1. Measurement of mobility of positive charge carriers in polyethylene J Zhao, G Chen and P L Lewin University of Southampton, Southampton, UK Positive charge packets The dependence of velocity on the applied electric field Introduction Experimental Conclusions References Space charge could be a big problem when polymeric insulation materials are used for dc transmission cables. It could create regions of high electric fields in the material, which may initiate partial discharge, treeing or cause failure of the insulation. Efforts have been made to investigate space charge dynamics in polymers under dc stress by laboratory experiments. The transport of charge carriers has been observed using the traditional space charge measurements. However the field dependence of charge carrier’s movement is not yet clearly understood. In this work, positive charge packets are observed in polyethylene from experiments using the pulse electro-acoustic (PEA) technique. The dependence of velocity on the applied dc electric field is obtained. Results indicate that there is a negative differential mobility of positive charge carriers. [1] N. Hozumi, Y. Muramoto, M. Nagao and Y. Zhang, IEEE Trans. Dielectr. Electr. Insul. 8(5), 849(2001). [2] J. P. Jones, J. P. Llewellyn and T. J. Lewis. IEEE Trans. Dielectr. Electr. Insul. 12(5), 951(2005).  The dynamics of positive charge packets is observed in polyethylene under various dc electric fields using the pulse electro-acoustic technique;  The decrease of velocity with electric field and negative differential mobility of positive charge carriers in polyethylene is firstly observed;  Negative differential mobility has been confirmed to be necessary for the formation of charge packet in the simulation.  Charge packet profiles After excitation, a packet of positive charge carriers is formed at the anode and it travels towards the cathode under the influence of electric field. The measured space charge profiles at dc electric field of 20 kVmm -1 after pulse excitation are shown in figure 2(a); It does not demonstrate clearly the behaviour of the charge packet. Hence a subtraction from the stable distribution prior to the excitation has been performed. The subtracted profiles are shown in figure 2(b). It clearly shows the dynamics of positive charge packets.  Pulse excitation method In the experiment, a thin film of polyethylene (100 µm ) is sandwiched between two flat electrodes which are a semiconducting polymer as the anode and aluminum as the cathode; dc voltages are applied across the film. Under lower electric fields, charge packets cannot be observed in polyethylene by traditional PEA method; A large pulse voltage is then added onto the bias dc voltage to initiate a charge packet in order to observe the dynamics of positive charge packets in polyethylene. The principle of this pulse excitation method is explained in figure 1. In experiments, the overall voltage including pulse voltage is up to 15 kV. Fig. 2. Space charge profiles at dc field of 20 kVmm -1 : (a) 3d plot; (b) after subtraction. Fig. 3. Charge packet profiles at dc field of 50 kVmm -1 : (a) 3d plot; (b) contour plot.  Velocity of charge carriers Subtracted space charge profiles at dc electric field of 50 kVmm -1 after pulse excitation are shown in figure 3(a); To describe the behavior of this packet of positive charge carriers, the velocity of positive charge packet is calculated using a contour plot of the dynamics of the charge packet shown in figure 3(b). It indicates that the packet travels at a speed of 0.23 µms -1. The field dependence of charge transport in dielectrics is difficult to describe by classic equations or theories. Therefore how the applied electric field affects the velocity of charge carriers is extracted from experimental observation of positive charge packets in polyethylene under dc electric fields. The dependence is shown in figure 4. It shows an interesting curve which does not always suggest an increase of velocity with electric field. The initial increase is followed by a drop at a critical field value and a second rise afterwards again. This dependence is firstly observed in experiments and is in agreement with T. J. Lewis’s comment on hole’s mobility in polyethylene. This curve resembles the ‘Gunn Effect’ on the velocity of charge carriers in semiconducting materials. Fig. 4. Dependence of velocity on the applied electric field Fig. 5. Dependence of mobility on the applied electric field Fig. 1. Principle of pulse excitation method Contact details : Junwei Zhao jz208r@ecs.soton.ac.uk University of Southampton, Highfield, Southampton, SO17 1BJ, UK The dependence of mobility on the applied electric field It is possibly to estimate the effective mobility from the velocity and applied field. The mobility as a function of electric field is shown in figure 5. It shows that positive charge carriers have lower mobility at increased electric field. This negative differential mobility differs from general consideration of an increased mobility at higher stress. Initial simulation based on the observed mobility shows that negative differential mobility is necessary for charge packet formation.