- Email: [email protected]
The electronic structure of tungsten impurities in diamond films
Solid State Communications,Vol. 102, No. 12, pp. 867-870, 1997 0 1997 Elsevier Science Ltd Printed in Great Britain. All tights reserved 0038-1098/‘97 $17.00+.00
PII: s0038-10!%(!37)00117-8
THE ELECTRONIC STRUCTURE OF TUNGSTEN IMPURITIES IN DIAMOND FILMS F.G. Anderson,“* T. Dallas,b S. Lal,b S. Gangopadhyayb and M. Holtzb ‘Department of Physics, University of Vermont, Burlington VT 05405, U.S.A. department of Physics, Texas Tech University, Lubbock, Texas, 79409-105 1, U.S.A. (Received 20 August 1996; revised 7 March 1997 by M.F. Collins)
A model for the electronic structure of the tungsten impurity in diamond is presented that explains recent photoluminescence results. The model is based on the Ludwig and Woodbury model for interstitial transition-metal impurities in silicon and includes Jahn-Teller coupling, which almost entirely quenches the orbital angular momentum. 0 1997 Elsevier Science Ltd states (localized), Keywords: D. electronic semiconductors, D. electron-phonon interactions.
Interest in diamond films stems from applications involving the electronic, optical and mechanical properties of these films. These properties are often influenced by the impurities present in the material. Chemical vapor deposition (CVD) growth yields high quality films with some control of the incorporation of impurities. Recently, a series of photoluminescence (PL) lines near 1.7 eV has been observed in arc-jet CVD diamond grown using tungsten or tungsten-carbide electrodes [l-4]. Since these lines have only been seen in samples for which tungsten is a possible contaminant, it has been concluded that these sharp lines near 1.7 eV are the result of tungsten incorporated into the diamond film [2]. The spectrum in the region of 1.7 eV is shown in Fig. 1. A description of the samples and experiment are given in [5]. The features are at energies 1.663, 1.668, 1.711, 1.723, 1.735, 1.741, 1.750, 1.754 and 1.759 eV. As we can see in Fig. 1, the main spectral features appear as a three line component (W 1, W2 and W3) and a two line component (W4 and W5). These main features are replicated in sidebands at lower energies. These sidebands are successively downshifted by about 24 meV. Hence, we attribute these sidebands to vibrational replicas in which a local band-resonant mode is excited during the relaxation to the ground state.
* To whom correspondence should be addressed.
C.
impurities
in
Studies of the temperature dependence of this spectrum revealed that the intensities of the sharp lines drop off about 100 K, with an implied activation energy of 37 meV. This is due to competition with non-radiative processes. The line width also increases above 100 K, commensurate with increasing phonon population. Most important is the observation that the relative intensities within the multiple lines are temperature independent and do not show a Boltzmann factor dependence. Thus, we interpret the splitting between the five main lines to be the result of a splitting in the ground state involved in the PL process. This present work details a model for the electronic structure of the ground state of the tungsten impurity in diamond films that explains the observed features in the PL spectrum. In addition, it serves as a guide for the electronic structure of other transition-metal impurities in diamond films. Firstly, we note that the spectral features in Fig. 1 are fairly sharp, possessing a line width on the order of 2.5 meV at 20 K. Since the sample from which this PL spectrum was obtained is polycrystalline, the sharpness of the spectral features strongly suggests that the W atoms occupy a high symmetry site in the lattice. If this were not the case, we would expect a splitting of the electronic states, with either a splitting or a broadening of the PL lines, resulting from the low symmetry crystal field and the variation in the distortions that would arise from the varying strains in the various crystals. We
867
TUNGSTEN
868
IMPURITIES
r=20 K
2.41 ev w51’1 wsl’ w,’ w,
1
I
I
1.60
1.65
I
1.70
I
1.75
1.80
Photon Energy (eV) Fig. 1. Spectrum obtained at 20 K in the region of 1.7 eV ascribed to a tungsten impurity in polycrystalline diamond. The main features are the two line component around 1.74 eV and the three line component around 1.755 eV. The lower energy features are vibrational replicas with characteristic energy 24 meV. continue under the assumption that the W impurity is located at either a substitutional or interstitial site. The original theory for the electronic structure of transition-metal impurities in silicon, another diamondstructure material, was set forth by Ludwig and Woodbury [6]. We use their model as a guide in developing a model for the electronic structure of the tungsten impurity in diamond. Following the Ludwig and Woodbury model, the two 6s electrons are transferred to the 5d shell. Our experimental results suggest the W occupies an interstitial site, in which case the W possesses a d6 configuration. In accordance with Hund’s rule, the ground state will be a 5D term. The tetrahedral crystal field splits the 5D term into ‘TI and 5E manifolds. The ‘T2 manifold has the lower energy, the interstitial site crystal field raising the electron energy of the e symmetric d states above that of the t2 symmetric d states. Within the 5T2 manifold, which has a spin S = 2 and an effective angular momentum L = 1, the spinorbit interaction creates manifolds with J = 1, 2 and 3, the J = 1 manifold being the ground state. Including the second-order spin-orbit interaction involving the excited 5E manifold, the J = 2 manifold is split into I’, and F4 manifolds; the J = 3 manifold splits into states spanning
IN DIAMOND
Vol. 102. No. 12
FILMS
the irreducible representations I’ i, F4 and Ps. The J = 1 manifold spans the Ps representation. So, we expect to observe up to six lines [7]. The second-order splitting of the J = 2 and J = 3 manifolds at first appears to be the two line/three line component splitting observed in experiment. However, experiment shows that the two line component has a lower energy than the three line component, in contradiction to the predicted ordering in this simple crystal-field model. The ordering of the various spin-orbit manifolds can be altered by inclusion of the Jahn-Teller effect. Strong JT coupling has been observed for various transitionmetal impurities in semiconductor (diamond structure) hosts. As is most often the case in semiconductor crystals, the coupling to tetragonal modes (E modes) of distortion is the dominant JT coupling and so we consider this form of coupling. In the case of strong JT coupling, it is conceptually easier to consider first the static limit of JT coupling and then to add a dynamic aspect to this coupling [8, 91. The effect of a tetragonal distortion in the static limit of JT coupling is to split the orbital triplet T2 into an orbital singlet, the ground state and an orbital doublet. In general, any one of the Tl states (5, r], r) can become the ground state and the distortion is determined by which one of these states is occupied, e.g. if the Tzr is occupied, the tetragonal distortion is along the z axis. This particular result is diagrammed in Fig. 2. Similar results hold for the TzE and Tt,, states. We note that the spin degeneracy remains unaffected by this JT coupling. In the static limit of JT coupling the states associated with one type of distortion cannot communicate with the states associated with a different distortion. Hence, we only consider matrix elements of the spin-orbit interaction taken between states associated with the same distortion. For a distortion along the z axis, the 5T2r
S,rl
z
ti8
Fig. 2. Diagram of the state splitting in the static limit of JT coupling for the particular case when the ‘Tzr state is occupied, giving rise to a tetragonal distortion along the z axis. The splitting of the spin states results from the second-order spin-orbit interaction as given by equation (1).
Vol. 102, No. 12
TUNGSTEN
IMPURITIES
IN DIAMOND
FILMS
869
ground state manifold only mixes with the excited ‘TIE and 5T2, states and with the ‘E states [lo]. The effect of such a second-order spin-orbit interaction, there is no first-order spin-orbit interaction, is described by the operator
2 K=_h+y JbJT
2
n
where 3E,r is the splitting between the orbital singlet and the orbital doublet resulting from the JT interaction and A(10 Dq) is the splitting between the orbital singlet and some average vibrational state of the 'E manifold. The second term on the right-hand side of equation (1) shifts al1 of the states equally. The first term splits the five-fold spin-degenerate ground manifold into two doublets and a singlet. For the ith distortion (i = x, y, 2). the splitting of the spin states that results can be found by diagonalizing the spin operator K&,, -$). The splitting of the spin states in the ground state for the case K < 0 is also shown in Fig. 2. We include a dynamic aspect to the JT coupling by allowing the system to tunnel from one distortion to another. This tunneling is driven by the spin-orbit interaction. As a result of this tunneling, the symmetry of the impurity site is an average over the three distorted symmetries, that is, the symmetry is the full tetrahedral symmetry of the diamond crystal. The matrix elements of the spin-orbit interaction taken between states associated with different distortions are reduced however from their usual value, resulting in an effective spinorbit parameter X* (0 < A* < X). This reduction results from the overlap between the vibrational components of the wave functions for states associated with different distortions [ 111. In the static limit of JT coupling this overlap vanishes. This mixing of states associated with different distortions results in manifolds of states that have the same symmetry as those previously given in the simple crystal-field model when JT effects are neglected, though the characters and ordering of these levels are initially different from those in the simple crystal-field model. The three singlets found in the static limit, one for each tetragonal distortion, span the irreducible representation Ps, the six states from the lower energy (when K < 0) doublets span the irreducible representations F4 and Ps and the six states from the higher energy doublets span the irreducible representations PI, I’ 3 and F4. Figure 3 shows the energies of the various states when dynamic JT effects are included. These energies are plotted as a function of the reduced spin-orbit parameter h* (X” > 0 as in the crystal-field model)
h* I K
Fig. 3. Variation of the energies of the spin states coming from the orbital ground state as the reduced spin-orbit parameter h* is increased, that is, as the JT coupling becomes more dynamic. This is plotted for cases in which K < 0 on the left and K > 0 on the right. scaled to the second-order spin-orbit parameter K found in equation (1). We note that as h* is increased, the levels regroup as the J = 1, 2 and 3 levels found in simple crystal-field theory. The best agreement with Wl through W5 occurs when X*IK= - 0.9, [12] in which case the predicted energy splittings are within 0.5 meV of the observed splittings. This fit has the interesting result that it predicts the presence of an additional line located at a higher energy of 1.777 eV. This line is associated with the Ps manifold associated with the J = 1 spin-orbit manifold. Analysis of this and other data shows that a weak feature may be present at this energy, but the weak intensity does not permit us to make a definitive identification. Lastly, we consider briefly the initial state for the luminescence. Following Ref. [5], the initial state is assumed to be a weakly bound electronic state. If the symmetry of the initial state is not either P4 or Ps, then transitions to only the P4 and/or Ps ground-state manifolds are allowed for either electric or magnetic dipole transitions. This results in fewer than five lines, in conflict with experiment and so we discard this possibility. For the case of electric (magnetic) dipole transitions, if the initial state is P4 (P5), then only five lines are allowed, as observed in experiment. The forbidden transition is that to the F, manifold. From Fig. 3 however, we see that if the P, manifold is removed, it is no longer possible to fit the experimental results for any value of X* lK.Hence, we conclude that the initial state for the luminescence must be Fs (F,) for electric (magnetic) dipole transitions, in which transitions to all six ground state manifolds are allowed, as we have assumed in our fit. A PL spectrum that results when tungsten is present during the growth of polycrystalline diamond thin films has been ascribed to tungsten impurities in the diamond lattice. We have proposed a model for the electronic
870
TUNGSTEN
IMPURITIES
structure of the tungsten impurity using the electronic structure model of Ludwig and Woodbury for transitionmetal impurities in silicon as a guide. Our experimental results suggest that the tungsten impurity occupies an interstitial position in the diamond lattice. Further, our model proposes that there is a strong Jahn-Teller coupling involving E modes of vibration that nearly quenches the orbital angular momentum. This model is quite similar to that of other transition-metal impurities in semiconductor hosts. We conclude that the usual models for transitionmetal impurities in narrow-gap semiconductors are also applicable to transition-metal impurities in diamond. Our model and the best fit results lead to several predictions. A result of the strong Jahn-Teller coupling involving E modes of vibration is that the application of uniaxial stress in single crystal samples would show a very definite splitting for stress applied along the [I 0 0] direction, but essentially no splitting of the lines for stress along the [l 1 l] direction. An additional prediction of the model is that the (isotropic) g-value in the ground state should be approximately 3, a result of the almost entirely quenched orbital angular momentum, rather than 3.5 as predicted by simple crystal-field theory without any JT coupling. Finally, the model predicts the presence of an additional peak with an approximate energy 1.777 eV. Further experimental work with single-crystal samples, including bulk diamond, possessing a range of tungsten concentrations is required to test these predictions. Acknowledgements-The Donors of the Petroleum Research Fund, administered by the American Chemical Society, are acknowledged for their partial support (T.D. and M.H.) of this work. Further support has come from the Texas Tech Center for Energy Research. Additional support (F.G.A.) has come from NSF/EPSCOR under Cooperative Agreement No. OSR-9350540.
IN DIAMOND
FILMS
Vol. 102, No. 12
REFERENCES 1.
Perry, T.A. and Beetz, C.P., SPIE Conf on Raman Scattering, Luminescence and Spectroscopic Inst. in Technol., 1055, 1989, 152. 2. Dallas, T., Gangopadhyay, S., Yi, S. and Holtz, M., in Applications of Diamond Films and Related Materials: Third International Conference (Edited by A. Feldman, Y. Tzeng, W.A. Yarbrough, M. Yoshikawa and M. Murakawa), p. 449. U.S. Government Printing Office, Washington, D.C., 1995. 3. Lal, S., Dallas, T., Holtz, M., Lichti, R. and Gangopadhyay, S., Bull. Am. Phys. Sot., 41, 1996,438. 4. Anderson, R.J., Fox, C. and Gray, K., Bull. Am. Phys. Sot., 41, 1996, 438. 5. Lal, S., Dallas, T., Yi, S., Gangopadhyay, S., Holtz, M. and Anderson, F.G., Phys. Rev., B54, 1996, 13428. 6. Ludwig, G.W. and Woodbury, H.H., Phys. Rev. Lett., 5, 1960, 98. 7. A similar analysis for the case of the W occupying a substitutional site yields that the ground state is a 3A2 manifold, which spans only the Ps spin-orbit manifold. Hence, we would expect to observe only a single line. 8. Anderson. F.G. and Ham, F.S., Mat. Sci. Forum, 38-41, (Proc. of 15th ICDS, Budapest, ed. G. Ferenczi), 305, 1989. 9. Hofmann, G., Anderson, F.G. and Weber, J., Phys. Rev., B43, 1991, 9711. 10. We assume the spin-orbit coupling involving terms other than ‘D is negligible due to the large termenergy splittings. 11. Ham, F.S., Phys. Rev., 138A, 1965, 1727. 12. A less compelling fit can be achieved when X*/K = 0.48. A feature about this fit is that the highest energy line is actually two lines separated by 1 meV that are not resolved.
PII: s0038-10!%(!37)00117-8
THE ELECTRONIC STRUCTURE OF TUNGSTEN IMPURITIES IN DIAMOND FILMS F.G. Anderson,“* T. Dallas,b S. Lal,b S. Gangopadhyayb and M. Holtzb ‘Department of Physics, University of Vermont, Burlington VT 05405, U.S.A. department of Physics, Texas Tech University, Lubbock, Texas, 79409-105 1, U.S.A. (Received 20 August 1996; revised 7 March 1997 by M.F. Collins)
A model for the electronic structure of the tungsten impurity in diamond is presented that explains recent photoluminescence results. The model is based on the Ludwig and Woodbury model for interstitial transition-metal impurities in silicon and includes Jahn-Teller coupling, which almost entirely quenches the orbital angular momentum. 0 1997 Elsevier Science Ltd states (localized), Keywords: D. electronic semiconductors, D. electron-phonon interactions.
Interest in diamond films stems from applications involving the electronic, optical and mechanical properties of these films. These properties are often influenced by the impurities present in the material. Chemical vapor deposition (CVD) growth yields high quality films with some control of the incorporation of impurities. Recently, a series of photoluminescence (PL) lines near 1.7 eV has been observed in arc-jet CVD diamond grown using tungsten or tungsten-carbide electrodes [l-4]. Since these lines have only been seen in samples for which tungsten is a possible contaminant, it has been concluded that these sharp lines near 1.7 eV are the result of tungsten incorporated into the diamond film [2]. The spectrum in the region of 1.7 eV is shown in Fig. 1. A description of the samples and experiment are given in [5]. The features are at energies 1.663, 1.668, 1.711, 1.723, 1.735, 1.741, 1.750, 1.754 and 1.759 eV. As we can see in Fig. 1, the main spectral features appear as a three line component (W 1, W2 and W3) and a two line component (W4 and W5). These main features are replicated in sidebands at lower energies. These sidebands are successively downshifted by about 24 meV. Hence, we attribute these sidebands to vibrational replicas in which a local band-resonant mode is excited during the relaxation to the ground state.
* To whom correspondence should be addressed.
C.
impurities
in
Studies of the temperature dependence of this spectrum revealed that the intensities of the sharp lines drop off about 100 K, with an implied activation energy of 37 meV. This is due to competition with non-radiative processes. The line width also increases above 100 K, commensurate with increasing phonon population. Most important is the observation that the relative intensities within the multiple lines are temperature independent and do not show a Boltzmann factor dependence. Thus, we interpret the splitting between the five main lines to be the result of a splitting in the ground state involved in the PL process. This present work details a model for the electronic structure of the ground state of the tungsten impurity in diamond films that explains the observed features in the PL spectrum. In addition, it serves as a guide for the electronic structure of other transition-metal impurities in diamond films. Firstly, we note that the spectral features in Fig. 1 are fairly sharp, possessing a line width on the order of 2.5 meV at 20 K. Since the sample from which this PL spectrum was obtained is polycrystalline, the sharpness of the spectral features strongly suggests that the W atoms occupy a high symmetry site in the lattice. If this were not the case, we would expect a splitting of the electronic states, with either a splitting or a broadening of the PL lines, resulting from the low symmetry crystal field and the variation in the distortions that would arise from the varying strains in the various crystals. We
867
TUNGSTEN
868
IMPURITIES
r=20 K
2.41 ev w51’1 wsl’ w,’ w,
1
I
I
1.60
1.65
I
1.70
I
1.75
1.80
Photon Energy (eV) Fig. 1. Spectrum obtained at 20 K in the region of 1.7 eV ascribed to a tungsten impurity in polycrystalline diamond. The main features are the two line component around 1.74 eV and the three line component around 1.755 eV. The lower energy features are vibrational replicas with characteristic energy 24 meV. continue under the assumption that the W impurity is located at either a substitutional or interstitial site. The original theory for the electronic structure of transition-metal impurities in silicon, another diamondstructure material, was set forth by Ludwig and Woodbury [6]. We use their model as a guide in developing a model for the electronic structure of the tungsten impurity in diamond. Following the Ludwig and Woodbury model, the two 6s electrons are transferred to the 5d shell. Our experimental results suggest the W occupies an interstitial site, in which case the W possesses a d6 configuration. In accordance with Hund’s rule, the ground state will be a 5D term. The tetrahedral crystal field splits the 5D term into ‘TI and 5E manifolds. The ‘T2 manifold has the lower energy, the interstitial site crystal field raising the electron energy of the e symmetric d states above that of the t2 symmetric d states. Within the 5T2 manifold, which has a spin S = 2 and an effective angular momentum L = 1, the spinorbit interaction creates manifolds with J = 1, 2 and 3, the J = 1 manifold being the ground state. Including the second-order spin-orbit interaction involving the excited 5E manifold, the J = 2 manifold is split into I’, and F4 manifolds; the J = 3 manifold splits into states spanning
IN DIAMOND
Vol. 102. No. 12
FILMS
the irreducible representations I’ i, F4 and Ps. The J = 1 manifold spans the Ps representation. So, we expect to observe up to six lines [7]. The second-order splitting of the J = 2 and J = 3 manifolds at first appears to be the two line/three line component splitting observed in experiment. However, experiment shows that the two line component has a lower energy than the three line component, in contradiction to the predicted ordering in this simple crystal-field model. The ordering of the various spin-orbit manifolds can be altered by inclusion of the Jahn-Teller effect. Strong JT coupling has been observed for various transitionmetal impurities in semiconductor (diamond structure) hosts. As is most often the case in semiconductor crystals, the coupling to tetragonal modes (E modes) of distortion is the dominant JT coupling and so we consider this form of coupling. In the case of strong JT coupling, it is conceptually easier to consider first the static limit of JT coupling and then to add a dynamic aspect to this coupling [8, 91. The effect of a tetragonal distortion in the static limit of JT coupling is to split the orbital triplet T2 into an orbital singlet, the ground state and an orbital doublet. In general, any one of the Tl states (5, r], r) can become the ground state and the distortion is determined by which one of these states is occupied, e.g. if the Tzr is occupied, the tetragonal distortion is along the z axis. This particular result is diagrammed in Fig. 2. Similar results hold for the TzE and Tt,, states. We note that the spin degeneracy remains unaffected by this JT coupling. In the static limit of JT coupling the states associated with one type of distortion cannot communicate with the states associated with a different distortion. Hence, we only consider matrix elements of the spin-orbit interaction taken between states associated with the same distortion. For a distortion along the z axis, the 5T2r
S,rl
z
ti8
Fig. 2. Diagram of the state splitting in the static limit of JT coupling for the particular case when the ‘Tzr state is occupied, giving rise to a tetragonal distortion along the z axis. The splitting of the spin states results from the second-order spin-orbit interaction as given by equation (1).
Vol. 102, No. 12
TUNGSTEN
IMPURITIES
IN DIAMOND
FILMS
869
ground state manifold only mixes with the excited ‘TIE and 5T2, states and with the ‘E states [lo]. The effect of such a second-order spin-orbit interaction, there is no first-order spin-orbit interaction, is described by the operator
2 K=_h+y JbJT
2
n
where 3E,r is the splitting between the orbital singlet and the orbital doublet resulting from the JT interaction and A(10 Dq) is the splitting between the orbital singlet and some average vibrational state of the 'E manifold. The second term on the right-hand side of equation (1) shifts al1 of the states equally. The first term splits the five-fold spin-degenerate ground manifold into two doublets and a singlet. For the ith distortion (i = x, y, 2). the splitting of the spin states that results can be found by diagonalizing the spin operator K&,, -$). The splitting of the spin states in the ground state for the case K < 0 is also shown in Fig. 2. We include a dynamic aspect to the JT coupling by allowing the system to tunnel from one distortion to another. This tunneling is driven by the spin-orbit interaction. As a result of this tunneling, the symmetry of the impurity site is an average over the three distorted symmetries, that is, the symmetry is the full tetrahedral symmetry of the diamond crystal. The matrix elements of the spin-orbit interaction taken between states associated with different distortions are reduced however from their usual value, resulting in an effective spinorbit parameter X* (0 < A* < X). This reduction results from the overlap between the vibrational components of the wave functions for states associated with different distortions [ 111. In the static limit of JT coupling this overlap vanishes. This mixing of states associated with different distortions results in manifolds of states that have the same symmetry as those previously given in the simple crystal-field model when JT effects are neglected, though the characters and ordering of these levels are initially different from those in the simple crystal-field model. The three singlets found in the static limit, one for each tetragonal distortion, span the irreducible representation Ps, the six states from the lower energy (when K < 0) doublets span the irreducible representations F4 and Ps and the six states from the higher energy doublets span the irreducible representations PI, I’ 3 and F4. Figure 3 shows the energies of the various states when dynamic JT effects are included. These energies are plotted as a function of the reduced spin-orbit parameter h* (X” > 0 as in the crystal-field model)
h* I K
Fig. 3. Variation of the energies of the spin states coming from the orbital ground state as the reduced spin-orbit parameter h* is increased, that is, as the JT coupling becomes more dynamic. This is plotted for cases in which K < 0 on the left and K > 0 on the right. scaled to the second-order spin-orbit parameter K found in equation (1). We note that as h* is increased, the levels regroup as the J = 1, 2 and 3 levels found in simple crystal-field theory. The best agreement with Wl through W5 occurs when X*IK= - 0.9, [12] in which case the predicted energy splittings are within 0.5 meV of the observed splittings. This fit has the interesting result that it predicts the presence of an additional line located at a higher energy of 1.777 eV. This line is associated with the Ps manifold associated with the J = 1 spin-orbit manifold. Analysis of this and other data shows that a weak feature may be present at this energy, but the weak intensity does not permit us to make a definitive identification. Lastly, we consider briefly the initial state for the luminescence. Following Ref. [5], the initial state is assumed to be a weakly bound electronic state. If the symmetry of the initial state is not either P4 or Ps, then transitions to only the P4 and/or Ps ground-state manifolds are allowed for either electric or magnetic dipole transitions. This results in fewer than five lines, in conflict with experiment and so we discard this possibility. For the case of electric (magnetic) dipole transitions, if the initial state is P4 (P5), then only five lines are allowed, as observed in experiment. The forbidden transition is that to the F, manifold. From Fig. 3 however, we see that if the P, manifold is removed, it is no longer possible to fit the experimental results for any value of X* lK.Hence, we conclude that the initial state for the luminescence must be Fs (F,) for electric (magnetic) dipole transitions, in which transitions to all six ground state manifolds are allowed, as we have assumed in our fit. A PL spectrum that results when tungsten is present during the growth of polycrystalline diamond thin films has been ascribed to tungsten impurities in the diamond lattice. We have proposed a model for the electronic
870
TUNGSTEN
IMPURITIES
structure of the tungsten impurity using the electronic structure model of Ludwig and Woodbury for transitionmetal impurities in silicon as a guide. Our experimental results suggest that the tungsten impurity occupies an interstitial position in the diamond lattice. Further, our model proposes that there is a strong Jahn-Teller coupling involving E modes of vibration that nearly quenches the orbital angular momentum. This model is quite similar to that of other transition-metal impurities in semiconductor hosts. We conclude that the usual models for transitionmetal impurities in narrow-gap semiconductors are also applicable to transition-metal impurities in diamond. Our model and the best fit results lead to several predictions. A result of the strong Jahn-Teller coupling involving E modes of vibration is that the application of uniaxial stress in single crystal samples would show a very definite splitting for stress applied along the [I 0 0] direction, but essentially no splitting of the lines for stress along the [l 1 l] direction. An additional prediction of the model is that the (isotropic) g-value in the ground state should be approximately 3, a result of the almost entirely quenched orbital angular momentum, rather than 3.5 as predicted by simple crystal-field theory without any JT coupling. Finally, the model predicts the presence of an additional peak with an approximate energy 1.777 eV. Further experimental work with single-crystal samples, including bulk diamond, possessing a range of tungsten concentrations is required to test these predictions. Acknowledgements-The Donors of the Petroleum Research Fund, administered by the American Chemical Society, are acknowledged for their partial support (T.D. and M.H.) of this work. Further support has come from the Texas Tech Center for Energy Research. Additional support (F.G.A.) has come from NSF/EPSCOR under Cooperative Agreement No. OSR-9350540.
IN DIAMOND
FILMS
Vol. 102, No. 12
REFERENCES 1.
Perry, T.A. and Beetz, C.P., SPIE Conf on Raman Scattering, Luminescence and Spectroscopic Inst. in Technol., 1055, 1989, 152. 2. Dallas, T., Gangopadhyay, S., Yi, S. and Holtz, M., in Applications of Diamond Films and Related Materials: Third International Conference (Edited by A. Feldman, Y. Tzeng, W.A. Yarbrough, M. Yoshikawa and M. Murakawa), p. 449. U.S. Government Printing Office, Washington, D.C., 1995. 3. Lal, S., Dallas, T., Holtz, M., Lichti, R. and Gangopadhyay, S., Bull. Am. Phys. Sot., 41, 1996,438. 4. Anderson, R.J., Fox, C. and Gray, K., Bull. Am. Phys. Sot., 41, 1996, 438. 5. Lal, S., Dallas, T., Yi, S., Gangopadhyay, S., Holtz, M. and Anderson, F.G., Phys. Rev., B54, 1996, 13428. 6. Ludwig, G.W. and Woodbury, H.H., Phys. Rev. Lett., 5, 1960, 98. 7. A similar analysis for the case of the W occupying a substitutional site yields that the ground state is a 3A2 manifold, which spans only the Ps spin-orbit manifold. Hence, we would expect to observe only a single line. 8. Anderson. F.G. and Ham, F.S., Mat. Sci. Forum, 38-41, (Proc. of 15th ICDS, Budapest, ed. G. Ferenczi), 305, 1989. 9. Hofmann, G., Anderson, F.G. and Weber, J., Phys. Rev., B43, 1991, 9711. 10. We assume the spin-orbit coupling involving terms other than ‘D is negligible due to the large termenergy splittings. 11. Ham, F.S., Phys. Rev., 138A, 1965, 1727. 12. A less compelling fit can be achieved when X*/K = 0.48. A feature about this fit is that the highest energy line is actually two lines separated by 1 meV that are not resolved.