Defect formation wave and damage in laser-excited media

Abstract

Resent progress on multishot laser damage ofwide-gap optical materials is linked with the idea of gradual or explosive accumulation ofpoint defects accompanied by some structural changes in a material (see Reviews [1,21). According to the quantitatively developed model of ReL[2J the F-center accumulation proceeds in explosive manner due to the decrease of the defect formation energy by selfconsistent medium stress. Multiphoton free carrier generation across the forbidden band gap and subsequent rapid cascade defect reactions, involving excited electrons and holes and leading eventually to F-center formation are other essential features of the model of multishot laser damage developed in this approach. According to Ref[2J these reactions occur in the following manner. Intensive laser light with quantum ofenergy two(Eg iflthXS multiphoton electron transitions into conduction band of a dielectric. Autolocalization of a free hole at some crystal site creates Vk -center, which then captures free electron with formation of a self-trapped exiton (STh). Recombination of autolocalized electron-hole pair leads to the STE decay accompanied by liberation of an energy sufficient for production of F-center (vacancy) and H-center (interstitial) in adjacent crystal sites. The cascade of above reactions with recombination4nduced vacancy production is completed by time scale of 1O_12 ÷ 10 s [3]. The generation of interstitials, accompaning F-center production, leads to the local expansion of crystal lattice [11,12], which decreases the F-center formation energy. The arising positive feedback leads to explosive F-center generation that may be considered as an absolute defect concentration instability developing locally. When the dilatative stress due to generated interstitials reaches the value of yield stress of a material then the damage threshold is supposed to be reached [2]. The model dependencies of the number of shots, leading to damage, on the photon flux in a laser pulse at different initial temperatures was shown to correspond well to experimental ones [2]. The model ofRef.[2] is relied implicitly on the assumption that the localization of a free carriers leading to a Vk -center and a STE formation occurs at regular crystal sites with the same rate as at defected ones. In this case the spatial distribution ofthe generated defects follows the laser intensity distribution in focal region. In this work we study another opportunity and assume that the rate of free carriers localization at defected sites is much bigger than at the regular sites (which at least in semiconductors certainly is the case [5]). We show that in this case one comes to the model ofexplosive F-center formation and resulting damage essentially differed from that of Ref. [2]. The physical essence of the proposed model consists in the following [6]. We assume the same cascade of reactions as in Ref.[2] to be responsible for F-centers (vacancies) production in a laser excited medium. We exploit the assumption that the above cascade reaction with defect production occurs much more rapidly near defected sites. Thus the above cascade reactions are initiated at initially present defects that leads to appearance of strain in their vicinity which decreases locally the defect formation energy. This leads to further enhancing of defect generation and appearance of strain. This defect generation-strain appearance cycle is repeated again and again in vicinity of newly formed centers, leading thus to defect formation wave (DFW) propagation in laser excited medium [6]. Thus instead of local (absolute) defect generation instability of Ref.[2] we develop here the model of distributed (convective) defect generation instability. We note that the strain induced positive feedback and corresponding vacancy generation-deformational instability (ODD developing in condition oflaser irradiation in strongly absorbintg metals and semiconductors was considered earlier in Ref.[7] and is shown to lead to formation of ordered defect structures (for review of GDI see Ref.[4]). The DFW model also takes into account the long range character of the medium deformation, which is shown here to lead to strain induced DFW propagation with steady velocity. The passage of this DFW switches the medium from the state with zero defect concentration (n= 0)to the F-center enriched state with F = X . Ifthe value of n exceeds the Critical defect concentration 4 iO' cni at which deformationinduced extended defects (voids) nucleation begins [4] then the switching wave ofpoint defect production is accompanied by switching wave of extended defect nucleation i.e. by mateiial damage. This work is dedicated to studies of the model of switching wave ofpoint defect generation. proposed in [6J. We apply the theoretical results obtained to the problem of multishot laser damage in transparent dielectrics. The present model is shown to be in a good agreement with the expeiimental results on dependency of the number of shots leading to damage on the photon flux in a laser pulse.