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The inclusion of space charge effects in simulations of the thermally stimulated discharge experiment
PERGAMON
Radiation Physics and Chemistry Radiation Physics and Chemistry 54 (1999) 199±201
The inclusion of space charge eects in simulations of the thermally stimulated discharge experiment M.J. Given a, *, R.A. Fouracre a, H.M. Banford b a
Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, UK b Scottish Universities' Research and Reactor Centre, East Kilbride, Scotland, UK
1. Introduction Thermally stimulated discharge current (TSDC) measurement is a technique for studying the behaviour of electrical polarization in non-conducting materials. The method has been used by engineers interested in the ageing processes in polymeric materials (Li et al., 1994, 1995). For example, it has been used to characterize the long-term eects of gamma and neutron radiation in electrical insulators where such radiation produces signi®cant changes in the TSDC thermograms (spectra) (Chen et al., 1991; Al-Attabi et al., 1992). Using the TSDC method it is possible to determine whether the relaxations in the polarisation are dipolar or as a result of charge migration within the polymer. In addition relaxation times and activation enthalpies (Booth, 1954; Given et al., 1992) can be determined from the spectra giving information on the changes occurring within the system. In more complicated systems where several polarization processes are present, the techniques of partial polarisation and thermal cleaning (Braunlich, 1979) have been used to resolve the structures within the spectra. These methods generally consider that each component of the polarization relaxes independently. Experimental results produced by the authors in irradiated epoxy (Al-Attabi et al., 1992) and polyimide (Banford et al., 1996) systems have shown ®eld dependencies in the TSDC spectra which might only be explained in terms of interactions between the polarisation components. Using ®nite dierence techniques, the authors have been developing computer simulations of the TSDC processes based on charge migration. The latest modi®cations to their model is the inclusion of charge injection from the electrodes.
* To whom correspondence should be addressed.
The model determines the polarization arising within a dielectric through the motion of charge carriers. At any instant in time, it is possible to calculate the ¯uxes of charge carriers in the system as a result of concentration gradients and the action of the local ®eld; the latter is the result of both space charge distributions and the applied external electric ®eld. From these ¯uxes, it is possible to determine the development of the distribution of charge carriers with time. More detailed descriptions of the basis of the models and the ¯ux calculations can be found in earlier papers (Given et al., 1992, 1995, 1996). Previously the models only considered two charged species in the system which were constrained by blocking electrodes. The latest simulations introduce a third charge carrier in the form of electrons injected from the electrodes through an activated process modi®ed by the external ®eld. The time dependence of the injected electron concentrations through the system can then be derived in a similar manner to the other two charge carrying species. Unlike the earlier models where overall charge neutrality was maintained throughout the simulation process, in this model a nett charge can be introduced into the dielectric during the simulation.
2. Results and discussion The system modelled contained two mobile charge carriers: the ®rst at a concentration of 1 1016 m ÿ 3 whose motion through the dielectric was de®ned by an activation energy of 0.5 eV; the second at a concentration of 1 1020 m ÿ 3 with an activation energy of 0.8 eV. Polarization was simulated in the model system with a ®eld of 10 kV mm ÿ 1 at a temperature of 300 K, and the TSDC spectra was derived over a temperature range 150±450 K using a heating rate of 6 degrees per minute. In the absence of electron injection
0969-806X/99/$19.00 # 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 9 8 ) 0 0 2 4 3 - 6
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M. Given et al. / Radiation Physics and Chemistry 54 (1999) 199±201
Fig. 1. Basic TSDC spectra and its modi®cation by charge injection from the electrode.
the simple two peak spectrum shown in Fig. 1 is derived. An important result is that although the more mobile species in the system has a much lower concentration its peak dominates the behaviour of the spectrum. Previous work (Given et al., 1995, 1996) had shown that the peak associated with the lower activation energy relaxes under the in¯uence of the local ®eld produced predominantly by the distribution of the less mobile charge carriers. This in¯uence increases the magnitude of the lower temperature peak and acts
to suppress, in part, the higher temperature peak of the less mobile species. When the electrodes are allowed to introduce electrons into the system, the presence of the additional component of charge further modi®es the TSDC spectra. The lower temperature peak is unaected, the region between the peaks is broadened and the second peak is narrower and slightly smaller. The behaviour of the system as the polarization ®eld was varied between 1 and 20 kV mm ÿ 1 was explored. The results obtained are displayed in Fig. 2. As the
Fig. 2. Behaviour of system as polarising ®eld is changed.
M. Given et al. / Radiation Physics and Chemistry 54 (1999) 199±201
®eld is increased, the height of the initial peak in the TSDC spectra associated with the more mobile species increases. The eect of the increase from 1 kV mm ÿ 1 to 5 kV mm ÿ 1 on peak height is much greater than that for the increase from 5 to 20 kV mm ÿ 1. This saturation could be the result of the almost complete polarization of the more mobile species as the ®eld is increased. The slight increase observed as the ®eld is increased beyond 5 kV mm ÿ 1 may occur due to an increase in the polarization component associated with the less mobile species. As a consequence, the ®eld seen by the more mobile species is increased during its relaxation. Once the ®eld has increased to 5 kV mm ÿ 1 little further change is observed in the appearance of the relatively ¯at region between the low temperature and high temperature peaks. The ®eld dependence for the higher temperature peak has become partially reversed. The peak height is at a maximum for a ®eld of 10 kV mm ÿ 1 and then decreases slightly as the ®eld is increased. This behaviour is similar to that observed by the authors in certain circumstances in polyimide samples that had been aged by combined gamma irradiation and thermal stressing (Banford et al., 1996). It has not been possible to determine at this point the interactions between the second species and the charge introduced from the electrodes during polarization. 3. Conclusions A computer simulation has been developed that models the generation of TSDC spectra. This model includes a simple treatment for the injection of space charge from the electrodes. The interactions between the various components of the polarization occur through the calculated electric ®eld and are shown to be complex as is the ®eld behaviour of the system. In the future the simulation will be used to explore systematically the parameters signi®cant to the model's behaviour. The relaxation of the individual components of the polarization will be explored as will the
201
behaviour of the transient polarising and depolarising currents.
References Al-Attabi, A., Fouracre, R.A., Banford, H.M., Tedford, D.J., 1992. High dose neutron and gamma-radiation eects in an epoxy resin. Radiat. Phys. Chem. 40, 411±419. Banford, H.M., Given, M.J., Tedford, D.J., 1995. TSDC spectra of polyimide aged in a simulated space environment. Conference record of the 1996 IEEE Symposium on Electrical Insulation, 369±372. Booth, A.H., 1954. Calculation of electron depths from thermoluminescence maxima. Can. J. Chem. 32, 214±215. Braunlich, P., 1979. Thermally stimulated relaxation in solids. Springer, Berlin. Chen, G., Fouracre, R.A., Banford, H.M., Tedford, D.J., 1991. The eects of gamma irradiation on the thermaly stimulated discharge current spectra in low density polyethylene. Radiat. Phys. Chem. 37, 523±530. Given, M.J., Fouracre, R.A., Banford, H.M., 1992. Modelling of space charge relaxation under the conditions used for thermally stimulated current measurements. Proc. 6th Dielectric Materials Measurements and Applications Conf. 131±134. Given, M.J., Fouracre, R.A., Banford, H.M., 1995. Modelling of TSDC spectra: The eect of local ®elds. Proc. 7th Dielectric Materials Measurements and Applications Conf. 42±45. Given, M.J., Fouracre, R.A., Banford, H.M., 1996. Modelling the eects of space charge distributions on TSDC spectra. Proc. 5th Int. Conf. Conduction and Breakdown in Solid Dielectrics, 164±167. Li, H.M., Fouracre, R.A., Crichton, B.H., Banks, V.A.A., 1994. The in¯uence of ions on the thermally stimulated discharge current spectra of water-treed additive-free low-density polyethylene. IEEE Trans. Dielec. Elec. Ins. 1, 1084± 1093. Li, H.M., Fouracre, R.A., Crichton, B.H., 1995. Transient current measurement for the detection of water tree growth in polymeric power cables. IEEE Trans. Dielec. Elec. Ins. 2, 866±874.
Radiation Physics and Chemistry Radiation Physics and Chemistry 54 (1999) 199±201
The inclusion of space charge eects in simulations of the thermally stimulated discharge experiment M.J. Given a, *, R.A. Fouracre a, H.M. Banford b a
Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, UK b Scottish Universities' Research and Reactor Centre, East Kilbride, Scotland, UK
1. Introduction Thermally stimulated discharge current (TSDC) measurement is a technique for studying the behaviour of electrical polarization in non-conducting materials. The method has been used by engineers interested in the ageing processes in polymeric materials (Li et al., 1994, 1995). For example, it has been used to characterize the long-term eects of gamma and neutron radiation in electrical insulators where such radiation produces signi®cant changes in the TSDC thermograms (spectra) (Chen et al., 1991; Al-Attabi et al., 1992). Using the TSDC method it is possible to determine whether the relaxations in the polarisation are dipolar or as a result of charge migration within the polymer. In addition relaxation times and activation enthalpies (Booth, 1954; Given et al., 1992) can be determined from the spectra giving information on the changes occurring within the system. In more complicated systems where several polarization processes are present, the techniques of partial polarisation and thermal cleaning (Braunlich, 1979) have been used to resolve the structures within the spectra. These methods generally consider that each component of the polarization relaxes independently. Experimental results produced by the authors in irradiated epoxy (Al-Attabi et al., 1992) and polyimide (Banford et al., 1996) systems have shown ®eld dependencies in the TSDC spectra which might only be explained in terms of interactions between the polarisation components. Using ®nite dierence techniques, the authors have been developing computer simulations of the TSDC processes based on charge migration. The latest modi®cations to their model is the inclusion of charge injection from the electrodes.
* To whom correspondence should be addressed.
The model determines the polarization arising within a dielectric through the motion of charge carriers. At any instant in time, it is possible to calculate the ¯uxes of charge carriers in the system as a result of concentration gradients and the action of the local ®eld; the latter is the result of both space charge distributions and the applied external electric ®eld. From these ¯uxes, it is possible to determine the development of the distribution of charge carriers with time. More detailed descriptions of the basis of the models and the ¯ux calculations can be found in earlier papers (Given et al., 1992, 1995, 1996). Previously the models only considered two charged species in the system which were constrained by blocking electrodes. The latest simulations introduce a third charge carrier in the form of electrons injected from the electrodes through an activated process modi®ed by the external ®eld. The time dependence of the injected electron concentrations through the system can then be derived in a similar manner to the other two charge carrying species. Unlike the earlier models where overall charge neutrality was maintained throughout the simulation process, in this model a nett charge can be introduced into the dielectric during the simulation.
2. Results and discussion The system modelled contained two mobile charge carriers: the ®rst at a concentration of 1 1016 m ÿ 3 whose motion through the dielectric was de®ned by an activation energy of 0.5 eV; the second at a concentration of 1 1020 m ÿ 3 with an activation energy of 0.8 eV. Polarization was simulated in the model system with a ®eld of 10 kV mm ÿ 1 at a temperature of 300 K, and the TSDC spectra was derived over a temperature range 150±450 K using a heating rate of 6 degrees per minute. In the absence of electron injection
0969-806X/99/$19.00 # 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 9 8 ) 0 0 2 4 3 - 6
200
M. Given et al. / Radiation Physics and Chemistry 54 (1999) 199±201
Fig. 1. Basic TSDC spectra and its modi®cation by charge injection from the electrode.
the simple two peak spectrum shown in Fig. 1 is derived. An important result is that although the more mobile species in the system has a much lower concentration its peak dominates the behaviour of the spectrum. Previous work (Given et al., 1995, 1996) had shown that the peak associated with the lower activation energy relaxes under the in¯uence of the local ®eld produced predominantly by the distribution of the less mobile charge carriers. This in¯uence increases the magnitude of the lower temperature peak and acts
to suppress, in part, the higher temperature peak of the less mobile species. When the electrodes are allowed to introduce electrons into the system, the presence of the additional component of charge further modi®es the TSDC spectra. The lower temperature peak is unaected, the region between the peaks is broadened and the second peak is narrower and slightly smaller. The behaviour of the system as the polarization ®eld was varied between 1 and 20 kV mm ÿ 1 was explored. The results obtained are displayed in Fig. 2. As the
Fig. 2. Behaviour of system as polarising ®eld is changed.
M. Given et al. / Radiation Physics and Chemistry 54 (1999) 199±201
®eld is increased, the height of the initial peak in the TSDC spectra associated with the more mobile species increases. The eect of the increase from 1 kV mm ÿ 1 to 5 kV mm ÿ 1 on peak height is much greater than that for the increase from 5 to 20 kV mm ÿ 1. This saturation could be the result of the almost complete polarization of the more mobile species as the ®eld is increased. The slight increase observed as the ®eld is increased beyond 5 kV mm ÿ 1 may occur due to an increase in the polarization component associated with the less mobile species. As a consequence, the ®eld seen by the more mobile species is increased during its relaxation. Once the ®eld has increased to 5 kV mm ÿ 1 little further change is observed in the appearance of the relatively ¯at region between the low temperature and high temperature peaks. The ®eld dependence for the higher temperature peak has become partially reversed. The peak height is at a maximum for a ®eld of 10 kV mm ÿ 1 and then decreases slightly as the ®eld is increased. This behaviour is similar to that observed by the authors in certain circumstances in polyimide samples that had been aged by combined gamma irradiation and thermal stressing (Banford et al., 1996). It has not been possible to determine at this point the interactions between the second species and the charge introduced from the electrodes during polarization. 3. Conclusions A computer simulation has been developed that models the generation of TSDC spectra. This model includes a simple treatment for the injection of space charge from the electrodes. The interactions between the various components of the polarization occur through the calculated electric ®eld and are shown to be complex as is the ®eld behaviour of the system. In the future the simulation will be used to explore systematically the parameters signi®cant to the model's behaviour. The relaxation of the individual components of the polarization will be explored as will the
201
behaviour of the transient polarising and depolarising currents.
References Al-Attabi, A., Fouracre, R.A., Banford, H.M., Tedford, D.J., 1992. High dose neutron and gamma-radiation eects in an epoxy resin. Radiat. Phys. Chem. 40, 411±419. Banford, H.M., Given, M.J., Tedford, D.J., 1995. TSDC spectra of polyimide aged in a simulated space environment. Conference record of the 1996 IEEE Symposium on Electrical Insulation, 369±372. Booth, A.H., 1954. Calculation of electron depths from thermoluminescence maxima. Can. J. Chem. 32, 214±215. Braunlich, P., 1979. Thermally stimulated relaxation in solids. Springer, Berlin. Chen, G., Fouracre, R.A., Banford, H.M., Tedford, D.J., 1991. The eects of gamma irradiation on the thermaly stimulated discharge current spectra in low density polyethylene. Radiat. Phys. Chem. 37, 523±530. Given, M.J., Fouracre, R.A., Banford, H.M., 1992. Modelling of space charge relaxation under the conditions used for thermally stimulated current measurements. Proc. 6th Dielectric Materials Measurements and Applications Conf. 131±134. Given, M.J., Fouracre, R.A., Banford, H.M., 1995. Modelling of TSDC spectra: The eect of local ®elds. Proc. 7th Dielectric Materials Measurements and Applications Conf. 42±45. Given, M.J., Fouracre, R.A., Banford, H.M., 1996. Modelling the eects of space charge distributions on TSDC spectra. Proc. 5th Int. Conf. Conduction and Breakdown in Solid Dielectrics, 164±167. Li, H.M., Fouracre, R.A., Crichton, B.H., Banks, V.A.A., 1994. The in¯uence of ions on the thermally stimulated discharge current spectra of water-treed additive-free low-density polyethylene. IEEE Trans. Dielec. Elec. Ins. 1, 1084± 1093. Li, H.M., Fouracre, R.A., Crichton, B.H., 1995. Transient current measurement for the detection of water tree growth in polymeric power cables. IEEE Trans. Dielec. Elec. Ins. 2, 866±874.