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VUV laser ablation of polymers
Applied Surface Science 168 (2000) 175±177
VUV laser ablation of polymers Photochemical aspect M.C. Castexa,*, N. Bityurinb, C. Oliveroa, S. Muraviovb, N. Bronnikovab, D. Riedela a
Laboratoire de Physique des Lasers, Universite Paris-Nord, 93430 Villetaneuse, France b Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia
Abstract A photochemical theory of laser ablation owing to the direct chain scission process is considered in quite general form taking into account the modi®cation of material. The formulas obtained can be used for estimating mechanisms of VUV laser ablation of polymers. # 2000 Elsevier Science B.V. All rights reserved. Keywords: VUV laser; Polymers; Ablation; Modeling
1. Introduction The development of VUV laser sources with wavelengths shorter than the usually employed excimer F2 lasers [1] provides new opportunity for laser treatment of materials with great accuracy and small lateral resolution. VUV ablation of polymers is one of the promising areas of application for this newly developed laser technique [2]. The advent of VUV lasers with photon energies as high as 10 eV and their use for irradiation of polymers increases once again the interest to the theory of laser ablation, where the most intriguing point is the interrelation between thermal and non-thermal processes. From the very beginning of UV laser ablation modeling, it was believed that polymer ablation is dominated by direct photochemical main-chain scission [3]. The comprehensive investigations [4] have shown, however, that, at least for the so largely studied and used polymer as PMMA, direct
photochemical main-chain scission can be really relevant to the laser ablation process only with VUV. The aim of the present publication is to construct a pure photochemical theory of laser ablation owing to direct photochemical chain breaking. We assume that the VUV ablation is a layer-by-layer process. The main chains at the boundary have to be broken into small fragments and only after that they leave the surface. An important feature of this model is that it takes into account the movement of the interface during laser pulse. We accept here the Stefan-type formulation of the problem with moving interface, thus, we ®x the position of the ablation front with a critical number density of broken bonds. This model takes into account such features of VUV irradiation as signi®cant modi®cation of material in¯uencing its optical properties. We consider both single-pulse and multiple-pulse ablation. 2. Photochemical theory of laser ablation
*
Corresponding author. Tel.: 33-1-49-40-3600; fax: 33-1-49-40-3200. E-mail address: [email protected] (M.C. Castex).
Let us consider a laser beam propagating along the x axis, the half-space x > 0 being occupied by the
0169-4332/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 0 ) 0 0 5 8 4 - 5
176
M.C. Castex et al. / Applied Surface Science 168 (2000) 175±177
dielectric media. We will employ the mathematical approach [5] for treating the problem of photochemical modi®cation of material with moving interface. It was shown there that this problem formulated in general form could be reduced to the set of two equations. Here we ®x the position of the interface with the critical number density of broken bonds which imposes the boundary condition at the ablation front x xS t. @S C SI; S xS S ; @t @I ÿa SI; I xS IS t @x
dh q t exp ÿaP h 1 ÿ R S dt ho k (1)
S is one of the photochemical variables (see [5]) which monotonically depends on time. S generally does not correspond to the number density of broken bonds. Nevertheless, by ®xing the number density of broken bonds, we ®x the value S as well. I is the light intensity measured in photon per cm2 s. The irradiation starts at t 0, xS 0 0. The material initially is homogeneous and the initial condition for S stands S x; 0 S0 , thus, the ablation velocity is zero while S 0; t 6 S. It is important [5] that at every point x xS t and, at any time t, the relation holds: Z S @S a S0 0 ÿC S dS (2) 0 @x S0 C S It is evident that
dS xS t; t @S x; t @S x; t V t dt @x xxS @t xxS
(3)
From Eqs. (1)±(3) it follows immediately Eq. (14) of [5]. In our case (S xS t; t S const) by the same way from these relations, it follows the main formula: V t R S S0
IS t dS0 a S0 =C S0
R S ho 0 dS= 1 ÿ R SC S. Here R(S) refers to the re¯ection coef®cient. If F < Fth the interface will move according R t to Eq. (4) if t > t . Here t obeys the relation 0 q t dt Fth . Since the interface starts moving, the surface intensity IS will be connected with q(t) through the extinction of the plume. Assuming the simplest model of plume extinction and t > t, we obtain: hoIS t q t exp ÿaP h t 1 ÿ R S . Together with (4) it yields:
IS t k
(4)
The last equality de®nes k as the number density of photons which should be absorbed at this particular point to produce critical number density of broken bonds at this point. Let us consider now single-pulse and multiple-pulse ablation kinetics within the photochemical ablation model. If q(t) is the laser power density and F refers to ¯uence, then at single-pulse irradiation there will be no ablation with F < Fth , where the single-pulse threshold ¯uence is Fth
(5)
Integrating this equation with initial condition h t 0 yields the dependence of resulting etch depth, H, per single pulse on pulse laser ¯uence: 1 aP F ÿ Fth 1 ÿ R S ln 1 (6) H aP ho k In special cases, when the re¯ection coef®cient is practically not in¯uenced by the modi®cation process, R S const R and a S const a, k Fth 1ÿ Ra=ho and (6) becomes H l n 1 aP F ÿ Fth = a Fth =aP , which coincides with the formula in [6]. Let us consider now multiple-pulse ablation kinetics. Here, we have no ablation at all for the number of pulses less or equal to [Fth/F], integer part of the number Fth/F, (incubation) and then, after the next pulse, we have S S at the boundary. Thus, each pulse, which ordinal number is greater than Fth =F 1, will etch absolutely the same depth, which can be easily found from Eq. (5) with initial condition h 0 0. This yields the resulting ablated depth for such pulse: 1 aP F 1 ÿ R S ln 1 (7) H aP ho k If we irradiate the material with a number of pulses much greater than Fth =F 1, then the averaged etch depth per pulse, can be estimated using Eq. (7). If R S const R and a S const a, Eq. (7) becomes: 1 aP F (8) H ln 1 aP a Fth The `photochemical law' H ln F=Fapp:th =aEff [3] is often used for interpreting the data on laser ablation kinetics. Here aEff is the effective absorption
M.C. Castex et al. / Applied Surface Science 168 (2000) 175±177
coef®cient and Fapp.th is apparent threshold. The relation (7) follows this law at high ¯uences. Here ho k=aP 1 ÿ R S or in the aEff aP and Fapp:th case (8) Fapp:th Fth a=aP . For smaller ¯uences (7) deviates from the logarithmic law, with H tending to zero when F ! 0. That corresponds qualitatively to the behavior of etch rate curves obtained in [2] for laser ablation of PMMA and Te¯on at l 125 nm. For small ¯uences the kinetics curve (7) follows linear ho k or in the case (8): law: H F 1 ÿ R S = H F= a Fth . Let us consider the simplest photoho chemical reaction A!B, see [5], and R const. Here A stands for the element of the initial material, and B denotes the product of a photochemical reaction. In our case this transition corresponds to chain breaking with simultaneous creation of by-products changing the optical properties of the material. The kinetics of modi®cation caused by this reaction is described by the set of equations: @n ZsA n0 ÿ nI; @t
@I ÿ sB n sA n0 ÿ nI @x (9)
Here n stands for the number density of broken bonds, n0 referring to the number density of initial bonds. sA stands for the absorption cross-section of initial material recalculated per the number density of initial bonds. sB refers to the absorption cross-section of products of photochemical reaction recalculated per the number density of broken bonds. Z is the quantum yield of photochemical bond breaking reaction. n stands for the critical number density of broken bonds providing ablation. We apply the mathematical approach developed in the previous section. It yields: k n 1 g=n, here g b 1=d ln 1=1 ÿ d ÿ 1,
177
b sB =sA ; d n =n0 , and (7) becomes 1 ZaP F 1 ÿ R ln 1 ; H aP ho n 1 g ho n 1 g ; Fapp:th ZaP 1 ÿ R ho 1 ln Fth ZsA 1 ÿ R 1ÿd For small d, d ! 0; g ! 0 and k n =Z, and this result corresponds to [7]. However, for real situations d can be quite close to unity and the effect of modi®cation is signi®cant. Let us estimate k for a typical situation n0 6 1021 cmÿ3. If d 1=2 then, for b 1 and Z 1 we have g 1:3 and k 4 1021 cmÿ3. If b 2 and Z 1 then g 1:6 and k 5 1021 cmÿ3. With k 5 1021 cmÿ3, ho 10 eV, and aP 107 cmÿ1 (see [2]), Fapp:th 1 mJ/ cm2, and with sA 10ÿ16 cm2, Fapp:th 10 mJ/cm2. For self-consistency of the pure photochemical model, temperature estimations are necessary. They will be published in a separate paper.
References [1] L. Museur, W.Q. Zheng, A.V. Kanaev, M.C. Castex, IEEE J. Sel. Top. QE 1 (1995) 900. [2] D. Riedel, M.C. Castex, Appl. Phys. A 69 (1999) 375. [3] H.H.G. Jelinnek, R. Srinivasan, J. Phys. Chem. 88 (1984) 3048. [4] M.C.K. Tinone, K. Tanaka, N. Ueno, J. Vac. Sci. Technol. 13 (1995) 1885. [5] N. Bityurin, Appl. Surface Sci. 138/139 (1999) 354. [6] K. Schildbach, Proc. SPIE 1279, 1990. [7] G.D. Mahan, H.S. Cole, Y.S. Liu, H.R. Phillip, Appl. Phys. Lett. 53 (1988) 2377.
VUV laser ablation of polymers Photochemical aspect M.C. Castexa,*, N. Bityurinb, C. Oliveroa, S. Muraviovb, N. Bronnikovab, D. Riedela a
Laboratoire de Physique des Lasers, Universite Paris-Nord, 93430 Villetaneuse, France b Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia
Abstract A photochemical theory of laser ablation owing to the direct chain scission process is considered in quite general form taking into account the modi®cation of material. The formulas obtained can be used for estimating mechanisms of VUV laser ablation of polymers. # 2000 Elsevier Science B.V. All rights reserved. Keywords: VUV laser; Polymers; Ablation; Modeling
1. Introduction The development of VUV laser sources with wavelengths shorter than the usually employed excimer F2 lasers [1] provides new opportunity for laser treatment of materials with great accuracy and small lateral resolution. VUV ablation of polymers is one of the promising areas of application for this newly developed laser technique [2]. The advent of VUV lasers with photon energies as high as 10 eV and their use for irradiation of polymers increases once again the interest to the theory of laser ablation, where the most intriguing point is the interrelation between thermal and non-thermal processes. From the very beginning of UV laser ablation modeling, it was believed that polymer ablation is dominated by direct photochemical main-chain scission [3]. The comprehensive investigations [4] have shown, however, that, at least for the so largely studied and used polymer as PMMA, direct
photochemical main-chain scission can be really relevant to the laser ablation process only with VUV. The aim of the present publication is to construct a pure photochemical theory of laser ablation owing to direct photochemical chain breaking. We assume that the VUV ablation is a layer-by-layer process. The main chains at the boundary have to be broken into small fragments and only after that they leave the surface. An important feature of this model is that it takes into account the movement of the interface during laser pulse. We accept here the Stefan-type formulation of the problem with moving interface, thus, we ®x the position of the ablation front with a critical number density of broken bonds. This model takes into account such features of VUV irradiation as signi®cant modi®cation of material in¯uencing its optical properties. We consider both single-pulse and multiple-pulse ablation. 2. Photochemical theory of laser ablation
*
Corresponding author. Tel.: 33-1-49-40-3600; fax: 33-1-49-40-3200. E-mail address: [email protected] (M.C. Castex).
Let us consider a laser beam propagating along the x axis, the half-space x > 0 being occupied by the
0169-4332/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 0 ) 0 0 5 8 4 - 5
176
M.C. Castex et al. / Applied Surface Science 168 (2000) 175±177
dielectric media. We will employ the mathematical approach [5] for treating the problem of photochemical modi®cation of material with moving interface. It was shown there that this problem formulated in general form could be reduced to the set of two equations. Here we ®x the position of the interface with the critical number density of broken bonds which imposes the boundary condition at the ablation front x xS t. @S C SI; S xS S ; @t @I ÿa SI; I xS IS t @x
dh q t exp ÿaP h 1 ÿ R S dt ho k (1)
S is one of the photochemical variables (see [5]) which monotonically depends on time. S generally does not correspond to the number density of broken bonds. Nevertheless, by ®xing the number density of broken bonds, we ®x the value S as well. I is the light intensity measured in photon per cm2 s. The irradiation starts at t 0, xS 0 0. The material initially is homogeneous and the initial condition for S stands S x; 0 S0 , thus, the ablation velocity is zero while S 0; t 6 S. It is important [5] that at every point x xS t and, at any time t, the relation holds: Z S @S a S0 0 ÿC S dS (2) 0 @x S0 C S It is evident that
dS xS t; t @S x; t @S x; t V t dt @x xxS @t xxS
(3)
From Eqs. (1)±(3) it follows immediately Eq. (14) of [5]. In our case (S xS t; t S const) by the same way from these relations, it follows the main formula: V t R S S0
IS t dS0 a S0 =C S0
R S ho 0 dS= 1 ÿ R SC S. Here R(S) refers to the re¯ection coef®cient. If F < Fth the interface will move according R t to Eq. (4) if t > t . Here t obeys the relation 0 q t dt Fth . Since the interface starts moving, the surface intensity IS will be connected with q(t) through the extinction of the plume. Assuming the simplest model of plume extinction and t > t, we obtain: hoIS t q t exp ÿaP h t 1 ÿ R S . Together with (4) it yields:
IS t k
(4)
The last equality de®nes k as the number density of photons which should be absorbed at this particular point to produce critical number density of broken bonds at this point. Let us consider now single-pulse and multiple-pulse ablation kinetics within the photochemical ablation model. If q(t) is the laser power density and F refers to ¯uence, then at single-pulse irradiation there will be no ablation with F < Fth , where the single-pulse threshold ¯uence is Fth
(5)
Integrating this equation with initial condition h t 0 yields the dependence of resulting etch depth, H, per single pulse on pulse laser ¯uence: 1 aP F ÿ Fth 1 ÿ R S ln 1 (6) H aP ho k In special cases, when the re¯ection coef®cient is practically not in¯uenced by the modi®cation process, R S const R and a S const a, k Fth 1ÿ Ra=ho and (6) becomes H l n 1 aP F ÿ Fth = a Fth =aP , which coincides with the formula in [6]. Let us consider now multiple-pulse ablation kinetics. Here, we have no ablation at all for the number of pulses less or equal to [Fth/F], integer part of the number Fth/F, (incubation) and then, after the next pulse, we have S S at the boundary. Thus, each pulse, which ordinal number is greater than Fth =F 1, will etch absolutely the same depth, which can be easily found from Eq. (5) with initial condition h 0 0. This yields the resulting ablated depth for such pulse: 1 aP F 1 ÿ R S ln 1 (7) H aP ho k If we irradiate the material with a number of pulses much greater than Fth =F 1, then the averaged etch depth per pulse, can be estimated using Eq. (7). If R S const R and a S const a, Eq. (7) becomes: 1 aP F (8) H ln 1 aP a Fth The `photochemical law' H ln F=Fapp:th =aEff [3] is often used for interpreting the data on laser ablation kinetics. Here aEff is the effective absorption
M.C. Castex et al. / Applied Surface Science 168 (2000) 175±177
coef®cient and Fapp.th is apparent threshold. The relation (7) follows this law at high ¯uences. Here ho k=aP 1 ÿ R S or in the aEff aP and Fapp:th case (8) Fapp:th Fth a=aP . For smaller ¯uences (7) deviates from the logarithmic law, with H tending to zero when F ! 0. That corresponds qualitatively to the behavior of etch rate curves obtained in [2] for laser ablation of PMMA and Te¯on at l 125 nm. For small ¯uences the kinetics curve (7) follows linear ho k or in the case (8): law: H F 1 ÿ R S = H F= a Fth . Let us consider the simplest photoho chemical reaction A!B, see [5], and R const. Here A stands for the element of the initial material, and B denotes the product of a photochemical reaction. In our case this transition corresponds to chain breaking with simultaneous creation of by-products changing the optical properties of the material. The kinetics of modi®cation caused by this reaction is described by the set of equations: @n ZsA n0 ÿ nI; @t
@I ÿ sB n sA n0 ÿ nI @x (9)
Here n stands for the number density of broken bonds, n0 referring to the number density of initial bonds. sA stands for the absorption cross-section of initial material recalculated per the number density of initial bonds. sB refers to the absorption cross-section of products of photochemical reaction recalculated per the number density of broken bonds. Z is the quantum yield of photochemical bond breaking reaction. n stands for the critical number density of broken bonds providing ablation. We apply the mathematical approach developed in the previous section. It yields: k n 1 g=n, here g b 1=d ln 1=1 ÿ d ÿ 1,
177
b sB =sA ; d n =n0 , and (7) becomes 1 ZaP F 1 ÿ R ln 1 ; H aP ho n 1 g ho n 1 g ; Fapp:th ZaP 1 ÿ R ho 1 ln Fth ZsA 1 ÿ R 1ÿd For small d, d ! 0; g ! 0 and k n =Z, and this result corresponds to [7]. However, for real situations d can be quite close to unity and the effect of modi®cation is signi®cant. Let us estimate k for a typical situation n0 6 1021 cmÿ3. If d 1=2 then, for b 1 and Z 1 we have g 1:3 and k 4 1021 cmÿ3. If b 2 and Z 1 then g 1:6 and k 5 1021 cmÿ3. With k 5 1021 cmÿ3, ho 10 eV, and aP 107 cmÿ1 (see [2]), Fapp:th 1 mJ/ cm2, and with sA 10ÿ16 cm2, Fapp:th 10 mJ/cm2. For self-consistency of the pure photochemical model, temperature estimations are necessary. They will be published in a separate paper.
References [1] L. Museur, W.Q. Zheng, A.V. Kanaev, M.C. Castex, IEEE J. Sel. Top. QE 1 (1995) 900. [2] D. Riedel, M.C. Castex, Appl. Phys. A 69 (1999) 375. [3] H.H.G. Jelinnek, R. Srinivasan, J. Phys. Chem. 88 (1984) 3048. [4] M.C.K. Tinone, K. Tanaka, N. Ueno, J. Vac. Sci. Technol. 13 (1995) 1885. [5] N. Bityurin, Appl. Surface Sci. 138/139 (1999) 354. [6] K. Schildbach, Proc. SPIE 1279, 1990. [7] G.D. Mahan, H.S. Cole, Y.S. Liu, H.R. Phillip, Appl. Phys. Lett. 53 (1988) 2377.