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Microelectronics Reliability 47 (2007) 347–353

Thermal simulation of UV laser ablation of polyimide

Peter Gordon *, Balint Balogh, Balint Sinkovics

Budapest University of Technology and Economics, Department of Electronics Technology, Goldmann ter 3, 1111 Budapest, Hungary

Received 6 December 2005Available online 19 May 2006

Abstract

The aim of our research is to provide a simulation tool for manufacturing processes that takes the influence of temperature distribu-tion thus the underlying copper pattern and pulse repetition frequency into account. To establish such simulation software, a finite ele-ment model was set up which is able to describe the thermal processes and ablation induced by laser irradiation of polymers. The etchrate description usually applied for excimer lasers was slightly altered to be adequate for Gaussian lasers by writing pulse energy insteadof fluence. This theoretical consideration was proved by experiments. The experiments also revealed the temperature dependence of etchrate and the influence of pulse repetition frequency on the amount of ablated material. The experimental, analytical and simulationresults are in good agreement.� 2006 Elsevier Ltd. All rights reserved.

1. Introduction

Laser processing of polymers has been subject to exten-sive scientific research now for more than two decades. Thework has, however, still far not been completed. The inter-action of the laser beam and the polymer material is rathercomplex, while modeling always comes with simplificationof reality. Papers published on this discipline usuallydescribe only some specific aspects of the ablation processor investigate e.g. etch rate in the function of a processingparameter or side-effect. At the same time models incorpo-rate laser sources with completely different beam character-istics, as well as material properties also change type bytype.

Our modeling and simulation work basically originatesfrom industry-initiated process optimization projects. Asfeature sizes decrease in today’s high-density flexible sub-strates and there is constant need to increase the produc-tion speed, process windows of laser micromachining getcritically narrow. Especially pad and pitch sizes of the pat-terned copper layer and focal spot diameters are within thesame order of magnitude. This also means that the laser

0026-2714/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.microrel.2006.01.013

* Corresponding author. Tel.: +36 1 463 27 48; fax: +36 1 463 41 18.E-mail address: gordon@ett.bme.hu (P. Gordon).

beam exposes inhomogeneous areas and volumes, thusparameters of the process need to be adjusted in accor-dance with the specific structure. The final goal of our basicresearch is to determine an adequate model for laser-mate-rial interaction, and to integrate it into the process controlsoftware of industrial laser machining appliances.

This paper deals with the 355 nm UV Nd:YAG laserlight interaction with flexible polyimide substrates. Themain outcome expected from our model is etch rate inthe function of the beam parameters as well as materialproperties and structure of the patterned or processedlayers. The model is supposed to give answer for our appli-cation: industry needs to introduce lasers for direct pro-cessing of polyimide foils to achieve high resolutionpatterning and controlled ablation of the substrate [1]. Atthe same time the flexible substrate is a multilayer struc-ture: laminated and patterned copper areas increase thenumber of factors that influence the interaction by makingthe substrate inhomogeneous as far as its thermal conduc-tivity is concerned. We have described in our previouswork, that the underlying copper pattern influences theablation of the polymer layer so its effect has to be compen-sated [2]. Such compensation requires a simulation toolthat cannot only calculate the temperature distributioninduced by laser and affected by the multilayer structure,

348 P. Gordon et al. / Microelectronics Reliability 47 (2007) 347–353

but it also has to be able to reckon with the temperaturedependency of ablation.

Former studies on UV beam—polymer interaction werecarried out with excimer lasers, recent publications alsodeal with frequency tripled Nd:YAG lasers as these havebeen commercially available now for almost a decade.Models established with excimer lasers are now subject tovalidation experimentally outside the operation ranges ofexcimer lasers and new models are composed specificallyconcentrating on the beam properties of solid state lasers.Even though the wavelength and pulse duration of an exci-mer can be close to those of a frequency tripled Nd:YAGlaser, their pulse repetition frequency (PRF) is limited toa few hundreds per second and the energy distribution inthe beam is completely different, too.

Frequency tripled Nd:YAG lasers only appeared com-mercially in the last decade. Their advantages over excimerlasers are obvious as far as our application is concerned.Direct patterning of polyimides with this laser source is,however still a new field of application and needs its back-ground to be explored. So far only Yung et al. publishedtheir theoretical and experimental results on the thermalaspects of this interaction [3–5]. The Gaussian beam shape,the effect of other layers of the structure are just some ofthe factors that were not considered in their work. As fea-tures of the structures to be produced are comparable withthe spot size of the beam the above issues cannot beneglected. Thus our model does respect the Gaussian beamshape, as well as the cumulative heat effect of consecutiveshots as result of high (up to 100 kHz) PRF.

One can experience either photo-thermal or photo-chemical effects or even both at the same time [6], whilemany other side-effects could be considered, like plume,plasma formation [7,8] resulting complex shielding, acous-tic waves due to explosion-like processes causing mechani-cal impact and stress [9], different heat transfer methods,different material properties in function of temperatureand state of matter. Our model, however, does not considerthese factors at this state of the work. Laser shots are trea-ted as one-time direct energy transfers into the material, nomolecular dynamics (MD) level considerations [10] areimplemented.

2. Basic theory for modeling

The purpose of our research work is to obtain a modeland its constants that could be built into the control soft-ware of laser machining systems. The following chapterswill describe how we established and verified the basicequations of our model and what our methods were toset up and verify the constants of the model for single-pulseablation. A properly determined model is expected to resultin similar characteristics to what we experience in our realexperiments. A properly determined set of constants isexpected to provide accurate absolute values.

As we prepare our model to be able to handle multilayerstructures, we also need to consider cumulative heat effect

and ablation. This purpose initiates the use of temperatureas the most informative variable of our model. Dealingwith temperature distribution inside the material is less ofa problem, three main laws of temperature dissipationdescribe the process. Coupling the energy of the laser beaminto the material and transfer it to heat need, however,some more considerations. As mentioned in the introduc-tion our model does not neglect the Gaussian energy distri-bution of the beam. All effects that in a way decrease theenergy of the beam before it is absorbed by the material(e.g. plume formation, reflection, etc.) is considered in thecoupling efficiency factor, CEF.

The energy is then absorbed exponentially by the mate-rial the Lambert–Beer Law, and then transformed to heatby an efficiency factor we refer here to as TEF, transformefficiency factor. Please note that TEF gives a good estima-tion on the ratio of thermal and chemical (bond-breaking)processes that take place during the 355 nm ablation ofpolyimide.

The complete loss of converting the original energy of alaser shot to heat is taken into account as CEF * TEF,which is ETF, energy-to-temperature transformation effi-ciency factor. In the discussion session of this paper, it willbe explained how to determine ETF and Tth by matchingthe experimental and modeling results.

As far as ablation is concerned, scientific papers usuallymention Fth (threshold fluence) to define an expressionand value above which the material is ablated [11].Fth, however, does not consider the cumulative heat effectof consecutive shots. Thus we introduced Tth (thresholdtemperature) which we define as a temperature abovewhich the material is ablated. This way all important vari-ables that describe the process of heat accumulation andablation are temperatures. This is a method that was notpresented previously by other scientists.

In the following chapter, we will deduce temperature riseas function of the pulse energy. Then we will make ablationthreshold tests at different ambient temperature, to obtainthreshold energy values as the function of temperature.ETF will then harmonize the analytical and experimentalvalues.

3. Description of light energy transformation to heat

The energy density, fluence distribution of a Gaussianlaser beam can be written as

F ðx; y; zÞ ¼ F 0 � e� x2þy2

2r2 �a�z� �

; ð1Þwhere a is the absorption coefficient, x, y, z are the spacecoordinates, so that the origin is at the centre of the beamand axis z is perpendicular to the surface of the material.The first term in the exponent describes the Gaussiandistribution of the laser beam and the second comesfrom the Lambert–Beer Law of absorption. The parameterof width (r) comes from the minimal spot diameterequation:

Fig. 1. Laser drilled holes in PI (Eimp = 36 lJ, PRF = 50 kHz, burst1–26).

P. Gordon et al. / Microelectronics Reliability 47 (2007) 347–353 349

4r ¼ dmin ¼ 2:44fM2k

D; ð2Þ

where dmin is defined as the position, where the intensitydrops to 1/e2 and f is the focal distance, D is the beamdiameter, M2 is a beam quality parameter which is 1 forthe TEM00 Gaussian beam and k is the wavelength [14].

F0 is the fluence at the centre of the beam and it can becalculated from the pulse energy (Eimp):

F 0 ¼CEF � Eimp

2pr2. ð3Þ

Since the pulse energy is the definite integral of the fluenceover the whole surface and it had to be decreased by CEF,

CEF � Eimp ¼Z 1

�1

Z 1

�1F 0e�

x2þy2

2r2 dxdy ¼ F 02pr2. ð4Þ

The energy (E) in a finite element of volume (a3) can becalculated based on (1)

E ¼ F � a2ð1� e�a�aÞ; ð5Þthus the temperature rise in a finite element of volume (a3)can be calculated by

DT ¼ TEF � Ecq � a3

; ð6Þ

where c is the specific heat capacity, q is the density andTEF was described previously. Its value is 0 if the ablationprocess is totally photo-chemical and 1 if the ablation issimply a photo-thermal process. At 355 nm laser ablationof polyimide both phenomena take place and their ratiois not known yet. If (3) is substituted in (6) the highest tem-perature rise can be calculated by the following expression:

DT max ¼ETF � Eimpð1� e�a�aÞ

2pr2cq � a ð7Þ

and if a is infinitesimally small it can be written as

DT max ¼a!0

ETF � Eimpa2pr2cq

. ð8Þ

As it will be described below the ablation rate was mea-sured at different substrate temperatures. The thresholdenergy (Eth) can be determined from these measurementsas the intersection point of the curve and the abscissa. IfEth is substituted in (8) and the calculated temperature riseis added to the initial temperature of the substrate (Tsub)then we get the ablation threshold temperature.

T th ¼ T sub þ DT max. ð9ÞThe final value of Tth depends highly on ETF. The purposeof measuring the ablation rate at different substrate tem-peratures is to find the right ETF value when the differencebetween the maximal temperature rises at different Eth arein accordance with the substrate temperature differencesthus Tth is constant.

ETF and Tth are the main constants of our model andare the main input values of our simulation. As mentionedabove our main goal is to set up a model with its constants

to be able to establish a simulation tool which is also capa-ble of handling multilayer structures, adjustable pulseparameters and moving laser spot.

4. Experimental

The experiments were carried out by a Coherent AVIA355-4500 frequency tripled, Q-switched Nd:YAG laser.The laser has a built in thermal lens compensation calledThermaTrack. The length of the resonator is optimized ateach pumping diode current—PRF pair to obtain the high-est output power and best beam quality. This means thatthe beam diameter and the energy distribution of the beamcan be considered independent from the pumping currenti.e. the pulse energy.

Positioning of the samples was realized by two PI trans-lation stages and the precise focal setting by a third one.The deflection of the beam was accomplished by a Razor-scan-10 galvo scan head, which uses an f-theta lens with100 mm focal length. The most important parameters ofthe laser system are

– wavelength: 355 nm,– beam diameter at 1/e2: 3.5 mm,– max. PRF: 100 kHz,– pulse length: 20–35 ns (depending on PRF and pumping

current),– max. pulse energy: 300 lJ,– min. spot diameter: �30 lm.

The base material of the test specimens was a polyimidefoil (UpilexTM) of 25 and 75 lm thickness, respectively.The optical inspections were accomplished by an OlympusBX-51 optical microscope, which has a maximal magnifica-tion of 1000.

The etch rate, i.e. the ablated depth per pulse, was deter-mined by drilling holes into a 25 lm thick polyimide(UpilexTM 25S) foil with bursts ranging from 1 to 30 shots,as it can be seen on Fig. 1. So the etch rate could be

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

experimental @186 oC

1 /α ln(E/E0) α=1 .4 μm-1 E0=1 .3μJ

Etch

rate

[µm

]

Pulse energy [μJ]

1 10

Fig. 4. Experimental etch rate and fitting curve at 186 �C and 50 kHzPRF. Eth = 1.3 lJ.

350 P. Gordon et al. / Microelectronics Reliability 47 (2007) 347–353

calculated by dividing the thickness of the foil by the lowestburst where it was perforated. The higher the etch rate themore inaccurate this method is, since the measuring errorcan be written as

e ¼ tb� 1

� tb¼ t

b2 � b; ð10Þ

where e is the error (the uncertainty of the etch depth perpulse), t is the thickness of the material and b is the lowestnumber of pulses at which perforation occurred.

5. Results

The etch rate dependence on pulse energy was measuredby the above described method. The PRF was 50 kHz andholes were drilled by pulse energies ranging from 5 to 61 lJ.In Fig. 2 the results of an experiment carried out at roomtemperature can be seen. Figs. 3 and 4 show how the etch

1 100.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

experimental @ 25 oC

1/αln(E/E0) α=1.4μm-1 E0=1.8 μJ

Etch

rate

[µm

]

Pulse energy [μJ]

Fig. 2. Experimental etch rate and fitting curve at 25 �C and 50 kHz PRF.Eth = 1.8 lJ.

1 10

1/αln(E/E0) α=1.4μm-1 E0=1.5μJ

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

experimental @ 110 oC

Etch

rate

[µm

]

Pulse energy [μJ]

Fig. 3. Experimental etch rate and fitting curve at 110 �C and 50 kHzPRF. Eth = 1.5 lJ.

rate increases if the polyimide foil is heated up to 110 �Cand 186 �C. Please note that the pulse energy is scaledlogarithmically on all graphs. The error bars growing lar-ger at higher pulse energies because of the lower burstneeded to drill through the whole foil means higher uncer-tainty (see Eq. (10)).

The etch rate of excimer lasers can be calculated by

d ¼ 1

aln

FF th

; ð11Þ

where d is the etch depth per pulse, F is the laser fluence(energy over area) and Fth is the ablation threshold[11,12]. The nearly homogeneous energy distribution ofexcimer lasers permits the use of fluence. However thereis little use to talk about fluence in general related to theGaussian beam of Nd:YAG lasers. There the fluence ofinfinitesimally small areas can be defined and it dependson the position of these areas. However since the quotientin the argument of the logarithm is dimensionless it is rea-sonable to write pulse energy over threshold energy in caseof Gaussian beams.

d ¼ 1

aln

EEth

. ð12Þ

To be able to fit the curves the absorption coefficient (a)had to be taken 1.4 lm�1. This value is slightly lower thanthe 2 lm�1 which can be found in [3]. Eth is given as theintersection point of the fitting curve and the axis ofabscissa. At 25 �C the threshold energy is 1.8 lJ while at110 �C it drops to 1.5 lJ and to 1.3 lJ at 186 �C. It meansthat the same laser pulse energy will result in more ablatedmaterial if the initial temperature of the substrate is ele-vated (see Fig. 5).

Eq. (12) describes precisely enough the ablated depth atrelatively low pulse energies. As it can be seen the fittingcurves are within the measuring error at low pulse energiesboth at room and elevated temperatures; however the 49and 61 lJ points are slightly above the theoretical curves

0.0

0.5

1.0

1.5

2.0

2.5

3.0

186 oC

110 oC

25 oC

Etch

rate

[µm

]

Pulse energy [μJ]

1 10

Fig. 5. Comparison of ablation rates at different substrate temperatures.

00 10 20 30 40 50

1

2

3

50kHz1kHz

Etch

rate

[µm

]

Pulse energy [μJ]

Fig. 6. Etch rate at 50 kHz and 1 kHz PRF.

P. Gordon et al. / Microelectronics Reliability 47 (2007) 347–353 351

in all three cases. A plausible explanation can be that thereis a break-point in material properties at high pulse ener-gies. To prove this theory it would have been necessaryto investigate how the etch rates evolve at higher pulseenergies, but 61 lJ was the highest pulse energy of our laserat 50 kHz, so such experiments could not been carried out.

6. Modeling the temperature distribution between

consecutive shots

In the basic theory section, the mode of energy conver-sion to heat was described. After the ablation is over theresidual heat will be dissipated by three modes (conduction,radiation, and transfer). This is how cells in our finite ele-ment simulation communicate with each other.

Thermal conduction is described by the Fourier law:

q ¼ k � A � gradT ð13Þwhere q is the heat flow, k is the thermal diffusivity, A is thearea.

Radiation, according to the Stefan–Boltzmann law isproportional with the fourth magnitude of temperature:

q ¼ e � r0 � T 4; ð14Þwhere e is the coefficient of radiation, r0 is the black bodyconstant. Heat transfer can be calculated according to (15),where aht is the heat transfer coefficient.

q ¼ aht � A � ðT body � T ambientÞ. ð15ÞThe model equations are applied to describe the thermal

processes induced by laser ablation. Our aim is to be ableto simulate laser manufacturing processes such as via dril-ling or large area scanning. To be able to obtain resultswithin a reasonable computation time the processes thatoccur during the few nanoseconds of laser pulse durationare not simulated. The laser pulse is considered to transmitits energy in a single time unit. The effects that take placeduring the ablation process, such as plasma shielding aretaken into account only on macroscopic scale and besidesheating energy also has photo-chemical effect, so less than

100% of the pulse energy is turned into heat. This is whatwe call energy-to-temperature transformation efficiencyfactor (ETF). The amount of ablated material is calculatedso that those material parts are considered to be ablatedwhere the temperature would increase above a certainthreshold. This threshold temperature description canqualitatively describe the PRF and substrate temperaturedependency of etch rate as it was published in our previouspaper [13].

The volume of material that is exposed by to laser irra-diance lower than the ablation threshold is not removedbut heated up. After the few nanosecond laser pulse is overthe residual material starts to cool down until the followingpulse. The time between consecutive shots equals to thereciprocal of PRF, thus the higher the PRF the shorterthe time the material has to cool down. As it has beenshown in Fig. 5 the elevated temperature results in higheretch depth, so it can be expected that the higher the PRFthe higher the etch rate is. Fig. 6 shows the results of anexperiment where the etch rate at 1 kHz and at 50 kHzare compared.

It can be clearly seen that the etch rate at 50 kHz ishigher than at 1 kHz. The elapsed time after the laser irra-diation is 0.02 ms and 1 ms at 50 kHz and 1 kHz, respec-tively. Thermal simulations have shown that temperaturedrop on the surface during this period is more than100 �C (see Fig. 7). This magnitude of temperature differ-ence can cause the variation in ablated depth as we couldsee in Fig. 5. It is not possible to deduce the frequencydependency of etch rate from the results of the simulationand the temperature dependent etch rate measurements atthis stage, since during the experiments the temperaturedependency was induced by elevating homogeneously theinitial temperature of the substrate. The frequency depen-dency can only be described by an inhomogeneous temper-ature distribution as can be seen in Fig. 7.

At the moment the complexity of our simulation toolenables to calculate the surface profile formed by punchingas it is demonstrated in Fig. 8.

0 2 4 60

100

200

300

400

500

10-5s

10-4s

10-3s

10-2s

10-1s

100s

Tem

pera

ture

[o C]

Depth [µm]

Fig. 7. Temperature of PI 10 ls–1 s after a single 10 lJ laser pulse, in themiddle line of the laser spot, perpendicular to the surface.

Fig. 8. Simulated surface profile of 10 lJ laser pulses.

Table 1Approximation of ETF based on temperature dependent etch ratemeasurements

Eth

(lJ)Tsub

(�C)ETF = 1 ETF = 0.132 ETF = 0.176

DTmax

(�C)Tth

(�C)DTmax

(�C)Tth

(�C)DTmax

(�C)Tth

(�C)

1.8 25 3866 3891 510 535 680 7051.5 110 3222 3332 425 535 567 6771.3 186 2792 2978 368 554 491 677

352 P. Gordon et al. / Microelectronics Reliability 47 (2007) 347–353

The previously described cumulative heat effect can beobserved on the simulation results. The diameter of theablated area increases shot by shot, even though the diam-eter of the focal spot is constant. The next step is to imple-ment a moving laser spot into our simulation so that wewill be able to calculate etch rates and surface profiles gen-erated by scanning or spiralling. The effect of the underly-ing copper pattern on the temperature distribution of thepolymer layer can be simulated.

7. Discussion

The experiments have proved that the higher the initialtemperature of the substrate the lower the ablation thresh-old energy is. If we substitute the 1.8, 1.5 and 1.3 lJ thresh-old energies in (8) we get the highest temperature rise in thematerial. In order to obtain the same ablation rates by sim-ulation as we observed in the experiments Tth has to bechosen in a way that the value of this maximal temperaturerise has to be added to the initial temperature of the sub-strate (see Table 1).

If ETF is considered to be 1 then the maximal tempera-ture rises are too high and they do not commensurate withthe temperature differences of the substrate. The 85 �C dif-ference between 1.8 and 1.5 lJ of Eth is observed betweenDTmax values if ETF is 0.132. In this case, the ablationthreshold temperature (Tth) is 535 �C, however, it is554 �C at 1.3 lJ. If ETF is 0.176 than the 76 �C substratetemperature difference is reflected between the maximaltemperature rise values at 1.5 and 1.3 lJ and Tth is677 �C in this case.

Based on the result it can be stated that ETF is between0.132 and 0.176, since in first case the temperature depen-dency of the etch rate between 25 and 110 �C, in the secondcase between 110 and 186 �C is presented correctly. Theinaccuracy of the experimental method and the littleamount of results did not let us to determine this factormore precisely, however it is already in good correlationwith the expected empirical results.

8. Conclusions

The etch rate of UV Nd:YAG lasers can be described bythe expression (12), which is similar to the equation used forthe description of excimer laser ablation (11). The differenceis that since fluence is hardly applicable for Gaussianbeams, in the argument of the logarithm quotient of pulseenergy and energy threshold is written instead of fluenceand fluence threshold. Our experiments proved that (12)describes the ablation process precisely if the pulse energyis below 49 lJ, however the reason of why the measureddata for high pulse energies are higher than expected needsfurther investigation.

The experiments have also shown that the ablation rateincreases if the initial temperature of the substrate is ele-vated. The results can formally be described by the temper-ature dependent threshold energy, which is 1.8, 1.5 and1.3 lJ at 25, 110 and 186 �C, respectively. In order to elim-inate this temperature dependent factor from the descrip-tion of the ablation process the ablation thresholdtemperature (Tth) was introduced.

The correlation between the ablation threshold energyand temperature was deduced analytically. SubstitutingEth in (8) the maximal temperature rise added to the initialsubstrate temperature formally results in Tth. However toobtain a physically correct value of Tth, ETF, the maininfluencing factor, has to be determined empirically.

P. Gordon et al. / Microelectronics Reliability 47 (2007) 347–353 353

An experimental method based on temperature depen-dent etch rate measurements has been developed to deter-mine ETF and Tth. Based on the results it can be statedthat ETF is between 0.132 and 0.176 while Tth is between535 and 677 �C.

Our model that incorporates Tth as the ablation thres-hold parameter instead of Fth has been verified bysimulation.

Having Tth as a characteristic parameter of the specificpolyimide material a more sophisticated simulation toolwill be developed, covering moving laser spot and pat-terned multilayer structures. The outcome of the simula-tion will then be compared to experimental results. Goodcorrelation would prove our basic theory. Poor correlationwill induce the consideration of neglected side-effects in themodel.

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