1. A Comparison between Electroluminescence Models and Experimental Results D. H. Mills 1*, F. Baudoin 2, G. Chen 1, P. L. Lewin 1 1 University of Southampton, Southampton, UK 2 University of Tolouse, France Models Results Introduction Experiment Setup Conclusions  Electroluminescence phenomena is the emission of visible photons from an electrically stressed polymer. This emission occurs before the onset of any other measurable sign of material ageing. A thorough understanding of the mechanisms behind EL would give a better understanding of the electrical ageing processes within polymeric insulation.  This poster presents a new model for the EL emission, comparing it with a previous model and EL measurements under various waveforms. dhm08r@ecs.soton.ac.uk University of Southampton, Highfield, Southampton, SO17 1BJ, UK Contact details :  Both models assume two kinds of charge carriers provided by either injection or extraction and assume charge is able to become trapped or recombine with trapped charges of the opposite polarity.  Charge carriers are provided for injection at both electrodes according to this functional approximation for current density (1): (1)  Poisson’s (2) equation and continuity (3) equation are used to calculate the net density of charges within the dielectric: (2) (3) where n is the number of trapped charge carriers, ɛ 0 ɛ r is the dielectric permittivity. Model 1  Model 1 assumes that EL emission under an ac field is an interfacial phenomenon rather than occurring within the bulk and so does not account for transport, diffusion or extraction of charge carriers from the electrodes.  It assumes all injected charge is uniformly distributed within a space charge region 10 nm from the electrode surface and remains constant over time (figure 2).  Charge is assumed to either be trapped or to recombine where the recombination density can be calculated using (4): and(4) where r e,m is the recombination density for mobile electrons, trapped holes. S e,h is the recombination coefficient and n is the number of trapped charge carriers.  The resultant EL intensity is proportional to the emission of light from both electrodes. Model 2  Model 2 uses an exponential distribution of trap levels (5) and calculates the space charge region using a 1500 element mesh tightened close to the electrodes (figure 3). (5) where ∆ is the trap depth and ∆ ≤ ∆ max, k is Boltzmann’s constant, T 0 is a shape parameter, ∆ max is the maximum trap depth  Two models showing the EL phenomena in LDPE under ac stress have been compared with experimental data.  Both models show a relatively good fit to the experimental data even though model 1 does not account for transport, diffusion and extraction of charges at the electrodes.  Model 2 accounts for transport and extraction of charge at the electrodes and provides other important information such as charge behaviour, the space charge profile in the region close to the electrodes and the shape of the conduction current but all at the cost of significant computation time.  The simulated data supports the theory of EL phenomena under ac stress as an interfacial phenomena and further work aims to simulate changes relating to sample ageing.  Figure 1 shows the experiment setup for collecting EL measurements.  A uniform electrode arrangement is achieved by coating low density polyethylene (LDPE) samples in semi-transparent 20 nm thick gold electrodes. Silicone rubber is placed around the edge of the gold to avoid measuring light from high electrical stresses.  Measurements are taken under 50 Hz sinusoidal fields in an inert, Nitrogen atmosphere.  In all cases two EL peaks for every ac cycle occur. Confirming EL relation with charge movement near the electrodes.  Measured EL emission for sinusoidal and triangular waveforms is lower than that of a square waveform.  Different waveforms result in the peak occurring in different locations.  Sinusoidal, EL emission is greatest before the peak.  Triangular, EL emission is greatest at or just after the peak.  Square waveform results in the peak occurring at the end of the applied field rise time.  Sinusoidal and triangular simulations both show good agreement between the different models.  Square waveform simulations show different profiles for the EL emission between model 1 and model 2.  Model 2 suggests an almost instantaneous increase in EL intensity and then a fast reduction.  Model 1 shows a slower increase in EL intensity and then a very slow reduction.  The measured emission is actually somewhere between these two simulations but with a less instantaneous peak.  Results shown below (figure 4) compare both models and experimental data under a 60kV pk /mm, 50Hz field for sinusoidal, triangular and square waveforms.  The simulated data is multiplied by a coefficient to allow all results to be presented on one figure. The intensity of the simulation is not being investigated just the ability to represent the shape of the EL emission.  The filtered EL data is the raw EL after applying a zero phase shift, low pass filter for easier comparison. Figure 4 - Simulated and experimental EL emission. (a)6kV pk, 50Hz, sinusoidal field. (b)6kV pk, 50Hz, triangular field (c)6kV pk, 50Hz, square field with 1ms rise time (a) (b) (c) Figure 2 – Geometry of study for model 1 Figure 3 – Geometry of study for model 2 Figure 1 – Electroluminescence experiment