- Email: [email protected]
FIBSIM – dynamic Monte Carlo simulation of compositional and topography changes caused by focused ion beam milling
Nuclear Instruments and Methods in Physics Research B 180 (2001) 125±129
www.elsevier.nl/locate/nimb
FIBSIM ± dynamic Monte Carlo simulation of compositional and topography changes caused by focused ion beam milling W. Boxleitner, G. Hobler
*
Institut fur Festkorperelektronik, Vienna University of Technology, A-1040 Vienna, Austria
Abstract A new simulation program is presented for focused ion beam (FIB) induced sputtering in two-dimensional targets. The model combines dynamic Monte Carlo simulation of the collision cascades with cell-based topography simulation. This approach takes the nonlocal nature of the sputtering process into account, and treats doping, damage formation and compositional changes self-consistently with the evolution of the surface. Two applications are presented: erosion of a sample edge, and milling of a hole into a multilayer target. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Focused ion beam; Ion beam milling; Sputtering; Monte Carlo simulation; Topography simulation
1. Introduction Focused ion beam (FIB) tools have found widespread use in semiconductor manufacturing. Applications include lithographic mask repair, modi®cation of metal connections in prototype integrated circuits, failure analysis, and sample preparation for transmission electron microscopy (TEM) [1,2]. In many cases the intended eect is the removal of material by local ion beam milling. Parasitic eects include implantation of the beam atoms (usually Ga), damaging and intermixing of layers of dierent material. Since during FIB processing usually highly nonplanar surfaces develop, these phenomena should be described in at least two spatial dimensions. *
Corresponding author. Fax: +43-1-588-013-62-91. E-mail address: [email protected] (G. Hobler).
Apart from analytical theories, two groups of sputtering models exist: In Monte Carlo codes [3] collisional processes are modeled on a physical basis. In the ``dynamic'' Monte Carlo codes [4±6] compositional changes of the target are taken into account as a function of ¯uence. They allow physics-based simulation of sputtering, deposition and mixing processes. However, these codes are restricted to one spatial dimension. On the other hand, topography simulation tools have been developed, mainly for use in semiconductor processing. In these codes the target geometry is described in two or three spatial dimensions by one of several methods, such as the string algorithm [7], cellular models [8] or the level set method [9]. The surface is moved according to an etch rate which in the case of ion beam milling depends on the incidence angle of the ions with respect to the local surface orientation. Extension
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 4 0 6 - 2
126
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
to FIB milling [10] is achieved in a straightforward manner by modulating the sputter rates with the local beam intensity. In these topography simulation tools shadowing and redeposition may be taken into account. However, they consider sputtering as a local process taking place at the impact point of the ion on the target surface. This might not be a good approximation for the highly nonplanar surfaces often forming during FIB processing. The Ga ions in a FIB tool are typically accelerated to 30±50 keV which corresponds to a projected range of about 30 nm in silicon. The points of sputter emission are therefore distributed over a correspondingly large area. The sputter rates depend on the exact geometry of the sample, e.g. whether the impact point is near an edge, within a planar segment of the surface, or at the bottom of a hole. It has been attempted to take this eect into account by a surface-curvature dependent sputtering yield [11]. However, the surface curvature is still a local property that may change considerably within the volume of the collision cascade. In addition, existing topography simulation tools do not treat implantation, damage formation, and intermixing eects self-consistently. The simulation of an ion implantation step in the ®nal structure [12] provides rough estimates at best. We have therefore developed a new simulation program, FIBSIM, which combines dynamic Monte Carlo binary collision simulation with cellbased topography simulation. Details of the program are described in the next section. In Section 3 we present two applications of the code: erosion of a sample edge with FIB, and milling of a hole into a multilayer target. 2. Simulation code The simulation domain is divided into cells by a two-dimensional rectangular grid with a typical cell size of 1 nm 1 nm. The target is de®ned by the concentrations of the atom species in each cell. In this structure a Monte Carlo collision cascade simulation is performed assuming amorphous target. The local target density is taken into account in the calculation of the maximum impact
parameter and the electronic stopping power. The universal ZBL potential [13] and the Lindhard stopping power [14] with correction factors where at known [15] are used. The free ¯ight path is 1 A energies below 100 eV and increases up to 3 A at higher energies. The displacement energy for recoil generation in the bulk is taken as 13 eV, and a planar surface potential is used for particles leaving the target. If known, an empirical factor frec can be used to correct the number of displaced atoms for damage calculations [16]. The cell concentrations are updated each time a particle comes to rest or a recoil is generated. Thus, compositional changes are dynamically taken into account. The surface is determined from the ®ll factors of the cells in the following way. First, the 50% isoconcentration line of the ®ll factors is constructed as a polygon. Then, the signed distance from this polygon is calculated on the grid points, with points outside the target being assigned negative values. The surface is de®ned by a certain During the simulavalue of the distance ( 6 A). tion of a trajectory, the distance value is interpolated on the grid at each collision point. If the the planar surface distance value falls below 6 A potential model is applied. The surface normal is readily obtained by calculation of the gradient of the distance function. The distance function is also used in the calculation of the cut-o energy for the ion trajectories. At distances smaller than 10 nm trajectories are terminated when the energy falls below a value slightly smaller than the surface binding energy. At larger distances a value corresponding to the displacement energy is used instead. The ®ll factor is de®ned by the ratio of the actual atom concentration and the atom concentration in an undisturbed solid. The latter is estimated by the sum of the pure element densities weighted with the relative abundance of each element in the cell. Currently we do not allow the target density to relax. One would expect cells with ®ll factors larger than unity to expand, and cells with ®ll factors smaller than unity to shrink. In two (or more) dimensions this is a non-trivial problem. The neglect of target density relaxation may cause some distortion in the geometry and of the details of the distribution of the atom species. On the other
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
hand, sputter rates and therefore the amount of removed material should not be aected to ®rst order, since the main eect of the density is to scale the spatial extent of the cascade (both nuclear and the electronic energy loss scale linearly with the target density), and the surface binding energy is independent of density. Inaccuracies of the sputter rates are only caused indirectly through the geometric distortion of the surface and the concentration ®elds, not by the incorrect densities themselves. Signi®cantly over®lled cells mainly occur in the case of low eective sputter yields, i.e. at normal incidence and/or in areas of signi®cant redeposition. 3. Applications 3.1. Erosion of a sample edge A typical example of FIB milling is the erosion of a sample edge. This is used, e.g. to cut out and thin samples for TEM. We compare two modes of
– – – – –
127
operation. In both modes the beam is moved along one direction (``scan'') which we assume perpendicular to the drawing plane. After a certain ion dose is delivered, the scan position is stepped perpendicular to the scan direction by a chosen distance. This is repeated until the prede®ned interval is covered. In the ``single-pass mode'' the scan positions are stepped only in one direction, and the process is ®nished when the scan position reaches the end of the interval. In the ``multi-pass mode'' this procedure is repeated many times, each time starting at the ®rst scan position. Fig. 1 shows the evolution of the surface when the edge of a Si sample covered with a thin W layer is eroded with a 30 keV Ga beam. The single-pass mode (left) is compared with the multi-pass mode (right). The contour is drawn after each ``scan'' which is de®ned here by 1/20th of the total dose. Although the total dose is the same in both cases, in the multi-pass mode more material is removed than in the single-pass mode. This is explained by the fact that in the multi-pass mode an angle between surface and beam is maintained which
– – – –
Fig. 1. Comparison of the surface evolution in the single-pass mode (left) and in a multi-pass mode (right) with the same total delivered dose. 30 keV Ga beam with a Gaussian intensity distribution with a radial standard deviation of 10 nm. The line dose per scan is 7143 atoms/nm, and the step distance is 14 nm. The target consists of bulk Si and a 20 nm thick W layer on top. Note the dierent scales in vertical and lateral direction.
128
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
allows a high sputtering yield, while in the singlepass mode the walls become so steep between the second and third scan at the same position that the sputtering yield decreases signi®cantly. Note that in Fig. 1 the lateral scale is stretched in order to show the details of the surface evolution better. On the bottom the ®nal contour is above some of the intermediate contours indicating redeposition of material. In Fig. 2 the implanted Ga distributions are shown after the 8th and the 20th scan of the singlepass mode of Fig. 1. The sidewall is doped at concentrations larger than 1020 cm 3 to a depth of 20 nm, while the maximum Ga concentration is slightly less than 3 1021 cm 3 . This is only 6% of the target density so that the neglect of density relaxations should not be a problem at the sidewall. There is more Ga doping at the bottom after the 20th scan than after the 8th scan or at the sidewalls, since the incidence angle of the ions is
Fig. 2. Deposited Ga distributions after the 8th and the 20th scan of the single-pass mode of Fig. 1.
closer to perpendicular at the bottom and since additional Ga ions are deposited there after re¯ection from the sidewall. 3.2. Milling of a hole into a multilayer target In this example a hole is milled into a multilayer target consisting of a 100 nm thick Au layer on GaAs with an intermediate Ti layer of 20 nm thickness. The total dose is delivered in 8 passes with 5 scans each. When the hole has penetrated the Ti layer, Au contaminates the GaAs surface and vice versa. While the GaAs contamination of the sidewalls persists while the hole is digged deeper, the Au contamination at the bottom of the hole gradually decreases. This is caused by the fact that no eective source of Au exists once the hole has penetrated the Au layer, while Au atoms continue to be sputtered from the bottom of the hole and have a chance to escape through the opening. At the stage shown in Fig. 3, the Au contamination at the bottom of the hole is still larger than 1021 cm 3 (shaded area in the upper part of Fig. 3) but smaller than 1022 cm 3 (lower part of the ®gure). The As contamination on the sidewalls (light lines) does not disappear since it has been implanted into the wall with some range that brings it outside the area of the beam, and since more As is redeposited during further milling of the hole. Ti is deposited at the sidewalls mainly during the time when the depth of the trench just reaches into the Ti layer. Therefore the sidewalls are more contaminated above the Ti layer than below (dark lines in the upper part of Fig. 3). The Ti concentrations below the Ti layer are partly caused by deposition of resputtered atoms from the opposite sidewalls. The ``nail heads'' formed by the 1022 cm 3 isoconcentration line of Ti (dark lines in the lower part of Fig. 3) are caused by ion beam mixing rather than redeposition. Redeposition of atoms originating from the other sidewall is expected to result in the same or a larger extension of the nail heads above than below the Ti layer. However, Fig. 3 shows a larger extension below than above which is consistent with the motion of Ti atoms predominantly in the forward direction of the beam.
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
Au
Ti GaAs
Depth [nm]
36 37 38 39 40
0 20 40 60 80 100 120 140 160 180 200 220
erosion of a sample edge, and milling of a hole. Among the useful information that can be extracted from these simulations are: comparison of operating modes of the FIB tool; prediction of the thickness of doped or damaged layers; contamination of the walls of a hole and the adjacent subsurface regions with atoms from dierent layers. Comparison with experimental data remains as future work as well as optimization with respect to computation times.
21
Au>10 cm–3 21 Ti>10 cm– 3 21 As>10 cm–3 40nm 40nm
Depth[nm]
36 37 38 39 40
0 20 40 60 80 100 120 140 160 180 200 220
129
Acknowledgements This work was supported by the European Commission under the HQ-SONATE project, Contract No. SMT4-CT97-2201.
References
22
Au>10 cm–3 22 Ti>10 cm–3 22 As>10 cm–3
Fig. 3. Redeposition during milling of a hole in a Au±Ti±GaAs multilayer structure. Eight passes with ®ve scans each (line dose per scan 10 000 atoms/nm). 50 keV Ga beam with a Gaussian intensity distribution and a radial standard deviation of 10 nm. The step distance between scans is 20 nm. The shaded area corresponds to Au concentrations larger than 1021 cm 3 (top) and 1022 cm 3 (bottom). The corresponding regions with Ti and As contamination are indicated by the dark and light isoconcentration lines, respectively.
4. Conclusions A new simulator has been developed for FIB milling. By combining Monte Carlo simulation of the collision cascades and cell-based topography modeling, it treats surface evolution, ion implantation, damaging, and intermixing self-consistently. Two examples have been given that demonstrate the capabilities of the simulator:
[1] D. Stewart, J. Casey, in: P. Rai-Choudhury (Ed.), Handbook of Microlithography, Micromachining, and Microfabrication, Vol. 2, 1997, Chapter 4. [2] H. Bender, Vac. Solutions 14 (2000) 11. [3] J. Biersack, W. Eckstein, Appl. Phys. A 34 (1984) 73. [4] W. M oller, W. Eckstein, Nucl. Instr. and Meth. B 2 (1984) 814. [5] W. M oller, W. Eckstein, J. Biersack, Comput. Phys. Commun. 51 (1988) 355. [6] Y. Yamamura, Nucl. Instr. and Meth. B 28 (1987) 17. [7] A.R. Neureuther, C. Liu, C. Ting, J. Vac. Sci. Technol. 16 (1979) 1767. [8] E. Strasser, S. Selberherr, IEEE Trans. Comput.-Aided Des. 14 (1995) 1104. [9] J. Sethian, D. Adalsteinsson, IEEE Trans. Semicond. Man. 10 (1997) 167. [10] F. Itoh, A. Shimase, S. Haraichi, J. Electrochem. Soc. 137 (1990) 983. [11] R. Smith, Atoms & Ion Collisions in Solids and at Surfaces, Cambridge University Press, 1997, Chapter 9. [12] T. Ishitani, H. Tsuboi, T. Yaguchi, H. Koike, J. Electron Microsc. 43 (1994) 322. [13] J. Ziegler, J. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985. [14] J. Lindhard, M. Schar, Phys. Rev. 124 (1961) 128. [15] G. Hobler, C. Murthy, in: Proceedings of the 13th International Conference on Ion Implantation Technology, IEEE, accepted. [16] G. Hobler, Nucl. Instr. and Meth. B 96 (1995) 155.
www.elsevier.nl/locate/nimb
FIBSIM ± dynamic Monte Carlo simulation of compositional and topography changes caused by focused ion beam milling W. Boxleitner, G. Hobler
*
Institut fur Festkorperelektronik, Vienna University of Technology, A-1040 Vienna, Austria
Abstract A new simulation program is presented for focused ion beam (FIB) induced sputtering in two-dimensional targets. The model combines dynamic Monte Carlo simulation of the collision cascades with cell-based topography simulation. This approach takes the nonlocal nature of the sputtering process into account, and treats doping, damage formation and compositional changes self-consistently with the evolution of the surface. Two applications are presented: erosion of a sample edge, and milling of a hole into a multilayer target. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Focused ion beam; Ion beam milling; Sputtering; Monte Carlo simulation; Topography simulation
1. Introduction Focused ion beam (FIB) tools have found widespread use in semiconductor manufacturing. Applications include lithographic mask repair, modi®cation of metal connections in prototype integrated circuits, failure analysis, and sample preparation for transmission electron microscopy (TEM) [1,2]. In many cases the intended eect is the removal of material by local ion beam milling. Parasitic eects include implantation of the beam atoms (usually Ga), damaging and intermixing of layers of dierent material. Since during FIB processing usually highly nonplanar surfaces develop, these phenomena should be described in at least two spatial dimensions. *
Corresponding author. Fax: +43-1-588-013-62-91. E-mail address: [email protected] (G. Hobler).
Apart from analytical theories, two groups of sputtering models exist: In Monte Carlo codes [3] collisional processes are modeled on a physical basis. In the ``dynamic'' Monte Carlo codes [4±6] compositional changes of the target are taken into account as a function of ¯uence. They allow physics-based simulation of sputtering, deposition and mixing processes. However, these codes are restricted to one spatial dimension. On the other hand, topography simulation tools have been developed, mainly for use in semiconductor processing. In these codes the target geometry is described in two or three spatial dimensions by one of several methods, such as the string algorithm [7], cellular models [8] or the level set method [9]. The surface is moved according to an etch rate which in the case of ion beam milling depends on the incidence angle of the ions with respect to the local surface orientation. Extension
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 4 0 6 - 2
126
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
to FIB milling [10] is achieved in a straightforward manner by modulating the sputter rates with the local beam intensity. In these topography simulation tools shadowing and redeposition may be taken into account. However, they consider sputtering as a local process taking place at the impact point of the ion on the target surface. This might not be a good approximation for the highly nonplanar surfaces often forming during FIB processing. The Ga ions in a FIB tool are typically accelerated to 30±50 keV which corresponds to a projected range of about 30 nm in silicon. The points of sputter emission are therefore distributed over a correspondingly large area. The sputter rates depend on the exact geometry of the sample, e.g. whether the impact point is near an edge, within a planar segment of the surface, or at the bottom of a hole. It has been attempted to take this eect into account by a surface-curvature dependent sputtering yield [11]. However, the surface curvature is still a local property that may change considerably within the volume of the collision cascade. In addition, existing topography simulation tools do not treat implantation, damage formation, and intermixing eects self-consistently. The simulation of an ion implantation step in the ®nal structure [12] provides rough estimates at best. We have therefore developed a new simulation program, FIBSIM, which combines dynamic Monte Carlo binary collision simulation with cellbased topography simulation. Details of the program are described in the next section. In Section 3 we present two applications of the code: erosion of a sample edge with FIB, and milling of a hole into a multilayer target. 2. Simulation code The simulation domain is divided into cells by a two-dimensional rectangular grid with a typical cell size of 1 nm 1 nm. The target is de®ned by the concentrations of the atom species in each cell. In this structure a Monte Carlo collision cascade simulation is performed assuming amorphous target. The local target density is taken into account in the calculation of the maximum impact
parameter and the electronic stopping power. The universal ZBL potential [13] and the Lindhard stopping power [14] with correction factors where at known [15] are used. The free ¯ight path is 1 A energies below 100 eV and increases up to 3 A at higher energies. The displacement energy for recoil generation in the bulk is taken as 13 eV, and a planar surface potential is used for particles leaving the target. If known, an empirical factor frec can be used to correct the number of displaced atoms for damage calculations [16]. The cell concentrations are updated each time a particle comes to rest or a recoil is generated. Thus, compositional changes are dynamically taken into account. The surface is determined from the ®ll factors of the cells in the following way. First, the 50% isoconcentration line of the ®ll factors is constructed as a polygon. Then, the signed distance from this polygon is calculated on the grid points, with points outside the target being assigned negative values. The surface is de®ned by a certain During the simulavalue of the distance ( 6 A). tion of a trajectory, the distance value is interpolated on the grid at each collision point. If the the planar surface distance value falls below 6 A potential model is applied. The surface normal is readily obtained by calculation of the gradient of the distance function. The distance function is also used in the calculation of the cut-o energy for the ion trajectories. At distances smaller than 10 nm trajectories are terminated when the energy falls below a value slightly smaller than the surface binding energy. At larger distances a value corresponding to the displacement energy is used instead. The ®ll factor is de®ned by the ratio of the actual atom concentration and the atom concentration in an undisturbed solid. The latter is estimated by the sum of the pure element densities weighted with the relative abundance of each element in the cell. Currently we do not allow the target density to relax. One would expect cells with ®ll factors larger than unity to expand, and cells with ®ll factors smaller than unity to shrink. In two (or more) dimensions this is a non-trivial problem. The neglect of target density relaxation may cause some distortion in the geometry and of the details of the distribution of the atom species. On the other
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
hand, sputter rates and therefore the amount of removed material should not be aected to ®rst order, since the main eect of the density is to scale the spatial extent of the cascade (both nuclear and the electronic energy loss scale linearly with the target density), and the surface binding energy is independent of density. Inaccuracies of the sputter rates are only caused indirectly through the geometric distortion of the surface and the concentration ®elds, not by the incorrect densities themselves. Signi®cantly over®lled cells mainly occur in the case of low eective sputter yields, i.e. at normal incidence and/or in areas of signi®cant redeposition. 3. Applications 3.1. Erosion of a sample edge A typical example of FIB milling is the erosion of a sample edge. This is used, e.g. to cut out and thin samples for TEM. We compare two modes of
– – – – –
127
operation. In both modes the beam is moved along one direction (``scan'') which we assume perpendicular to the drawing plane. After a certain ion dose is delivered, the scan position is stepped perpendicular to the scan direction by a chosen distance. This is repeated until the prede®ned interval is covered. In the ``single-pass mode'' the scan positions are stepped only in one direction, and the process is ®nished when the scan position reaches the end of the interval. In the ``multi-pass mode'' this procedure is repeated many times, each time starting at the ®rst scan position. Fig. 1 shows the evolution of the surface when the edge of a Si sample covered with a thin W layer is eroded with a 30 keV Ga beam. The single-pass mode (left) is compared with the multi-pass mode (right). The contour is drawn after each ``scan'' which is de®ned here by 1/20th of the total dose. Although the total dose is the same in both cases, in the multi-pass mode more material is removed than in the single-pass mode. This is explained by the fact that in the multi-pass mode an angle between surface and beam is maintained which
– – – –
Fig. 1. Comparison of the surface evolution in the single-pass mode (left) and in a multi-pass mode (right) with the same total delivered dose. 30 keV Ga beam with a Gaussian intensity distribution with a radial standard deviation of 10 nm. The line dose per scan is 7143 atoms/nm, and the step distance is 14 nm. The target consists of bulk Si and a 20 nm thick W layer on top. Note the dierent scales in vertical and lateral direction.
128
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
allows a high sputtering yield, while in the singlepass mode the walls become so steep between the second and third scan at the same position that the sputtering yield decreases signi®cantly. Note that in Fig. 1 the lateral scale is stretched in order to show the details of the surface evolution better. On the bottom the ®nal contour is above some of the intermediate contours indicating redeposition of material. In Fig. 2 the implanted Ga distributions are shown after the 8th and the 20th scan of the singlepass mode of Fig. 1. The sidewall is doped at concentrations larger than 1020 cm 3 to a depth of 20 nm, while the maximum Ga concentration is slightly less than 3 1021 cm 3 . This is only 6% of the target density so that the neglect of density relaxations should not be a problem at the sidewall. There is more Ga doping at the bottom after the 20th scan than after the 8th scan or at the sidewalls, since the incidence angle of the ions is
Fig. 2. Deposited Ga distributions after the 8th and the 20th scan of the single-pass mode of Fig. 1.
closer to perpendicular at the bottom and since additional Ga ions are deposited there after re¯ection from the sidewall. 3.2. Milling of a hole into a multilayer target In this example a hole is milled into a multilayer target consisting of a 100 nm thick Au layer on GaAs with an intermediate Ti layer of 20 nm thickness. The total dose is delivered in 8 passes with 5 scans each. When the hole has penetrated the Ti layer, Au contaminates the GaAs surface and vice versa. While the GaAs contamination of the sidewalls persists while the hole is digged deeper, the Au contamination at the bottom of the hole gradually decreases. This is caused by the fact that no eective source of Au exists once the hole has penetrated the Au layer, while Au atoms continue to be sputtered from the bottom of the hole and have a chance to escape through the opening. At the stage shown in Fig. 3, the Au contamination at the bottom of the hole is still larger than 1021 cm 3 (shaded area in the upper part of Fig. 3) but smaller than 1022 cm 3 (lower part of the ®gure). The As contamination on the sidewalls (light lines) does not disappear since it has been implanted into the wall with some range that brings it outside the area of the beam, and since more As is redeposited during further milling of the hole. Ti is deposited at the sidewalls mainly during the time when the depth of the trench just reaches into the Ti layer. Therefore the sidewalls are more contaminated above the Ti layer than below (dark lines in the upper part of Fig. 3). The Ti concentrations below the Ti layer are partly caused by deposition of resputtered atoms from the opposite sidewalls. The ``nail heads'' formed by the 1022 cm 3 isoconcentration line of Ti (dark lines in the lower part of Fig. 3) are caused by ion beam mixing rather than redeposition. Redeposition of atoms originating from the other sidewall is expected to result in the same or a larger extension of the nail heads above than below the Ti layer. However, Fig. 3 shows a larger extension below than above which is consistent with the motion of Ti atoms predominantly in the forward direction of the beam.
W. Boxleitner, G. Hobler / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 125±129
Au
Ti GaAs
Depth [nm]
36 37 38 39 40
0 20 40 60 80 100 120 140 160 180 200 220
erosion of a sample edge, and milling of a hole. Among the useful information that can be extracted from these simulations are: comparison of operating modes of the FIB tool; prediction of the thickness of doped or damaged layers; contamination of the walls of a hole and the adjacent subsurface regions with atoms from dierent layers. Comparison with experimental data remains as future work as well as optimization with respect to computation times.
21
Au>10 cm–3 21 Ti>10 cm– 3 21 As>10 cm–3 40nm 40nm
Depth[nm]
36 37 38 39 40
0 20 40 60 80 100 120 140 160 180 200 220
129
Acknowledgements This work was supported by the European Commission under the HQ-SONATE project, Contract No. SMT4-CT97-2201.
References
22
Au>10 cm–3 22 Ti>10 cm–3 22 As>10 cm–3
Fig. 3. Redeposition during milling of a hole in a Au±Ti±GaAs multilayer structure. Eight passes with ®ve scans each (line dose per scan 10 000 atoms/nm). 50 keV Ga beam with a Gaussian intensity distribution and a radial standard deviation of 10 nm. The step distance between scans is 20 nm. The shaded area corresponds to Au concentrations larger than 1021 cm 3 (top) and 1022 cm 3 (bottom). The corresponding regions with Ti and As contamination are indicated by the dark and light isoconcentration lines, respectively.
4. Conclusions A new simulator has been developed for FIB milling. By combining Monte Carlo simulation of the collision cascades and cell-based topography modeling, it treats surface evolution, ion implantation, damaging, and intermixing self-consistently. Two examples have been given that demonstrate the capabilities of the simulator:
[1] D. Stewart, J. Casey, in: P. Rai-Choudhury (Ed.), Handbook of Microlithography, Micromachining, and Microfabrication, Vol. 2, 1997, Chapter 4. [2] H. Bender, Vac. Solutions 14 (2000) 11. [3] J. Biersack, W. Eckstein, Appl. Phys. A 34 (1984) 73. [4] W. M oller, W. Eckstein, Nucl. Instr. and Meth. B 2 (1984) 814. [5] W. M oller, W. Eckstein, J. Biersack, Comput. Phys. Commun. 51 (1988) 355. [6] Y. Yamamura, Nucl. Instr. and Meth. B 28 (1987) 17. [7] A.R. Neureuther, C. Liu, C. Ting, J. Vac. Sci. Technol. 16 (1979) 1767. [8] E. Strasser, S. Selberherr, IEEE Trans. Comput.-Aided Des. 14 (1995) 1104. [9] J. Sethian, D. Adalsteinsson, IEEE Trans. Semicond. Man. 10 (1997) 167. [10] F. Itoh, A. Shimase, S. Haraichi, J. Electrochem. Soc. 137 (1990) 983. [11] R. Smith, Atoms & Ion Collisions in Solids and at Surfaces, Cambridge University Press, 1997, Chapter 9. [12] T. Ishitani, H. Tsuboi, T. Yaguchi, H. Koike, J. Electron Microsc. 43 (1994) 322. [13] J. Ziegler, J. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985. [14] J. Lindhard, M. Schar, Phys. Rev. 124 (1961) 128. [15] G. Hobler, C. Murthy, in: Proceedings of the 13th International Conference on Ion Implantation Technology, IEEE, accepted. [16] G. Hobler, Nucl. Instr. and Meth. B 96 (1995) 155.