(a) The schematic diagram shows the direction of the ion beam relative to the surface. The beam direction is defined by two angles: , referred to as the incident angle, is the angle between the average surface normal and the beam direction; is the angle of the projected beam direction onto the surface with respect to a certain crystallographic direction of the surface (if the surface is crystalline). (b) The surface morphology of a surface after bombardment by ions, with . Periodic ripples perpendicular to the beam direction develop from an originally smooth surface after the removal of of material (Ref. 6).
Kinetic phase diagram for pattern formation on Cu(001)/Ag(001) surfaces. Each region in the diagram represents a different form of pattern formation behavior. The characteristics of the patterns formed in each region are labeled on the diagram. The table below the figure shows the sputtering conditions and the original reference for each data point appearing in the diagram.
Surface morphology of a Cu(001) surface after sputtering with Ar at and azimuthal angles of (a) and (b) relative to the  direction. The insert shows the autocorrelation function of the surface. The arrow indicates direction of ion beam projected onto the surface. The sputtering temperature is and the flux is .
Ag(001) surfaces bombarded at different temperatures, indicating the transition of morphology from (a) pits aligned with the ⟨110⟩ directions of the surface to (b) ripples aligned with the ion beam direction . The surface is bombarded with ions with . The white arrow indicates the ion beam direction projected onto the surface (Ref. 4).
STM topology of defects induced by single ion impacts on a Pt(111) surface. The surface is bombarded with ions at . The image was taken after an ion fluence of , corresponding to an average of 24 impacts on the area shown (Ref. 70).
MD simulations of the defect structure created by the impact of (a) Ne and (b) Xe on a Pt(111) surface. The upper figures show the distribution of surface adatoms and vacancies after the bombardment, and the lower figures show the location of atoms that have been displaced by more than 0.4 lattice parameters during the impact. Larger craters and clusters are formed by bombardment with the heavy ion, while individual defects are formed by bombardment with the light ion (Ref. 67).
Schematics showing the defect evolution after an ion impact. (a) When an ion bombards the solid, defects are created both in the bulk and on the surface. At the same time, some atoms are sputtered, which leaves vacancies on the surface. (b) After the impact, defects can annihilate and recombine through bulk and surface diffusion. The bulk defects can also diffuse to the surface and become surface defects.
The average surface defect yield per ion as a function of temperature observed by RHEED on Ge(001) surfaces. The surface is bombarded with Ar and Xe ions at an incident angle 60° away from surface normal. The solid line is a fit to a continuum model discussed in Ref. 82. The yield drops rapidly at a temperature around , indicating a rapid recombination of adatoms and vacancies above this temperature. At high temperature, a yield approximately equal to the sputter yield is observed, which implies that primarily sputter-induced vacancies remain on the surface (Ref. 82).
(a) A schematic diagram showing how the height at can be affected by an ion impact at . The elliptical contours represent how the energy of an ion is deposited inside the bulk in the Sigmund model. (b) In the BH model, more ion energy is deposited at areas with a positive curvature, causing these areas to be sputtered faster than areas with a negative curvature.
Schematic diagrams indicate (a) surface smoothening by surface diffusion current and (b) surface roughening by the ES instability. The notations and refer to the mass current due to surface diffusion and the ES barrier, respectively.
Typical values for and as a function of . The coefficients and are normalized by the product of erosion velocity and the ion range , which makes it dimensionless. The orientation of ripples changes by 90° at the critical angle . The parameters used are .
(a) AFM morphology of a Si(001) surface after bombardment by Ar ions at and . (b) The power spectral density (PSD) of the surface, measured by an in situ light scattering technique at different times during sputtering. The sample temperature was with the same ion beam parameters. A peak develops at , corresponding to the formation of ripples with a well-defined periodicity. (c) The amplitude of the ripples as a function of time calculated from a series of PSD spectra similar to those shown in (b). This set of data was measured at . The line on the semilog plot shows the initial exponential growth regime (Refs. 45 and 56).
(a) An AFM image of self-organized ripples formed on a Si(001) surface. The surface was sputtered at room temperature with ions at a 15° incident angle. The ion flux is with a total fluence of . The circle indicates a defect found in the ripple structure. (b) The Fourier transform of the image. Multiple higher order peaks can be seen, indicating that the ripple structure has a high degree of uniformity (Ref. 154).
Ripple growth rate normalized by the ion flux against the ripple wave vector. Results are obtained from (a) experiments on Cu(001) surfaces and (b) KMC simulation. The details of the sputtering conditions can be found in Refs. 47 and 105. The solid line is a fit to Eq. (14). The unit is the nearest neighbor distance used in the KMC simulation. The value of the coefficient of the roughening term can be determined from the fitting.
STM micrographs of graphite surface eroded by ions at different incident angles. The surface was maintained at during sputtering. The black arrow indicates the projected direction of the ions. The ripples changes from an orientation with wave vector parallel to the beam at to an orientation with wave vector perpendicular to the beam at (Ref. 53).
The experimentally measured wavelength (circular points) as a function of incident angle for the ripples shown in Fig. 15. The lines are the wavelength for each mode of ripple, normalized by the wavelength at , calculated from the BH theory using the ion beam parameters determined by SRIM (these values are shown in the insert). The vertical line indicates the critical angle where ripple rotation is expected to be observed. The wavelength is expected to follow the solid line for and the dashed line for (Ref. 53).
Schematics showing how the ripples translate during sputtering. The region with a positive slope has a smaller incident angle than the region with a negative slope. If the erosion velocity is an increasing (decreasing) function of , the ripples will move in a direction opposite to (same as) the beam direction.
(a) Temperature dependence of the ripple wavelength on Cu(001) surfaces with . The surface was bombarded by ions at . The flux dependence of the ripple wavelength at different temperatures is shown for (b) and (c) . The solid lines are results of fitting the data to Eq. (18). Different temperature and flux dependences are found in the high and low temperature regimes, which are explained by different defect formation mechanisms dominating in the two kinetic regimes (Ref. 123).
KMC simulation results for the relationship between the ripple lateral velocity (normalized by ion flux) and the wave vector of the ripples. The solid line indicates a fit to the continuum model using higher order terms in the BH/MBC model (see Ref. 105 for more details).
KMC simulation results for the spatial average of the surface defect concentration (both adatom and surface vacancy) during simulated ion bombardment. The concentration is approximately proportional to . These data can be used to analyze the effect of defects on the ripple wavelength as described in the text (Ref. 105).
The flux dependence of the ripple wavelength found in the KMC simulation measured at four different temperatures. At higher temperatures, the ripple wavelength decreases more rapidly with flux. The solid line is a fit to the continuum model [Eq. (16)], with the concentration determined from the data shown in Fig. 20 (Ref. 105).
Cross-sectional TEM images (with different magnifications) of a Si(001) surface sputtered by ions. (c) and (d) are higher magnification images of the regions 2 and 1 labeled in (b), respectively. An amorphous layer (lighter in color) is formed on the single-crystalline Si. The layer is thicker on the slope that is facing the ion beam [the ion beam direction is indicated in (a)]. Bubble/cavitylike structures can be found near the surface (Ref. 176).
STM images of the Ag(001) surface after sputtering by ions at normal incidence [(a) and (b)]. (c) and (d) are the “photographic negative” of the images (a) and (b). The morphology after Ag deposition is shown in (e) and (f). The image sizes for morphology shown on the left column and the right column are and , respectively. The sample temperatures are indicated in the figures (Ref. 94).
The morphology of a Ag(001) surface sputtered at three different temperatures: (a) , (b) , and (c) by Ar ions at normal incidence. The image sizes for (a), (b), and (c) are , , and , respectively. (d) The rms roughness of the surface as a function of temperature bombarded with Ar ions (solid squares) and Ne ions (open squares). A constant fluence is used at each temperature, with the values indicated in the figure (Ref. 36).
Images of Ag(110) surfaces sputtered by ions at (image size: ). The incident angle is 45° and the projected beam direction is indicated by the white arrows. The ripples always align along the ⟨001⟩ direction (shown as a white marker) independent of the azimuthal angle used (Ref. 30).
Morphology of a Ag(110) surface after the sputtering by ions with image size equal to for (a) and (b), and for (c)–(e). The incident angle is 0°. The sample temperatures are (a) , (b) , (c) , (d) , and (e) , and the orientation of the surface is indicated in the figures (Ref. 30).
AFM images of Cu(001) surfaces sputtered at 327 and and . The flux used is with a total fluence equal to . The direction of the ion beam is shown as the white arrow in the image. The PSD of the image is shown in the small figure.
Experimental measurements of the transition between the BH instability and the ES instability. The open (closed) circle represents conditions in which ripples (array of pits) are observed. The total fluence used in all experiments ranges from .
(a) Specular RHEED intensity evolution in the out-of-phase condition during Xe bombardment of Si(100). At temperatures of 470 and , step flow erosion occurs and the intensity maintains a steady-state level. At , layer-by-layer erosion occurs. Each oscillation represents the removal of 1 ML (monolayer) of atom. (b) Intensity oscillations of the specular beam measured by x-ray scattering. The sample was Au(111) sputtered by Ar ions at . Over 100 intensity oscillations were observed (Refs. 201 and 202).
(a) The exponential growth rate of the sputter ripples on Cu(001) surfaces as a function of flux. The surface is sputtered by Ar ions at 70° incident angle. The sample temperatures are indicated in the graph. The growth rate goes to zero below a threshold flux, in contradiction with predictions of the instability model. (b) KMC simulation results for the exponential growth rate of the ripples as a function of flux for three different temperatures. The solid line is the predicted rate from the instability model. The growth rate in the simulation deviates from the prediction of the continuum theory in the low flux regime.
The transition between nonroughening and roughening behaviors in experiments of sputtering and growth on Cu(001) and Ag(001) surfaces. For each point, the error bar represents the temperature range in which the evolution is observed to undergo a transition from layer-by-layer erosion/growth to roughening. Data points are obtained from the references stated in the legend. The closed symbols represent data from sputtering and the open symbols represent data from growth. The solid line is the transition temperature as a function of flux calculated using the Tersoff model.
The ratio of the surface rms roughness to the pattern wavelength as a function of time for a number of systems. The pattern usually saturates with an aspect ratio on the order of 0.1-1. For some systems, a steady-state aspect ratio with respect to time is maintained in the nonlinear regime.
(a) SEM image of well-organized quantum dots forming on a GaSb surface during bombardment by ions at normal incidence. (b) The autocorrelation function of image (a) showing the hexagonal and long-range ordering of the QDs. (c) Cross-sectional TEM image of the dots. The aspect ratio of the dots is on the order of unity (Ref. 7).
(a) A diamond cutting tool and (b) a circular diamond pillar created using FIB machining. Different ion-induced morphologies can be observed on different surfaces of the structure. Locally, the incident angle of the ion depends on the normal direction of a particular surface (Ref. 16).
(a) SEM image of a circular pit, with diameter and depth, fabricated on a Si surface by FIB. (b) SEM image of the pit after uniform irradiation of ions across the whole surface. The fluence is . As the pit grows, the slope of the sidewall is maintained at a constant value while it moves outward (Ref. 110).
STM images of Pt(111) surfaces bombarded by at at 83°. The images are taken after the erosion of (a) 0.5 ML, (b) 1ML, and (c) 2ML of Pt. The white arrow indicates the ion beam direction. The individual craters developed from single impacts line up along the ion beam direction due to channeling. These craters turn into periodic ripples after the removal of a few monolayers of atoms (Ref. 178).
Cross-sectional TEM image showing a FIB-sputtered diamond surface under grazing incident . The surface evolves into a “step-terrace” morphology where the terrace is nearly parallel to the ion beam direction and the step is normal to the beam direction. The terrace has a sputter yield orders of magnitude lower than the step, and the surface is eroded through the movement of the steps (Ref. 16).
Comparison of roughening parameter measured experimentally with theoretical prediction for several materials systems. The theoretical value is calculated with ion beam parameters obtained from SRIM. (Ref. 65).
Experimentally observed flux and temperature dependence of the ripple wavelength. Parameters and are defined in Eq. (17).
Comparison of the saturation amplitude of ripples formed on Si(001) surfaces bombarded with Ar ions at different energies and temperatures. The ripples formed by higher energy ions have a larger saturation amplitude and wavelength.
Theoretical predictions of the scaling exponents for various continuum equations. The exponents for the KS equation are determined by numerical methods.
Scaling exponents measured experimentally on various surfaces.
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