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By considering the rapid change of standing-wave electric-field and assuming the interface defect distribution, an improved model is developed to analyze the defect density distribution and assess the damage performance of high-reflective coatings. Two kinds of high-reflective coatings deposited by e-beam evaporation (EBE) and ion beam sputtering (IBS) techniques are analyzed with this method. The lower overall damage threshold is the major feature for the coatings deposited by IBS method according to the defect parameters extracted from the model. Typical damage morphologies of coatings are also measured and analyzed. The assumption of interface defects is supported by the damage behavior. The damage mechanisms of two high-reflective coatings are attributed to the formation of molten pool and mechanical ejection. The influence of the incident angle on the damage probability is also considered and numerically calculated. The defect analysis model improved here is suitable for high-reflective coatings.
© 2015 Optical Society of America
1. Introduction
Nanoscale defect dispersed in the optical components have been recognized as a major laser damage precursor in the 355nm wavelength [1–4]. The effort to identify the precursors and understand the damage mechanism is very important to mitigate the defects and improve the laser induced damage threshold [3, 5]. Due to the difficulty of directly detecting the defects, nondestructive measurement such as photothermal microscopy [6, 7] and Total Internal Reflection microscopy [8], artificial defects of known size and properties [9–12], and various statistical models [13–15] are widely developed to study the damage behaviors. As a fundamental component used in the high power laser system, high-reflective (HR) coatings have attracted extensive interest in the recent years [16–18]. Stolz et al. investigated the damage mechanism of multilayer coatings containing the nodular defects and presented a nodular defect planarization method to improve the laser resistance of the mirror [17, 18]. Suratwala and Miller et al. characterized the subsurface defects on the fused silica and proposed an advanced mitigation process to eliminate the dangerous precursors [19]. Based on the optimized acid etching process and damage density extracted from of the damage test, fluence-limiting defects and high fluence ones were identified [3].
In our previous work, Yu et al. found that high absorption defects existed in the weak electric field region could still influence the damage performance of the HR coatings [20]. Zhu et al. investigated the influence of silica overcoat layer and electric distribution on the damage morphology of the HR coatings. Their results indicated that the invisible nano-absorbing defects around the interface between silica and hafnia with strong electric field were the major limiting factors [21]. Therefore, defect analysis with regarding the feature of HR coatings should be developed. As we know, Krol et al. have developed a statistical model to investigate nano-precursors threshold distribution for single layer or substrate that without distinct interference [15]. They also considered the influence of field distribution on the damage probability by calculating the critical volume where the local fluence is greater than intrinsic fluence and summing over all the volumes [22]. The defect density is assumed to be uniform in the volume of the same material. Frankly, it is a state-of-art model to analyze the defect distribution for arbitrary film structure. However, only the numerical examples for multilayer coatings are given. Specific consideration with the feature of HR coatings including electric field (e-field) modulation and damage behavior will be more beneficial and appropriate to illustrate the real damage phenomenon. At first, no damage has been observed in the overcoat layer commonly consisted of low refractive index material, which is suffering the highest laser intensity [21]. In addition, the interface absorption was reported to be much higher than the bulk absorption according to the calorimetric method developed by Temple [23]. Recently Lu and Cheng et al. separated the interface and volume absorption in hafnia single layer by a photothermal common-path interferometer [24]. Moreover, reasonable assumption can be made to simplify the amount of fitting parameters and improve the accuracy of fluence-limiting precursors as well as the implement efficiency of the fitting procedure.
In this paper, an improved model of defect analysis is proposed with some assumption and simplification according to our experimental results and discussion above. Firstly the basic defect statistical model is reviewed, and the major improvement is given. Then sample preparation, damage test and damage morphology characterization are performed to support our assumption and apply our improved model. Discussion is also made to analyze the damage mechanism and investigate the influence of the incident angle on the damage probability. The conclusion of our work is given in the last part.
2. Theoretical background and experiments
2.1 Theoretical background
To extract the defect density distribution from the laser damage probability curve, much work has been done with the statistical model [3, 15, 22]. The fundamental idea of the statistical models is based on the assumption that the probability of a defect appearing inside the laser spot obeys the Poisson Law [13]. Therefore the basic relationship between the damage probability and expected defect number is
Different statistical models are mainly dependent on the different assumption of, such as Delta distribution, Power distribution and Gaussian distribution [13]. We mainly concentrate on the Gaussian model developed by Krol et. al. [15] with assuming that the defect density as a function of damage threshold obeys the Gaussian distribution, which can be presented as
In Eq. (2), andare average threshold and threshold standard deviation respectively, andis the total defect density. Thus the expected defect number under the irradiation fluencecan be expressed aswherein whichis the effective area of the laser spot.However, Eq. (3) and Eq. (4) are restricted to the case that the electric field changes slowly. In fact, the standing-wave e-field in the basic periodical unit of the HR coatings rapidly changes from zero to maximum, then to zero at the central wavelength of rejection band. To correct the influence of the value and shape of e-field in each layer of the coatings, Krol et al. considered the influence of field distribution on the damage probability by calculating the critical volume where the local fluence is greater than intrinsic fluence and summing over all the volumes [22]. By assuming a uniform defect densityin a single layer, the expected defect number is
wherein which z is the depth relative to the air-film interface.Then the total expected defect number in a real coatings is given by
where i is the ith layer of the coatings.As mentioned in the introduction, some improvement based on the specific consideration with the feature of HR coatings can be made. Firstly we assume that the defect is mainly distributed in the interface between the different coating materials, which can be supported by the predominantly interface absorption with very little of absorption taking place in the bulk of the film according to the results of Temple [23] and Lu et al. [24]. Secondly, considering the periodical structure of HR coatings, we assume that all the interface defect distribution between coating materials is the same, which can be denoted as, and can be referred to Eq. (2). The air-film interface absorption and film-substrate interface absorption are ignored because of the relatively weak absorption in the air-film interface and very weak e-field in the film-substrate interface. Therefore the expected defect number at the kth interface can be given by
in whichandis the normalized squared e-field intensity at the kth interface that can be solved with thin film theory [25]. Then we sum over all the interface and the total expected defect number under one irradiation with the fluencecan be expressed asCombining with Eq. (1), Eq. (8) and Eq. (9), the damage probability curve for arbitrary coatings with known interface defect distributioncan be calculated and vice versa.
2.2 Sample preparation and laser damage test
Two HR coatings deposited by e-beam evaporation (EBE) and ion beam sputtering (IBS) techniques are denoted as A and B respectively. The detail parameters of the samples are listed in Table 1. The coating materials are Al2O3 and SiO2. The symbols H and L represent a quarter wavelength of the high refractive index material and low refractive index material respectively. All the substrates were ultrasonic cleaned before deposition. The laser damage test was carried out in the “1-on-1” mode according to ISO standard 11254. The third harmonic wavelength of Nd: YAG laser system with S polarization was used to irradiate the sample with the pulse duration of 8ns full-width at half maximum (FWHM). The effective laser spot area for sample A and sample B is 0.077mm2. The damage testing system was introduced in detail in our previous work [26]. The damage morphologies were characterized by scanning electron microscope (SEM).
Table 1. Sample parameters
3. Results and discussion
3.1 Standing-wave e-field and interface defect distribution
The standing-wave e-field in the two coatings are calculated and shown in Fig. 1. The e-field changes rapidly as a function of depth. The position of zero e-field and peak e-field appears at the SiO2 over Al2O3 interface and the Al2O3 over SiO2 interface respectively. The peak values for the two samples are different at each interface. As we can see from Fig. 1, sample B shows much higher e-field peak values at each Al2O3 over SiO2 interface than that of sample A. In addition, the peak values decay much slower in the design of sample B and the laser can penetrate much deeper.
Fig. 1 Normalized electric field intensity (squared) in the coatings for (a) sample A and (b) sample B.
The interface defect distributionwith three fitting parameters,andis applied to fit the damage test results of the two sample obtaining from the damage test. The damage probability curve and corresponding defect distribution extracted from the fitting procedure are shown in Fig. 2(a) and Fig. 2(b) respectively. It is found that the model improved in Section 2.1 can fit the experimental results well, as shown in Fig. 2(a). The measured damage threshold of sample B is roughly half of that of sample A. Interface defect distributions of two samples are extracted from the damage probability curve and the defect densityas a function of threshold for two samples is show in Fig. 2(b). The corresponding defect parameters are displayed in Table 2. From Table 2, it can be seen that the total defect density d and threshold standard deviation ΔT of two samples are similar. Therefore, the interface defects are mainly determined by the bonding of two coating materials. The major difference is the average threshold, which can reflect the overall level of the damage threshold. The damage threshold of the damage precursor is dependent on the absorptivity of the defect and the mechanical strength of the surrounding matrix.
Fig. 2 (a)Damage probability curve and (b) defect distribution of two samples extracted from the improved model.
Table 2. Fitting parameters extracted from the model
Comparing with the previous work of Krol et al. [15, 22], the model improved by us is suitable for investigating the defect distribution in the HR coatings with simplified fitting parameters and reasonable defect assumption.
3.2 Damage morphology and mechanism analysis
To further illustrate the interface defects, the damage morphology caused by destructive defects under ultraviolet irradiation is investigated and shown in Fig. 3. It is clear that damage morphologies of two samples consist of many microscale pits induced by the nano-precursors from the first Al2O3 over SiO2 interface, where is the highest e-field peak value. Most damage precursors are originating from the interface, which can be seen in Fig. 3, and it is in consistence with our assumption. Moreover, the scale of the damage sites also indicates that the damage is caused by nano-precursors, which is consistence with the previous work [1, 3]. As we can see from Fig. 3(b), the material around the defect are melted or boiled, and no delamination can be observed. This is attributed to the super compactness of the coatings deposited by IBS method as well as the adhesion. The possible processes happened during the laser irradiation was that the interface precursor absorbed the laser energy initially and transferred the surrounding matrix into absorptive material when the matrix reached a critical temperature. With the laser energy deposited by the matrix around the defect, more and more material are melted or boiled. The heating process continued until the mechanical strength of the system is reached or the molten pool is formed [9]. The damage mechanism for the coatings deposited by IBS method is mainly due the formation of the molten pool. In addition, molten core surrounded by delamination layer is the major feature of coatings deposited by EBE method. Due to the weak adhesion of the layer interface, heating process is suspended by the delamination caused by the thermal stress.
Fig. 3 Damage morphologies of (a) sample A at F = 15.0 J/cm2 with (b) high magnification local pits and (c) sample B at F = 22.8 J/cm2.
It is very interesting that only the shallow molten pits are found in the coatings deposited by IBS method, as shown in Fig. 4(a). These shallow pits are also found in the sample A, and their dimensions are similar, which can be seen in Fig. 4(b). Therefore, formation of molten pool is the major mechanism for these shallow pits. However, the deeper defects in the sample B cannot absorb enough energy to melt all the material above the defects and the mechanical strength is so strong that the local molten material cannot erupt from the inner part because of the super compactness. Therefore, a possible inference is that increasing the thickness of the overcoat layer will be beneficial to improve the damage threshold of the HR coatings deposited by IBS via suppressing the molten material ejection of the shallow pits. Nevertheless, molten material can still eject from the surrounding of deeper defects due to poor mechanical strength and adhesion for sample A, as shown in Fig. 4(c) and Fig. 4 (d). Furthermore, the heating time for sample A by the laser is significantly affected by the mechanical strength of the coatings as well as the area of molten core.
Fig. 4 Damage morphologies of (a) sample A at F = 9.9 J/cm2 and other typical damage morphologies of sample B: (b), (c), (d) at F = 22.8 J/cm2.
According to the analysis above, the damage threshold of HR coatings deposited by IBS method is not only dependent on the absorptivity of the precursors but also the mechanical compactness needed to suppress the ejection of the molten material. However, more experiments are needed to explore the influence of the thickness of overcoat layer on the damage behavior of the HR coatings deposited by IBS method.
3.3 Influence of the incident angle on the damage probability curve
The interface defect density distributionextracted from the damage probability curve with improved model reflected the intrinsic property determined by the specific coatings by correcting the influence of the standing-wave e-field. In this part, only the numerical results are given for incident angle from 0° to 50° with S polarization. Since the incident angle affects the laser spot and standing-wave e-field in the film stack, the results of different incident angles with the interface defect density distributionextracted in the Table 2 for sample B are depicted in Fig. 5. It is obvious that the influence of the incident angle on the damage probability is small for angle less than 30°and significant for angle above 30°. The best method to verify this method is to conduct an experiment by investigating the same HR coatings with different central wavelength irradiated by corresponding incident angle. Nevertheless, the phenomenon depicted by Fig. 5 is needed to be examined by experiments in our future work.
Fig. 5 Numerical damage probability curve calculated with the same g(T) for sample B under different incident angles.
4. Conclusion
A defect analysis model adapted to the HR coatings is improved by correcting the influence of the standing-wave e-filed and considering the factual damage feature. The assumption of interface defect is supported by the damage morphology and can simplify the fitting procedure. The improved model is used to analyze the damage test results and extract the corresponding defect parameters. It is found that the overall level of the damage threshold of the HR coatings deposited by IBS method is lower than that deposited by EBE method. Typical damage morphologies are summarized and the corresponding damage mechanism is also discussed. The damage mechanism of the HR coatings is attributed to the formation of molten pool and mechanical ejection. Only the shallow molten pits are observed due to the super compactness of coatings deposited by IBS methods. The possible method to improve the damage threshold is proposed. The influence of incident angle for HR coatings deposited by IBS method on the damage probability is numerically analyzed. The defect analysis model improved here is suitable for HR coatings. The results also indicated a method to verify our improved model in the future work.
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