Topography of Solid Surfaces Modified by Fast Ion Bombardment

ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS.VOL 79

Topography of Solid Surfaces Modified by Fast Ion Bombardment D. GHOSE AND S. B. KARMOHAPATRO Sahu Institute of Nucleur Physics Culcurtu, India

I. Introduction . . . . . . . . 11. Basic Ion Bombardment Processes . A. Ion Penetration and Stopping . B. Channeling. . . . . . . . C. Sputtering . . . . . . . . D. Radiation Damage . . . . . 111. Ion-Induced Surface Modifications . A.Cone.. . . . . . . . . B. Faceting. . . . . . . . . C. Blistering . . . . . . . . IV. Summary. . . . . . . . . . Acknowledgments. . . . . . . References . . . . . . . . .

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I . INTRODUCTION Fast ion bombardment modifies the topography of solid surfaces as a result of a number of different effects, the most important being the sputtering. Since the surfaces are not always perfectly planar, the variation in sputtering yield with angle of ion incidence causes the surface to be eroded more rapidly where the angle of incidence is higher. Also, the presence of impurities on the surface, the inhomogeneity of the target material, and radiation damage lead to nonuniform etching of the surface. All these result in the development of surface structures. The second effect that can give rise to changes in surface topography is caused by implanation of insoluble gas ions. The phenomenon called radiation blistering is most easily observed with light ions, principally hydrogen and helium, because their range is large compared with the depth of erosion during bombardment and it is therefore possible to accumulate high gas concentrations in the near-surface region before the gas is released by erosion. The formation of voids caused by radiation damage also contributes to the modification of surfaces in some cases. The interest in the studies of the modifications of surface topography by ion bombardment stems partly from the intrinsic fundamental aspects of ion-solid interaction processes and partly from the possible technological applications. 73

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D. GHOSE AND S. B. KARMOHAPATRO

Since the initial observation of sputtering process in glow discharge tubes by Grove in 1852,it has become increasingly recognized that the phenomenon causes both atomic-scale and larger-scale morphological changes on surfaces. As the dose of the bombarding ion increases, the surface of the solid is eroded away successively and then some characteristic etch patterns, such as conical protrusions, grooves, and pits are developed on the surface of the sputtered area. In early investigations, the existence of surface structure was detected by studying the light reflected from the surface. The presence of structures with certain dimensions was indicated by the occurrence of Rayleigh scattering. These observations were subsequently supplemented by optical microscopy, though many of the features were beyond the resolution of these microscopes. Later, the electron microscope was used, involving both the replica and scanning techniques. The resolution limit was in that way extended below 1000 A. The practical resolution limit of the scanning electron microscope (SEM) is, however, -100 A. With the advent of the scanning tunneling microscope (STM), it is now possible to study subnanometer- or atomic-scale topography (Feenstra and Oehrlein, 1985a,b; Wilson et al., 1989). It may be mentioned that the scanning ion microscope (SIM), besides its application to elemental localization by secondary ion mass spectrometry, can also be used to obtain high-quality images of the surface topography by collecting ioninduced secondary electron or ion signals (Levi-Setti et al., 1983, 1986). Using finely focused beams from liquid metal ion sources (Ga), one can obtain lateral resolution of -200 A. Fetz (1942) was the first to discover the dependence of sputter yield on angle of ion incidence. For thin wires sputtered in a low-pressure plasma, sputtering yields were always found to be above the corresponding values for plane targets. One of the implications of this observation, the formation of submicroscopic surface cones, was reported in the same year by Giintherschulze and Tollmien (1942). Textured surfaces formed by ion beam sputtering have a number of characteristic properties that make them suitable for a large and diversified number of applications. Auciello (1981, 1984a, 1986) listed the following fields in which texturing has possible applications and relevances: (i) microelectronics, (ii) surface acoustical and optical technologies, (iii) solar energy conversion technology, (iv) ion beam surface analysis, (v) thermonuclear fusion, (vi) field ion emission and electron microscopy, (vii) surface-enhanced Raman scattering spectroscopy, and (viii) biomedicine (implantology). It has been demonstrated that textured surfaces already are used in some technologies, have the potential to be useful in others, and are relevant on either a detrimental or a beneficial basis in various experimental techniques. The emphasis on blistering studies, in the 1970s, arose mainly from its potential importance in the erosion of the inner walls of the controlled

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thermonuclear reactors (CTR) exposed to ion bombardment (D, T, and He) from hot hydrogenic plasmas. The erosion of the wall surface due to blistering and flaking is orders of magnitude higher than that due to sputtering and introduces heavy impurity atoms, which has the detrimental effect of cooling down the plasma by radiative collision processes. In a CTR machine, the first wall will be bombarded by thermalized helium ions escaping the plasma edge (the temperature of which is nearly 100 eV) and by the nascent 3.5 MeV helium ions from the D-T reaction, which have some probability of directly escaping the magnetic field. The thermalized ions, having a broad angular distribution, are very unlikely to blister the surface (Behrisch and Scherzer, 1983). They mainly contribute to wall sputtering. In contrast, the high-energy helium ions have a high probability of causing surface modifications by blistering, exfoliation, and flaking. Blister formation from the hydrogen isotopes is, however, unlikely for the ion dose rates and wall temperatures found in practice. Recently, a new branch of materials science called plasma surface interaction (PSI) has emerged, which includes various atomic collision processes of plasma particles (ions and charge exchange neutrals) with the first wall structures. The surface deformations induced by high-fluence helium implantation is a narrow field of PSI, and a number of experiments are aimed at assessing the helium-induced blistering problem by bombarding monoenergetic beams of helium ions on a large variety of probable (and improbable) first wall materials. Aside from the technological implications, these experiments have permitted a better understanding of basic phenomena in ion-solid interaction processes (Ullmaier, 1983). A n important parameter for the understanding of bubble growth processes and the subsequent formation of blisters on helium-irradiated materials is the pressure or density of helium in the bubbles. The most direct method for characterizing He bubbles in metals is transmission electron microscopy (TEM). The other methods, which give indirect information, are small-angle x-ray (SAXS) or neutron (SANS) scattering, and the spectroscopic techniques such as vacuum ultraviolet absorption spectroscopy (VUVAS) and electron energy-loss spectroscopy (EELS). A discussion of various experimental methods can be found in the article by Donnelly (1985). The surface modifications due to gas pressure in the bubble can be investigated by optical microscopy and also by SEM. They are often combined with nuclear methods such as Rutherford backscattering spectroscopy (RBS) and nuclear reaction analysis (NRA) to yield information about blister lid thickness and depth profiles of implanted helium. (See, for instance, Scherzer e l al., 1983.) In the present work, following fundamental aspects of ion-solid interactions, the ion bombarded surface modifications in the form of cones, faceting, and blistering are reviewed, along with the progress of the subject in recent years.

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11. BASICION BOMBARDMENT PROCESSES

A . Ion Penetration and Stopping

When a beam of fast ions encounters a solid target, a fraction of the ions backscatters from the surface, while most of the ions penetrate and lose energy in the solid until their energy has fallen below about 24 eV, when they become trapped by the cohesive forces of the solid. The slowing down of the penetrating ion is due mainly to inelastic electronic and elastic nuclear collision processes. The first type of interaction occurs at high energies where the velocity of the projectile is generally greater than the orbital velocity of the lattice electrons, resulting in excitation and ionization processes of both the incident projectile and the target atom, and the collision is said to be inelastic in the sense that the total kinetic energy of the participating particles is not conserved. On the other hand, the second type of interaction, i.e., the elastic nuclear collision, is more frequent at low energies and involves the mechanics of hard-sphere collision between incident ion and lattice atom. In general, the stopping of an energetic projectile in a solid is caused by the sum of these two components; the importance of one over the other is, however, dependent on energy. The varieties of physical phenomena observed during ion bombardment of solids all originate from the energy expended by the ions in the solid. The path length of penetration R , , i.e., the range of the projectile into a solid, is related to the total stopping power by the relation dE’ (-dE’/dx),’

where ( - dE’/dx), is the total stopping power or the specific energy loss

(-,):

(-

(-

+ ~)..c...i.‘ Since energy is lost by the projectile in a series of discrete collisions, the specific energy loss and consequently the path length have a statistical spread of values leading to a near-Gaussian type of range distribution. The trajectory of the penetrating ion is almost straight when electronic stopping dominates, but it follows a zigzag path as it is slowed down by nuclear collisions. As a result, at lower energies, the projected range R , measured along the incident ion direction can be considerably less than the total path length or range, R , . The projected range and the straggling both parallel ( A R , ) and perpendicular ( A R , ) to the ion direction are more useful practical range parameters than those relating to the total path length. =

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For light ions such as H, D and He at energies that are not too low,

( - dE’/dx)e,ec,ronic >> ( -dE’/dx)nuc,ear. A useful rule of thumb is that the en-

ergy loss is predominantly electronic whenever the energy of the bombarding particle in keV is greater than its atomic weight. For energies that are not too high, the electronic stopping cross-section is proportional to projectile velocity, the specific dependence (Lindhard and Scharff, 1961) being given by

Here, Z , and Z 2 are the atomic numbers of projectile and target, respectively. The projectile velocity is v, e is the electronic charge, and a, and uo the Bohr radius of the hydrogen atom and the Bohr velocity respectively. The data for hydrogen and helium stopping powers and ranges in all elements have been compiled by Andersen and Ziegler (1977; Ziegler, 1977).

B. Channeling A number of processes occur during ion bombardment of solid targets, e.g., sputtering of solid and its damage, backscattering, energy loss of ions, secondary electron emission, x-ray production by inner-shell ionization and nuclear reactions. If the solid is homogeneous and isotropic, the results of the interaction of ions with the solid will not be influenced by the direction of the beam and the target. When the target is a single crystal, the interaction will be strongly dependent upon the relative orientation of the crystal and the ion beam. The effect is due to the channeling of ions through crystals, and it is dependent upon the degree of inhomogeneity, anisotropy, and lack of randomness of the crystalline solid. Lindhard (1965) developed a continuum model of directional effects in which the potential of a row or plane of atoms is considered as smeared out, forming a continuous potential. When a charged particle moves along a major crystallographic direction, under certain conditions it may not be able to feel the interaction caused by individual atoms sitting at various lattice sites, but rather experiences a collective effect of all the atoms sitting along a particular axial or planar direction, so that the moving particle will experience the action of potentials associated with continuous strings or planes. A channeled particle loses energy only by electronic collisions, and since it cannot come close to atomic positions, all physical effects that require a close collision between the projectile and target atom are greatly reduced. Axial channeling can be established only for ions incident at less than a critical angle II/ with respect to a row of lattice atoms. For low projectile

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energies this angle is given by (Lindhard, 1965)

where d’ is the distance between the atoms along the axis, E is the incident energy, and uTF is the Thomas- Fermi screening radius. Typical critical angles of keV heavy ions are of the order of ten degrees. The continuum scattering from planes is somewhat weaker and less well defined than for strings of atoms, because in the plane, the distance between scattering centers is random. Lindhard (1965) proposes that the continuum scattering remains valid so long as the maximum angle of deflection in any single collision at a distance y from the plane does not exceed the transverse angle required to reach y. This leads to slowly varying values of the distance of minimum approach, generally of the order of the screening length uTF at high energies, and increasing with decreasing energy. Because of the relatively slow variation of the continuum potential, Y(y), with y, it is assumed that the potential barrier of a plane is not higher than Yefr = Y(0)/2.However, for quite low energies, the barrier becomes somewhat lower than the above value. The concept of channeling is applied to predict the cone apex angle, which is described in Section III.A.4. C . Sputtering

Sputtering, i.e., the ejection of atomic and molecular particles, is known to be a universal phenomenon, which occurs when a solid target is bombarded with energetic ions. The most essential quantity to characterize the sputtering effect at a solid surface is the sputtering yield or the sputtering ratio S , i.e., the average number of atoms ejected per incoming ion. S depends on a number of parameters, e.g., ion energy, type of the incident ion, angle of incidence, material to be sputtered, target temperature, surface condition and, if single crystals are used, the orientation of the exposed crystal face. The experimental values of S lie usually in the range between 1 O - j and 10” atoms/ions, dependent on ion and target (Andersen and Bay, 1981). The phenomenon of sputtering in an isotropic solid can be understood qualitatively in the following way: When a projectile enters a solid target, it collides several times with the target atoms and creates a generation of primary recoil atoms, also called primary knock-on atoms (PKA). The recoils that have sufficient energy are able to transfer momenta to other target atoms, thereby creating another generation of recoil atoms, and so on. During slowing down, the projectile may also backscatter towards the surface and again produce recoils along its path. In this way, a collision cascade is

-

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generated in a space-time frame of reference. The recoil target atoms that lie close to the surface and have sufficient energy to overcome the surface binding energy will leave the surface. Sigmund (1969a) developed a theory of sputtering for random targets within the framework of transport theory. He showed that the sputtering yield at depth x is given by s(x) = A * F D ( ~ ) ,

(5)

where A is a material constant and F,(X) is the deposited energy distribution function. A is given by

where N is the density of target atoms and V, the surface binding energy. For the case of backsputtering, x = 0 and FD(0)is mathematically expressed by the formula FD(o)

= aD(M2/Ml

9

?) ’

’ Sn(E),

(7)

where S n ( E ) is the nuclear stopping cross-section and aD is a dimensionless quantity depending on the mass ratio between the target atom mass M, and the impinging ion mass MI and the angle of incidence 6, (q = cose). For perpendicular incidence of the bombarding particles, i.e., for cose = 1, S is given by S

= 0.042-

aDSn(E)

v,A2

.

The ciD function in Sigmund’s theory determines the multiple-scattering character of the sputtering phenomenon, and it plays a decisive part when the variation of yield with angle of incidence is studied. In a single-scattering theory, the yield is expected to rise as

simply because of the longer pathlength close to the surface, while the dependence within the multiple-scattering-based theory is expressed through the ciD function. For not-too-oblique ion incidence, Sigmund gives

where m

‘Y

3 for M2/Ml 5 3, and m tends to unity for M , << M , .

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The angular dependence of S plays the prime role in the development of conical protrusions on sputtered surfaces, which is discussed in Section III.A.2. In the case of monocrystalline sputtering, there is a considerable influence of the lattice structure on the collision cascade. In the later stages of the development of collision cascade, when the energy of the knock-on lattice atoms has fallen to below about 100 eV, the kinds of collisions that occur are extremely sensitive to the lattice structure, as the mean free path is roughly equal to the lattice spacing. Silsbee (1957) suggested that under these conditions, correlated sequences of collisions would propagate along closepacked lines of atoms in the crystal, and the atoms would be ejected preferentially along those directions. The experimental observations of the preferential ejection of sputtered atoms from monocrystals indeed suggest that the sputtering process in monocrystals is mainly governed by these correlated processes. D. Radiation Damage

The radiation-damage phenomena are classified as displacement damage or impurity damage according to the type of interactions between the radiation and lattice atoms: (i) The bombarding particles transfer recoil energy E , to the lattice atoms. If E , exceeds the value Ed, the threshold energy for displacement, a vacancy-interstitial pair is created provided that the displaced atom moves far enough from the vacant site to avoid recombination. In the second step, the energetic primary knock-on atoms (PKA) produce a cascade of point defects that is called a displacement cascade. When the kinetic energy of the colliding atoms has dropped below E d , the displacement events stop. However, the energy per atom in the cascade may be quite high; in terms of temperature, some lo4 degrees. In the last step, this energy is dissipated by random atomic collisions until the temperature has fallen below the melting point, and subsequently the flow of phonons out of the cascade reduces further the temperature down to ambient temperatures. Finally, the relaxation of the atomic arrangement results in a stable defect pattern. The vacancies and interstitials that are produced by the displacement damage can interact in two ways. Vacancies and interstitials can be annihilated by recombination or by going to sinks such as the target surface, grain boundaries, etc. The other possibility is that the aggregates of vacancies or interstitials can nucleate and grow. Three basic morphologies of the clustering of point defects exist. Interstitials can aggregate into two-dimensional platelets or interstitials dislocation loops that can subsequently evolve into a dislocation network with increasing dose of ion bombardment. On the other hand, the vacancies that

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survive recombination can form either two-dimensional aggregates called vacancy loops or a three-dimensional empty space called a void. The void morphology is, however, formed at high irradiation temperature where both the vacancies and interstitials are highly mobile. (ii) The second type of damage is associated with impurity atoms introduced either by transmutation of the target nucleus or when the bombarding ions come to rest in the specimen. For example, helium impurities up to 30 at ”/, concentrations can be introduced into metals by tritium decay, (n, a) reactions, or direct a-implantations, Since the solubility of He in metals is less than a part per million, He tends to segregate in the form of small bubbles. In a fast reactor such a phenomenon plays a crucial role in degradation of material properties (Ullmaier and Schilling, 1980). In the displacement damage, the average number of displacements N, produced by an incident ion or an energetic recoil atom can be estimated from the knowledge of the deposited energy, r (E), not lost to electronic excitation, and the size of the displacement cascade, which is 10-1000 A for ions in the 1-100 keV energy range. The modified Kinchin and Pease (1955) collisional model gives Nd as (Sigmund, 1969b)

A necessary condition for the development of surface structure due to the displacement damage has been proposed by Hermanne (1973). During sputtering, if the surface that is continuously eroded approaches one of the extensive defects, e.g., dislocations, these cause a preferential erosion of the defect area with respect to neighbour zones. The consequent spatial variation of sputtering yield would then give rise to undulations at the surface (Hermanne and Art, 1970). Other regular surface features associated with the symmetry of the crystal, which may also develop, are the crystallographic etch pits and conical protrusions. The basic criterion for the possible appearance of the damaged-induced surface structure is that the time for formation of extensive defects must be less than the time for recession of the surface to their level, i.e.,

where d , is the depth of damage peak below the surface, v, is the velocity of surface recession by sputtering, dd is the distance between two neighbouring extensive defects, and u, is the average velocity of migration of defects. It is argued that the distance travelled on average by a point defect to an extensive defect is add.

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v, can be calculated directly from the sputtering yield S . d d is approximated by the mean projected range R , as calculated by Lindhard et al. (1963). The distance de depends on the number of extensive defects formed per unit volume, an estimate of which can be made on the basis of the Kinchin and Pease (1955) model of defect production and on the amount of point defects present at the concerned level. Thus, the minimum value for the migration velocity of defects is obtained (Hermanne, 1973),

where I is the ion dose rate, E ion energy, ro the radius of the defect, and IC a numerical constant. The criterion of whether radiation-damage-related surface structure appears or not thus depends on whether the defect migration velocity u, is larger or smaller than vmin given in Eq. (13). The value of urndepends primarily on the local temperature of the region where the migration takes place, but it is rather difficult to estimate reliably. It is recognized that the above theoretical treatment gives only an order-of-magnitude estimate of conditions under which surface structure will appear.

111. ION-INDUCED SURFACE MODIFICATIONS A . Cone

1. A Brief Review of the Works on Cone Formation Solid surfaces exposed to an energetic ion beam erode and frequently acquire well-defined topography. Cones, pyramids, pits, hillocks, steps, etc., have been observed, and there are evidences that they are closely related to the initial surface irregularities, impurities, intrinsic or ion-beam-induced defects, and variations in the sputtering yield as a function of the angle of ion beam incidence to the surface. The cones or pyramids are the most commonly recurring surface features produced by sputtering. Several review articles have appeared on this subject (NavinSek, 1972, 1976; Wilson, 1974, 1989; McCracken, 1975; Townsend et al., 1976; Carter et al., 1983, 1985a, 1987; Auciello and Kelly, 1984; Whitton, 1986). Giintherschiilze and Tollmien (1942) first reported and described the formation of submicroscopic cones on glow discharge cathodes of various polycrystalline materials. They found well-developed cones on Mg, Zn, Cd, Al, Sn, Pb, Sb, and Bi, and in some cases, they appeared on Cu and Ag, but

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surfaces of Au, Ni, Fe, and Pt were almost free of cones. The dimension of the cones increases during sputtering, and the cone apex angle is different for each metal. It was also observed that on some cathodes, cones were absent when the bombardments were made at higher temperatures. Later, Spivak er ~ 1 1 .(1953) described the cone development at high current densities on ion-etched a 1umi n i um. With the advent of the SEM with its three-dimensional capability, the interest in the field of surface ion-bonibnrdment effects has grown considerably. Stewart (1962) studied the formation of cones on ion-bombarded surfaces of Al, Si, W, and Sn with an early model of the SEM. He proposed that cones or spikes are caused either by inclusions or precipitates with a lower sputtering yield than the surrounding material, or by particles resting on the surface. When the shielding particle had been eroded away, a sharp spike or cone of matrix material remained. If the bombardment was continued, the spikes decreased in size and eventually disappeared. Similar behaviour has been reported for iron oxide particles on i r o n by Pease el uI. (1965)and for line dust particles of Al, Ag. or Si o n NaCl crystals by Marinkovii and NavinSek (1965). The shielding principle for cone forniation has been substantiated by the work of Wehner and Hajicck (1971). They found that cones formed when groups of low-sputter-yield atoms, M o or W, lay on the surface of high-yield material such as Cu, Ag, or ALLThe combinations such as C u - Ag or C u C, however. showed no sign of cone formation. They also noted the importance of solubility and activation energyfor migration of the low-yield atoms on the high-yield material. For low-yield carbon atoms seeded on a high-yield CLI substrate, cones d o not form under ion bombardment. When low-yield M o atoms replace the c' atoms, conical structures form. The M o a t o m not only protect the underlying C u from being sputtered, but also arc constantly replenished via surface migration. Wilson and Kidd (1971) studied the devclopment of cones on gold surfaces by 5 to 20 keV Ar' and Xe' ion bombardment. A high cone density was found to be characteristic of mechanically polished surfaces, whilst a low cone density with height contrast of the individual grains was discovered on polycrystalline etched surfaces. The cones were found to have hexagonal facets, and in the case of ii polycrystnlline specimen, two families of cones were found. These phenomena were attributed to single crystal effects. The cone angles were found t o vary only slowly with the ion energy. Similar bombardment of single crystals produced no cones, probably as a result of channeling of the incident ion beam. Conditions of cone formation on the sputtered surfaces of Cu, Ni. Mo, W, CdS and CdSe single crystals with respect to the ion dose, face orientation, and ion beam incidence angle were investigated by Gvosdover Pt 111. ( I 976). Intense

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formation of cones was observed only when impure metal atoms were present on the sputtered surface. Such impurity either was a part of the target material or was sputtered from outside. As the ion irradiation dose increased, the cone heights and their surface density also increased. The cone density was, however, a function of crystallographic orientation of the sputtered face. This density appeared to be higher for less close-packed faces than for more closepacked ones. From the analysis of the data obtained, the authors concluded that the cone-like configurations appeared as a result of the three simultaneous processes of surface migration, growth, and sputtering. The main process responsible for cone formation was attributed to a growth process such that the sputtering in the course of ion bombardment shaped the cones into a form stable against sputtering. Recently, two groups, Whitton et al. (1977, 1978, 1980a; Whitton, 1986) and Auciello et al. (1979,1980; Kelly and Auciello, 1980; Auciello, 1982),made systematic investigations of the development of energetic ion-bombardmentinduced surface features on copper crystal, in which many interesting results were obtained. Whitton et al. (1977, 1978, 1980a; Whitton, 1986) bombarded superpure polycrystalline Cu by 40 keV Ar’ ions to a total dose of 1 x 10” ionslcm’ at room temperature. Cones were observed to develop on some grains but not on others, although all had the same conditions of bombardment. The individual grains were x-rayed to produce Laue patterns, the analyses of which showed that only of grains having orientation of, or near to, the high index direction of (11 3 1) were cones formed. Similar results were obtained for other f.c.c. metals (Whitton et al., 1984).The cones were later termed as pyramids since the observed features were of faceted shapes, having octagonal bases with triangular sides meeting at a point. For suitably oriented single crystalline targets, etch pits were always found to be the forerunners of pyramids. These observations led them to the conclusion that the mechanism of initiation of pyramid formation was associated with defects such as dislocations rather than impurities. The most critical parameter was that of crystal orientation. Pyramids were formed only of surfaces with orientations close to or of (11 3 1) crystallographic plane. Whitton et al. (1980a; Whitton, 1986) also suggested the following range of parameters within which pyramid-covered surfaces on (11 3 1) surfaces could be produced: total dose of 10’’ to 2 10” ions/cm’, temperature range 100-550 K, beam current > 100 pA/cm’, beam energy 10-41 keV, working pressure between 5 x and 5 x lo-’ mm of Hg. Auciello et al. (1979, 1980; Kelly and Auciello, 1980; Auciello, 1982) studied the morphological evolution of pyramids developed on polycrystalline Cu bombarded by 12 keV Kr’ ions as a function of ion doses. Their observations revealed that the initial surface topography was very important as far as the nucleation and development of pyramids were concerned. The presence of asperity or convex-up irregu-

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larity on unbombarded surface was the prime factor for the development of pyramid. Such asperities can in principle be formed as a result of mechanical treatment, chemical treatment, inclusions, surface impurities, ionbombardment-induced damage associated with preferential erosion, or other causes, the precise details being unimportant. A one-to-one correlation was demonstrated between pre-existing asperities and pyramids. Sequential bombardments and SEM observations of the same features showed that pyramids are not an equilibrium structure. They disappear at high enough doses. The authors also obtained strong experimental evidence for the importance of secondary and tertiary effects in the evolution of pyramids, which involved scattered ions, reflected ions, and energetic sputtered atoms from the pyramids’ surface and the inclined walls of the grooves underlying the pyramids, respectively. Alexander et al. (1981) investigated the geometric relations between the orientation of the crystals, the faceted cones, and the sputtered spot patterns for Ag, Al, Au, and Pb single crystals with (1 11) surfaces bombarded with 13 keV Ar ions, not analyzed with respect to mass and charge. The crystals of approximately 1 mm thickness were cut from massive rods by means of a diamond wire saw and then cleaned by ion etching in a sputtering chamber. A scanning electron micrograph of the crystal surface cleaned in the above way showed high density of impurities on the surface. The impurities were either condensed cracking products produced during ion etching, or residues from the diamond saw. Intense cone formation was observed when the crystals were bombarded to a total dose of 2 10’’ ions/cm’. Different kinds of cones were found to develop on the bombarded surface-namely, cones with a small apex angle with or without impurities on top, cones with a small angle at the bottom but with a wider apex angle at the top, and completely faceted cones with a wider apex angle. The last type of cones exhibits a six-fold symmetry, ie., three main facets, each being structured into two subfacets. This type of symmetry is similar to that in the sputtered spot patterns. Electron channeling pattern studies showed that the bombarded surface remained single crystalline with the same structure and orientation as the original surface. Ghose et al. (1983a,b, 1984a) studied cone formation on various metals bombarded by Ar+ ions at different doses ranging from 1019to 10” ions/cm2. The metals were polycrystalline Cu and Ni and single cyrstals of Ag with faces parallel to (111) and (100) planes respectively. The results obtained from 30 keV 40Ar+-bombarded Ag single crystals seem to be quite interesting (Ghose et al., 1984a). These are: (a) The cone density is orientation-dependent; it is found to be lower on the (100) face than on the (1 11)face under the same dose of ion bombardment. Onderdelinden (1 968) showed that the sputtering yield S is considerably reduced along low index directions due to the channeling of ions. It is known that the cone is formed in such a way that its surface normal

86

D. CHOSE AND S. B. KARMOHAPATRO

makes an angle 0’ with the ion beam corresponding to the maximum sputtering yield in the angular dependence of the sputtering yield curve (see the following section). Since for an f.c.c. crystal (100) is a more close-packed direction than ( 1 1 l), the rate of erosion of the cones relative to that of the surrounding surface plane will be faster in the case of the (100) face than in the case of the (1 11) face. This implies that cones on the (100)face, if formed, would rapidly disappear with subsequent ion bombardment. Another possibility is that in the low index direction, the range of the ion is long, therefore the energy deposition and near-surface defect production rate are small, resulting in a lower probability of cone formation (Whitton et al., 1980a). (b) Cones are not an equilibrium structure consistent with the observations of Auciello et al. (1980; Auciello and Kelly, 1979). (c) In the latter stages of cone evolution the cones become faceted and pits develop at the bottom. The faceting indicates not only that the angle of ion incidence with respect to the local surface normal is important, but also that the orientation of the local crystal axis to the ion beam plays a significant role in the formation of cones. (d) At low doses of ion bombardment, grain boundaries develop and cones appear on some grains, while on others they are completely absent, as shown in Fig. 1. This is probably due to the fact that the polishing procedure tends to produce randomization of the surface grains that is revealed only at low ion doses where the erosion is small. This phenomenon did not occur when the crystals were bombarded with high ion doses. Finally, (e) a few cones on the (1 11) face are found to bend as shown in Fig. 2. There have been only a few reports of SEM observations of bent cones (Wilson et al., 1984).Belson and Wilson (1982) attributed the effect to bending under the stress associated with the surface tension.

2. Theoretical Considerations The most often proposed mechanisms, which relate to different experimental conditions, for the formation of cones on ion-bombarded solids are the following. In the first mechanism (Wehner and Hajicek, 1971; Stewart and Thompson, 1969), the plateau surface discontinuities caused by lowersputtering-yield impurities shielding the underlying material are modified into conical protrusions during erosion, as a result of the variation in sputtering yield with angle of ion beam incidence. The second mechanism (Gvosdover et al., 1976) is that the surface impurity is necessary for nucleation while the cone later grows by the interplay between sputtering and surface atom migration. Wehner (1985) recently has shown that the impurities need not have a lower sputtering yield as widely believed, but rather a higher melting point. The third mechanism (Whitton et al., 1977, 1978, 1980a) considers the initiation of surface discontinuities by intrinsic or ion-beam-induced defects followed by erosion to produce the final conical or pyramidal protuberance. A

FIG.1. Electron micrograph of the sputtered area of Ag(100) face after 1 x 10'' 30 keV Ar' ions/cm2. The viewing angle in the microscope is 33.5". (a) shows different cone densities on different grains; some grains are completely devoid of cones. White markers = 10 p n . (b) shows cones on one grain at high magnification. White markers = I pn. [After Chose et a/., 1984a.l

FIG 2. Bent cones on Ag(l1 I ) face bombarded by 30 keV Ar' ions to a dose of I x 10'' ions/cm2 The viewing angle in the microscope 15 3 3 5 White markers = I pm.

88

D. CHOSE AND S. B. KARMOHAPATRO

I

I

8'

0

I

so*

9-

FIG.3. Schematic diagram of the angular dependence of sputtering yield S(0).

fourth mechanism was advocated by Auciello et al. (1980; Kelly and Auciello, 1980; Auciello, 1982) where cones originate from pre-existing asperities on the surface combined with the erosion process caused by sputtering. In all the mechanisms of cone formation, the dependence of the sputtering yield on angle of ion incidence plays the major role. If 8 is the angle between the incident ion beam and the surface normal, then the sputtering yield S ( 8 ) follows a sec 8 law only over a limited range for small 8. At large values of 8, S ( 0 ) deviates from the sec 8 dependence, passes through a maximum at 8' between 60 and 80°, and falls towards zero at 8 = 90"as shown in Fig. 3. Such a variation is typical for amorphous and polycrystalline solids, while for single crystals the effect of channeling changes the curve significantly. In the following, the different theories of cone formation are described, where it is assumed that surface changes occur only as a result of atomic ejection, i.e., other processes such as surface diffusion, local variation of binding energy over a surface, and redeposition of sputtered material are ignored. Also, none of the theories take account of directional effects and they are, therefore, only applicable to isotropic materials. Belson and Wilson (1980,1981) have recently published calculations on contour changes of asperities by taking redeposition of atoms sputtered from the area adjacent to the feature into account. Chadderton (1979) has discussed the role of surface energy minimization in the development of the faceted cone or pyramid. a. The Theory of Stewart and Thompson Motion of the intersection between two plane surfaces due to ion-induced erosion was studied by Stewart and Thompson (1969). Figure 4 shows a surface consisting of two inclined planes A and B intersecting at 0.Angles of incidence of ions on the planes A and B are c( and p, respectively. Sputtering changes the positions of the planes

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

89

Ion Beam

FIG. 4. Motion of the intersectionbetween two plane surfaces during erosion. [By permission from Stewart and Thompson, Chapman and Hall,0 1969.1

to A‘ and B’ with the point of intersection moved to 0’.The angle 6 is defined as the angle between the direction of the incident ion and the line 00’.The distances a, b, c, and d are respectively defined as that advanced by the two planes A and B, by the point of intersection, and by the movement of the intersection transverse to the direction of incidence. Each of the planes is bombarded with the flux of ions CDcosa or CD cos 8, where Q, is the flux per unit area normal to the surface. It is evident from Fig. 4 and the geometry of the system that 1 a = -Q, cos as(‘%)= c cos(a

N

1 b = -CDcosps(p) N

+ 6) (14)

=

ccos(8 - 6),

where N is the density of atoms per unit volume. The ratio &a, i.e., the ratio of the distance due to transverse motion of the intersection and the distance of advancement of A, is

Three kinds of movement of the intersection can occur. (i) If S(a) = S(B), d = 0 and 00’does not move laterally; (ii) If S(a) > S(j), d < 0 and 00’moves towards B; (iii) If S(a) < S(B), d > 0 and 00’moves towards A.

Had the angle between A and B been acute instead of obtuse viewed from above as shown in Fig. 4, the direction of motion would have been reversed. In

90

D. CHOSE AND S . B. KARMOHAPATRO

FIG. 5. Evolution of a surface step under ion bombardment. [By permission from Stewart and Thompson, Chapman and Hall, 0 1969.1

conclusion, the crest of a ridge and the foot of a valley will move towards the side for which S(O) is least or greatest, respectively. Figure 5 shows the erosion of a surface step, where the profile 1 can be considered as an assembly of small planar facets such as 0,02on the convex part of the step and O,O, on the concave part of the surface. Applying the above criterion to the corners at O,, O,, 0,, and O,, one can deduce: (i) if 0 <

0, and 0, move to the right 0, and 0, move to the right;

(ii) if 0 > 0'

0, and 0, move to the left 0, and 0 , move to the left;

(iii) if 8 = 0'

0, moves to the left 0, moves to the right

I

and the facet grows;

0, moves to the right 0, moves to the left

I

and the facet shrinks.

Thus, the convex part of the step forms a facet with angle of incidence 0'. The concave part develops a smaller radius of curvature as the corners where 8 < 8' move towards to those for which 0 > O', thereby making a single concave corner. Finally, the profile 3 is obtained, where a single facet at 0' moves across the surface. Using the above results, Stewart and Thompson (1969) have proposed various stages in the formation of a conical structure as shown in Fig. 6. The experimental investigations of Witcomb (1974a) indicate that the cone development schematized in Fig. 6 is essentially correct. If a foreign particle, inclusion, or precipitate located on the surface is exposed to an ion beam, a

A-*-?i-

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

Impur ity. 2:riit-A-

91

FIG. 6 . Cone evolution according to the model of Stewart and Thompson (1969). [By permission from Stewart and Thompson, Chapman and Hall, 0 1969.1

step will first form under the edge of the particle. As the particle itself shrinks, the step will be inclined at an angle 8'. After removal of the shielding particle, the step further contracts inwards forming a cone of apex angle (n - 28') with its axis in the direction of ion incidence. At this stage, the cone tends to rapidly disappear since it erodes in the direction of the ion beam at a rate faster than the surrounding surface plane. b. The Theory of' Curter et al. Carter et al. (1971,1973; Nobes et ul., 1969) have analyzed the evolution of a line contour under ion bombardment when I ions/sec/unit length in the Ox direction bombard a surface in the - 0 y direction, in the plane xOy (Fig. 7). To determine the equilibrium configuration, one should consider the time variation of the spatial location of two points A and B on the surface generator y = f ( x , t ) at t = 0. A t A, the rate of bombardment per unit length of the generator is I cos 8 and the normal rate of recession of the surface is ( I I N ) S(8)cos8; here N is the number of atoms per unit area. The effective rate of recession in the Oy direction is thus

ay

I N

- _ = -S(8)-

at

'1

0

case = -IS ( 8 ) . coso

N

I o n Bomm

11111111

/y-f(x~O)

X

FIG. 7. Geometry of the evolution of a line contour under ion bombardment. [By permission from Nobes er al., Chapman and Hall, 0 1969.1

92

D. GHOSE AND S. B. KARMOHAPATRO

At B, the rate of recession in the Oy direction is -"Y at+ 6 x . g ) = ; s ( 0 + b t ( )

Subtracting Eqs. (16) and (17) and proceeding to the limit lead to the result 1 ay

a

I dS(0) 60 N d0 '6x'

a

Since the surface recedes only in the y direction, -(6x) at

= 0. Therefore,

I dS(0) d0 N d0 dx aY or, since tan 0 = -,

ax a0 I dS(0) d0 _ - _ _ cos2 0d0

N

at

dx

or, again, since S(0) is given approximately by S(0) sec 0 for small 0, a0 I d0 _ - - -S(O)sin0at

N

dx

(0 small).

These are equivalent expressions for the time evolution of the slope of the surface. In equilibrium, the slope of the surface does not change with time, i.e.,

a

-(ay/ax) = 0 for all X . It follows from Eq. (18a) at

I dS(0) d0 = 0. N d0 dx

If S is independent of 0, then either of the solutions of Eq. (19) predicts that a continuous contour of initial slope 0, will recede in the - y direction maintaining a constant slope. Since S is a function of 0, the surface topography changes during sputtering, except in the case of a plane surface. However, dS/d0 = 0 for 0 = 0, 0', and n/2,according to Fig. 3. Therefore, regions of curves initially at these slopes will remain unaltered. For angles other than the above, the change of slope can be followed from Fig. 8 showing a concavedownward surface bombarded in the Oy direction. 0 is initially greater and less

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

93

Sputtered contour after a short t i m e

I

A9 dx

I -V.

FIG. 8. Evolution of a concave-downward surface under ion bombardment. [By permission from hbbes etal., Chapman and Hall, 0 1969.1

d8 dS than 8' in the left and right portion of A respectively. For 6' > O', -, - and dx d8

a

eventually -(ay/ax) are negative. Hence the slope decreases until it reaches at

8 = 8'. Similarly in the 8 < 8' region dH/dx is negative, but dSld8 is positive,

a

so that -(ay/dx) is positive. Hence, the slope increases until the equilibrium at

condition is achieved, i.e., 0 = 8'. The equilibrium topography of a concave downwards curve thus becomes a straight line with a single slope of 8', the same conclusion obtained by Stewart and Thompson (1969). For a concave upward surface, similar arguments show that the equilibrium configuration would be a horizontal line, i.e., 6' = 0 if 0 initially is less than 8' all over the surface, but a vertical line, i.e., 6' N 7r/2 if 8 > 8'. Thus, in the case of a surface contaminated with material of low sputtering yield, a hillock will first develop at the site of each contaminant atom or atom cluster. The surface is then analogous to the concave downward surface of Fig. 8 and will degenerate with bombarding time into a cone of semivertical angle ( x / 2 - 8'). The above theoretical discussion on the changes of surface topography considers a two-dimensional surface. Smith et al. (1981; Smith and Walls, 1980)have proposed a three-dimensional theory of the development of surface topography during ion bombardment, which also includes the effects of surface crystallinity and the multiple stationary points evident in the angular dependence of the sputtering yield of monocrystalline solids.

94

D.CHOSE AND S. B. KARMOHAPATRO

A quite different approach based on the concept that a sputtered surface behaves as a wavefront in kinematic or nonlinear wave theory has been developed recently by Carter and Nobes (1984; Carter, 1986). It was recognized earlier (Carter et al., 1973) that Eq. (18b) had the form of propagating wave in the variable 8, but the effective wave velocity, instead of being constant, was varied with 8. Formalisms for the study of space-time developing wavefronts with nonconstant wave velocity have been developed. Solutions of the wave equation are used to determine the trajectories in space or characteristics that link positions on the surface at successive intervals of time. In geometrical optics, these characteristics have the meaning of optical rays. It was shown that the characteristic method could give important information about the development of edges, facets, and other surface gradient discontinuities.

c. The Theory of Barber et al. For isotropic solids there is a distinct similarity between chemical and ion-beam etching. Barber et al. (1973) realized this and applied Frank‘s kinematic theory of chemical dissolution of crystals (Frank, 1958, 1972) to sputter etching. Frank’s two theorems state: (i) The locus of an elemental area of crystal surface with a particular orientation is a straight line during etching (assuming that the etch rate is only a function of orientation). This line is termed a dissolution trajectory. (ii) The trajectory of this elemental area is parallel to the normal of the polar diagram of the reciprocal of the etch rate at the point of similar orientation (defining the etch rate as measured normal to the actual crystal surface). Before deducing the changes in surface topography during sputtering, Barber et al. (1973) plot the reciprocals of the sputtering ratio S(8)cosfl/S(O) on polar graph paper in accordance with the second theorem of Frank. This curve is called the erosion-slowness curve. Now taking a drawing of the surface of interest, they superimpose the erosion-slowness curve on it and draw the orientation trajectories parallel to the direction of the normals to the slowness curve at corresponding orientations. Finally, the depth eroded is measured along the direction of erosion at points along the surface using the known values of S(8). Thus, the new surface at any given time during bombardment is constructed, and this may be done at successive times to determine how the surface topography develops. The advantage of Barber et al.’s graphical method is that it can in principle be applied to a surface of arbitrary shape. But the shape of the S(8)-8 curve must be known before the evolution of surface topographies can be predicted in detail. d. The Theory of Sigmund Sigmund (1973) described a mechanism that can lead to microroughening of the surface. If an ion is incident non-normally

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

95

on a surface, since it has a finite range, the maximum sputtering effect will not occur at the very point of impact, but further “downstream”. This effect will lead to nonuniform sputtering rates. Applying his earlier sputtering theory (Sigmund, 1969a), Sigmund showed that on a length scale of the order of the penetration depth of the ions, a microscopically flat surface is unstable under high-dose ion bombardment, and cones or grooves develop from small irregularities. It is possible that atom migration could smooth out this effect, so that it should be temperature-dependent. Such hypothetical microscopic features are at the resolution limit of the SEM. Recent investigations of the cone apex region by TEM (Kubby and Siegel, 1986a,b) have shown evidence that supports the mechanism operating on the length scale of ion range. It has been asserted that this mechanism provides a link between the events taking place on an atomic scale and those features that can be predicted from the macroscopic variation of the sputtering yield with the direction of ion incidence. 3. Critical Doses of Cone Evolution

In all the models described above, the secondary and tertiary effects are not included. The secondary effect involves the scattered ions, reflected ions and energetic sputtered atoms from the surfaces of cones, while the tertiary effect involves the energetic sputtered atoms from the inclined grooves’ walls underlying the cones. These effects are very important in modifying the shape of the cones during evolution. More recently, Kelly and Auciello (1980) developed a model in which the effects of secondary and tertiary particles have been included, although in a semi-empirical form only. Kelly and Auciello (1980)considered the evolution of asperities of convexup curvature on an ion-bombarded surface (Fig. 9). Such asperities may initially be present on the surface, or they may originate from intrinsic or ionbeam-induced defects or impurities, the details of which are unimportant. The asperities interfere with the uniformity of sputtering process in two ways. (i) Primary effect: Owing to the existence of a maximum rate of sputtering, S(O’), for a particular large angle O‘, there is a tendency for the surfaces of convex-up features (Fig. 9a) to rotate until facets at angle 0‘ develop and the overall shape becomes conical (Fig. 9b). (ii) Secondary effect: Scattered ions, reflected ions and energetic sputtered atoms from the edges of cones can enhance the sputtering at the bottom. The potentiality for such effects is supported rather well by the work of Reid et al. (1976, 1980) in which experimental evidence is presented for the existence of a significant component of energetic (10- lo3 eV) sputtered atoms from surfaces that were bombarded obliquely. As a result, the cones tend to become better-defined and develop

96

D. GHOSE AND S. B. KARMOHAPATRO ION BEAM

Cb b b b b 4 bC b

+

deflected ions energetic target species C

energetic target {species

FIG. 9 . Schematic diagram showing different stages of cone evolution from a convex-up asperity under ion bombardment. (a) represents an asperity of height h , . This is convex-up at its center and passes through a slope 8‘ at some intermediate width g and height h. [After Auciello er al., 1980. By permission from Gordon and Breach Science Publishers Inc.]

grooves around them as depicted in Fig. 9c. In real systems, however, the shapes of 9b and 9c would develop concurrently. Now the tertiary effect consisting of energetic sputtered atoms from the groove walls comes into play. These particles hit the cones, producing enhanced erosion, which leads to enlargement of the apex angles (Fig. 9d) and their ultimate disappearance. Finally, the ever-enlarging pit remains, as shown in Fig. 9e. Using the formalism of Carter et al. (1971, 1973; Nobes et al., 1969) discussed in the previous section, Kelly and Auciello (1980) derived approximate expressions for the critical bombardment dose of cone formation and disappearance, which is described below: Considering the asperity shown in Fig. 9a, it is evident from the analysis in Section III.A.2 that the top of the asperity where 8 = 0 and the position with 8 = 8’ act as reference points of unchanging 8. For a fully conical shape to

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

97

come out, the following conditions should be met: K(8’)t + h , cot 8‘ = g

or

c K@’)

V,(O)l t

+ h, cot 8‘

(20a)

(20b) where q(8’) is the horizontal velocity of the real or extrapolated intersection of the position with 6 = 6’ and the substrate. The vertical velocity K(8) of a reference point is given by Eq. (16).The horizontal velocity VJ6) of a reference point is determined with the help of Eq. (16) as -

= h, 9

ax I K(6) = - = -S(8)cot 8. at N Since the intersection has both a vertical and horizontal component, it follows (Bayly, 1972) that

The critical dose for cone formation is now obtained from Eqs. (20a), (20b), and (21b) as the larger of ( I t ) , = 0,= N [ g tan 8’ - h ,

+ h2]/[S(8’)- S(O)]

(224

or (It), = 0 1 = N h z / [ S ( B ’ ) - S(O)],

-

(22b)

where O is the number of ions/cm2. In most cases, 8’ 65” and tan 8’ ‘v 2. Then it can be shown that Eq. (22a) corresponds to a “flat” asperity with 29 > h , , while Eq. (22b) corresponds to a “tall” one with 29 < h,. Both Eqs. (22a) and (22b), can be approximated as 2.

N h l / [ S ( O ’ ) - S(O)].

(224

For determination of the dose for disappearance of the cone, the following argument is considered. The vertical velocity of the center of a flat-topped asperity relative to that of the surrounding surface would be initially zero and would remain small until full conical shape is evolved. At this stage the relative vertical velocity would be K(0’) - K(O), and the condition that a cone of height h would disappear is

[V,(8’) - V,(O)]r ‘v h + j , (23) where j is the depth of the groove underlying the cone. Thus Eq. (23) includes the overall effect of secondary and tertiary particles. The total critical dose for cone existence O3can be considered as the sum of those for formation,

98

D. G H O S E AND S. B. KARMOHAPATRO

Eq. (22c), and disappearance given by

Q2,

derivable from Eq. (23). It is approximately

Q3 = N ( 2 h

+ j ) / [ S ( 8 ' ) - S(O)]

(244

or, assuming h = j , Q3 N

3 N h / [ S ( 8 ' ) - S(O)].

Kelly and Auciello (1980) found that the doses calculated with Eq. (24) are in reasonable agreement with the experimental values. 4. Cone Apex Angle From the theories of cone formation described in Section III.A.2, it appears that the variation of the sputtering yield with the angle of ion incidence plays an important role in the formation of surface cones, and the apex angle, a,, of such cones is given by the relationship a, = 180" - 28'.

(25)

The angle 8' is generally believed to be that critical angle beyond which the incoming ion has a probability of being reflected from the potential barrier presented by the surface atoms. As the value of (8 - 8') increases, both ion penetration and the sputter yield of the target rapidly decrease. Such a case of ion reflection can be considered somewhat analogous to channeling. Consequently, the theoretical analysis of directional effects in penetration of charged particles through crystal lattices by Lindhard (1965) lends itself to the problem. As 8' is generally in the range 60-80", it is assumed that the channel direction is very close to the surface. If t,b is the critical angle of channeling with respect to the target surface, then

8' = 900

- t,b.

(26)

Stewart and Thompson (1969) first determined the value of a, using Lindhard's theory of channeling. Later, Witcomb (1974b), generalizing their approach, described different methods of calculation to compute 8' and hence a,. In the following we discuss first the calculations of Witcomb (1974b) and then our own (Ghose, 1979). All the calculations that predict the cone apex angle are based on the same calculated planar potential from Lindhard (1965):

where N is the atomic density of the plane, y the distance of the ion from the plane, and V ( R )the ion-atom potential for separation R .

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

99

Using Lindhard’s standard atomic potential (Lindhard, 1965), Eq. (27) becomes Y(y)

=~

z Z , Z , ~ ’ N ~ ’ ~+[ 3u-f,)”’ (~’

-

y],

(28)

where uTF= 0.8853~,(2:’~ + Z:’3)-1’2.the Thomas-Fermi screening length. Thus in the surface plane, i.e., y = 0, the potential has a finite value, Y(0)

=

~ZZ,Z,~’N’’~&U~~.

(29)

From transverse energy and collision time considerations, the minimum distance of approach of an ion of energy E to a surface target atom is determined by the relation Y(0) = E sin’ t+h.

(30)

Equation (30) assumes that the deflection in the single collision is smaller than the total scattering angle. To a first approximation, $ can be written as

where e has been replaced by the Rydberg energy E, through the relation e’ = 2aoE,, and t,b is given in degrees. Since the continuous planar potential barrier of the plane is generally not nigher than = Y(0)/2, we have from Eqs. (26) and (31)

x,,

where 9‘ is in degrees, E in eV, and N in A units. This is essentially the expression quoted by Stewart and Thompson (1969),but with a square root in the denominator and a factor 347 instead of 443. The difference is due to use of an inverse-square form of the ion-atom potential (Thompson, 1969). At the lower-energy bombardment range, the barrier height becomes somewhat lower, and hence one would expect a somewhat smaller multiplication factor than 347 in Eq. (32). Since the extent of this reduction is not known, Eq. (32) is assumed to hold over the whole energy and atomic-number range, and the expression for the cone apex angle obtained from Eqs. (25) and (32) is

100

D. CHOSE AND S. B. KARMOHAPATRO

When compared with the experimental data collected by Witcomb (1974b), Eq. (33) gives satisfactory results only in the energy range between 20 and 30 keV. Below 20 keV the calculated values of a, are always greater than the measured values. The discrepancy between the theoretical and experimental values is also seen to increase rapidly with the decreasing value of Z2IZl. The second expression for a, can be obtained by a more rigorous solution of Eq. (27). If it is assumed that the incident particle happens to have a lattice atom directly below its orbit at the minimum approach distance, it can be shown (Lindhard, 1965) that the solution takes the form of

where i= ymin/fiaTFis a dimensionless parameter and E , = ( Z , Z 2 e 2 ) / (2n3&a&NZi3). Witcomb treats this basic inequality as an equality, substitutes the string expression rmin= d'$ for yminrand calculates values of $. The relevant solution of (34) is given by

Substituting the necessary values into the above equation yields the expression

To obtain a value for a,, Witcomb takes the value of d' as the closest packing distance between atoms in the string and finds that the cone apex angle can well be predicted by Eq. (36) in the energy range 0.2 to 30 keV for all types of incident ions and target elements. A further case is considered by Witcomb at very low energies, i.e., below 1 keV where the more appropriate interatomic potential is the Born-Mayer potential V(R) = A exp( - R/a,,), where A and aBMare usually determined phenomenologically, say by fitting the elastic moduli. In the surface plane, y = 0, the continuum planar potential (27) takes the form

:l

Y(0)= 2rtAN2I3 =2

R eXp( -R/a,,)dR

n ~ ~ * a;M. /3.

(37)

Applying Eq. (30) and assuming as previously that the effective potential Xff = Y(O)/2,it can be shown that a, = 203[

~

~

2

'

]

3 112 ~

;

~

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

101

Using the values proposed by Andersen and Sigmund (1965) for A = 52(Z,Z2)314 eV and for aBM= 0.219 A, it is found that although Eq. (38) produces reasonable values at 1 keV, at other ion energies the calculated values are much inferior to those obtained from Eq. (36). From the above analysis of Witcomb, it appears that the cone apex angle can best be determined by Eq. (36). However, one should note that Witcomb’s expression contains two target lattice characteristics, namely, N , the number of atoms per unit volume, and d’, the distance between the atoms in a string. A fit with the experimental values is obtained by taking the d’ values as close-packed values. This can only be justified for single crystals where atoms are found to be ejected along low-index crystallographic directions. When a polycrystalline material is bombarded with energetic ions, no such preferential ejection of atoms occurs owing to the presence of grains of various orientations. Thus, it would be more appropriate to choose some form of statistical average atom spacing rather than the closest packing separation. It therefore seems questionable to use Witcomb’s relation with a randomly oriented target. In order to derive (Ghose, 1979) an expression for 8’, it is also important to choose an appropriate potential function. Published data reveal that for a certain projectile- target system, 8‘ varies slowly with projectile energy. This fact is also supported by Wilson and Kidd (1971),who obtained 8‘values from the measurement of the apex angle of cones developed on polycrystalline gold surfaces under argon and xenon ion bombardment at 5 to 20 keV. For this reason, they suggested that the interaction potential between the incoming ion and the target atom should be very sensitive to separation. One may, therefore, proceed with a power law potential function for the calculation of 8’. Onderdelinden (1968) used a R - 3 power potential in his theory of sputtering, which is suitable in the low-energy region. This potential has the form 3 ZlZ2e2a& V ( R )= (39) 2 R3 ’ The average planar potential corresponding to this interatomic potential is obtained from Eq. (27) as

In planar channeling, the projectile is steered by planes of lattice atoms. If one takes the mean separation of successive atoms in the plane along the projectile path as N - 1 / 3(Francken and Onderdelinden, 1970), then from the condition for continuum approximation one obtains (41)

102

D. CHOSE A N D S. B. KARMOHAPATRO TABLE I COMPARISON BETWEEN PREDICTED 0'. EQ. (42), OBSERVED

8'

VALUES OF OECHSNER

Projectile and target

E (keV)

@(theor) (degrees)

Ar+-AI Ar+-Ti Ar+-Ni He+-Cu Ne+-Cu Ar+-Cu Kr+-Cu Xe+,-Cu Xe+-Cu Xe+-Cu Xe+-Cu Ar+-Zr Ar+-Pd Ar+-Ag Ar+-Ta Ar+-Au

1.05 1.05 1.05 1.05 1.05 I .05 1.05 2.05 1.55 1.05 0.55 1.05 1.05 1.05 1.05 1.05

71.7 69.8 65.1 76.6 68.9 65.5 61.3 65 62.6 58.8 51.4 69.3 65 66.2 64.1 63.8

Substitution of the value of the expression

AND

(1973.1975)

B'(expt) (degrees) 70.5 70.5 71 71 70 61.5 65.5 70 65 60.5 56 68 60.5 61.5 65 58

II/ in Eq. (26) and further simplification yield

For illustration, the values obtained from Eq. (42) are compared with the results of Oechsner (1973, 1975) (Table I) and Evdokimov and Molchanov (1968) (Table 11). It is evident from Tables I and I1 that the agreement between calculated and measured 8' values is quite satisfactory at both low and high keV energies and also for different projectile- target systems. Thus, the approximation of the mean separation of lattice atoms with a suitable interaction potential can well replace the close-packed spacing d', which is actually not necessary for a polycrystalline target. In all the calculations described above, the angle 8' represents the critical angle for ion reflection. Chadderton (1977) has pointed out a mistake regarding the measurement of this angle. The resemblance between the ion reflection and channeling is more conspicuous when one studies the angular variation of sputtering yield normalized to the yield for normal ion incidence. The curve shows a characteristic shoulder as well as a characteristic trough (Fig. 10). While the former is caused by a process similar to quasichanneling,

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103

TABLE I1 COMPARISON BETWEEN PREDICTED 0', Ey. (42). AND OBSERVED 0' VALUESOF EVDOKIMOV AND MOLCHANOV ( 1968) Projectile and target

E (keV)

O'( theor) (degrees)

Ne+-Ni Ar+-Ni Kr'-Ni Ar'-Cu Kr+-Cu Ne+-Mo Ar+-Mo Ne*-Ag Ar'-Ag Kr+-Ag

30 30 25 21 25 30 21 30 30 25

83 81.8 79.8 81.7 80 83.3 81.8 83.3 82.2 80.2

O'(expt) (degrees) 83 81 79 80 80 82 80 82.5 81 79

t * 1 S(0)

-

0

0-

e'

e' so.

FIG. 10. Schematic diagram of the angular dependence of normalized sputtering yield S(@/S(O). The "trough" is characterized by the critical angle 8". [After Chadderton, 1977. By permission from Gordon and Breach Science Publishers Inc.]

the latter is generated by ion reflection following correlated collisions with surface atoms. At the angle O', for which the maximum in the shoulder is reached, the ions penetrate and violently sputter the target, whereas at the angle t)", measured at half-minimum corresponding to the oneset of the trough, the ions are not able to surmount the potential barrier presented by the surface atoms. Hence the calculated value of O', although apparently agreeing with 8' (expt.), actually corresponds to the angle at half-minimum rather than the maximum in the shoulder. However, experimentally it is difficult to resolve

104

D. GHOSE AND S . B. KARMOHAPATRO

TABLE 111 COMPARISON BETWEEN PREDICTED ac, EQ. (43), AND OBSERVED a, VALUES OF WILSON AND KIDD(1971) FOR POLYCRYSTALLINE AIJ Bombarding ion type

E (keV)

a,(theor) (degrees)

aSexpt) (degrees)

Ar Ar Ar Xe

5 10 20 20

31.1 24.68 19.59 25.93

36.5 k 0.5 33.0 0.5 27.5 0.3 40+ 1 59k 1

+ +

the dilemma of whether the cone apex angle relates to the angle 8' or 8", as the errors in the measured values are relatively large compared to the small difference between the angles. The cone apex angle calculated from Eq. (42) is given by

Tables I11 and IV show the comparison between the predicted a, values from Eq. (43) and the observed a, values of Wilson and Kidd (1971) for Ar- and Xebombarded gold and of Tanovik et d. (1978) for Ar-bombarded copper. The latter one shows that the agreement between the two sets of values is reasonable. Some comments are required regarding the influence of various factors on the apex angle of cones. First, one must consider the effects of secondary and tertiary particles on the cone apex angle a,. As discussed in Section III.A.3, TABLE IV COMPARISON BETWEEN PREDICTED a,, EQ. (43), AND OBSERVED a, VALUES OF TANOVIC ET AL. (1978) Ar+ + CU E (keV)

a,( theor) (degrees)

a,(expt) (degrees)

20 40 60 80

18.3 14.8 12.1 11.5

23 k 3 18k3 15 2 13k2

+

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

105

these particles tend to increase the value of a, with the increasing dose of ion bombardment. This is experimentally shown by Auciello and Kelly (1979) in the dose range -(6 x 10'' to 3 x lOI9 ions/cm2). Tanovic and Tanovic (1987), on the other hand, noted enlargement of cone apex angle only in a limited range of ion dose - ( 5 x 10'' to 2 x 10" ions/cm*). After reaching a certain maximum value, the apex angle decreases and finally maintains a certain stable value at higher ion doses k 7 x lOI9 ions/cm2. In the dose range 3.4 x 10l6 to 3.4 x 10'' ions/cm2, Nindi and Stulik (1988) observed an initial faster increase of the average apex angle before the angle levels off at doses greater than about 2.3 x 10'' ions/cm2. Other relevant factors that may change the position of the sputter-yield peak, O', and hence the value of ac,are the target temperature and the anisotropy of the collision cascades at low keV energies (Witcomb 1977a,b).Finally, it should be noted that though the cone apex angle is weakly dependent on ion energy, it has a much stronger dependence on the crystal orientation as observed for Cu (Tanovic, 1981)and Pb (Erlenwein, 1977) crystals. This is in conformity with the finding that in single crystals the final pyramid form is dictated largely by the crystallographic habit (Whitton et al., 1980a).

5. Experimental Techniques and an "Ideal Experiment "

Usually cones are formed by impurity contamination of the target surface during sputtering. In the absence of impurities, ion bombardment in properly chosen high index crystal directions can result in a high density of cone formation (Whitton et al., 1980a). Techniques to prepare surfaces with dense arrays of cones in low-gas-pressure plasmas created with RF, or in DC diode or DC triode discharges, were described by Wehner and Hajicek (1971; Wehner, 1985), Berg and Kominiak (1976), and Kelly and Auciello (1980). Rossnagel and Robinson (1982a; Robinson and Rossnagel, 1982) used a broad-beam high-intensity ion source such as a Kaufman ion source for impurity-induced sputter cone formation. It is noted that the temperature of the sample is critical for surface mobility of impurity atoms or adatoms, which is inevitable to initiate the formation of conical structures. Recently, Linders et al. (1986a,b) described the method of contamination lithography for the generation of microcones. The target surfaces are first provided with defined three-dimensional carbonaceous deposits at desired positions by electron-beam-induced contamination in an SEM, and then sputtered with 12.5-24 kV Ar' ions. The contamination process depends on beam size, current density, electron energy, residual gas composition, target surface condition, and temperature. For a great height-to-diameter ratio of the contaminant, a stationary focused electron beam is necessary, whereas a scanning

106

D. GHOSE AND S. B. KARMOHAPATRO

beam generates high-volume contaminants. For perpendicular ion incidence, microcones are obtained. For oblique incidence of 25" and target rotation around the surface normal it is possible to obtain cylindrical microstructures, and for irradiation under 45" with target rotation, one obtains double cone structures. Wilson (1974)and Naviniek (1976)described the conditions of an "ideal" ion bombardment experiment in which no surface features should develop. In such an experiment, the target should be a random one, ultrapure and with a smooth and homogeneous surface. No gas contamination of the surface from the environment is allowed. The ion beam should be magnetically analyzed, chemically inert, and normally incident on the target. When such conditions are fulfilled, one can decide what perturbation of the surface will be introduced in order to follow the development of cones in isolation from other effects. In real systems, however, the target surface tends to become more or less contaminated. Hence, a careful preparation of clean and smooth surface is necessary. The experiment should also be performed in an ultrahigh vacuum system ( p < lo-' torr). Whitton (1978) discussed the role of various factors related to the beam and target in the determination of depth profiles by sputtering. He showed that the beam impurity, changes in beam current, angular divergence of the beam, orientation effect of the target crystal, lattice defects, surface impurity, departure from the flatness of the surface, and bad vacuum in the target chamber-each of these tends to produce cones, pyramids, and etch pits, which often obliterate the underlying physics of the development of topography. One therefore demands a well-defined beam on a well-defined target in well-defined environments. Roberts (1963) and Verhoeven (1979) have reviewed different techniques to obtain atomically clean surfaces and their relative advantages and disadvantages. Before installation in an ultrahigh vacuum system, a pretreatment of the sample is required. After mechanical, chemical, or electropolishing and washing in alcohol, trichloroethylene, or acetone in an ultrasonic cleaner, the sample is finally cleaned in the vacuum system. There are several methods of cleaning: high-temperature heating, gas-solid surface reactions, sputter ion cleaning, electron-stimulated desorption, and cleaving. Even in high vacuum, one can maintain a dynamically clean surface, if the rate of removal of the atoms from the surface by sputtering exceeds the rate of contamination by the residual gases. In order to minimize the contamination of the target surface by foreign atoms sputtered from the beam-defining apertures, the final aperture is usually kept at a large distance, say 40 mm (Whitton et al., 1977), from the target. In addition, sometimes diaphragms made of the same materials as the targets are used (Auciello et al., 1980). Most of the experiments reported so far are a two-step process, i.e., one bombards the sample in the ion beam system to the specific dose level and then

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

107

transfers it to the electron microscope for observation. However, in order to follow the development of conical structures and the evolution with successive ion bombardment, i.e., for a quasidynamic investigation, in-situ bombardment and observation are required. Such an arrangement, i.e., an SEM with a builtin ion source, was first used by Stewart (1962), and later several such on-line systems have been reported (Stewart and Thompson, 1969; Weissmantel et al., 1974; Dhariwal and Fitch, 1977; Hauffe, 1978; Lewis et al., 1979, 1980a,b; Carter et al.,1984; Goto and Suzuki, 1988). Buger et al. (1978) used an SEM that was equipped with an energy-dispersive x-ray (EDX) spectrometer to detect the type of the impurity atom and its concentration at the top of the cones. Finally, it should be noted that in many experiments, development of any surface structure during ion bombardment is deleterious to the problem under study. Sample rocking and rotation are the techniques that are used to minimize the growth of unwanted topography when using ion beams to mill or thin samples (Lewis et al., 1986). The use of two static ion beams symmetrically inclined about the surface normal also partially alleviates the formation of ion-induced sputtering structures (Makh et al.,1982). Reactive ions such as N:, O:, and C1' sputtering, or a suitable choice of gas mixture, e.g., Ar/O, sputtering, are found to be beneficial for obtaining a comparatively smooth surface (Hofer and Liebl, 1975; Tsunoyama et al., 1974, 1976; Begemann et al.,1986; Katzschner er al., 1984).

B. Fuceting The term faceting includes various surface structures such as steps, terraces, furrows, channels, facets, pits, etc. The phenomenon of ionbombardment-induced reorientation of crystallites in thin films has also been discussed, by Auciello (1984b), in the context of faceting. The earlier works by a number of authors (Ogilvie, 1959; Haymann and Waldburger, 1962; Fluit and Datz, 1964; Cunningham and Ng-Yelim, 1969; Hermanne and Art, 1970; Elich et al., 1971) have shown that faceting during ion bombardment of single crystals is a general phenomenon. The {loo} and ( 1 1 1 ) faces of f.c.c. single crystals are generally most stable under ion bombardment (Ogilvie, 1959; Fluit and Datz, 1964; Chadderton et al., 1972; Lyon and Samorjai, 1967; Nelson and Mazey, 1967; Rhead, 1962). In addition to the thermodynamic stability of the crystal face, the focusing and channeling effect and the presence of reactive gases such as mercury and oxygen during ion bombardment seem to be principally linked to the development and enhancement of facets. Wehner (1958) presented an early evidence of characteristic etch-pattern formation in Ge bombarded by 100 eV Hg' ions. He observed pits having

108

D. CHOSE AND S. B. KARMOHAPATRO

FIG. 11. Pit formation in Ge after Ar' bombardment at adose > 10'' ions/cm*. The viewing angle in the microscope is 33.5". White markers = 10 pm (Ghose, 1982).

four-, three-, and two-fold symmetry on (loo), (1 1 l), and (1 10) surfaces respectively. Ghose (1982) observed regular pit formation in Ge by highenergy (20-30 keV) Ar' sputtering (Fig. 11). Symmetric pit formation, similar to that of Wehner (1958), in Cu single crystals was reported by Tanovic and Perovic (1976). Detailed examination of pit shapes revealed that pits are square or eight-angular on the (100) plane, triangular or six-angular on the (1 11) plane, and rectangular or trapezoidal on the (1 10) plane. The symmetry of these microrelief figures is strongly correlated with that of sputtering ejection patterns from the respective planes. The authors also noted that on well-polished and very clean single crystal samples, the surface relief structures were weakly expressed and uniformly distributed over the whole surface in accordance with the model of Hermanne and Art (1970; Hermanne, 1973). Ghose et al. (1984a) found that pits on 30 keV Ar+-bombarded Ag ( 1 11) crystal were conical and strongly faceted with a sixfold symmetry similar to that in the sputtered ejection pattern from the same face (Fig. 12). This similarity suggests that the alternate facets of the pits correspond to (110) planes, while the remaining facets are the (100) planes. According to the analysis of Smith et al. (1981), each of the facets of the pit corresponds to the direction of the minima of the angular dependence of the sputtering yield curve for a monocrystalline solid. Close inspection of Fig. 12 also reveals that the facets contain fine-scale ripples with a spacing of about 10,000 A. Similar background ripple morphology was found in major etch pit regions (Whitton et al., 1977), near protruding pyramids (Whitton et al., 1978; Stewart and Thompson, 1969) and also on the pyramid facets (Erlenwein, 1978). It is generally concluded that this is associated with elaboration of the subsurface

FIG. 12. (a-c) are electron micrographs showing faceted pits on the Ag(ll1) surface with a sixfold symmetry. (a) is after 5 x lo" 30 keV Art ions/cm2, and (b) and (c) after 3 x l O I 9 30 keV Ar' ions/cm*.The viewing angle in the microscope is 33.5".White markers = 1 pm. (d) shows the sputtered spot pattern from an Ar-bombarded Ag(l11) surface. [After Chose et al., 1984a.l

110

D. CHOSE AND S . B. KARMOHAPATRO

dislocation network that forms to relieve stress generated by ion-beaminduced defects. In the same experiment of Ghose et al. (1984a), it was also observed that when the bombarding ion dose is very high ( N 10" ions/cm2), terrace steps are developed. Fig. 13 shows typical terrace steps on an Ag(100) surface after 8.3 x 10'' ions/cm2. These are probably formed according to the mechanism proposed by Bayly (1972).When a curved surface is exposed to an ion beam, the rate of rotation of the surface tangent caused by sputtering is given by Eq. (18). Considering the enhancement of the particle flux at the foot of steep slopes due to scattered ions and energetic sputtered atoms, it can be shown (Bayly, 1972) that pits where the local slope initially exceeds 8' will develop with bombarding time into steps of 90" walls and 0" bases. In many sputtering experiments, polycrystalline targets are used. When such a target is bombarded by energetic ions, there will be a differential sputtering due to the presence of individual grains. As a result, a stepped surface topography usually develops, as shown by Tortorelli and Altstetter (1980) in Ar+-bombarded Nb (Fig. 14). Sometimes surface structures may develop on some grains, while other grains remain completely unaffected (Mazey et al., 1968).

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

111

FIG. 13. Electron micrograph showing terrace steps on an Ag( 100)surface after 8.3 x 30 keV Ar' ions/cm2.The viewing angle in the microscope is 33.5". White markers = 10 pm, [After Ghose et al., 1984a.1

FIG. 14. Electron micrograph of a polycrystalline Nb surface sputtered with 7 x 10" 15 keV Ar' ions/cmz.The angle of ion incidence is 22'. [After Tortorelli and Altstetter, 1980. By permission from Gordon and Breach Science Publishers Inc.]

1. InJuence of Facering o n Sputtering

Solid surfaces subject to energetic particle bombardment generally develop characteristic surface structures due to sputtering. Once the structures grow, on subsequent bombardment they must give rise to changes in the integral and differential sputtering yield from that of a flat surface. This is the consequence of two competing effects: a yield increase by an enhanced

112

D. GHOSE AND S. B. KARMOHAPATRO

effective projectile incidence angle, and a yield reduction by recapture of obliquely ejected particles by the protruding elements of the structure. Gurmin et al. (1969) first calculated the effect of surface structures on sputtering yield and showed that even heavily structured surfaces reflect the same emission distribution from a flat surface. Their conclusion that the topography has no influence on the differential yield was drawn because some special cases were generalized that had been taken as representative of the phenomenon as a whole. The analytical calculations of Littmark and Hofer (1978), on the other hand, show that surface structure exerts a profound influence on the sputtering yield. The calculation is based on the following assumptions: (i) The surface structures are stable under the chosen irradiation conditions. That means the facet angles remain unaltered during bombardment, though the individual facet may move across the surface. (ii) The facet planes are large enough so that edge effectscan be neglected. (iii) Only the ascending branch of the yield vs. incidence angle curve, which extends from zero to about 70"(see Fig. 3), is included in the calculation. This means that reflection of projectiles from facet planes, and therefore enhanced sputtering from facet bottoms, is neglected.

In Fig. 15 the faceted surface is characterized by the facet planes A and B, which are inclined at the angles tl and /Ito the nominal (macroscopic) surface plane of the crystal. A polar coordinate system is constructed on each of these three planes where the surface normals are the polar axes and the plane of symmetry of the facets is the azimuthal reference plane. B indicates the direction of bombardment or the direction of observation, as the case may be. All quantities related to facets A or B are indicated by the respective superscripts, while those referring to the nominal surface have no index. The

FIG. 15. Definition of structure parameters, coordinatesystems, and reference planes. [By permission from Littmark and Hofer, Chapman and Hall, 0 1978.1

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

kton c,'

h.cota

'

113

h.cotp

FIG. 16. Characterization of the variables E and x , shadowing limit E(x), and beam partition. [By permission from Littmark and Hofer, Chapman and Hall, 0 1978.1

relation between 8* or OB and 8 is given by cos BA = cos 8 cos a - sin 8 sin LY cos cp cos ON = cos 8 cos p

+ sin 6 sin fl cos cp.

(44)

The shadowing effect, i.e., the recapture of sputtered particles by the neighbouring facet plane, can be understood in Fig. 16, which is the projection of Fig. 15 on the symmetry plane for the facets. The angle that the direction of bombardment or the direction of sputtering emission makes with the nominal surface normal is denoted here by E. E is connected to the polar coordinates by tan(a - E ) = tan BA cos rpA

- cos 8 sin a + sin 8 cos LY cos cp -

tan@

+

cos 8 cos a - sin 8 sin a cos rp

E)

= tan dBcos cpR

- cos 8 sin p - sin 8 cos p cos cp

c o s B c o s ~+ sin8sinpcoscp'

(45)

The directional region where sputtered material from part of plane A is shadowed by plane B is n c0 > - - p

or

2

-1

< cos cp, < - cot pcot O0

(case I). (46)

Similarly, the directional region of shadowing by plane A is E,

n

< a -2

or

cot a cot 8, < cos cpo < 1

(case 111),

(47)

114

D. GHOSE AND S. B. KARMOHAPATRO

and the region where sputtering emission is not hindered is 71

71

2

2

C ( - - < E , < - - ~

or

-cotpcot8,
(caseII). (48)

The differential sputtering yield dS(Fi,Fo)/dR, is defined as the number of particles emitted per solid angle element dQo around eo per projectile impinging on the surface from direction Fi. Provided that the shape of the emission distribution for a flat surface is not dependent on the projectile incidence angle, the differential yield from a flat surface can be written as dS(Fi,e,) = fi(Fi)f,(F,) dRo

= fi(C0s ei)jo(coseo)m,.

(49)

In Eq. (49) it is further assumed that the emission distribution has no azimuthal dependence, which is quite reasonable for amorphous and polycrystalline targets and even for single crystals where random emission always dominates preferential emission. Now, the sputtering from a faceted surface can be calculated as the linear superposition of the sputtering from the A and B planes separately, taking into account the shadowing effects. After some trigonometric calculations it can be shown that

--

-

dQ0

I

cos 8B + f i ( C 0 S e;)---fo(cos cos ei

COS e; er)--f0(~~~ e:)cOS ei

~~(COS

0:) cos 6, cOS

e:

sin u sin(u 8)

+

case 11, and

case 111.

From Eq. (50) the total yield S is obtained by integration over the whole free space of emission, i.e., c1 - 1 < E, 1- B. To perform the integration one must know the form of emission distribution function. Experimentally it is found (Vossen, 1974; Oechsner, 1975) that for polycrystalline targets under perpendicular ion bombardment, particle ejection occurs symmetrically to the target normal, changing from an undercosine distribution at bombarding energies of some 100 eV to an overcosine shape at energies above some keV. Emmoth and Braun (1977) have

-=

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

1 15

shown that the angular distribution function can be fitted to a sum of a c1 cos 0 and a c2 cos20 term, where c1 and c2 are arbitrary constants but depend on bombarding energy and ion-target combinations. Accordingly, Littmark and Hofer (1978) considered a power form of fo, fo(cos 0,) = (COS OO)mo,

m, = 1,2.

From these two terms one may construct undercosine as well as overcosine distributions. The incoming projectile flux distribution is of the form fi(c0~ ei) = ci(cose i ) m l ,

mi < 0,

(52)

where ci is a constant depending on energy and the type of ion and target. Since only the ascending branch of fi(cos Oi) is considered, the relation based on Eq. (52)is limited to Of,0; ,< 70". Inserting Eqs. (51) and (52) in (50),one can obtain the explicit expression for the differential yield, and by integration the total yield. Several interesting conclusions can be drawn by examining Eq. (50) for various combinations of rn, and mi as discussed in detail by Littmark and Hofer (1978). For most of the experimental data at medium to high projectile energy, mo = 1, which gives SA+B/S > 1 for mi < - 1. Since mi usually lies between - 1 and - 2, the results show that the yield from a faceted surface always exceeds the yield from a flat surface. Furthermore, provided the projection of the beam on the nominal surface does not coincide with the line of intersection of the facet planes, it can be shown that there are remarkable distortions in the shape of the emission distributions caused by the influence of faceting when the projection of the direction of observation on the nominal surface is away from the line of intersection of the facet planes, particularly along the line normal to it. The inferences drawn for a faceted surface topography are equally pertain to cone/pyramid-covered surface. The relative importance of yield enhancement due to oblique ion incidence at the cone surface and the yield reduction due to shadowing by the neighbouring forest of cones obviously depends on a number of factors-namely, crystallographic structures of the cones, cone heights, cone apex angles, and the density of cones over the surface, the overall effect of which is reflected in the emission distribution and the total yield. Thus, Whitton et al. (1980b) observed -50% greater overall sputtering yield from the pyramid-covered (11 3 1) Cu surface than from the flat surface of the same orientation. Besocke et al. (1982) also reported similar results in the case of Ag sputtering. Mattox and Sharp (1979),on the other hand, found 30-40% lower yield in the case of needle-like cone morphology, indicating the prevalence of the recapture of released sputtered particles. Kundu et al. (1985) have measured the angular distribution of sputtered Ag particles at high-ion-dose-induced sputtering where conical protrusions

116

FIG.17. (a) Angular distribution of sputtered Ag atoms after 7 x 10" 30 keV Ne+ ions/cmz bombardment, the angle of ion incidence being40". Curve I shows thedistribution in the plane of incidence, and curve I1 in the plane perpendicular to it. Open circles are the experimental points, while the solid curves through the data points show the trend of experimental variation. (b) Scanning electron micrograph of the sputtered Ag surface showing cones. The ions are incident from the right. The viewing angle in the microscope is 0".White markers = 1 pm. [After Kundu et a/., 1985.1

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

117

are formed at the surface. The angular distribution is found to be symmetric with respect to the surface normal, and overcosine at normal angle of ion incidence, whereas at an oblique angle of ion incidence, the distribution is asymmetric in the plane of incidence and symmetric in the orthogonal plane. Fig. 17 shows a typical angular distribution curve for 30 keV Ne' bombardment at oblique incidence of 40°, and the corresponding electron micrograph of the Ag surface. The cones are seen to be aligned along the direction of the beam. The results can be understood qualitatively from the above analysis of Littmark and Hofer (1978). Yamada et al. (1979) also estimated surface microstructural effects on the angular distribution and showed that the grain size has an influence both on the surface topographic changes and the angular distributions. 2. Surface Modijications in Semiconductors Semiconductor materials have wide applications in the microelectronics industry-the trend of which is towards the fabrication of integrated circuits with increasingly high density and devices with progressively smaller features (Lee, 1979). Microelectronic circuit fabrication is based on the ability to remove and add material selectively from and to the surface of a suitable substrate. At present wet chemical, plasma and sputtering methods are used to etch the required structures. To sputter-etch the target material, an ion beam etching or ion milling technique is utilized in which bombardment is by lowenergy ions such as Ar'. This technique has several advantages. Firstly, ion beams can be used to etch any material, even those with a multilayer structure that might be difficult using wet chemical etching and other dry etching techniques. Secondly, its high controllability allows the generation of patterns down to submicrometer dimensions (Melliar-Smith, 1976; Somekh and Casey, 1977). Since the geometrical and electronic properties of etched surfaces affect device characteristics, it is important to study the damage and topography generated by ion bombardment. Low-energy ion bombardment also has important application in the analysis of electronic materials, such as by secondary ion mass spectrometry (SIMS). Inert-gas or reactive-gas ions are used as primary excitation agent in SIMS to obtain the depth distribution of dopants and contaminants in semiconductors. The development of any topography during bombardment may constitute resolution limitations in depth profiling. Thus care should be taken in the choice of primary ions and also the dose for minimizing topography development. In semiconductor technology, Si is most widely used material because silicon devices exhibit much lower leakage currents. Recently, compound semiconductor technology has got attention for having electrical and optical properties that are absent in silicon. These semiconductors, e.g., GaAs and InP, are used mainly for microwave and photonic applications.

118

D. GHOSE AND S. B. KARMOHAPATRO

Wilson (1973) pioneered the systematic investigation of the topography of a number of semiconductors after 40 keV Ar' bombardment. Si, Ge, GaAs. and InP exhibit relief structures in the form of undulating surface and narrowangled cones, which, however, can be removed by continued sputtering. Such a behaviour is consistent with an amorphous surface. The other group of materials studied, namely, CdTe, CdS, and Gap, are found to retain their crystal structure at the surface after sputtering, and the topography developed depends sensitively on the beam orientation. In the case of InSb, the surface appears to undergo a chemical change and tall whiskers grow from the indium-rich areas. Among the semiconductor materials, Si is the most widely studied element both by inert-gas ions such as Ar' and reactive-gas ions such as 0; and Cs' ions. The group of Carter et al. (1977, l982,1984,1985b,c;Lewis et al., 1980b; Begemann et al., 1986) studied extensively inert-gas irradiation-induced topographic changes of Si. The surface morphology development critically depends upon ion fluence or depth eroded. In the fluence range 1019lo'' ionsjcm', following an initial period of the production and expansion of individual etch pits, these overlap to form a terraced or corrugated ripple structure, the amplitude and wavelength of which increase with increasing ion fluence and mean eroded depth. A sequence of micrographs of Ar+-sputtered Si surface with ions incident at 45" to the surface normal is shown in Fig. 18 to exemplify this behaviour, as a function of increasing ion fluence. The ripple habit alignment lies transverse to the projection of the ion flux on the surface plane. For 70"to normal incidence a corrugated appearance also persists, but habit alignment is now parallel to the surface projection of the flux. At normal incidence, however, there are only few etch pits and the surface appears relatively plane. It was further noted (Lewis et al., 1986) that surface terracing or rippling no longer occurs over the mean sputtered surface under sample rocking and rotation or distributed ion flux conditions. Surface topography minimization also occurs if the surface is pre-irradiated at low ion fluence (Carter et al., 1984). For 0' irradiation no clearly definable microscopic morphological evolution was obtained up to fluences of lo'' ions/cm' (Carter et al., 1984). The results are consistent with those of Tsunoyama et al. (1980) for 20 keV 0; + Si at a dose of 3.2 x lOI9 ions/cm2 as well as for Ge to a dose of 1.4 x 1019 ionsjcm'. A tentative explanation for the observed surface features was given by Carter et al. (1984). For inert-gas ion bombardment, it is thought that stresses are developed parallel to the surface between the surface zone in which collision-induced recoils are generated and the underlying substrate. This initiates microcracks, the precursors of pits that ultimately evolve into corrugated structures. For oxygen irradiation, because of the comparatively high binding energy of the oxygen atom to the target atom (8.3 eV) (Tsunoyama et al., 1980), a near-surface silicon oxide layer is formed, N

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

I19

FIG. 18. Corrugated surface structure developed upon Si by 7 keV Ar+ ion bombardment at 45’ incidence to the surface normal. The sequence (a)-(d) shows the increase in amplitudeand wavelength of surface facets as a function of increasing ion fluence: (a) fluence = 2 x 10l8ions/cm’; (b) fluence = 1.6 x 10’’ ions/cmz;(c) fluence I6 X 10’’ ions/cm2,and (d) fluence = 8 x 10” ions/cm’. The magnification of all the micrographs is 5000 X . [Reprinted by permission from Vacuum 34, Carter, G., “Some problems and prospects in high erosion yield sputtering.” Copyright 0 1984, Pergamon Press PLC.]

which relieves the stresses developed, and hence pits and subsequent development of topography are inhibited. It may be mentioned that cone formation in Si is rare unless large contaminants or asperities are present on the surface (Wilson, 1973; Morishita et a/., 1988). Duncan et al. (1983, 1984) systematically studied the effects of 5.5 keV ion bombardment on some important electronic materials such as Si( 100), Crdoped semi-insulating GaAs(100), and Fe-doped InP( 100). The primary ion species used are 0;and Cs’ since these enhance the electropositive and

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D. GHOSE AND S. B. KARMOHAPATRO

electronegative ion yields, respectively, in SIMS analysis. Relatively high doses of 1019 ions/cm2 to lozoions/cm2 have been used to ensure that the observed features are properly developed. In general, the microtopography observed to occur in all three materials with 0 ; bombardment is a stepped and faceted structure somewhat resembling that observed with inert-gas ion bombardment in Si (Carter et al., 1984).The structure is found to be better defined on Si(100) and InP(100) than on GaAs(100). In each case, the pitch and the magnitude of the morphological features increase with the depth of erosion. In passing, it may be mentioned that for Si, Carter et al. (1984) observed almost featureless surface after bombardment of 7 keV 0' ion. Duncan et al. (1983), however, noted that if the bombarding 0 ; energy is increased (10 keV), the Si surface remains almost featureless except for the occurrence of occasional faceted pits. Since the sputtering yield for a diatomic molecule at 2E is approximately twice the yield for the corresponding atomic ion at E (Andersen and Bay, 1981), the differences in the depth of erosion and the implanted oxygen concentration may be responsible for the difference of topography in the two cases. In contrast to 0 ; bombardment, Cs' bombardment has been shown to produce an overall smoother surface on Si(100)and GaAs(100) both at comparable ion doses and, more particularly, at comparable erosion depths. However, at a very high dose of lo2' ions/cm2, ripple topography begins to appear in the GaAs(100) surface. In contrast, Cs+-bombarded InP(l00) surface shows a complete different topography, which is cones appearing singly or in groups. The cones are first observed at relatively low doses (10" ions/cm2), and their size and density increase with increasing dose. The cause of cone formation is presumably the presence of predoped highmelting Fe impurity (Wehner, 1985) and the preferential sputtering of the P-component. Quite recently, Stevie et al. (1988) studied the correlation of changes in secondary ion yields to changes in topography during 0 ; and Cs+ ion bombardment of Si and GaAs crystals. For 0 ; bombardment of Si, the onset of ripple topography is indicated by a 68% increase of 28Si+ion yield, which occurs around a depth of 3 pm. For GaAs, change of ion yield was found over a depth interval of 0.3 to 1 pm, where the surface topography changes from a very lightly rippled to a furrowed structure. Neither change in ion yield nor surface topography occurs for Cs+ bombardment over a depth of 9 pm in Si and 1.9 pm in GaAs. Homma et al. (1985) found the development of small rounded protrusions of -0.1 pm dimension on the surfaces of Cs+-bombarded Si(lOO), GaAs(100), and InP(100). The bombardment was made in a SIMS instrument. The doses were not high enough to produce ripple topography. 0; and Ar+ bombardment also show similar microtopographies only in InP. It is thought that the formation of an altered layer by preferential sputtering of the high-

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vapor-pressure component in compound semiconductors, especially in InP, plays an important role in the development of topography. Cone formation on InP crystal was reported by Linders et al. (1986~)for Ar' and 0;ions sputtering in the energy range 3-10 keV. Three types of microstructures occurred during ion bombardment: contamination-induced surface roughness, densely standing cones of height and mean distance 5 to 25 pm, and regions of closely packed small cones of height and mean distance 0.2 pm. X-ray microanalysis reveals that sputtered Ta impurities from the beam-defining diaphragm are responsible for cone formation. It is interesting to note that the formation of a small cone region can be prevented by air exposure after irradiation with low ion doses. Such regions can also be eliminated when etched by a mixture of 75% Ar and 25% 0, ions (Katzschner et al., 1984). Wada (1984) bombarded InP crystals with 500eV Ar ions at normal incidence from a Kaufman ion source. Following the formation of small globules, sharp cones of 9.5" half-angle were obtained after prolonged irradiation. Auger analysis of the etched surface shows P deficiency and In accumulation in the surface layer of about 150 A thickness. It is theorized that these In atoms form minute globules and possibly act as nuclei for formation of sharp cones. When the bombardment is made at glancing angle, a nearly stoichiometric planar surface morphology is obtained. Topographical changes in the surfaces of GaAs( 100)crystal produced by 30 keV Ar' beam sputtering at various temperatures were studied by Bhattacharya et al. (1987). It was found that the bombarded surface remains almost featureless except for the formation of a few isolated pits for samples that were not externally heated (Fig. 19)and a few isolated conical protrusions

FIG. 19. Electron micrograph of a pit on a GaAs( 100)surface sputtered with 1 x 10'' 30 keV Ar+ ions/cm2. The viewing angle in the microscope is 0". White markers = 1 pm. [After Bhattacharya et a/.,1987.1

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D. CHOSE AND S. B. KARMOHAPATRO

FIG.20. A cone formed on a CaAs(100) surface sputtered with 1 x l O I 9 30 keV Ar+ ions/cm2; target temperature = 225°C. The viewing angle in the microscope is 33.5”. White markers = 1 pm. [After Bhattacharya ef al., 1987.1

for samples bombarded at high temperatures (Fig. 20). However, one observed a high density of cones when the sample was bombarded with simultaneous seeding with Cu at high temperature. It is thought that high-melting-point CuO is responsible for such cone formation (Wehner, 1985). In a compound target, the elements contained may also serve as seed material for cone formation. This may happen by preferential sputtering of one component and surface diffusion and clustering of the other component. The stoichiometry of GaAs was found to be unchanged during bombardment; this might be the reason for the absence of cones without the introduction of foreign atoms.

3. Colour Changes in Ion-Bombardment-Induced Textured Targets An ion-induced textured target often exhibits different colour when light falls on it. Depending upon the size and spacings of the microstructures, the topography may act as a total photon sink, sometimes selectively absorbs lights of particular wavelengths, and sometimes causes total reflection in a particular direction. The colour of the bombarded surface is found to be dependent on the direction of observation since metallic reflection also plays a role in it (Jenkins and White, 1957). In an early study of Si bombardment, Nelson and Mazey (1968) observed colour changes on the bombarded part with increasing ion dose. Faint blue or pink hues are observed initially which eventually saturate into a characteristic “milky white” appearance as the dose builds up. It is thought that Rayleigh scattering of the incident white light by the ion-induced disorder zones is

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responsible for such colour changes. Similar “milky spot” was also observed by Elich et al. (1971)in a Cu(100) crystal turned around a (100) axis when the incident ion beam made an angle of 39” with the surface normal. A replica of the bombarded surface in an electron microscope shows the presence of faceted surface structures, the width of which has the order of magnitude of the wavelength of visible light. A number of authors (Wehner and Hajicek, 1971; Kerkdijk and Kelly, 1978; Mattox and Sharp, 1979; Linders et al., 1986c) observed that closely spaced cone-covered surfaces of various solids, e.g., Cu, Mg, Be, and InP, are optically very absorptive and appear black when viewed perpendicular to the surface. The mean height and relative separation of such cones are 0.20.5 pm. Whitton et a/. (1978), however, observed selective absorption of light where only red light is reflected in a pyramid-covered (1 1 3 1) Cu surface. The pyramid apex angle is presumed to cause such selective absorption, which, in turn, should be projectile energy-dependent. The possible use of ion-bombardment-induced textured surface as a “solar absorber” was investigated by Berg and Kominiak (1976) and Rossnagel and Robinson (1982b).The selective absorption of light and low optical reflectance are thought to be due to multiple reflection between the facets of the structures, which are on the same physical scale as the wavelength of light. Dendritic needlelike structures on a tungsten surface formed by chemical vapour deposition (CVD) also show similar properties (Cuomo et al., 1975; DiStefano et a/., 1979). DiStefano et al. (1979) described a geometric optical model in which light is decomposed into components of multiply scattered light according to the order or the number of reflections it has undergone, as shown in Fig. 21. The total reflectance &( 0), for I, light incident on the surface at an angle 8 is

where the nth component is due to light of wavelength A that has been reflected n times from the facets of the surface structure. The coefficients a,(0) represent the fraction of rays that are scattered n times before escape, with X u n = 1. R(A,8)is the reflectance for light incident at an angle 0 on a smooth surface. At most wavelengths, second-order reflection is found to dominate the reflectance up to 8 60°, beyond which the first-order reflection becomes important. The model can predict the reflectance of a textured surface once the parameters characterizing the surface geometry are known. Though the model is applicable for light of wavelengths appreciably smaller than the dendrite spacing, it is approximately correct for wavelengths larger than the spacing.

-

124

D. GHOSE AND S. B. KARMOHAPATRO

FIG.21, Schematic representation of a dendritic-tungsten surface obtained by CVD. The first-, second-, and third-order reflections of incident light are indicated. [After DiStefano et al., 1979.1

C . Blistering 1. Introduction

Blistering is the name used to describe the surface deformation caused by insoluble gas ion implantation in solid materials. The main criterion for this type of surface deformation is that the implanted gas profile must have a peak at least 10 nm below the surface. This is usually achieved by light ions, e.g., H + or He+ with E > 1 keV. Such low-energy light ions also have very low sputtering yields S << 1; consequently, the small erosion due to sputtering does not release the previously implanted gas. Further conditions are that the loss

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of gas due to diffusion, thermal desorption, and ion-induced reemission must be small. Although blistering was observed as early as 1912 by Stark and Wendt (1912), the first detailed analysis of blistering phenomena was made by Primak (1963; Primak and Luthra, 1966).In this work blister heights, diameters, shell thickness, and depth of cavities left after exfoliation were measured for both He' and H + bombardment of corundum and other minerals, magnesium oxide, Cu, and Ni. He also developed a quantitative model of blister formation associated with coalescence of small bubbles. Kaminsky (1964) first reported mass spectrometric observations of gas bursts released from ruptured blisters. Since then a lot of work has been done in this field, as can be seen in the review work of Das and Kaminsky (1976) and more recently in the work of Scherzer (1983, 1986). Readers are also referred to the blistering section of the proceedings of the international conferences on "Plasma Surface Interactions in Controlled Fusion Devices", all published in J . Nucl. Muter. (1974, 1976, 1978, 1980, 1982). Scherzer (1983, 1986) gave an account of keV-energy He-trapping and surface modification in different dose ranges. Initially, He doses of 10'4-10'7 ions/cm2 create damage in the form of point defects sufficient in number to trap all migrating heliums. Dislocations quickly grow into loops, after which a dislocation tangle is formed and small gas bubbles appear. No modifications of the surface structure are observed, but the bombarded surface expands outward due to swelling. Upon further implantation (21 10'7-10'8 ions/cm2), the peak helium concentration continues to build up until saturation is reached. At this stage the implanted helium starts to be reemitted, and at the same time the surface is deformed by blistering or flaking. Proceeding to very high implantation doses ( > 1OI8 ions/cm2), a repetition of blistering and flaking may occur. They are eventually eroded away by sputtering, and the final surface structure resembles that due to sputtering. At this stage, no further generation of blistering is possible because the helium-saturated layer is now exposed to the surface, and the condition that the peak should lie at some distance from the surface is no longer satisfied. 2. Factors Aflecting Blister Formation Mezey et al. (1982, 1987) have given the following classifications of morphologies due to He bombardment to avoid some confusion in the terminology. (i) Blistering: This formation dominates in the low-energy region

( N _ 1 keV- 1 MeV).

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D. GHOSE AND S. B. KARMOHAPATRO

(ii) Exfoliation: This is a large formation similar in shape to blistering but covering almost the whole implanted spot. This formation usually occurs at high energy ( > 1 MeV). (iii) Flaking: This formation takes place when almost the total area of the implanted spot leaves the surface with practically uniform thickness. Flaking can be induced at all energies under special implantation conditions, i.e., elevated target temperature and prolonged irradiation after blister rupture. Figure 22 shows some typical electron micrographs of these three types of surface deformation. Das and Kaminsky (1976) and Scherzer (1983) have listed the parameters affecting the gas-ion-induced surface modifications in detail and have reviewed extensively the experimental observations supporting the influencing factors. Following is a brief survey of the influence of some of the most important parameters on blistering. It must be stated at the outset that solubility and diffusivity of the implanted gas in metals are two of the important parameters affecting the blistering process. In general, hydrogen isotopes have higher solubility and diffusivity in most metals than inert gases such as helium, which is reflected in the fact that the dose rate and critical dose for blistering under hydrogen irradiation are considerably higher than that for helium. Moreover, in certain metals, e.g., Ti, Zr, Nb, and Ta, hydrogen reacts exothermically and forms a strong chemical bond with the surface (Scherzer, 1983). For these reasons, most of the work on blistering is concerned with He ions. The projectile energy determines the depth of implantation and hence the blister skin thickness, or “deckeldicke”, t , and the blister diameter D.One wellknown effect is that the ratio of blister lid thickness to projected helium range falls with energy from 3 for E < 5 keV towards unity above 100 keV (Roth, 1976; Risch et al., 1977). The fact that t , is 2-3 times larger than R , at low energies is a controversial point on the blistering models. The “deckeldicke” t , is often measured directly in units of distance by SEM or in units of target atoms/unit area by RBS. The direct measurements are affected to some extent by swelling of blister skin as discussed by St.-Jacques et al. (1978).This partly accounts for the thicker “deckeldicke” observed at low energies where relative swelling is expected to be larger. Emmoth (1983) compared the thicknesses of flakes measured by SEM and RBS for A1 and stainless steel in the energy range 20-80 keV. The SEM-measured values are always largest over the whole energy range, while the RBS measured values correspond very well with the projected range. This is in agreement with the earlier observations of Whitton et al. (1981), who noted a 30% greater thickness of Inconel-625 flakes measured by SEM when compared to that measured by RBS. It is further noted (Emmoth, 1983) that the relative swelling for flakes increases with

-

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127

FIG.22. Scanningelectron micrographs showing examples of (a) blister formation on an N b single crystal bombarded in random direction by 15 keV He+ ions [after Roth et a/., 19751; (b) exfoliation on Inconel type INCO-625 after 1 MeV He' bombardment [after Paszti et al., 1983al; and (c) flaking on Inconel type EP-753 after 1 MeV He' implantation [after Paszti et a/.. 1983al.

decreasing energy, being 10-20% at higher energies and 50-60X at lower energies. Quite recently, Whitton et al. (1988) pointed out that the skin thickness at the perimeter of the blister may be different from that near the center because of the change of angle of ion incidence to the blister surface during the growth phase. The diameter of the blister is roughly proportional to the energy of the projectile, and above a certain energy ( E > 1 MeV), only

128

D. GHOSE AND S. B. KARMOHAPATRO

one large blister occupies almost the whole bombarded area (Das and Kaminsky, 1974). It is further proportional to t: with 0.85 Irn I1.5 (Scherzer, 1983). Temperature is one of the most important factors influencing the surface deformation. There appear to be four temperature ranges in which quite different blistering behaviour occurs (McCracken, 1975).At low temperatures (up to 300-400 K) regular hemispherical blisters occur; some of the blisters have caps that are lifted at the edges or lost completely. At intermediate temperatures (700-900 K) the surface flakes in a very irregular form. At high temperatures (- 1100 K) the surface again produces hemispherical blisters that tend to be larger than at low temperature. At very high temperatures (1500-1600 K), the surface is typified by a pinhole or spongelike configuration that should not be considered as blisters at all. No detailed mechanisms have been suggested to describe these features. They are possibly related to differences in the bubble growth mechanisms at different temperatures, and partly to changes in plasticity and yield strengths of the materials concerned. The critical dose determines the concentration of the implanted gas atoms needed for blistering. The maximum concentration is, however, limited by particle reflection and surface regression due to sputtering. The critical dose is found to increase slowly with the projectile energy (Das and Kaminsky, 1976; Saidoh et al., 1981).It is also observed that the dose for onset of the implanted gas reemission during bombardment approximately coincides with the critical dose for blister appearance (Erents and McCracken, 1973).Bauer (1978) summarized the critical dose behaviour of seven metals that were He-implanted at energies from 20 to 300 keV. The critical helium lattice concentration Cg, (expressed as He/metal ratio) for blistering is a strong function of the homologous temperature T/T, (T, is the melting temperature) and is given by (Wilson, 1984) (54) for T/T, I0.4. Armstrong et al. (1981) studied the dependence of the critical dose for 200 keV D + blistering in Cu on target temperature. They observed three well-defined temperature regions between 120 and 380 K such that each region is characterized by a particular value of the critical dose that is independent of temperature. Blister morphology also changes abruptly in going from one temperature region to another. The flux of incident ions determines the rate of gas buildup near the implant depth, which is, however, affected by the rate of diffusion of the implanted gas to the bulk and to the surface. Because of the extremely low solubility and comparatively lower diffusivity of He in metals, helium blistering is relatively insensitive to incident flux. Conversely, because of the C$, = 0.5 - (T/T,),

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129

high diffusivity and solubility of hydrogen in metals, the likelihood of blistering is determined by a competition between the accumulation of hydrogen and its loss from the implant depth by diffusion. Therefore, the critical dose for hydrogen blistering depends on the flux density (Verbeek and Eckstein, 1974; Behrisch et al., 1976a; Moller et al., 1976). Another effect of high flux density is the formation of a local thermal spike in the bombarded spot, which in turn may change the blister morphology. The morphology of blisters formed in monocrystalline targets depends on the channeling of projectiles. Kaminsky and Das (1972, 1973a) investigated blistering of Nb monocrystals irradiated at 1173 K with 0.5 MeV He' ions. The results indicate a strong dependence of the blister shape and the orientation of the blisters with respect to each other on the crystallographic orientation of the target. The blister shape on the (1 11) surface plane reveals a threefold symmetry, and the prongs are aligned perfectly along the traces of (1 10) planes of the lattice. The blister density is lower by approximately two orders of magnitude for the channeled helium projectiles as compared to unchanneled ones. The average blister size is larger for axially channeled ions than for unchanneled ions. Similar observations were also made by Verbeek and Eckstein (1974), Roth et al. (1974), and Risch (1978). No detailed explanation for this directional effect has yet been put forward. In the following section, the formation and growth of bubbles are discussed, which is important for understanding the mechanism of blister formation. 3. Bubble Formation and Growth Bubbles are formed in solids by introducing insoluble gases to a high concentration of approximately one gas atom per bulk atom. Helium bubbles are observed in a large number of metals, and it is now an established fact that the bubbles are the precursor of blistering and flaking. It is known that helium is highly mobile as long as it occupies interstitial positions; the activation energy for interstitial migration of He in f.c.c. metals range from 0.1 to 0.4 eV (Reed, 1977; Melius et al., 1978).But it becomes deeply trapped in vacancies or at other lattice defects such as dislocations, grain boundaries, impurities, or precipitates because of the high binding energies; e.g., the binding energy of an He atom to a vacancy is 2.6 eV in Ni (Wilson et al., 1981).Small helium bubbles are thought to nucleate from the agglomeration of approximately six helium atoms in one lattice vacancy. These helium-vacancy clusters then grow by trap mutation. The term bubble is used for a gas-vacancy complex containing more vacancies than helium atoms. Surface modifications due to bubbles are easily understandable from the estimation of pressure of the implanted gas inside the bubble. If it is assumed

130

D. GHOSE AND S. B. KARMOHAPATRO

that a bubble of radius R,, which contains gas at a pressure P, is in equilibrium under expansion because of the pressure and the surface energy increase, the relation between a bubble’s pressure and its radius is written as

where y is the bubble surface energy per unit area. For Ni, y = 2000 erg/cm2 (Trinkaus, 1982) yields an equilibrium gas pressure of 35 kbar for a typical radius R, = 12 8. This pressure is an order of magnitude higher than that obtained in laboratory experiments carried out to measure the equation of state (EOS) of gaseous helium. Empirical equations of state, such as the van der Waals’ law, which have been fitted to experimental data, cannot be extrapolated with confidence to “gas pressures”, which are close to solid-state pressures. A satisfactory empirical EOS based on experimental measurements has been developed by Mills et al. (1980)in the pressure range 2-20 kbar and temperature range 75-300 K. They express the molar volume V in cm3 within an accuracy of f0.3% in the above-specified range as V = (22.575

+ (-

+ 0.0064655T - 7.2645T-’/2)P-’/3

12.483 - 0.024549T)P-2’3

+ (1.0596 + 0.10604T - 19.641T-’” + 189.84T-’)P-’,

(56)

where P is the pressure in kbar and T is the absolute temperature. Attempts have also been made to derive an analytical expression for EOS for helium and other inert gases at high pressures. A nonattractive hard-sphere approximation represented by virial expansion in terms of reduced parameters z and w is a possible approach to a theoretical description of imperfect fluids. Ree and Hoover (1964) gave the first few accurately known virial coefficients in the form

z= 1

+ 4~ + lowz + 1 8 . 3 6 ~+~2 8 . 2 +~ ~3 9 . 5 +~ ~56.5w6**.,(57)

where z = PV/NkT is called compressibility and w = m3N/6V is called the packing fraction; s is the hard-sphere diameter. A few closed-form expressions of Eq. (57) have been used to find the EOS agreeing with the results of molecular dynamic simulation experiments on an ensemble of hard spheres. The assumption of a gas atom as a hard sphere at a high pressure leads to inaccurate results. The more realistic approach is to derive the hard-sphere diameter varying with density from a realistic potential and to use it in one of the closed-form expressions of Eq. (57). Accordingly, Wolfer (1981) used Beck’s interatomic potential of helium (Beck, 1968) to derive a theoretical EOS starting from the hard-sphere approximation of Carnahan and Starling

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131

(1969) with s varying with temperature and pressure. Trinkaus (1983) has calculated an EOS based on the adjustment of both the virial coefficients to agree at low densities and the empirical compressibility on freezing. For gaseous or fluid He, the final form is

where P=

VIP,

V, = 56T-”4exp(-0.145T+1’4)

in units of

A3,

z1 = 0.1225V1T0*555,

B = 170T-”3 - 1750/T z;V,

2:

in units of

A3,

-50.

For room temperature liquid He, Eq. (56) from Mills et a/. (1980) agrees with the calculations of Trinkaus [Eq. (58)l to within a few percent. Furthermore, Eq. (56), when used at a pressure 50 times higher than the range of its experimental validity, gives pressures for a given V differing from the theoretical values by no more than 50% even for solid helium. At present the EOS given by Eqs. (56) and (58) give the most acceptable values with a reasonable fit to the theory and experiment. Generally, it is difficult to determine the pressure of the bubbles directly; rather, one measures the density of the gas within the bubble and then uses the EOS for density-to-pressure conversion. The helium density NH, in a spherical bubble with radius R, is given by (Van Swijgenhoven et a/., 1983a)

where 0 is the implanted dose, f is the fraction of the implanted dose precipitated into the visible bubbles, A R p is the range straggling, and C , is the bubble density. Donnelly (1985) has reviewed the density and pressure of helium in bubbles, including a comprehensive discussion on the EOS formulated by different authors. At high temperatures where enough thermal vacancies are available, there will be a continual arrival of vacancies tending to make the bubble grow, and at the same time an equal rate of departure tending to make it shrink. The bubbles are thus in thermal equilibrium, and the gas pressure inside the bubble is given by Eq. (55). While at low temperatures

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D. GHOSE AND S. B. KARMOHAPATRO

because of the absence of sufficient vacancy mobility, the bubbles are found to be overpressurized so that P > 2y/R,, and instead of a further increase in the volume of the bubble to an extent satisfying Eq. ( 5 5 ) , the free energy is stored as a pure shear strain around the bubble. Gas pressures in the range of tens to hundreds of kbar in the helium bubbles pressurized above the equilibrium level almost surely exist in some metals at least. Formation of solid Ar, Kr and Xe bubbles in various f.c.c. metals (vomFelde et al., 1984;Templier et al., 1984; Evans and Mazey, 1985) provides clear indication of the remarkably high pressures generated during bubble-growth processes by these gases also. An upper limit of pressure in an overpressurized helium bubble in Ni implanted with multienergy He ions ( E I 5.2 MeV) is measured by Haubold and Lin (1982) from a small-angle X-ray scattering study. They obtained a value of 300 kbar, which corresponds to a He density in the bubble of 2 helium per vacancy (He/V) using the EOS of Mills et al. (1980). Donnelly (1985) has compiled the values of maximum helium densities in bubbles in several metals determined from various experimental investigations with various ion doses. These values range between 0.3 and 5 He/V, which corresponds to 2.5 x 4.5 x loz3He-atom/cm3, some of which are derived on the assumption that all the implanted gas is concentrated in the observable bubbles. The question as to whether all the helium atoms reside in the observable bubbles, or a major fraction resides in small submicroscopic clusters distributed between the bubbles, is important for understanding the surface-modification and gasrelease processes. There are contradictory conclusions from experimental results; for example, for He in Al, Jager et al. (1982)found evidence that above 6 at % He concentration, most of the He is trapped in observable bubbles, whereas Johnson and Mazey (1980a,b) in an experiment involving He in Cu concluded that most of the gas is trapped outside the visible bubbles. The nonmonotonic variation of He density with ion dose at both low- and highenergy implants observed by Fenske (1979) reveals an enormously high pressure ( 6 Mbar) corresponding to the highest density (- 5 He/V) which is incompatible with the mechanical properties of metals. The conclusion is therefore drawn that a large percentage of the implanted helium, depending on the dose, is trapped in the submicroscopic defects. The recent study, by Van Swijgenhoven et al., of the bubble growth in Ni during 5 keV He' implantation (1983a,b; Van Swygenhoven and Stals, 1983) indicates that about 35% k 25% of the implanted helium precipitates into visible bubbles at the dose of 1017 ions/cm2, while the percentage increases to about 55% f 28% at the critical dose for blistering (5 x lOI7 ions/cm2). During He ion irradiation of Mo, Sass and Eyre (1973)first observed not only that high concentrations of nearly equally sized bubbles ( R , = 10 A) are developed, but also that the bubbles are mostly ordered on a space lattice in

-

-

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT 0 0 0 0 0 . 0

0

0 0 0 .

0

0 0 0 0

0

0 0

0 0 0 . 0 0 0 0 0 0

0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 .

0 . 0 0 .

133

0 0

FIG.23. Illustration of bubble growth by loop punching. (a) Excess bubble pressure deforms surrounding atom planes. (b) Shunting process allows expansion of bubble and creation of interstitial loop. [After Evans, 1978.1

the host metal. Subsequent studies (Mazey et al., 1977; Johnson and Mazey, 1980a,b; Jager and Roth, 1980; Johnson et al., 1983) have shown that in the case of metals having a high degree of crystalline perfection within grains, the bubble superlattice was formed in all metals representing the three main crystal structures b.c.c., f.c.c., and h.c.p. at temperatures <0.3Tm. The mechanism of bubble growth depends on the number of external vacancies, either created thermally or by radiation damage during implantation. At low temperatures ( T < O.3Tm)where only insufficient radiation induced vacancies are available, a loop punching mechanism (Greenwood et al., 1959) has been proposed that would allow the bubbles to grow without the help of external vacancies by the emission of a cluster of interstitials (or dislocation loop), as sketched in Fig. 23. An alternative process of creating vacancies is the emission of self-interstitial atoms (SIA). This latter process requires a pressure an order of magnitude greater than that for the loop punching process and is therefore less favourable for bubble growth, but it is suggested to be operational only in the bubble nucleation phase. The punching of prismatic dislocation loops (i.e., burger vector normal to the plane of the loop) as a mechanism for stress relief was originally discussed by Seitz (1950). Lally and Partridge (1966) reported the first observation of such loops associated with gas bubbles in Mg quenched from high temperature in an atmosphere of Ar contaminated with air and moisture. They concluded that the observed loops had been punched out by hydrogen bubbles formed during the quench as a result of the decreasing solubility of hydrogen with temperature, which was subsequently confirmed by Wampler et al. (1976). Recently Evans et al. (1981, 1983) observed punching of loops from helium platelets and showed that such a mechanism can also be initiated by electron-beam effects during observation in TEM. For loop punching to be energetically possible, the free energy of a circular prismatic dislocation loop can be equated, following Greenwood et al. (1959), with the work done in expanding the bubble volume by AV. This yields the

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D. CHOSE AND S. B. KARMOHAPATRO

minimum pressure, PLp,at which loop punching can occur:

--+

2Y PLP RB

Pb ln-,RDL 2xR,(1 - V) ro

where p is the shear modulus, v the Poisson ratio, b the burger vector of the emitted dislocation loop, ro ( 1:b) the core radius of the dislocation, and RDL ( N RB) the radius of the dislocation loop. There are variations in Eq. (60) found in the literature. For small bubbles of radii R, in the range 2b < R, < lob, Eq. (60) is replaced by 2Y PLP= Rn

Pb +Rn

‘v

2Y (5 to lo)-. R,

In a theoretical treatment, Trinkaus (1983), however, has concluded that Eq. (61) may only be correct to within a factor of two. The mechanism of loop formation is still not well understood. It is not clear why for small-size bubbles the expelled interstitials form threedimensional clusters near the bubble, whereas the self-interstitial atoms exceeding a number 13 form two-dimensional platelets (Ingle et al., 1981). In the derivation of Eq. (60), the elastic interactions between successively punched dislocations are ignored; such interactions have the effect of increasing the maximum pressure. Besides that, the assumption of an undamaged lattice is not a reasonable approximation since the lattice may also have small He clusters along with the visible bubbles. The bubbles cannot grow to an unlimited size. A mechanism for material failure in the surrounding of overpressurized bubbles was put forward by Auciello (1976), and the associated pressure was evaluated by Evans (1977, 1978). Over this critical pressure, interbubble fracture occurs, triggering the blister formation. Evans (1977, 1978) considers a set of identical coplanar overpressurized bubbles at some depth below the surface of a semi-infinite medium. The tensile stresses at the bubble surface will combine to give a resulting tensile stress in a direction perpendicular to the plane containing the bubbles and therefore tending to part the material at this plane. The pressure at which such a process occurs is obviously dependent on bubble density C , and the fracture strength of the material oF.The pressure PF for fracture between the bubbles is given by

A comparison of Eqs. (61) and (62)as a function of bubble radius shows that below a certain critical radius R;, PLpis always less than PF.That means for R, < R ; the bubble will relieve its excess internal pressure by loop punching

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until the two equations converge at R ; . At or above R ; , the interbubble fracture will occur. 4. Models of Blister Formation Two sets of condition have to be fulfilled for the appearance of blistering. (i) A peak of helium concentration must set up beneath the target surface. (ii) The He concentration at the peak must reach at least about 0.3 Helmetal. The first condition usually demands a monoenergetic ion with perpendicular angle of incidence, while the second condition defines the helium dose at which blister formation is initiated. Qualitative models for the formation of blisters have been suggested by a number of authors. These fall into two major categories. One is the gas pressure model, in which the buildup of excess gas pressure in the implant region of maximum gas concentration is the main driving force for the surface deformation leading to blister appearance. The other is the integrated lateral stress model, in which it is suggested that the large lateral stress introduced in the implanted layer leads to elastic instability and buckling of the implanted surface layer above the weakened interface region, and thus gas pressure is not the driving force behind the surface deformation. The experimental evidences on which the gas pressure model are based are (i) the observation of gas bursts and their correlation with the number of pits observed on the surface (Kaminsky, 1964; Thomas and Bauer, 1973);(ii) high symmetry of the blisters and the occurrence of blisters on both front and rear faces of a thin wedge-shaped Mo sample bombarded with He ions (Evans and Eyre, 1977); (iii) formation of extremely large blisters due to the lateral coalescence of small blisters with high density (Das and Kaminsky, 1973; Paszti et al., 1981; Saidoh et al., 1981); and (iv) the fact that at E > 100 keV, blister lid thickness (“deckeldicke”) is approximately the same as the mean range of the implanted ion (Kaminsky and Das, 1973b). Blistering was initially attributed to a sudden coalescence of small bubbles, which occurs when the density increases sufficiently to allow bubbles to touch (McCracken, 1975).This happens, of course, at a depth corresponding to the mean range of the incident ions. The coalescence of two bubbles at constant volume results in an excess internal pressure in the large bubble, because of the fall in the term 2y/R,. The situation is a runaway one until the pressure is relieved at the surface, by which time a blister is formed. Assuming the blister as a thin spherical shell clamped at its periphery with an internal pressure P, the blister diameter D is given by D = 4a,tB/P,

(63)

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where tB is the blister lid thickness equal to R , , the projected range of the ion, and c,, is the yield strength of the material. Equation (63) predicts a linear relationship between blister diameter and lid thickness. The principal argument against the above model is that the lid thickness is appreciably larger than the depth of the helium peak, especially for E < 100 keV. To resolve the thick deckeldicke controversy, Evans (1977, 1978) developed a model in which blistering is initiated by the interbubble fracture of highly overpressurized helium bubbles. As discussed earlier, in the initial phase, the bubble grows by athermal processes such as loop punching, but with increasing bubble size the growth is governed by an interbubble fracture mechanism. At some critical depth from the irradiated surface, a layer of bubbles may have internal pressure equal to that required for interbubble fracture, PF.This creates an internal crack. If the pressure difference between the gas in the crack and gas in the bubble adjacent to the crack is sufficient, a process of “unzipping” layers of bubbles can take place, being able to start deforming the layer of material above the crack to give the final blister crosssection. The sequence of events is schematically outlined in Fig. 24. One important result of this model concerns the position of fracture plane; because of the usual displacement of damage and helium peaks relative to depth, this plane can lie well beyond the peak of the deposited helium distribution. This

BUBBLE P E S S U R L

(C

1

td)

w)

FIG.24. Interbubble fracture mechanism: (a) high density of overpressurized bubbles, (b) crack formation, (c) bubbles adjacent to original crack become involved to widen crack and increase pressure, (d) penny-shaped crack that either extends to cause flaking or (e) forms blister. [After Evans, 1978.1

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removes the difficulty, inherent in previous gas models, of reconciling measurements of blister lid thickness with the helium range. In passing it should be noted that the idea of interbubble fracture was first proposed by Auciello (1976). Here the fracture does not run parallel to the surface as in the Evans’ model (1977, 1978). However, Auciello’s model (1976) appears to be the only one that can explain rupture of blisters around the periphery and on the top of the cover as observed by Erents and McCracken (1973). Though the lateral stress model was originally developed to explain the low energy discrepancy between blister lid thickness and helium range (Behrisch et al., 1975a), the proponents of this model have criticized the gas pressure model also on the basis that (i) it cannot explain the relationship Dmpa t i / 2 between the most probable blister diameter Dmpand blister skin thickness t , (Roth, 1976), and (ii) only a small fraction of the total implanted helium is actually emitted during blistering (Behrisch et al., 1975b). The formation of lateral stress observed during bombardment is associated with the local helium-bubble swelling. For small bubble radii ( 510 A), the volume swelling is independent of bubble size and depends only on the helium lattice concentration. At bubble radii larger than about 30 A, the volume swelling for a given lattice concentration of helium atoms increases with the bubble size (Roth, 1976). Because of the proximity of the metal surface, the swelling can expand in the direction of the surface normal, while parallel to the surface no swelling is possible because of the contact to the nonimplanted material. EerNisse and Picraux (1977) measured the lateral stress integrated over the thickness of the implanted layer, oi, in He+bombarded Mo, Nb, and Al as a function of the implanted dose @, which shows a linear variation at low doses followed by a sublinear stage before falling relatively sharply in the region where surface blistering is initiated. The low-fluence results provide values for the induced volume expansion per implanted He atom. At high fluences, the integrated stress saturates and relieves. The saturation value, oi,max,is proportional to the yield stress o, of the material and is independent of the helium projected range. Considering the elastic instabilities of a circular plate subjected to lateral forces in the plane of the plate, it can be shown (EerNisse and Picraux, 1977) that the critical lateral force per unit length, oi,cr,at which buckling occurs is given by

where YM is the Young’s modulus, v is the Poisson ratio, tB and D are the thickness and diameter of the plate, respectively, and K is a geometric factor that ranges from 1.4 to 4.9 for elastic edge conditions ranging from a simply supported edge to a clamped edge, respectively. In the case of He-implanted layers, assuming that oi,cr = oi,max and also that the shear failure takes place at

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D. CHOSE AND S. B. KARMOHAPATRO

the interface between the implanted layer and the bulk, it follows from Eq. (64) that D cc ti’’. Contrary to the gas pressure model, which necessitates “overpressurized” helium bubbles, this model does not require an explicit description of the microscopic behaviour of He in metals, though the origin of the stresses is the He in the lattice. The relation between the blister diameter and cover thickness, i.e., Dmpcc ti5,is considered as important evidence for the stress model. Das et al. (1978) measured the relation experimentally in Be, V, Ni, and Nb with great care for the diversity of the blister diameter in a given sample, which seems to have been neglected in the earlier data compilations. The results showed that the exponent of t B is strongly dependent on the type of the material (e.g., value of exponent varies from 0.85 for V to 1.25 for Be) and also on the target temperature; this does not support the lateral stress model. With this in view, Kamada and Higashida (1979) developed an interbubble fracture model of blistering that criticizes the objections raised against the gas pressure model. This model is based on the stress fields around a large lenticular bubble of diameter 2RLB parallel to a free surface at a depth h g . The bubble is loaded with a gas of pressure P. The components of the stress field are found to have square root singularities at the bubble tip. This means in real materials, plastic deformation must take place in such a region, which is called the plastic zone. This plastic zone must spread as the radius of the bubble increases. Since the lenticular bubble is similar to the tensile crack whose surfaces are subject to internal gas pressure, the plastic zone at the bubble tip extends farthest in the direction normal to the bubble surface. When the boundary of the plastic zone touches the free surface, the subsurface layer over the bubble may suffer general yielding and deform into a dome-shaped blister. It is shown that the blistering process can be separated into two factors: One is determined only by the geometry of the lenticular bubble, namely, by (hB/RLB),and the other is determined by physical properties of the materials and expressed as ( P / c , ) ~ . This latter factor, which is dependent on both the ion energy and the target materials, is responsible for the nonlinear dependence of the blister diameter on the cover thickness. Though this model clears some of the objections against the gas pressure model, the mechanism of the growth of the lenticular gas bubble is not satisfactorily understood. It cannot be formed by a simple crack extension mechanism in ductile materials, as the estimated internal gas pressure is far lower than the pressure necessary to satisfy the Griffith’s condition. In conclusion, controversy still exists regarding the two mechanisms to explain blistering. No model as yet can describe blister shape, size, and cover thickness in a quantitative way. Exact experimental data are also lacking to compare the models. While effects of lateral stress are identified as playing a major role in flaking, effects of gas pressure seem to be a dominant influence in

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blistering at lower temperature. However, it is now certain that both the stress and gas pressure are involved in evaluating the physical mechanism of surface deformation (Wolfer, 1980). 5. Flaking and Exfoliation Risch (1978) investigated blistering and flaking in Nb bombarded with 100 keV Hef ions. The current density at the critical dose of blistering seems to determine whether small discrete blisters are formed or flaking over a large area occurs. A high current density (-400 pA/cm2) shortly before reaching the critical dose results in flaking, whereas a low current density ( - 20 pA/cm2) results in small discrete blisters. Emmoth (1983) noted that for 75 keV Hef bombardment of 304 stainless steel, blisters are formed at room temperature, but at elevated temperature, above 373 K, the surface flakes. During 40 keV He+ irradiation of polycrystalline Al at 325 K, Braun and Emmoth (1976) observed a rapid -250-fold enhancement of optical photon intensity from sputtered excited Al atoms at a critical dose of 4 x 10'' Hef/cm2. It was shown that this effect is associated with a sudden increase in the erosion rate of the target due to flaking and also due to a rapid oxidation of the newly exposed surfaces. At very high dose and controlled target temperature (in the range 0.2Tm-0.4T,), multiple flaking may occur. While Kaminsky and Das (1978) demonstrated 15 successive generations of flaking from 316 stainless steel bombarded at 723 K with 100 keV He' to a total dose of 1.25 x lo2' ions/cm2, Whitton et al. (1981) observed as many as 39 repetitions in Inconel 625 with a dose of 3 x 10'' 100 keV Hef ions/cm2. The latter authors also observed a strong dose-rate dependence of the maximum number of flakes generated; decreasing the beam current from 640 pA/cm2 to 64 pA/cm2 results in a factor of 20 fewer flakes being generated for the same total dose. During repeated flaking, the crater area that is left decreases rapidly. When the crater diameter reduces to a minimum, the flaking eventually comes to an end (Emmoth, 1983). A comparative study of blistering and flaking induced in the same bombarded spot in the case of 200 keV D + bombardment of Cu (Johnson and Jones, 1984) reveals that the fracture plane of flakes is situated at somewhat shallower depth than that of blisters. Terreault (1980) studied the question of repetitive flaking in detail and predicted various blistering regimes by the ratio of the range profile width (FWHM) to the mean projected range R,. According to him, blistering or flaking will be repetitive as long as FWHMIR, < 0.7. The works of Martel et al. (19741, Behrisch et al. (1976b) and Gusev et al. (1979), however, show that at high enough doses, blisters disappear and a sponge-like equilibrium surface structure is developed. These observations led them to the conclusion that the blistering process is transient and not continuous.

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Studies of surface deformations caused by MeV energy helium implantation in which mainly exfoliation and flaking dominated are relatively scarce. The Hungarian group (Mezey et al., 1987)have done some work in this direction. The transition energy at which the blistering process turns into exfoliation is found to be material-dependent. While gold exhibits helium exfoliation at 2 MeV (Mezey et al., 1982), for Inconel and stainless steel the transition energy at room temperature is below 1 MeV (Paszti et al., 1983a). On the basis of the results of 3.25 MeV helium exfoliation in a gold target, Paszti et al. (1981) concluded that the relationship between blister skin thickness and diameter experienced at lower bombarding energies seems to be invalid at high bombarding energies. The only limiting factor in the diameter is the size of the implanted spot. They also gave a speculative model for highenergy blister formation. Bhattacharya et al. (1988) bombarded a 100-pmthick W sheet with 2.6 x lo'* 28.7 MeV 01 particles/cm2 from the Calcutta variable-energy cyclotron. The projected range of the ion is comparable to the thickness of the specimen. A large elongated exfoliation (length 1500 pm and breadth 1000 pm) with rupture at some portion of the cover was observed only on the reverse unbombarded surface (Fig. 25). This observation lends support to the gas pressure model of blister formation. Metallic glasses, however, show different behaviour with MeV helium implantation (Manuaba et al., 1982; Paszti et al., 1983b,c).The surfaces flake immediately the critical dose is reached. Blistering occurs only when the bombardment is done at elevated temperature. On the surface left behind the flaked layer, a peculiar wave pattern formation can be observed. A similar pattern accompanied by

-

-

FIG.25. Scanning electron micrograph showing exfoliation on the rear unbombarded face of a W sample after 28.7 MeV ct bombardment. The viewing angle in the microscope is 70". White markers = 100 pm.[After Bhattacharya et al.,1988.1

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FIG.26. Wave structure on Metglass 2826A after flaking induced by 2 MeV He+ bombardment. White scale marker is 20 pn. [After Manuaba el al., 1982.1

flaking was also observed in a helium-implanted silicon surface (Paszti et al., 1985). The waves consisted of elevations of asymmetric triangular crosssection and were formed only at temperatures below the crystallization temperature. Figure 26 shows an example of very regular pattern formation on Metglass 2826A after flaking. This can be compared with the ripple structure observed in Si surface eroded by very high-dose heavy-ion sputtering (Carter et al., 1977). The periodicity of the wave structure can extend to several mm in length. The wavelength varies between 0.9 and 1.8 pm. In some cases the pattern is characterized by diffraction, interference and island-like formation. Hajdu et al. (1987; Hajdu, 1988) proposed a mechanical stress model to explain the phenomena. It is thought that the large lateral stresses developed by ion implantation, as discussed by EerNisse and Picraux (1977), are relaxed by forming wrinkles and corrugations if not relaxed otherwise, e.g., by forming blisters. An approximate analytical calculation gives the wavelength of wrinkling as (Hajdu, 1988) =

10.2 A R p ,

(65)

where A R p is the projected range straggling. This model, like the stress model of blistering, suggests the evolution of the wave pattern around the depth of maximum ion penetration, and unless it is near the surface, the pattern will be observable after removal of the uppermost layers. Such a topography once

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formed is not lost even if a thickness greater than the projected range is removed. Finally, it should be noted that formation of voids can also result in topographical changes, which is discussed in the following section. 6. Surface Modification due to Void Swelling Cawthorne and Fulton (1967) discovered the void swelling phenomenon during examination of stainless steel fuel claddings exposed to high doses of fast neutrons in a reactor. The development of internal porosity in the form of small cavities (- 100 A) results in an overall volume increase, i.e., swelling of the irradiated materials from a few percent to an order of 10% in specific cases. In most of the materials voids generally form and grow in the temperature range of 0.3T, to O S T , . At very low temperatures (<0.3Tm),the mobility of vacancies is small so that recombination with interstitials is more prominent than migration to a sink to form a void. At very high temperatures ( > 0.5 T , ) , radiation-induced vacancies are fewer in number than thermal vacancies, prohibiting the supersaturation of vacancies that provides the driving force for void nucleation and growth. The sufficient conditions for void swelling to occur in the appropriate temperature range are the presence of biased sinks such as dislocations for interstitials and of neutral sinks such as gas bubbles. The growth rate of voids depends on the competition from all other sinks. Consequently, not every vacancy migrates to form a void. In fact, nearly one in one thousand of the vacancies produced accounts for the volume change, since significant swelling in excess of nearly 0.1% is observed at displacement doses of 1 to 10 displacements per atom (dpa) (Nelson, 1976). The use of ion beams to study void swelling was introduced by Nelson and Mazey (1969; Nelson et al., 1970) at Harwell. They showed prior implantation of helium is effective in aiding void nucleation. Many other workers followed the Harwell group with ions with H+ to Ta' in the energy range to lo-' 100 keV to -50 MeV and the atom displacement rates from (dpa) s-' (Johnston and Rosolowski, 1976). Intense electron beams of energies between 0.5 and 1 MeV from a high-voltage electron microscope (HVEM) are also used for void studies (Norris, l970,1971a, b), where in-situ production and observation of damage structure can be performed. Such experiments are initiated with a view to simulating the damages produced by fast neutrons in reactor materials. Marwick (1975) showed that nickel-ion-induced displacement damages are a close approximation to reactor damages, while Johnston et al. (1973, 1974) showed that void swellings produced by Ni-ion bombardments are similar in terms of void densities, void diameters, and total swellings to those in-reactor when compared at the same damage level and at the respective peak-swelling temperatures.

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Similar to ordering of gas bubbles, voids can form a regular array on the host lattice as observed first by Evans (1971a, b) in a high-purity Mo single crystal irradiated with 2 MeV nitrogen ions. The void superlattices have the same symmetry and alignment as the host lattices. The average void radius is typically a few tens of angstroms, and the lattice constant ranges from one to a few hundred angstroms, which is, however, much higher than for bubble lattices (Krishan, 1982). It has been suggested (Stoneham, 1975) that void ordering takes place mainly in four stages: (i) the initial formation of many small voids distributed at random; (ii) growth of large voids by coalescence of smaller voids; (iii) development of small local regions where voids start having spatially ordered correlations; and (iv) spreading of these ordered local regions to the adjacent ones. In the case of a bubble superlattice, similar stages are proposed, but in addition to these four stages a fifth stage has been observed in which some bubbles are interconnected forming pipe-like channels close to the surface (Johnson and Mazey, 1980b; Jager and Roth, 1980).Quite recently, Evans (1985,1987) proposed that void and bubble lattice formation in metals could be explained by the two-dimensional diffusion of self-interstitial atoms on close-packed planes. Since the stress model of gas blistering accounts some of the experimental results, one may expect analogous surface structures involving void swelling, where the stress systems should be similar. In cases of large void swelling (greater than 20%), Johnston and Rosolowski (1976) could show that the integrated swelling is totally reflected in the step height between bombarded and shielded regions. These authors also observed some interesting changes in surface topography in void-swelling studies, which are not related to sputtering phenomena because of the high energies and temperatures used. Different elevations of grain surfaces, gross unevenness at large swellings, development of facets on certain grain surfaces, and formation of ridges at grain boundaries are the characteristic features of Ni-ion-bombarded stainless steel surfaces. Very recently, Ghose er al. (1984b, 1987)reported blister-like structures on both sides of Ta foils during 30-40 MeV a-particle bombardment. The blisters are mainly three-pronged, mixed with a substantial number of one-pronged and two-pronged ones (Fig. 27), and have a close similarity with the gas blisters previously observed on Nb single crystals bombarded by 0.5 MeV Hef ions at 1173 K (Kaminsky and Das, 1972,1973a). Since the foil thickness was much less compared to the projected range of the ion, the observed features are not related to gas bubbles. These may be attributed to void swelling, which provides great compressive stress parallel to the surface. It is thought that in addition to the displacement damage, the formation of a beam-induced local thermal spike and the presence of oxygen accentuate the swelling phenomenon, the collective effect of which is manifested in the form of surface structures. In passing it should be mentioned that Wilson (1982,

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FIG.27. (a) Electron micrograph of 40 MeV a-bombarded Ta foil showing pronged blisters. (b) is a higher magnification micrograph of the u-bombarded Ta foil containing two threepronged and one two-pronged blisters. The viewing angle in the microscope is 33.5". White markers = 1 pm. [After Ghose et a[.,1987.1

1989 also observed topographical changes due to voids in case of low-energy heavy-ion-implanted semiconductors. Holes first appear in the surface at relatively low doses. As the ion dose increases, the holes grow to form a cellular structure that coarsens until a dynamic equilibrium is established. It is proposed that the cellular structure is the result of void formation combined with sputter etching.

IV. SUMMARY

To summarize, this review presents some pertinent aspects of ion-induced surface modifications. The first part deals with surface structures developed by ion-beam sputtering. A frequently appearing phenomenon in sputtering

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experiments is the development of cones or pyramids. Though the involvement of impurities in the formation of conical protrusions is well documented, the exact mechanism for nucleation of cones is still not well understood. It is not clear whether “intrinsic” effects, which arise from interactions of the ionsolid system alone, and “extrinsic” effects, which arise from perturbations of the ion-solid interactions caused by the presence of impurities and convex-up asperities on the solid surface, act separately or in concert in the development of cones. The wide belief that the impurities should have lower sputtering yields than the matrix materials is not always correct, as recently pointed out by Wehner (1985), where it is shown that only in the cases where the seed materials have a higher melting point are the cones formed. However, it is established that whatever the mechanism of cone nucleation is, it is the angular dependence of the sputtering yield of the cone material that largely determines the final shape of the cone. The formalism of Carter et al. (1971, 1973; Nobes et al., 1969) most clearly explains the evolution of cones and can be applied to predict the critical doses for cone formation and disappearance. A more complete description of the evolution of cones, however, needs the introduction of secondary and tertiary effects, the redeposition of sputtered materials, and the effects of crystallinity. An important aspect is the question of stability of cones under prolonged bombardment. It is known that isolated cones are generally not stable under ion bombardment. But under certain conditions, e.g., continual supply of seed atoms, or particular target crystallography, e.g., (1 1 3 1) (Whitton, 1986), the dense arrays of cones formed are found to be stable. This apparent stability is suggested to be due to continuous disappearance and regeneration of individual cones. Alternatively, if one considers the erosion by primary beam only, then for a dense array of cones there is no reference slope with respect to which the cones could recede (Auciello, 1982); consequently, the array would be stable. It is interesting to note that the semiconductors are not as susceptible to cone formation as the metals. This indicates that the structural state of the target influences the type of the topographical features. It has been demonstrated by Whitton and Grant (1981) that solids that cannot retain long-range order of the crystal structure under ion bombardment are very unlikely to develop conical features. The cone or faceted surface morphology has a strong influence in the angular distribution of sputtering yield as well as the total yield measurements. It also gives rise to poor depth resolution in some surface analytical techniques such as SIMS. The theory of Littmark and Hofer (1978) presents some qualitative information on these aspects. The second part of the present work concerns the surface modifications due to gas ion implantation, namely, blistering. Helium blistering is more easily observed than hydrogen blistering. Though the nucleation of helium gas bubbles is more or less understood, whether all implanted helium is accommodated in bubbles, or whether a considerable fraction of the implanted helium resides in clusters outside the bubble, is still a matter of debate. There

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are several proposals as to how bubbles gain vacancies by athermal processes that include SIA emission and dislocation loop punching, but exact details are not yet available. However, there is ample evidence that helium bubbles are pressurized far beyond the equilibrium level. The controversy between the gas-driven and stress-driven mechanisms of blistering is not resolved, but the final description seems to be a kind of in-between. Since the stress system in void swelling is similar to that of gas bubbles, there is no reason why analogous stress-induced relief structures should not also develop in this case. In fact, the work of Johnston and Rosolowski (1976) indicates that surface topography could also be developed for large void swelling. More investigations in this subject are needed. An important question is sometimes raised whether the blistering process is transient or continuous. It has been found that under certain circumstances blistering and flaking are repetitive, but the evidence is not conclusive. Recent experiments suggest that multiple energy multiangle ion bombardment and a rough surface can reduce blistering. These conditions prevail in a CTR machine; consequently, the blistering phenomena may not be a serious problem in fusion as was initially envisaged. Nevertheless, such experiments deserve attention on their own merit, since these will improve the understanding of the underlying mechanism of particle interaction with solids.

ACKNOWLEDGMENTS The authors thank Mr. M. C. Das for his untiring assistance in the preparation of several versions of the manuscript.

REFERENCES Alexander, V., Lippold, H.-J., and Niedrig, H. (1981). Radiat. Efl. 56, 241. Andersen, H. H. and Bay, H. L. (1981).In Sputtering by Particle Bombardment I (R. Behrisch, ed.), p. 145. Springer-Verlag, Berlin. Andersen, H. H. and Sigmund, P. (1965). Nucl. Instrum. Methods 38,238. Andersen, H. H. and Ziegler, J. F. (1977). In The Stopping and Ranges of Ions in Matter (organized by Z. F. Ziegler), Vol. 3. Pergamon Press, New York. Armstrong, T. R., Corliss, R. C., and Johnson, P. B. (1981). J. Nucl. Mater. 98, 338. Auciello, 0.(1976). Radiat. Efl. 30, 11. Auciello, 0.(1981). J. Vac. Sci. Technol. 19, 841. Auciello, 0.(1982). Radiat. FfS.60, I. Auciello, 0.(1984a). In Ion Bombardment ModiJcalion of Surfaces (0.Auciello and R. Kelly, eds.), p. 435. Elsevier, Amsterdam. Auciello, 0.(1984b).In Ion Bombardment Mod$cation qf Surfaces (0.Auciello and R. Kelly, eds.), p. 1. Elsevier, Amsterdam.

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