Is the VUV laser ablation of polymers a pure photochemical process?

Applied Surface Science 197±198 (2002) 805±807

Is the VUV laser ablation of polymers a pure photochemical process? M.C. Castexa,*, N. Bityurinb a

Laboratoire de Physique des Lasers, Universite Paris-Nord, 93430 Villetaneuse, France b Institute of Applied Physics, Russian Academy of Sciences, Nizhnii Novgorod, Russia

Abstract Within the pure photochemical model of laser ablation of polymers, developed in our previous publications, we estimate the value of the surface temperature at the ablation front for several important examples. Derived formulas allow probing physical self-consistency of the pure photochemical ablation model. # 2002 Elsevier Science B.V. All rights reserved. Keywords: VUV laser; Ablation; Photochemical model; Heating

1. Introduction The development of VUV laser sources [1] provides new opportunity for laser treatment of materials with great accuracy and small lateral resolution [2]. In particular, the advent of VUV lasers with photon energies as high as 10 eV and their use for irradiation of polymers increase once again the interest in the theory of laser ablation, where the most intriguing point is the interrelation between thermal and non-thermal processes. With VUV photons with energy well exceeding the energy of covalent bond, one can anticipate that photochemical mechanism should dominate laser ablation. In [3,4], photochemical ablation was considered within the photochemical modi®cation model, which, in quite general case, can be reduced to the form [3]: @S @I ˆ C…S†I; ˆ a…S†I; S…x; 0† ˆ S0 ; @t @x (1) I…0; t† ˆ I0 …t†; *

Corresponding author. Tel.: ‡33-1-49-40-36-00; fax: ‡33-1-49-40-32-00. E-mail address: [email protected] (M.C. Castex).

where S is a photochemical variable, I is photon ¯ux, and a is absorption coef®cient. Ablation starts when S reaches its critical value S that is associated with a critical number of broken bonds. After the start of ablation, the position of the moving interface between solid and gaseous phases, xs, can be found, according to model derived in [4], from the Stefan-like condition S…xs …t†† ˆ S. It was shown in [4] that the ablation velocity, V ˆ dxs =dt, is proportional to the laser intensity at the ablation front: Z S Is …t† a…S0 † 0 ; k dS ˆ constant; (2) V…t† ˆ 0 k S0 C…S † where Is(t) can be evaluated knowing I0(t) and plume absorption, as it is discussed in [4]. The question about heating of the material during photochemical ablation is very important from the point of view of self-consistency of pure photochemical model. With VUV photons, we have effective bond scission. However, the energy of the photon is much larger than the energy of the broken covalent bond. If the excess of energy went to heat, a temperature rise would be high enough to make the applicability of a

0169-4332/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 2 ) 0 0 4 4 8 - 8

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M.C. Castex, N. Bityurin / Applied Surface Science 197±198 (2002) 805±807

pure photochemical model questionable. In the present communication, we assume that the photochemical model works and estimate the surface temperature. Quite general formulas are obtained. It is evident that if this estimation yields the value of the temperature high enough to provide thermal destruction of material, then the photochemical model is not relevant.

tion when I s ˆ constant, and ablation velocity V ˆ constant. The temperature distribution within the moving reference frame (z) ®xed with the ablation front obeys the equation: @T @ 2 T hoL…S†I…z; t† @T ˆ DT 2 ‡ ; ‡V @t @z cP r @z

(6)

2. Adiabatic approximation

where z ˆ 0 corresponds to the interface. It can be checked directly that Eqs. (1) and (2) of paper [4] yield:

Let us start with the single pulse ablation and perform estimation from the previous discussions for the surface temperature, neglecting heat diffusion. In this case, the temperature rise, T, can be estimated from the equation (see Eq. (1)):

@ …F…S†I†; L…S†I…z; t† ˆ @z RS ‰L…S0 †=C…S0 †Š dS0 F…S† ˆ RSS0 : 0 0 0 S0 ‰a…S †=C…S †Š dS

@T ho  ˆ L…S†I; @t cP r

It follows from Eq. (7) that the right part of Eq. (6) is a full derivative with respect to z:   @T @ @T hoF…S†I…z; t† ˆ DT ‡ VT : (8) @t @z @z cP r

L…S†  a…S†

e…S† C…S†; ho

(3)

where cP refers to the speci®c heat, and r is the density of the material. In what follows, for simplicity, we will regard them as constants. Here, e(S) is the endothermic effect of photochemical transitions. It follows from Eq. (3) that, in this case, temperature can be regarded as one of the Si-variables [3]. Formalism developed in [3,4] allows one to immediately obtain the expression for surface temperature, Tadiabat, at the ablation front in this adiabatic approximation: Z  ho S L…S†  dS: (4) Tadiabat ˆ cP r S0 C…S† Here, and also later on, we put the ambient temperature equal to zero. Putting the enthalpy e equal to 0, and using de®nition of k, Eq. (2) yields the estimation: Ts ˆ

ok h : cP r

(5)

It should be noted that Eqs. (4) and (5) are valid only for single-pulse ablation. Indeed, while temperature relaxes between pulses due to heat diffusion, Si-variables assumed to be not relaxing [3]. 3. Stationary-wave ablation Let us now consider the case when the heat diffusion is signi®cant. First, we consider stationary abla-

(7)

With I s ˆ constant, and V ˆ constant, the temperature distribution tends to stationary one obeying Eq. (8) with @T=@t ˆ 0. Integrating the right part of Eq. (8) over z, from z to in®nity, yields the equation for the stationary temperature distribution: DT

@T @z

hoF…S†I ‡ VT ˆ 0: cP r

(9)

If we assume the boundary condition for the temperature to be @T=@z ˆ 0, which is valid for Stefan-like models (see [5,6], where photothermal Stefan-like models are discussed), then Eq. (9) immediately yields the expression for the stationary value of the surface temperature, Tstationary, (see Eqs. (2), (7), and (9)): Z  hoF…S †Is ho S L…S† dS: ˆ T…0; t†  Tstationary ˆ cP r S0 C…S† VcP r (10) Eq. (10) for Tstationary coincides exactly with Eq. (4) for Tadiabat. It suggests that this estimation is good for single pulse well-developed ablation. It is important that according to formula in Eq. (10), Tstationary does not depend on intensity and heat diffusivity, DT.

M.C. Castex, N. Bityurin / Applied Surface Science 197±198 (2002) 805±807

4. Estimations and discussions In fact, when we speak about the photochemical ablation, we assume implicitly that the surface layers are etched before they are heated up to high temperature. Eq. (10) provides a test for such an assumption. Consider the example of direct photochemical chain scission model discussed in [4]. Here S ˆ n number density of broken bonds: C ˆ ZsA …n0

n†;

a ˆ sB n ‡ sA …n0 n†;     sB n 1 1 ln ; dˆ ; gˆb bˆ 1 ; d 1 d sA n0  n e  Z ; k ˆ …1 ‡ g†; L ˆ sB n ‡ sA …n0 n† 1 ho Z 

e is the endothermic effect of photochemical chain scission and accompanying reactions, Z stands for number of broken bonds per photon absorbed by non-broken bond (see [4]). The other parameters are introduced in [4]. Temperature elevation (Eq. (10)) can be expressed as:   Z  ho n L…n†  k eZ Tstationary ˆ dn ˆ ho : cP r 0 C…n† cP r 1‡g (11) If we assume that e  0, then it follows from the fact that g  0: k … ho cP r

eZ†  Tstationary

k ho :  cP r

(12)

In [4], for typical values of parameters it was estimated that k  4  1021 cm 3. If we assume that the endothermic effect can be estimated as the energy

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of the bond, e ˆ Ebond  3 eV, then, for typical value cP r  2 J/cm3 K, at l ˆ 125 nm (ho ˆ 10 eV), and Z ˆ 1, (Eq. (12)) yields: 2:2  103 K  T stationary  3:2  103 K. Of course, this value of surface temperature is too high to speak about the self-consistent photochemical model. These estimations show that if k > 1021 cm 3 both stationary and adiabatic VUV ablation hardly can be considered as pure photochemical if there is no process, which makes Z signi®cantly greater than unity. The physical nature of such process should be discussed separately. Non-adiabatic non-stationary regimes of photochemical ablation can be relevant even with relatively large k and small Z. These regimes will be considered in a separate paper. Acknowledgements Authors thank Dr. N. Arnold for an interesting discussion. N. Bityurin thanks Russian Foundation for Basic Research (grant 00-02-16411-a) and International Cooperation Program of the University ParisNord for ®nancial support. 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] N. Bityurin, Appl. Surf. Sci. 138-139 (1999) 354. [4] M.C. Castex, N. Bityurin, C. Olivero, S. Muraviov, N. Bronnikova, D. Riedel, Appl. Surf. Sci. 168 (2000) 175. [5] N. Arnold, N. Bityurin, Appl. Phys. A. 68 (1999) 615. [6] N. Bityurin, Proc. SPIE 4423 (2001) 197.