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J. Phys. Chem. B 2005, 109, 23386-23394
The Influence of Defects on the Morphology of Si (111) Etched in NH4F Hui Zhou, Joseph Fu, and Richard M. Silver* National Institute of Science and Technology, Gaithersburg, Maryland 20899 ReceiVed: May 9, 2005; In Final Form: October 3, 2005
We have implemented a kinetic Monte Carlo (KMC) simulation to study the effects of wafer miscut and wafer defects on the morphologies of Si (111) surfaces etched in NH4F. Although a conventional KMC simulation reproduced previously published results, it failed to produce the morphologies observed in our experiments. By introducing both dopant sites and lattice defect sites into the model, we are able to simulate samples having different dopant elements and densities as well as different defect concentrations. Using the modified KMC simulation, the simulated surface morphologies agree well with the morphologies observed in our experiments. The enhanced model also gives insights to the formation mechanism for multiple level stacking pits, a notable morphology on the etched surfaces of samples with very small miscut angles.
1. Introduction Silicon etching, especially anisotropic etching such as hydroxide-based silicon etching, has played a substantial role throughout the history of the semiconductor industry. Despite the large number of studies over the past decade or two, there is little fundamental understanding of the etching mechanisms at the microscale in the literature. In fact, most (if not all) anisotropic etchants were developed by trial and error.1 In standard chemistry nomenclature, hydroxide-based silicon etching is commonly written as a redox reaction:
Si + 2OH- + 4H2O f Si(OH)22+ f 2H2 + 4(OH)- (1) However, the above equation does not account for the fact that the reaction rate for silicon atoms from different surface orientations and different lattice structures can vary by as much as several orders. And it is these site-dependent reaction rate differencesscommonly known as anisotropic etchingsthat account for many of the essential applications in the semiconductor industry. To fundamentally understand the mechanism of anisotropic silicon etching and ultimately control the etching process, more than just knowledge of the etch rates of the silicon surfaces from various crystal orientations is needed. It is necessary to study the anisotropic etching at the atomic level, where the surface step distribution and crystal defects become important. Anisotropy is due to the difference in chemical reactivity among various specific surface site classes, which is a result of the different structural configurations. In the study of these sitespecific chemical etching dynamics, the traditional chemical analysis method falls short due to the lack of sensitivity. Following the invention and widespread use of scanning probe microscopy (SPM), a different method, based on the study of surface morphology, has shown its unique strength in exploring the chemical dynamics.2-5 Studying the Si surface morphology has been shown to be an effective tool in exploring NH4F-based etching of Si (111) surfaces. Si (111) surfaces etched by 40% NH4F can be atomically smooth and a scanning probe microscope (SPM) can then be used to directly study the various surface sites and atomic configurations. Due to the slow etch rates while the
surface is being etched, an STM can be used to image the surface in real time.4 On the basis of ex situ SPM studies, the mechanism of NH4-based etching of Si (111) has been explained as a competition between step-flow and surface-pit initiation.2 There have been two different approaches in the theoretical study of the evolution of the surface morphology. The first approach is based on the kinematic wave theory introduced almost simultaneously by Frank6 and Cabrera.7 In this approach, individual atomic surface steps are treated as the fundamental entity, and their migration and nucleation are used to explain the resulting surface morphology. The second approach is based on a solid-on-solid (SOS) model and was used by Hines et al. in their kinetic Monte Carlo simulations.8 The atomic surface step approach describes directly how the surface morphology evolves during etching, but usually involves a number of assumptions based on empirical observations rather then being based on the fundamental theory or simulations. The SOS method, on the other hand, starts from a more fundamental understanding and has proven to be an effective method to link the surface morphology to the atomic mechanisms at work. KMC studies in the literature, however, have been typically limited to surfaces with miscut facing either the 〈112h〉 direction or the 〈112〉 direction and miscut angles greater than 0.1°. As reported previously, the wafer miscut configuration has profound effects on the etching dynamics and resulting surface morphology.9 In particular, surfaces with large miscut angles can easily achieve long-range steps and terraces, while significant pitting effects appear on surfaces with small miscut angles. Since pitting is one of the crucial components in the etching mechanism, it is desirable to apply the KMC simulation to surfaces with low miscut angles where parameters that affect pitting, such as the terrace-site etch rate, have a more noticeable effect. To directly simulate the surfaces as used in our experiments, we have implemented a KMC simulator and algorithm that is optimized for nonorthogonal and small miscut angle configurations. The validity of our simulator has been verified by reproducing previously published results using the same parameters as in the literature. With the ability to simulate arbitrary sample configurations based on site-specific etch rates, experiments from different wafer configurations can be directly compared. In our study, we have found that without expanding the
10.1021/jp0524072 CCC: $30.25 © 2005 American Chemical Society Published on Web 11/19/2005
Morphologies of Si (111) Surfaces Etched in NH4F
J. Phys. Chem. B, Vol. 109, No. 49, 2005 23387 TABLE 1: The Miscut Information for Samples Used in Our Experiments sample A B C
Figure 1. Illustrations showing the surface miscut orientations on Si (111): (a) miscut angle and (b) miscut orientation angle.
existing model, it is difficult to account for the etch rate differences obtained by analyzing the experimental results, and we have been unable to account for the appearance of multilevel etch pits observed on samples with small miscut angles. In this paper, we attribute the formation of etch pits largely to the increased reactivity of crystal defects and dopant sites. By considering both the dopant sites and defect sites in the model, we have implemented a more comprehensive simulation tool and are now able to obtain much better agreement between the computation-based morphology results and those observed in the experiments. On surfaces with low miscut angles, the formation of etch pits is an overwhelming effect. It should be noted that the etch pits discussed throughout this study are formed on single atomic layers and are a few nanometers to a few hundred nanometers in size. They are distinctly different than the “macropits” which result from rapid etching. Although they resemble one another in geometrical shape, the macropits are much larger and deeper. While both the macropits and the single-layer pits discussed in this paper may share a similar origin such as crystal defects, they are developed under significantly different etching conditions.
miscut angle miscut orientation (R), deg angle (β), deg 0.12 0.09 0.02
15 2 60
dopant
resistivity, Ω‚cm
boron phosphorus boron
3-6 0.1 5-15
procurement, rather the wafer miscut is a random result subsequently determined directly from sample measurements. The samples were prepared by using a pre-cleaning procedure as described in a previous paper9 followed by etching in 40% NH4F solution for 15 min in an ambient environment. The NH4F solution was sparged with Ar for 45 min before the final etching. During the 15 min etching period, the solution is not stirred to increase the repeatability of the results. Following a quick rinse (a few seconds) in deionized (DI) water after etching, the samples were imaged immediately with an atomic force microscope (AFM). Figure 2 shows three AFM images of the above-described samples. The samples with miscut angles of 0.12° and 0.09° both exhibit long-range steps and terraces, although the sample with a miscut angle of 0.09° shows more zigzagged steps, with a few triangular pits appearing on the terraces. For the sample with the extremely small miscut angle (0.02°), long-range terraces are not present and the etch pits dominate the surface; furthermore, multiple level stacked pits with nominally the same center are also seen in the image. After 15 min of etching, both samples with 0.12° and 0.09° evolved to a steady state. That is the overall morphology no longer changed with additional etching time. The samples with 0.02°, however, still evolved with additional etching time. Although long-range terraces or steps never form on the 0.02°miscut sample, some of the multilevel pits did grow larger in size. Figure 3 shows a multilevel pit formation that developed after 3 h of etching. From these experimental results, the dependence of surface morphology on the wafer miscut angle is apparent. This dependence can be interpreted with the step-flow theory as follows. A flat surface with a larger miscut angle has a larger step density, and as a result it takes less time to etch away a single monolayer from the surface given a constant step-flow velocity. Assuming a constant rate of pit initiation, fewer pits are initiated during the time period that a monolayer exists and thus the number of pits and their effects on the overall morphology are suppressed. For a smaller miscut angle, it takes
2. Experimental Section Silicon (111) samples from three different wafers were used in the experiments reported here. Each wafer had a different miscut angle and miscut orientation, as defined next. In this paper, the miscut angle refers to the angle between the sample surface plane and the (111) plane, and the miscut orientation angle refers to the angle between the miscut vector projected on the (111) plane and the 〈112h〉 direction, as shown in Figure 1. Both the miscut angle and miscut orientation angle for the samples used in these experiments were estimated by measuring the average surface step spacing and step orientation from SPM images of samples prepared either through NH4F etched sample preparation or by thermal annealing in ultrahigh vacuum. A summary of the miscut information of the samples used in our experiments is given in Table 1. The doping specifications of the wafers are also listed. As a note, the miscut of the wafers used in the experiments reported here was not specified during
Figure 2. AFM images produced from samples with different miscut angles. All the samples were etched in 40% NH4F for 15 min.
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Figure 3. AFM image of a stacking pit on a sample with a miscut angle of 0.02° after 3 h of etching. The image has been enhanced by an edge detection algorithm.
more time to etch away a single monolayer of the surface, and therefore, more pits are initiated during a given time period and the pits have more time to grow in size before they merge into the advancing steps. As seen in Figure 2b, the steps have a distribution of triangular kinks that result from the advancing step-pit collisions. For samples with very small miscut angles, the pits have time to grow large enough to have second-level pit growth in their interior. Long-range steps never form due to the constant collision of large sized pits. Although the above interpretation explains our experimental observations satisfactorily, it is empirical in nature. Without significantly more data, it is difficult to use the above empirical approach to describe the surface evolution and morphology for a given etching period of a silicon surface with arbitrary miscut configuration. For example, given a sample with a miscut angle of 0.07°, this model would predict that the resulting morphology should have more pits and zigzagged steps than that of samples with a miscut angle of 0.09° as seen in Figure 2b. However, it is difficult to predict whether long-range terraces and steps will form other than by doing additional experiments to find out. From a practical perspective, to obtain a full range of wafers and samples with appropriate miscut angles and miscut orientations would be very expensive and time consuming. To gain a more quantitative and broad understanding, we have utilized kinetic Monte Carlo simulations. 3. Computational Section 3.1. Classic KMC Simulation. In this section, we refer to Monte Carlo simulations based on the model described in ref 8 as the classic KMC simulation. The new KMC simulation approach reported here differs from the classic KMC simulation in that it includes additional parameters for dopants and defects. Although our implementation of the classic KMC simulator is based on the same physical model and essentially the same simulation algorithms, since it was developed independently, the detailed implementation, data structure, and computation algorithm is likely to be different from that in the reference. In this section, we describe the details of our implementation. 3.1.1. Data Representation. The silicon lattice is a diamond lattice structure (Figure 4a) and the silicon (111) surface can be viewed as a stack of bilayers. If we denote the lattice sites with A, B, and C as illustrated in Figure 4, the silicon crystal
Figure 4. Illustration of the Si (111) surface lattice. (a) A ball-andstick model showing the Si (111) lattice as a network of “chair” configuration. (b) A top view of Si (111) lattice sites. The surface lattice essentially consists of three sets of hexagonal lattices: A, B, and C. Each bilayer is a combination of two sets of lattice sites. The crystal lattice is an AB-BC-CA-... structure.
has a stacking pattern of AB-BC-CA-AB-.... If we assume that the etching is a layer-by-layer mechanism, which is to say that, during etching, no over-hang or under-cut structures are formed, the silicon surface can always be represented by a 2-dimensional lattice structure as illustrated in Figure 4b, in which only the relative position of the topmost surface atoms are recorded. This 2-D lattice is then stored as an integer array, where each integer represents the height of the topmost silicon surface atom at that particular lattice point. Each surface atom, assuming that the surface remains hydrogen terminated during etching, is categorized into the following classes: terrace monohydride, step monohydride, vertical dihydride, horizontal dihydride, terrace trihydride, step trihydride, kink, and point sites (Figure 5). Each site class is assigned a site-specific etch rate. The following rates have been used in the literature to best reproduce the surface morphology of Si (111) etched in 40% NH4F:
kkink ) 1 kpt ) 0.1 kdi ) 0.01 kmono ) 5 × 10-4 kterr ) 10-7 An infinite etch rate is used for all other species.11
(2)
Morphologies of Si (111) Surfaces Etched in NH4F
J. Phys. Chem. B, Vol. 109, No. 49, 2005 23389 A second random number is then generated to select a particular etch site within the species. To increase the efficiency of selecting atoms, another array of data is used to store the surface lattice indexed by the site species. During etching, a significant amount of computation time is required to update the reference array, which involves updating not only the site species of the atom being etched but also the site species of its neighboring sites, as those species are likely to be modified as a result of the removal of the atom at the selected site. 3.1.3. Etch Time. The simulation algorithm described above is referred to as the n-fold method of Monte Carlo simulation,10 in which the computation time of the simulation is no longer proportional to the real time that is being simulated. Thus, the actual time elapsed during etching must be tracked throughout the simulation. In our simulation, after each removal of a surface atom, the total etch time is updated by an accumulated quantity ∆t that can be calculated from the average surface etch rate kh with the formula
∆t )
1 Ntotalkh
(4)
where
Ntotalkh )
Figure 5. Atomic structure of a hydrogen-terminated Si (111) surface.
3.1.2. The Etch Algorithm. The site-specific etch rate ki characterizes the etch rate for all of the sites of species i. If there are a total of Ni sites of species i, then Niki sites are assumed to be etched per unit time. Following the convention established in the literature, the time unit was chosen so that kkink ) 1. By referring the simulation results to actual experiments, the actual value of the time unit can be determined. A comprehensive time-dependent study of silicon etching with the KMC model will be published in another paper. In this paper, this unit is simply refereed to as the “time unit”. As long as the same set of site-specific etch rates are used, the time unit remains a constant across different runs of the simulation. During the simulation, a random number is first generated to determine which site species will be selected for etching; this is done according to the probabilities calculated from the following equation:
Pi )
Niki
∑j Njkj
(3)
∑j Njkj
(5)
Although in the literature the recalculation of k after each etching event was regarded as too difficult and some approximation for the time-keeping process was used in the literature, we found this task to be not overly cumbersome in our implementation. The total etching time obtained in this way is given in units of the simulation “time unit”. As long as the site-specific etch rates used in the simulation are constant, the cumulative etching time has a constant time unit, which enables meaningful time-dependent comparisons of simulation results between different simulations. In principle, the etching time used in the simulation can be determined empirically, and consequently the physical values for the site-specific etch rates in real time units can also be derived. 3.1.4. Cyclic Boundary Conditions. Although the algorithm only involves the computation of the surface atoms, it requires a significant amount of memory to simulate even a small surface area. For example, to simulate a 1 µm × 1 µm area of the surface, nominally 70 megabytes of memory is required, while simulation of a 5 µm × 5 µm area requires 1.75 gigabytes. Without a proper, rigorous method to treat the boundary sites in the simulation, due to the lack of an acceptable method for treating the neighboring atom sites, the boundary sites behave like permanent defect sites which are etched either too frequently or too infrequently. As a result, the effects of those “boundary defects” would eventually propagate into the center area of the surface due to the step-flow mechanism. By exploiting the symmetry of the crystal lattice, however, it is possible to employ cyclic boundary conditions,8 a strategy that maps one edge of the simulation area to the opposite edge. The entire silicon surface is treated as a repeated tiling of the same simulation area (Figure 6). Due to the existence of miscut, the opposite edges of the simulation area are usually not at the same level (height). Thus, to satisfy the cyclic boundary condition, it ordinarily not only requires a height shift but also a lattice shift. The height shift refers to
h(x b) ) h(x b + B) l + dh
(6)
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Figure 7. Simulated steady-state etch morphologies of Si (111) surfaces with miscut 0.35° etched in NH4F. (a) The surface is miscut toward the 〈112h〉 direction. (b) The surface is miscut toward the 〈112〉 direction. In both images, the surface has been etched for 10 monolayers.
Figure 6. Illustrations of boundary conditions in the simulation: (a) a rectangular simulation are, and (b) a parallelogram simulation area. The boundary condition often requires the opposite edge of the simulation area have a different surface level, which demands a lattice pattern shift due to the silicon diamond lattice structure.
where h(x b) is the height of the site at b x, Bis l the vector from one edge to the opposite edge, and dh is the height difference between the two edges. The lattice shift refers to the fact that after one bilayer height difference, the A lattice shifts into the B lattice for downward steps or shifts into the C lattice for upward steps. Although rectangular simulation areas have largely been used in the literature, in our implementation, rectangular cyclic boundary conditions were used since these work well as long as the miscut angle is perpendicular to one of the edges of the rectangle. In this situation, the cyclic boundary conditions cause the above shift in only one pair of edges. For an arbitrary miscut orientation, the cyclic boundary conditions become rather cumbersome to deal with, since the intrinsic lattice no longer has orthogonal symmetry in the reference frame, which then often results in a tiling shift as described in Figure 6a. To utilize the symmetry of the surface lattice, we use a simulation area in our program the shape of a parallelogram, with its corner angles equal to 60° or 120° (Figure 6b). This approach enables us to treat the cyclic boundary conditions in both directions symmetrically, which greatly simplifies the computation algorithm. 3.2. Classic KMC Simulations. 3.2.1. Simulations on Surfaces with 0.35° Miscut. To evaluate our implementation of the KMC simulator, we performed a set of simulations using the same sample miscut configurations as well as the same set of site-specific etch rates as used in refs 11 and 12. Samples
Figure 8. (a) Experimental results of steady-state etched morphology on a surface with 0.12° miscut angle and 10° misorientation. (b) Simulated results obtained with kterr ) 10-7. (c) Simulated results obtained with kterr ) 10-9. (d) Simulated results obtained with kterr ) 10-10. Image size 700 × 500 nm2.
with 0.35° miscut angles toward either the 〈112h〉 or the 〈112〉 direction were used. Figure 7 shows the morphologies produced by our simulator. The morphology with miscut of 0.35° toward 〈112h〉 has straight steps and a limited number of etch pits a few nanometers in size (Figure 7a). The morphology with the same miscut but toward the 〈112〉 direction has steps distributed with hillocks, with few etch pits visible (Figure 7b). These morphologies agree well with those in ref 11. 3.2.2. 0.12° Miscut. The largest miscut angle used in our experiments was nominally 0.12°. Figure 8 shows both the experimental and simulated morphologies from a Si (111) sample with 0.12° miscut and 10° misorientation. Here, the misorientation refers to the angle between the miscut direction and the 〈112〉 direction. Simulation results from the same etching parameters found in refs 11 and 12 with the appropriate miscut angles yielded the surface shown in Figure 8b. These results are in apparent disagreement with our experimental results as seen by the comparison of panels a and b in Figure 8. The etch pits and step edge roughness are much more pronounced in the simulations than those observed in the experiments. To reduce the pitting effects and achieve satisfactory visual comparisons, the etch rate for terrace sites must be lowered by 2-3 orders of magnitude as shown in the lower two panels (c and d) in Figure 8. 3.2.3. Etch Rate Differences between the Various Experiments. The morphologies of the samples with 0.12° miscut and 10° misorientation in our experiments have a similar appearance to the morphologies reported in ref 11. However, as we have previously reported, the miscut angle and miscut orientation have a profound effect on the resulting morphology of the etched
Morphologies of Si (111) Surfaces Etched in NH4F surfaces.9 And, for the samples described here, the underlying etching kinetics are, in fact, very different despite the similar appearance of the final morphologies. By using the KMC simulation package, the site-specific etch rates for each of the experiments can be evaluated and compared revealing a discrepancy in the terrace-site etch rates as large as 2 orders of magnitude (1 × 10-7 versus 1 × 10-9). A comparison of the experimental details between the experiments in ref 11 and those reported here shows a number of differences. Among them, the most noticeable is the likely difference in the dissolved oxygen concentration in the etchants. As first reported by Wade and Chidsey,13 dissolved oxygen in the etchants leads to an increase in the initiation of etch pits. In the experiments reported here, the NH4F solution was sparged with pure argon for 45 min immediately prior to final etching so as to deplete the dissolved oxygen. And during the final etching, the solution was specifically not disturbed throughout the duration of etching. However, the experiments in ref 11 involved a stirred solution whose etchant, therefore, likely contained a large amount of dissolved oxygen resulting in a larger terrace-site etch rate. However, in another study reported by the same group, the terrace etch rates extracted from their experiments with an oxygen free etchant were reported as 4 × 10-8, a value still much larger than those estimated from our experiments, 1 × 10-9. There were additional subtle differences in the experimental details as well as differences in the samples, such as dopant concentration, dopant type, and defect distributions. As stated above, the experiments reported in ref 11 were performed in a stirred solution, while those reported here were performed in a quiescent solution. In addition, the wafers used in our experiments have lower dopant densities and possibly differences in the defect distributions which result from variations in the sample pre-cleaning and handling procedures The effects of dopants and defects on the etched surface morphology are of particular interest due to their effects on the etching dynamics as discussed next. To investigate these effects, we have extended the conventional KMC simulation model to include parameters for dopants and defects. 3.3. Extended KMC Simulation Model. 3.3.1. Dopant Sites. The dopant atoms share the same chemical bonding structure as the native atoms, and do not break the lattice structure from an algorithm point of view. Due to the apparent different atomic sizes and bonding strengths, the chemical structure near the dopant sites is more stressed than the structure in pure crystalline silicon. This structural stress increases the reactivity around the dopant sites. These dopant effects on etch rates have been observed by Maher15 and Ukraintsev.16 The dopant sites are represented in our model by randomly selected sites to which a higher etch rate is assigned as compared to the normal terrace sites. Strictly speaking, the dopant effects on the etch rates are not limited to just the individual dopant atoms. However, this neighboring effect is omitted in our simulation to simplify the computation. As a consequence, the dopant etch rate obtained in the simulation will be higher than the actual etch rate since the neighboring effects are rolled in. Dopant sites are not persistent during etching, i.e., the locations of dopant sites change from layer to layer. To simulate this effect in the simulation algorithm, after etching a single dopant site, a new site is randomly selected and assigned to be a new dopant site. Typical doping densities in silicon wafers range from 1016 to 1018 cm-3, and nominally, there will be a dopant atom every 107 to 105 silicon atoms, respectively. Since the dopant sites are randomly distributed on each atomic layer,
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Figure 9. Simulated steady-state morphology for surfaces with 0.09° miscut and misorientation of 2°. The etch rates used in these simulations are (a) Fdopant ) 10-4, kdopant ) 10-3, kterr ) 0; (b) Fdislocation ) 10-7, kdislocation ) 10-4, kterr,eff ) 0; (c) Fdislocation ) 10-7, kdislocation ) 10-4, kterr,eff ) 10-8; and (d) Fdislocation ) 10-7, kdislocation ) 10-4, kterr,eff ) 10-7.
the surface morphologies which result from simulations that include dopant etching resemble those which are obtained from the classic KMC simulation having no dopant etching (Figure 9a). For every etching event, the algorithm selects a site to etch according to the relative etch rate Rj ) kj × Nj. Thus, the etch rate and final morphology which results from Rterr,eff ) kterr × Nterr + kdopant × Ndopant is not sensitive to the individual components or etch rates. That is, the simulations are mathematically equivalent for different values of terrace or dopant etch rates and only depend on the combined value. The etching is therefore determined by the effective terrace site etch rate,
kterr,eff ) kterr + kdopant‚Fdopant
(7)
where Fdopant is the relative concentration of dopant. To obtain agreement between the KMC simulation and our experimental results, a value of kterr,eff ≈ 10-9 is required. The actual value for Ndopant can be determined from the dopant density of the silicon wafer, which can be roughly estimated from resistivity measurements. It is more difficult, however, to accurately determine what the independent values for kterr and kdopant should be. Since the results only depend on kterr,eff, for this study, we have used kterr,eff ) 10-9. 3.3.2. Extended Defects. In general, lattice defects include point defects and dislocations. The former are localized and typically refer to single atomic defects such as vacancies and interstitials. The role of atomic point defects in etching is very similar to the effects of dopants, as discussed previously. In fact, dopants are often classified as a particular type of point defect. Dislocation defects, including edge dislocations and screw dislocations, on the other hand, are more extensive in scale, often extending beyond a few micrometers. In fact, the conventional method for revealing dislocation defects is to etch the surface several micrometers. However, there is little mention in the literature with regard to defects that are larger than point defects but yet primarily localized as compared to large-scale dislocations. In our simulation study, we have found it not possible to generate multilevel pits in the simulations unless persistent defects are embedded in the algorithm. However, it is an important point that the defects only need to extend over several nanometers to induce multilevel etch pit formation. In fact, as long as the defects persist over a few monolayers, multilevel etch pits can be effectively seeded and their further growth can be sustained by regular step-flow etching. As a result, our experiments imply
23392 J. Phys. Chem. B, Vol. 109, No. 49, 2005 defect densities of this type in the range of 10-8 or 1 µm-2. A typical commercial wafer nominally has a structural defect concentration
