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Received 20 October 1999; accepted 24 January 2000. In this article we present a novel method for absolute quantification of the flux and angular distribution of ...
Novel method for absolute quantification of the flux and angular distribution of a radical source for atomic hydrogen T. Schwarz-Selinger,a) A. von Keudell, and W. Jacob Max-Planck-Institut fu¨r Plasmaphysik, EURATOM Association, D-85748 Garching, Germany

共Received 20 October 1999; accepted 24 January 2000兲 In this article we present a novel method for absolute quantification of the flux and angular distribution of a beam source for atomic hydrogen or atomic deuterium. It is based on quantitative determination of the erosion of an amorphous, hydrogenated carbon 共a-C:H兲 film. A heated tungsten capillary serves as the radical source. Atomic hydrogen is produced in this capillary by thermal dissociation of hydrogen molecules. A large-area a-C:H film is exposed to the source at a substrate temperature of 650 K. Interaction of atomic hydrogen with the a-C:H film causes erosion. From the spatial variation of the erosion rate one can deduce the angular distribution of the impinging hydrogen atoms. This angular distribution was also measured by mass spectrometry and showed excellent agreement with the erosion profile. The absolute flux of atomic hydrogen was also determined by mass spectrometry. With the absolute flux of atomic hydrogen known from mass spectrometry, measurement of the lateral variation of the erosion rate can be directly used as a probe for absolute quantification of the angular distribution of the impinging H 共D兲 flux. The erosion yield is (2⫾0.7)⫻10⫺2 , which is consistent with the microscopic erosion mechanisms of a-C:H by atomic hydrogen known from the literature. © 2000 American Vacuum Society. 关S0734-2101共00兲01003-4兴

I. INTRODUCTION The interaction of atomic hydrogen 共H兲 with solid surfaces is of great interest for many basic surface science studies such as the adsorption of H on metals1 or semiconductors2,3 and for measurement of reaction rates such as those in hydrogen–deuterium 共HD兲 exchange.4 In order to study these basic surface mechanisms quantitatively, a quantified source for atomic hydrogen is necessary. A pure source for atomic hydrogen can easily be implemented on the basis of thermal dissociation of hydrogen molecules in a small heated volume with a known throughput of hydrogen molecules. Atomic hydrogen can then leave this heated volume via a small orifice and effuse into a sample chamber. If a 100% degree of dissociation in the heated volume can be achieved, the atomic hydrogen flow can be calculated from the known input flow of H2 molecules. Several different implementations of this source principle have been realized.5,6 The most advanced were developed by Van Zyl and Gealy7 and by Bischler and Bertel.8 They used a small tungsten capillary as the heated volume and the tip of the capillary was heated by electron bombardment. Bischler and Bertel obtained a flow of atomic hydrogen in the range of ⬃3⫻1014 s⫺1. Recently, this source design was further developed by Horn and co-workers,9 who used resistive heating of the capillary to exclude any disturbing production of energetic ions due to ionization of the neutral gas by the electron bombardment. Our study features a similar radical source, but with the additional option of varying the length of the heated capillary tip. a兲

Author to whom correspondence should be addressed; electronic mail: [email protected]

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In many experimental studies based on the use of a capillary source, it is only the beam density7 or total flow8 of atomic hydrogen that is quantified, not the angular distribution of the effusing atomic species. In order to determine the flux density on a substrate, it is also necessary to know the angular distribution of the particles. Just recently, Tschersich and von Bonin10 and Eibl et al.11 investigated beam formation in a hot capillary in detail. Tschersich and von Bonin measured the angular distribution of atomic hydrogen with a mass spectrometer which could be rotated around the exit orifice of the capillary. Their experimental results were successfully compared with the theoretical predictions of beam formation first formulated by Clausing12,13 and later expanded by Dayton14 and by Gottwald.15 An experiment designed to measure surface reactions based on interaction of an absolutely quantified radical flux with a sample requires, in principle, two experimental setups: the first is dedicated to surface studies of the sample of interest, and the second is dedicated solely to measurement of the flux and angular distribution of the radicals. This complication of having two setups was obviated by Eibl et al.,11 who determined the angular distribution of the emitted atomic hydrogen by adsorbing H on a gold foil placed on a movable substrate holder. The hydrogen coverage was afterwards quantified by thermal desorption spectroscopy 共TDS兲. With this approach, however, the angular resolution for determining the angular distribution is limited by the size of the gold foil sample. Several alternative approaches to quantification of the atomic hydrogen flux are mentioned in the literature and are briefly reviewed in Ref. 16, but most of them achieve only poor angular resolution, or involve the neces-

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Schwarz-Selinger, von Keudell, and Jacob: Method for absolute quantification of a radical source for a -C:H

sity of an additional experimental setup to characterize the beam. In this article we present a much simpler method of measuring the angular distribution and absolute flux of atomic hydrogen by using the erosion of an amorphous, hydrogenated 共a-C:H兲 carbon film as the probe for an impinging H flux. A large-area a-C:H film is placed in front of the radical source. Since the erosion yield for the interaction of H 共D兲 with a-C:H films at elevated substrate temperatures is well known, the absolute flux and angular distribution can easily be calculated from measurement of the spatial variation of the erosion rate. Characterization of the atomic hydrogen flux density can, therefore, be reduced to a thickness measurement. The measurement of the angular distribution and absolute flux of atomic hydrogen by means of a mass spectrometer is compared with the measurement of the angular distribution by means of an a-C:H film as the probe. This comparison gives the absolute yield for the erosion of the probe. It agrees very well with the known values from literature and confirms the feasibility of this method also for quantitative measurements. The variation of the angular distribution with the length of the heated capillary is presented as an example and application of this method. II. EXPERIMENT A heated tungsten capillary was used to produce H 共D兲 at the hot walls of the capillary via thermal dissociation of H2 共D2兲 molecules. Its length L is 50 mm and its inner diameter d is 1 mm. To heat the tip of the capillary, we applied resistive heating in a design similar to that of Horn et al.9 Our design has the additional option of varying the length of the heated volume in the capillary and the temperature gradient. A flow of hydrogen molecules in a range of 0.02–1.0 sccm 共1 sccm ⬃4.5⫻1017 atoms s⫺1兲 through the capillary was adjusted by means of a mass flow controller 共MKS M330兲. The pressure p i on the high-pressure side of the capillary was measured by a baratron gauge in the gas line and was in the range of 0.2–2.5 mbar at room temperature. The capillary is mounted in a water-cooled socket, and the tip of the capillary is shielded by a cooled copper aperture to protect the substrates from radiative heating. The temperature of the capillary is measured along its length with a disappearing filament pyrometer. In addition, the temperature was also measured inside the orifice of the capillary tip, which can be considered to be a blackbody emitter. From these data the absolute temperature gradient along the capillary was determined. The radical source was mounted on an ultrahigh vacuum 共UHV兲 system with a base pressure of 10⫺10 mbar. At the maximal H2 共D2兲 flow, the chamber pressure p 0 reached ⬃9⫻10⫺6 mbar. The experimental setup for measuring the angular distribution using mass spectrometry is shown schematically in Fig. 1共a兲. The angular distribution of the emitted H 共D兲 atoms and H2 共D2兲 molecules was measured by a Hiden Analytical HAL 201 quadrupole mass spectrometer in direct line of sight of the capillary orifice. The mass spectrometer could be rotated around the tip of the capillary. The contribution of J. Vac. Sci. Technol. A, Vol. 18, No. 3, MayÕJun 2000

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FIG. 1. Schematic illustration of the two experimental setups for measuring the angular distribution of the beam particles: 共a兲 mass spectrometry and 共b兲 erosion of a dense a-C:H film.

atomic hydrogen to the flux emitted was directly measured by ionization threshold mass spectrometry 共ITMS兲17 with an electron energy in the ionizer of the mass spectrometer of 14 eV and by standard mass spectrometry with an electron energy of 70 eV. The mass spectrometer was differentially pumped with two cascaded turbopumps that maintained the pressure in the mass spectrometer chamber below 10⫺8 mbar during the experiment. A graphite capillary with an inner diameter of 1 mm and a length of 10 mm was used as a conductance filter for the entrance orifice between the source chamber and the mass spectrometer chamber. This conductance filter enhances the contribution of species reaching the ionizer of the mass spectrometer in direct line of sight of the hot capillary. For beam particles the capillary acts just as an aperture, for background particles entering from random directions it acts as a conductance with a transmission probability 共Clausing factor兲 of only 10%. The angle resolution of the setup is 1°. The use of graphite instead of a metal for the conductance filter reduces recombination of atomic hydrogen on the inner walls.18 In order to distinguish between signals in the mass spectrometer originating from particles emerging from the hot capillary in direct line of sight and signals originating from the background, a shutter could be moved in front of the graphite conductance filter to block the directed beam of particles from the capillary into the mass spectrometer. To overcome our mass spectrometer’s experimental problem of having an unambiguous detection of mass 1, deuterium was used instead of hydrogen for our mass spectrometry and consequently also for the erosion measurements. The results obtained for D can be transferred qualitatively

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to H, but the absolute values for the degree of dissociation and angular distribution differ slightly since the thermal velocity of D is smaller than that of H at the same temperature. For the erosion yield no difference is found, in agreement with the literature where no isotope effect for this chemical erosion step is mentioned.19 We used two different approaches for detecting atomic deuterium: First, we applied ITMS17 at an electron energy of 14 eV in the ionizer of the mass spectrometer. A signal for mass 2 can originate from three different reactions20 when the electron energy is higher than the threshold E th , ⫺





D⫹e →D ⫹2e ,

E th⫽13.6 eV,

D2⫹e ⫺ →D⫹⫹D⫺⫹e ⫺ , H2⫹e



⫺ →H⫹ 2 ⫹2e ,

E th⫽15.4 eV,

E th⫽17.3 eV.

共1兲 共2兲 共3兲

Therefore, at an electron energy of 14 eV, mass 2 can only be produced via direct ionization of D by reaction 共1兲. This suppresses the background signal from the dissociative ionization of D2 关reaction 共2兲兴 and the ionization of H2 关reaction 共3兲兴 since these reactions can only occur at electron energies above the threshold E th . It is conceivable that the threshold for dissociative ionization shifts with increasing internal energy of the particles to lower energies, thus leading to overestimation of the amount of hydrogen for higher capillary temperatures. In order to exclude this possibility, as a second approach we applied detection of atomic deuterium by the mass spectrometer at an electron energy of 70 eV. The cracking pattern of D2 molecules is determined at a capillary temperature where no dissociation occurs. On the assumption that this cracking pattern does not change with the temperature of the molecules, the signal originating from atomic deuterium in the mass spectra can be deduced for higher capillary temperatures where dissociation takes place. Both methods yield the same results within the accuracy of the measurements. The equivalent setup for measuring the angular distribution by means of erosion of an amorphous, hydrogenated carbon film is shown in Fig. 1共b兲. A dense a-C:H film several hundred nm thick was placed in front of the radical source. The a-C:H films were deposited on single-crystal silicon substrates by means of a rf discharge from methane with a dc self-bias of ⫺200 V and a pressure of 0.02 mbar. Details of the deposition setup are given elsewhere.21 The film composition and structure were measured by ion-beam analysis. Proton-enhanced cross-sectional scattering 共PES兲 was applied to determine the carbon content and elastic recoil detection 共ERD兲 was used for the hydrogen content, described in Refs. 22 and 23. New cross-sectional data reported by Amerikas et al.24 for PES and by Baglin et al.25 for ERD were chosen for the analysis. The carbon density of the films was determined to be 9.2⫻1028 m⫺3. The hydrogen-tocarbon ratio of the film was 0.41, typical of so-called ‘‘hard’’ carbon films. It is necessary to use these kinds of hard films because they are thermally stable up to a substrate temperature of 800 K,26 in contrast to polymer-like, hydrogen-rich films, where thermal desorption already starts at 600 K.27 JVST A - Vacuum, Surfaces, and Films

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During exposure of these films to the atomic hydrogen flux emitted from the radical source, the substrate temperature was kept at 650 K since chemical erosion of a-C:H by D 共H兲 is a thermally activated process. The substrate temperature was measured by thermocouples. The variation in film thickness was measured ex situ by ellipsometry before and after exposing the film to the D 共H兲 source. From the spatial variation of the film thickness and the exposure time it was possible to determine the variation of the erosion rate. III. RESULTS AND DISCUSSION A. Angular distribution and total flux measured by mass spectroscopy

For quantification of the atomic hydrogen flux emanating from the capillary source three quantities have to be measured: the absolute gas flow through the capillary, the degree of dissociation, and the angular distribution. This quantification is described in the following. Beam formation in a long capillary was first theoretically described by Clausing12,13 and since then has often been treated in the literature.14,28–31 Very recently, Tschersich and von Bonin10 resumed the work of Dayton14 and Gottwald15 and considered the problem of partial molecular flow inside a capillary source. This theory is based on the transport of species inside the capillary along a linear pressure gradient in a molecular flow regime at the end of the capillary via adsorption of the species at the wall and desorption in random directions. The main parameter determining the shape of the angular distribution is the effective length L eff of the volume at the end of the capillary in which the pressure p m is low enough 共with respect to the capillary diameter兲 for molecular flow to occur. The angular distribution of the emitted species can then easily be obtained by integrating over the diffuse emission of species starting at the inner walls of the capillary in a volume with length L eff . This is illustrated in Fig. 2: 共i兲 for large L eff 关Fig. 2共a兲兴, particles originating from the walls of a large volume with length L eff extending deep into the capillary contribute to the angular distribution. All the particles starting with a small angle ␪ (L eff) relative to the axis at x⫽L eff are able to reach the exit orifice without any gas phase collision, leading to a rather peaked angular distribution; 共ii兲 at small L eff 关Fig. 2共b兲兴, most of the particles that contribute to the angular distribution originate from the wall of a small volume near the exit orifice only. Most of the particles starting at positions x greater than L eff inside the capillary, where collisional flow dominates, will not reach the exit of the capillary without any further collision. This leads to a broad angular distribution, indicated by a large opening angle ␪ (L eff). The composition of the emitted flux derived from this consideration is shown in Fig. 2共c兲: particles emerging from the capillary at angles smaller than ␪ (L eff) originate mainly from the part of the capillary where x⭓L eff and reach the exit orifice without any collision with the wall in the volume with length L eff . Their fraction of the total particle flux is marked by region 1 in Fig. 2共c兲. Particles emerging at angles larger than ␪ (L eff) originate only from the walls of the volume within the section x⬍L eff .

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FIG. 3. Angular distribution of atomic deuterium normalized to 1 for four different throughputs, measured by angle-resolved mass spectrometry for a capillary temperature of 2250 K. The solid lines are calculations according to the equation of Tschersich 共Ref. 10兲 with L eff as the only fit parameter. The values of L eff and the corresponding pressure p i are 3.5d/4.6 mbar, 7d/1.4 mbar, 9d/0.85 mbar, and 13d/0.2 mbar. For comparison, the angular distribution of a Knudsen emitter is shown.

FIG. 2. Schematic illustration of the formation of a particle beam 共a兲 for a high value of L eff 共small throughput兲 and 共b兲 a low value of L eff 共large throughput兲. 共c兲 Illustration of the fact that most of the particles in direct line of sight did not hit the wall in the molecular flow regime L eff 共regime 1 between the dashed and the solid lines兲. The fraction of particles that hits the wall in L eff is very small 关regime 共2兲 under the solid line兴 but increases with the angle of emergence until ␪ (L eff) is reached. For angles greater than ␪ (L eff) all emerging particles must have hit the wall. The equations taken for the plot are from Ref. 10.

Because of the fixed geometry, a larger throughput of particles leads to a higher pressure p i at the entrance x⫽L of the capillary. This causes a steeper pressure gradient inside the capillary and consequently p m shifts to the exit of the capillary, which means that L eff gets smaller. The dependence of the angular distribution of atomic deuterium on the pressure p i at the entrance of the capillary was measured by angle-resolved mass spectrometry. Figure 3 presents the angular distributions measured as a function of the deuterium gas flow. Since the effective length L eff depends not only on the particle throughput but also on the mean free path of the molecules, the measurements were made for a fixed temperature profile, with a maximum temperature of 2250 K. It can be seen that for low throughput, corresponding to a low pressure p i , the angular distribution of the emitted D is very sharp, whereas at high throughput 共pressure p i 兲 the angular distribution becomes broad. Figure 3 also clearly shows that in all cases presented the angular distribution of emitted species is much narrower than the cosine distribution shown by the dotted line. The measurements are fitted with the analytical expression presented by Tschersich and von Bonin10 to determine L eff for each throughput 共shown by the solid lines in Fig. 3兲. Experiment and theory show excellent agreement. With a diameter d of the capillary, one obtains an effective length L eff⫽3.5⫻d for the highest deuterium throughput of 1.0 sscm (pressure⫽4.6 mbar) and an effective length L eff J. Vac. Sci. Technol. A, Vol. 18, No. 3, MayÕJun 2000

⫽13⫻d for the lowest throughput of 0.03 sccm (pressure⫽0.2 mbar). In order to quantify the absolute flux of atomic hydrogen, the degree of dissociation ␣ inside the heated capillary has to be determined. ␣ is defined as:32 ␣ ⫽n D /(n D⫹2n D2兲, whereas n D and n D2 are the densities of atomic and molecular species. According to Tschersich,33 for a constant throughput of D2 the flow of atomic D is then proportional to ⌫ D⬀

2 冑␣ 1⫺ ␣ ⫹ 冑2 ␣

.

A value for the dissociation degree is obtained by measuring the variation of the D signal with the variation of the capillary temperature. In order to determine the degree of dissociation from the D signal, the variation of the detection sensitivity of the particles in the ionizer of the mass spectrometer has to be taken into account. With increasing capillary temperature the velocity of the emitted species increases as the square root of the capillary temperature and, therefore, the measured intensity, has to be divided by the square root of the capillary temperature. From the saturation of the corrected D signal with the variation of the capillary temperature it is concluded that 100% dissociation occurs. This is observed for maximum capillary temperatures higher than 2400 K at the lowest flow of 0.03 sccm and at higher temperatures at flow of 0.1 sccm, as shown in Fig. 4. In addition, chemical equilibrium calculations33 are shown in Fig. 4 as solid lines for pressures of 1⫻10⫺3 and 6 ⫻10⫺3 mbar. These pressures have to be considered as fictitious values since there is no constant pressure inside the capillary. However, the good agreement between the chemical equilibrium calculations and the measurements justifies the assumption of thermal equilibrium in a small part of the capillary. Recently, Tschersich34 was also able to achieve

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FIG. 5. Erosion profile of the a-C:H film probe measured by ellipsometry. Twelve parallel scans across the sample along the x axis were made in y step sizes of 0.2 mm. The maximum erosion of 57.5 nm is in the center opposite the capillary exit. Parameters: T cap⫽2250 K and ⌫(D2 )⫽0.33 sccm for erosion time of 45 min.

FIG. 4. Normalized intensity measured with the mass spectrometer line of sight as a function of temperature for two different deuterium throughputs. The signal is divided by the square root of the capillary temperature to account for the changing particle velocity. The saturation of the signal is assigned to 100% dissociation. The solid lines correspond to equilibrium calculations for the pressure p equ⫽1⫻10⫺3 mbar for ⌫(D2 )⫽0.03 sccm, and p equ⫽6⫻10⫺3 mbar, for ⌫(D2 )⫽0.1 sccm.

good agreement between measurements and chemical equilibrium calculations by using a constant pressure as the only fit parameter. Finally, for quantification of the D flux the D2 flow has to be determined. The absolute throughput of D2 molecules through the capillary is controlled by a mass flow controller. The accuracy of the system is declared to be 1% of the full range. Since all D2 molecules are dissociated into D above 2400 K for the smallest throughput used, the total flow of D then corresponds to twice the input flow of D2. With this calibration, the absolute D flux density can be calculated from the mass spectrometer measurements for varying capillary temperatures and gas flows. The error in the flux measurement is determined by the accuracy of the flow controller, the repeatability of the mass spectrometry measurements, and the applicability of the description of the angular distribution. B. Angular distribution measured by an a-C:H film as probe

An amorphous, hydrogenated carbon film was placed in front of the radical source and heated to 650 K. At this substrate temperature, the flux-dependent chemical erosion of a-C:H by atomic hydrogen for a D 共H兲 flux of ⬃1016 cm⫺2 s⫺1 is at its maximum, as is known from the literature.35,36 The D2 flow through the capillary was set at 0.33 sccm, which yields a capillary temperature of 2250 K a D flux density of (1.0⫾0.3)⫻1016 cm⫺2 s⫺1 at the position of the probe, 46 mm away from the capillary exit. The interaction of D with the a-C:H film leads to etching, which varies locally according to the angular distribution of the emitted D species. The etching is already visible by eye due to JVST A - Vacuum, Surfaces, and Films

the variation of interference color of the thin film. This variation of the erosion rate was measured ex situ by ellipsometry in two dimensions, as shown in Fig. 5. Twelve parallel scans across the rectangular sample in step widths of 0.2 mm were performed. From the measured ellipsometric angles, the film thickness and the complex refractive index of the film was determined by means of an optical model. A mask was used to expose only a circular area 共50 mm in diameter兲 of the sample to the D beam. It can be seen that the erosion rate is highest in the center, which is exactly opposite the exit orifice of the capillary. For larger distances from this center or, accordingly, larger angles to the surface normal of the exit orifice, the erosion rate drops off significantly. With the optical constants of the film of n⫽2.17 and k⫽0.13 at the measured wavelength of 632 nm an erosion depth of 57.5 nm in the center of the probe was determined. The erosion yield, determined from the known carbon density of the a-C:H film of (9.2⫾0.9)⫻1028 m⫺3, the erosion rate of 57.5 nm in 45 min, and the measured D flux of (1.0⫾0.3)⫻1016 cm⫺2 s⫺1, was found to be (2⫾0.7) ⫻10⫺2 at 650 K. The erosion yield predicted for interaction of a-C:H films with atomic hydrogen is 1% for a low H flux of around 1.9⫻1013 cm⫺2 s⫺1 at a substrate temperature of 650 K, with CH3 and CH4 as the main erosion products.9 For larger fluxes in the range of ⬃1016 cm⫺2 s⫺1, a higher erosion yield of ⬃4% was observed by Vietzke et al. at a substrate temperature of 470 K.35 We ascribe the differences in these values to the uncertainty of the flux determination. Our measurement is therefore in very good agreement with that in the literature. Figure 6共a兲 shows a comparison of the erosion rate on a central scan across a sample with the angular variation of the D flux measured by mass spectrometry under identical conditions. It is important to note that the flux measured by mass spectrometry has to be converted from spherical to plane geometry because the mass spectra were taken on the surface of a sphere around the exit orifice of the capillary, whereas the erosion profile is measured on a plane sample facing the capillary 共see Fig. 1兲. It can be seen that the shape of the erosion profile agrees very well with the measured angular distribution of the D flux. This demonstrates the feasibility of using an a-C:H film as the probe for measuring the angular

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FIG. 6. Influence of the length of the heated volume on the angular distribution of atomic deuterium for a central scan measured with angle-resolved mass spectrometry and the erosion probe 共solid line兲. The mass spectrometry measurement is corrected for the plane geometry. 共a兲 For a large heated volume the angular distribution is peaked at the center whereas 共b兲 a hollow profile appears when the heated volume is smaller than the area of molecular flow. The throughput of D2 was 0.03 sccm in both cases which corresponds to an effective length of 13 d. In 共a兲 the capillary temperature increased from 2000 K at x⫽0 to 2250 K at x⫽15 mm and then decreased with 25 K/mm; the erosion time was 220 min. In 共b兲 the temperature decreased from 2000 K at x⫽1 with a gradient of 80 K/mm; the erosion time was 300 min.

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tributions results in the total angular distribution illustrated in Fig. 2共c兲. However, if the capillary is heated only at its very end, the production of atomic deuterium via thermal dissociation occurs only in a very small region of the wall near the exit orifice of the capillary. With small particle throughput, it is possible for the effective length L eff of the volume in which molecular flow occurs to become larger than the length of the capillary where dissociation can occur. Therefore, the dominant contribution to the emitted particles in the beam at large angles to the capillary axis is made by D atoms and at small angles by D2 molecules. If the heated volume of the capillary is larger than the region with molecular flow, atomic deuterium will already be produced at x⫽L eff and D will also contribute to the flux emitted for small angles. As a consequence, the angular distribution of the emitted atomic species can be modified by varying the length of the heated volume inside the capillary. Figure 6 shows the measurement of the angular distribution by mass spectroscopy as well as by the erosion probe for a small and a large heated volume inside the capillary for a D2 flow of 0.03 sccm. For a large heated volume of the capillary 关Fig. 6共a兲兴, the angular distribution is peaked at the center. However, for a small heated volume of the capillary 关Fig. 6共b兲兴, the angular distribution shows a hollow profile since atomic deuterium is preferentially emitted at large angles. On the axis itself, predominantly D2 contributes to the emitted flow, which does not lead to etching of the a-C:H film. From comparison of Figs. 6共a兲 and 6共b兲 it is evident that one can easily obtain a flat beam profile that leads to constant flux over a wide range just by varying the length of the heated volume at constant throughput. Furthermore, Fig. 6共b兲 shows again that the measurement of the angular distribution by mass spectrometry agrees excellently with the measurement by the erosion probe. IV. CONCLUSION

distribution of D emitted from the radical source. The detection limit for atomic hydrogen depends only on the exposure time of the probe and the accuracy of the thickness measurement. The angular resolution is defined by the distance between the furnace capillary and the probe and the minimum step width for the thickness measurement. C. Variation of the angular distribution with the length of the heated volume

As mentioned above, the variation of the effective length of the volume inside the capillary in which molecular flow occurs leads to a variation of the angular distribution. On the basis of this dependence, it is possible to assign to each angle of the emitted species with respect to the axis of the capillary that part of the capillary on which these species start and reach the orifice without any collision with the wall. This is illustrated in Fig. 2: 共a兲 species emitted from the source at very small angles are mainly emitted from surface areas deep inside the capillary (x⭓L eff); 共b兲 species emitted from the source at large angles can only originate from surface areas near the exit orifice (x⬍L eff). Overlapping of all these conJ. Vac. Sci. Technol. A, Vol. 18, No. 3, MayÕJun 2000

A radical source for atomic hydrogen was constructed on the basis of the thermal dissociation of D2 共H2) in a heated tungsten capillary. The angular distribution of atomic deuterium 共hydrogen兲 was measured by mass spectrometry as well as by using the erosion of an amorphous hydrogenated carbon film at elevated substrate temperature as a novel probe. The angular distribution can be calculated directly from measurement of the spatial variation of the erosion rate of the a-C:H film. The determined yield of (2⫾0,7)⫻10⫺2 eroded C atoms per H atom at 650 K can be used to determine the absolute flux of atomic hydrogen as well. The main advantage of using an a-C:H film as the H probe is the fact that this method can easily be implemented in any experimental setup and the H measurement is reduced to a simple film thickness measurement. ACKNOWLEDGMENTS The authors would like to thank A. Horn and T. Kammler for their assistance with the construction of the radical source and K. G. Tschersich for many fruitful discussions concerning beam formation.

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1

J. Boh, G. Eilmsteiner, K. D. Rendulic, and A. Winkler, Surf. Sci. 395, 98 共1998兲. 2 S. J. Pearton, J. W. Corbett, and M. Stavola, Hydrogen in Crystalline Semiconductors, Springer Series in Materials Science Vol. 16 共Springer, Berlin, 1992兲. 3 N. M. Jonson, C. Doland, F. Ponce, J. Walker, and G. Anderson, Physica B 170, 3 共1991兲. 4 F. J. Aoiz, L. Banares, V. J. Herrero, V. S. Rabanos, and I. Tanarro, J. Phys. Chem. 101, 6165 共1997兲. 5 M. M. Eisenstadt, Rev. Sci. Instrum. 36, 1878 共1965兲. 6 W. E. Lamb and R. C. Retherford, Phys. Rev. 79, 549 共1950兲. 7 B. Van Zyl and M. W. Gealy, Rev. Sci. Instrum. 57, 359 共1986兲. 8 U. Bischler and E. Bertel, J. Vac. Sci. Technol. A 11, 458 共1993兲. 9 A. Horn, T. Kammler, and M. Kappel, German Patent No. DE 19757851 C1. 10 K. G. Tschersich and V. von Bonin, J. Appl. Phys. 84, 4065 共1998兲. 11 C. Eibl, G. Lackner, and A. Winkler, J. Vac. Sci. Technol. A 16, 2979 共1998兲. 12 P. Clausing, Z. Phys. 66, 471 共1930兲. 13 P. Clausing, Ann. Phys. 共Leipzig兲 12, 961 共1932兲. 14 B. B. Dayton, Vak.-Tech. 7, 7 共1958兲. 15 B. A. Gottwald, Vak.-Tech. 22, 106 共1973兲. 16 K. C. Harvey and C. Fehrenbach, Jr., Rev. Sci. Instrum. 54, 1117 共1983兲. 17 G. C. Eltenton, J. Chem. Phys. 15, 455 共1947兲. 18 J. Ku¨ppers, Surf. Sci. Rep. 22, 249 共1995兲. 19 E. Vietzke, K. Flaskamp, V. Philipps, G. Esser, P. Wienhold, and J. Winter, J. Nucl. Mater. 145–147, 443 共1987兲.

JVST A - Vacuum, Surfaces, and Films

20

1001

H. M. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, J. Phys. Chem. Ref. Data Suppl. 6, 1 共1997兲. 21 A. Annen, M. Sass, R. Beckmann, A. von Keudell, and W. Jacob, Thin Solid Films 312, 147 共1998兲. 22 D. Boutard, W. Mo¨ller, and B. M. U. Scherzer, Phys. Rev. B 38, 2988 共1988兲. 23 D. Boutard, B. M. U. Scherzer, and W. Mo¨ller, J. Appl. Phys. 65, 3833 共1989兲. 24 R. Amerikas, D. N. Jamieson, and S. P. Dooley, Nucl. Instrum. Methods Phys. Res. B 77, 110 共1993兲. 25 J. E. E. Baglin, A. J. Kellock, M. A. Crockett, and A. H. Shih, Nucl. Instrum. Methods Phys. Res. B 64, 469 共1992兲. 26 W. Wang, W. Jacob, and J. Roth, J. Nucl. Mater. 245, 66 共1997兲. 27 K. Maruyama, W. Jacob, and J. Roth, J. Nucl. Mater. 264, 56 共1999兲. 28 J. A. Giordemaine and T. C. Wang, J. Appl. Phys. 31, 463 共1959兲. 29 P. Zugenmaier, Z. Angew. Phys. 20, 184 共1966兲. 30 H. C. W. Beijerinck and N. F. Verster, J. Appl. Phys. 46, 2083 共1975兲. 31 D. M. Murphy, J. Vac. Sci. Technol. A 7, 3075 共1989兲. 32 P. W. Atkins, Physical Chemistry 共Oxford University Press, Oxford, 1998兲. 33 K. G. Tschersich, J. Appl. Phys. 87, 2565 共2000兲. 34 I. Barin, Thermochemical Data of Pure Substances 共VCH, Weinheim, 1995兲, Vol. 1. 35 E. Vietzke, V. Philipps, K. Flaskamp, P. Koidl, and Ch. Wild, Surf. Coat. Technol. 47, 156 共1991兲. 36 A. Horn, A. Schenk, J. Biener, B. Winter, C. Lutterloh, M. Wittmann, and J. Ku¨ppers, Chem. Phys. Lett. 231, 193 共1994兲.