- Email: [email protected]
Simulation study of secondary electron images in scanning ion microscopy
Nuclear Instruments and Methods in Physics Research B 202 (2003) 305–311 www.elsevier.com/locate/nimb
Simulation study of secondary electron images in scanning ion microscopy K. Ohya a
a,*
, T. Ishitani
b
Faculty of Engineering, The University of Tokushima, Tokushima 770-8506, Japan b Naka Division, Hitachi High-Technologies Corp., Ibaraki 312-8504, Japan
Abstract The target atomic number, Z2 , dependence of secondary electron yield is simulated by applying a Monte Carlo code for 17 species of metals bombarded by Ga ions and electrons in order to study the contrast difference between scanning ion microscopes (SIM) and scanning electron microscopes (SEM). In addition to the remarkable reversal of the Z2 dependence between the Ga ion and electron bombardment, a fine structure, which is correlated to the density of the conduction band electrons in the metal, is calculated for both. The brightness changes of the secondary electron images in SIM and SEM are simulated using Au and Al surfaces adjacent to each other. The results indicate that the image contrast in SIM is much more sensitive to the material species and is clearer than that for SEM. The origin of the difference between SIM and SEM comes from the difference in the lateral distribution of secondary electrons excited within the escape depth. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 79.20.Ap; 79.20.Rf Keywords: Secondary electron emission; Monte Carlo simulation; Scanning ion microscopy; Focused ion beam
1. Introduction Focused gallium ion beams have been used to prepare cross-sectional samples in semiconductor microfabrication processes and subsequently to observe them, where a scanning ion microscope (SIM) is employed as an observational tool, like a scanning electron microscope (SEM). In many cases, the material contrast in the SIM image is opposite to that for SEM [1,2]. Recent Monte Carlo calculations of the secondary electron
*
Corresponding author. Tel./fax: +81-886-56-7444. E-mail address: [email protected] (K. Ohya).
emission of Al (Z2 ¼ 13), Cu (Z2 ¼ 29) and Au (Z2 ¼ 79) have revealed the origin of the difference in the material contrast between SIM and SEM images [2,3]. For bombardment of light targets with Ga ions, a large fraction of the total energy deposited in electron excitation is due to collisions between recoiled target atoms and target electrons. The heavier target atoms transfer less energy to the electrons, thus leading to a poorer multiplication of other electrons in cascade processes. As observed in [2], however, a fine structure probably relating to the periods of the periodic system, is superimposed on the monotonous change in the secondary electron yield with Z2 . To investigate the fine structure of the Z2 dependence, we have
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)01874-8
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K. Ohya, T. Ishitani / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 305–311
conducted a Monte Carlo calculation of the secondary electron emissions of 17 species of metals. The results are also compared with the Z2 dependence of sputtering and ion reflection. Furthermore, two different metals, Au and Al, adjacent to each other were scanned by 30 keV Ga ions and 10 keV electrons, where the difference between SIM and SEM image characteristics is discussed.
2. Monte Carlo simulation of heavy ion induced secondary electron emission Ion-induced secondary electron emission can be ascribed to the processes of potential emission and kinetic emission. Ga ion bombardment will not lead to potential emission because of its low ionisation potential (6.0 eV), according to BaragiolaÕs empirical formula [4]. In the case of kinetic emission, the electron excitation can be caused by three collision processes in the target material: one due to collisions between projectile ions and target electrons, one due to collisions between recoiled target atoms and target electrons, and one due to collisions between excited electrons and other target electrons. The basic concept of our Monte Carlo code is to simulate trajectories of a projectile ion penetrating into the target bulk and of recoiled target atoms and excited electrons travelling towards the surface on the basis of the binary collision approximation with given mean free paths (MFP) for elastic and inelastic collisions. Details of the model are presented in [2,3]. One of the important physical quantities is the inverse MFP for electron excitation by projectile ions or the recoiled target atoms with velocity v [5], i.e., 1 X 1 1 3pnv X ¼ pffiffiffi 2 ð2l þ 1Þð2m þ 1Þ kinel 4 2vF l¼0 m¼0 f1 cos 2dl ðEF Þ cos 2dm ðEF Þ þ cos½2ðdl ðEF Þ dm ðEF ÞÞ g Z 1 1=2 ð1 xÞ Pl ðxÞPm ðxÞ dx:
ð1Þ
1
Here, dl;m is the phase shift for the scattering of a conduction band electron at the Fermi energy, EF , by the potential of the intruding ion or the
recoiled target atom at rest, assuming the impact of slow ions (v vB , vB : the Bohr velocity); for 30 keV Ga ions, v ¼ 0:13 vB . The quantities n, Pl;m and vF are the density of conduction band electrons, the Legendre polynomials and the Fermi velocity, respectively. By means of the partial wave expansion technique [6], the scattered wave function is decomposed into partial waves and the radial wave equation with a spherical symmetric scattering potential and solved using the Numerov algorithm. The phase shift in each partial wave is determined. Since the scattering potential is approximated by an analytical potential of neutral solid-state atoms obtained by Salvat and Parellada [7], the effect of the ion charge state on the MFP is not taken into account. The inverse MFP is directly proportional to v and n, so that the number of excited electrons increases with increasing v and depends upon the electron shell structure of the target atoms, and the atomic number, Z2 . The density, n, is deduced from experimental vF values compiled by Ziegler et al. [8], by use of the rela1=3 tionship, vF ¼ h=me ð3p2 nÞ . The motions of projectile ions and recoiled target atoms are treated in the same way; the straight free flight path is determined from the total MFP, ktot , defined as 1=ktot ¼ 1=kel þ 1=kinel , using a random number. The elastic MFP, kel , is fixed at N 1=3 where N is the atomic density of the target. Depending on each of the inverse MFPs, kel and kinel , either elastic collision or inelastic collision (i.e. electron excitation) is chosen using another random number. If elastic collision is chosen, the scattering angle is determined using an asymptotic procedure of atomic collisions in the Ziegler–Biearsack–Littmark interatomic potential [9], and the elastic energy loss is calculated. In each elastic collision, a new recoiled target atom is generated. If inelastic collision is chosen, the particle loses its energy and excites an electron. The energy of the excited electron is equal to the energy loss of the 2 particle, DE ¼ 2me ½v þ ðvF =2Þ [10], which is calculated from a head-on collision of the particle with a conduction electron. The initial directional angle of the excited electron is calculated using the energy and momentum conservation law. The excited electrons interact with the target through elastic collisions with the target atoms,
K. Ohya, T. Ishitani / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 305–311
and through inelastic collisions, i.e. excitations of conduction electrons and inner-shell electrons. The electron transport process is calculated using a direct simulation Monte Carlo model [11], which is used as well for secondary electron emission under electron bombardment. The trajectory of each electron is chosen as a series of random numbers to determine the path length between collision events, the type of collision that has taken place and the energy loss or the scattering angle. In each inelastic process, secondary electrons are excited, so that an electron cascade is generated. The elastic MFP is calculated using the screened Rutherford formula where the energy-dependent screening parameters for 17 species of metals are determined using the parameters for C, O, Al, Cu, Ag and Au calculated by Fitting and Reinhardt [12] by interpolation. For individual and collective (plasmon) excitation of conduction electrons, the differential inverse MFP, sðE; xÞ, of an electron with an energy E is described by the complex dielectric response function, Im½ 1=eðx; kÞ , i.e., 1 sðE; xÞ ¼ pE
Z
kþ
k
dk 1 Im
; k eðx; kÞ
ð2Þ
and the integration of sðE; xÞ over the allowed values of k yields the inverse MFP, 1=kinel . Here x and k are the energy and momentum pffiffiffipffiffiffiffitransfers pffiffiffiffiffiffiffiffiffiffiffiffito conduction electrons, and k ¼ 2 E E x in atomic units. In the previous papers [2,3] the MFP is calculated using the Lindhard dielectric function for eðx; kÞ according to Tung and Ritchie [13], but in the present simulation, optical data of the target material for the k ¼ 0 limit, eðx; 0Þ [14,15], is connected to eðx; kÞ according to an ‘‘optical-data’’ model developed by Ashley [16,17]. The advantage of this treatment is that, since eðx; 0Þ is based on the experimental result, it includes complicated processes of the inter-band, intra-band and some other transition mechanisms automatically, in addition to the individual and bulk-plasmon excitation of conduction electrons, which can be treated by the Lindhard dielectric function. The kinetic emission mechanism is conventionally subject to an impact energy threshold calculated from the condition that the energy
307
transfer from a projectile ion in a head-on collision with a conduction electron is equal to the surface barrier. The surface barrier is generally taken to be the energy difference between the bottom of the conduction band and the vacuum level, i.e. EF þ U (U: the surface work function) [18]. The surface barrier energy results in an extremely high threshold energy for Ga ions, e.g. 10.7, 18.8 and 26.6 keV for Al, Cu and Au targets, respectively, which are inconsistent with experimental observations for heavy ions such as Kr (Z1 ¼ 36), and Xe (Z1 ¼ 54) [4,19,20], as well as Ga (Z1 ¼ 31). Until recently, some models [21,22] were available for kinetic emissions below the conventional threshold energy. In this study, however, a lowering in the threshold energy is considered as a reduction in the apparent surface barrier between EF þ U and U [3]. According to the classical planar surface barrier model, excited and cascade electrons coming to the surface are emitted in the vacuum with reduced energy in a refracted direction due to the surface barrier energy. For the 17 species of metals used for this calculation, the values of EF obtained from different theoretical studies [23] are averaged, and the values of U are taken from [24]. The projectile ions and the recoiled target atoms are followed as well, until their energies falls below a predetermined energy or until they overcome the surface binding energy and escape into the vacuum; socalled ‘‘ion reflection’’ and ‘‘sputtering’’, respectively. The cohesive energy of atoms [25] is taken as the predetermined energy or the surface binding energy.
3. Results and discussion In Fig. 1(a), the secondary electron yield below the conventional threshold energies is simulated for the apparent surface barrier energy of 0:5EF þ U which has been arbitrarily chosen. The influence of the surface barrier energy on the secondary electron yield has been investigated in a previous study [3]: the decrease in the surface barrier energy from EF þ U towards U increases the secondary electron yields for both Ga ions and electrons, but retains the Z2 dependence of the
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Fig. 1. Projectile energy dependence of (a) secondary electron yield, ion reflection coefficient and sputtering yield, and (b) secondary electron yield and electron reflection coefficient of Al and Au, due to the impact of Ga ions and electrons, respectively.
Fig. 2. Target atomic number dependence of (a) secondary electron yield, ion reflection coefficient and sputtering yield, and (b) secondary electron yield and electron reflection coefficient of Al and Au, due to the impact of Ga ions and electrons, respectively. The solid, dotted and dashed lines are only intended as a guide for the eye.
secondary electron yields. In the calculation of the secondary electron yield for electrons (Fig. 1(b)), the surface barrier energy is taken as EF þ U. The secondary electron yield for Ga ion bombardment generally decreases with increasing Z2 whereas the secondary electron yield for electrons (>2 keV) increases. This can explain the reason for contrast reversal of secondary electron images observed between SIM and SEM. A fine structure is calculated not only for the secondary electron yield for Ga ion and electron bombardments, but also for the sputtering yield, as shown in Fig. 2. The fine Z2 dependence of the sputtering yield is strongly correlated to the surface binding energy. The lower the surface binding energy, the higher the sputtering yield. The secondary electron yield for electron bombardment is found to correlate to the density of conduction band electrons. These cor-
relations to the surface binding energy and the density of conduction electrons show dominant contributions of the surface and bulk properties of the material to sputtering and secondary electron emission, respectively. A similar trend in the secondary electron yield as for electron bombardment is calculated for Ga ions, although its strong decrease with increasing Z2 hides the fine structure. The reflection coefficient is less correlated to such physical parameters due to the dominant contribution of large angle scatterings through elastic collision sequences, where both the ZBL analytical interatomic potential for ion scattering and the screened Rutherford cross-section for electron scattering are used in this calculation and monotonously change with Z2 . To investigate brightness changes of the secondary electron images in SIM and SEM due to
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Fig. 3. Changes in (a) secondary electron yield, ion reflection coefficient and sputtering yield, and (b) secondary electron yield and electron reflection coefficient, due to scanning by 30 keV Ga ions and 10 keV electrons, respectively, near the boundary between Au and Al.
changes in target material, a sample surface, which is half made of Al and half made of Au, is scanned in the perpendicular direction to the boundary by 30 keV Ga ions and 10 keV electrons. In Fig. 3, large differences in secondary electron yield between Au and Al for Ga ion bombardment in comparison to electron bombardment can be seen. When the Ga ion beam moves from the Au surface to the Al surface, the secondary electron yield increases monotonously in a thin layer of 20 nm near the boundary, whereas for electrons there is an unexpectedly slow increase in the Au side, which is accompanied by a sharp decrease in the Al side. The two-dimensional plots of excitation points of secondary electrons that are emitted from the surfaces reveal the origin of the slow increase for electron bombardment, as well as the difference of the yield changes between Ga ion and electron bombardments. As shown in Fig. 4, the excited electrons by electrons in Au are much more distributed, in particular, in the lateral direction, because a much larger amount of energy is transferred from the projectile to electrons than for Ga ions. This causes the electron excitation to distribute in the Al, even in the case of the bombardment of Au. Since elastic and inelastic MFPs of low energy electrons are larger for Al than for Au, the escape depth is larger for Al. Even at a position well away from the boundary, a large number of secondary electrons are excited in Al by the bombardment of Au, which results in an increase in the total number of electrons escaping in
the vacuum. By the bombardment of Al, however, the large MFPs for elastic and inelastic scatterings cause projectile electrons to penetrate much deeper over the escape depth of the excited electrons, which results in a smaller secondary electron yield for Al than for Au. On the other hand, the total MFP, ktot , of low-energy ions slowed down and recoiled target atoms are the order of the average atomic distance of the target material. Therefore, both the lateral and depth distributions are localized. As a result, the ion reflection coefficient and the sputtering yield vary only in a very thin layer of thickness less than 10 nm near the boundary (Fig. 3(a)). The difference in the change in the secondary electron yields between Ga ions and electrons indicates that image contrasts in SIM are much more sensitive to the material species or the atomic number, Z2 and is clearer than that for SEM. This has been noticed by some SIM and SEM users as pointed out in [2]. Fig. 4(a) shows another interesting feature of the electron excitation by heavy ions, such as Ga ions: one due to electron excitation by a projectile ion, one due to electron excitation by recoiled target atoms, and one due to electron excitation by electron cascade. The three components contribute equally to the total secondary electron yield of low-Z2 material (Al). For high-Z2 material (Au), however, the electron excitation by the projectile ions dominates the total secondary electron yield, and the components by the recoiled target atoms and electron cascade contribute much less.
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Fig. 4. Plots of excitation points of electrons escaped from the surface, one half made of Au and the other half made of Al, due to the impacts of (a) 30 keV Ga ions and (b) 10 keV electrons. The arrows indicate the bombarding points on the surface. The number of projectile particles is 104 . In figure (a), the electrons are excited by projectile ions (black), recoiled target atoms (white) and electron cascades (gray).
Furthermore, very near the boundary between Au and Al, some synergetic effects, e.g. the particle reflection and absorption at the boundary and materials mixing due to transport of recoiled target atoms over the boundary, act on the enhancement and suppression of the secondary electron emission from both sides of the boundary.
References [1] Y. Sakai, T. Yamada, T. Suzuki, T. Sato, H. Itoh, T. Ichinokawa, Appl. Phys. Lett. 73 (1998) 611.
[2] T. Ishitani, Y. Madokoro, M. Nakagawa, K. Ohya, J. Electron Microsc. 51 (2002) 207. [3] K. Ohya, T. Ishitani, Surf. Coat. Technol. 158–159 (2002) 8. [4] R.A. Baragiola, E.V. Alonso, J. Ferr on, A. Oliva-Florio, Surf. Sci. 90 (1979) 240. [5] I. Nagy, A. Anau, P.M. Echenique, Phys. Rev. B 38 (1988) 9191. [6] S.E. Koonin, D.C. Meredith, Computational Physics, Addison-Wesley, Redwood, 1990, p. 103. [7] F. Salvat, J. Parellada, J. Phys. D 17 (1984) 1545. [8] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985, p. 264. [9] J.P. Biersack, L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 256.
K. Ohya, T. Ishitani / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 305–311 [10] M. R€ osler, in: R.A. Baragiola (Ed.), Ionization of Solids by Heavy Particles, Plenum, New York, 1993, p. 27. [11] K. Ohya, J. Kawata, Scanning Microsc. 9 (1995) 331. [12] H.J. Fitting, J. Reinhardt, Phys. Status Solidi A 88 (1985) 245. [13] C.J. Tung, R.H. Ritchie, Phys. Rev. B 16 (1977) 4302. [14] E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic, Boston, 1985. [15] E.D. Palik (Ed.), Handbook of Optical Constants of Solids II, Academic, Boston, 1991. [16] J.C. Ashley, J. Electron Spectrosc. Relat. Phenom. 50 (1990) 323. [17] K. Nishimura, J. Kawata, K. Ohya, Nucl. Instr. and Meth. B 164–165 (2000) 903. [18] R.A. Baragiola, E.V. Alonso, A. Oliva-Florio, Phys. Rev. B 19 (1979) 121.
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[19] B. Svensson, G. Holmen, J. Appl. Phys. 52 (1981) 6928. [20] P.C. Zalm, L.J. Beckers, Philipps J. Res. 39 (1984) 61. [21] R.A. Baragiola, in: Rabalais (Ed.), Low Energy IonSurface Interactions, John Wiley & Sons, Chichester, 1994, p. 187. [22] J. L€ orincık, Z. Sroubek, H. Eder, F. Aumayr, H. Winter, Phys. Rev. B 62 (2000) 16116. [23] K.-H. Hellwege, J.L. Olsen (Eds.), Electron states and Fermi surfaces of elements, Numerical Data and Functional Relationships in Science and Technology, Vol. 13, Springer, Berlin, 1984. [24] D.R. Lide (Ed.), Handbook of Chemistry and Physics, CRC, Boca Raton, 1993. [25] C. Kittel, in: Introduction to Solid State Physics, sixth ed., John Wiley & Sons, New York, 1986, p. 248.
Simulation study of secondary electron images in scanning ion microscopy K. Ohya a
a,*
, T. Ishitani
b
Faculty of Engineering, The University of Tokushima, Tokushima 770-8506, Japan b Naka Division, Hitachi High-Technologies Corp., Ibaraki 312-8504, Japan
Abstract The target atomic number, Z2 , dependence of secondary electron yield is simulated by applying a Monte Carlo code for 17 species of metals bombarded by Ga ions and electrons in order to study the contrast difference between scanning ion microscopes (SIM) and scanning electron microscopes (SEM). In addition to the remarkable reversal of the Z2 dependence between the Ga ion and electron bombardment, a fine structure, which is correlated to the density of the conduction band electrons in the metal, is calculated for both. The brightness changes of the secondary electron images in SIM and SEM are simulated using Au and Al surfaces adjacent to each other. The results indicate that the image contrast in SIM is much more sensitive to the material species and is clearer than that for SEM. The origin of the difference between SIM and SEM comes from the difference in the lateral distribution of secondary electrons excited within the escape depth. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 79.20.Ap; 79.20.Rf Keywords: Secondary electron emission; Monte Carlo simulation; Scanning ion microscopy; Focused ion beam
1. Introduction Focused gallium ion beams have been used to prepare cross-sectional samples in semiconductor microfabrication processes and subsequently to observe them, where a scanning ion microscope (SIM) is employed as an observational tool, like a scanning electron microscope (SEM). In many cases, the material contrast in the SIM image is opposite to that for SEM [1,2]. Recent Monte Carlo calculations of the secondary electron
*
Corresponding author. Tel./fax: +81-886-56-7444. E-mail address: [email protected] (K. Ohya).
emission of Al (Z2 ¼ 13), Cu (Z2 ¼ 29) and Au (Z2 ¼ 79) have revealed the origin of the difference in the material contrast between SIM and SEM images [2,3]. For bombardment of light targets with Ga ions, a large fraction of the total energy deposited in electron excitation is due to collisions between recoiled target atoms and target electrons. The heavier target atoms transfer less energy to the electrons, thus leading to a poorer multiplication of other electrons in cascade processes. As observed in [2], however, a fine structure probably relating to the periods of the periodic system, is superimposed on the monotonous change in the secondary electron yield with Z2 . To investigate the fine structure of the Z2 dependence, we have
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)01874-8
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conducted a Monte Carlo calculation of the secondary electron emissions of 17 species of metals. The results are also compared with the Z2 dependence of sputtering and ion reflection. Furthermore, two different metals, Au and Al, adjacent to each other were scanned by 30 keV Ga ions and 10 keV electrons, where the difference between SIM and SEM image characteristics is discussed.
2. Monte Carlo simulation of heavy ion induced secondary electron emission Ion-induced secondary electron emission can be ascribed to the processes of potential emission and kinetic emission. Ga ion bombardment will not lead to potential emission because of its low ionisation potential (6.0 eV), according to BaragiolaÕs empirical formula [4]. In the case of kinetic emission, the electron excitation can be caused by three collision processes in the target material: one due to collisions between projectile ions and target electrons, one due to collisions between recoiled target atoms and target electrons, and one due to collisions between excited electrons and other target electrons. The basic concept of our Monte Carlo code is to simulate trajectories of a projectile ion penetrating into the target bulk and of recoiled target atoms and excited electrons travelling towards the surface on the basis of the binary collision approximation with given mean free paths (MFP) for elastic and inelastic collisions. Details of the model are presented in [2,3]. One of the important physical quantities is the inverse MFP for electron excitation by projectile ions or the recoiled target atoms with velocity v [5], i.e., 1 X 1 1 3pnv X ¼ pffiffiffi 2 ð2l þ 1Þð2m þ 1Þ kinel 4 2vF l¼0 m¼0 f1 cos 2dl ðEF Þ cos 2dm ðEF Þ þ cos½2ðdl ðEF Þ dm ðEF ÞÞ g Z 1 1=2 ð1 xÞ Pl ðxÞPm ðxÞ dx:
ð1Þ
1
Here, dl;m is the phase shift for the scattering of a conduction band electron at the Fermi energy, EF , by the potential of the intruding ion or the
recoiled target atom at rest, assuming the impact of slow ions (v vB , vB : the Bohr velocity); for 30 keV Ga ions, v ¼ 0:13 vB . The quantities n, Pl;m and vF are the density of conduction band electrons, the Legendre polynomials and the Fermi velocity, respectively. By means of the partial wave expansion technique [6], the scattered wave function is decomposed into partial waves and the radial wave equation with a spherical symmetric scattering potential and solved using the Numerov algorithm. The phase shift in each partial wave is determined. Since the scattering potential is approximated by an analytical potential of neutral solid-state atoms obtained by Salvat and Parellada [7], the effect of the ion charge state on the MFP is not taken into account. The inverse MFP is directly proportional to v and n, so that the number of excited electrons increases with increasing v and depends upon the electron shell structure of the target atoms, and the atomic number, Z2 . The density, n, is deduced from experimental vF values compiled by Ziegler et al. [8], by use of the rela1=3 tionship, vF ¼ h=me ð3p2 nÞ . The motions of projectile ions and recoiled target atoms are treated in the same way; the straight free flight path is determined from the total MFP, ktot , defined as 1=ktot ¼ 1=kel þ 1=kinel , using a random number. The elastic MFP, kel , is fixed at N 1=3 where N is the atomic density of the target. Depending on each of the inverse MFPs, kel and kinel , either elastic collision or inelastic collision (i.e. electron excitation) is chosen using another random number. If elastic collision is chosen, the scattering angle is determined using an asymptotic procedure of atomic collisions in the Ziegler–Biearsack–Littmark interatomic potential [9], and the elastic energy loss is calculated. In each elastic collision, a new recoiled target atom is generated. If inelastic collision is chosen, the particle loses its energy and excites an electron. The energy of the excited electron is equal to the energy loss of the 2 particle, DE ¼ 2me ½v þ ðvF =2Þ [10], which is calculated from a head-on collision of the particle with a conduction electron. The initial directional angle of the excited electron is calculated using the energy and momentum conservation law. The excited electrons interact with the target through elastic collisions with the target atoms,
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and through inelastic collisions, i.e. excitations of conduction electrons and inner-shell electrons. The electron transport process is calculated using a direct simulation Monte Carlo model [11], which is used as well for secondary electron emission under electron bombardment. The trajectory of each electron is chosen as a series of random numbers to determine the path length between collision events, the type of collision that has taken place and the energy loss or the scattering angle. In each inelastic process, secondary electrons are excited, so that an electron cascade is generated. The elastic MFP is calculated using the screened Rutherford formula where the energy-dependent screening parameters for 17 species of metals are determined using the parameters for C, O, Al, Cu, Ag and Au calculated by Fitting and Reinhardt [12] by interpolation. For individual and collective (plasmon) excitation of conduction electrons, the differential inverse MFP, sðE; xÞ, of an electron with an energy E is described by the complex dielectric response function, Im½ 1=eðx; kÞ , i.e., 1 sðE; xÞ ¼ pE
Z
kþ
k
dk 1 Im
; k eðx; kÞ
ð2Þ
and the integration of sðE; xÞ over the allowed values of k yields the inverse MFP, 1=kinel . Here x and k are the energy and momentum pffiffiffipffiffiffiffitransfers pffiffiffiffiffiffiffiffiffiffiffiffito conduction electrons, and k ¼ 2 E E x in atomic units. In the previous papers [2,3] the MFP is calculated using the Lindhard dielectric function for eðx; kÞ according to Tung and Ritchie [13], but in the present simulation, optical data of the target material for the k ¼ 0 limit, eðx; 0Þ [14,15], is connected to eðx; kÞ according to an ‘‘optical-data’’ model developed by Ashley [16,17]. The advantage of this treatment is that, since eðx; 0Þ is based on the experimental result, it includes complicated processes of the inter-band, intra-band and some other transition mechanisms automatically, in addition to the individual and bulk-plasmon excitation of conduction electrons, which can be treated by the Lindhard dielectric function. The kinetic emission mechanism is conventionally subject to an impact energy threshold calculated from the condition that the energy
307
transfer from a projectile ion in a head-on collision with a conduction electron is equal to the surface barrier. The surface barrier is generally taken to be the energy difference between the bottom of the conduction band and the vacuum level, i.e. EF þ U (U: the surface work function) [18]. The surface barrier energy results in an extremely high threshold energy for Ga ions, e.g. 10.7, 18.8 and 26.6 keV for Al, Cu and Au targets, respectively, which are inconsistent with experimental observations for heavy ions such as Kr (Z1 ¼ 36), and Xe (Z1 ¼ 54) [4,19,20], as well as Ga (Z1 ¼ 31). Until recently, some models [21,22] were available for kinetic emissions below the conventional threshold energy. In this study, however, a lowering in the threshold energy is considered as a reduction in the apparent surface barrier between EF þ U and U [3]. According to the classical planar surface barrier model, excited and cascade electrons coming to the surface are emitted in the vacuum with reduced energy in a refracted direction due to the surface barrier energy. For the 17 species of metals used for this calculation, the values of EF obtained from different theoretical studies [23] are averaged, and the values of U are taken from [24]. The projectile ions and the recoiled target atoms are followed as well, until their energies falls below a predetermined energy or until they overcome the surface binding energy and escape into the vacuum; socalled ‘‘ion reflection’’ and ‘‘sputtering’’, respectively. The cohesive energy of atoms [25] is taken as the predetermined energy or the surface binding energy.
3. Results and discussion In Fig. 1(a), the secondary electron yield below the conventional threshold energies is simulated for the apparent surface barrier energy of 0:5EF þ U which has been arbitrarily chosen. The influence of the surface barrier energy on the secondary electron yield has been investigated in a previous study [3]: the decrease in the surface barrier energy from EF þ U towards U increases the secondary electron yields for both Ga ions and electrons, but retains the Z2 dependence of the
308
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Fig. 1. Projectile energy dependence of (a) secondary electron yield, ion reflection coefficient and sputtering yield, and (b) secondary electron yield and electron reflection coefficient of Al and Au, due to the impact of Ga ions and electrons, respectively.
Fig. 2. Target atomic number dependence of (a) secondary electron yield, ion reflection coefficient and sputtering yield, and (b) secondary electron yield and electron reflection coefficient of Al and Au, due to the impact of Ga ions and electrons, respectively. The solid, dotted and dashed lines are only intended as a guide for the eye.
secondary electron yields. In the calculation of the secondary electron yield for electrons (Fig. 1(b)), the surface barrier energy is taken as EF þ U. The secondary electron yield for Ga ion bombardment generally decreases with increasing Z2 whereas the secondary electron yield for electrons (>2 keV) increases. This can explain the reason for contrast reversal of secondary electron images observed between SIM and SEM. A fine structure is calculated not only for the secondary electron yield for Ga ion and electron bombardments, but also for the sputtering yield, as shown in Fig. 2. The fine Z2 dependence of the sputtering yield is strongly correlated to the surface binding energy. The lower the surface binding energy, the higher the sputtering yield. The secondary electron yield for electron bombardment is found to correlate to the density of conduction band electrons. These cor-
relations to the surface binding energy and the density of conduction electrons show dominant contributions of the surface and bulk properties of the material to sputtering and secondary electron emission, respectively. A similar trend in the secondary electron yield as for electron bombardment is calculated for Ga ions, although its strong decrease with increasing Z2 hides the fine structure. The reflection coefficient is less correlated to such physical parameters due to the dominant contribution of large angle scatterings through elastic collision sequences, where both the ZBL analytical interatomic potential for ion scattering and the screened Rutherford cross-section for electron scattering are used in this calculation and monotonously change with Z2 . To investigate brightness changes of the secondary electron images in SIM and SEM due to
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Fig. 3. Changes in (a) secondary electron yield, ion reflection coefficient and sputtering yield, and (b) secondary electron yield and electron reflection coefficient, due to scanning by 30 keV Ga ions and 10 keV electrons, respectively, near the boundary between Au and Al.
changes in target material, a sample surface, which is half made of Al and half made of Au, is scanned in the perpendicular direction to the boundary by 30 keV Ga ions and 10 keV electrons. In Fig. 3, large differences in secondary electron yield between Au and Al for Ga ion bombardment in comparison to electron bombardment can be seen. When the Ga ion beam moves from the Au surface to the Al surface, the secondary electron yield increases monotonously in a thin layer of 20 nm near the boundary, whereas for electrons there is an unexpectedly slow increase in the Au side, which is accompanied by a sharp decrease in the Al side. The two-dimensional plots of excitation points of secondary electrons that are emitted from the surfaces reveal the origin of the slow increase for electron bombardment, as well as the difference of the yield changes between Ga ion and electron bombardments. As shown in Fig. 4, the excited electrons by electrons in Au are much more distributed, in particular, in the lateral direction, because a much larger amount of energy is transferred from the projectile to electrons than for Ga ions. This causes the electron excitation to distribute in the Al, even in the case of the bombardment of Au. Since elastic and inelastic MFPs of low energy electrons are larger for Al than for Au, the escape depth is larger for Al. Even at a position well away from the boundary, a large number of secondary electrons are excited in Al by the bombardment of Au, which results in an increase in the total number of electrons escaping in
the vacuum. By the bombardment of Al, however, the large MFPs for elastic and inelastic scatterings cause projectile electrons to penetrate much deeper over the escape depth of the excited electrons, which results in a smaller secondary electron yield for Al than for Au. On the other hand, the total MFP, ktot , of low-energy ions slowed down and recoiled target atoms are the order of the average atomic distance of the target material. Therefore, both the lateral and depth distributions are localized. As a result, the ion reflection coefficient and the sputtering yield vary only in a very thin layer of thickness less than 10 nm near the boundary (Fig. 3(a)). The difference in the change in the secondary electron yields between Ga ions and electrons indicates that image contrasts in SIM are much more sensitive to the material species or the atomic number, Z2 and is clearer than that for SEM. This has been noticed by some SIM and SEM users as pointed out in [2]. Fig. 4(a) shows another interesting feature of the electron excitation by heavy ions, such as Ga ions: one due to electron excitation by a projectile ion, one due to electron excitation by recoiled target atoms, and one due to electron excitation by electron cascade. The three components contribute equally to the total secondary electron yield of low-Z2 material (Al). For high-Z2 material (Au), however, the electron excitation by the projectile ions dominates the total secondary electron yield, and the components by the recoiled target atoms and electron cascade contribute much less.
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Fig. 4. Plots of excitation points of electrons escaped from the surface, one half made of Au and the other half made of Al, due to the impacts of (a) 30 keV Ga ions and (b) 10 keV electrons. The arrows indicate the bombarding points on the surface. The number of projectile particles is 104 . In figure (a), the electrons are excited by projectile ions (black), recoiled target atoms (white) and electron cascades (gray).
Furthermore, very near the boundary between Au and Al, some synergetic effects, e.g. the particle reflection and absorption at the boundary and materials mixing due to transport of recoiled target atoms over the boundary, act on the enhancement and suppression of the secondary electron emission from both sides of the boundary.
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