Observation of negative differential mobility and charge packet in polyethylene

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2011 J. Phys. D: Appl. Phys. 44 212001

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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 44 (2011) 212001 (4pp) doi:10.1088/0022-3727/44/21/212001

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Observation of negative differentialmobility and charge packet inpolyethyleneGeorge Chen and Junwei Zhao

Faculty of Physical and Applied Science, University of Southampton, Southampton, SO17 1BJ, UK

Received 28 March 2011, in final form 29 March 2011Published 4 May 2011Online at stacks.iop.org/JPhysD/44/212001

AbstractCharge packet has been observed on many occasions but its physical mechanisms have neverbeen properly understood. One of the models proposed by Lewis et al shows the presence ofnegative differential mobility with an electric field in semicrystalline polyethylene. In thispaper we have observed the negative differential mobility using the transient space chargeprofile measured by the pulsed electroacoustic technique. By superimposing a short pulsevoltage to a dc voltage, it is possible to obtain the velocity of holes at different applied fields.To the best of our knowledge we have for the first time observed negative differential mobilityin polyethylene. This observation provides crucial evidence to support Lewis’s model andallows one to simulate charge packet and its behaviours.

(Some figures in this article are in colour only in the electronic version)

Polymeric materials have been widely used as insulationin power engineering due to their excellent dielectricproperties. With the advances in manufacturing and processingtechnology, the defects in these materials have been reducedsignificantly over the years. Accordingly, the operating electricfield of the materials has been increased steadily to minimizethe cost of power equipment and devices. On the otherhand, electrical phenomena under high electric field becomeof significant importance as they are not only scientificallyinteresting but also related to the reliable operation of manydevices. It has been recognized that the reliability issue of theinsulation materials operating at high electric field is closelyrelated to space charge formation and its dynamics.

The formation of space charge in dielectric materialsat high electric field is a well-known phenomenon and hasbeen a hot topic of scientific research in the last few yearsthanks to the significant developments in space charge mappingtechniques. The presence of space charge will distort theapplied electric field and may lead to a more severe electricfield enhancement resulting in material degradation/ageing [1].On the other hand, space charge dynamics in the materialhave been used as an ageing marker to assess the status of

the material [2, 3]. One of the observed and well-publishedphenomena in space charge research is charge packet and itsdynamics [4–10]. A charge packet can be loosely defined as apulse of net charge that propagates across the material underthe influence of electric field while maintaining its shape. It hasbeen termed as an unexpected phenomenon and usually formedunder high electric field and propagates through the materialfrom one electrode to the other. In many cases, positive chargepacket was reported although negative charge packet was alsoobserved. Different mechanisms have been put forward toexplain various features of charge packet. In a recent paper byLewis et al [11], they proposed the velocity–field characteristicfor holes based on their charge transport model in polyethylene.The velocity of holes increases initially with the field andreaches its maximum at the threshold field ET. After ET thevelocity of holes decreases with the increasing electric fieldas shown in figure 1. When the applied field is lower thanET, any injected holes from the anode will modify the appliedfield. The embryo of charge packet is characterized by the fieldEA (rear) and EB (front) with EB > EA. The correspondingvelocities are VA and VB. From figure 1, it can be seen thatVA < VB, meaning the charge packet will disperse during its

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J. Phys. D: Appl. Phys. 44 (2011) 212001 Fast Track Communication

Figure 1. Velocity–field relationship for holes in polyethylene [11].

propagation. However, when the applied field is above ET thevelocities of rear and front charge packet change to V ′

A and V ′B.

As V ′A > V ′

B the charge packet will increase. The growingpacket reduces E′

A and increases E′B until the corresponding

velocity becomes the same, i.e. V ′A = V ′

B = VP.The characteristic described above is similar to part of

the Gunn effect [12] observed in semiconductors but themechanisms are probably very different. For the Gunn effect,it is believed that electrons can exist in a high-mass lowvelocity state as well as their normal low-mass high velocitystate in semiconductors. The normal states can be forced intothe high-mass state by an electric field of sufficient strength.In this state electrons form clusters or domains which crossthe region at a constant rate causing current to flow as apulse. The detailed mechanism can be traced back to twoconduction band energy levels, � (normal lower valley) andL (satellite valley). In the lower � valley, electrons exhibita small effective mass and very high mobility while in thesatellite valley electrons possess a large effective mass andvery low mobility. The two valleys are separated by a smallenergy gap. Initially, most electrons reside near the bottomof the lower � valley and they can readily be acceleratedin a strong electric field to the energy in the order of the�-L inter-valley separation. Electrons are then able to scatterinto the satellite valley, resulting in a decrease in the averageelectron mobility. Above the threshold field ET, most electronsreside in the L valley. In polyethylene, the energy landscapefor semiconductors may not apply. According to the modelproposed by Lewis et al [11], hole transport in polyethylenecan only occur via electron vacancies in or closely associatedwith the valence band and is consequently confined to polymerchains. Continuous movement of holes requires inter-chainhole transfer via tunnelling between closely adjacent polymerchains including chains in amorphous regions. Therefore,hole conduction process is more sensitive to morphology ofpolyethylene. When an electric field is applied to the material,reorganization of molecular chains in amorphous regions willtake place due to induced mechanical stress. They haveconcluded that the above process would have adverse influenceon hole tunnelling, consequently reducing hole mobility andencouraging hole trapping, leading to the proposed velocity–field diagram shown in figure 1.

The above velocity and field characteristic has been usedin simulation of charge packet behaviour in polyethylene [13].

Figure 2. Transient space charge profile and velocity estimation forholes.

However, there is no convincing experimental evidence so farto verify the model. In this paper, we report the velocity–field characteristic in polyethylene for holes based on transientspace charge profiles. The pulsed electroacoustic (PEA)technique was utilized for space charge measurement and theapplied field ranges from 10 to 70 kV mm−1. Additive-freelow-density polyethylene (LDPE) films with a thickness of100 µm were used in this study. All the measurements werecarried out at room temperature.

Different methods have been used to measure chargemobility in solid dielectrics such as the time-flight method,transient space-charge-limited current method and surfacepotential decay method. Recently, Hozumi et al [14] haveproposed a new method to estimate mobility based on transientspace charge measurement. By superimposing a pulse voltageto the applied dc voltage, it is possible to generate a chargepacket that moves under the influence of the electric field. Theschematic principle of the method is shown in figure 2.

When the external applied field is high enough, chargeinjection takes place due to either Schottky injection ortunnelling. The injected charge will move under the influenceof the electric field and may reach a quasi-equilibrium aftera period of time. In addition to the material itself, this timealso depends on the applied field strength and temperature.An electric pulse is then applied and an extra charge packetwill be initiated and move across the material. By subtractingthe steady-state charge profile the small charge packet due tothe pulse voltage becomes clearly visible and its movementcan be used to estimate the velocity of the charge as shown infigure 2. It has been reported [4] that the semicon electrode(polyethylene loaded with carbon black) injects more easilythan the electrodes such as aluminium or gold. So in the present

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J. Phys. D: Appl. Phys. 44 (2011) 212001 Fast Track Communication

Figure 3. Transient space charge profiles at 20 kV mm−1 after pulse excitation: (a) before subtraction and (b) after subtraction.

Figure 4. Transient space charge profiles subtracted from stable distribution at 50 kV mm−1: (a) 3D plot and (b) contour plot.

case the semicon was used as the anode and aluminium asthe cathode to promote hole injection, and therefore, positivecharge packet.

Figure 3 shows the transient charge distribution at anapplied field of 20 kV mm−1 and subtracted plots. Themagnitude of the pulse voltage is about 10 kV with a pulsewidth of 0.25 s. The pulse magnitude is decreased when theapplied voltage is increased while the pulse width remainsthe same. The packet charge is not obvious without thesubtraction, but it can be clearly seen that the movement ofcharge packet goes towards the cathode after the subtractionas shown in figure 3(b). The velocity of holes depends on theapplied field as shown in figure 4 where the applied field is50 kV mm−1. It can be seen that the velocity of the chargepacket is faster compared with that at 20 kV mm−1. On theother hand, the injected negative charge seems to move veryfast.

A range of applied electric fields from 10 to 70 kV mm−1

were investigated and the velocity obtained is illustrated infigure 5. Each data point is the average of at least threemeasurements. When the applied field exceeds 70 kV mm−1

it takes a longer time to achieve the steady state. Therefore,the present results are limited to 70 kV mm−1. However, it

Figure 5. Dependence of hole velocity on the applied electric field.

becomes very clear that the proposed characteristic of thevelocity–field by Lewis et al [11] has been, to the best of ourknowledge, for the first time experimentally observed. Thevelocity and electric field relationship in figure 5 deviatesslightly from the one where the applied field is exceeding60 kV mm−1. Instead of decreasing continuously the velocityof holes increases. The shape is strikingly similar to the Gunneffect occurring in semiconductors.

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J. Phys. D: Appl. Phys. 44 (2011) 212001 Fast Track Communication

The Gunn effect is responsible for the negative differentialresistance observed in semiconductor materials. The aboverelationship may be directly related to the negative differentialresistance observed in polyethylene reported many years ago[15, 16] where the current and voltage characteristics of verythin polyethylene film with varying thickness from 10 to50 nm were investigated. Negative differential resistance wasobserved and the onset of the negative differential resistancewas found to be as low as 27 kV mm−1. Crine [17] hastermed the negative differential resistance in polyethylene asone of the unexplained disturbing phenomena in the electricalproperties of dielectric polymers. Based on the result obtainedin this paper, the negative differential resistance observedin polyethylene can be attributed to the change in chargecarrier mobility. As mentioned earlier, the charge packethas been observed under a wide range of conditions, thenegative differential mobility obtained in this work may beresponsible for those observed in the electric field range below80 kV mm−1. It is believed that electron injection takes placeas well, especially when the positive charge packet movesclose to the cathode. However, injected electrons seemto move very fast which may contribute to the formationof charge packet. On the other hand, the real chargepacket always changes its shape during the propagation, i.e.diffused. This may be related to recombination of holes andelectrons. The charge packet observed above 100 kV mm−1

may take place based on the different mechanisms suchas a consequence of charge injection, ionization andrecombination. Currently, simulations using the velocity–fieldcharacteristic are underway to study charge packet behavioursin polyethylene. More importantly, the mobility versus electricfield in aged polyethylene will also be investigated to unravelthe relationship between ageing and charge mobility.

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