Objective Comparison of Scanning Ion and Scanning Electron Microscope Images

SCANNING Vol. 19, 489 497 (1997) Received December 1, 1996 FAMS, Inc. Accepted with revision January 6, 1997 Objective Comparison of Scanning Ion and Scanning Electron Microscope Images TOHRU ISHITANI AND HIDEKI TSUBOI* Instrument Division, Hitachi, Ltd., *Techno Research Laboratory, Hitachi Instruments Engineering Co., Ltd., Hitachinaka, Japan Summary: Common and different aspects of scanning electron microscope (SEM) and scanning ion microscope (SIM) images are discussed from a viewpoint of interaction between ion or electron beams and specimens. The SIM images [mostly using 30 kev Ga focused ion beam (FIB)] are sensitive to the sample surface as well as to low-voltage SEM images. Reasons for the SIM images as follows: (1) no backscatteredelectron excitation; (2) low yields of backscattered ions; and (3) short ion ranges of 20 40nm, being of the same order of escape depth of secondary electrons (SE) [=(3 5) times the SE mean free path]. Beam charging, channeling, contamination, and surface sputtering are also commented upon. Key words: scanning electron microscope, scanning ion microscope, focused ion beam, Monte Carlo simulation, scattering Introduction Scanning electron microscopes (SEM) and transmission electron microscopes (TEM) have been used for structural observation of microdevices, advanced materials, and biological specimens. In recent years, a focused ion beam (FIB) has been used for preparing their cross-sectional samples (Ishitani et al. 1994, 1996 a, b; Nikawa 1991; Steave et al. 1995). Here, the FIB works both as a milling beam and as a probe for a scanning ion microscope (SIM). SIM images are in good use during the whole milling processes, that is, drawing of the milling area, milling monitoring, and confirmation of the final milling. The SIM image resolution has been improved, and 10 nm or better resolution is achievable at present (Ishitani et al. 1996, Kubena et al. 1991). Since both FIB milling and SIM observation are carried out in one FIB system, SIM observation is gradually replacing SEM observation, mostly for the FIB cross-sectioned samples. Figure 1 Address for reprints: Tohru Ishitani Instrument Division Hitachi, Ltd. 882 Ichige, Hitachinaka Ibaraki 312, Japan shows typical SIM images of FIB cross-sectioned microdevice and diatom samples. Although the contrast mechanism present in the SIM image is similar to that in SEM, there are some differences. While SIM advantages include high contrast sensitivity to surface topography and crystal grain (channeling), drawbacks include sample surface damage and ion implantation. To the authors knowledge, one report has been published regarding the SIM contrast (Olson et al. 1992). In the present paper, SIM and SIM images will be discussed from a viewpoint of interaction between ion or electron beams and specimens. In addition, beam charging, contamination, and surface sputtering will be commented upon. Scanning Ion Microscope Imaging Ion beam irradiation on a target generates electrons, positive and negative secondary ions, photons, and neutrals particles. The positive or negative particles are collected to form SIM images. The yields of secondary electrons (SE) are, in general, far larger than those of negative or positive secondary ions (SI), so the negative particle signal is essentially the SE signal. Here, SIM images in the present study have used the SE signal. Both FIB milling and SIM imaging are performed mostly using 25 30 kev gallium (Ga) beams. Thus, the ion species of interest is Ga in the present study. Monte Carlo Simulations of Electron and Ion Trajectories Interaction of electron or ion beams with solid samples is complex. Before ultimately losing their energies or escaping the sample, each incident electron or ion may undergo a large number of scattering events, distributed between elastic and inelastic processes. While elastic collisions result from collisions of energetic electrons or ions with nuclei of the target atoms and alter their undergoing directions, inelastic collisions result in transfer of their energies to the target, leading to generation of SE, Auger electrons, photons, electron hole pairs, and so forth. (Here, elastic and inelastic collisions are defined as the collisions satisfying and unsatisfying the energy and momentum conservation rule, respectively.) The

490 Scanning Vol. 19, 7 (1997) Monte Carlo (MC) method using a stepwise simulation of various scattering events is useful to both macro- and microscopically understood beam interactions (refer to the special issue on electron beam/specimen interaction modeling in Scanning 17, No. 4 & 5, 1995). Monte Carlo programs also allow to estimate the various signals, their yields, distributions, and so forth. Electron and Ga ion trajectories are MC simulated so that their beam interactions are visually understood. Figure 2a and b shows their trajectories in silicon (Si) and tungsten (W) targets, respectively, where beam energies Eo are 30 and 1.5 kev for electrons and 30 kev for Ga ions. Here, Si and W are chosen as typical lighter and heavier atomic mass elements relative to Ga (i. e., atomic mass M = 28.1, 69.7, and 183.5 amu for Si, Ga, and W, respectively). A mass ratio of the strike to struck particles much governs the elastic scattering, as will be discussed further on. Both MC programs for electrons and ions employed here are based on a single scattering model proposed by Joy (1988), and by Ishitani et al. (1983) and Ishitani and Kaga (1995), respectively. Only 50 trajectories are drawn for each plot in Figure 2 so as not to be heavily overlapped. Several thousands trajectories also have been simulated to attain a decent feeling for their interaction volumes. Noticeable differences among MC results are as follows: Si target 30 kev Electrons 5 µm Si target 1.5 kev Electrons 30 kev Ga ions (a) 10 µm (a) 0.2 µm 30 kev Electrons W target 0.5 µm 1.5 kev Electrons 30 kev Ga ions W target 0.01 µm 5 µm (b) FIG. 1 Scanning ion microscope images of focused ion beam crosssectioned samples; (a) microdevice, (b) diatom. (b) FIG. 2 Monte Carlo simulations of 30 kev and 1.5 kev electron and 30 kev Ga + ion trajectories in the targets; (a) Si target, (b) W target. The number of trajectories drawn for each plot is 50.

T. Ishitani and H. Tsuboi: Objective comparison of SIM and SEM images 491 1. Range: Electron interaction volume indicates little dependency on Eo and atomic number of the target atoms (,) except for its scale magnification. The 30 kev ranges R are about 6 and 0.6 µm for Si and W, respectively, and 1.5 kev R are about 0.05 and 0.01 µm for Si and W, respectively. Although a factor of 10 exists in 30keV R between Si and W targets, there is only a slight difference between their reduced mass ranges in µg/cm 2. It is known that an approximately -independent mass range is valid at Eo = 10 100 kev (Reimer 1993). On the other hand, 30keV ion R are as short as about 0.04 and 0.02 µm for Si and W, respectively, and are roughly the same as 1.5 kev electron R. In addition, a -independent mass range is no longer valid for ion R. 2. Backscattering: The larger the sample, the higher the backscattering yield η is for electron beam. On the other hand, ion η is rather low compared with electron. This is expected from that Ga ions are never deflected in backward direction at Ga-Si elastic collisions because of M Si /M Ga < 1 (see Appendix). 3. Total path length: As to total path length (defined as an accumulated path length along each zigzag trajectory of the electrons or ions stopped in the sample), there is little difference among the electrons. The reason is that electrons suffer negligible energy loss in elastic two-body collisions because of M target-atom /M electron >> 1. On the other hand, the larger the ion deflection angle, the larger is the ion energy loss (see Appendix). Thus, the ion range after the large-angle scattering becomes short on average. If the energy transferred from the ion to the target atom exceeds a sharp threshold energy, the target atom is displaced and is added to the cascade with kinetic energy. This cascade brings about lattice damage and sputtering. Excitation of Secondary Electrons There is a common view of the secondary electron (SE) emission event which is split into three stages: (1) Primary excitation by incident electrons or ions during penetration, as well as secondary excitation by energetic secondary particles; (2) migration on of some of the liberated electrons to the surface; and (3) escape of these electrons through potential barriers at the surface. Only the first stage is different in aspect between electron and ion beam irradiation. Secondary Electron Excitation by Electron Beam Irradiation Scanning electron microscope imaging has been described in textbooks by Goldstein et al. (1981) and Reimer (1993). Important points in SEM imaging are outlined below. Secondary electrons are produced as a result of interactions between primary electrons (PE) and weakly bound conduction electrons. The resulting SE energy distribution shows a peak at about 2 5 ev and a long tail as shown in Figure 3. The distribution will be compared with ion-induced emission lat- er. (Here, by convention, emitted electrons with exit energies of <50 ev are called SE.) Secondary electrons can escape from a small depth, where their escape probability decreases exponentially: ρ exp( z / λ) (1) where z is the depth below the surface where the SE generation takes place and λ is the mean free path of SE. Here, λ is about 1 nm for metals and up to 10 nm for insulators. The SE escape depth is taken as 3 5 times λ. Although λ is dependent on SE energy, the λ values given above are sufficient for rough estimation. The SE generally contains two components. The first, conventionally labelled SE1, consists of SE excited by the PE, as shown in Figure 4. Since these SE are directly related to the beam position, it is this component that carries high-resolution information about the sample. The second group, SE2, consists of SE produced by backscattered electrons (BSE). These are generated both from the surface illuminated by the incident beam and from depths of up to 0.3 0.5 times the electron range R, typically to 0.1 3 µm at Eo = 10 30 kev, depending on the target material. The surface distribution of SE showing the SE1 and SE2 components are schematically shown in Figure 5. This will be compared with ion-induced emission further on. The quality of SEM images depends on relative magnitudes and information contents of these two components. The total SE yield δ is expressed as which can be rewritten as δ = δ SE1 + δ SE2 (2) δ = δ SE1 (1 + βη) (3) where η is a bulk backscattering coefficient and β is a factor which represents relative efficiency of BSE that generate SE. The β is always greater than 1 because BSE have energy J(E) (arbitrary units) 0 50 Electron-induced emission Ion-induced emission Eo E [ev] FIG. 3 Comparison of schematic energy spectrum (in arbitrary units) of total electrons emitted from the specimen for electron-induced emission and ion-induced emission.

492 Scanning Vol. 19, 7 (1997) lower than those of PE and because they approach the surface over a wide range of angles. In general, the β is of the order of 2 4. The η is weakly dependent on Eo (over the range of 1 100 kev), but is a monotonous function of, which can be approximated by a function as (Reimer 1993) η = (2.54E 2) + (1.6E-2) (1.86E 4) 2 + (8.31E 7) 3 (4) Taking β = 3 and the calculated η values of 0.16 and 0.48 for Si and W, respectively, δ SE2 /δ SE1 values are 0.48 and 1.4 for Si and W, respectively. In the SEM images made with the δ signal, the δ SE1 term will be dominant for the signal for low targets, while the δ SE2 term will be dominant for high targets. The total electron yield σ (= δ+ η) for normal incidence of the beam varies with Eo, as schematically shown in Figure 6a. Starting at Eo = 0, σ rises with Eo, reaching 1 at Eo = E 1 (about 1 kev). A peak, slightly above 1 for metals and as high as 3 for nonmetals, is observed in the range 0.5 1 kev (Plies 1994). With further increase in Eo, σ decreases and passes through 1 again at Eo = E 2 (1 3 kev), and continues to decrease with increasing Eo to a value of about 0.1 for metals and Eo = 20 kev. As Eo is reduced, electron range R falls and σ rises. Thus, at Eo 1 kev, SE1 and SE2 contributions to the spatial resolution become indistinguishable since R is compatible with the SE escape depth (Joy 1987). In case of a practical probe with a finite diameter, the SE spatial distribution is given approximately by a convolution of a response SE spatial distribution for zero diameter probe (shown in Fig. 5) with its probe-intensity spatial distribution. Secondary Electron Excitation by Ion Beam Irradiation Secondary electron excitation by ion beam irradiation has been reviewed in several papers (Hofer 1990, Schou 1988). The SE emission processes for a metal target are divided into two different types, that is, potential emission and kinetic emission, depending on whether or not the emitted SE are liberated by conversion of potential or kinetic energy of the projectile ion. Since the kinetic emission generally becomes more efficient with increasing Eo, it is of equal importance to σ in the Eo range of 0.5 10 kev with the potential emission (Nishimura et al. 1996). A typical σ Eo curve (at Eo < several tens kev) is schematically shown in Figure 6b. The σ increases monotonically with Eo, in contrast to electron-induced emission. The ion beam does not logically excite BSE. The yield for backscattered ions (BSI) is much smaller than BSE yield for electron bombardment. Then, the expected SE spatial distribution is described by δ SE1 component only as shown in Figure 4. Therefore, SIM images available with an ion probe of 30 kev Ga are very sensitive to surface just like low-voltage SEM images. Details of these behavior for the ion specimen interaction can be described by using MC simulation taking account of SE excitation (Nishimura et al. 1996, Ohya and Kawata 1995). Magnetic Contrast There are two types of magnetic contrast (Reimer 1993): In the contrast type 1, external magnetic stray fields above ferromagnetic domains or magnetic recording media can act on SE trajectories by Lorentz force and result in a small tilt of SE PE BSE Je(r) (Arbitrary units) Specimen SE2 SE1 Range R SE escape depth SE1 Electron-induced emission SE2 Ion-induced emission FIG. 4 Excitation of backscattered electrons (BSE) and two groups of secondary electrons (SE1 and SE2) by irradiation of primary electrons (PE). Volume of electron penetration, BSE trajectories, and SE escape region are shown with increasing density of gray levels. 0 r FIG. 5 Comparison of the surface distribution of secondary electrons showing the SE1 and SE2 components under electron-induced emission and under ion-induced emission.

T. Ishitani and H. Tsuboi: Objective comparison of SIM and SEM images 493 exit, which can be observed as magnetic contrast. The magnetic contrast type 2 is caused by Lorentz force of internal magnetic induction on BSE trajectories. Since Ga ion is about 1.3E+5 times heavier and about 3.6E+2 times less sensitive to the magnetic field than electrons, the type 2 contrast is of no interest for the SIM. Charging When insulator samples are bombarded by high-energy electrons (Eo > E 2 in Fig. 5), a strong negative charging results because of σ < 1, exhibiting charging artifacts on SEM images. It is thus desirable to operate at E 1 < Eo < E 2, which results in weak positive charging. Under such conditions, uncoated insulators can be examined. Here, sample tilt, that is, non-normal incidence, is not taken into account. As the tilt angle α increases, δ increases approximately, obeying a secant relationship: δ(α) = δ(0) sec α (5) Therefore, specimen tilting is often used in SEM to permit charge-free operation even with energies Eo >E 2 (α=0). On the other hand, ion bombardment (e. g., Ga + beam) brings about a strong positive charging on insulators. Both positive ion bombardment and negative SE emission do charge the surface positively. Lowering the Eo method is no longer effective for charge-free SIM imaging. Subsequently, the following two methods are used in practice: (1) Conductive coating: an FIB-assisted deposition is often used for locally coating the FIB milling area. (2) Low-energy electron spraying to cancel the positive charge: since the SE detector takes in the sprayed electrons as well as the true SE, the positive SI signal is employed instead of the SE signal. It is experimentally known that the Ga implanted layer is so effective that it reduces the surface charge which is, in practice, enough for SIM imaging with a low probe current of a few pa or less. What will happen if a polarity of ion beam is negative? The δ value at Eo > a few kev is presumably little dependent on the polarity and is larger than 1. In secondary ion mass spectrometry (SIMS) using an oxygen-negative ion beam (O - ), a stable positive charging of only a few ev has been achieved both by setting a semi-spherical grid in front of the sample and by applying the same potential to both the grid and the sample holder (Fig. 7) (Tamura 1983). The positive charging makes a high-energy (E) SE pass filter of the grid, where the high-e SE part corresponding to the unity yield can go through the grid and the low-e part corresponding to the yield of σ - 1 is sent back to the surface. Finally, the SI mass spectrum has been obtained to satisfaction. σ Negative ion beam 1 SE grid 0 0 E1 E2 (a) Electron-induced emission E0 SI SE σ Sample holder Nonconductive sample 0 ~1kV (b) Ion-induced emission FIG. 6 Total emitted electron yield σ (in arbitrary units) as a function of electron/ion beam energy Eo; (a) electron-induced emission (E1 1keV and E2 = 2 3keV), (b) ion-induced emission. E0 FIG. 7 Schematic illustration of negative ion bombardment for secondary ion mass spectrometry analysis. SE = secondary electrons, SI = secondary ions (positive). Charge equilibrium state is achievable by setting a hemispherical metal-grid, with the specimen holder potential, in front of the nonconductive specimen.

494 Scanning Vol. 19, 7 (1997) Channeling Through crystal channeling (orientation or grain) contrast of the SEM image, grains in polycrystalline specimens are seen with BSE contrast that depends sensitively on the specimen tilt (Reimer 1993). This sensitivity results from the dependence of the BSE yield η on the orientation of the primary beam relative to the lattice planes and is caused by the primary Bloch wave field. Due to the sensitivity of the η variation on the surface, the channeling contrast can decrease with an increasing electron-probe focusing angle which should not exceed 1 10 mrad. The depth of average channeling varies with, but for most elements, the additional contribution to the contrast is very small from depths > 50 nm. The channeling contrast is also very sensitive, either on an amorphous surface oxide layer or on multiple scattering in the crystal. As to the directional effects of kinetic ion electron emission, experimental and theoretical work has been reviewed by Brusilovsky (1985). Fast particles entering crystalline materials in low-index lattice directions are steered into the interior of the target by many small-angle scattering collisions. This causes a drastic δ-reduction for two reasons: first, kinetic electron emission depends on inelastic energy loss and channeled ion transfers relatively small energy in each collision along its path; second, electrons generated deep in the material have difficulty in escaping to the surface. Channeling also reduces sputtering yield S because a fraction of the projectiles is steered into regions so deep in the crystal that there is no more momentum in the arrival of these projectiles at the surface. Only direct hits, that is, small-impact parameter collisions with surface atoms, result in atom ejection events. A typical SIM image showing the channeling contrast from the aluminum (Al) surface is shown in Figure 7. The dark grains with low δ correspond to the channeled grains and to the low S grains. Such a clear contrast has been obtained after removing the native oxide surface layer with a high δ. On angular δ curves, dependence of dip half-width Ψ w is approximately in accordance with the Lindhard critical channeling angle (Dearnaley et al. 1973). Ψ c (Z 1 /Eo) 1/2 (6) The experimental Ψ w values mostly range from several to about 20, which are sufficiently larger than the FIB focusing angles of a few mrad. Since this wide Ψ c produces several contrast levels corresponding to various channeling orientations, the SIM image is useful in practice to evaluate the grain sizes with various crystal planes. Contamination and Ion Sputtering Contamination is caused by damage and polymerization of organic molecules on the electron-irradiated area. Thin deposits of contamination result in darkening of the irradiated area and in decreasing contrast of surface structures in the SEM image. Ion beams also polymerize the organic molecules, but Ga beams provide a higher sputtering rate than a deposition rate of contamination; that is, the sample surface suffers from sputtering rather than contamination. Here, the deposition or sputtering yield of 1 atoms/ion corresponds to their rate of 0.12 µm 3 /na s when N = N(Si). A positive application of ion radiation damage is FIB-assisted deposition. An appropriate precursor gas, usually metal carbonyl or organometallic molecules, is introduced near the surface through a capillary tube. The deposition occurs when the FIB dissociate the absorbed gas molecules. Local deposition using numerous precursor gases has been employed in microelectronics fabrication such as photo mask and x-ray mask repairs, as well as circuit restructuring, customization, and repair. The local coating of the conductive layer to reduce the surface charge, as mentioned before, is one of these applications. For a review of the subject and citations of literature, see references in Gamo and Namba (1990) and Melngailis (1991). Scanning ion microscopy imaging encounters a surface topography change due to ion sputtering as the SIM probe beam is common to the milling heavy ion beam. The sputtering rate is strongly dependent on ion species, beam energy, angle of incidence, and target materials. Typical values are in the range of 0.2 0.8µm 3 /na s for the combination of 30 kev Ga ion and Si target. This topography change brings about the upper limit in SIM magnification. Crystalline Damage Assuming that the ion range profile is approximately equal to the damage profile, the damage profile is about 40 nm in depth and about 10 nm in half width for the 30 kev Ga ion bombardment on the Si target. The FIB cross sectioning also forms the damage layer of about 10 nm in thickness (Ishitani et al. 1994; 1996a, b). The question is the extent of the damage density. This is determined in a first approximation by total balance between the accumulating damage profile and the surface recession due to ion sputtering (Ishitani et al. 1996b). Keeping the channeling contrast up to a high ion dose, which has often been observed in metal samples, verifies that the damage is sparse and not completely amorphous. The damage density must be sensitive to the displacement energy of a lattice atom, depending on the target material. As to a local temperature rise due to the FIB power, an analytical calculation has been reported (Ishitani and Kaga 1995). Conclusions To the following contrast types of SEM image, several distinctive aspects of SIM contrast type are added and summarized. Here, the most important contributors (SE or BSE) to SEM are listed: 1. Topographic contrast (SE and BSE) 2. Material or compositional contrast (BSE and SE)

T. Ishitani and H. Tsuboi: Objective comparison of SIM and SEM images 495 3. Grain (channeling) contrast (BSE and SE) 4. Magnetic contrast type 1 (SE) of external and type 2 (BSE) of internal magnetic fields. One of essential parameters is information depth of SE and BSE in both SEM and SIM. In high-voltage SEM, information depth and exit volume of BSE are much larger than those for SE1 generated by the PEs. This makes for a large difference between SE and BSE images, although these signal contains the group SE2 generated by BSE. In low-voltage SEM, the information volume becomes more similar to the SE escape depth (defined as 3 5 times the SE mean free path). BSE contrast observable at high energies disappears or is reduced. Scanning ion microscope images using Ga ion probes, on the other hand, are sensitive to the sample surface just like low-voltage SEM images. The reasons are: (1) short ion ranges of 20 40 nm that are of the same order as the SE escape depth; (2) no BSE excitation; and (3) low BSI yields. SIM images provide also distinct channeling contrast because of the large channeling-critical angle of several to about 20, in contrast to 1 10 mrad for SEM images. Far from the surface contamination, ion beams sputter away the surface native oxide layer, which keeps the channeling SIM image in good contrast. In the two types of magnetic contrast (types 1 and 2), there is no type 2 contrast for SIM because of the heavy mass of Ga ions. As to charge-up for nonconductive samples, optimum probe energies to balance between entering and outgoing charges do exist in SEM, but not in SIM using a positive ion probe. FIG. 8 Typical channeling scanning ion microscope image of aluminum film deposited on silicon substrate. (The letters HITACHI on the surface were focus ion beam-milled.) Further studies will be undertaken using SEM and SIM images for the common samples. Monte Carlo simulations taking account of SE excitation and collision cascade will also be useful to understand their imaging. Acknowledgments The authors acknowledge Drs. T. Nagumo and F. Mitsuhasi of The Nippon Dental University for supplying them with a sample of their diatom, and Mr. K. Kanda of Instrument Division, Hitachi Ltd., for using the Microsoft- Windows program of electron MC-simulation, which was originally developed by Dr. D. C. Joy (1988). It should also be mentioned that the SIM images were obtained with the Hitachi FIB system, developed by H. Hirose, H. Koike, T. Ohnishi, and other colleagues. References Brusilovsky BA: Directional effects in kinetic ion-emission. Vacuum 35, 595 615 (1985) Dearnaley G, Freeman JH, Nelson RS, Stephen J: Ion Implantation. North-Holland Publishers, Amsterdam (1973) Ding ZJ, Shimizu R: A Monte Carlo modeling of electron interaction with solids including cascade secondary electron production. Scanning 18, 92 113 (1996) Gamo K, Namba S: Ion beam assisted etching and deposition. J Vac Sci Technol B8, 1927 1931 (1990) Goldstein JI, Newbury DE, Joy DC, Fiori C, Lifshin E: Scanning Electron Microscopy and X-ray Microanalysis. Plenum Press, New York (1981) Hofer WO: Ion-induced electron emission from solids. Scan Microsc (suppl) 4, 265 310 (1990) Ishitani T: Monte Carlo simulation of ion bombardment at low glancing angles. Jpn J Appl Phys 34, 3303 3306 (1995) Ishitani T, Kaga H: Calculation of local temperature rise in focused-ionbeam sample preparation. J Electron Microsc 44, 331 336 (1995) Ishitani T, Shimase A, Hosaka S: Monte Carlo simulation of energetic ion behavior in amorphous targets. Jpn J Appl Phys 22, 329 334 (1983) Ishitani T, Tsuboi H, Yaguchi T, Koike H: Transmission electron microscope sample preparation using a focused ion beam. J Electron Microsc 43, 322 326 (1994) Ishitani T, Yaguchi T, Koike H: Focused ion beam system for TEM sample preparation. Hitachi Rev 45, 19 24 (1996a) Ishitani T, Yaguchi T: Cross-sectional sample preparation by focused ion beam: A review of ion sample interaction. Microsc Res Techn 35, 1320 333 (1996b) Joy DC: Low voltage scanning electron microscopy. Inst Phys Conf Ser No. 90, 175 180 (1987) Joy DC: An introduction to Monte Carlo simulations. Inst Phys Conf Ser No. 93, 1, 23 32 (1988) Kubena RL, Ward JW, Stratton FP, Joyce RJ, Atkinson GM: A low magnification focused ion beam system with 8 nm spot size. J Vac Sci Technol B 9, 3079 3083 (1991) Melngailis J: Focused ion beam induced deposition: A review. SPIE Proc 1465, 36 49 (1991) Nikawa K: Applications of focused ion beam technique to failure analysis of very large scale integrations: A review. J Vac Sci Technol B 9, 2566 2577 (1991) Nishimura K, Ohya K, Kawata J: Contribution of kinetic and potential emission to kev singly charged on induced electron emission from a metal surface. Jpn J Appl Phys 35, 2284 2289 (1996)

496 Scanning Vol. 19, 7 (1997) Ohya K, Kawata J: Simulation of electron emission from beryllium under electron and ion bombardments. Scan Microsc 9, 331 353 (1995) Olson TK, Lee RG, Morgan JC: Contrast mechanisms in focused ion beam imaging. Proc 18th Int Symp Testing & Failure Analysis, 373 380 (1992) Plies E: Electron optics of low-voltage electron beam testing and inspection. Part I: Simulation tools. Adv Opt Electron Microsc 13, 123 242 (1994) Reimer L: Image Formation in Low-Voltage Scanning Electron Microscopy. SPIE Optical Engineering Press, Washington (1993) Ryssel H, Ruge I: Ion Implantation. John Wiley & Sons, New York (1986) Schou J: Secondary electron emission from solids by electron and proton bombardment. Scan Microsc 2, 607 632 (1988) Steve FA, Shane TC, Kahora PM, Hull R, Bahnck D, Kannan VC, David E: Application of focused ion beams in microelectronics production, design, and development. Surf Interface Anal 23, 61 68 (1995) Tamura H: Analysis of insulating materials by negative ion microprobe. Sinku (Vacuum) 26, 179 188 (1983) (in Japanese) Appendix: Electron/Ion Scattering Elastic Collision It is appropriate both to describe interaction of two colliding particles as that of a collision of two point masses (M 1 for the incident electron or ion, M 2 for the struck particle) and to set up and solve the classical mechanical dynamic equations of motion under a central force constraint (see Fig. A1). When the incident particle is elastically scattered through an angle θ relative to the direction of motion of the center of mass (CM), the incident particle with kinetic energy E loses energy by T = E {(1 A)/(1 + A)} 2 sin 2 (θ/2) (A1) where A = M 2 /M 1. This energy loss is equal to postcollision energy of the struck atom. The T value is maximum at θ = 2π (i. e., a head-on collision), T max = {(1 A)/(1+A)} 2 E M1, E T M1, E M2 Θ (A2) Only when T is larger than atom displacement energy ( 25 ev for metal) in ion-atom collisions, target atoms are knocked out from their lattice positions. When struck atoms have sufficient kinetic energies to generate secondary collisions, they initiate a cascade of atomic collisions, causing irradiation damage and sputtering. The center of mass scattering angle θ is converted to the scattering angle Θ in the laboratory (Lab.) system using a simple relation such as cos Θ = (1 + A cos θ)/(1 + 2A cos θ + A 2 ) 1/2 (A3) The direction of motion of the postcollision struck atom in the Lab. system, at angle Φ to the locus of CM is given by Φ = (π θ)/2 (A4) In Eq. (A3), when θ = 0, Θ = 0, and when θ = π, Θ = 0 or π, depending upon whether A < 1 or A > 1, that is, the incident ion, which is heavier than the struck atom (i. e., A < 1), is always scattered forward in the Lab. system (i. e., 0 Θ π/2). On the other hand, collisions for A > 1 cover a full range of 0 Θ πso that backward scattering (i. e., π/2<θ π) can also occur. Here, both Ga ion W target atom and electron target atom collisions of interest correspond to the case of A > 1. Especially in the latter collision (at E < 100 kev), both Θ θ and Τ 0 are satisfied at any θ because of A»1. In other words, electrons can change their directions without losing their kinetic energies through elastic collisions. No target atoms are knocked out from their lattice positions. Inelastic Collision Regarding the approach to ion inelastic scattering, the continuous slow-down approximation has been widely used. A schematic representation of the stopping power combines two energy regimes. The stopping power increases from zero, passes through a maximum when the incident velocity V is of the order of orbital velocities of lattice electrons ( 2/3 V B ), and finally falls off inversely as the first power of energy. Here, V B = 2.2E + 6 m/s is the velocity of Bohr electron in the hydrogen atom. In the lower velocity region (i. e., V < Z 1 2/3 VB, 2/3 V B ), a V-proportional stopping power is derived. The velocity of V = Z 1 2/3 V B is converted to energy of E [kev] 25Z 1 4/3 M 1 [amu], which corresponds to 25 kev for H ion and 170 MeV for Ga ion. Using dimensionless energies and distances, V-proportional electronic stopping power is given by Dearnaley et al. (1973) and Ryssel and Ruge (1986), Φ ( dε/dρ) electronic = kε 1/2 (A5) M2, T where FIG. A1 A collision of two particles in a laboratory system. M 1 =incident or moving electron/ion mass, M 2 =struck particle mass). ε = E(a/Z 1 e 2 )(M 2 /(M 1 +M 2 ) (A6)

T. Ishitani and H. Tsuboi: Objective comparison of SIM and SEM images 497 ρ = R N 4π a 2 M 1 M 2 /(M 1 +M 2 ) 2 (A7) κ = ξ e [0.0793 {Z 1 1/2 1/2 /(Z 1 2/3 + 2/3 ) 3/4 } x{(m 1 +M 2 ) 3/2 /(M 1 3/2 M 2 1/2 )}], (ξ e = Z 1 1/6 ) (A8) a = 0.885 a B /(Z 1 2/3 + 2/3 ) 1/2 (Thomas-Fermi radius) (A9) a B = 0.053 nm (Bohr radius), and N is the number of target atoms per unit volume. At high ion velocities V >> Z 1 V B, inelastic energy loss to lattice electrons through excitation and ionization dominates and electronic stopping power is given by Bethe formula (Dearnaley et al. 1973): (de/dr) = (4π Z 1 2 e 4 /m e V 2 ) N ln(2m e V 2 /I AV ) (A10) where m e is the electron mass and I AV is the average ionization energy. The Eo of several tens kev for Ga ion beam is too low to excite x-ray emission, in contrast to the electron beam. Energy Loss figure. The Sn(ε) curve shows its maximum at ε 1/2 0.5 0.6 and is larger than Se(ε) at ε 1/2 <1.2 and 1.9 for Ga ions in W and Si targets, respectively. It is found that Sn(ε) is dominant in energy loss for the 30 kev-ga ion penetration in Si and W targets. As to the electron stopping power, the nuclear term in Eq. (A11) is negligible as discussed before. The electron inelastic stopping powers for gold (Au) and copper (Cu) targets (Ding and Shimizu 1996) are shown in Figure A2 (b). The stopping power has a maximum plateau of 60 100 ev/nm in a range of 0.1 kev < E < 1keV. The Bethe equation is valid only at sufficiently high electron energies, that is, E >3keV (Reimer 1993). (de/dr) = (2π e 4 N/E) ln(1.166e/i). (A13) It was found that the electron stopping powers at Eo = 1 30 kev are smaller by 1 to 2 orders of magnitude than those for Ga ions. This predicts that Ga ion ranges are shorter by 1 2 orders of magnitude than electron ranges under the same incident energies. 10 3 The stopping of an energetic particle in solid results from a sum of two components (i. e., the nuclear and electronic stopping), which may be taken in good approximation as independent of each other, and the total stopping power is given by ( de/dr) total = ( de/dr) nuclear + ( de/dr) electronic (A11) 10 2 10 Au Cu The nuclear stopping depends on the cumulative effect of statistically independent elastic scattering of the incident particle and the target atom. The stopping power is given by 1 10 10 2 Bethe 10 3 10 4 10 5 ( de/dr) i = ( dε/dρ) i (ρ/r)/(ε/e) (A12) where i = nuclear, electronic, or total. Here, ( dε/dρ) i is the i- component universal stopping power per atom. Values of ε/e, ρ/r, and κ for combination of Ga ion with Si and W targets are given in Table IA. The curves of Sn(ε) [ ( dε/dρ) nuclear ] and Se(ε) [ ( dε/dρ) electronic ] versus ε are shown in Figure A2 (a). The E and ( de/dr) axes, which are reduced for the combinations of Ga ion with Si and W targets, are also given in the TABLE IA Various important parameters in the beam-specimen interactions Atomic Atomic Target number mass Density LSS parameters element Z M[amu] ρ[g/cm 3 ] M/M Ga ε/e[kev] ρ/r[µm] κ Si 14 28.086 2.42 0.40 5.44E 3 18.7 0.117 W 74 183.85 19.3 2.64 1.96E 3 11.8 0.287 Ga = Z Ga = 31, M Ga = 69.72. -de/dr [kev/nm] S(ε) 0.5 3 1.5 0.4 2 1 0 1.0 0.5 0.0 0.3 0.2 0.1 0.0 0 1 2 3 0 100 0 Sn(ε) Sn(ε) (Ga in W) Sn(ε) (Ga in Si) 400 1000 2000 1000 4000 FIG. A2 Comparison of stopping power between electron and ion; (a) electron stopping powers for Au and Cu targets (Ding and Shimizu 1996), and (b) ion stopping powers. 4 E [kev] Ga in Si E [kev] Ga in W