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Proposals for producing novel periodic structures by ion bombardment sputtering
ARTICLE IN PRESS
Vacuum 77 (2004) 97–100 www.elsevier.com/locate/vacuum
Proposals for producing novel periodic structures by ion bombardment sputtering G. Carter Joule Physics Laboratory, Institute of Materials, University of Salford, Salford M5 4WT, UK Received 3 June 2004; received in revised form 28 July 2004; accepted 30 July 2004
Abstract It is proposed, and confirmed analytically that if multiple ion fluxes are incident simultaneously, all at the same oblique polar angle but at different azimuthal angles, on to a target then the individual ripple patterns generated by sputtering are superimposed to produce novel surface structures. It is also shown that single focused ion fluxes incident on to rotating targets can produce circular ripple patterns. r 2004 Published by Elsevier Ltd. Keywords: Sputtering; Multiple ion fluxes; Superimposed ripple patterns; Rotating targets; Circular ripple patterns
It has been known for many years that ion bombardment at oblique incidence of amorphous materials such as glass [1] or semiconductors [2,3] and insulators [4], which are amorphised by ion irradiation can produce regular repetitive and periodic surface structures in the form of ripples. For ion incidence angles between about 301 and 601 to the surface normal these ripples are formed with their wave vector parallel to the projection of the ion flux on to the surface but for larger incidence angles the wave vector is rotated to be perpendicular to the ion flux projection [5]. Recently several studies [6–9] have revealed that low energy ion bombardment normal to the surface of different semiconductors can lead to E-mail address: [email protected] (G. Carter). 0042-207X/$ - see front matter r 2004 Published by Elsevier Ltd. doi:10.1016/j.vacuum.2004.07.082
the production of regular arrays of conical or pyramidal features. In the case of metals, which are not amorphised by irradiation but become loaded with defects, both ripple and pyramidal features can be produced not only for oblique but also for normal ion incidence, the exact structure being dependent upon the irradiated substrate temperature [10–13]. These general behaviours, if not all the specific details, can be understood [14–16] in terms of the competition between sputtering erosion phenomena which, due to the dependence of sputtering yield upon local angle of ion incidence [17,18], can lead to surface smoothing whilst, due to the dependence of the yield upon local surface
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G. Carter / Vacuum 77 (2004) 97–100
curvature, can lead to surface roughening [5,19,20] and higher order spatial derivatives of surface height can lead to surface smoothing [21], and surface relaxation phenomena such as diffusion [5], which can be radiation mediated [22], can have preferred directionality [10–13] and biased due to the Ehrlich-Schwoebel effect [23–25] and viscous flow [4]. All of these effects can be encompassed in the deceptively simple equation for the time rate of change of local surface height, h, qh=qt ¼
J Y ðy; b; R; rn hÞ þ K 1 r4 h þ K 2 rj s þ Z; N (1)
where J is the ion flux density incident at polar angle y and azimuthal angle b on to a substrate of atomic density N, Y ðy; b; R; rn hÞ is the local sputtering yield at a point of radius of curvature R and is a function of higher order spatial derivatives of the local surface height, K 1 r4 h represents surface diffusion and/or viscous flow, K2js represents any biased surface diffusion process with a biased diffusion current js and Z represents the random or noisy nature of ion arrival and the sputtering process. For not too large angles of ion incidence and relatively low amplitudes of any emerging surface features Y can be expanded in low order linear derivatives of the surface height [5,21] but for larger values of angles and amplitude non-linear terms in powers of these derivatives must be included [26]. In the former case, and in the absence of biased surface diffusion, the linear form of equation (1) can be readily solved [5,26] to show that surface waves with all possible wavelengths will develop but the one with the fastest growing amplitude will dominate and a well defined ripple structure with increasing amplitude and constant wavelength will emerge. In particular the wave vectors will be parallel to the projection of the ion flux for not too large ion incidence angles and ripple amplitudes but perpendicular to this projection for larger incidence angles. For large increase in ripple amplitude non-linear terms become effective and the surface is predicted [26] to roughen kinetically with time but it has also been predicted that for even larger amplitudes [27]
ripples may again emerge but with wave vectors rotated from their original direction. Unlike the low amplitude behaviour, which has been observed many times experimentally [5,14,15] the large amplitude behaviour has not yet been confirmed empirically. The dependence of sputtering yield on the surface height derivatives can be measured experimentally or calculated as can the constant K1 and the resulting values of ripple wavelength, orientation and rate of increase of amplitude correspond reasonably well, for amorphous materials, with experimental data [14,15]. In the case of metals diffusion rates can vary between different crystal directions and be temperature dependent so that ripple orientations can vary with this parameter as observed experimentally [10–13,15] as can the growth of pyramids when biased surface diffusion becomes effective. The results for low energy normally incident ion bombardment of semiconductors are unusual because theory suggests [5] that minor random roughening of the surface should occur but computational simulations have suggested [28] that fourth order height derivative processes involved in the sputtering yield can lead to omnidirectional diffusion-like effects and reordering of the surface. The purpose of the preceding review has been to show that repetitive surface features with translational symmetry can be understood and their habits and evolution quite well predicted and realised experimentally if ion bombardment parameters (flux density, energy, species, incidence angle) and substrate material parameters (diffusivity, temperature) can be controlled and known or estimated. Thus features with repetition lengths in the nanometre to submicrometre range can be achieved [14,15]. However the above discussion refers only to the case of mono-directional ion fluxes and stationary ion fluxes or substrates. It is now the purpose of subsequent discussion to suggest how novel surface structures may be produced if these constraints are removed. Firstly, in the case of amorphisable substrates where surface diffusion and viscous flow are isotropic, erosion phenomena dictate ripple habit and evolution [5,14,15,16] and are controllable by the polar angle of ion incidence which defines the
ARTICLE IN PRESS G. Carter / Vacuum 77 (2004) 97–100
direction of the ripple wave vector. That this is the case has been demonstrated in studies [29] with ion irradiated Si at fixed oblique polar angle and an initial azimuthal angle to produce ripples with wave vector parallel to the projection of the ion flux. The substrate was then rotated through a right angle and radiation recommenced and the initial ripple structure was gradually eradicated and a new ripple structure developed with wave vector orthogonal to the earlier one. It is clear that the two morphologies were independent and any resulting surface structure obtained during the second, sequential, radiation would be difficult to anticipate. However, precisely because of this independence, if two (or more) irradiations were performed simultaneously with ion fluxes deployed at different azimuthal angles the ensuing morphology would be the sum of the independent individual morphologies. Thus, for example, two orthogonally deployed ion fluxes would lead to orthogonally developed ripple structures with the appearance of four sided pyramidal features. Nonorthogonal ion fluxes would result in four sided features also but with rotated habit while three ion fluxes would lead to trigonal features. Even more deployed ion fluxes could result in more exotic structures while modification of one or more ion incidence polar angles, ion flux densities, energies and species could result in a range of tailored micro-features. The same could be true for metal substrates provided that substrate temperature was so controlled as to minimise directional and biased diffusion processes [10–13,15]. Turning now to non-stationary systems it is well known that if targets are continuously rotated during irradiation the surface can be smoothed [30–32] and ripple formation inhibited. [33,34]. Essentially the latter occurs because, as noted above, ripple wave vector is controllable, for fixed polar angle, by the incident azimuthal angle and if, as in continuous target rotation all such angles are explored no dominant mode can develop. The above is valid if the whole substrate is irradiated during rotation. It is now proposed that if only a part of the substrate is irradiated by a focused ion flux such as a line beam or a spot beam then a different scenario would occur. For example with
99
a line beam centred on and obliquely incident to the centre of rotation of the target ripples transverse or parallel (depending on the polar incidence angle) would form independently at each azimuthal angle during rotation. In this way a circular ripple pattern centred on the centre of rotation would develop. If, on the other hand, a spot beam was used only an annular ring (or rings if the spot was successively moved to different radial positions) of ripples would develop. Again variation of ion incidence conditions could be used to control ripple directions and sizes. In summary therefore it is proposed that use of multiple ion fluxes in parallel could be used to create surface structures with different translational symmetries from the overlapping of individual ripple structures and circular ripple structures by using focused ion fluxes and rotating targets. Unfortunately the author does not possess, currently, experimental facilities to confirm these proposals but believes them to be valid based upon the predictable behaviour with systems of single orientation and broad ion fluxes. It is considered worthwhile to explore these suggestions in view of their potential for generating surface structures in, for example, micro-electronic, microelectronic mechanical and opto-electronic systems applications.
References [1] Navez M, Sella C, Chaperot D. Comptes Rendus 1962;254:240. [2] Nelson RS, Mazey DJ. Ion Surface Interactions, Sputtering and Related Phenomena. London: Gordon and Breach; 1973. p. 199. [3] Carter G, Nobes MJ, Paton F, Williams JS, Whitton JL. Radiat Eff 1977;65:33. [4] Umbach CC, Headrick RL, Chang Kee C. Phys Rev Lett 2001;87:246104. [5] Bradley RS, Harper JM. J Vac Sci Technol 1988;A6:2390. [6] Facsko S, Kurz H, Dekorsky T. Phys Rev 2001;B63:165329. [7] Facsko S, Dekorsky T, Koerdt C, Trapp C, Kurz H, Vogt A, Hartnagel HL. Science 1999;285:1551. [8] Facsko S, Bobek T, Dekorsky T, Kurz H. Phys Status Solidi 2001;b224:539. [9] Gago R, Vazquez L, Cuerno R, Varela M, Ballesteros C, Albella JM. Appl Phys Lett 2001;78:3316.
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[10] Constantini B, B de Mongeot F, Boragno C, Valbusa U. Phys Rev Lett 2001;86:838. [11] Rusponi S, Constantini G, B de Mongeot F, Boragno C, Valbusa U. Appl Phys Lett 1999;75:3318. [12] Rusponi S, Boragno C, Valbusa U. Phys Rev Lett 1997;78:2795. [13] B de Mongeot F, Constantini G, Boragno C, Valbusa U. Phys Rev Lett 2001;84:2425. [14] Carter G. J Phys D 2001;34:R1–22. [15] Valbusa U, Boragno C, B de Mongeot F. J Phys Cond Matter 2002;14:8153. [16] Makeev M, Cuerno R, Barabasi A-L. arXiv: cond-mat/ 0007354 v1 20 July 2000. [17] Sigmund P. Phys Rev 1969;84:383. [18] Oechsner H. Appl Phys 1975;8:185. [19] Sigmund P. J Mater Sci 1973;8:1545. [20] Carter G, Nobes MJ, Webb RP. J Mater Sci 1981;16:2091. [21] Makeev M, Barabasi A-L. Appl Phys Lett 1997;71:2800. [22] Carter G. J Mater Sci 1976;11:1091.
[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34]
Villain J. J Phys 1991;I(1):19. Ehrlich G, Hudda FG. J Chem Phys 1966;44:1039. Schwoebel RL, Shipsey EJ. J Appl Phys 1968;40:614. Cuerno R, Barabasi A-L. Phys Rev Lett 1995;74: 4746. Park S, Kahng B, Jeong H, Barabasi A-L. Phys Rev Lett 1999;85:3486. Kahng B, Jeong H, Barabasi A-L. Appl Phys Lett 2001;78:805. Carter G, Vishnyakov V, Martynenko Yu V, Nobes MJ. J Appl Phys 1995;78:3559. Barber DJ, Frank FC, Moss M, Steeds JW, Tsong IST. J Mater Sci 1973;8:1030. Smith R, Valkering TP, Walls JM. Phil Mag 1981;A44:879. Carter G, Nobes MJ, Cruz SA. J Mater Sci Lett 1984;3:523. Bradley RM, Cirlin E-H. Appl Phys Lett 1996;68:3722. Sykes DE, Chew A. Surf Interface Anal 1994;21:231.
Vacuum 77 (2004) 97–100 www.elsevier.com/locate/vacuum
Proposals for producing novel periodic structures by ion bombardment sputtering G. Carter Joule Physics Laboratory, Institute of Materials, University of Salford, Salford M5 4WT, UK Received 3 June 2004; received in revised form 28 July 2004; accepted 30 July 2004
Abstract It is proposed, and confirmed analytically that if multiple ion fluxes are incident simultaneously, all at the same oblique polar angle but at different azimuthal angles, on to a target then the individual ripple patterns generated by sputtering are superimposed to produce novel surface structures. It is also shown that single focused ion fluxes incident on to rotating targets can produce circular ripple patterns. r 2004 Published by Elsevier Ltd. Keywords: Sputtering; Multiple ion fluxes; Superimposed ripple patterns; Rotating targets; Circular ripple patterns
It has been known for many years that ion bombardment at oblique incidence of amorphous materials such as glass [1] or semiconductors [2,3] and insulators [4], which are amorphised by ion irradiation can produce regular repetitive and periodic surface structures in the form of ripples. For ion incidence angles between about 301 and 601 to the surface normal these ripples are formed with their wave vector parallel to the projection of the ion flux on to the surface but for larger incidence angles the wave vector is rotated to be perpendicular to the ion flux projection [5]. Recently several studies [6–9] have revealed that low energy ion bombardment normal to the surface of different semiconductors can lead to E-mail address: [email protected] (G. Carter). 0042-207X/$ - see front matter r 2004 Published by Elsevier Ltd. doi:10.1016/j.vacuum.2004.07.082
the production of regular arrays of conical or pyramidal features. In the case of metals, which are not amorphised by irradiation but become loaded with defects, both ripple and pyramidal features can be produced not only for oblique but also for normal ion incidence, the exact structure being dependent upon the irradiated substrate temperature [10–13]. These general behaviours, if not all the specific details, can be understood [14–16] in terms of the competition between sputtering erosion phenomena which, due to the dependence of sputtering yield upon local angle of ion incidence [17,18], can lead to surface smoothing whilst, due to the dependence of the yield upon local surface
ARTICLE IN PRESS 98
G. Carter / Vacuum 77 (2004) 97–100
curvature, can lead to surface roughening [5,19,20] and higher order spatial derivatives of surface height can lead to surface smoothing [21], and surface relaxation phenomena such as diffusion [5], which can be radiation mediated [22], can have preferred directionality [10–13] and biased due to the Ehrlich-Schwoebel effect [23–25] and viscous flow [4]. All of these effects can be encompassed in the deceptively simple equation for the time rate of change of local surface height, h, qh=qt ¼
J Y ðy; b; R; rn hÞ þ K 1 r4 h þ K 2 rj s þ Z; N (1)
where J is the ion flux density incident at polar angle y and azimuthal angle b on to a substrate of atomic density N, Y ðy; b; R; rn hÞ is the local sputtering yield at a point of radius of curvature R and is a function of higher order spatial derivatives of the local surface height, K 1 r4 h represents surface diffusion and/or viscous flow, K2js represents any biased surface diffusion process with a biased diffusion current js and Z represents the random or noisy nature of ion arrival and the sputtering process. For not too large angles of ion incidence and relatively low amplitudes of any emerging surface features Y can be expanded in low order linear derivatives of the surface height [5,21] but for larger values of angles and amplitude non-linear terms in powers of these derivatives must be included [26]. In the former case, and in the absence of biased surface diffusion, the linear form of equation (1) can be readily solved [5,26] to show that surface waves with all possible wavelengths will develop but the one with the fastest growing amplitude will dominate and a well defined ripple structure with increasing amplitude and constant wavelength will emerge. In particular the wave vectors will be parallel to the projection of the ion flux for not too large ion incidence angles and ripple amplitudes but perpendicular to this projection for larger incidence angles. For large increase in ripple amplitude non-linear terms become effective and the surface is predicted [26] to roughen kinetically with time but it has also been predicted that for even larger amplitudes [27]
ripples may again emerge but with wave vectors rotated from their original direction. Unlike the low amplitude behaviour, which has been observed many times experimentally [5,14,15] the large amplitude behaviour has not yet been confirmed empirically. The dependence of sputtering yield on the surface height derivatives can be measured experimentally or calculated as can the constant K1 and the resulting values of ripple wavelength, orientation and rate of increase of amplitude correspond reasonably well, for amorphous materials, with experimental data [14,15]. In the case of metals diffusion rates can vary between different crystal directions and be temperature dependent so that ripple orientations can vary with this parameter as observed experimentally [10–13,15] as can the growth of pyramids when biased surface diffusion becomes effective. The results for low energy normally incident ion bombardment of semiconductors are unusual because theory suggests [5] that minor random roughening of the surface should occur but computational simulations have suggested [28] that fourth order height derivative processes involved in the sputtering yield can lead to omnidirectional diffusion-like effects and reordering of the surface. The purpose of the preceding review has been to show that repetitive surface features with translational symmetry can be understood and their habits and evolution quite well predicted and realised experimentally if ion bombardment parameters (flux density, energy, species, incidence angle) and substrate material parameters (diffusivity, temperature) can be controlled and known or estimated. Thus features with repetition lengths in the nanometre to submicrometre range can be achieved [14,15]. However the above discussion refers only to the case of mono-directional ion fluxes and stationary ion fluxes or substrates. It is now the purpose of subsequent discussion to suggest how novel surface structures may be produced if these constraints are removed. Firstly, in the case of amorphisable substrates where surface diffusion and viscous flow are isotropic, erosion phenomena dictate ripple habit and evolution [5,14,15,16] and are controllable by the polar angle of ion incidence which defines the
ARTICLE IN PRESS G. Carter / Vacuum 77 (2004) 97–100
direction of the ripple wave vector. That this is the case has been demonstrated in studies [29] with ion irradiated Si at fixed oblique polar angle and an initial azimuthal angle to produce ripples with wave vector parallel to the projection of the ion flux. The substrate was then rotated through a right angle and radiation recommenced and the initial ripple structure was gradually eradicated and a new ripple structure developed with wave vector orthogonal to the earlier one. It is clear that the two morphologies were independent and any resulting surface structure obtained during the second, sequential, radiation would be difficult to anticipate. However, precisely because of this independence, if two (or more) irradiations were performed simultaneously with ion fluxes deployed at different azimuthal angles the ensuing morphology would be the sum of the independent individual morphologies. Thus, for example, two orthogonally deployed ion fluxes would lead to orthogonally developed ripple structures with the appearance of four sided pyramidal features. Nonorthogonal ion fluxes would result in four sided features also but with rotated habit while three ion fluxes would lead to trigonal features. Even more deployed ion fluxes could result in more exotic structures while modification of one or more ion incidence polar angles, ion flux densities, energies and species could result in a range of tailored micro-features. The same could be true for metal substrates provided that substrate temperature was so controlled as to minimise directional and biased diffusion processes [10–13,15]. Turning now to non-stationary systems it is well known that if targets are continuously rotated during irradiation the surface can be smoothed [30–32] and ripple formation inhibited. [33,34]. Essentially the latter occurs because, as noted above, ripple wave vector is controllable, for fixed polar angle, by the incident azimuthal angle and if, as in continuous target rotation all such angles are explored no dominant mode can develop. The above is valid if the whole substrate is irradiated during rotation. It is now proposed that if only a part of the substrate is irradiated by a focused ion flux such as a line beam or a spot beam then a different scenario would occur. For example with
99
a line beam centred on and obliquely incident to the centre of rotation of the target ripples transverse or parallel (depending on the polar incidence angle) would form independently at each azimuthal angle during rotation. In this way a circular ripple pattern centred on the centre of rotation would develop. If, on the other hand, a spot beam was used only an annular ring (or rings if the spot was successively moved to different radial positions) of ripples would develop. Again variation of ion incidence conditions could be used to control ripple directions and sizes. In summary therefore it is proposed that use of multiple ion fluxes in parallel could be used to create surface structures with different translational symmetries from the overlapping of individual ripple structures and circular ripple structures by using focused ion fluxes and rotating targets. Unfortunately the author does not possess, currently, experimental facilities to confirm these proposals but believes them to be valid based upon the predictable behaviour with systems of single orientation and broad ion fluxes. It is considered worthwhile to explore these suggestions in view of their potential for generating surface structures in, for example, micro-electronic, microelectronic mechanical and opto-electronic systems applications.
References [1] Navez M, Sella C, Chaperot D. Comptes Rendus 1962;254:240. [2] Nelson RS, Mazey DJ. Ion Surface Interactions, Sputtering and Related Phenomena. London: Gordon and Breach; 1973. p. 199. [3] Carter G, Nobes MJ, Paton F, Williams JS, Whitton JL. Radiat Eff 1977;65:33. [4] Umbach CC, Headrick RL, Chang Kee C. Phys Rev Lett 2001;87:246104. [5] Bradley RS, Harper JM. J Vac Sci Technol 1988;A6:2390. [6] Facsko S, Kurz H, Dekorsky T. Phys Rev 2001;B63:165329. [7] Facsko S, Dekorsky T, Koerdt C, Trapp C, Kurz H, Vogt A, Hartnagel HL. Science 1999;285:1551. [8] Facsko S, Bobek T, Dekorsky T, Kurz H. Phys Status Solidi 2001;b224:539. [9] Gago R, Vazquez L, Cuerno R, Varela M, Ballesteros C, Albella JM. Appl Phys Lett 2001;78:3316.
ARTICLE IN PRESS 100
G. Carter / Vacuum 77 (2004) 97–100
[10] Constantini B, B de Mongeot F, Boragno C, Valbusa U. Phys Rev Lett 2001;86:838. [11] Rusponi S, Constantini G, B de Mongeot F, Boragno C, Valbusa U. Appl Phys Lett 1999;75:3318. [12] Rusponi S, Boragno C, Valbusa U. Phys Rev Lett 1997;78:2795. [13] B de Mongeot F, Constantini G, Boragno C, Valbusa U. Phys Rev Lett 2001;84:2425. [14] Carter G. J Phys D 2001;34:R1–22. [15] Valbusa U, Boragno C, B de Mongeot F. J Phys Cond Matter 2002;14:8153. [16] Makeev M, Cuerno R, Barabasi A-L. arXiv: cond-mat/ 0007354 v1 20 July 2000. [17] Sigmund P. Phys Rev 1969;84:383. [18] Oechsner H. Appl Phys 1975;8:185. [19] Sigmund P. J Mater Sci 1973;8:1545. [20] Carter G, Nobes MJ, Webb RP. J Mater Sci 1981;16:2091. [21] Makeev M, Barabasi A-L. Appl Phys Lett 1997;71:2800. [22] Carter G. J Mater Sci 1976;11:1091.
[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34]
Villain J. J Phys 1991;I(1):19. Ehrlich G, Hudda FG. J Chem Phys 1966;44:1039. Schwoebel RL, Shipsey EJ. J Appl Phys 1968;40:614. Cuerno R, Barabasi A-L. Phys Rev Lett 1995;74: 4746. Park S, Kahng B, Jeong H, Barabasi A-L. Phys Rev Lett 1999;85:3486. Kahng B, Jeong H, Barabasi A-L. Appl Phys Lett 2001;78:805. Carter G, Vishnyakov V, Martynenko Yu V, Nobes MJ. J Appl Phys 1995;78:3559. Barber DJ, Frank FC, Moss M, Steeds JW, Tsong IST. J Mater Sci 1973;8:1030. Smith R, Valkering TP, Walls JM. Phil Mag 1981;A44:879. Carter G, Nobes MJ, Cruz SA. J Mater Sci Lett 1984;3:523. Bradley RM, Cirlin E-H. Appl Phys Lett 1996;68:3722. Sykes DE, Chew A. Surf Interface Anal 1994;21:231.