Energy transfer into the growing film during sputter deposition: An investigation by
`calorimetric measurements and Monte Carlo simulations
`Tilo P. Drüsedau, Torsten Bock, Thomas-Maik John, Frank Klabunde, and Wolfgang Eckstein
`
`Citation: Journal of Vacuum Science & Technology A 17, 2896 (1999); doi: 10.1116/1.581957
`View online: http://dx.doi.org/10.1116/1.581957
`View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/17/5?ver=pdfcov
`Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
`
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`LMBTH-000118
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`
`Energy transfer into the growing film during sputter deposition:
`An investigation by calorimetric measurements
`and Monte Carlo simulations
`Tilo P. Dru¨sedau,a) Torsten Bock, Thomas-Maik John, and Frank Klabunde
`Institut fu¨r Experimentelle Physik, Otto-von-Guericke-Universita¨t Magdeburg,
`PF 4120, 39016 Magdeburg, Germany
`Wolfgang Eckstein
`Max-Planck-Institut fu¨r Plasmaphysik, 85748 Garching, Germany
`~Received 29 January 1999; accepted 30 April 1999!
`
`The power density at the substrate during sputter deposition was measured by a calorimetric
`method. In combination with measurements of the atomic deposition rate, the total amount of the
`energy input per incorporated atom was determined. The measured values range from 18 eV for
`aluminum to about 1000 eV maximum per atom for carbon. There is, for all elements investigated,
`a general trend for a linear increase of the energy per atom with increasing sputtering argon pressure
`over the range from 0.2 to 7 Pa. The energy per atom decreases with increasing power of the
`sputtering discharge. The application of a negative bias to the substrate reduces the total energy per
`atom to the values measured at low pressure of 0.4 Pa or below. The total energy flux in the low
`pressure range ~0.4 Pa or less! can be well described by contributions due to plasma irradiation, the
`heat of condensation of the deposited atoms, their kinetic energy, and the kinetic energy of the
`reflected argon neutrals. The latter two components are a priori calculated by TRIM.SP Monte Carlo
`simulations. There is good agreement between the a priori calculated and the measured values. The
`combination of experimental and theoretical data result in empirical rules for the energies of the
`sputtered and reflected species, which allow an estimate of the energy input during sputter
`deposition for every elemental target material in the low pressure range. In a first approximation, the
`energy per incorporated atom is proportional to the ratio between target atomic mass and sputtering
`yield. © 1999 American Vacuum Society. @S0734-2101~99!05405-6#
`
`I. INTRODUCTION
`
`Over the past 3 decades, magnetron sputtering ~MSP! has
`been established as one of the most important tools in thin
`film deposition technology ~see for example Ref. 1!. There is
`a large variety of applications of the MSP technique, as for
`example hard and protective coatings, metallic interconnects
`in microelectronics or thin film solar cells and optical and
`decorative layers.1 The growth of sputtered films leading to
`the formation of special types of microstructure is known to
`be strongly affected by the sputtering argon pressure.1,2 In
`recent years, new or improved thin film materials have be-
`come widely used. It is found that sputter deposition of some
`of these films results in ‘‘strange’’ effects as, for example,
`the formation or turnover of texture or a special crystal struc-
`ture as observed in titanium nitride,3 molybdenum,4 zinc
`oxide5 or boron nitride.6 These effects are often connected to
`the appearance of lateral inhomogeneities of other film prop-
`erties over the substrate area. It is assumed that all these
`effects result from variations in the energetic bombardment
`of the growing film. However, there is rather small knowl-
`edge about the energy input into the growing film during
`sputter deposition as a function of the target material and the
`process parameters. Twenty years ago, Thornton7 performed
`
`a!Author to whom correspondence should be addressed; electronic mail:
`tilo.druesedau@physik.uni-magdeburg.de
`
`a pioneering work studying the total energy input into the
`growing film by a calorimetric method. The results of this
`work are discussed in terms of a quantitative model. From
`the present point of view, there is a variety of open questions
`regarding the results in the literature.7 These concern the role
`of the discharge power and pressure on the energy flux.
`Thornton7 reported on a pressure-independent energy per
`atom in the range from 0.1 to 1.3 Pa. In addition, the contri-
`bution of reflected argon neutrals to the energy input was not
`investigated quantitatively because of the lack of experimen-
`tal or theoretical data. The role of reflected argon neutrals is
`of special interest, as argon bombardment can influence the
`chemical composition, crystallite size and the microscopic
`properties of thin films as demonstrated for Mo by Ensinger.8
`Argon bombardment is also essential for the deposition of
`‘‘zero-stress’’ films.9 The aim of the present work is the
`reexamination and improvement of the calorimetric measure-
`ments performed by Thornton. The experimental results are
`discussed by means of
`transport of
`ions in matter—
`sputtering ~TRIM.SP! Monte Carlo simulations. The reader of
`the present work should be given a tool to estimate the total
`energy input into the growing film and the contributions of
`incorporated sputter atoms and reflected neutrals.
`
`II. EXPERIMENTAL SETUP
`For this investigation, two types of magnetron sputtering
`equipment were used. With the exception of carbon deposi-
`
`2896
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`J. Vac. Sci. Technol. A 17(cid:132)5(cid:133), Sep/Oct 1999
`
`0734-2101/99/17(cid:132)5(cid:133)/2896/10/$15.00
`
`©1999 American Vacuum Society
`
`2896
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`tion, dc sputtering was applied. The magnetron sources used
`are all manufactured by von-Ardenne Anlagentechnik. The
`target to substrate distance was d ST58 cm in every case.
`Germanium and carbon films were deposited by dc or 13.56
`MHz rf sputtering, respectively, in an LA 440S commercial
`sputtering apparatus equipped with 125 mm diam magne-
`trons ~for details see the previous work10!. The other depo-
`sition apparatus is computer-controlled multichamber depo-
`sition equipment designed for
`the deposition of metal/
`semiconductor multilayers, which is described in detail in
`Refs. 4 and 11. Two chambers contain PPS-90UV magne-
`trons with 90 mm diam targets of silicon or metal ~Al, Mo,
`W! targets, respectively. With the exception of the single
`crystalline Si targets and the glassy carbon target, all targets
`used are polycrystalline.
`For the films prepared, the deposition rate was determined
`by measuring the films’ thickness and density via x-ray re-
`flectometry ~see Ref. 4 for experimental details! and the
`deposition time. The x-ray measurements also gave addi-
`tional information about the film properties ~besides density,
`surface roughness, crystallite size, etc.!. It was found12 that
`for sputtering a variety of elemental targets in argon atmo-
`sphere, the pressure-dependent atomic deposition rate F at is
`well described by the Keller–Simmons formula:13
`
`F 12exp2
`
`F at5F 0
`
`~pd!0
`pdST
`
`G.
`
`pdST
`~pd!0
`
`~1!
`
`Here F 0 is the zero-pressure flux at the substrate and (pd) 0
`is the characteristic pressure-distance product ~PDP! which is
`element specific.12 In a first approximation and neglecting
`gas density reduction effects, it can be assumed to be pro-
`portional to the product of target atomic mass, the energy of
`sputtered atoms and their thermal mean free path in argon.12
`The measurements of the energy input during sputter
`deposition were performed applying the calorimetric method
`after Thornton.7 For the single-chamber apparatus, the heat
`flux was measured using a molybdenum dummy substrate
`the size of 25323 mm2, the mass of 667 mg and defined heat
`capacity. Temperature control was performed using a 0.25
`mm diam Ni–CrNiAl coaxial thermocouple attached with
`silver paste to the substrate. Measurements were performed
`by a computer-controlled voltmeter Fluke 8842. For the mul-
`tichamber apparatus, the substrate heating was measured by
`means of a 15315 mm2, 0.5 mm thick Al substrate. Tem-
`perature measurements were performed by a PT 100 ther-
`moresistor, which was electrically connected by 50 mm diam
`gold wires. It was operated at a voltage of 0.2 V. By means
`of the self-heating of the thermoresistor ~at a voltage of 2 V!,
`the heat capacity of the whole probe was determined to be
`0.835 J/K. Using the gradient method after Thornton,7 the
`heat loss due to conduction via the wires or the thermo-
`couple, respectively, and due to irradiation, can be deter-
`mined. The incoming power density at the substrate during
`deposition I tot is then deduced from the effective heating of
`the substrate per unit area. Normalizing the power density to
`the atomic deposition rate results in the total energy input per
`incorporated atom ^E t&
`
`JVST A - Vacuum, Surfaces, and Films
`
`FIG. 1. Total energy input per atom as a function of argon pressure for ~a!
`silicon and carbon, ~b! aluminum. The data were taken at different sputter-
`ing powers, which are given in the legend. The solid lines are linear fit
`curves.
`
`^E t&5I tot /F at .
`~2!
`The simulation of the sputter process was performed using
`the ~TRIM.SP! Monte Carlo program.14 The principle of the
`program is to calculate collision cascades generated by an
`argon projectile penetrating the target material. The model is
`based on the binary collision approach ~for more details, the
`reader is referred to Ref. 15!. For each target voltage 5
`3105 sputtering events were simulated on an IBM worksta-
`tion. This calculation typically took 3 h. ~Note that the target
`voltage in V is assumed identical to the ion energy in eV—
`see, for example Refs. 16 and 17!. The targets were assumed
`amorphous and perpendicular incidence of the projectiles
`was chosen.
`
`III. RESULTS: CALORIMETRIC MEASUREMENTS
`Figure 1~a! shows the measured energy flux for carbon
`and silicon. With increasing argon pressure there is an in-
`crease of the total energy input per atom up to maximum
`values of 1030 and 540 eV for C and Si, respectively. For the
`case of Al @Fig. 1~b!# the energy input per atom reaches a
`maximum of 152 eV. It can be seen from Fig. 1~b! that the
`
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`TABLE I. Parameter of the linear fit curves ^E t&5c 01c 1p, which are shown
`in Figs. 1~a!–3~a!, describing the functional dependence of the total energy
`flux per atom deposited ^E t& on pressure p for different elements and sput-
`tering powers investigated.
`
`Element
`
`Power ~W!
`
`c 0 ~eV!
`
`c 0 ~eV/Pa!
`
`C
`Al
`Al
`Al
`Al
`Si
`Ge
`Ge
`Mo
`Mo
`Mo
`Mo
`W
`W
`
`900
`50
`100
`200
`300
`50
`50
`500
`20
`50
`100
`200
`20
`100
`
`302.89
`12.43
`10.78
`16.09
`14.89
`17.56
`24.46
`21.04
`77.39
`64.35
`58.07
`50.60
`152.88
`136.67
`
`172.59
`21.37
`18.95
`11.18
`9.43
`105.08
`16.40
`4.14
`5.16
`6.86
`4.23
`2.98
`44.86
`1.41
`
`increase of energy input is also power dependent with the
`highest values obtained for minimum power. With decreas-
`ing pressure, the curves taken for different power converge
`into identical values, which amount to 18.660.5 eV at 0.4 Pa
`argon pressure. A decrease of the pressure to 0.2 Pa results
`only in a minor decrease of the energy input
`to 16.4
`60.3 eV. The functional dependence of the energy input on
`pressure is well described by linear fit curves. These are
`shown in Figs. 1~a! and 1~b!. The extrapolation of the linear
`curves to zero pressure results in values in the range of 10.8–
`16.1 eV for Al ~Table I!. No clear effect of power on these
`extrapolated values can be observed. For Si the extrapolation
`results in an energy of 17.6 eV at zero pressure. The obser-
`vation of a pressure-dependent energy per atom is in contra-
`diction with the measurements performed by Thornton.7 He
`reported on a pressure-independent energy flux in the range
`between 0.13 and 1.3 Pa. In contrast, over the range from 0.2
`to 1.0 Pa the measured values in Fig. 1 increase by a factor
`of about 2. Figure 2~a! shows for the sputter deposition of
`germanium also a linear increase of the energy input per
`atom with pressure. The linear extrapolation of the fit curves
`results in values of 24.5 and 21.0 eV for discharge powers of
`50 and 500 W, respectively ~Table I!. As in the case of Al,
`the effect of pressure on the energy input decreases with
`increasing power of the discharge. There is only a weak in-
`crease of the energy per atom from 22.2 to 25.4 eV when the
`pressure increases from 0.25 to 1 Pa. This behavior, in con-
`trast with the above results for Al and Si, is in agreement
`with Thornton’s measurements.7 The energy input as a func-
`tion of pressure measured for molybdenum is also roughly
`described by a linear fit curve as shown in Fig. 2~b!. The
`experimental findings for tungsten deposition @Fig. 3~a!# are
`quite different from the results for the other elements. For the
`lowest power of 20 W, there is also a linear increase of the
`total energy per atom with pressure ~with the exception of
`the highest pressure values investigated, where the energy
`approaches a constant value—see Table I!. At increased dis-
`charge power, the energy per atom is no longer a function of
`
`J. Vac. Sci. Technol. A, Vol. 17, No. 5, Sep/Oct 1999
`
`FIG. 2. Total energy input per atom as a function of argon pressure for ~a!
`germanium and ~b! molybdenum. The data were taken at different sputtering
`powers, which are given in the legend. The solid lines are linear fit curves.
`
`pressure. In addition, the energy per atom is power indepen-
`dent and amounts to 136 eV. As a key experiment to ratio-
`nalize the results of the calorimetric measurements, the ex-
`periment was repeated for molybdenum. However,
`the
`substrate was no longer kept at ground potential but biased
`with 230, 210 and 110 V versus ground. The result of the
`experiment is shown in Fig. 3~b!. For negative potential, the
`measured values are always below the previously measured
`values. With the exception of the value taken at 7 Pa, the
`data points for 210 and 230 V are practically coincident. At
`the lowest pressure of 0.2 Pa, the data values coincide also
`with that taken at ground potential. By increasing the pres-
`sure from 0.2 to 1.0 Pa, the energy flux of the negatively
`biased sample does not increase in agreement with Thorn-
`ton’s results.7 For the positive bias, the energy input shows a
`strong increase. From this experiment @Fig. 3~b!# it is clearly
`evident that, with the exception of the low-pressure region,
`the measured values of the energy per atom are affected by
`negatively charged particles.
`
`IV. RESULTS: TRIM.SP SIMULATIONS
`As a test for the results of the TRIM.SP calculations, the
`sputtering yields obtained are compared to experimental
`
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`yields from the early work of Laegreid and Wehner.18 It is
`evident from Fig. 4~a! that for the selected elements ~and
`also for the others, which are not shown! there is fair agree-
`ment between experiment and calculation. This test is con-
`sidered as a hint for the reliability of the TRIM.SP simulations
`also for the other results discussed below.
`
`A. Energy of sputtered atoms
`
`The average kinetic energies of the sputtered atoms de-
`rived from the TRIM.SP simulation are shown in Fig. 4~b!. As
`evident, the functional dependence of the average energy on
`the target voltage ~projectile energy! is well described by a
`power law. Table II contains the parameters of the fit curves.
`With the exception of carbon, the powers are around 1/2 ~in
`agreement with experimental observations1! and show a qua-
`dratic dependence on the target atomic mass with a minimum
`at 118 amu ~see Table II!. Because of the power-law depen-
`dence, there is only a small increase of the kinetic energies at
`voltages above 400 V. The average energies calculated agree
`well with the experimental values given by Thornton7 and
`Dembovski et al.19 This is an additional indication for the
`reliability of the calculations performed.
`
`FIG. 4. Sputtering yields ~TRIM.SP calculations! of selected elements as a
`function of target voltage in comparison to experimental data taken from the
`work of Laegreid and Wehner ~a!. The average energy of the sputter-ejected
`atoms of selected elements as a function of target voltage ~b!. The solid lines
`are linear ~a! and power-law ~b! fit curves, respectively.
`
`In addition, the average energy of the sputtered atoms can
`be calculated in principle by an analytical integration for a
`given energy distribution f (E) and the maximum transferred
`16,20,21 by
`energy E max
`
`^E at&5E
`
`Emax
`
`0
`
`f ~E!E dEY E
`
`Emax
`
`0
`
`f ~E!dE,
`
`~3!
`
`f ~E!5
`
`E
`~E1U 0!312m .
`The potential parameter m for power interaction is chosen to
`be m51/6.22,23 U 0 is the surface binding energy.15,24 Note
`that f is slightly different from the Thompson distribution,1
`which was derived under the assumption of hard sphere col-
`lisions (m50).
`The energy distribution of the sputter-ejected atoms was
`found to satisfactorily obey the distribution function f. For
`projectile energies of 200 eV, the simulated energy distribu-
`tions of the atoms start around energies equivalent to 3U 0 to
`fall below the distribution function f. For projectile energies
`of 400 eV, the validity of the distribution function is ex-
`
`FIG. 3. Total energy input per atom as a function of argon pressure for ~a!
`tungsten and ~b! molybdenum. The data ~a! were taken at different sputter-
`ing powers ~see legend!. The data ~b! were taken at different substrate bias
`~see legend!. The solid lines are fit curves.
`
`JVST A - Vacuum, Surfaces, and Films
`
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`
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`TABLE II. Parameters of the fit curves ^E at&5(V/V C) g describing the energy of the sputtered atoms ^E at& ~in
`eV! as a function of target voltage V @Fig. 4~b!#. For a target voltage of 400 V, the maximum energy E max and
`the factor k are determined by adjusting the results of the analytical calculations according to Eq. ~3! to the
`TRIM.SP results @Fig. 5~a!#.
`
`Element
`
`Parameter V C
`~V!
`
`Parameter g
`
`E max ~eV!
`(E 05400 eV)
`
`Factor k
`(E 05400 eV)
`
`k3G
`(E 05400 eV)
`
`C
`Al
`Si
`V
`Ge
`Mo
`Sn
`Ta
`W
`
`18.1
`11.8
`11.2
`4.31
`2.82
`0.85
`1.62
`1.13
`1.21
`
`0.72
`0.55
`0.60
`0.51
`0.47
`0.44
`0.43
`0.50
`0.51
`
`24.2
`28.2
`31.2
`37.0
`62.7
`66.2
`122.3
`89.9
`86.8
`
`0.111
`0.082
`0.093
`0.107
`0.182
`0.220
`0.416
`0.413
`0.407
`
`0.079
`0.079
`0.090
`0.106
`0.166
`0.183
`0.314
`0.245
`0.239
`
`~4!
`
`E max5kGE 02U 0 , G5
`
`tended to energies of about 9U 0 . These observations are in
`general agreement with experimental and theoretical findings
`by Brizzolara et al.,25 Dembovsky et al.,19 and Yamamura
`and Ishida,26 respectively.
`The main problem when using Eq. ~3! is the determina-
`tion of E max , which is the upper limit of the integral.
`Eisenmenger-Sittner et al.21 proposed to determine E max by
`4M ArM
`~ M Ar1M !2 .
`Here the factor k considers the energy dissipation in the col-
`lision cascade, E 0 is the projectile energy, and M and M Ar
`are the atomic masses of the target and argon. Comparing
`to TRIM simulations, k50.4 is
`analytical calculations
`proposed21 for sputtering Cu and Ni with 0.5 and 1 keV
`argon projectiles, respectively.
`It is possible to determine the quantity of the factor k
`comparing the average atomic energies obtained by TRIM.SP
`with those from the analytical solution of Eq. ~3!. For this
`purpose, the upper limits of the integrals have to be varied
`until identical values of the kinetic energy are obtained. The
`derived values of the factor k are shown in Fig. 5~a! as a
`function of the target atomic mass and at a projectile energy
`of 400 eV. The factor k amounts to 0.1 for masses up to 60
`amu, then steeply increases and reaches a value of 0.4 around
`120 amu. This behavior is well described by a step function,
`which is shown as a fit curve in Fig. 5~a!. Comparing the
`results to the above cited values of k50.4 for Cu and Ni
`sputtering,21 one should keep in mind that the latter are ob-
`tained for higher projectile energies, which might influence
`the quantity of k. Figure 5~a! shows also the quantity kG,
`which mainly determines the value of E max , as a function of
`the target mass. It can be seen that, under the conditions
`simulated, the upper integration limit amounts only to E max
`50.1E 0 for light elements below 80 amu. It reaches a maxi-
`mum at 121 amu with E max50.3E 0 . At higher masses the
`upper limit gradually decreases to E max50.24E 0 at 200 amu.
`The dependence of the quantity kG on the target mass shows
`that the energy transfer in the sputtering process is not sym-
`metric with respect to the ratio of M /M Ar . This result was
`already predicted from previous TRIM.SP simulations.20
`
`J. Vac. Sci. Technol. A, Vol. 17, No. 5, Sep/Oct 1999
`
`To get a functional dependence of the average kinetic
`energy of the sputtered atoms, consideration of the analytical
`solution of Eq. ~4! is less helpful because of its complicated
`structure. For the case of E max@U0 a dependence according
`
`1/3 is derived.20 Calculations of the averageto ^E at&}U 02/33E max
`
`kinetic energies as a function of U 0 and for E max as a param-
`eter ~varying from 30 to 120 eV! from the analytical solution
`of Eq. ~4! were performed. It was found that the dependence
`^E at&}U 0
`2/3 is a reasonable approximation also for lower pro-
`jectile energies. For surface binding energies between 2 and
`4 eV, which are typical for most elements, and for maximum
`energies varying between 30 and 120 eV, the validity of the
`relation ^E at&}E max
`1/3 was ascertained from the analytical so-
`lutions. The average energies calculated by TRIM.SP are plot-
`1/3 in Fig. 5~b!. There is indeedted as a function of U 02/33E max
`
`
`
`1/3 in agreementa linear dependence on the quantity U 02/33E max
`
`with experimental data. Therefore, for typical projectile en-
`ergies investigated in this study, the average kinetic energies
`of the sputtered atoms ~in eV! will be approximated by the
`expression
`1/3 ,^E at&5U 02/33E max
`
`
`~5!
`where U 0 and E max are given in eV. Although Eq. ~5! is
`obtained for a target voltage up to 400 V, it should be also
`valid for higher voltages used in magnetron sputtering.
`
`B. Energy of reflected neutrals
`
`The contribution of the energy of the reflected neutrals to
`the total energy becomes especially pronounced for the
`heavy elements. This is obvious from the calculated particle
`and energy reflection coefficients R N and R E , respectively,
`which are shown in Figs. 6~a! and 6~b! as a function of target
`voltage. These particular data are in agreement with the de-
`tailed simulations of projectile reflection.27 The particle re-
`flection coefficients monotonically decrease from 0.4 ~W!
`down to 0.1 ~V!. The energy reflection coefficients are
`smaller and average 0.12 for W and Ta and decrease down to
`0.005 for vanadium. The increase of the reflection coeffi-
`cients with decreasing target voltage is a general trend for
`noble gas bombardment.27 It results from the fact that the
`
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`FIG. 5. Factor k of Eq. ~4! determined from analytical calculations according
`to Eq. ~3! and TRIM.SP simulations as a function of the target atomic mass.
`The solid line is a fit curve using a step function. ~b! The average kinetic
`energies of sputtered atoms derived by TRIM.SP calculations at a projectile
`energy of 400 eV as a function of a mathematical expression of surface
`binding energy and maximum transferred energy. Experimental data
`adopted from the literature are shown for comparison ~see legend!.
`
`FIG. 6. Particle ~a! and energy reflection coefficients ~b! for the backscat-
`tered argon neutrals as a function of target voltage obtained from the TRIM.SP
`calculations for selected elements. The solid lines represent fit curves ac-
`cording to the equations given.
`
`typical values for magnetron sputtering. The data shown
`agree quite well with earlier TRIM.SP and molecular dynamics
`simulations and also with experimental measurements.27–30
`The functional dependence of the reflection coefficients on
`the atomic mass of the target is well described by the ana-
`lytical expressions, which are represented by the solid lines
`in Fig. 7 as
`
`R N5S M 2M Ar
`
`M N
`
`
`
`D h, R E5S M 2M Ar
`
`M E
`
`D g
`
`.
`
`~7!
`
`~6!
`
`The values of the fit curves in Fig. 7 are M E5806 amu,
`M N5775 amu, h51.26, and g50.59. In addition, Fig. 7
`shows also the ratio r5R E /R N as a function of target mass.
`The value of r is of interest, as it determines the average
`energy of the reflected neutrals ^E Ar&5rE 0 . 27 As shown in
`Fig. 7, there is a linear dependence of the quantity r ~at E 0
`5400 eV) on the target mass
`
`~8!
`
`,
`
`M M
`
`R
`
`r5r 01
`
`JVST A - Vacuum, Surfaces, and Films
`
`probability for backscattering decreases with the penetration
`depth of the incoming Ar, which increases with energy. The
`functional dependence of the reflection coefficients on the
`target voltage V T can ~in the range investigated! be well
`described by the analytical expressions:
`
`R N512S V T
`
`
`
`D n, R E512S V T
`
`D e
`
`.
`
`V E
`V N
`For the particle reflection, the fit parameter V N is around
`6500 V for V, Ge and Mo and it is about 20 000 V for the
`heavier elements. The parameter nis approximately 0.1. For
`the energy reflection, the fit parameters V E are similar to V N .
`The power eis 0.001 and 0.006 for V and Ge, respectively,
`and 0.014 for Mo and Sn. It is 0.031 and 0.037 for Ta and W,
`respectively. From the validity of Eq. ~6! with the values for
`nand eit is clear that an increase of the target voltage to say
`500 V has little influence on the reflection coefficients.
`Therefore, the values of R N and R E at 400 eV, shown in Fig.
`7 as a function of target atomic mass, can be considered as
`
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`FIG. 7. Particle and energy reflection coefficients and the ratio of both for
`backscattered argon neutrals obtained from the TRIM.SP calculations at a
`target voltage of 400 V. The data are plotted as a function of target atomic
`mass. The fit curves are according to Eqs. ~7! and ~8!.
`
`with r 0520.0319 and M R5527 amu. This relationship is
`quite different from the parabolic dependence of the energy
`of the reflected neutrals on atomic mass suggested by Thorn-
`ton and Hoffman.31
`
`V. DISCUSSION
`
`A. Comparison between experiment and calculation
`
`In Sec. III it was argued that the general trend of energy
`to decrease with decreasing pressure results from the elec-
`tronic contribution to the heating of the substrates. There-
`fore, in the following it will be assumed that at the lowest
`pressure of 0.4 Pa, where the plasma was sustained for all
`combinations of powers and target materials, the contribu-
`tions of electrons to the measured values can be neglected.
`From the fit curves shown in Figs. 1–3 it is evident that this
`assumption is very rough for the case of carbon. Therefore,
`this result will be excluded from the quantitative discussion.
`Improving the model established by Thornton7 the total en-
`ergy per incorporated atom ^E t& can be calculated by16
`R E
`Y
`
`~9!
`
`^E t&5U 01^E at&1E 0
`
`1^E P&.
`
`Here the first and second terms are the contribution of the
`heat of condensation and the average atomic energy of the
`incorporated atoms, respectively. The third term represents
`the contribution of the reflected neutrals ~per sputtered
`atom!. This quantity depends on the sputtering yield and the
`particle reflection coefficient ~see also above and Ref. 16!.
`The forth term is the contribution of plasma irradiation,
`which was given by Thornton7 in a rough estimate to be
`^E P&55.33/Y ~with ^E P& in eV and Y in atoms/ion!. Note
`that Eq. ~9! implicitly assumes identical angular distributions
`of sputtered and reflected atoms. In addition, any inhomoge-
`neities due to the specific erosion profiles of the magnetrons
`are ignored. Comparing the calculated with the experimental
`
`J. Vac. Sci. Technol. A, Vol. 17, No. 5, Sep/Oct 1999
`
`FIG. 8. Measured total energy input per atom ~sputter-deposition at 0.4 Pa!
`in comparison with theoretical values resulting from the TRIM.SP calculations
`as a function of target voltage ~discharge power! for ~a! aluminum and ~b!
`germanium. Open symbols are the contribution of ~i! the kinetic energy of
`the sputter-ejected atoms, ~ii! the kinetic energy of the reflected neutrals
`~normalized per incorporated atom!, and ~iii! the plasma irradiation @see
`legend and Eq. ~9!#. The lines drawn are visual guides.
`
`values, one also has to keep in mind that the particles on
`their way between target and substrate experience collisions
`with the argon atoms of the sputtering atmosphere, which
`cause an energy loss of these atoms. This loss in energy ~at
`the chosen argon pressure of 0.4 Pa! is less than 30% based
`on the data taken from Somekh.32 For two reasons, the effect
`of thermalization will be ignored. First, there are very few
`experimental investigations on the characteristic pressure–
`distance product of thermalization for specific elements ~see
`the work by Ball et al. for Cu!.33 Second, with increasing
`discharge power the effect of gas density reduction becomes
`significant.34–36 This makes an exact determination of the
`energy loss difficult even for a given pressure–distance prod-
`uct.
`Neglecting the effect of gas density reduction, the influ-
`ence of sputtering power on the energy flux can be simply
`described via the power-dependent
`target voltage. This
`makes a direct comparison between calculated and experi-
`mental data possible. Figure 8 shows this for the case of Al
`
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`FIG. 9. Measured total energy input per atom ~sputter deposition at 0.4 Pa!
`in comparison with theoretical values resulting from the TRIM.SP calculations
`as a function of target voltage ~sputtering power! for ~a! molybdenum and
`~b! tungsten. Open symbols are the contribution of: ~i! the kinetic energy of
`the sputter-ejected atoms, ~ii! the kinetic energy of the reflected neutrals
`~normalized per incorporated atom!, and ~iii! the plasma irradiation @see
`legend and Eq. ~9!#. The lines drawn are visual guides.
`
`FIG. 10. Total energy input per atom as a