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On determining the spot size for laser fluence measurements
Applied Surface Science 252 (2006) 4728–4732 www.elsevier.com/locate/apsusc
On determining the spot size for laser fluence measurements B. Farkas *, Zs. Geretovszky Department of Optics and Quantum Electronics, University of Szeged, P.O. Box 406, H-6701 Szeged, Hungary Received 3 May 2005; accepted 13 July 2005 Available online 27 October 2005
Abstract Energy fluence, defined as pulse energy over irradiated area, is a key parameter of pulsed laser processing. Nevertheless, most of the authors using this term routinely do not realize the problems related to the accurate measurement of the spot size. In the present paper we are aiming to approach this problem by ablating crystalline Si wafers with pulses of a commercial KrF excimer laser (l = 248 nm, t = 15 ns) both in vacuum and at ambient atmosphere. For any pulse energy, the size of the ablated area monotonously increases with increasing number of pulses. The difference in the ablated area could be as high as a factor of three when 2000 consecutive pulses impinge on the surface. The existence and extent of the gradual lowering of multi-pulse ablation threshold queries the applicability of routinely used procedure of dividing the pulse energy with the size of the ablated area exposed into either carbon-paper or a piece of Si with one or a few pulses when determining the fluence. A more quantitative way is proposed allowing comparison of results originating from different laboratories. # 2005 Elsevier B.V. All rights reserved. Keywords: PLA; PLD
1. Introduction Pulsed laser deposition (PLD) is a uniquely versatile technique for preparing high quality thin films of the widest range of materials. In the film growth process energy fluence, defined as pulse energy over irradiated area, is a key parameter [1]. Along with other experimental conditions, it determines the growth rate, film composition, directionality of the plasma plume and thus the thickness distribution in the plane of the substrate. Most of the authors do not give enough details on the measurement of the spot size and though using energy fluence routinely do not realize the inherent problems related to it. The derivation of the energy fluence, defined above raises several delicate questions [2] hence one has to be careful when comparing results originating from different groups [3,4]. Surface ablation studies of different materials have reported that the fluence required to initiate surface damage drops significantly with multi-pulse irradiation [2,5–11]. Although the mechanisms of ablative material removal can be quite different, i.e., thermal, mechanical, photophysical and photo-
* Corresponding author. Tel.: +36 62 544274; fax: +36 62 544658. E-mail address: [email protected] (B. Farkas). 0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.07.111
chemical, and involve several steps (e.g., defect generation, bond breaking, plasma formation and shielding) that are dominant under different experimental conditions [12] it was found that the overall effect could be well correlated to the accumulation model proposed by Jee et al. [11]. Moreover, for laser machining with a beam of Gaussian intensity distribution, it has been shown that the diameter of the ablated region increases with the number of pulses for a given laser fluence and the rate of increase in the diameter with each laser pulse is related to the width of the Gaussian profile and the incubation parameter of the material in question [7–9]. For measurements of the spot size of Gaussian laser pulses, Liu proposed a fairly simple method [13]. Laser beams of nonGaussian fluence distribution are more complex to measure, and still excimer lasers, one of the most popular from this family, find numerous applications in materials processing, including a large number of the PLA and PLD studies. In the present paper, a quantitative way is proposed for the determination of the spot size of tightly focused excimer laser pulses along with a procedure to reproducibly determine the applied fluence. The former allows regular checking of the condition of the laser, while the latter is essential for allowing comparison of, e.g., PLD results originating from different laboratories. We exemplify our results on silicon mainly as it is readily available in all laboratories. However, the model is
B. Farkas, Zs. Geretovszky / Applied Surface Science 252 (2006) 4728–4732
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general in the sense that it can also be used on any other material, i.e., the target material of a specific PLA or PLD study.
the same fluence belongs: n m dx dy ¼ : wx wy
2. Experimental
If we plot corresponding ln(dy) and ln(dx) data pairs, we should get a straight line. The slope, mA and intercept, bA of this straight line can be used to calculate n, and wy via the following equations: m n¼ ; (4) mA
A commercial nanosecond KrF excimer laser (Spectra Physik, LPX 105) was used to ablate polished crystalline Si wafers at 248 nm and 1 Hz repetition rate. The laser beam was focused by a UV grade fused silica lens of 47.3 cm focal length on to the surface of the target at 458 angle of incidence. The pulse energy at the target surface was varied from 43.7 to 63.6 mJ by means of an attenuator (Optec SA, AT 4020). The ablation experiments were carried out in vacuum and at ambient atmosphere. The low-pressure ambience in the vacuum chamber was achieved by evacuating the chamber to a base pressure of 1–2 105 Pa by a turbomolecular pump, and then increasing the pressure to 101 Pa by flushing the system with high purity (99.999%) N2 gas, in a flow configuration. The lateral dimensions of each ablation crater were determined by optical microscopy. The images taken on the craters were evaluated by a picture analysing programme, after proper calibration. The beam intensity distribution was also determined by a CCD camera (ML 3300, Metrolux GmbH). 3. Results 3.1. Incubation model for excimer lasers For the sake of generalization, let us assume that the spatial fluence distribution of an excimer laser beam exhibits superGaussian distribution along both of its symmetry axis and therefore described by the following function: m
n
Fðx; yÞ ¼ F0 eðx=rx Þ eðy=ry Þ ;
(1)
where rx and ry are half of the 1/e diameters of the beam, wx and wy while m and n are the characteristic exponents along the xand y-axis, respectively. The peak laser fluence, F0 is related to the laser pulse energy, E by: F0 ¼
E
; 1 1 wx wy G 1 þ m G 1 þ n
(2)
where G is the Euler gamma function. E is the total energy of the laser beam, usually measured by a larger area detector. We have no reason to suppose that the process of ablation, and therefore the ablation threshold itself has a directional dependence. If so, the ablation contours, on any surface, will precisely follow the fluence contours of the beam, assuming that the energy of the laser pulse is high enough, i.e., its peak fluence is above the ablation threshold of the material under study. In this case, a simple geometrical relationship exists between the diameter of contours, dx and dy to which
(3)
wy ¼ wm=n ebA : x
(5)
According to the accumulation model proposed by Jee et al. [11] incubation, i.e., defect generation at sub-threshold fluences, will gradually reduce the damage threshold of the irradiated material according to: Fth ðNÞ ¼ Fth ð1ÞN j1 ;
(6)
where j is the incubation parameter, while Fth(1) and Fth(N) are the single-pulse and N-pulse threshold fluences, respectively. While the single-pulse threshold fluence characterizes the lasermatter interaction, the incubation parameter, j describes the incubation process. It is noted, that the value of j = 1 indicates that the ablation threshold does not change with the pulse number, i.e., there is no incubation. This corresponds to the case of ablating the material with pulses of uniform fluence, which is a case not treated here. When performing the experiment with a laser beam of inhomogeneous intensity distribution j differs from 1. The more homogeneous the intensity distribution is, or more precisely the steeper is the rise and fall of intensity around the edges of the pulse the smaller the effect of incubation, as also demonstrated experimentally by Coyne et al. by comparing ablation results obtained with pulses of Gaussian and homogenized intensity profiles [8]. When ablating a sample with consecutive pulses of inhomogeneous fluence distribution incubation will result in a gradual increase in the dimension of the ablation crater. The evolution of the dimensions of the ablation crater is given by combining Eqs. (1), (2) and (6) Fth ð1ÞN j1 ¼
E
m
n
eðdx ðNÞ=wx Þ eðdy ðNÞ=wy Þ ; wx wy G 1 þ m1 G 1 þ 1n
(7)
where we introduced dx(N) and dy(N), i.e., the dimension of the craters at a certain number of laser pulses, denoted by N. Taking the natural logarithm of both sides and applying the geometrical constrain between the two axis of the laser beam, as given by Eqs. (3) and (5), result in: ðdx ðNÞÞm wm wm ¼ x ð1 jÞ lnðNÞ þ x 2 2
E ln : ðm=nÞþ1 bA Fth ð1Þwx e G 1 þ m1 G 1 þ 1n
(8)
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When plotting (dx(N))m as a function of ln(N) at different pulse energies, we must get parallel straight lines with identical slopes of: mB ¼
wm x ð1 jÞ 2
(9)
and energy dependent intercepts: wm E : bB ¼ x ln 2 ðm=nÞþ1 bA Fth ð1Þwx e G 1 þ m1 G 1 þ 1n (10) Finally, the pulse energy dependence of bB, as described by Eq. (10), is used to determine wx, the waist of the laser beam on the sample surface, via measuring the slope, mC and intercept bC of the bB versus ln(E) function: mC ¼
wm x ; 2
(11)
wm 1 1 ðm=nÞþ1 bA x bC ¼ ln Fth ð1Þwx e G 1þ G 1þ : m n 2 (12) 3.2. Ablation of Si In this section, we will show our experimental results on ablating polished Si samples at 248 nm and apply the above detailed accumulation model to the experimental results. We use silicon as a model material, as it is readily available in all laboratories, but the model is applicable to any other target material. Silicon samples, kept under low vacuum (101 Pa nitrogen), were irradiated with consecutive pulses at four different pulse energies between 43.7 and 63.6 mJ. Number of pulses were increased as a power of 2, between 2 and 2048. Fig. 1 shows selection of top-view optical micrographs of the series made at 63.6 mJ. Images were taken at the same magnification to allow
direct comparison. At this energy 2 and 4 pulses were hardly enough to fully resolve the shape of the laser pulse. From the micrographs taken between 8 and 2048 laser pulses it is obvious that the size of the ablation spot was not saturated, not even when 2048 consecutive pulses were fired on the same sample surface. This result is in perfect harmony with our model, namely that incubation and the inhomogeneous intensity distribution of the laser pulses cause a steady increase in the size of ablation craters. Debris formation, i.e., re-deposition of the ablated material around the ablated area becomes obvious at pulse numbers above 32, while discolouration of the Si surface, as a clear evidence of film growth via the inverse PLD process [14,15], materializes when more than 128 pulses hit the Si surface. Similar data sets were obtained for other pulse energies differing from this one only in the pulse numbers were the characteristic changes appear in the processed area. In general, the lower the energy the larger the pulse numbers where the processed surface exhibits the above exemplified characteristic changes. Furthermore, at 49.7 and 43.7 mJ energies no measurable ablation of the Si took place at two pulses, but only rapid melting and resolidification of the surface was obvious and therefore no ablation crater were seen. Then, wherever it was possible, the characteristic dimensions of the ablation craters (dx(N) and dy(N)) were measured on each micrograph. The ln(dy(N)) versus ln(dx(N)) represenatation of the data in Fig. 2 proves that crater dimensions of all the four energies scatter around the same straight line, which was fitted with a slope of mA = 0.53188 and an intercept of bA = 0.61551. Approximating the fluence distribution of our excimer beam with super-Gaussian functions is therefore proved to be realistic. The above representation provides information only on the ratio of the two super-Gaussian exponents, m and n. However, it is reasonable to assume that the intensity distribution of a typical excimer beam is close to Gaussian along its shorter axis. Independent CCD measurements, performed on the un-focused beam, proved that this assumption is fairly good. Hence, in the followings, we will assume, that the fluence distribution along
Fig. 1. Top-view optical micrographs of ablation craters made at 63.6 mJ (l = 248 nm, t = 15 ns). The number of pulses used are N = 4, 8, 16, 32, 128 and 1024. The scale bar (indicated on the first micrograph) is the same for all images.
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Table 1 Slopes and intercepts of straight lines obtained when applying the incubation model to experimental data on ablating Si samples by different number of (between 2 and 2048) KrF excimer laser pulses at four different energies (between 43.7 and 63.3 mJ) mA bA mB bB,43.7 bB,49.7 bB,56.9 bB,63.6 mC bC
0.53188 0.61551 0.05185 0.05035 0.09957 0.10892 0.14719 0.23670 0.83802
(43.7 mJ) (49.7 mJ) (56.9 mJ) (63.6 mJ)
For the definition of each value please see text. Fig. 2. Relationship between the natural logarithm of crater dimensions, dx(N) and dy(N) at four pulse energies and variuos number of pulses between 2 and 2048. All data scatter around the same straight line, also shown as solid line.
the x direction is Gaussian, i.e., m = 2. The dataset was then used to construct the (dx(N))2 versus ln(N) plot and finally, the bB versus ln(E) plot. The former is shown in Fig. 3 (where the experimentally obtained data are plotted with different symbols for the four pulse energies), while the slopes and intercepts of the three graphs prepared are summarized in Table 1. From the parameters of the fitted lines, we calculated the following values of each parameter, using the equations given after each one in parentheses: n = 3.76 (Eq. (4)), wx = 0.688 mm (Eq. (11)), wy = 1.517 mm (Eq. (5)), j = 0.781 (Eq. (9)), and finally Fth(1) = 4.13 J cm2 (Eq. (12)). After determining all the characteristic parameters of our laser beam, i.e., m, n, wx and wy, as well as the single-pulse threshold fluence, Fth(1) and the incubation parameter, j describing the laser-matter interaction we can calculate the dx(N) and dy(N) diameters from Eqs. (8) and (5), respectively. The calculated (dx(N))2 values are plotted as straight lines in Fig. 3 and compare fairly well with the experimentally measured data (plotted with symbols).
Fig. 3. The square of crater diameter (along the Gaussian axis) as a function of the natural logarithm of pulse number. Measured data for the four pulse energies are plotted with different symbols. Values, calculated according to Eq. (8), are also given as straight lines for each pulse energy.
Further to these experiments ablation of Si samples was also carried our under ambient conditions. The most noticeable difference between the ablation craters made at atmospheric air is that the size of the craters is bigger than those made in vacuum under identical conditions, which is in agreement with other reported results [12]. For example, when comparing craters made with the same number of pulses at the highest pulse energy the size of the crater made in air is about a factor of 1.8 and 1.5 bigger than those ones obtained in vacuum, in the Gaussian and super-Gaussian directions, respectively. Furthermore debris formation, discolouration of the nearby areas are all observed at much lower pulse numbers than in vacuum, hindering the determination of accurate crater dimensions, especially at pulse numbers larger than 512. 4. Discussion Ideally, ablation experiments should be done with pulses of uniform fluence distribution above the wavelength and pulse duration dependent single-pulse threshold fluence of the ablated material. However, this is almost never the case, and the vast majority of PLA and PLD studies are done with raw or apertured laser beams. The inhomogeneity in the intensity distribution of these beams gives rise to incubation, which causes lateral spread in the ablated area as the number of pulses increases. Our results on ablating polished Si surfaces with nonhomogenised UV pulses (l = 248 nm, t = 15 ns) are in perfect harmony with the model proposed in Section 3.1 for excimer beams, one of the most popular choice of laser for materials processing, especially for ablation or laser assisted thin film growth. The steady increase of the size of the ablation crater was confirmed up to 2048 consecutive pulses and the calculated dimensions were in good agreement with the experimentally measured ones. Due to the logarithmic nature of the process, one may not notice this steady increase in size when performing spot size measurement only at few, small number of pulses. Even those experimentalists, rigorous enough to perform multi-shot experiments for converting the pulse energy to fluence, do not typically use more than a few tens of pulses, not to mention the general practice of firing one or a few focused pulses onto an untreated target surface and simply use the area of the affected
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surface to divide the pulse energy with. Moreover, even when the highest number of pulses used is around 50, one may easily get the misleading tendency of a quickly saturating increase in spot size, which is clearly not the case for inhomogeneous pulses. It is worth mentioning that even textbooks dealing with ablation in detail [12] assume that everyone knows how to measure laser fluence. In order to overcome these problems and allow reproducible determination of the fluence one need to follow a standard procedure. Based on our results, we recommend the following approach for calculating the fluence of focused excimer laser pulses: Perform a similar spot-size study like the one detailed above. Using several pulse numbers and at least a few pulse energies is sufficient. Estimate, that on average how many pulses, Nmax hit the surface of the target material and calculate dx,max = dx(Nmax) and dy,max = dy(Nmax) for that number of pulses using the fitted parameters. These will provide the maximum ablation area during your experiment. Measure, if possible, or estimate the single-pulse dx,min = dx(1) and dy,min = dy(1) with the same procedure. These data will allow you to calculate the minimum ablation area during your experiment. Calculate the values (minimum and maximum) of the ablation area. Choosing from shapes of a rectangle (with area of AR = dx(N)dy(N)) or an ellipse (with an area of AE = (p/4)dx(N)dy(N) = (p/4)AR) is most probably sufficient. Provide the fluence as a range, citing the minimum and maximum fluences together with your selection of rectangular or elliptical shape estimate. (Correction of pulse energy for reflection losses may also be necessary.) Due the difference of the ablation results obtained in vacuum and air, it is advised to use diameters for the fluence calculations that were measured on ablation craters made under process pressures. Finally, this procedure yields a fluence value that depends on the material to be ablated. By using wx and wy, also obtained from the model, material independent laser fluence can also be easily derived. 5. Conclusion We showed that the inhomogeneous intensity distribution of laser pulses causes a steady increase in the size of ablation
craters via gradually decreasing the multi-pulse ablation threshold of Si around the perimeter of the craters. We derived a procedure, tailor made to the lateral fluence profile of an excimer laser with super-Gaussian intensity distribution along its axis of symmetry, to allow the determination of beam parameters (such as waist and one of the super-Gaussian exponent) together with the material dependent single-pulse ablation threshold and the incubation parameter. Experiments performed in low vacuum (101 Pa) fit nicely to the predicted behaviour. Results, obtained at atmospheric pressures, suggest that experiments for the determination of ablated area should be performed under process pressures. Finally, on the basis of our results we recommend a procedure for calculating the fluence of experiments performed with focused excimer laser pulses.
Acknowledgements The financial support of the Hungarian Scientific Research Fund under contract number OTKA TS 049872 is kindly acknowledged. One of the authors (ZsG) is also indebted to Katalin Varju´ for stimulating discussions.
References [1] Douglas B. Chrisey, Graham K. Hubler (Eds.), Pulsed Laser Deposition of Thin Films, John Wiley & Sons, Inc., New York, 1994. [2] A. Rosenfeld, M. Lorenz, R. Stoian, D. Ashkenasi, Appl. Phys. A 69 (1999) S373. [3] T. Szo¨re´nyi, J.-P. Stoquert, F. Antoni, E. Fogarassy, Surf. Coat. Technol. 180–181 (2004) 127. [4] R. Danyi, T. Szo¨re´nyi, Appl. Phys. A 79 (2004) 1373. [5] D. Ashkenasi, R. Stoian, A. Rosenfeld, Appl. Surf. Sci. 154–155 (2000) 40. [6] D. Ashkenasi, M. Lorenz, R. Stoian, A. Rosenfeld, Appl. Surf. Sci. 150 (1999) 101. [7] P.T. Mannion, J. Magee, E. Coyne, G.M. O’Connor, T.J. Glynn, Appl. Surf. Sci. 233 (2004) 275. [8] E. Coyne, J.P. Magee, P. Mannion, G.M. O’Connor, T.J. Glynn, Appl. Surf. Sci. 229 (2004) 148. [9] J. Bonse, J.M. Wrobel, J. Kru¨ger, W. Kautek, Appl. Phys. A 72 (2001) 89. [10] J. Bonse, P. Rudolph, J. Kru¨ger, S. Baudach, W. Kautek, Appl. Surf. Sci. 154–155 (2000) 659. [11] Y. Jee, M.F. Becker, R.M. Walser, J. Opt. Soc. Am. B 5 (1988) 648. [12] D. Ba¨uerle, Laser Processing and Chemistry, Springer-Verlag, Berlin, 2000. [13] J.M. Liu, Opt. Lett. 7 (1982) 196. [14] T. Szo¨re´nyi, B. Hopp, Zs. Geretovszky, Appl. Phys. A 79 (2004) 1207. [15] T. Szo¨re´nyi, Zs. Geretovszky, Thin Solid Films 484 (2005) 165.
On determining the spot size for laser fluence measurements B. Farkas *, Zs. Geretovszky Department of Optics and Quantum Electronics, University of Szeged, P.O. Box 406, H-6701 Szeged, Hungary Received 3 May 2005; accepted 13 July 2005 Available online 27 October 2005
Abstract Energy fluence, defined as pulse energy over irradiated area, is a key parameter of pulsed laser processing. Nevertheless, most of the authors using this term routinely do not realize the problems related to the accurate measurement of the spot size. In the present paper we are aiming to approach this problem by ablating crystalline Si wafers with pulses of a commercial KrF excimer laser (l = 248 nm, t = 15 ns) both in vacuum and at ambient atmosphere. For any pulse energy, the size of the ablated area monotonously increases with increasing number of pulses. The difference in the ablated area could be as high as a factor of three when 2000 consecutive pulses impinge on the surface. The existence and extent of the gradual lowering of multi-pulse ablation threshold queries the applicability of routinely used procedure of dividing the pulse energy with the size of the ablated area exposed into either carbon-paper or a piece of Si with one or a few pulses when determining the fluence. A more quantitative way is proposed allowing comparison of results originating from different laboratories. # 2005 Elsevier B.V. All rights reserved. Keywords: PLA; PLD
1. Introduction Pulsed laser deposition (PLD) is a uniquely versatile technique for preparing high quality thin films of the widest range of materials. In the film growth process energy fluence, defined as pulse energy over irradiated area, is a key parameter [1]. Along with other experimental conditions, it determines the growth rate, film composition, directionality of the plasma plume and thus the thickness distribution in the plane of the substrate. Most of the authors do not give enough details on the measurement of the spot size and though using energy fluence routinely do not realize the inherent problems related to it. The derivation of the energy fluence, defined above raises several delicate questions [2] hence one has to be careful when comparing results originating from different groups [3,4]. Surface ablation studies of different materials have reported that the fluence required to initiate surface damage drops significantly with multi-pulse irradiation [2,5–11]. Although the mechanisms of ablative material removal can be quite different, i.e., thermal, mechanical, photophysical and photo-
* Corresponding author. Tel.: +36 62 544274; fax: +36 62 544658. E-mail address: [email protected] (B. Farkas). 0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.07.111
chemical, and involve several steps (e.g., defect generation, bond breaking, plasma formation and shielding) that are dominant under different experimental conditions [12] it was found that the overall effect could be well correlated to the accumulation model proposed by Jee et al. [11]. Moreover, for laser machining with a beam of Gaussian intensity distribution, it has been shown that the diameter of the ablated region increases with the number of pulses for a given laser fluence and the rate of increase in the diameter with each laser pulse is related to the width of the Gaussian profile and the incubation parameter of the material in question [7–9]. For measurements of the spot size of Gaussian laser pulses, Liu proposed a fairly simple method [13]. Laser beams of nonGaussian fluence distribution are more complex to measure, and still excimer lasers, one of the most popular from this family, find numerous applications in materials processing, including a large number of the PLA and PLD studies. In the present paper, a quantitative way is proposed for the determination of the spot size of tightly focused excimer laser pulses along with a procedure to reproducibly determine the applied fluence. The former allows regular checking of the condition of the laser, while the latter is essential for allowing comparison of, e.g., PLD results originating from different laboratories. We exemplify our results on silicon mainly as it is readily available in all laboratories. However, the model is
B. Farkas, Zs. Geretovszky / Applied Surface Science 252 (2006) 4728–4732
4729
general in the sense that it can also be used on any other material, i.e., the target material of a specific PLA or PLD study.
the same fluence belongs: n m dx dy ¼ : wx wy
2. Experimental
If we plot corresponding ln(dy) and ln(dx) data pairs, we should get a straight line. The slope, mA and intercept, bA of this straight line can be used to calculate n, and wy via the following equations: m n¼ ; (4) mA
A commercial nanosecond KrF excimer laser (Spectra Physik, LPX 105) was used to ablate polished crystalline Si wafers at 248 nm and 1 Hz repetition rate. The laser beam was focused by a UV grade fused silica lens of 47.3 cm focal length on to the surface of the target at 458 angle of incidence. The pulse energy at the target surface was varied from 43.7 to 63.6 mJ by means of an attenuator (Optec SA, AT 4020). The ablation experiments were carried out in vacuum and at ambient atmosphere. The low-pressure ambience in the vacuum chamber was achieved by evacuating the chamber to a base pressure of 1–2 105 Pa by a turbomolecular pump, and then increasing the pressure to 101 Pa by flushing the system with high purity (99.999%) N2 gas, in a flow configuration. The lateral dimensions of each ablation crater were determined by optical microscopy. The images taken on the craters were evaluated by a picture analysing programme, after proper calibration. The beam intensity distribution was also determined by a CCD camera (ML 3300, Metrolux GmbH). 3. Results 3.1. Incubation model for excimer lasers For the sake of generalization, let us assume that the spatial fluence distribution of an excimer laser beam exhibits superGaussian distribution along both of its symmetry axis and therefore described by the following function: m
n
Fðx; yÞ ¼ F0 eðx=rx Þ eðy=ry Þ ;
(1)
where rx and ry are half of the 1/e diameters of the beam, wx and wy while m and n are the characteristic exponents along the xand y-axis, respectively. The peak laser fluence, F0 is related to the laser pulse energy, E by: F0 ¼
E
; 1 1 wx wy G 1 þ m G 1 þ n
(2)
where G is the Euler gamma function. E is the total energy of the laser beam, usually measured by a larger area detector. We have no reason to suppose that the process of ablation, and therefore the ablation threshold itself has a directional dependence. If so, the ablation contours, on any surface, will precisely follow the fluence contours of the beam, assuming that the energy of the laser pulse is high enough, i.e., its peak fluence is above the ablation threshold of the material under study. In this case, a simple geometrical relationship exists between the diameter of contours, dx and dy to which
(3)
wy ¼ wm=n ebA : x
(5)
According to the accumulation model proposed by Jee et al. [11] incubation, i.e., defect generation at sub-threshold fluences, will gradually reduce the damage threshold of the irradiated material according to: Fth ðNÞ ¼ Fth ð1ÞN j1 ;
(6)
where j is the incubation parameter, while Fth(1) and Fth(N) are the single-pulse and N-pulse threshold fluences, respectively. While the single-pulse threshold fluence characterizes the lasermatter interaction, the incubation parameter, j describes the incubation process. It is noted, that the value of j = 1 indicates that the ablation threshold does not change with the pulse number, i.e., there is no incubation. This corresponds to the case of ablating the material with pulses of uniform fluence, which is a case not treated here. When performing the experiment with a laser beam of inhomogeneous intensity distribution j differs from 1. The more homogeneous the intensity distribution is, or more precisely the steeper is the rise and fall of intensity around the edges of the pulse the smaller the effect of incubation, as also demonstrated experimentally by Coyne et al. by comparing ablation results obtained with pulses of Gaussian and homogenized intensity profiles [8]. When ablating a sample with consecutive pulses of inhomogeneous fluence distribution incubation will result in a gradual increase in the dimension of the ablation crater. The evolution of the dimensions of the ablation crater is given by combining Eqs. (1), (2) and (6) Fth ð1ÞN j1 ¼
E
m
n
eðdx ðNÞ=wx Þ eðdy ðNÞ=wy Þ ; wx wy G 1 þ m1 G 1 þ 1n
(7)
where we introduced dx(N) and dy(N), i.e., the dimension of the craters at a certain number of laser pulses, denoted by N. Taking the natural logarithm of both sides and applying the geometrical constrain between the two axis of the laser beam, as given by Eqs. (3) and (5), result in: ðdx ðNÞÞm wm wm ¼ x ð1 jÞ lnðNÞ þ x 2 2
E ln : ðm=nÞþ1 bA Fth ð1Þwx e G 1 þ m1 G 1 þ 1n
(8)
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When plotting (dx(N))m as a function of ln(N) at different pulse energies, we must get parallel straight lines with identical slopes of: mB ¼
wm x ð1 jÞ 2
(9)
and energy dependent intercepts: wm E : bB ¼ x ln 2 ðm=nÞþ1 bA Fth ð1Þwx e G 1 þ m1 G 1 þ 1n (10) Finally, the pulse energy dependence of bB, as described by Eq. (10), is used to determine wx, the waist of the laser beam on the sample surface, via measuring the slope, mC and intercept bC of the bB versus ln(E) function: mC ¼
wm x ; 2
(11)
wm 1 1 ðm=nÞþ1 bA x bC ¼ ln Fth ð1Þwx e G 1þ G 1þ : m n 2 (12) 3.2. Ablation of Si In this section, we will show our experimental results on ablating polished Si samples at 248 nm and apply the above detailed accumulation model to the experimental results. We use silicon as a model material, as it is readily available in all laboratories, but the model is applicable to any other target material. Silicon samples, kept under low vacuum (101 Pa nitrogen), were irradiated with consecutive pulses at four different pulse energies between 43.7 and 63.6 mJ. Number of pulses were increased as a power of 2, between 2 and 2048. Fig. 1 shows selection of top-view optical micrographs of the series made at 63.6 mJ. Images were taken at the same magnification to allow
direct comparison. At this energy 2 and 4 pulses were hardly enough to fully resolve the shape of the laser pulse. From the micrographs taken between 8 and 2048 laser pulses it is obvious that the size of the ablation spot was not saturated, not even when 2048 consecutive pulses were fired on the same sample surface. This result is in perfect harmony with our model, namely that incubation and the inhomogeneous intensity distribution of the laser pulses cause a steady increase in the size of ablation craters. Debris formation, i.e., re-deposition of the ablated material around the ablated area becomes obvious at pulse numbers above 32, while discolouration of the Si surface, as a clear evidence of film growth via the inverse PLD process [14,15], materializes when more than 128 pulses hit the Si surface. Similar data sets were obtained for other pulse energies differing from this one only in the pulse numbers were the characteristic changes appear in the processed area. In general, the lower the energy the larger the pulse numbers where the processed surface exhibits the above exemplified characteristic changes. Furthermore, at 49.7 and 43.7 mJ energies no measurable ablation of the Si took place at two pulses, but only rapid melting and resolidification of the surface was obvious and therefore no ablation crater were seen. Then, wherever it was possible, the characteristic dimensions of the ablation craters (dx(N) and dy(N)) were measured on each micrograph. The ln(dy(N)) versus ln(dx(N)) represenatation of the data in Fig. 2 proves that crater dimensions of all the four energies scatter around the same straight line, which was fitted with a slope of mA = 0.53188 and an intercept of bA = 0.61551. Approximating the fluence distribution of our excimer beam with super-Gaussian functions is therefore proved to be realistic. The above representation provides information only on the ratio of the two super-Gaussian exponents, m and n. However, it is reasonable to assume that the intensity distribution of a typical excimer beam is close to Gaussian along its shorter axis. Independent CCD measurements, performed on the un-focused beam, proved that this assumption is fairly good. Hence, in the followings, we will assume, that the fluence distribution along
Fig. 1. Top-view optical micrographs of ablation craters made at 63.6 mJ (l = 248 nm, t = 15 ns). The number of pulses used are N = 4, 8, 16, 32, 128 and 1024. The scale bar (indicated on the first micrograph) is the same for all images.
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Table 1 Slopes and intercepts of straight lines obtained when applying the incubation model to experimental data on ablating Si samples by different number of (between 2 and 2048) KrF excimer laser pulses at four different energies (between 43.7 and 63.3 mJ) mA bA mB bB,43.7 bB,49.7 bB,56.9 bB,63.6 mC bC
0.53188 0.61551 0.05185 0.05035 0.09957 0.10892 0.14719 0.23670 0.83802
(43.7 mJ) (49.7 mJ) (56.9 mJ) (63.6 mJ)
For the definition of each value please see text. Fig. 2. Relationship between the natural logarithm of crater dimensions, dx(N) and dy(N) at four pulse energies and variuos number of pulses between 2 and 2048. All data scatter around the same straight line, also shown as solid line.
the x direction is Gaussian, i.e., m = 2. The dataset was then used to construct the (dx(N))2 versus ln(N) plot and finally, the bB versus ln(E) plot. The former is shown in Fig. 3 (where the experimentally obtained data are plotted with different symbols for the four pulse energies), while the slopes and intercepts of the three graphs prepared are summarized in Table 1. From the parameters of the fitted lines, we calculated the following values of each parameter, using the equations given after each one in parentheses: n = 3.76 (Eq. (4)), wx = 0.688 mm (Eq. (11)), wy = 1.517 mm (Eq. (5)), j = 0.781 (Eq. (9)), and finally Fth(1) = 4.13 J cm2 (Eq. (12)). After determining all the characteristic parameters of our laser beam, i.e., m, n, wx and wy, as well as the single-pulse threshold fluence, Fth(1) and the incubation parameter, j describing the laser-matter interaction we can calculate the dx(N) and dy(N) diameters from Eqs. (8) and (5), respectively. The calculated (dx(N))2 values are plotted as straight lines in Fig. 3 and compare fairly well with the experimentally measured data (plotted with symbols).
Fig. 3. The square of crater diameter (along the Gaussian axis) as a function of the natural logarithm of pulse number. Measured data for the four pulse energies are plotted with different symbols. Values, calculated according to Eq. (8), are also given as straight lines for each pulse energy.
Further to these experiments ablation of Si samples was also carried our under ambient conditions. The most noticeable difference between the ablation craters made at atmospheric air is that the size of the craters is bigger than those made in vacuum under identical conditions, which is in agreement with other reported results [12]. For example, when comparing craters made with the same number of pulses at the highest pulse energy the size of the crater made in air is about a factor of 1.8 and 1.5 bigger than those ones obtained in vacuum, in the Gaussian and super-Gaussian directions, respectively. Furthermore debris formation, discolouration of the nearby areas are all observed at much lower pulse numbers than in vacuum, hindering the determination of accurate crater dimensions, especially at pulse numbers larger than 512. 4. Discussion Ideally, ablation experiments should be done with pulses of uniform fluence distribution above the wavelength and pulse duration dependent single-pulse threshold fluence of the ablated material. However, this is almost never the case, and the vast majority of PLA and PLD studies are done with raw or apertured laser beams. The inhomogeneity in the intensity distribution of these beams gives rise to incubation, which causes lateral spread in the ablated area as the number of pulses increases. Our results on ablating polished Si surfaces with nonhomogenised UV pulses (l = 248 nm, t = 15 ns) are in perfect harmony with the model proposed in Section 3.1 for excimer beams, one of the most popular choice of laser for materials processing, especially for ablation or laser assisted thin film growth. The steady increase of the size of the ablation crater was confirmed up to 2048 consecutive pulses and the calculated dimensions were in good agreement with the experimentally measured ones. Due to the logarithmic nature of the process, one may not notice this steady increase in size when performing spot size measurement only at few, small number of pulses. Even those experimentalists, rigorous enough to perform multi-shot experiments for converting the pulse energy to fluence, do not typically use more than a few tens of pulses, not to mention the general practice of firing one or a few focused pulses onto an untreated target surface and simply use the area of the affected
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surface to divide the pulse energy with. Moreover, even when the highest number of pulses used is around 50, one may easily get the misleading tendency of a quickly saturating increase in spot size, which is clearly not the case for inhomogeneous pulses. It is worth mentioning that even textbooks dealing with ablation in detail [12] assume that everyone knows how to measure laser fluence. In order to overcome these problems and allow reproducible determination of the fluence one need to follow a standard procedure. Based on our results, we recommend the following approach for calculating the fluence of focused excimer laser pulses: Perform a similar spot-size study like the one detailed above. Using several pulse numbers and at least a few pulse energies is sufficient. Estimate, that on average how many pulses, Nmax hit the surface of the target material and calculate dx,max = dx(Nmax) and dy,max = dy(Nmax) for that number of pulses using the fitted parameters. These will provide the maximum ablation area during your experiment. Measure, if possible, or estimate the single-pulse dx,min = dx(1) and dy,min = dy(1) with the same procedure. These data will allow you to calculate the minimum ablation area during your experiment. Calculate the values (minimum and maximum) of the ablation area. Choosing from shapes of a rectangle (with area of AR = dx(N)dy(N)) or an ellipse (with an area of AE = (p/4)dx(N)dy(N) = (p/4)AR) is most probably sufficient. Provide the fluence as a range, citing the minimum and maximum fluences together with your selection of rectangular or elliptical shape estimate. (Correction of pulse energy for reflection losses may also be necessary.) Due the difference of the ablation results obtained in vacuum and air, it is advised to use diameters for the fluence calculations that were measured on ablation craters made under process pressures. Finally, this procedure yields a fluence value that depends on the material to be ablated. By using wx and wy, also obtained from the model, material independent laser fluence can also be easily derived. 5. Conclusion We showed that the inhomogeneous intensity distribution of laser pulses causes a steady increase in the size of ablation
craters via gradually decreasing the multi-pulse ablation threshold of Si around the perimeter of the craters. We derived a procedure, tailor made to the lateral fluence profile of an excimer laser with super-Gaussian intensity distribution along its axis of symmetry, to allow the determination of beam parameters (such as waist and one of the super-Gaussian exponent) together with the material dependent single-pulse ablation threshold and the incubation parameter. Experiments performed in low vacuum (101 Pa) fit nicely to the predicted behaviour. Results, obtained at atmospheric pressures, suggest that experiments for the determination of ablated area should be performed under process pressures. Finally, on the basis of our results we recommend a procedure for calculating the fluence of experiments performed with focused excimer laser pulses.
Acknowledgements The financial support of the Hungarian Scientific Research Fund under contract number OTKA TS 049872 is kindly acknowledged. One of the authors (ZsG) is also indebted to Katalin Varju´ for stimulating discussions.
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