Comments on ?The equilibrium topography of sputtered amorphous solids?

Ishitani, Tohru; Kato, Masahiro; Shimizu, Ryuichi

doi:10.1007/bf00737856

Cited by 41 publications

(31 citation statements)

References 4 publications

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“…These computations have been carried out with successively more complete descriptions, e.g., for fixed ion angle of incidence without redeposition 23,24 ; fixed angle including redeposition and surface diffusion 25,26 ; and rotation of the substrate with redeposition, surface diffusion, shadowing, and other boundary conditions. The ion energy is of order of one keV, the current density is assumed to be uniform at about 0.1 mA/cm 2 , and the rare gas ion is usually Ar.…”

Section: A Large Area Sputteringmentioning

confidence: 99%

Mathematical modeling of focused ion beam microfabrication

Nassar

Vasile

Zhang

1998

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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Depth control of focused ion-beam milling from a numerical model of the sputter process A mathematical model for sputtering a shape or cavity with an arbitrary cross-sectional profile has been developed for focused ion beam milling. The ion beam is assumed to have a Gaussian intensity distribution and a submicron width. The model solves for ion beam dwell times on a pixel grid which yields the desired feature depth as a function of the pixel (x,y) coordinate. The solution is unique and accounts for the ion beam flux contribution at any point from all other pixels in the address matrix. A semiempirical sputter yield treatment allows for a very wide range of ion beam/ solid combinations and for yield variations with ion energy and angle of incidence. Solutions have been obtained for parabolic surfaces of revolution, a parabolic trench ͑with a plane of symmetry͒ and a hemispherical pit. Either a square or a circular pixel matrix was used for the parabolic shapes. Correspondence between the predictions of the model and experimental 20 keV Ga ϩ sputtering of a parabolic cross-section trench in Si͑100͒ was within the limits of the accuracy of the experimental control.

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Section: A Large Area Sputteringmentioning

confidence: 99%

Mathematical modeling of focused ion beam microfabrication

Nassar

Vasile

Zhang

1998

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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“…where grad, = (dlan,, alan,, dldn3) and ni are the components of the normal fi. Simultaneous integration of the set of ordinary differential equations (7) or its equivalent set (8) under the initial condition equation (2) define loci of points from successive surfaces, which are called characteristic trajectories or simply characteristics. These characteristics link points on incrementally successive surfaces.…”

Section: For Example Under Ion Beam Erosion Of a Solid Q = -J(xy Zmentioning

confidence: 99%

“…Specifically, a = 2 : J0 corresponds to a current density of 0-6 mA cmP2 and the total evolution time is 40 min. Characteristic trajectories, evaluated according to equations (7) and corresponding to arbitrarily selected initial points are presented also.…”

Section: For Example Under Ion Beam Erosion Of a Solid Q = -J(xy Zmentioning

confidence: 99%

“…Note that it is the points of tangency which lie on the evolving wavefront. However, any attempt to analytically find the common tangent envelope requires that the surface S=O at any one time be smooth, in which case it is easily shown24 that this common tangent envelope is analytically given by the set of equations (7), i.e. the Huygens construction and the formalism presented above are identical for smooth surfaces.…”

Section: Principle Of Numerical Simulation Based On the Huygens Princmentioning

confidence: 99%

“…The same result is also apparent from visual comparison of the two simulations where the first one stops almost at the end of the fifth cycle, whereas the second stops shortly after the beginning of the fifth cycle. Figures 1 and 2, where the evolving profiles were simulated with the above algorithm and the characteristic trajectories were independently calculated from equation (7) and subsequently superimposed, present a direct comparison between theory and simulation. In Figure 3(b) the evolving profile was again simulated and Huygens wavelets were constructed at arbitrary points on the initial profile.…”

Section: Specific Examples Using the Simulation Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

The modelling of surface evolution during growth and erosion

Katardjiev

Carter

Nobes

1990

Int J Numerical Modelling

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SUMMARYWhen the erosion or growth of a surface that occurs in semiconductor device processing can be considered as everywhere continuous in space and time, the equations of motion of the surface may be specified and determined numerically using a kinetic model of surface evolution. In this review the fundamental concepts of the kinematic model of surface evolution are discussed. Detailed consideration of the theory of characteristics reveals its limitations which are overcome by recent theoretical development based on the Huygens principle of wavefront reconstruction. Correct interpretation of the nature of the basic wavelet, coupled with contemporary ideas of surface and edge propagation, form the essence of a new numerical algorithm. Numerical analysis and consequent numerical procedures derived from the generalized kinematic model are presented. Examples of surface evolution, with particular reference to ion beam induced erosion are given to show the advantages and potential of the method as opposed to existing models and theoretical prediction.When evolution processes are discontinuous and localized, other approaches, particularly those that use numerical modelling, are required. Such approaches are also reviewed here.

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Cross-sectional sample preparation by focused ion beam: A review of ion-sample interaction

Ishitani

Yaguchi

1996

Microsc. Res. Tech.

110

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A focused ion beam (FIB) was applied for cross‐sectional sample preparation with both transmission electron microscopes (TEM) and scanning electron microscopes (SEM). The FIB sample preparation has the advantage of high positioning accuracy for cross sections. On the other hand, a broad ion beam (BIB) has been conventionally used for thinning TEM samples. Although both FIB and BIB use energetic ion beams, they are essentially different from each other in many aspects such as beam size, beam current density, incident angle of the beam with respect to cross sections, and beam scanning (i.e., dynamic or static beam). In this study, FIB cross‐sectioning is compared with BIB thinning. We review inherent characteristics such as positioning accuracy and uniformity of cross section, radiation damage, and beam heating. Discussion is held from a viewpoint of ion beam and sample interaction. © 1996 Wiley‐Liss, Inc.

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Comments on ?The equilibrium topography of sputtered amorphous solids?

Cited by 41 publications

References 4 publications

Mathematical modeling of focused ion beam microfabrication

Mathematical modeling of focused ion beam microfabrication

The modelling of surface evolution during growth and erosion

Cross-sectional sample preparation by focused ion beam: A review of ion-sample interaction

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