous studies have shown how internal microcavities can be produced in silicon by implanting helium and an— nealing.8 In the study described here, silicon samples containing internal microcavities were equilibrated with D2 gas. In these experiments, the D goes into solution at the external Si surface, then diffuses through the Si lattice to the microcavities where it forms Si-D bonds on the cavity surfaces. The amount of D bonded to the cavity surfaces was measured using D(3He,p)4He nuclear reac- tion analysis. In equilibrium with the gas, the fraction of Si— bonds on the cavity surfaces which are terminated with D depends on the Si-D bond strength relative to the gas and on the gas pressure. By measuring the amount of D bonded to the cavity surfaces in equilibrium with gas 4492 © 1993 The American Physical Society 48 SURFACE SILICON-DEUTERIUM BOND ENERGY FROM GAS- . . . at various pressures, both the strength of the Si-D surface bond and the number of bond sites can be determined. This method avoids the problem of surface contamina— tion, since the internal microcavity surfaces under inves- tigation are not exposed directly to the gas, and only the D is mobile enough to reach the cavities by diffusion through the silicon lattice. The number of bonding sites calculated from the total cavity surface area observed with transmission electron microscopy (TEM) is compa- rable to the number of D atoms detected at the cavities. II. EXPERIMENTAL METHOD The samples used in this study were n-type silicon with a room-temperature resistivity of 2 kfl cm, a polished (001) surface, and dimensions of 12X12X0.25 mm3. A new sample was used for each measurement to avoid the possibility of D trapping at lattice damage from the analysis beam. The silicon was first implanted at room temperature with 30-keV helium to a fluence of 1017 He/cm2 and then annealed in vacuum at 800°C for 10 h to stabilize the microstructure and remove lattice dam- age. Calculations based on the known solubility and difl'usivity of He in Si show that after annealing at 800°C for 10 h the amount of helium remaining in the cavities is negligible. 8 Thus the cavities can be considered as empty voids. Cross-section TEM shows that the above procedure produces microcavities from about 150—350 nm beneath the surface as seen in Fig. 1.10 This distribution is con- sistent with the He implantation profile calculated using the TRIM-90 Monte Carlo particle transport code. 11 Fig- ure 1 shows a TEM image of the cavities in a cross- sectioned sample. A detailed analysis of TEM images was carried out to determine the size and number per unit area of the cavities. 10 Thickness contrast fringes ob- FIG. 1. A [110] cross-section TEM image of cavities beneath the (001) surface of silicon after implanting with helium and an- nealing. The depth beneath the implanted surface is indicated at the bottom of the picture. 4493 tained with two-beam conditions and stereo imaging were used to determine the thickness of the imaged region. The results are an average cavity diameter of 15 nm, a cavity surface area per sample surface area of 4.8i0.7, and a cavity volume per sample surface area of 17 nm3/nm2. Many cavities were faceted, with predom- inantly {111] surfaces and a smaller amount of {100} surfaces. Samples were soaked at 800°C in D2 gas at pressures from 0.65 to 650 Torr until equilibrium was reached be— tween the gas phase and D at the cavities. This was done as follows. Samples were placed in a quartz tube which was evacuated to about 10‘7 Torr. The tube and sample were then heated by a cylindrical furnace to 800°C. The tube was then filled with high-purity (impurity concentra— tion <20 ppm) deuterium gas to the desired pressure. After equilibrating, the sample was cooled by sliding the furnace back from the quartz tube. The cooling rate of ~100°/min was fast enough to prevent any‘significant change in the amount of D at the cavities during the cooldown. Soak times were 1—3 h which is long com- pared to the time required to reach equilibrium8 calculat— ed using the known solubility and difi‘usivity of hydrogen in silicon. 12 Measurement of the amount of D at the cav- ities after tripling the soak time confirmed that equilibri- um had been reached. Since soak times were much less than the 10 h used for the initial vacuum anneal, evolu- tion of the cavity microstructure during the soak should be negligible. The temperature of 800°C was chosen as the optimum for the equilibration because at lower temperatures the time to reach equilibrium becomes very long, especially for the low gas pressures needed only to partially popu— late the surface sites, and at higher temperatures incon- veniently high gas pressures are required to approach full occupation of the sites. Furthermore, at temperatures above 800°C evolution of the microstructure of the cavi- ties becomes a concern. _ After equilibration the samples were rinsed in buffered hydrofluoric acid to remove residual D from the external surface, and then mounted in a target chamber for mea- surement of the amount of D at the cavities. An analysis beam of 700 keV 3‘He was directed onto the sample. En- ergetic protons from the D(3He,p)4He nuclear reaction were counted using a solid-state detector which subtend- ed a solid angle of 0.77 sr centered at a scattering angle of 135°. A stainless—steel range foil 0.25 mm thick between the sample and detector prevented all charged particles except the 13—MeV protons from the 3He-D reaction from reaching the detector. Since the nuclear reaction cross section is known, 13 the number of D atoms at the cavities per unit area of the sample surface, i.e., the areal density of D, can be calculated from the measured proton yield. With an analysis beam energy of 700 keV, protons will be produced from D at depths from the surface down to about 1 ,um beneath the surface, which includes the en- tire region containing the cavities. Due to the very low solubility of D in Si, the proton yield from the small amount of D in solution in the Si lattice is negligible. Furthermore, the amount of D2 gas inside the cavities after equilibration with the external gas is equal to the 4494 cavity volume times the atomic density of the gas which is 1.2 ><1019 D/cm3 at 650 Torr and 800 “C assuming the ideal gas law. The amount of D2 gas inside the cavities is therefore less than 2X 1013 D/cmz, and is much less than the amount of D bound to the cavity surfaces. Thus the analysis accurately measures the D bound to the cavity surfaces. III. RESULTS AND ANALYSIS OF DATA The results from the measurements of the areal density of D at the cavities in equilibrium with D2 gas are plotted in Fig. 2 versus the square root of the gas pressure during soaking. The Si-D bond strength and the number of Si- dangling bonds on the cavity surfaces per unit area of the sample surface ( N T) can be extracted from this data us- ing the following model. The model assumes there is a single value for the Si-D surface bond strength, and that in equilibrium the fraction 0 of surface sites bonded to D is related to the atomic fraction C of D in solid solution by a Boltzmann population distribution 6/(1—6)=C/(1—C)exp[(ES—ET)/kT] , where T is the temperature, and ES~ET is the energy gained by taking a D atom from a solution site and bond- ing it to a surface silicon atom. E S is the energy gain per atom in moving D from solution to the molecular state, i.e., the energy of solution, and ET is the energy gain per D atom in taking D from the surface state to the molecu- lar state. Implicit in this model is the assumption that the entropy term in the free energy is the same for D at a solution site and D bound to a surface Si atom. The concentration of D in solution in equilibrium with D2 gas at pressure P is given by12 C =P1/2C0exp( —ES /kT) , (2) where ES=1.86 eV and C0=0.0035 D/(Si Torr”). .5 DEUTERIUM (10‘5/cm2) 1111.111 0 5 10 15 1220 25 30 PV2 (Torr) / FIG. 2. The measured areal density of deuterium at the cavi— ties after gas-phase equilibration vs square root of the gas pres- sure (dots). The solid curve shows the least-squares fit of the model described in the text to the data. The dashed curves were calculated using values for the Si-D bond strength differing by $0.05 eV from the fitted value. W. R. WAMPLER, S. M. MYERS, AND D. M. FOLLSTAEDT 48 Here we assume that the solubility of D in Si is the same as that of H. The number of D atoms at the cavities per unit area of the sample surface, which is what is mea- sured here, can therefore be expressed as N=NT9=NT/{1+1/[P1/2C06Xp(—ET/kT)]} . (3) The solid curve in Fig. 2 shows a least-squares fit to the data using Eq. (3), with ET and NT as adjustable parame- ters which are determined from the fit. The parameter values obtained from the fit and their estimated uncer- tainties are ET: —0. 37i0.1 eV and NT=61i10 nm_2. The negative sign of ET signifies that the surface state is lower in energy than the gas phase. The features of the data which mainly determine the parameter values are the saturation level at high pressures for N T and the slope at low pressures for ET. The method of gas—phase equilibration provides a very sensitive measurement of the surface Si-D bond energy as shown by the dashed curves in Fig. 2 which were calcu- lated using NT=6l/nm‘2 and ET: —0.37:0.05 eV. This sensitivity is largely due to the fact that the refer— ence state, i.e., the gas phase, is close in energy to the sur- face state. IV. DISCUSSION A. Si-D bond energy The surface Si-D bond energy EB is the energy re— quired to separate a D atom from a surface silicon atom, leaving a surface silicon atom with a dangling bond and a D atom in vacuum, i.e., the energy for the reaction Si-D—>Si-+D. The value of E B can be determined directly from our measurement of ET. The relationship between them is E, =§ER —ET , (4) as shown in Fig. 3. E R is the energy required to dissoci- ate a D2 molecule, which has the well-established value14 of 4.60 eV. Equation (4) with our value of ET gives E B =2. 67i0. 1 eV for the surface Si-D bond energy. This value agrees with the value of EB=2.5i0.2 eV for the Si-D bond energy determined in our earlier measure- ments of the thermal release of D from internal micro- cavities in silicon. 8 B. Adsorption, desorption, and the activation energy for adsorption Adsorption and desorption of deuterium on silicon in- volves not only the formation and dissociation of Si-D bonds but also the dissociation and formation of D2 mole- cules. Figure 3 illustrates the energetics of the adsorption and desorption processes. Thermal desorption of H2 from monohydride states on external (100) and (111) Si surfaces has been studied by several groups, and their ac- tivation energies are in fairly good agreement. In the case of the (100) surface, values of 2.0 and 2.5 eV were re- ported.6’7 In porous Si, where IR spectroscopy indicated Si-H bonding similar to that on the (100) surface, the re— 48 SURFACE SILICON-DEUTERIUM BOND ENERGY FROM GAS- . . . ENERGY (eV) VACUUM SURFACE FIG. 3. Energetics of adsorption and desorption of deuteri- um on silicon. The total energy is indicated for the transition between the surface state 2(Si-D) and the molecular state D2+ZSi—. E D and E A are activation energies for desorption and adsorption, respectively. Also shown is the bond energy E R of the D2 molecule. sult was 2.8 eV.15 For the (111) surface, activation ener- gies of 2.7, 2.6, 2.5, and 2.4 eV were obtained.6’16“3 Here we will not distinguish between the (100) and (111) surfaces, since the respective ranges of values of E D over- lap; instead, we use the average value E D =2.5i0.3 eV, and we assume that E D is the same for H and D. The activation energy for desorption is much larger than the energy difference between the initial and final (i.e., adsorbed and molecular) states, indicating that the reaction passes through a higher-energy intermediate configuration. A consequence of this is that adsorption is inhibited by a large activation barrier. This contrasts with adsorption and desorption of hydrogen on metals where the barrier to adsorption is usually very small. 19 The activation energy E A for dissociative adsorption of D2 onto silicon is related to E D and E T by EA 2E0 +2ET , (5) as shown in Fig. 3. With our value for ET, Eq. (5) gives E A = 1.8 eV for the activation barrier to dissociative ad— sorption of D2 onto a Si surface. This large value for E A is consistent with the experimental observation that H2 does not easily adsorb onto silicon surfaces, Whereas thermally dissociated atomic H does adsorb.20 At sufficiently high temperatures, the activation barrier to dissociative adsorption can be overcome and equilibri- um can be reached between D2 gas and surface states. However, the fact that the surface states are only 0.4 eV lower in energy than the gas phase means that relatively high gas pressures are required to populate a significant fraction of the surface states at the high temperatures where equilibrium can be achieved. Difficulties with maintaining clean surfaces and measuring H surface cov— erage in the presence of high gas pressures have prevent- ed the use of gas-phase equilibration to study Si-H bonds on external surfaces. The use of internal microcavities in the present experiment avoids the problem of surface contamination, since the surfaces under investigation are not exposed directly to the gas, and only D is mobile 4495 enough to reach the cavities by diffusion through the sil- icon lattice. C. Reaction paths for desorption and adsorption The result that the surface Si-H bond strength and the activation energy for thermal desorption have similar values (EBzED) points to a possible reaction path for thermal desorption of H, in which the first and rate- determining step is the thermal dissociation of an Si-H bond followed by the exothermic reaction between the released H atom and a second Si-H to form a H2 mole- cule and two Si- dangling bonds according to 2(Si-H)—>Si-H+Si-+H*4>ZSi—+H2 . (6) The intermediate state in this reaction then consists of one surface Si-H, one surface Si— dangling bond, and one H atom, which may still be weakly bound to the surface. The energy of the intermediate state relative to the molecular state (see Fig. 3) is EA=2ET+ED=2ET+EB+E* , (7) where E*=ED—EB is the energy of the H atom in the intermediate state relative to a H atom in free space. Ad- sorption from the molecular state would occur via the in- verse process with an activation energy of E A. This pro- posed reaction path is consistent with the notion that, on a H—terminated silicon surface, the H is localized by the Si-H bonds which are strong and highly directional, and the H atoms are much farther apart [0.38 nm on Si(111)] than in a H2 molecule (0.074 nm), so that a Si-H bond must first be broken before two H atoms can get close enough together to form a H2 molecule. The above reac- tion path is also consistent with the conclusions of Wise et 01.6 and Boland“ that desorption from the Si(100) monohydride surface occurs by recombination of pairs of hydrogen atoms from the same dimer unit. The initially released H atom will have the highest probability for recombination with its nearest neighboring H, which on the Si(lOO) surface is the other H on the dimer unit. The above reaction path for recombination is not specific to a particular surface structure and is compatible with both first-order release kinetics from correlated recombination due to islanding or pairing of surface H, and with second—order release kinetics from recombination by ran- dom encounters of mobile H. An alternative mechanism has been proposed by Sinni- ah et al.7 in which desorption proceeds via an irreversi- ble excitation of H from a Si-H bond to a delocalized state which is still bound to the surface by 1.95 eV. H in their delocalized bound state then reacts with a second Si-H, resulting in desorption of a H2 molecule. They pro- posed a delocalized bound state to reconcile their mea- sured activation energy for thermal desorption (ED: 1.95 eV) with their assumption (in the absence of any direct measurement) that the surface Si—H bond strength is 3.9 eV. Our new measurement of E B =2.67i0.1 eV, together with recent thermal desorp- tion studies6 giving higher values of E D =2.67-l_-0. 17 eV for Si(lll) and ED=2.51i0.09 for Si(100), show that 4496 binding of the H atom in the intermediate state to the surface is weak, |E*|=|ED —EBI <0.l6 eV in the con- text of our proposed reaction path. The above mechanism for desorption of immobile H covalently bonded to surface Si atoms contrast with desorption of H from metal surfaces where the adsorbed hydrogen atoms are very mobile, allowing a continuous transition from separated H atoms close to the metal sur- face, to a molecule where the H atoms are close to each other and far from the metal surface. Thus in the case for metals, typically E A << E D ~ ZEB -ER. D. Similarity between Si-H on internal cavities and external surfaces The areal density of Si- dangling bonds available for at- tachment of D can be estimated from the observed mi- crostructure of the cavities. TEM shows that the cavity surface area per sample front surface area is 4.8:O.7, with mostly { 111} surfaces. 1° The number of Si-H bonds per unit area for monohydride terminated silicon surfaces is 7.8/nm2 for the (111) surface and 6.23/an for the (100) surface. The number of dangling bonds on the cavity sur- faces per sample surface area should therefore be about (4.8X7.8)~4O/nm2. This value agrees reasonably well with the value of 61i10/nm2 determined from our gas- phase equilibration measurements. This agreement shows that the number of sites available for D attach- ment at the cavities per unit area of cavity surface is simi- lar to that of a monohydride on an external surface. Next, we discuss the questions of whether the Si-H states on the internal cavities are representative of Si-H states on external surfaces, and the extent to which vari- ous crystallographic orientations of the cavity surfaces might influence the Si-H bond energy. The infrared- absorbtion spectrum has been measured for Si samples with internal cavities similar to ours. 22 After soaking in hydrogen gas, two strong peaks appeared at wave num- bers of 2084 and 2100 cm”1 for samples with cavities. IR-absorbtion peaks at these frequencies have also been observed for H on external Si surfaces, and are associated with stretch vibration of the surface monohydride on the (111) and (100) surfaces, respectively. 1’“ We therefore believe that the surface monohydride states on the cavity surfaces are essentially the same as those on external sur- faces. The IR spectroscopy also shows that, as the sam- ples are annealed to successively higher temperatures, these two peaks both disappear at the temperature where hydrogen leaves the cavities. This indicates that the sur- face monohydride bond strength is essentially the same for the (100) and (111) surfaces. In view of the different arrangement of Si atoms on these two surfaces, we take this as evidence that the Si-H bond energy depends pri- marily on what the other three bonds of the Si atom are attached to. In particular, we suggest that the Si-H bond strength may be similar for surface silicon atoms bonded to three other silicon atoms, and depend only weakly on the longer-range ordering of the Si lattice. Since dangling W. R. WAMPLER, S. M. MYERS, AND D. M. FOLLSTAEDT 48 bonds are a high-energy configuration, silicon surfaces tend to reconstruct to minimize the number of dangling bonds; for example, the dimerization of the (100) surface reduces the number of dangling bonds from two to one per Si atom. For this reason it is likely that very few of the surface atoms in the cavities have more than one dan‘ gling bond. Thus it is not surprising that we find a well— defined value for the Si-H bond energy at the cavities in spite of the various surface orientations within the cavi— ties. Finally, while it is possible to attach more than one hy— drogen to a surface Si atom to form dihydride or trihy— dride states, for example, by exposure to atomic hydro— gen, these higher hydride states are less strongly bound than the monohydride.“ This is shown by the fact that desorption from dihydride and trihydride states occurs at substantially lower temperatures than desorption from the monohydride configuration. 24 In our gas-phase equilibration experiment, the fraction of surface Si atoms with a D atom attached depends very strongly on the bond energy, as shown in Fig. 2. Thus the more weakly bound multihydride states will not be occupied and should not play any significant role in our experiments. The bond strength determined by our experiments is that of the most strongly bound, i.e., the monohydride, state. V. CONCLUSIONS The experiments described here and in Ref. 8 provide direct measurements of the bond energy of monohydride Si-D bonds on a silicon surface. A value of ET: —0.37i0. 1 eV is obtained for the surface Si-D bond strength referenced to the D2 molecule. From this result, the bond energy of surface Si—D referenced to the D atom in vacuum EB =2.67i0.1 eV is obtained direct- ly, since E T and E B differ only by the dissociation energy of D2 which is well known. This agrees with the value E B =2.5i0.2 eV determined recently by a different ex- perimental method,8 but is much smaller than the bond energy of H in silane of 3.9 eV which has been assumed in the past to indicate the strength of the surface Si-H bond. The fact that E B is comparable to the activation energy ED=2.5iO.3 eV for thermal desorption of H from Si suggests a possible reaction path for desorption in which the first step is the dissociation of an Si-H bond followed by an exothermic reaction between the released H atom and a second Si-H to form a H2 molecule. Our result has the additional implication that the inverse process of dis— sociative adsorption of H2 on silicon is impeded by a large activation barrier E A = 1.8 eV. This conclusion is supported by the experimental observation that H2 does not easily adsorb onto silicon surfaces unless it is first dis- sociated into atoms. ACKNOWLEDGMENT This work was supported by the US. Department of Energy under Contract No. DE-AC04-76DPOO789. 48 SURFACE SILICON-DEUTERIUM BOND ENERGY FROM GAS- . . . 1G. S. Higashi, Y. J. Chabal, G. W. Trucks, and K. Raghava- chari, Appl. Phys. Lett. 56, 656 (1990). 2H. Hirayama and T. Tatsumi, Appl. Phys. Lett. 54, 1561 (1989). 3P. M. Garone, J. C. Sturm, P. V. Schwartz, S. A. Schwarz, and B. J. Wilkens, Appl. Phys. Lett. 56, 1275 (1990). 4D. Graf, M. Grundner, R. Schulz, and L. Mfihlhofl‘, J. Appl. Phys. 68, 5155 (1990). 5S. H. Wolff, S. Wagner, J. C. Bean, R. Hull, and J. M. Gibson, Appl. Phys. Lett. 55, 2017 (1989). 6M. L. Wise, B. G. Koehler, P. Gupta, P. A. Coon, and S. M. George, Surf. Sci. 258, 166 (1991). 7K. Sinniah, M. G. Sherman, L. B. Lewis, W. H. Weinberg, J. T. Yates, Jr., and K. C. Janda, J. Chem. Phys. 92, 5700 (1990). 8S. M. Myers, D. M. Follstaedt, H. J. Stein, and W. R. Wampler, Phys. Rev. B 45, 3914 (1992); 47, 13 380 (1993). 9K. Christmann, O. Schober, G. Ertl, and M. Neumann, J. Chem. Phys. 60, 4528 (1974). 10D. M. Follstaedt, S. M. Myers, W. R. Wampler, and H. J. Stein, in Proceedings of the 50th Annual Meeting of the Elec- tron Microscopy Society of America, edited by G. W. Bailey, J. Bentley, and J. A. Small (San Francisco Press Inc., San Fran- cisco, 1992), pp. 334—335. 11J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping 4497 and Range of Ions in Solids (Pergamon, New York, 1985), Vol. 1; J. F. Ziegler (private communication). 12A. Van Wieringen and N. Warmoltz, Physica 22, 849 (1956). 13W. Mc'iller and F. Besenbacher, Nucl. Instrum. Methods 168, l 1 1 (1980). 14G. Herzberg, J. M01. Spectrosc. 33, 147 (1970). 15P. Gupta, V. L. Colvin, and S. M. George, Phys. Rev. B 37, 8234 (1988). 16B. G. Koehler, C. H. Mak, D. A. Arthur, P. A. Coon, and S. M. George, J. Chem. Phys. 89, 1709 (1988). 17G. Schulze and M. Henzler, Surf. Sci. 124, 336 (1983). 18G. A. Reider, U. Hofer, and T. F. Heinz, J. Chem. Phys. 94, 4080 (1991). 19H. P. Steinriick, M. Luger, A. Winkler, and K. D. Rendulic, Phys. Rev. B 32, 5032 (1985). 20Z. H. Lu, K. Grifliths, P. R. Norton, and T. K. Sham, Phys. Rev. Lett. 68, 1343 (1992). 21]. J. Boland, J. Vac. Sci. Technol. A 10, 2458 (1992). 22H. J. Stein, S. M. Myers, and D. M. Follstaedt, J. Appl. Phys. 73, 2755 (1992). 23Y. J. Chabal, Surf. Sci. 168, 594 (1986). 24C. C. Cheng and Y. T. Yates, Jr., Phys. Rev. B 43, 4041 (1991). FIG. 1. A [110] cross-section TEM image of cavities beneath the (001) surface of silicon after implanting with helium and an— nealing. The depth beneath the implanted surface is indicated at the bottom of the picture. ...
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