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Simulations of relaxation phenomena in dielectric materials
Radiat. Phys. Chem. Vol. 48, No. I, pp. 133-134, 1996
Pergamon
S0969-806X(96)00027-8
Copyright© 1996Publishedby ElsevierScienceLtd Printed in Great Britain.All rightsreserved 0969-806X/96 $15.00+ 0.00
SIMULATIONS OF RELAXATION PHENOMENA IN DIELECTRIC MATERIALS M. J. GIVEN, ~ R. A. F O U R A C R E l and H. M. B A N F O R D 2 ~C_¢ntre for Electrical Power Engineering, University of Strathclyde, Glasgow G1 IXW, Scotland and 2scottish Universities Research and Reactor (~entre, East Kilbride G75 0QU, Scotland
The technique of thermally stimulated discharge current measurement (TSDC) is widely used to determine the properties of dipolar relaxations and the depths of electronic traps within a polymer. Measurement of the changes in these properties as a function of ageing has also provided insights into the underlying degradation mechanisms. The process is based on first polarising the material by applying a voltage at an elevated temperature, cooling the sample, then allowing the polarisation to relax as the sample temperature is increased linearly. Depolarisation is monitored by measuring the short circuit current flowing between the sample electrodes. Activation energies and pre-exponential terms for the dipolar relaxations can be derived from the TSDC data using well known equations which model the process. If the polarigation has arisen from a space charge however the relaxation is more complex and it is difficult to obtain an analytical model. It has often been assumed however that the form of a charge related peak in the TSDC spectra would be similar to that for a dipolar relaxation. The authors are interested in developing computer simulations of depolarisation processes for several reasons. In experimental-work they have observed
1E-03
200 K
shifts in the position of peaks in the TSDC spectra as the polarisation voltage was varied. This shift is not inherent in the standard equations and the authors believe that it is due to modifications to the relaxation process caused by local fields set up within the polarised material. In addition the structure of TSDC spectra are frequently complicated due to the summing of several polarisation components and a simulation may be able to show if interactions occur between these components during depolarisation. A semi-infinite slab of dielectric is considered in the model which is subdivided into thinner cells. Two species of charge carrier with opposite polarity are present which are able to move within the sample. The electrodes are blocking. By considering the external field and the concentration profiles of two carriers within the slab it is possible through Poisson's equation to derive the value of the local electric field at each cell boundary. In an earlier model the motion of the charge carriers across the cell boundaries was calculated in terms of a simple mobility. However this model did not accurately simulate the expected behaviour of the system. The present model includes the effects of concentration gradients and the cell boundaries was calculated in terms of a simple mobility.
240K
280K 320K 360K
8E-0A
6E-04 o
..I
4E-04 2E-04 0E+00 0.0000001
0.00001
0.001
0.1
10
Frequency (Hz) Fig. 1. Loss peaks from charging transients, 0.5eV, as function of temperature. 133
1000
134
The Fourth Castellani Seminar--Extended Abstracts
O.OE+O0 -5.0E-07 -1,0E-06 -1.5E-06 o
l
-2.0E-06 -2.5E-06 -3.0E-06 -3.5E-06 150
0.8eV 0.7eV 0.6eV
0.5eV I 200
I 300
I 250
Temperature
I 350
I 400
I 450
I 500
(K)
Fig. 2. TSDC spectra obtained for differing activation energies
However this model did not accurately simulate the expected behaviour of the system. The present model includes the effects of concentration gradients and the field dependence of the mobilities. The polarisation within the sample at a given instant of time can be calculated from the distributions of these two charge carriers and the currents in the system can be calculated from the rate of change in polarisation. Transient currents resulting from polarisation or depolarisation at a constant temperature have been simulated as have TSDC spectra. Charging transients were simulated over a range of temperatures and the corresponding loss peaks derived using the Hamon transformation. Figure 1 shows a set of loss peaks for a system where the charge carrier mobilities were defined by an activation energy of 0.5 eV. It can be seen that the peak shifts to higher frequencies as the temperature is increased. By examining the behaviour of this peak shift it is possible to calculate the underlying activation energy for the process. The calculated values are very close to the actual parameters used.
Figure 2 shows a series of TSDC spectra derived by the model for different activation energies. The simulated polarisations were performed at a temperature of 400 K. The general form of the TSDC spectra is as expected with a single peak present which shifts to higher temperatures as the activation energy for the charge transport process is increased. Activation energies for the relaxation process have been derived by the standard technique from Arrhenius plots of the initial i s e of the currents. The behaviour of the TSDC spectra as the heating rate is changed has also been simulated and these results allow the activation energy to be calculated. Again a close correlation betwen the derived and expected activation energies was observed. The model appears to be capable of accurately simulating transient current and TSDC experiments for simple systems. It is now being applied to systems where the charge carriers have more than one activation energy to explore how accurately the underlying behaviour of the system can be derived from experimental current transients and TSDC spectra.
Pergamon
S0969-806X(96)00027-8
Copyright© 1996Publishedby ElsevierScienceLtd Printed in Great Britain.All rightsreserved 0969-806X/96 $15.00+ 0.00
SIMULATIONS OF RELAXATION PHENOMENA IN DIELECTRIC MATERIALS M. J. GIVEN, ~ R. A. F O U R A C R E l and H. M. B A N F O R D 2 ~C_¢ntre for Electrical Power Engineering, University of Strathclyde, Glasgow G1 IXW, Scotland and 2scottish Universities Research and Reactor (~entre, East Kilbride G75 0QU, Scotland
The technique of thermally stimulated discharge current measurement (TSDC) is widely used to determine the properties of dipolar relaxations and the depths of electronic traps within a polymer. Measurement of the changes in these properties as a function of ageing has also provided insights into the underlying degradation mechanisms. The process is based on first polarising the material by applying a voltage at an elevated temperature, cooling the sample, then allowing the polarisation to relax as the sample temperature is increased linearly. Depolarisation is monitored by measuring the short circuit current flowing between the sample electrodes. Activation energies and pre-exponential terms for the dipolar relaxations can be derived from the TSDC data using well known equations which model the process. If the polarigation has arisen from a space charge however the relaxation is more complex and it is difficult to obtain an analytical model. It has often been assumed however that the form of a charge related peak in the TSDC spectra would be similar to that for a dipolar relaxation. The authors are interested in developing computer simulations of depolarisation processes for several reasons. In experimental-work they have observed
1E-03
200 K
shifts in the position of peaks in the TSDC spectra as the polarisation voltage was varied. This shift is not inherent in the standard equations and the authors believe that it is due to modifications to the relaxation process caused by local fields set up within the polarised material. In addition the structure of TSDC spectra are frequently complicated due to the summing of several polarisation components and a simulation may be able to show if interactions occur between these components during depolarisation. A semi-infinite slab of dielectric is considered in the model which is subdivided into thinner cells. Two species of charge carrier with opposite polarity are present which are able to move within the sample. The electrodes are blocking. By considering the external field and the concentration profiles of two carriers within the slab it is possible through Poisson's equation to derive the value of the local electric field at each cell boundary. In an earlier model the motion of the charge carriers across the cell boundaries was calculated in terms of a simple mobility. However this model did not accurately simulate the expected behaviour of the system. The present model includes the effects of concentration gradients and the cell boundaries was calculated in terms of a simple mobility.
240K
280K 320K 360K
8E-0A
6E-04 o
..I
4E-04 2E-04 0E+00 0.0000001
0.00001
0.001
0.1
10
Frequency (Hz) Fig. 1. Loss peaks from charging transients, 0.5eV, as function of temperature. 133
1000
134
The Fourth Castellani Seminar--Extended Abstracts
O.OE+O0 -5.0E-07 -1,0E-06 -1.5E-06 o
l
-2.0E-06 -2.5E-06 -3.0E-06 -3.5E-06 150
0.8eV 0.7eV 0.6eV
0.5eV I 200
I 300
I 250
Temperature
I 350
I 400
I 450
I 500
(K)
Fig. 2. TSDC spectra obtained for differing activation energies
However this model did not accurately simulate the expected behaviour of the system. The present model includes the effects of concentration gradients and the field dependence of the mobilities. The polarisation within the sample at a given instant of time can be calculated from the distributions of these two charge carriers and the currents in the system can be calculated from the rate of change in polarisation. Transient currents resulting from polarisation or depolarisation at a constant temperature have been simulated as have TSDC spectra. Charging transients were simulated over a range of temperatures and the corresponding loss peaks derived using the Hamon transformation. Figure 1 shows a set of loss peaks for a system where the charge carrier mobilities were defined by an activation energy of 0.5 eV. It can be seen that the peak shifts to higher frequencies as the temperature is increased. By examining the behaviour of this peak shift it is possible to calculate the underlying activation energy for the process. The calculated values are very close to the actual parameters used.
Figure 2 shows a series of TSDC spectra derived by the model for different activation energies. The simulated polarisations were performed at a temperature of 400 K. The general form of the TSDC spectra is as expected with a single peak present which shifts to higher temperatures as the activation energy for the charge transport process is increased. Activation energies for the relaxation process have been derived by the standard technique from Arrhenius plots of the initial i s e of the currents. The behaviour of the TSDC spectra as the heating rate is changed has also been simulated and these results allow the activation energy to be calculated. Again a close correlation betwen the derived and expected activation energies was observed. The model appears to be capable of accurately simulating transient current and TSDC experiments for simple systems. It is now being applied to systems where the charge carriers have more than one activation energy to explore how accurately the underlying behaviour of the system can be derived from experimental current transients and TSDC spectra.