Nanoscale Morphology Evolution in Ion Sputter Erosion
Nanoscale Morphology Evolution in Ion Sputter Erosion
Very small ("nanoscale") structures, which are the building blocks of future technologies, are exceedingly difficult to fabricate by conventional materials processing methods and are often much less stable than their macroscopic counterparts. The reduced stability arises because the time constant for the decay of a structure by atomic diffusion scales as a large power (3rd, 4th, or 5th power depending on whose theory you believe) of the feature size. We are performing research to illuminate the basic materials science phenomena that govern what kinds of small features can be made, and how small they can be made, by nonequilibrium wafer-compatible processing methods such as ion bombardment.
Sputter Rippling: Surface Self-Organization During Ion Sputter Erosion
Guided Self-Organization
Physical Origin of Self-Organization
Shocking Developments in Ion Sputtering
Stability of a Flat Surface Reconsidered
Where do we go from here?
Application: Materials for imaging extrasolar planets: are the "little green men" really green?
Application: Fabrication of nanopore single-molecule detectors for rapid DNA sequencing
Application: Materials for novel liquid crystal displays
Selected Publications
More Complete Research Bibliography
Literature References
Sputter Rippling: Surface Self-Organization During Ion Sputter Erosion
If you simply take a fresh silicon wafer and uniformly irradiate it at non-normal incidence with inert ions that have kinetic energies of keV, the surface doesn't stay flat (Fig. 1). The spontaneously arising topographic pattern that arises is determined by the physics of the ion bombardment and the material response. Little is known about that response and we are pursuing a fundamental understanding of it. Understanding implies control.
Sometimes these patterns can be highly uniform, and sometimes they can be dots instead of ripples, as shown in Fig. 2. We currently don't have the ability to predict what kind of pattern will form, how uniform it will be, or even whether a pattern will form, under any particular set of conditions, and we'd like to do something about that. The formation of these topographic features is not specific to any particular material; they arise on semiconductors, metals, and insulators (Fig. 2). Sometimes the features can be highly uniform, and sometimes they are quite disordered. Under some circumstances the feature size can be as small as 15 nm (Fig. 2b), which is smaller than you can make with standard lithographic mass-production methods, so this begs the question, "Can we understand and control this phenomenon well enough to make it into a general nanofab mass production 'tool'?"
Fig. 2(a) Ordered dot pattern from facsko, now in powerpoint in plan view
Fig. 2(b) Cross section of same
Fig. 2(c) Ordered Si ripples from Brown and Erlebacher
Fig. 2(d) Disordered Si ripples
Fig. 2(e) Rippled Metals
Fig. 2(f) SiO2 ripples
Fig. 2(g) Spirals, from Ziberi
Fig. 2(h) Two length scales, from George's thesis, p. 114, Fig. 4.2
Fig. 2(i) Dots showing 2 length scales, from Ziberi, InSb
Fig. 2(j) Undirected ripples, from Ziberi, CaF2
Even the most uniform spontaneously-arising features stay in registry only over length scales that are small compared to typical wafer sizes, so mass production at wafer size scales becomes unreliable. We reliably produce things on wafers using standard lithographic techniques, in which a single made (an increasingly time-consuming and expensive process as feature sizes shrink and wafer-sizes grow), but the extent of miniaturization is limited. Suppose we could make a pattern at these limited miniaturization length scales that extends reliably across an entire wafer by some simple non-lithographic technique, such as setting up an optical standing wave to expose photoresist and develop a series of lines at length scales near the wavelength of light. Suppose we could do this in two orthogonal directions, as shown in the lower-left of Fig. 3. Suppose the boundaries thus created served as lateral templates during uniform sputter erosion for the morphology evolution of the domain within the boundaries in a controllable and predictable way, as shown in the images going from left to right across the bottom of the figure. You might then have a controllable and predictable pattern that's the same within each domain. You might then be able to take advantage of capillary and chemical configurational forces to develop a technology of creating blobs on top of blobs, as shown in the sequence along the top of the figure, without having to write each individual blob. That's not too different from what you find in a modern SRAM device, as shown in the lower right, except the current SRAM device is made by conventional lithography and the self-organized method might permit a couple of orders of magnitude higher packing density of the blobs.
We have taken the initial steps in this direction by making a grating by conventional lithography and irradiating uniformly with inert keV argon ions. As shown in Fig. 4, the pattern that develops in between the templated boundaries is much better organized than the pattern that develops under the same ion beam just outside the templated region. The full research report on this is readable by any non-specialist scientist or science student; see Publication 163 in Advanced Materials, and a much broader review article in Publication 176 in MRS Bulletin. At this time, however, we don't know enough to answer the question "How much control can you have over the pattern that develops within a region by controlling only the boundaries and then uniformly treating the entire region? We simply must get a better fundamental understanding of the morphology evolution process if we are to make progress on this question.
Physical Origin of Self-Organization
The physical origin of the instability leading to a characteristic spacing is believed to be the dependence on surface curvature of the sputter yield (yield = atoms out per ion in). When a keV ion impacts a solid, the distribution of deposited damage is maximized a bit below the surface instead of at the surface, as shown in Fig. 5. The average ion first loses energy to the electrons in the solid, slowing down the ion. As it slows down, the cross-section for a head-on nuclear collision goes up. Eventually there is a nuclear collision that displaces an atom within the target and leading to a nuclear collision cascade below the surface. The Sigmund theory of sputtering6 posits that the erosion velocity, vn, at position x is proportional to all the energy EN the surface at point x receives from all the nuclear collision cascades centered at all the other points x' on the surface:
A crude model for the shape of this cascade is a Gaussian ellipsoid7 , which decays like the square of the distance from the center of the cascade. It is evident from the figure that a point at the bottom of a valley is closer to the neighboring cascades than is a point at the top of a hill. Hence concave regions should erode faster than convex regions of a solid surface under uniform ion irradiation. Opposing the instability is capillarity-driven surface diffusion, which acts to return the surface to flatness. The dependence on wavelength of these two effects is different, leading to a single fastest-growing wavelength, as shown8 by the Bradley-Harper linear stability theory , which we call the "classical theory of sputter rippling". Publication 173 reviews the development of the linear stability theory based on this mechanism, as well as nonlinear extensions. It also points out the shortcomings of the theory, e.g. it predicts incorrectly that any flat surface under any irradiation conditions is unstable to the development of ripples.
Our experiments on sputter ripples of crystalline Si(001) at high temperature are entirely consistent with this picture (Publication 111). But in order to reconcile the theory to our results quantitatively, we had to be creating a surface with a concentration of mobile point defects that is independent of flux and temperature. Directly observing these point defects in situ at high temperature is not possible, but we could infer their existence and behavior by considering the various processes that could create and annihilate mobile species on a surface, as shown in Fig. 6. At the high flux of our experiments, the concentration is determined only by the characteristics of an individual ion collision cascade, which don't depend on flux or temperature.
Shocking Results in Ion Sputtering
A lot of the excitement about ion sputtering comes from Focused Ion Beams (FIBs), which are being used for nanofabrication of tall, steep features at length scales too small for optical lithography. But the understanding of morphology evolution during ion irradiation of tall, steep features is in its infancy. For this purpose, theoretical approaches involving perturbations from a flat surface, which have dominated the sputter patterning theoretical literature, are probably doomed to failure. A rather large example of a tall, steep feature fabricated by a FIB, which has little hope of being modeled by a perturbative approach, is shown in Fig. 7.
We discovered a new regime of ion beam sputtering that occurs for sufficiently steep slopes, see Publication 165. High slopes propagate over large distances without dissipating the steepest features. Both the propagation velocity and the dynamically selected slope are universal, independent of the details of the initial shape of the surface. The resulting behavior can be understood as the propagation of a shock front that self-selects a stable slope, as has been previously observed in thin-film fluid flows.
The story of this discovery has a number of twists. Originally Wei Zhou, a visiting scientist working with us, observed propagative behavior during uniform ion bombardment of an initially flat commercial magnesium alloy, as shown in this movie (Fig. 8) . This told us that we really needed to understand the nonlinear physics of propagating fronts involving large slope changes. We showed this to our collaborator Michael Brenner , who supervised Ph.D. student Henry Chen from the Physics department in developing a nonlinear non-perturbative theory for his thesis. Henry's theory said that the morphology evolution depended sensitively on the "yield curve" (sputter yield vs. angle of incidence). Because the yield curve has been measured for silicon, we went back into the lab to test Henry Chen's theory by machining a variety of structures in silicon using the FIB and then uniformly irradiating them and measuring the topography quantitatively using a confocal optical profilometer. This was done by undergraduate researchers Omar Urquidez, Stefan Ichim, and Humberto Rodriguez. The result is the striking confluence of theory and experiment described in Publication 165.
The image in Fig. 9 shows a pit with with a steep wall that has been micromachined into silicon using a Focused Ion Beam, and then uniformly rastered over an area to observe the propagation of the "experimental edge". A shock front is observed with a slope that is smaller than the originally machined slope. At the same time, the originally shallow slope of the fracture surface develops a self-sharpening shock front with higher slope.
The left panel of Fig. 10 shows predictions of Henry Chen's theory of sputter morphology evolution that is applicable to arbitrarily large slopes when the curvature is small. Under uniform ion irradiation the pit wall, initially at t =0, propagates laterally and, for this particular set of conditions, evolves to maintain a uniform slope that is steeper than the original slope. The theory also predicts that sufficiently shallow slopes dissipate, which is the conventionally observed behavior. The experimental sequence in Fig. 10 , obtained with the optical profilometer, shows striking confirmation of the predictions of the theory. For the prospects of nanofabrication, an important implication of the transition from dissipative behavior to propagative behavior at high slopes is that a structure (e.g. line or dot) can be fabricated at a large length scale and, with uniform ion irradiation, reduced to a smaller length scale while preserving, or even sharpening, the steepest features.
Stability of a Flat Surface Reconsidered
The classical theory of sputter rippling predicts the instability of any flat surface under uniform ion irradiation at any incidence angle. Experimentally, we see that sometimes flat surfaces are unstable, sometimes they are completely stable, and sometimes they are "metastable" (i.e. stable against small perturbations but unstable against sufficiently large perturbations). We now believe that the erroneous prediction is a consequence of the Gaussian ellipsoid approximation of the ion collision cascade ( Fig. 5). Single ion impacts on a flat surface are sometimes observed to cause craters with rims, as shown in Fig. 11 , which cannot be obtained from Gaussian ellipsoids.
We have examined the implications for linear stability of changes to response of the surface topography to a single ion impact. For a broad class of perturbations of the Gaussian ellipsoid response the surface remains linearly unstable - hence the predictions of the classical theory are robust over a wide domain of potential responses. But for at least some shapes of craters with rims, as well as for momentum momentum transfer stimulated downhill surface diffusion, the flat surface can become stable, as described in Publication 181 .
• Now that we have identified classes of ion impact responses that can stabilize a flat surface, the next challenge is to develop predictive capabilities for what conditions actually stabilize the flat surfaces that we observe to be stable. The critical problem is to determine which of the potential physical effects is operating in experiments; the answer almost certainly depends on the material, the ion mass and energy, etc.
• Once we have the linear stability problem under control, as evidenced by a convergence of theory and experiment, we will be in a position to understand pattern formation, which is a nonlinear problem. It is well known that correctly identifying the linear behavior is critical for deriving a nonlinear theory that can actually predict the fully developed pattern.
• There are so-called "secondary effects" which will be very important for understanding the evolution of tall, steep features. Atoms sputtered off of the surface at one point can re-deposit at another point a long way away; incoming ions can be scattered away from the surface only to hit the surface again at another point a long way away. In Publication 165 we focused on the evolution of convex regions of the surface, where these effects should be minimized. We need to understand these effects in order to understand the evolution of concave regions of the surface, e.g. the trailing edge of shock fronts seen in the experimental images, but not in the model, in Fig. 10 . The results may also have significant implications for linear stability of a flat surface.
Selected Publications
173. M.J. Aziz, "Nanoscale Morphology Control Using Ion Beams", Matematisk-Fysiske Meddelelser / udg. af Det Kongelige Danske Videnskabernes Selskab 52 , 187 (2006); Ion'06 Proceedings, Ed. P. Sigmund.
176. D.P. Adams, M.J. Aziz, G. Hobler, W.J. MoberlyChan, T. Schenkel, " Fundamentals of FIB Nanostructural Processing: Below, At and Above the Surface ", MRS Bulletin 32 (5), 424-32 (2007).
165. H.H. Chen, O.A. Urquidez, S. Ichim, L. Humberto Rodriguez, M.P. Brenner and M.J. Aziz, "Shocks in Ion Sputtering Sharpen Steep Surface Features", Science 310 , 294 (2005).
163. A. Cuenat, H.B. George, K.-C. Chang, J.M. Blakely and M.J. Aziz, "Lateral Templating for Guided Self-Organization of Sputter Morphologies", Advanced Materials 17 , 2845 (2005).
111. J.D. Erlebacher, M.J. Aziz, E. Chason, M.B. Sinclair, and J.A. Floro, "Spontaneous Pattern Formation on Ion Bombarded Si(001)", Physical Review Letters 82 , 2330 -2333 (1999).
More Complete Research Bibliography
86. J.D. Erlebacher and M.J. Aziz, "Morphological Equilibration of Rippled and Dimpled Crystal Surfaces: The Role of Terrace-Width Fluctuations", Surface Science 374 , 427 -442 (1997).
95. J.D. Erlebacher and M.J. Aziz, “Ion-Sputter Induced Rippling of Si(111)”, Materials Research Society Symposium Proceedings 440 , 461-466 (1997).
96. J.D. Erlebacher and M.J. Aziz, “Surface Relaxation Mechanisms in the Morphological Equilibration of Crystal Surfaces”, Materials Research Society Symposium Proceedings 440 , 59-64 (1997).
111. J.D. Erlebacher, M.J. Aziz, E. Chason, M.B. Sinclair, and J.A. Floro, "Spontaneous Pattern Formation on Ion Bombarded Si(001)", Physical Review Letters 82 , 2330 -2333 (1999).
113. J.D. Erlebacher, M.J. Aziz, E. Chason, M.B. Sinclair, and J.A. Floro, "Nonlinear Amplitude Evolution During Spontaneous Patterning of Ion-Bombarded Si(001)", Journal of Vacuum Science and Technology A 18 , 115 -120 (2000).
130. E. Chason, J. Erlebacher, M.J. Aziz, J.A. Floro and M.B. Sinclair, "Dynamics of Pattern Formation During Low Energy Ion Bombardment of Si(001)", Nuclear Instruments & Methods B 178 , 55-61 (2001).
136. J. Li, D. Stein, C. McMullan, D. Branton, M.J. Aziz, and J.A. Golovchenko, "Ion-Beam Sculpting at Nanometre Length Scales", Nature 412 , 166 -177 (2001).
138. A. Cuenat and M.J. Aziz, "Spontaneous Pattern Formation from Focused and Unfocused Ion Beam Irradiation", Materials Research Society Symposium Proceedings 696 , N2.8.1-N2.8.6 (2002).
144. E. Chason and M.J. Aziz, "Spontaneous Formation of Patterns on Sputtered Surfaces" Scripta Materialia , 49 , 953 (2003).
145. W. Zhou, A. Cuenat and M.J. Aziz, "Formation of Self-organized Nanostructures on Ge During Focused Ion Beam Sputtering", in Microscopy of Semiconducting Materials 2003: Proceedings of the 13th International Conference on Microscopy of Semiconducting Materials , eds. A. G. Cullis and P. A. Midgley (Institute of Physics and IOP Publishing Limited, 2003).
146. D. Margetis, M.J. Aziz, and H.A. Stone, "Continuum Description of Profile Scaling in Nanostructure Decay", Physical Review B 69 , 041404 (2004).
154. D. Margetis, M.J. Aziz, and H.A. Stone, "Continuum Approach to Self-Similarity and Scaling in Nanostructure Decay", Phys. Rev. B 71 , 165432 (2005).
155. A.D. Brown, H.B .George, M.J. Aziz and J.D. Erlebacher, "One and Two-Dimensional Pattern Formation on Ion Sputtered Silicon", Materials Research Society Symposium Proceedings 792 , R7.8 (2004).
157. S. Ichim and M.J. Aziz, "Lateral templating of self-organized ripple morphologies during focused ion beam milling of Ge", Journal of Vacuum Science and Technology B 23 , 1068-1071 (2005) .
163. A. Cuenat, H.B. George, K.-C. Chang, J.M. Blakely and M.J. Aziz, "Lateral Templating for Guided Self-Organization of Sputter Morphologies", Advanced Materials 17 , 2845 (2005).
165. H.H. Chen, O.A. Urquidez, S. Ichim, L. Humberto Rodriguez, M.P. Brenner and M.J. Aziz, "Shocks in Ion Sputtering Sharpen Steep Surface Features", Science 310 , 294 (2005).
167. H.B. George, A.-D. Brown, M.R. McGrath, J. Erlebacher, and M.J. Aziz, "Quantifying the order of spontaneous ripple patterns on ion-irradiated Si(111)", Mater. Res. Soc. Symp. Proc. 908E , OO2.4 (2005).
168. K. Otani, X. Chen, J.W. Hutchinson, J.F. Chervinsky, and M.J. Aziz, "Three Dimensional Morphology Evolution of SiO2 Patterned Films Under MeV Ion Irradiation", Journal of Applied Physics 100 , 023535 (2006).
170. Y.-R. Kim, P. Chen, M.J. Aziz, D. Branton, and J.J. Vlassak, "Focused Ion Beam Induced Deflections of Freestanding Thin Films", Journal of Applied Physics 100 , 104322 (2006).
173. M.J. Aziz, "Nanoscale Morphology Control Using Ion Beams", Matematisk-Fysiske Meddelelser / udg. af Det Kongelige Danske Videnskabernes Selskab 52 , 187 (2006); Ion'06 Proceedings, Ed. P. Sigmund.
174. D. Margetis, P.-W. Fok, M.J. Aziz, and H.A. Stone, "Continuum Theory of Nanostructure Decay via a Microscale Condition", Phys. Rev. Lett. 97 , 096102 (2006).
176. D.P. Adams, M.J. Aziz, G. Hobler, W.J. MoberlyChan, T. Schenkel, " Fundamentals of FIB Nanostructural Processing: Below, At and Above the Surface ", MRS Bulletin 32 (5), 424-32 (2007).
181. B. Davidovitch, M.J. Aziz, and M.P. Brenner, "On the Stabilization of Ion Sputtered Surfaces", Phys. Rev. B , in press (2007).
Literature References
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3S. Rusponi, G. Costantini, C. Boragno, and U. Valbusa, "Scaling Laws of the Ripple Morphology on Cu(110)", Physical Review Letters 81 , 4184 (1998).
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6P. Sigmund, "Theory of Sputtering .I. Sputtering Yield of Amorphous and Polycrystalline Targets", Physical Review 184 , 383 (1969).
7P. Sigmund, "A Mechanism of Surface Micro-Roughening by Ion Bombardment", J. Mater. Sci. 8 , 1545 (1973).
8R.M. Bradley and J.M. Harper, "Theory of Ripple Topography Induced by Ion Bombardment", J. Vac. Sci. Technol. A 6 , 2390 (1988).
9D.P. Adams, M.J. Vasile, T.M. Mayer, and V.C. Hodges, "Focused Ion Beam Milling of Diamond: Effects of H 2 O on Yield, Surface Morphology and Microstructure", J. Vac. Sci. Technol. B 21 , 2334 (2003).
10E.M. Bringa, K. Nordlund, and J. Keinonen, "Cratering-Energy Regimes: From Linear Collision Cascades to Heat Spikes to Macroscopic Impacts", Phys. Rev. B 64 , 235426 (2001).
11G. Costantini, F. Buatier de Mongeot, C. Boragno, and U. Valbusa, "Is Ion Sputtering Always A "Negative Homoepitaxial Deposition?" Physical Review Letters 86 , 838 (2001).