Knudsen layer formation in laser induced thermal desorption
Akihiko Ikeda, Masuaki Matsumoto, Shohei Ogura, Tatsuo Okano, Katsuyuki Fukutani
aa r X i v : . [ c ond - m a t . m t r l - s c i ] M a r Knudsen layer formation in laser induced thermal desorption
Akihiko Ikeda, a) Masuaki Matsumoto, Shohei Ogura, Tatsuo Okano, and Katsuyuki Fukutani b) Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo, 153-8505,Japan (Dated: 8 October 2018)
Laser induced thermal desorption of Xe atoms into vacuum from a metal surface following the nano-secondpulsed laser heating was investigated by the time-of-flight (TOF) measurement. The desorption flow wasstudied at a wide range of desorption flux by varying the initially prepared Xe coverage Θ (1 ML = 4 . × atoms/m ). At Θ = 0 . > . T D and a stream velocity u . With T D fixed at 165 K, u was found to increase from 80 to 125 m/ s with increasingΘ from 1.2 to 4 ML. At Θ > u become constant at 125 m/ s. The converging feature of u was found to be consistent with analytical predictions and simulated results based on the Knudsen layerformation theory. We found that the Knudsen layer formation in laser desorption is completed at Knudsennumber Kn < . I. INTRODUCTION
Laser induced desorption of atoms and moleculesfrom solid surfaces is a vital phenomenon to investi-gate fundamentals such as surface electronic structuresand dynamics.
Besides, laser desorption is an essentialtechnique for pulsed laser deposition used in thin filmgrowth and mass spectrometry of protein employ-ing matrix-assisted laser desorption ionization. Whendesorption flux is small, the velocity distribution of des-orbed atoms is directly governed by the desorption mech-anism. When the desorption flux is large enough, on theother hand, the post-desorption collision between des-orbed particles may become significant and modify thevelocity distribution in the vicinity of the surface afterthe desorption.Manifestations of the collision effect in laser induceddesorption have been reported both by experiments andsimulations as the modifications of the angular and ve-locity distribution of desorbing atoms and molecules.
Cowin et al. investigated the angular dependence of thetranslational temperature of D desorbed from tungstensurfaces under a pulsed laser irradiation. The trans-lational temperature of D desorbed in the surface nor-mal direction was higher than those in oblique directions.They attributed the variation of the translational tem-perature to the collision effect. Noorbatcha et al. usedthe direct Monte Carlo simulation of desorbing atomsto investigate the collision effect. They showed thateven in the sub-monolayer regime the collision notice-ably modifies the final angular, velocity and rotational-energy distributions. However, there has not been a) E-mail: [email protected] b) E-mail: [email protected] any model that can quantitatively estimate the degreeof modification by the post-desorption collision in laserdesorption so far.Knudsen layer formation theory has been developedin rarefied gas dynamics to model the steady flow ofthe strong evaporation from the surface.
As shownin Fig. 1, the initial velocity distribution of thermallydesorbed species at the surface is well described by a
Surface Knudsen layer
T v z S T v z K u (a)(b) FIG. 1. (a) A schematic sketch of the Knudsen layer formedabove the surface following the laser induced thermal des-orption. The desorption flux is assumed to be large enoughfor the post-desorption collisions to take place and to furtherform the Knudsen layer. The arrows denote the velocity vec-tors of desorbed atoms at the surface and at the end of theKnudsen layer. (b) Schematic plots of the velocity distribu-tion of the desorbed atoms in the z (surface normal) directionat the surface and at the end of the Knudsen layer. T S , T K and u denote the surface temperature, the translational tem-perature of the desorbed atoms at the end of the Knudsenlayer and the stream velocity, respectively. ”half-range” Maxwell-Boltzmann velocity distribution. In the Knudsen layer theory, as a result of intensive post-desorption collisions, the half-range velocity distributionat the surface is thermally equilibrated to a full-rangeMaxwell-Boltzmann velocity distribution with a streamvelocity at some distance from the surface. This thermal-ization layer is defined as the Knudsen layer. The theoryanalytically predicts for monoatomic gas that the ratioof the translational temperature at the end of Knudsenlayer T K to the surface temperature T S and the Machnumber of the desorption flow at the end of the Knudsenlayer become 0.65 and 1.0, respectively. Kelly and Dreyfus discussed that the Knudsen layerformation theory may be applicable to the pulsed des-orption flow with a large desorption flux. However, itis not straightforward because the pulsed desorption in-volves complex time evolution of the density and velocitydistributions of desorbed atoms. Sibold and Urbassekhave shown by means of the Monte Carlo simulation ofthe Boltzmann equation that the pulsed desorption flowat an intense flux is well characterized by the above val-ues predicted by the Knudsen layer formation theory.Although previous experimental studies recognized thecollision effect in laser desorption, the formation ofthe Knudsen layer in laser desorption has been discussedonly by theory and simulations.
So far, any exper-imental confirmation of Knudsen layer formation in laserdesorption has not been presented. For an experimen-tal verification of the theory, a systematic observation ofthe translational temperature and stream velocity of thedesorption flow as a function of the desorption flux isstrongly required.In the present paper, we investigated the laser inducedthermal desorption (LITD) of Xe from an Au(001) sur-face by means of the time-of-flight (TOF) measurementas a function of the wide range of desorption flux byvarying the initial Xe coverage Θ. We found that at Θclose to 0 ML, the TOF was well analyzed by a Maxwell-Boltzmann velocity distribution. Hence, the desorptionat Θ close to 0 ML is rationalized by the thermal des-orption followed by the collision-free flow. At Θ close tomonolayer, we observed that the peak positions of theTOF spectra shift towards smaller values. Assuring thatthe desorption is only thermally activated, we regard thismodification of the TOF as the manifestation of the col-lision effect. At larger Θ, the peak positions of the TOFspectra become constant. We deduced the Mach number M of the desorption flow to be 0.96 at large Θ under theassumption that T K /T S = 0 .
65. The obtained value of M and the saturating behavior of u at Θ > Substrate on a cold headQMS PD LaserTriggerOscilloscope
Lens ApartureBS
C. Amp.
FIG. 2. A schematic drawing of the experimental setup for thetime-of-flight measurement of Xe following the laser inducedthermal desorption from Au surfaces. C. Amp., PD and BSdenote fast current amplifier, photo diode and beam splitter,respectively.
II. EXPERIMENT
The Au specimen and the physisorbed Xe layers wereprepared in the following manner. An Au disk with 001orientation was cut out from a single-crystal rod and waschemically and mechanically polished. The Au disk wasput into an ultra high vacuum (UHV) chamber with abase pressure of 2 × − Pa. The sample surface wascleaned by several cycles of Ar + sputtering and anneal-ing at 700 K in the UHV by the electron bombardment.The cleanliness of the specimen was confirmed by theobservation of a clear reconstructed (5 ×
20) pattern bylow-energy electron diffraction and no contamination inthe Auger electron spectrum. The sample temperaturewas monitored with a Chromel-Alumel type thermocou-ple directly spot-welded to the side of the Au disk. Thedisk was cooled down and kept at 23 K by a closed-cycleHe compressor type refrigerator during all LITD experi-ments.The Xe gas was dosed onto the Au surface by back-filling the chamber. The Xe coverage Θ was monitoredby the LITD yield. The LITD yield showed a linear de-pendence on the Xe exposure in the present experimentalcondition. The saturation coverage at the sample tem-perature of 80 K was defined to be 1 ML = 4 . × atoms/m as in Ref. 31. Θ was varied by varying thedosage of Xe gas onto the Au surface. We note thatthe desorption flux is defined as Θ devided by the meandesorption period τ . On the basis of the result employ-ing the LITD simulation, τ was shown to be constant atabout 4 ns at Θ concerned in the present study. Hence,the desorption flux can be varied by varying Θ.The TOF measurement of the LITD of Xe from an Ausurface was carried out in the following manner. The ex-perimental setup is schematically shown in Fig. 2. AnArF excimer laser (Lambda Physik) was used as a pulsed
30 1.00.50.0 Time of Flight (ms) Θ = 0.3 ML20100 Θ = 1.7 ML100500 Θ = 6.7 ML3002001000 Θ = 10 ML Exp. Shifted M-B----- M-B I n t en s i t y ( A r b . un i t s ) FIG. 3. Time-of-flight (TOF) spectra of Xe from Au surfacesfollowing pulsed laser irradiations. The Xe coverage Θ are10, 6.7, 1.7 and 0.3 ML from top to bottom, respectively.The dashed curves and the solid curves are the Maxwell-Boltzmann (M-B) velocity distribution and the shifted M-Bvelocity distribution fitted to the experimental results, respec-tively. The vertical dashed line and the arrows indicate thepeak position of each spectrum. laser source. The wavelength was 193 nm and the timeduration was 8 ns. The incidence angle was 25 ◦ fromthe surface normal direction. The irradiated area on thesample disk was ∼ . The laser pulse was guidedon to the surface through an aperture and a quartz win-dow. The laser power absorbed by the sample was fixedat 80 mJ/cm in all experiments taking the reflectivityinto consideration. At this laser power absorbed by thesample, the LITD of Xe is the dominant desorption pro-cess as shown in Ref. 32. The reflected light escapesthe UHV chamber through another quartz window. Aquadrupole mass spectrometer (QMS: Balzers QMA125)was placed in the surface normal direction at a distanceof 10 cm from the Au specimen. The QMS was tunedfor a high-sensitive detection of Xe with a low mass se-lectivity. The ion current of the QMS was amplified witha fast current amplifier (Keithley 427) and sent to an os-cilloscope (Tektronixs: TDS620B). The desorption of Xefrom the Au(001) surface was induced with only one laserpulse in each LITD experiment. The respective TOF was u ( m / s ) Θ (ML) FIG. 4. The stream velocity u of the desorbed Xe atomsfrom Au surfaces following the pulsed laser irradiations as afunction of the Xe coverage Θ. The data are obtained by an-alyzing the time-of-flight spectrum with the shifted Maxwell-Boltzmann velocity distribution. The solid line is a guide foreyes. u become constant at above 4 ML which is denoted bythe arrow. recorded using the oscilloscope with a single acquisitionmode. III. RESULTS
We obtained a series of TOF spectra of desorbed Xefrom Au surfaces following pulsed laser irradiation asshown in Fig. 3. The TOF spectrum of Xe from theAu surface at Θ = 0 . J ( v ) dv = Av exp (cid:18) − mv kT D (cid:19) dv, (1)where m , k and v are the mass of a Xe atom, the Boltz-mann constant and the velocity of Xe atoms, respec-tively, and A and T D are fitting parameters. In theanalysis, we convert Eq. (1) to a TOF function forthe density sensitive detector, which results in the form f ( t ) dt = at − exp( − bt − ) dt . By fitting Eq. (1) to theTOF of Xe at Θ = 0 . T D of 255 K asillustrated by the dashed curve at the bottom of Fig. 3.At the top and middle of Fig. 3, the TOF spectraof desorbed Xe at Θ = 10 to 1.7 ML are shown. Wenote that the peak positions of those TOF spectra, whichare indicated by the arrows, are shifted towards smallervalues with increasing Θ compared with that of Θ = 0.3ML. It was found that the peak positions of the TOFspectra become constant at about 0.34 ms at Θ ≥ . IV. DISCUSSIONA. Desorption mechanism
We first discuss that the observed desorption proceedsonly via thermal activation. In the previous study, weinvestigated the same system by varying the photon flu-ence at Θ = 1 ML. At the small fluence region wherethe laser power is below 20 mJ/cm , we observed a des-orption of Xe only at a photon energy of 6.4 eV and nodesorption at 2.3 eV. We assigned this photodesorptionas a non-thermal desorption via a transient Xe − forma-tion. At a large fluence region where laser power exceeds60 mJ/cm we observed, on the other hand, that thermaldesorption is the dominant desorption process regardlessof the photon energy. These observations are confirmedby comparing the experimentally observed T D and Xedesorption yield with the results of LITD simulations.Therefore, we regard that the initial desorption is onlythermally activated in the present experiment. B. Analysis of TOF spectra
In order to analyze the TOF spectra at Θ > . u . Generally, the ve-locity distribution in a desorption flux shows an angulardistribution and is expressed by the elliptical distribu-tion which involves an angular dependent translationaltemperature as described in Ref. 34. In the present ex-periment, the detector was fixed in the surface normaldirection. Therefore, the translational temperature onlyin this direction is detected in the present experiment.In this case, the shifted Maxwell-Boltzmann velocity dis-tribution in a flux from a thermal source is expressedas, J ( v ) dv = Av exp (cid:26) − m ( v − u ) kT D (cid:27) dv. (2)Under the condition of u = 0, Eq. (2) is identical to Eq.(1). In the analysis, Eq. (2) was also converted to a TOFfunction for the density sensitive detector.The TOF spectra at Θ > . T D and u . The spectra were well repro-duced with an arbitrary value of T D from 165 to 310 K byadjusting u from 125 to 0 m/s. We note that, with a fixedvalue of T D between 165 and 310 K, the obtained value of u monotonically increases with increasing Θ from 0.3 to4 ML and becomes constant at Θ > T D fixed at 165 K, of which the fitting curvesare shown as solid curves in Fig. 3. C. Moderate desorption at Θ ≃ ML At Θ ≃
0, the observed feature of the TOF can berationalized with a model employing thermal desorptionfollowed by collision-free flow. At the instance of thermaldesorption, the desorbed Xe gas is in thermal equilibriumwith the surface at the temperature T S . Here, it is rea-sonable to consider the half-range Maxwell-Boltzmannvelocity distribution for desorbed Xe expressed as f ( v ) d v = A exp (cid:18) − m v kT S (cid:19) d v ,v z > A and v are a normalization factor and the velocityvector of Xe atoms in the Cartesian coordinate, respec-tively. We note that in Eq. (3) the velocity componentin the z direction has a distribution only at v z > assuming the z axis to be the surface normal direction.Given the desorption period is much shorter than theflight time and the irradiation diameter is much smallerthan the flight distance, Eq. (3) can be, as a velocity dis-tribution in a flux from a thermal source, transformed tothe same form as Eq. (1). Thus, we notice that T D = T S at Θ ≃ For a qualitative analysis, we estimated the surfacetemperature during the present LITD experiment usingthe first order desorption rate equation, assuming thatthe desorption activation energy is 240 meV and thatthe desorption period is 4 ns. The calculated resultsshow that the required surface temperature is 260 K,which is in good agreement with the obtained value of T S = 255 K at Θ = 0 . ≃
0, in good accordance with the results by Cowin and Wedler . D. Intensive desorption at Θ > ML At Θ > Several the-oretical studies have speculated that the so-called Knud-sen layer is formed in the vicinity of the surface as a resultof collisions.
As schematically drawn in Fig. 1,in the Knudsen layer model, the initial velocity distri-bution is in thermal equilibrium with the surface at T S except that there is no distribution at v z < z = 0 be-comes thermally equilibrated at some distance from thesurface to a full-range Maxwell-Boltzmann velocity dis-tribution with a stream velocity u . The model alsorequires that, at the end of the Knudsen layer, the tem-perature of the flow becomes identical ( T K ) in all degreesof freedom. Hence, at the end of the Knudsen layer, the TABLE I. Mach number M obtained in the present studyand previously reported values by simulation and theory onthe Knudsen layer.Method M ConditionExperiment a a Present study velocity distribution may be described as f ( v ) d v = A exp " − m { v x + v y + ( v z − u K ) } kT K d v , (4)where v i , u K and T K are the velocity component in theCartesian coordinate, stream velocity and the tempera-ture at the end of the Knudsen layer, respectively. Un-der the condition that the flight distance is sufficientlylonger than the thickness of the Knudsen layer besidesthe conditions described above, Eq. (4) is converted, asa velocity distribution from a thermal source, to the iden-tical form to Eq. (2). Thus, we see that T D = T K and u = u K at Θ > > u ,indicates that the experimental result at Θ > E. Mach number of the flow
We further examine the results at Θ > u K withprevious theoretical reports on Knudsen layer forma-tion in the steady strong evaporation and the pulseddesorption from plane surfaces. We compare u K interms of the Mach number M at the end of the Knudsenlayer. M is defined as M = u K c = u K r mγkT K , (5)where c and γ are the local velocity of sound and theheat capacity ratio of the gas, respectively, the latter ofwhich is 5/3 for monoatomic gas as in the present case.Ytrehus and Cercignani formulated M and T K /T S by finding a solution to the Boltzmann equation underthe Knudsen layer formation model assuming the con-servation of the particle number, momentum and the en-ergy flux between the surface and the end of the Knudsenlayer. Sibold and Urbassek estimated M and T K /T S us-ing the Monte Carlo simulation of the Boltzmann equa-tion in one-dimension for both pulsed flow and steadyflow conditions. Those reports have stated that at theend of the Knudsen layer, M should always be close tounity and that T K /T S is at around 0.65. As discussed in IV. B, it was difficult to unambiguouslydetermine the value of T D . Here, we assume the relationof T K /T S = 0 .
65 following the theoretical studies andevaluate the Mach number. With the value of T S = 255K, we obtain the value of T K to be 165 K. With T K = 165K and Eq. (5), we obtain the value of M to be 0.96. Ascan be seen in Table I, the previously reported valuesof M show a quantitative agreement with the obtainedvalue of M in the present study. This indicates that theobserved trend of u at Θ > With adiabatic expansion, M should well exceedunity. We note that we observed the saturationof M at around unity at Θ > u at Θ > F. Knudsen number of the flow
In order to generalize the present result, we tentativelyconsider mean gas density ¯ n , mean free path λ and Knud-sen number Kn in the vicinity of the surface at the mo-ment of desorption as a function of Θ. Kn is definedby Kn = λl z = 1 √ nσl z , (6)where l z and σ are the representative length of the systemand the Van der Waals collision cross section of Xe (1 . × − m ), respectively.Here, we simply regard that l z is the mean thicknessof the gas cloud above the surface. It, then, reads that l z = ¯ v z τ , where ¯ v z is the mean thermal velocity of des-orbed Xe in the z direction and τ is the mean desorptionperiod. We further take ¯ v z = p kT S /πm and estimatethat ¯ n = Θ /l z . By substituting ¯ n in Eq. (6), we obtaina simple relation Kn = a/ ( √ a are the relative coverage ˜Θ = Θ / Θ S withthe monolayer saturation coverage Θ S and the ratio ofthe area occupied by an atom at Θ S to σ described as a = 1 / ( σ Θ S ), respectively.Now, we see that Kn depends simply on ˜Θ and a .Therefore, we can discuss the required condition for theformation of Knudsen layer in LITD for general systemsin terms of Kn. We fixed τ = 4 ns. On the basis of theresult employing the LITD simulation, τ showed littledependence on Θ in the region concerned in the presentstudy.In Table II, we summarized the obtained ¯ n , λ and Knas a function of Θ. Kn can also be understood as aninverse of mean collision times per each atoms. In thepresent study, we observed the formation of the Knudsenlayer at Θ > < ∼ . TABLE II. Mean gas density ¯ n , mean free path λ and Knud-sen number Kn in the vicinity of the surface at the momentof laser desorption as a function of Θ.Θ (ML) ¯ n (10 atoms/m ) λ (nm) Kn0.3 3.3 2114 5.24.0 45 159 0.3910 111 63 0.16 manifestation of collision effects is observed at Θ > . > .
2. The results coin-cide with the previous theoretical work by Sibold andUrbassek that the Knudsen layer is formed at Θ = 2 . .
25 ML, respec-tively. The obtained values of Kn also agree well with theprevious experimental observation of the collision effectin LITD of D /W at Θ = 1 ML reported by Cowin etal. . They also coincide with the theoretically estimatedcollision number of 2.9 per atom at Θ = 1 ML reportedby Noorbatcha et al. . Lastly, we note the observed feature at Θ ≃ ≃ al-though any analytical formulation for the flow at Θ ≃ ≃ V. CONCLUSION
In conclusion, we observed the TOFs of Xe from aAu(001) surface by LITD at a wide range of Θ. AtΘ ≃ . > . > u under the as-sumption that T K /T S = 0 .
65 became constant at around125 m/s, which corresponds to M = 0 .
96, being in goodagreement with the prediction by the Knudsen layer for-mation theory. In the LITD experiment, we found thatthe collision effect already appears at Kn ≃ . < .
39, which cor-responds to a mean collision number of greater than 2.6per atom for general systems.
ACKNOWLEDGMENTS
This work was supported by Grant-in Aid for Scien-tific Research (A) of Japan Society for the Promotion ofScience (JSPS). A. I. acknowledges support from a Re-search Assistant of Global COE Program ”The PhysicalSciences Frontier”, MEXT, Japan and TEPCO MemorialFoundation. H.-L. Dai and W. Ho,
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