- Email: [email protected]
Characterisation of laser ablation of silicon using a Gaussian wavefront and computer generated wavefront reconstruction
Applied Surface Science 229 (2004) 148–160
Characterisation of laser ablation of silicon using a Gaussian wavefront and computer generated wavefront reconstruction E. Coynea,b,*, J.P. Mageeb, P. Mannionb, G.M. O’Connorb, T.J. Glynnb a
Analog Devices, Raheen, Limerick, Ireland National Center for Laser Applications (NCLA), National University of Ireland-Galway, Galway, Ireland
b
Received 19 December 2003; received in revised form 23 January 2004; accepted 23 January 2004 Available online 21 March 2004
Abstract The work described in this paper characterises the laser ablation of wafer grade silicon, using both a Gaussian beam and the reconstructed wavefront of a femtosecond laser. The reconstructed wavefront was produced by transmission through a computer generated hologram (CGH). The laser used was a chirped pulsed amplification (CPA), Ti:sapphire system, operating at a centre wavelength of 775 nm, and with a average pulse duration of 150 fs. The dependence of the size of the ablated region on the number of pulses, used over a range of fluences, enabled the ablation threshold as a function of the number of pulses to be determined, for different beam profiles. With the Gaussian profile of the femtosecond laser, it was observed that the ablation threshold for silicon changes with the number of pulses used. The ablation threshold for a single laser pulse was determined as 0.45 J cm2 as compared to 0.18 J cm2 for 20 laser pulses. This behaviour can be attributed to the incubation parameter for silicon, which was estimated to be 0.7. In high resolution scanning electron microscope (SEM) images of the silicon surface, it was possible to observe the progression of the ablated area, within the Gaussian profile of the laser, from surface features such as circular ripples, machined with 2 laser pulses at the centre of the beam, to larger diameter laser holes, machined with 20 laser pulses. To improve the lateral precision of the ablated region over a range of pulses and fluences, a CGH was designed and constructed to transform the Gaussian profile of the laser beam into a more uniform fluence distribution. The reconstructed wavefronts produced from different CGH transmission structures were evaluated and the most successful was used to demonstrate improved laser machining of silicon. It was observed that the reconstructed beam was not Gaussian and that the ablated holes converged to a constant diameter with higher pulse fluences and pulse numbers. # 2004 Elsevier B.V. All rights reserved. Keywords: Characterisation; Laser ablation; Silicon
1. Introduction The use of femtosecond laser pulses for improved material ablation has been the subject of many studies *
Corresponding author. Tel.: þ351-61-495726; fax: þ351-61-302436. E-mail address: [email protected] (E. Coyne).
[1–4]. It has been shown that laser machining with sub-picosecond pulses reduces the thermal damage to neighbouring structures, lowers the pulse energy required to initiate ablation and, as a result, improves the quality of the laser-machined features. This increased control over the delivery of energy to the target has found many practical applications in areas such as micro machining, material edits, and surface
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.01.068
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
structuring [5,6]. Silicon is the most widely used material for the substrate of integrated circuits and it forms the basis of the modern semiconductor industry. Its properties have been thoroughly characterised and the importance of this material has led to many investigations on its response to femtosecond laser pulses [6,7]. Surface ablation studies of InP, PMMA and other dielectric materials using femtosecond pulses [8–10], have reported that the ablation fluence required to initiate surface damage drops significantly with multi-pulse irradiation. The mechanism proposed to explain this effect is based upon the creation of defect centres in the material with each successive laser pulse. The accumulation of these defect sites facilitates the transfer of energy from the excited electronic system to the lattice and thereby reduces the amount of energy needed to break the atomic bonds around the defect sites in order to ablate the structure. When laser machining with a Gaussian fluence 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. To avoid the dependency of the diameter on multipulse irradiation, it is necessary to irradiate the entire surface of the sample with the same energy, independent of position across the beam. This more uniform radial distribution of laser energy could have the form of a top-hat profile. The importance of reshaping the laser wavefront for improved machining has been the subject of previous studies [11–15]. The use of diffractive optical elements (DOEs) to reshape the laser wavefront, with the additional option of a using a refractive lens to focus the profile to a small spot size, is an established method. With CO2 and other laser sources [12,13], this method has been shown to produce the desired wavefront profile with satisfactory laser machining capabilities. Another method reported in [14] was to use a diffractive optical element to create a collimated Airy pattern. This pattern was focused with a refractive lens to produce the flat top fluence profile. Here, the refractive lens performs a Fourier transform on the incident Airy wavefront and converts it into a flat top profile at the focal plane. A simpler approach is to use a mask or aperture to spatially filter or change the profile of the laser and then project it onto the target
149
material for laser machining. However, this has the restriction of limiting the overall energy available in the laser beam after passing through the spatial filter. In this work, computer generated holographic transmission profiles were designed and fabricated with the intention of transforming the previously characterised Gaussian distribution of the untreated laser beam into an ideal flat top profile for more precise control over the lateral extension of ablation. The advantage of using a computer to generate the wavefront reconstruction is that the diffractive optic or hologram can be designed to reconstruct the unique profile of the incident laser beam into any mathematically defined wavefront that is required. To evaluate the effectiveness of this method, the reconstructed wavefront was analysed with a CCD camera and its lateral ablation profile was compared to that produced with the initial Gaussian distribution.
2. Background The method used in this paper to produce the computer generated hologram was to model the propagation of the laser beam through the optical system and to determine the distribution of the final amplitude at the plane of the holographic diffraction plate. The programming software used for the generation of the model was MATLAB. The optical system for the wavefront reconstruction consisted of a telescopic arrangement of a diverging and collimating lens, which was used in order to expand the laser beam to cover the entire width of the CGH. The computer program for the optical system was written to initially calculate the limited diffraction pattern produced by the Gaussian profile at a pinhole and then to formulate a series of transformation equations for each of the lenses, based upon their geometry and optical properties. Each set of transformation equations mapped the intensity distribution before and after each lens and this was repeated sequentially along the optical system. Any possible attenuation of the laser beam was neglected since only the relative amplitude was of interest. The final amplitude distribution illuminating the holographic plate was then calculated, Ar(x, y). It is this distribution that acts as the theoretical reference beam when generating the computer hologram and should correspond to the radial distribution of the real laser beam as seen with the CCD camera.
150
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
Next the amplitude of the object beam A0(x, y), at the holographic diffraction plate was calculated. For the purpose of the computer program, the ideal flat top profile was visualised as a circular aperture or point source, emitting a uniform monochromatic light source with a constant spatial amplitude and the resultant wavefront that propagated from this aperture or point source corresponded to the object beam. The theoretical distance between the source of the object beam and the holographic plate defined the focal length for the reconstructed wavefront. Then each point from the object beam interferes with each point from the reference beam across the surface of the computer defined holographic plane and the resulting intensity distribution I(x, y), (1), is used to define the transmission profile of the CGH. Iðx; yÞ ¼ jðAr ðx; yÞ þ A0 ðx; yÞÞj2 Iðx; yÞ ¼ ðA0 A0 þ Ar Ar Þ þ ðA0 Ar þ A0 Ar Þ
(1)
T / Iðx; yÞ The transmission profile T, was then physically mapped onto a transparent object to enable practical wavefront reconstruction. During the wavefront reconstruction phase, the real laser or reference beam will illuminate the holographic diffraction plane and interfere to produce the object beam, which should converge to produce the source at the focal point. This wavefront then acts as the real image for the hologram. A diverging conjugate wavefront will also be produced with the transmission hologram and this will act as the virtual image. AT ðx; yÞ ¼ Ar Iðx; yÞ AT ðx; yÞ ¼ ½Ar ðA0 A0 þ Ar Ar Þ þ A0 ðAr Ar Þ þ A0 Ar 2 Þ
(2) The first term in Eq. (2) Ar ðA0 A0 þ Ar Ar Þ, for the transmission profile AT(x, y), represents the direct beam, the second term represents the object beam A0 or the desired wavefront times a constant Ar Ar , and the last term represents the virtual or conjugate image A0 A2r . 3. Experimental The laser system used for the experiments reported in this paper was a Clark chirped pulse amplification
(CPA-2001) Ti:sapphire laser. The operating conditions of the laser were arranged for pulse durations of 150 fs. The energy of the pulses was controlled with a rotary wave plate and quarter wave polarising cube. A pinhole aperture was used to spatially filter the initial elliptical shape of the laser beam to produce a more symmetrical profile. The diffraction pattern created by the pinhole could be ignored for diameters of 3 mm or greater, but pinholes with smaller diameters could be used at lower intensities. Using the untransformed Gaussian laser wavefront for machining, a converging lens with a focal length of 120 mm was then used to focus the laser beam and a CCD camera confirmed that the beam had a Gaussian intensity distribution prior to laser machining. The silicon samples were placed on a computer-controlled stage for precision xyz movements. To monitor the ablation produced by the lateral profile of a given laser wavefront for multi-pulse irradiation, a mechanical shutter was used in conjunction with the frequency of the laser to control the number of pulses used at a given laser fluence. A computer program for the sample stage was written to machine a grid array of laser holes, where the number of pulses per hole increased, in increments of 2, from 2 to 20 pulses for each row. The lateral dimensions of each laser hole were then measured with high-resolution SEM surface imaging and from this it was possible to characterise the Gaussian distribution of the laser beam over a range of fluences for a given number of pulses. Two methods were used to produce the computergenerated hologram. The first method to physically create the transmission profile was to write a program for the xyz stage to use the femtosecond laser to machine the profile onto a planar sheet of thin glass. The transmission capability of glass was reduced after laser machining in air at atmospheric pressure and as a result of this property, it could be used to attenuate the laser beam and create the required transmission profile for the CGH. The required sinusoidal variation in the transmission profile as a function of radial position was achieved by dividing the computer generated transmission profile into a series of segments and then using the computer program to machine a number of laser lines in each segment that would be inversely related to its transmission. Therefore for opaque segments where the transmission is zero, the density of laser machined lines would be continuous with no
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
spaces between them. For more transparent sections, the number of lines would then decrease with increasing transparency until completely transparent segments would have no laser lines. This method then produced a series of concentric circles whose radial density varies as a direct function of the computer generated transmission profile. The second method was to print an enlarged version of the CGH and then project the image down onto a high resolution photographic film. A reduction factor of 32 was used to scale down the printed transmission profile and as a result more complex patterns with higher resolution for wavefront reconstruction could simply be produced. This method is only restricted by the quality of the printed hardcopy and of the resolution of the photographic film. By using the reconstructed wavefront from each method at the focal point, it is possible to determine and compare to what extent the original Gaussian profile had been transformed or remains a part of the transmitted wavefront.
4. Results and discussion 4.1. Development of wavefront reconstruction The transmission profile of the first CGH to be constructed was based on the reconstruction of the raw laser beam into a wave front that would converge
151
as a flat top profile with a diameter of 60 mm at a focal distance of 120 mm. This was done by modelling the wavefront that would propagate from a theoretical 60 mm wide aperture at the focal point, and then interfering it with the profile of the femtosecond laser beam to determine the resultant intensity pattern of the CGH. Since the required spatial resolution for this theoretical transmission pattern did not require any structure smaller then the minimum feature size obtainable using an 80 mm focal length lens, it was possible to use the femtosecond laser to machine the transmission profile onto a glass slide, Fig. 1. The incident Gaussian wavefront was then passed through the CGH and the reconstructed wavefront was directly observed with the CCD camera without any refractive lenses. With this reconstructed wavefront, it was possible to identify the three separate components associated with holographic images: (i) the straight through image as the beam passed through the CGH, (ii) the real image formed where one component of the reconstructed wavefront converged as a step profile at the focal point, and finally (iii) the conjugate image, where a beam appears to have originated from a circular source behind the CGH and expanded out. All three component are superimposed. However, since only the real component converges to a high fluence at the focal point, every other component could be neglected for the purpose of laser machining. With the CCD images of the reconstructed wavefront at different positions passing through the focal point, it
Fig. 1. Low magnification optical (a) and high resolution SEM image (b), showing the variation in the radial density of the laser ablated circles. This transmission profile is designed to reconstruct a planar wavefront into an approximate flat top profile with a diameter 60 mm at a focal distance of 120 mm.
152
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
Fig. 2. CCD image and profiles of the reconstructed wavefront: (a) 5 cm before the focal point, (b) at the approximate focal point, and (c) 3 cm after the focal point. Here it is possible to identify the straight through, real and conjugate images produced with the holographic transmission profile. The real image converges to a high fluence at the focus.
is possible to see the formation and divergence of each component image, as shown in Fig. 2. Trials showed that the energy of the laser pulse was being attenuated by the limited transmission of CGH and by reflections from the glass surface. As a result of these practical restrictions, the reconstructed wavefront was unable to reach the ablation threshold fluence for silicon at the focal point. Therefore the lateral ablation of silicon with this reconstructed profile could not be characterised. To reduce the beam diameter at the focal point and increase the laser fluence to the ablation threshold, a second CGH was designed. In this case, the 1/e2 diameter of the raw Gaussian laser beam along the xaxis was measured to be approximately 2.5 mm with the CCD camera and this profile was then used in the model to interfere with a wavefront propagating from a point source at a focal distance of 70 mm. The transmission profile produced from the resultant interference pattern should then reconstruct and focus the original Gaussian profile down to the minimum focal spot size, for the focal length with the initial laser beam diameter used. The minimum feature size that could be machined with the femtosecond laser on a glass slide was too large for the detail required with this CGH transmission profile, which is shown in Fig. 3. Therefore, an enlarged printed hardcopy of the transmission profile was scaled down by a factor of 32 on to a photographic film. The photographic film then contained all the information of the original pattern on a scale that was appropriate to reconstruct the wavefront.
When the initial beam was then passed through the photographic film, the maximum transmitted energy of the reconstructed wavefront was similarly restricted because of the limited transmission of the CGH. This energy was then further divided among the real, conjugate and straight through images of the reconstructed wavefront, while only the energy from the real image was used for machining. However, the fluence of the real image at the focal point was above the ablation threshold for silicon and therefore characterisation of the lateral ablation profile was possible. Also, by reducing the laser energy to its minimum value, it was possible to directly observe the reconstructed wavefront at the approximate focal point with the CCD camera, as shown in Fig. 4. The steep sides of the fluence distribution are evident from the profile. 4.2. Comparison of laser ablation with Gaussian and reconstructed beam profiles 4.2.1. Gaussian beam profile The characterisation method described in this paper to study the lateral ablation of silicon by Gaussian femtosecond laser pulses is based upon the condition that the spatial fluence distribution f(r) of the laser beam is characterised by the Gaussian profile (3), as a function of radial position r. 2r 2 fðrÞ ¼ f0 exp 2 (3) w0
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
153
Fig. 3. Variation in the transmission profile as a function of radial position (3 mm radius) for the computer generated interference pattern between a Gaussian profile with a 1/e2 radius of 2.5 mm and the wavefront propagating from a point source at a focal distance of 70 mm. Here the transmission is linearly proportional to the relative intensity of the interference pattern.
where w0 is the 1/e2 radius of the distribution and f0 represents the peak fluence. With the experiments reported in this paper, this condition was valid because a pinhole aperture spatially filters the elliptical shape
of the laser beam and a CCD camera is used to confirm the Gaussian profile prior to all laser machining. By defining the ablation threshold fth for silicon, Eq. (3) can be redefined to describe the diameter of the laser
Fig. 4. CCD planar image (a) of the reconstructed wavefront close to the focal point after being passed through a filter, and the corresponding relative intensity profile along the x-axis (b). The steep sides of the relative intensity distribution are evident, where the top of the profile converges to a point beyond the saturation point of the CCD camera. The horizontal line through the intensity distribution 4(b), represents the average intensity across the CCD camera.
154
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
machined holes D as a function of the peak laser fluence. D2 ¼ 2w20 ln
f0 fth
(4)
Then, by plotting the log of the laser fluence as a function of the diameter squared, it is possible to determine the width of the laser beam w0 from the slope and the threshold of ablation fth, by extrapolating the measurements for the diameter back to the intercept. The peak laser fluence f0 is related to the laser pulse energy Ep by: f0 ¼
2Ep pw20
(5)
For this experiment, an array of laser holes was constructed, where the number of pulses used to machine each hole at a given laser fluence increased in increments of 2, from 2 to 20. The diameters of each laser hole forming the arrays were measured with the
scanning electron microscope (SEM), and the data is plotted in Fig. 5. From Fig. 5 it can be seen that for each number of pulses the slope of the linear relation remains the same. When viewed in conjunction with the Eq. (3) for the Gaussian distribution, this result was anticipated because the same 120 mm focal length lens was used to machine all the laser holes and as a result the spatial distribution of the laser would remain the same independent of the pulse energy and the number of pulses used. From the slope of the graph a mean value of 30:9 0:4 mm was obtained for the 1/e2 radius of the distribution, w0 . This value was used to calculate the effective area of the laser pulse to convert the energy readings into fluence. An examination of the intercept, as a function of the number of pulses used to machine the laser holes, shows that the ablation threshold decreases with an increasing number of pulses. Using the experimental data for the line machined with 2 laser pulses, a value of 0.37 J cm2 was obtained for the ablation threshold
Fig. 5. Graph of the log of the pulse energy as a function of the diameter squared over the array of pulses. The graph starts with the 2 pulse line and continues down to 20 in increments of 2 pulses. The data for each set of pulses is fitted to a straight line, according to Eq. (4).
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
155
Fig. 6. Graph of the log (Nfth(N)) against the log(N), showing the best fit linear relation defined by the incubation parameter for silicon.
and this decreases to a value of 0.18 J cm2 for 20 pulses. Therefore there is an accumulation of defects occurring in the crystalline lattice for ablation and this process is described using the incubation model [9]. This model relates the ablation threshold fth(N)
for a given number of pulses N to the single pulse ablation threshold fth(1), with the incubation parameter x fth ðNÞ ¼ fth ð1ÞN x1
(6)
Fig. 7. SEM images of the ripples on the surface of the silicon wafer produced with 2 pulses of linearly polarised laser light with a wavelength 775 nm at a fluence of 0.4 J cm2. The images show how the ripples can be seen to radiate out in a circular pattern from a disturbance at their source 7(a), and produce interference patterns 7(b).
156
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
Fig. 8. SEM cross sectional images of the ripple structure produced with 2 pulses of linearly polarised light with a wavelength 775 nm at a fluence of 0.51 J cm2. The images show how the depth of each ripple trench decreases with distance away from the center of the Gaussian distribution.
By graphing the logarithm of Nfth(N) against the logarithm of N, as shown in Fig. 6, it is possible to determine the incubation parameter for silicon from the slope of the linear relation and the ablation threshold for a single laser pulse from the intercept, Fig. 6.
From Fig. 6, a value of 0.7 was obtained for the incubation parameter with silicon and a value of 0.45 J cm2 was found for the ablation threshold with a single pulse. By examining the ablated surface with high resolution SEM images it was possible to observe
Fig. 9. Graph of the laser ablated diameter as a function of the number of pulses using experimental data for a fluence of 0.8 J cm2, with the theoretical curve calculated with an incubation parameter of 0.72 and a single pulse ablation threshold of 0.45 J cm2.
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
the accumulation of damage on the silicon surface by increasing number of pulses used at constant laser fluence. It was observed that the Gaussian distribution for the laser energy defined the nature and progression of damage to the crystal lattice across the radial profile of the laser ablated region. Initially damage to the surface of the wafer was observed with the formation of ripples near the centre of the laser pulse with the highest peak fluence. For 2 laser pulses, these ripples can be seen to radiate out in a circular pattern from a disturbance at their source [16]. Interference with other surface ripples that originate from different locations was also observed, as shown in Fig. 7. Analysis of this symmetrical ripple structure found that their wavelength of approximately 0.6– 0.7 mm was comparable to the laser wavelength. SEM cross sectional imaging of the ripples showed that the depth of each ripple trench decreases with distance away from the centre of the Gaussian dis-
157
tribution with the higher laser fluences. In these cross sectional images, as shown in Fig. 8, it can be seen that the peak of each ripple is at the same level, which is the surface of the silicon wafer. Therefore the formation of the periodic ripple pattern appears to be from ablation only with no accumulation of material at the peaks. As the number of pulses is increased, more material at the centre of the laser pulse is removed and the diameter of the laser ablated region increases. The level of damage to the silicon surface also varies with radial position according to the Gaussian profile and the number of pulses. Therefore, there exists an accumulation effect with the ablation of silicon when irradiated repeatedly by laser pulses. With each laser pulse, the damage builds up in the lattice structure at the edge of the Gaussian distribution, which then causes an increase in the ablated diameters with pulse numbers. Since the number of pulses N and the ablation threshold are related according to (6), then
Fig. 10. Graph of laser hole x-axis diameters squared as a function of the log of the pulse energy used for machining over the pulse range (2–20) for transmitted energies of 22, 24.1, 27.4, 29.7 and 32.5 mJ. At higher pulse energies or with a higher number of pulses, the diameters of the laser-ablated holes converges to a constant value.
158
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
the diameter of the ablated holes D can now be expressed in terms of the number of pulses used by combining Eqs. (6) and (4). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f0 D ¼ w0 2 ln (7) fth ð1ÞN x1 This provides a separate method for determining the incubation parameter that was shown in ref. [9] and can now be applied to measurements obtained for silicon. This method compares the experimental data to the values calculated with Eq. (7) and adjusts the value for the incubation parameter that produces the best fit between both sets of data. Fig. 9 shows the experimental data for the diameters of the laser holes machined with a fluence of 0.8 J cm2, plotted with the theoretical values obtained from Eq. (7). Here the profile of the theoretical curve agrees with the experimental data with an incubation parameter of 0.72. This value is comparable to the value of 0.7 that was originally obtained with Eq. (6).
Therefore, for a given laser fluence, the diameter of the ablated region increases as a function of the number of pulses. The rate of increase is dependent on the material, and on the 1/e2 radius of the Gaussian profile, which limits the lateral precision achieved when laser machining with a Gaussian profile over a range of pulses and fluences. 4.2.2. Reconstructed beam profile To compare the lateral ablation attained with the reconstructed wavefront, the same procedure was used as described for the original Gaussian distribution. An array of laser holes was machined with the reconstructed wavefront, where the number of pulses used to machine each column of the array increased from 2 to 20 in increments of 2. The experiment was repeated over the energy range of 22–32 mJ, where ablation of the silicon surface was first observed when the total transmitted energy of all the reconstructed wavefront was 22 mJ. The total transmitted energy is used as a measurement because using the three separate compo-
Fig. 11. Graph of laser hole x-axis diameter as a function of the number of pulses for a transmitted energy of 29.7 mJ. The measured diameter only varies by an average of 20 nm per pulse over the range of pulses from 8 to 20.
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
nents of the CGH it was unreliable to estimate what percentage of the energy formed the real component. The x-axis and y-axis diameters of the laser holes were then recorded independently as a function of the number of pulses, where the x-axis values are shown in Fig. 10. The x-axis was chosen because the CGH was designed for the Gaussian distribution along the x-axis. Due to the elliptical shape of incident laser beam, data for the y-axis was similar but slightly less correlated. Here it can be seen that, at higher pulse energies or withahighernumberofpulses,thediametersofthelaserablated holes converges to a constant value. This behaviour is not what would be expected from a Gaussian distribution as defined in Eq. (5). For the holes that were machined with a transmitted pulse energy of 29.7 mJ, the measured diameter remains almost constant over the rangeofpulsesfrom8to20,asshowninFig.11.Overthis pulse range the diameter of the holes only varies by an average of 20 nm per pulse. Since the number of pulses used for machining defines the ablation threshold, and the ablation threshold defines the boundary of the observed laser holes, this implies that an almost constant diameter laser hole over a range of pulses would require a fluence distribution with the steep sides of a step profile at the diameter of the laser holes as shown in Fig. 4. However for holes machined with less then eight pulses the diameter decreases, as shown in Fig. 11. This may be due to a less-than-ideal top-hat shape in the laser pulse and some curvature at the centre of the modified beam.
5. Conclusion Based on the experimental results for the variation in the ablated diameter over a range of energies and pulses for a Gaussian distribution, it can be concluded that laser machining with a Gaussian fluence distribution does limit the lateral precision of the ablated boundary. With multiple pulse laser holes, each successive laser pulse results in a progressive increase in the diameter of the laser machined feature according to the absorption of energy as defined by the Gaussian profile. This process is characterised by the incubation parameter for the material, which defines the change in the ablation threshold in terms of the number of pulses used. Even when keeping the number of pulses constant and varying the pulse energy, it was observed
159
that the ablated diameter of the laser holes changes according to the Gaussian distribution. Therefore to fully realize the lateral precision of the femtosecond laser for machining, it is necessary to reshape the laser beam for a more uniform fluence distribution. Reshaping the laser beam for a more precise spatial distribution of energy was produced with a CGH that was designed to transform the Gaussian profile into a ‘‘top-hat’’ profile. The initial method described in this paper to physically create the CGH was achieved by using the femtosecond laser to machine the transmission profile onto a sheet of glass. However, this method does limit the spatial resolution of the holographic profile to the minimum feature size that the laser is able to machine. This restriction is easily solved for more complicated patterns requiring higher resolution, by projecting the computer generated image of the transmission profile onto a photographic film and then using the film to reconstruct of the original laser wavefront. With the reconstructed wavefront it was possible to observe the holographic real image in the form of a step fluence distribution, its conjugate image and the straight through beam. In principle, this technique can be used to transform the wavefront of a given laser beam into any other wavefront that can be mathematically defined and expressed in appropriate computer code. The primary difficulty with using a CGH to reshape the laser wavefront is that a large percentage of the pulse energy is lost in the process. To further optimise the transmission efficiency of the CGH, an antireflection coating for the 775 nm wavelength should be added and a better transmission medium for this wavelength could be used.
References [1] M.D. Shirk, P.A. Molian, A review of ultrashort pulsed laser ablation of materials, J. Laser Appl. 10 (1) (1998) 18–28. [2] W. Kautek, J. Kruger, Femtosecond-pulse laser ablation of metallic, semiconducting, ceramic, and biological materials, SPIE 2207 (1994) 600–611. [3] H. Varel, M. Wahmer, A. Rosenfeld, D. Ashkenasi, E.E.B. Campbell, Femtosecond laser ablation of sapphire: time-offlight analysis of ablation plume, Appl. Surf. Sci. 127–129 (1998) 128–133. [4] S. Nolte, C. Momma, H. Jacobs, A. Tunnermann, B.N. Chichkov, B. Wellegehausen, H. Welling, Ablation of metals by ultrashort laser pulses, J. Opt. Soc. Am. B 14 (10) (1997) 2716–2722.
160
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
[5] P.P. Pronko, S.K. Dutta, J. Squier, J.V. Rudd, D. Du, G. Mourou, Machining of sub-micron holes using a femtosecond laser at 800 nm, Opt. Commun. 114 (1995) 106–110. [6] J.E. Carey, C.H. Crouch, E. Mazur, Femtosecond-laserassisted microstructuring of silicon surfaces, Optics Photonics News, 02 (2003) 32–36. [7] Gambirasio, M. Bernasconi, L. Colombo, Laser induced melting of silicon: a tight-binding molecular dynamics simulation, Phys. Rev. B 61 (12) (2000) 8233–8237. [8] J. Bonse, J.M. Wrobel, J. Kruger, W. Kautek, Ultrashort-pulse laser ablation of indium phosphide in air, Appl. Phys. A 72 (2001) 89–94. [9] J. Bonse, S. Baudach, J. Kruger, W. Kautek, Femtosecond laser micromachining of technical materials, Proc. SPIE 4065 (2000) 161–172. [10] A. Rosenfeld, M. Lorenz, R. Stoian, D. Ashkensai, Ultrashortlaser-pulse damage threshold of transparent materials and the role of incubation, Appl. Phys. A 69 (1999) S373–S376.
[11] S. Rane, G. Cheriaux, S. Ferre, J.P. Chambaret, Importance of spatial quality of intense femtosecond pulses, Appl. Phys. B 70 (2000) S181–S187. [12] F.M. Dickey, S.C. Holswade, Gaussian laser beam profile shaping, Opt. Eng. 35 (11) (1996) 3285–3295. [13] J.R. Ledger, S. Makki, Z. Wang, Laser beam relaying with phase-conjugate diffractive optical element, Appl. Opt. 36 (20) (1997) 4749–4755. [14] K. Kanzler, Transformation of a Gaussian laser beam to an airy pattern for use in focal plane intensity shaping using diffractive optics, SPIE Proc. 4443-09 (2000). [15] E. Bricchi, J.D. Mills, P.G. Kazansky, B.G. Klappauf, Birefringent Fresnel zone plates in silica fabricated by femtosecond laser machining, Opt. Lett. 27(24) (2002). [16] G. Zhou, P.M. Fauchet, A.E. Siegman, Growth of spontaneous periodic surface structures on solids during laser illumination, Phys. Rev. B 10 (26) (1982) 5366– 5381.
Characterisation of laser ablation of silicon using a Gaussian wavefront and computer generated wavefront reconstruction E. Coynea,b,*, J.P. Mageeb, P. Mannionb, G.M. O’Connorb, T.J. Glynnb a
Analog Devices, Raheen, Limerick, Ireland National Center for Laser Applications (NCLA), National University of Ireland-Galway, Galway, Ireland
b
Received 19 December 2003; received in revised form 23 January 2004; accepted 23 January 2004 Available online 21 March 2004
Abstract The work described in this paper characterises the laser ablation of wafer grade silicon, using both a Gaussian beam and the reconstructed wavefront of a femtosecond laser. The reconstructed wavefront was produced by transmission through a computer generated hologram (CGH). The laser used was a chirped pulsed amplification (CPA), Ti:sapphire system, operating at a centre wavelength of 775 nm, and with a average pulse duration of 150 fs. The dependence of the size of the ablated region on the number of pulses, used over a range of fluences, enabled the ablation threshold as a function of the number of pulses to be determined, for different beam profiles. With the Gaussian profile of the femtosecond laser, it was observed that the ablation threshold for silicon changes with the number of pulses used. The ablation threshold for a single laser pulse was determined as 0.45 J cm2 as compared to 0.18 J cm2 for 20 laser pulses. This behaviour can be attributed to the incubation parameter for silicon, which was estimated to be 0.7. In high resolution scanning electron microscope (SEM) images of the silicon surface, it was possible to observe the progression of the ablated area, within the Gaussian profile of the laser, from surface features such as circular ripples, machined with 2 laser pulses at the centre of the beam, to larger diameter laser holes, machined with 20 laser pulses. To improve the lateral precision of the ablated region over a range of pulses and fluences, a CGH was designed and constructed to transform the Gaussian profile of the laser beam into a more uniform fluence distribution. The reconstructed wavefronts produced from different CGH transmission structures were evaluated and the most successful was used to demonstrate improved laser machining of silicon. It was observed that the reconstructed beam was not Gaussian and that the ablated holes converged to a constant diameter with higher pulse fluences and pulse numbers. # 2004 Elsevier B.V. All rights reserved. Keywords: Characterisation; Laser ablation; Silicon
1. Introduction The use of femtosecond laser pulses for improved material ablation has been the subject of many studies *
Corresponding author. Tel.: þ351-61-495726; fax: þ351-61-302436. E-mail address: [email protected] (E. Coyne).
[1–4]. It has been shown that laser machining with sub-picosecond pulses reduces the thermal damage to neighbouring structures, lowers the pulse energy required to initiate ablation and, as a result, improves the quality of the laser-machined features. This increased control over the delivery of energy to the target has found many practical applications in areas such as micro machining, material edits, and surface
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.01.068
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
structuring [5,6]. Silicon is the most widely used material for the substrate of integrated circuits and it forms the basis of the modern semiconductor industry. Its properties have been thoroughly characterised and the importance of this material has led to many investigations on its response to femtosecond laser pulses [6,7]. Surface ablation studies of InP, PMMA and other dielectric materials using femtosecond pulses [8–10], have reported that the ablation fluence required to initiate surface damage drops significantly with multi-pulse irradiation. The mechanism proposed to explain this effect is based upon the creation of defect centres in the material with each successive laser pulse. The accumulation of these defect sites facilitates the transfer of energy from the excited electronic system to the lattice and thereby reduces the amount of energy needed to break the atomic bonds around the defect sites in order to ablate the structure. When laser machining with a Gaussian fluence 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. To avoid the dependency of the diameter on multipulse irradiation, it is necessary to irradiate the entire surface of the sample with the same energy, independent of position across the beam. This more uniform radial distribution of laser energy could have the form of a top-hat profile. The importance of reshaping the laser wavefront for improved machining has been the subject of previous studies [11–15]. The use of diffractive optical elements (DOEs) to reshape the laser wavefront, with the additional option of a using a refractive lens to focus the profile to a small spot size, is an established method. With CO2 and other laser sources [12,13], this method has been shown to produce the desired wavefront profile with satisfactory laser machining capabilities. Another method reported in [14] was to use a diffractive optical element to create a collimated Airy pattern. This pattern was focused with a refractive lens to produce the flat top fluence profile. Here, the refractive lens performs a Fourier transform on the incident Airy wavefront and converts it into a flat top profile at the focal plane. A simpler approach is to use a mask or aperture to spatially filter or change the profile of the laser and then project it onto the target
149
material for laser machining. However, this has the restriction of limiting the overall energy available in the laser beam after passing through the spatial filter. In this work, computer generated holographic transmission profiles were designed and fabricated with the intention of transforming the previously characterised Gaussian distribution of the untreated laser beam into an ideal flat top profile for more precise control over the lateral extension of ablation. The advantage of using a computer to generate the wavefront reconstruction is that the diffractive optic or hologram can be designed to reconstruct the unique profile of the incident laser beam into any mathematically defined wavefront that is required. To evaluate the effectiveness of this method, the reconstructed wavefront was analysed with a CCD camera and its lateral ablation profile was compared to that produced with the initial Gaussian distribution.
2. Background The method used in this paper to produce the computer generated hologram was to model the propagation of the laser beam through the optical system and to determine the distribution of the final amplitude at the plane of the holographic diffraction plate. The programming software used for the generation of the model was MATLAB. The optical system for the wavefront reconstruction consisted of a telescopic arrangement of a diverging and collimating lens, which was used in order to expand the laser beam to cover the entire width of the CGH. The computer program for the optical system was written to initially calculate the limited diffraction pattern produced by the Gaussian profile at a pinhole and then to formulate a series of transformation equations for each of the lenses, based upon their geometry and optical properties. Each set of transformation equations mapped the intensity distribution before and after each lens and this was repeated sequentially along the optical system. Any possible attenuation of the laser beam was neglected since only the relative amplitude was of interest. The final amplitude distribution illuminating the holographic plate was then calculated, Ar(x, y). It is this distribution that acts as the theoretical reference beam when generating the computer hologram and should correspond to the radial distribution of the real laser beam as seen with the CCD camera.
150
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
Next the amplitude of the object beam A0(x, y), at the holographic diffraction plate was calculated. For the purpose of the computer program, the ideal flat top profile was visualised as a circular aperture or point source, emitting a uniform monochromatic light source with a constant spatial amplitude and the resultant wavefront that propagated from this aperture or point source corresponded to the object beam. The theoretical distance between the source of the object beam and the holographic plate defined the focal length for the reconstructed wavefront. Then each point from the object beam interferes with each point from the reference beam across the surface of the computer defined holographic plane and the resulting intensity distribution I(x, y), (1), is used to define the transmission profile of the CGH. Iðx; yÞ ¼ jðAr ðx; yÞ þ A0 ðx; yÞÞj2 Iðx; yÞ ¼ ðA0 A0 þ Ar Ar Þ þ ðA0 Ar þ A0 Ar Þ
(1)
T / Iðx; yÞ The transmission profile T, was then physically mapped onto a transparent object to enable practical wavefront reconstruction. During the wavefront reconstruction phase, the real laser or reference beam will illuminate the holographic diffraction plane and interfere to produce the object beam, which should converge to produce the source at the focal point. This wavefront then acts as the real image for the hologram. A diverging conjugate wavefront will also be produced with the transmission hologram and this will act as the virtual image. AT ðx; yÞ ¼ Ar Iðx; yÞ AT ðx; yÞ ¼ ½Ar ðA0 A0 þ Ar Ar Þ þ A0 ðAr Ar Þ þ A0 Ar 2 Þ
(2) The first term in Eq. (2) Ar ðA0 A0 þ Ar Ar Þ, for the transmission profile AT(x, y), represents the direct beam, the second term represents the object beam A0 or the desired wavefront times a constant Ar Ar , and the last term represents the virtual or conjugate image A0 A2r . 3. Experimental The laser system used for the experiments reported in this paper was a Clark chirped pulse amplification
(CPA-2001) Ti:sapphire laser. The operating conditions of the laser were arranged for pulse durations of 150 fs. The energy of the pulses was controlled with a rotary wave plate and quarter wave polarising cube. A pinhole aperture was used to spatially filter the initial elliptical shape of the laser beam to produce a more symmetrical profile. The diffraction pattern created by the pinhole could be ignored for diameters of 3 mm or greater, but pinholes with smaller diameters could be used at lower intensities. Using the untransformed Gaussian laser wavefront for machining, a converging lens with a focal length of 120 mm was then used to focus the laser beam and a CCD camera confirmed that the beam had a Gaussian intensity distribution prior to laser machining. The silicon samples were placed on a computer-controlled stage for precision xyz movements. To monitor the ablation produced by the lateral profile of a given laser wavefront for multi-pulse irradiation, a mechanical shutter was used in conjunction with the frequency of the laser to control the number of pulses used at a given laser fluence. A computer program for the sample stage was written to machine a grid array of laser holes, where the number of pulses per hole increased, in increments of 2, from 2 to 20 pulses for each row. The lateral dimensions of each laser hole were then measured with high-resolution SEM surface imaging and from this it was possible to characterise the Gaussian distribution of the laser beam over a range of fluences for a given number of pulses. Two methods were used to produce the computergenerated hologram. The first method to physically create the transmission profile was to write a program for the xyz stage to use the femtosecond laser to machine the profile onto a planar sheet of thin glass. The transmission capability of glass was reduced after laser machining in air at atmospheric pressure and as a result of this property, it could be used to attenuate the laser beam and create the required transmission profile for the CGH. The required sinusoidal variation in the transmission profile as a function of radial position was achieved by dividing the computer generated transmission profile into a series of segments and then using the computer program to machine a number of laser lines in each segment that would be inversely related to its transmission. Therefore for opaque segments where the transmission is zero, the density of laser machined lines would be continuous with no
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
spaces between them. For more transparent sections, the number of lines would then decrease with increasing transparency until completely transparent segments would have no laser lines. This method then produced a series of concentric circles whose radial density varies as a direct function of the computer generated transmission profile. The second method was to print an enlarged version of the CGH and then project the image down onto a high resolution photographic film. A reduction factor of 32 was used to scale down the printed transmission profile and as a result more complex patterns with higher resolution for wavefront reconstruction could simply be produced. This method is only restricted by the quality of the printed hardcopy and of the resolution of the photographic film. By using the reconstructed wavefront from each method at the focal point, it is possible to determine and compare to what extent the original Gaussian profile had been transformed or remains a part of the transmitted wavefront.
4. Results and discussion 4.1. Development of wavefront reconstruction The transmission profile of the first CGH to be constructed was based on the reconstruction of the raw laser beam into a wave front that would converge
151
as a flat top profile with a diameter of 60 mm at a focal distance of 120 mm. This was done by modelling the wavefront that would propagate from a theoretical 60 mm wide aperture at the focal point, and then interfering it with the profile of the femtosecond laser beam to determine the resultant intensity pattern of the CGH. Since the required spatial resolution for this theoretical transmission pattern did not require any structure smaller then the minimum feature size obtainable using an 80 mm focal length lens, it was possible to use the femtosecond laser to machine the transmission profile onto a glass slide, Fig. 1. The incident Gaussian wavefront was then passed through the CGH and the reconstructed wavefront was directly observed with the CCD camera without any refractive lenses. With this reconstructed wavefront, it was possible to identify the three separate components associated with holographic images: (i) the straight through image as the beam passed through the CGH, (ii) the real image formed where one component of the reconstructed wavefront converged as a step profile at the focal point, and finally (iii) the conjugate image, where a beam appears to have originated from a circular source behind the CGH and expanded out. All three component are superimposed. However, since only the real component converges to a high fluence at the focal point, every other component could be neglected for the purpose of laser machining. With the CCD images of the reconstructed wavefront at different positions passing through the focal point, it
Fig. 1. Low magnification optical (a) and high resolution SEM image (b), showing the variation in the radial density of the laser ablated circles. This transmission profile is designed to reconstruct a planar wavefront into an approximate flat top profile with a diameter 60 mm at a focal distance of 120 mm.
152
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
Fig. 2. CCD image and profiles of the reconstructed wavefront: (a) 5 cm before the focal point, (b) at the approximate focal point, and (c) 3 cm after the focal point. Here it is possible to identify the straight through, real and conjugate images produced with the holographic transmission profile. The real image converges to a high fluence at the focus.
is possible to see the formation and divergence of each component image, as shown in Fig. 2. Trials showed that the energy of the laser pulse was being attenuated by the limited transmission of CGH and by reflections from the glass surface. As a result of these practical restrictions, the reconstructed wavefront was unable to reach the ablation threshold fluence for silicon at the focal point. Therefore the lateral ablation of silicon with this reconstructed profile could not be characterised. To reduce the beam diameter at the focal point and increase the laser fluence to the ablation threshold, a second CGH was designed. In this case, the 1/e2 diameter of the raw Gaussian laser beam along the xaxis was measured to be approximately 2.5 mm with the CCD camera and this profile was then used in the model to interfere with a wavefront propagating from a point source at a focal distance of 70 mm. The transmission profile produced from the resultant interference pattern should then reconstruct and focus the original Gaussian profile down to the minimum focal spot size, for the focal length with the initial laser beam diameter used. The minimum feature size that could be machined with the femtosecond laser on a glass slide was too large for the detail required with this CGH transmission profile, which is shown in Fig. 3. Therefore, an enlarged printed hardcopy of the transmission profile was scaled down by a factor of 32 on to a photographic film. The photographic film then contained all the information of the original pattern on a scale that was appropriate to reconstruct the wavefront.
When the initial beam was then passed through the photographic film, the maximum transmitted energy of the reconstructed wavefront was similarly restricted because of the limited transmission of the CGH. This energy was then further divided among the real, conjugate and straight through images of the reconstructed wavefront, while only the energy from the real image was used for machining. However, the fluence of the real image at the focal point was above the ablation threshold for silicon and therefore characterisation of the lateral ablation profile was possible. Also, by reducing the laser energy to its minimum value, it was possible to directly observe the reconstructed wavefront at the approximate focal point with the CCD camera, as shown in Fig. 4. The steep sides of the fluence distribution are evident from the profile. 4.2. Comparison of laser ablation with Gaussian and reconstructed beam profiles 4.2.1. Gaussian beam profile The characterisation method described in this paper to study the lateral ablation of silicon by Gaussian femtosecond laser pulses is based upon the condition that the spatial fluence distribution f(r) of the laser beam is characterised by the Gaussian profile (3), as a function of radial position r. 2r 2 fðrÞ ¼ f0 exp 2 (3) w0
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
153
Fig. 3. Variation in the transmission profile as a function of radial position (3 mm radius) for the computer generated interference pattern between a Gaussian profile with a 1/e2 radius of 2.5 mm and the wavefront propagating from a point source at a focal distance of 70 mm. Here the transmission is linearly proportional to the relative intensity of the interference pattern.
where w0 is the 1/e2 radius of the distribution and f0 represents the peak fluence. With the experiments reported in this paper, this condition was valid because a pinhole aperture spatially filters the elliptical shape
of the laser beam and a CCD camera is used to confirm the Gaussian profile prior to all laser machining. By defining the ablation threshold fth for silicon, Eq. (3) can be redefined to describe the diameter of the laser
Fig. 4. CCD planar image (a) of the reconstructed wavefront close to the focal point after being passed through a filter, and the corresponding relative intensity profile along the x-axis (b). The steep sides of the relative intensity distribution are evident, where the top of the profile converges to a point beyond the saturation point of the CCD camera. The horizontal line through the intensity distribution 4(b), represents the average intensity across the CCD camera.
154
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
machined holes D as a function of the peak laser fluence. D2 ¼ 2w20 ln
f0 fth
(4)
Then, by plotting the log of the laser fluence as a function of the diameter squared, it is possible to determine the width of the laser beam w0 from the slope and the threshold of ablation fth, by extrapolating the measurements for the diameter back to the intercept. The peak laser fluence f0 is related to the laser pulse energy Ep by: f0 ¼
2Ep pw20
(5)
For this experiment, an array of laser holes was constructed, where the number of pulses used to machine each hole at a given laser fluence increased in increments of 2, from 2 to 20. The diameters of each laser hole forming the arrays were measured with the
scanning electron microscope (SEM), and the data is plotted in Fig. 5. From Fig. 5 it can be seen that for each number of pulses the slope of the linear relation remains the same. When viewed in conjunction with the Eq. (3) for the Gaussian distribution, this result was anticipated because the same 120 mm focal length lens was used to machine all the laser holes and as a result the spatial distribution of the laser would remain the same independent of the pulse energy and the number of pulses used. From the slope of the graph a mean value of 30:9 0:4 mm was obtained for the 1/e2 radius of the distribution, w0 . This value was used to calculate the effective area of the laser pulse to convert the energy readings into fluence. An examination of the intercept, as a function of the number of pulses used to machine the laser holes, shows that the ablation threshold decreases with an increasing number of pulses. Using the experimental data for the line machined with 2 laser pulses, a value of 0.37 J cm2 was obtained for the ablation threshold
Fig. 5. Graph of the log of the pulse energy as a function of the diameter squared over the array of pulses. The graph starts with the 2 pulse line and continues down to 20 in increments of 2 pulses. The data for each set of pulses is fitted to a straight line, according to Eq. (4).
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
155
Fig. 6. Graph of the log (Nfth(N)) against the log(N), showing the best fit linear relation defined by the incubation parameter for silicon.
and this decreases to a value of 0.18 J cm2 for 20 pulses. Therefore there is an accumulation of defects occurring in the crystalline lattice for ablation and this process is described using the incubation model [9]. This model relates the ablation threshold fth(N)
for a given number of pulses N to the single pulse ablation threshold fth(1), with the incubation parameter x fth ðNÞ ¼ fth ð1ÞN x1
(6)
Fig. 7. SEM images of the ripples on the surface of the silicon wafer produced with 2 pulses of linearly polarised laser light with a wavelength 775 nm at a fluence of 0.4 J cm2. The images show how the ripples can be seen to radiate out in a circular pattern from a disturbance at their source 7(a), and produce interference patterns 7(b).
156
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
Fig. 8. SEM cross sectional images of the ripple structure produced with 2 pulses of linearly polarised light with a wavelength 775 nm at a fluence of 0.51 J cm2. The images show how the depth of each ripple trench decreases with distance away from the center of the Gaussian distribution.
By graphing the logarithm of Nfth(N) against the logarithm of N, as shown in Fig. 6, it is possible to determine the incubation parameter for silicon from the slope of the linear relation and the ablation threshold for a single laser pulse from the intercept, Fig. 6.
From Fig. 6, a value of 0.7 was obtained for the incubation parameter with silicon and a value of 0.45 J cm2 was found for the ablation threshold with a single pulse. By examining the ablated surface with high resolution SEM images it was possible to observe
Fig. 9. Graph of the laser ablated diameter as a function of the number of pulses using experimental data for a fluence of 0.8 J cm2, with the theoretical curve calculated with an incubation parameter of 0.72 and a single pulse ablation threshold of 0.45 J cm2.
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
the accumulation of damage on the silicon surface by increasing number of pulses used at constant laser fluence. It was observed that the Gaussian distribution for the laser energy defined the nature and progression of damage to the crystal lattice across the radial profile of the laser ablated region. Initially damage to the surface of the wafer was observed with the formation of ripples near the centre of the laser pulse with the highest peak fluence. For 2 laser pulses, these ripples can be seen to radiate out in a circular pattern from a disturbance at their source [16]. Interference with other surface ripples that originate from different locations was also observed, as shown in Fig. 7. Analysis of this symmetrical ripple structure found that their wavelength of approximately 0.6– 0.7 mm was comparable to the laser wavelength. SEM cross sectional imaging of the ripples showed that the depth of each ripple trench decreases with distance away from the centre of the Gaussian dis-
157
tribution with the higher laser fluences. In these cross sectional images, as shown in Fig. 8, it can be seen that the peak of each ripple is at the same level, which is the surface of the silicon wafer. Therefore the formation of the periodic ripple pattern appears to be from ablation only with no accumulation of material at the peaks. As the number of pulses is increased, more material at the centre of the laser pulse is removed and the diameter of the laser ablated region increases. The level of damage to the silicon surface also varies with radial position according to the Gaussian profile and the number of pulses. Therefore, there exists an accumulation effect with the ablation of silicon when irradiated repeatedly by laser pulses. With each laser pulse, the damage builds up in the lattice structure at the edge of the Gaussian distribution, which then causes an increase in the ablated diameters with pulse numbers. Since the number of pulses N and the ablation threshold are related according to (6), then
Fig. 10. Graph of laser hole x-axis diameters squared as a function of the log of the pulse energy used for machining over the pulse range (2–20) for transmitted energies of 22, 24.1, 27.4, 29.7 and 32.5 mJ. At higher pulse energies or with a higher number of pulses, the diameters of the laser-ablated holes converges to a constant value.
158
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
the diameter of the ablated holes D can now be expressed in terms of the number of pulses used by combining Eqs. (6) and (4). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f0 D ¼ w0 2 ln (7) fth ð1ÞN x1 This provides a separate method for determining the incubation parameter that was shown in ref. [9] and can now be applied to measurements obtained for silicon. This method compares the experimental data to the values calculated with Eq. (7) and adjusts the value for the incubation parameter that produces the best fit between both sets of data. Fig. 9 shows the experimental data for the diameters of the laser holes machined with a fluence of 0.8 J cm2, plotted with the theoretical values obtained from Eq. (7). Here the profile of the theoretical curve agrees with the experimental data with an incubation parameter of 0.72. This value is comparable to the value of 0.7 that was originally obtained with Eq. (6).
Therefore, for a given laser fluence, the diameter of the ablated region increases as a function of the number of pulses. The rate of increase is dependent on the material, and on the 1/e2 radius of the Gaussian profile, which limits the lateral precision achieved when laser machining with a Gaussian profile over a range of pulses and fluences. 4.2.2. Reconstructed beam profile To compare the lateral ablation attained with the reconstructed wavefront, the same procedure was used as described for the original Gaussian distribution. An array of laser holes was machined with the reconstructed wavefront, where the number of pulses used to machine each column of the array increased from 2 to 20 in increments of 2. The experiment was repeated over the energy range of 22–32 mJ, where ablation of the silicon surface was first observed when the total transmitted energy of all the reconstructed wavefront was 22 mJ. The total transmitted energy is used as a measurement because using the three separate compo-
Fig. 11. Graph of laser hole x-axis diameter as a function of the number of pulses for a transmitted energy of 29.7 mJ. The measured diameter only varies by an average of 20 nm per pulse over the range of pulses from 8 to 20.
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
nents of the CGH it was unreliable to estimate what percentage of the energy formed the real component. The x-axis and y-axis diameters of the laser holes were then recorded independently as a function of the number of pulses, where the x-axis values are shown in Fig. 10. The x-axis was chosen because the CGH was designed for the Gaussian distribution along the x-axis. Due to the elliptical shape of incident laser beam, data for the y-axis was similar but slightly less correlated. Here it can be seen that, at higher pulse energies or withahighernumberofpulses,thediametersofthelaserablated holes converges to a constant value. This behaviour is not what would be expected from a Gaussian distribution as defined in Eq. (5). For the holes that were machined with a transmitted pulse energy of 29.7 mJ, the measured diameter remains almost constant over the rangeofpulsesfrom8to20,asshowninFig.11.Overthis pulse range the diameter of the holes only varies by an average of 20 nm per pulse. Since the number of pulses used for machining defines the ablation threshold, and the ablation threshold defines the boundary of the observed laser holes, this implies that an almost constant diameter laser hole over a range of pulses would require a fluence distribution with the steep sides of a step profile at the diameter of the laser holes as shown in Fig. 4. However for holes machined with less then eight pulses the diameter decreases, as shown in Fig. 11. This may be due to a less-than-ideal top-hat shape in the laser pulse and some curvature at the centre of the modified beam.
5. Conclusion Based on the experimental results for the variation in the ablated diameter over a range of energies and pulses for a Gaussian distribution, it can be concluded that laser machining with a Gaussian fluence distribution does limit the lateral precision of the ablated boundary. With multiple pulse laser holes, each successive laser pulse results in a progressive increase in the diameter of the laser machined feature according to the absorption of energy as defined by the Gaussian profile. This process is characterised by the incubation parameter for the material, which defines the change in the ablation threshold in terms of the number of pulses used. Even when keeping the number of pulses constant and varying the pulse energy, it was observed
159
that the ablated diameter of the laser holes changes according to the Gaussian distribution. Therefore to fully realize the lateral precision of the femtosecond laser for machining, it is necessary to reshape the laser beam for a more uniform fluence distribution. Reshaping the laser beam for a more precise spatial distribution of energy was produced with a CGH that was designed to transform the Gaussian profile into a ‘‘top-hat’’ profile. The initial method described in this paper to physically create the CGH was achieved by using the femtosecond laser to machine the transmission profile onto a sheet of glass. However, this method does limit the spatial resolution of the holographic profile to the minimum feature size that the laser is able to machine. This restriction is easily solved for more complicated patterns requiring higher resolution, by projecting the computer generated image of the transmission profile onto a photographic film and then using the film to reconstruct of the original laser wavefront. With the reconstructed wavefront it was possible to observe the holographic real image in the form of a step fluence distribution, its conjugate image and the straight through beam. In principle, this technique can be used to transform the wavefront of a given laser beam into any other wavefront that can be mathematically defined and expressed in appropriate computer code. The primary difficulty with using a CGH to reshape the laser wavefront is that a large percentage of the pulse energy is lost in the process. To further optimise the transmission efficiency of the CGH, an antireflection coating for the 775 nm wavelength should be added and a better transmission medium for this wavelength could be used.
References [1] M.D. Shirk, P.A. Molian, A review of ultrashort pulsed laser ablation of materials, J. Laser Appl. 10 (1) (1998) 18–28. [2] W. Kautek, J. Kruger, Femtosecond-pulse laser ablation of metallic, semiconducting, ceramic, and biological materials, SPIE 2207 (1994) 600–611. [3] H. Varel, M. Wahmer, A. Rosenfeld, D. Ashkenasi, E.E.B. Campbell, Femtosecond laser ablation of sapphire: time-offlight analysis of ablation plume, Appl. Surf. Sci. 127–129 (1998) 128–133. [4] S. Nolte, C. Momma, H. Jacobs, A. Tunnermann, B.N. Chichkov, B. Wellegehausen, H. Welling, Ablation of metals by ultrashort laser pulses, J. Opt. Soc. Am. B 14 (10) (1997) 2716–2722.
160
E. Coyne et al. / Applied Surface Science 229 (2004) 148–160
[5] P.P. Pronko, S.K. Dutta, J. Squier, J.V. Rudd, D. Du, G. Mourou, Machining of sub-micron holes using a femtosecond laser at 800 nm, Opt. Commun. 114 (1995) 106–110. [6] J.E. Carey, C.H. Crouch, E. Mazur, Femtosecond-laserassisted microstructuring of silicon surfaces, Optics Photonics News, 02 (2003) 32–36. [7] Gambirasio, M. Bernasconi, L. Colombo, Laser induced melting of silicon: a tight-binding molecular dynamics simulation, Phys. Rev. B 61 (12) (2000) 8233–8237. [8] J. Bonse, J.M. Wrobel, J. Kruger, W. Kautek, Ultrashort-pulse laser ablation of indium phosphide in air, Appl. Phys. A 72 (2001) 89–94. [9] J. Bonse, S. Baudach, J. Kruger, W. Kautek, Femtosecond laser micromachining of technical materials, Proc. SPIE 4065 (2000) 161–172. [10] A. Rosenfeld, M. Lorenz, R. Stoian, D. Ashkensai, Ultrashortlaser-pulse damage threshold of transparent materials and the role of incubation, Appl. Phys. A 69 (1999) S373–S376.
[11] S. Rane, G. Cheriaux, S. Ferre, J.P. Chambaret, Importance of spatial quality of intense femtosecond pulses, Appl. Phys. B 70 (2000) S181–S187. [12] F.M. Dickey, S.C. Holswade, Gaussian laser beam profile shaping, Opt. Eng. 35 (11) (1996) 3285–3295. [13] J.R. Ledger, S. Makki, Z. Wang, Laser beam relaying with phase-conjugate diffractive optical element, Appl. Opt. 36 (20) (1997) 4749–4755. [14] K. Kanzler, Transformation of a Gaussian laser beam to an airy pattern for use in focal plane intensity shaping using diffractive optics, SPIE Proc. 4443-09 (2000). [15] E. Bricchi, J.D. Mills, P.G. Kazansky, B.G. Klappauf, Birefringent Fresnel zone plates in silica fabricated by femtosecond laser machining, Opt. Lett. 27(24) (2002). [16] G. Zhou, P.M. Fauchet, A.E. Siegman, Growth of spontaneous periodic surface structures on solids during laser illumination, Phys. Rev. B 10 (26) (1982) 5366– 5381.