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Stress generation during ion beam-assisted pulsed laser deposition of thin AlN films
Thin Solid Films 415 (2002) 285–289
Stress generation during ion beam-assisted pulsed laser deposition of thin AlN films S. Sixa,*, B. Rauschenbachb a
¨ Physik, Universitat ¨ Augsburg, Experimentalphysik IV, D-86135 Augsburg, Germany Institut fur b ¨ Oberflachenmodifizierung, ¨ Institut fur Permoserstraße 15, D-04318 Leipzig, Germany Received 19 January 2001; received in revised form 11 April 2002; accepted 11 April 2002
Abstract AlN films, grown by nitrogen or argon ion beam-assisted pulsed laser deposition, exhibit very high stresses at a certain ion energy. These stresses are mainly caused by ion beam-induced defects. The magnitude of stress is found to depend not only on the ion energy, but also on the deposition temperature and the ion incidence angle. To explain the relation of the observed film stresses and the appropriate deposition parameters, a simple model was developed. The model takes into account the annealing of a certain fraction of the ion beam-induced point defects by thermal diffusion towards the film surface, which acts like a sink of the defect concentration. This model allows us to predict the ion energy where the point defect concentration in a film reaches a maximum in agreement with the experimental observation of the stress maximum. 䊚 2002 Published by Elsevier Science B.V. Keywords: Laser ablation; Ion beam-assisted deposition; AlN; Film stress
1. Introduction AlN is an electrical insulator due to its wide electronic band gap of 6.2 eV w1x. The suitability of AlN films as a basic material for surface acoustic wave filters (SAWs) w2x and pyroelectric sensors w3x has been demonstrated. Very thin AlN layers are also an ideal buffer material for an improved growth of GaN on sapphire substrates, because the lattice misfit of hexagonal AlN and csapphire is smaller than the lattice misfit of GaN and csapphire w4x. Bragg reflectors, based on AlNyGaN quaterwave layers, are recently fabricated to realize vertical cavity surface emitting laser structures w5x. For these applications epitaxial AlN films of an enhanced crystalline quality are necessary. It is generally known, that ion beam bombardment of a growing film makes it possible to influence important film properties, e.g. crystalline texture w6,7x, hardness w8x and stresses w9x. Recently, it has been shown, that argon ion beam irradiation during film deposition is able to enhance the *Corresponding author present address. Carl Zeiss SMT AG, D73446 Oberkochen, Germany, Tel.: q49-821-5983498; fax: q49821-5983425. E-mail address: [email protected] (S. Six).
epitaxy of AlN on c-plane oriented sapphire substrates w10x. In this article, a detailed study of the influence of low energy ion bombardment and substrate temperature on the stress generation at the deposition of AlN films on sapphire substrates is presented. The aim is to explain the dependency of the intrinsic stress on the deposing conditions on the base of ion beam-induced defects. 2. Experimental Aluminum nitride thin films were produced by the ion beam-assisted pulsed laser deposition (IBA-PLD) method. A KrF-excimer laser (pulse energy 300 mJ, pulse length 40 ns) was used for ablation from a sintered, stoichiometrical AlN target. The deposition rate could be estimated to be 0.01 nm per laser pulse and the substrate temperature ranged between 650 and 850 8C. Additionally, the growing AlN films were irradiated with argon or nitrogen ions. The argon ion beam was generated by a radio frequency (r.f.) ion source. For nitrogen irradiation the r.f. ion source was replaced by a Kaufman type ion source, enabling a higher nitrogen ion flux. The applied ion energies were between 100
0040-6090/02/$ - see front matter 䊚 2002 Published by Elsevier Science B.V. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 2 . 0 0 3 5 8 - 9
286
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289
Fig. 1. XRD uy2u measurements on the AlN (0002)-reflection peak for films produced without ion irradiation and under 500 and 400 eV argon ion bombardment.
and 700 eV for both ion sources. An ion current density between 100 and 200 mAycm2 was obtainable. It should be mentioned, that the number of incoming ions at an ion current density of 200 mAycm2 is nearly half of the amount of the deposited atoms at a laser pulse frequency of 20 Hz. A more detailed description of this deposition technique can be found elsewhere w10,11x. To analyze the crystalline structure and the stress of AlN films, X-ray diffraction (XRD) measurements in Bragg–Brentano geometry w12x were carried out, using Cu Ka radiation with a wavelength of 0.15406 nm. Additionally, Rutherford backscattering (RBS) measurements were performed, employing a tandem accelerator and 1.5 MeV Heq ions to determine the film composition. 3. Results and discussion AlN films deposited by IBA-PLD at temperatures greater than 400 8C are crystalline. They only consist of the hexagonal wurtzitic AlN phase. AlN grows epitaxially on c-sapphire substrates with its c-axis perpendicular to the substrate w11,13x. For films produced without ion irradiation, compressive thermal stress is dominating w14x. The lattice parameters differ only little from those of unstressed bulk material, if the film thickness is above 50 nm. To investigate the influence of ion energy on the crystalline properties of AlN, films were produced under argon and under nitrogen ion bombardment of various ion energies. As an example, Fig. 1 shows uy2u XRD measurements on the AlN (0002)-reflection peak of films prepared without and with argon ion bombardment at 400 and at 500 eV, respectively. A deposition temperature of 700 8C and a fixed ion incidence angle of 308 to the film surface was chosen for all of these films. The thickness of the films was between 100 and 200 nm. It can be seen clearly, that the AlN (0002)-peak is shifted to smaller 2u-angles as a consequence of ion irradiation. This means, the AlN c-axis is expanded
relative to the lattice constant of unstressed bulk material. The peak width enables us to determine an average coherence length of the diffracted X-rays along the caxis between 40 and 50 nm, similar for all films. For example, stacking faults may be responsible for this limitation. As Fig. 2 shows, argon ion irradiation during film deposition leads to an extremely expanded AlN c-axis at an ion energy of 500 eV. For higher ion energies the observed strain of the films decreases again. Above 800 eV all deposited material is sputtered by the ions and no film can be produced any more. The maximum caxis expansion of nearly 2% at 500 eV indicates, that only ion beam-induced defects can be responsible for these intrinsic stresses. This result and its influence on epitaxy was reported in detail previously w10x. Compared with argon ion bombardment, nitrogen ion irradiation causes an even stronger c-axis expansion at more than 300 eV ion energy (Fig. 2). At 500 eV crystalline quality of the films becomes worse and at higher nitrogen ion energies the films exhibit only comparatively poor crystalline quality with small grain sizes. AlN films were also produced at different substrate temperatures but the same argon ion energy of 500 eV. From 700 to 800 8C the film strain decreases strongly. For temperatures less than 700 8C the c-axis expansion is nearly equal at approximately 1.8% w10x. An example of a RBS-spectrum is offered in Fig. 3, which allows to determine the elementary composition of a film. All investigated films are found to consist of stoichiometric AlN. The argon content of films, grown under argon ion bombardment, is always below 800 ppm. There exists no dependency of the c-axis expansion on the argon concentration. Therefore, the ion beaminduced film stress results rather from lattice defects, which are caused by argon ions, than from the implanted argon atoms. Davis w15x has proposed a model of compressive stress, induced by ion beam-assisted film deposition,
Fig. 2. Relative expansion of the AlN c-axis at different ion energies for argon (black line) and nitrogen ion irradiation (gray line).
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289
Fig. 3. Helium ion (1.5 MeV) RBS-spectrum of an AlN film deposed on sapphire substrate under argon ion irradiation. The inset shows the helium ions, backscattered on the argon atoms of the film.
independent of the temperature. Effects, like surface sputtering and defect diffusion, are ignored. By application of this model a stress maximum for nitrogen ion irradiation of AlN at an ion energy of less than 100 eV can be predicted. Here, the loss of ion beam-induced point defects by their diffusion towards the film surface and the influence of temperature and re-sputtering are considered. Fig. 4 summarizes the events, which take place during ion beam-assisted film deposition. Knock-on cascades of atomic collisions induced by an incoming ion lead to point defects, e.g. vacancies and interstitials w16x. The parameter describing the average depth of these defects should be called l. Further atoms are removed from the surface by sputtering. The local average sputtering depth at the ion impact region should be represented by the symbol j. It is necessary to take respect of the point defect mobility at those high temperatures, where film deposition takes part. The film surface acts like a sink for the concentration of point defects like interstitials. That is the reason, why a certain fraction of these ion beam-induced defects disappears at the surface, before the next layer of atoms is deposited. To investigate the defect diffusion, it is necessary to recognize the depth profiles of the ion beam-induced defects g(z). Here the parameter z represents the distance to the film surface. g(z) as well as surface sputtering can be calculated with the SRIM algorithm w17x—a Monte Carlo simulation of the ion–solid interactions— for different ion energies and ion incidence angles. Finally, to find out the remaining defect density n in a growing film, the diffusion equation wEq. (1)x has to be solved for a given diffusion coefficient D(T) and continuing defect generation with the rate g(z). ≠n Žz,t.sDŽT.Ø=2nŽz,t.qgŽz. ≠t
(1)
The temperature dependency of the diffusion coefficient D(T) can be described by an Arrhenius equation wEq. (2)x.
287
Fig. 4. Scheme of an ion beam-assisted film deposition. The parameter j describes the average depth of the ion beam-induced point defects and the parameter l represents the removed fraction of the surface by sputtering. B
DŽT.sD0ØexpCy D
UE F kT G
(2)
The values of the activation energy U and the diffusion constant D0 for defects can be estimated by comparing the remaining defect density n, calculated for various diffusion coefficients D(T), and the measured AlN c-axis expansion for different deposition temperatures (Fig. 5). Measurement and calculation show the best agreement for Us3.2 eV and D0s1 cm2 ys. According to the results of SRIM simulations, the average depth l of the ion beam-induced point defects increases proportional to the square root of the ion energy EIon wEq. (3)x and the sputtered fraction of the surface j increases directly proportional to EIon for ion energies less than 1 keV wEq. (4)x. Both parameters—l and j—depend on the incidence angle a of the ions. Especially for small angles a, sputtering becomes important, while the average defect depth is less than for normal incidence of the ions. lsclØsinaØyEIon
(3)
jscjŽa.ØEIon
(4)
Table 1 offers a survey of the coefficients cl and cj (308) as a result of SRIM simulations w17x.
Fig. 5. The circles show the measured expansion of the AlN c-axis, caused by stress, at different substrate temperatures (all films produced under 500 eV argon ion irradiation). The gray line indicates the calculated point defect density which remains in a growing AlN film, irradiated with argon ions of the same energy.
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289
288
Table 1 Proportional constants cl for the average depth of defects l wEq. (3)x and cj for the sputtered fraction j of the surface wEq. (4)x in the case of argon and nitrogen ion irradiation
cl wnmyyeVx cj(308) wnmyeVx
Argon ion bombardment
Nitrogen ion bombardment
0.025 4.8=10y4
0.034 3.2=10y4
Now it is possible to estimate the remaining defect concentration n. This magnitude is proportional to the difference of the total point defect generation rate gs
|
gŽz.dzAEIonZ and the loss rate of defects by diffusion
to the film surface wEq. (5)x. The second term contains not only the diffusion coefficient D(T), but also the effective defect average depth lyj. In this term the numerical constant 0.38 results from integrating the gradient n(z)y(lyj) of the defect concentration. B n UE ØD0expCy F´n lyj kT G D g s B D0 UE Rq0.38 expCy F lyj kT G D
nØRsgy0.38Ø
(5)
Because l and j depend on the ion energy, the effective defect average depth—and therefore the remaining defect concentration—undergoes a maximum. Fig. 6 shows the calculated dependency of the remaining defect density on the ion energy for argon and nitrogen ions. There is a maximum of the defect density for argon ion irradiation at approximately 500 eV ion energy. Nitrogen ion bombardment, on the other hand, leads to a much stronger increasing defect concentration. This behavior is caused by the longer range of nitrogen ions due to their smaller energy loss in AlN. As a
Fig. 6. Calculated point defect concentration at different ion energies for argon (black line) and nitrogen (gray line) ion irradiation at a deposition temperature of 750 8C and a film growth rate of 0.1 nmys.
consequence defects are induced deeper beneath the film surface, wherefrom less of them can reach the surface. These results confirm the experimental observations of film strain (Fig. 2). Differently from the theoretical predictions the measured c-axis expansion increases very strongly at 400 eV. This can be understood, when it is taken into account, that a point defect hinders the diffusion of other defects next to it. Beyond a critical concentration the diffusion coefficient finally drops drastically (for a detailed discussion see Six w18x). 4. Summary and conclusions Argon or nitrogen ion bombardment of a growing AlN film leads to an extreme expansion of the AlN caxis. Above 500 eV the strain caused by argon ion irradiation decreases again, while in the case of nitrogen ion bombardment the films start to lose their crystalline order for an ion energy of more than 500 eV. The observed strain of AlN films, produced by ion beam-assisted deposition, can be described qualitative correctly by a simple model. This model considers effects like surface sputtering and diffusion of ion beaminduced point defects towards the film surface. The decrease of the film strain at higher deposition temperatures can be explained in the same way. An activation energy of approximately 3.2 eV for defect self-diffusion could be estimated by comparing the c-axis expansion of films, grown at various temperatures, and defect calculations for different diffusion coefficients. The presented model seems to be suitable also for other ion species and distinct materials. References w1x S.J. Pearton, GaN Relat. Mater. 2 (1997) 233. w2x J. Meinschien, G. Behme, F. Falk, H. Stafast, Appl. Phys. A 69 (1999) 683. w3x V. Fuflyigin, E. Sally, A. Osinsky, P. Norris, Appl. Phys. Lett. 77 (19) (2000) 3075. w4x S.C. Jain, M. Willander, J. Narayan, R. Van Overstraeten, J. Appl. Phys. 87 (2000) 965. w5x H.M. Ng, T.D. Moustakas, S.N.G. Chu, Appl. Phys. Lett. 76 (2000) 2818. w6x F.A. Smidt, Intern. Mater. Rev. 35 (1990) 61. w7x B. Rauschenbach, S. Sienz, S. Six, J.W. Gerlach, Surf. Coat. Technol. 142y144 (2001) 371. w8x P.J. Martin, R.P. Netterfield, W.G. Sainty, J. Appl. Phys. 55 (1984) 235. w9x H. Windischmann, J. Appl. Phys. 45 (1974) 4760. w10x S. Six, J.W. Gerlach, B. Rauschenbach, Surf. Coat. Technol. 142y144 (2001) 397. w11x S. Six, J.W. Gerlach, B. Rauschenbach, Thin Solid Films 370 (2000) 1. w12x H.P. Klug, L.E. Alexander, X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials, Wiley, New York, 1974, p. 656.
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289 w13x J. Meinschien, F. Falk, R. Hergt, H. Stafast, Appl. Phys. A 70 (2000) 215. w14x J. Keckes, S. Six, J.W. Gerlach, B. Rauschenbach, J. Cryst. Growth 240 (2002) 80. w15x C.A. Davis, Thin Solid Films 226 (1992) 30.
289
w16x P. Siegmund, in: R. Behrisch (Ed.), Sputtering by Particle Bombardment, Springer, Berlin, 1981, p. 49. w17x J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Ranges of Ions in Solids, Pergamon Press, New York, 1996. w18x S. Six, Thesis Universitat ¨ Augsburg 2001, published in Mensch und Buch Verlag, Berlin, 2001.
Stress generation during ion beam-assisted pulsed laser deposition of thin AlN films S. Sixa,*, B. Rauschenbachb a
¨ Physik, Universitat ¨ Augsburg, Experimentalphysik IV, D-86135 Augsburg, Germany Institut fur b ¨ Oberflachenmodifizierung, ¨ Institut fur Permoserstraße 15, D-04318 Leipzig, Germany Received 19 January 2001; received in revised form 11 April 2002; accepted 11 April 2002
Abstract AlN films, grown by nitrogen or argon ion beam-assisted pulsed laser deposition, exhibit very high stresses at a certain ion energy. These stresses are mainly caused by ion beam-induced defects. The magnitude of stress is found to depend not only on the ion energy, but also on the deposition temperature and the ion incidence angle. To explain the relation of the observed film stresses and the appropriate deposition parameters, a simple model was developed. The model takes into account the annealing of a certain fraction of the ion beam-induced point defects by thermal diffusion towards the film surface, which acts like a sink of the defect concentration. This model allows us to predict the ion energy where the point defect concentration in a film reaches a maximum in agreement with the experimental observation of the stress maximum. 䊚 2002 Published by Elsevier Science B.V. Keywords: Laser ablation; Ion beam-assisted deposition; AlN; Film stress
1. Introduction AlN is an electrical insulator due to its wide electronic band gap of 6.2 eV w1x. The suitability of AlN films as a basic material for surface acoustic wave filters (SAWs) w2x and pyroelectric sensors w3x has been demonstrated. Very thin AlN layers are also an ideal buffer material for an improved growth of GaN on sapphire substrates, because the lattice misfit of hexagonal AlN and csapphire is smaller than the lattice misfit of GaN and csapphire w4x. Bragg reflectors, based on AlNyGaN quaterwave layers, are recently fabricated to realize vertical cavity surface emitting laser structures w5x. For these applications epitaxial AlN films of an enhanced crystalline quality are necessary. It is generally known, that ion beam bombardment of a growing film makes it possible to influence important film properties, e.g. crystalline texture w6,7x, hardness w8x and stresses w9x. Recently, it has been shown, that argon ion beam irradiation during film deposition is able to enhance the *Corresponding author present address. Carl Zeiss SMT AG, D73446 Oberkochen, Germany, Tel.: q49-821-5983498; fax: q49821-5983425. E-mail address: [email protected] (S. Six).
epitaxy of AlN on c-plane oriented sapphire substrates w10x. In this article, a detailed study of the influence of low energy ion bombardment and substrate temperature on the stress generation at the deposition of AlN films on sapphire substrates is presented. The aim is to explain the dependency of the intrinsic stress on the deposing conditions on the base of ion beam-induced defects. 2. Experimental Aluminum nitride thin films were produced by the ion beam-assisted pulsed laser deposition (IBA-PLD) method. A KrF-excimer laser (pulse energy 300 mJ, pulse length 40 ns) was used for ablation from a sintered, stoichiometrical AlN target. The deposition rate could be estimated to be 0.01 nm per laser pulse and the substrate temperature ranged between 650 and 850 8C. Additionally, the growing AlN films were irradiated with argon or nitrogen ions. The argon ion beam was generated by a radio frequency (r.f.) ion source. For nitrogen irradiation the r.f. ion source was replaced by a Kaufman type ion source, enabling a higher nitrogen ion flux. The applied ion energies were between 100
0040-6090/02/$ - see front matter 䊚 2002 Published by Elsevier Science B.V. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 2 . 0 0 3 5 8 - 9
286
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289
Fig. 1. XRD uy2u measurements on the AlN (0002)-reflection peak for films produced without ion irradiation and under 500 and 400 eV argon ion bombardment.
and 700 eV for both ion sources. An ion current density between 100 and 200 mAycm2 was obtainable. It should be mentioned, that the number of incoming ions at an ion current density of 200 mAycm2 is nearly half of the amount of the deposited atoms at a laser pulse frequency of 20 Hz. A more detailed description of this deposition technique can be found elsewhere w10,11x. To analyze the crystalline structure and the stress of AlN films, X-ray diffraction (XRD) measurements in Bragg–Brentano geometry w12x were carried out, using Cu Ka radiation with a wavelength of 0.15406 nm. Additionally, Rutherford backscattering (RBS) measurements were performed, employing a tandem accelerator and 1.5 MeV Heq ions to determine the film composition. 3. Results and discussion AlN films deposited by IBA-PLD at temperatures greater than 400 8C are crystalline. They only consist of the hexagonal wurtzitic AlN phase. AlN grows epitaxially on c-sapphire substrates with its c-axis perpendicular to the substrate w11,13x. For films produced without ion irradiation, compressive thermal stress is dominating w14x. The lattice parameters differ only little from those of unstressed bulk material, if the film thickness is above 50 nm. To investigate the influence of ion energy on the crystalline properties of AlN, films were produced under argon and under nitrogen ion bombardment of various ion energies. As an example, Fig. 1 shows uy2u XRD measurements on the AlN (0002)-reflection peak of films prepared without and with argon ion bombardment at 400 and at 500 eV, respectively. A deposition temperature of 700 8C and a fixed ion incidence angle of 308 to the film surface was chosen for all of these films. The thickness of the films was between 100 and 200 nm. It can be seen clearly, that the AlN (0002)-peak is shifted to smaller 2u-angles as a consequence of ion irradiation. This means, the AlN c-axis is expanded
relative to the lattice constant of unstressed bulk material. The peak width enables us to determine an average coherence length of the diffracted X-rays along the caxis between 40 and 50 nm, similar for all films. For example, stacking faults may be responsible for this limitation. As Fig. 2 shows, argon ion irradiation during film deposition leads to an extremely expanded AlN c-axis at an ion energy of 500 eV. For higher ion energies the observed strain of the films decreases again. Above 800 eV all deposited material is sputtered by the ions and no film can be produced any more. The maximum caxis expansion of nearly 2% at 500 eV indicates, that only ion beam-induced defects can be responsible for these intrinsic stresses. This result and its influence on epitaxy was reported in detail previously w10x. Compared with argon ion bombardment, nitrogen ion irradiation causes an even stronger c-axis expansion at more than 300 eV ion energy (Fig. 2). At 500 eV crystalline quality of the films becomes worse and at higher nitrogen ion energies the films exhibit only comparatively poor crystalline quality with small grain sizes. AlN films were also produced at different substrate temperatures but the same argon ion energy of 500 eV. From 700 to 800 8C the film strain decreases strongly. For temperatures less than 700 8C the c-axis expansion is nearly equal at approximately 1.8% w10x. An example of a RBS-spectrum is offered in Fig. 3, which allows to determine the elementary composition of a film. All investigated films are found to consist of stoichiometric AlN. The argon content of films, grown under argon ion bombardment, is always below 800 ppm. There exists no dependency of the c-axis expansion on the argon concentration. Therefore, the ion beaminduced film stress results rather from lattice defects, which are caused by argon ions, than from the implanted argon atoms. Davis w15x has proposed a model of compressive stress, induced by ion beam-assisted film deposition,
Fig. 2. Relative expansion of the AlN c-axis at different ion energies for argon (black line) and nitrogen ion irradiation (gray line).
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289
Fig. 3. Helium ion (1.5 MeV) RBS-spectrum of an AlN film deposed on sapphire substrate under argon ion irradiation. The inset shows the helium ions, backscattered on the argon atoms of the film.
independent of the temperature. Effects, like surface sputtering and defect diffusion, are ignored. By application of this model a stress maximum for nitrogen ion irradiation of AlN at an ion energy of less than 100 eV can be predicted. Here, the loss of ion beam-induced point defects by their diffusion towards the film surface and the influence of temperature and re-sputtering are considered. Fig. 4 summarizes the events, which take place during ion beam-assisted film deposition. Knock-on cascades of atomic collisions induced by an incoming ion lead to point defects, e.g. vacancies and interstitials w16x. The parameter describing the average depth of these defects should be called l. Further atoms are removed from the surface by sputtering. The local average sputtering depth at the ion impact region should be represented by the symbol j. It is necessary to take respect of the point defect mobility at those high temperatures, where film deposition takes part. The film surface acts like a sink for the concentration of point defects like interstitials. That is the reason, why a certain fraction of these ion beam-induced defects disappears at the surface, before the next layer of atoms is deposited. To investigate the defect diffusion, it is necessary to recognize the depth profiles of the ion beam-induced defects g(z). Here the parameter z represents the distance to the film surface. g(z) as well as surface sputtering can be calculated with the SRIM algorithm w17x—a Monte Carlo simulation of the ion–solid interactions— for different ion energies and ion incidence angles. Finally, to find out the remaining defect density n in a growing film, the diffusion equation wEq. (1)x has to be solved for a given diffusion coefficient D(T) and continuing defect generation with the rate g(z). ≠n Žz,t.sDŽT.Ø=2nŽz,t.qgŽz. ≠t
(1)
The temperature dependency of the diffusion coefficient D(T) can be described by an Arrhenius equation wEq. (2)x.
287
Fig. 4. Scheme of an ion beam-assisted film deposition. The parameter j describes the average depth of the ion beam-induced point defects and the parameter l represents the removed fraction of the surface by sputtering. B
DŽT.sD0ØexpCy D
UE F kT G
(2)
The values of the activation energy U and the diffusion constant D0 for defects can be estimated by comparing the remaining defect density n, calculated for various diffusion coefficients D(T), and the measured AlN c-axis expansion for different deposition temperatures (Fig. 5). Measurement and calculation show the best agreement for Us3.2 eV and D0s1 cm2 ys. According to the results of SRIM simulations, the average depth l of the ion beam-induced point defects increases proportional to the square root of the ion energy EIon wEq. (3)x and the sputtered fraction of the surface j increases directly proportional to EIon for ion energies less than 1 keV wEq. (4)x. Both parameters—l and j—depend on the incidence angle a of the ions. Especially for small angles a, sputtering becomes important, while the average defect depth is less than for normal incidence of the ions. lsclØsinaØyEIon
(3)
jscjŽa.ØEIon
(4)
Table 1 offers a survey of the coefficients cl and cj (308) as a result of SRIM simulations w17x.
Fig. 5. The circles show the measured expansion of the AlN c-axis, caused by stress, at different substrate temperatures (all films produced under 500 eV argon ion irradiation). The gray line indicates the calculated point defect density which remains in a growing AlN film, irradiated with argon ions of the same energy.
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289
288
Table 1 Proportional constants cl for the average depth of defects l wEq. (3)x and cj for the sputtered fraction j of the surface wEq. (4)x in the case of argon and nitrogen ion irradiation
cl wnmyyeVx cj(308) wnmyeVx
Argon ion bombardment
Nitrogen ion bombardment
0.025 4.8=10y4
0.034 3.2=10y4
Now it is possible to estimate the remaining defect concentration n. This magnitude is proportional to the difference of the total point defect generation rate gs
|
gŽz.dzAEIonZ and the loss rate of defects by diffusion
to the film surface wEq. (5)x. The second term contains not only the diffusion coefficient D(T), but also the effective defect average depth lyj. In this term the numerical constant 0.38 results from integrating the gradient n(z)y(lyj) of the defect concentration. B n UE ØD0expCy F´n lyj kT G D g s B D0 UE Rq0.38 expCy F lyj kT G D
nØRsgy0.38Ø
(5)
Because l and j depend on the ion energy, the effective defect average depth—and therefore the remaining defect concentration—undergoes a maximum. Fig. 6 shows the calculated dependency of the remaining defect density on the ion energy for argon and nitrogen ions. There is a maximum of the defect density for argon ion irradiation at approximately 500 eV ion energy. Nitrogen ion bombardment, on the other hand, leads to a much stronger increasing defect concentration. This behavior is caused by the longer range of nitrogen ions due to their smaller energy loss in AlN. As a
Fig. 6. Calculated point defect concentration at different ion energies for argon (black line) and nitrogen (gray line) ion irradiation at a deposition temperature of 750 8C and a film growth rate of 0.1 nmys.
consequence defects are induced deeper beneath the film surface, wherefrom less of them can reach the surface. These results confirm the experimental observations of film strain (Fig. 2). Differently from the theoretical predictions the measured c-axis expansion increases very strongly at 400 eV. This can be understood, when it is taken into account, that a point defect hinders the diffusion of other defects next to it. Beyond a critical concentration the diffusion coefficient finally drops drastically (for a detailed discussion see Six w18x). 4. Summary and conclusions Argon or nitrogen ion bombardment of a growing AlN film leads to an extreme expansion of the AlN caxis. Above 500 eV the strain caused by argon ion irradiation decreases again, while in the case of nitrogen ion bombardment the films start to lose their crystalline order for an ion energy of more than 500 eV. The observed strain of AlN films, produced by ion beam-assisted deposition, can be described qualitative correctly by a simple model. This model considers effects like surface sputtering and diffusion of ion beaminduced point defects towards the film surface. The decrease of the film strain at higher deposition temperatures can be explained in the same way. An activation energy of approximately 3.2 eV for defect self-diffusion could be estimated by comparing the c-axis expansion of films, grown at various temperatures, and defect calculations for different diffusion coefficients. The presented model seems to be suitable also for other ion species and distinct materials. References w1x S.J. Pearton, GaN Relat. Mater. 2 (1997) 233. w2x J. Meinschien, G. Behme, F. Falk, H. Stafast, Appl. Phys. A 69 (1999) 683. w3x V. Fuflyigin, E. Sally, A. Osinsky, P. Norris, Appl. Phys. Lett. 77 (19) (2000) 3075. w4x S.C. Jain, M. Willander, J. Narayan, R. Van Overstraeten, J. Appl. Phys. 87 (2000) 965. w5x H.M. Ng, T.D. Moustakas, S.N.G. Chu, Appl. Phys. Lett. 76 (2000) 2818. w6x F.A. Smidt, Intern. Mater. Rev. 35 (1990) 61. w7x B. Rauschenbach, S. Sienz, S. Six, J.W. Gerlach, Surf. Coat. Technol. 142y144 (2001) 371. w8x P.J. Martin, R.P. Netterfield, W.G. Sainty, J. Appl. Phys. 55 (1984) 235. w9x H. Windischmann, J. Appl. Phys. 45 (1974) 4760. w10x S. Six, J.W. Gerlach, B. Rauschenbach, Surf. Coat. Technol. 142y144 (2001) 397. w11x S. Six, J.W. Gerlach, B. Rauschenbach, Thin Solid Films 370 (2000) 1. w12x H.P. Klug, L.E. Alexander, X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials, Wiley, New York, 1974, p. 656.
S. Six, B. Rauschenbach / Thin Solid Films 415 (2002) 285–289 w13x J. Meinschien, F. Falk, R. Hergt, H. Stafast, Appl. Phys. A 70 (2000) 215. w14x J. Keckes, S. Six, J.W. Gerlach, B. Rauschenbach, J. Cryst. Growth 240 (2002) 80. w15x C.A. Davis, Thin Solid Films 226 (1992) 30.
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w16x P. Siegmund, in: R. Behrisch (Ed.), Sputtering by Particle Bombardment, Springer, Berlin, 1981, p. 49. w17x J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Ranges of Ions in Solids, Pergamon Press, New York, 1996. w18x S. Six, Thesis Universitat ¨ Augsburg 2001, published in Mensch und Buch Verlag, Berlin, 2001.