Current Oscillations in Iodine-doped Polyethylene Film BY G. T. JONES AND T. J. LEWIS School of Electronic Engineering Science University College of North Wales Dean Street Bangor Gwynedd North Wales Received 25th July I974 Very low frequency Hz) regular current oscillations may be induced in iodine-doped polyethylene films when subjected to electric fields in excess of about 3 x lo7 V m-'. The oscillations are similar whether iodine is introduced from aqueous KI electrodes or from the dry vapour. The frequency depends on film thickness and iodine concentration and has an activation energy of -1.2 eV. Most significantly it decreases with increasing field suggesting that space charge domains are propagating in the films encouraged by a negative differential charge carrier mobility-field char- acteristic.This is confirmed by direct measurement. The acceptor action of iodine probably generates mobile electron vacancies in the polymer chains the effective mass of which increases with field to give the negative characteristic. It has been demonstrated already that the electrical conductivity of thin poly- ethylene films will increase by several orders of magnitude when they absorb iodine by contact with aqueous sodium iodide solutions. It appears that neutral iodine rather than iodine ions diffuse into the polyethylene and the current growth at con- stant applied electric field follows a Fickian diffusion law.2 Neutral iodine is known to be preferentially absorbed in the amorphous regions of the polymer film and at the same time it appears that electron transfer from polymer molecules to vacant acceptor levels in the iodine system generates mobile "holes " in the polymer chain which leads to enhanced conduction2 Swan has also shown that when the field applied exceeded about 4 x lo7 V in-' regular slow current oscillations were superimposed on the steady background current the frequency of these depending on temperature iodine concentration and field strength.Swan considered the possibility that the oscillations might be due to the propagation of space charge domains across the film but concluded because the static (current voltage) characteristics did not appear to show negative differential character- istics that high field accumulation domains as observed in more conventional semi- conductors were not occurring.McCumber and Chynoweth have shown however that the absence of such characteristics is not in fact evidence against the existence of high field domain propagation in a solid. Our present studies of a system similar to that of Swan confirm the existence of oscillations with the same characteristics. We have also found that oscillations may be generated in a dry system in which iodine is diffused directly into the polyethylene from the vapour and also in a polyethylene+sulphuric acid system. Furthermore we have been able to make direct determinations of the charge carrier mobility in such systems and to show that this parameter exhibits a strong negative differential coeffi- cient with respect to the field such as would be required for the establishment of space charge instabilities in conventional semiconductors.The implications of this for curl.icr iiiotion in organic systems generally is briefly discussed. 192 G. T. JONES AND T. J. LEWIS EXPERIMENTAL The arrangement for most of the experiments was essentially similar to that used earlier.Z* Samples of low density polyethylene film without additives in the thickness range 50-350 pm were cleaned of surface grease by washing in methanol and sealed between p.t.f.e. cups each normally containing an aqueous 1 M solution of KI with iodine added and arranged so that a surface area of 0.32cm2 of the solution was in contact with the film on either side. Iodine added to the KI solutions in known concentrations was allowed to diffuse into the polymer thereby increasing the conductivity by orders of magnitude.Contact to the aqueous KI solution in each cup was made via tungsten leads and the whole cell could be housed in an oven of which the temperature could be controlled to 0.1"C. Dry samples were prepared by first outgassing the films for several hours at a pressure of about 10 N and then immersing in iodine vapour until saturated and excess iodine appeared on the surfaces. The excess was removed by gentle washing with methanol. The sample was then placed between flat copper electrodes one fitted with an insulated guard ring. This system was difficult to control since high field measurements had to be made under a vacuum in order to avoid surface leakage and consequently the iodine content of the sample gradually fell with time.Some improvement in stability was achieved by pre- iodizing the copper electrodes before making contact to the sample. This stabilised the contact and prevented an iodine deficiency adjacent to the electrodes. Gold electrodes were also tried but without success the surfaces deteriorating rapidly. A stabilised controlled voltage source was used to apply selected fields to the samples and currents (lo-" A to loe6 A) were measured by electrometer. RESULTS CURRENT OSCILLATIONS Provided the film thickness was greater than 50 pm and less than about 350 pm sustained slow current oscillations could be obtained for the "wet " system when the field was raised above a threshold value Et.A typical example is shown in fig. I where the threshold field lay between 3.9 and 4.3x lo7 V m-l. When the sample was thin (-50 pm) current oscillations could be induced only at high iodine concentra- tions (100 g/l. 1 M KI solution). At lower concentrations oscillations were inter- mittent and were rapidly damped out. The general chracteristics present in fig. 1 and time (intervals = 10 s) FIG.1.-Typical (current time) characteristic at the onset of oscillaticms. Polyethylene film 127 pm thick. Iodine concentration 10 g in 1 1. of 1 M KI solution at 30°C. At point A the field is changed from below threshold (3.9 x lo7 V m-l) to just above (4.3x lo7 V m-l). Note that the oscillations begin by a downward swing of current (B). present in all cases are as follows.On raising the field to the threshold value a fast capacitative transient is generated which does not appear to have any influence on the subsequent oscillations. Following the transient oscillations commence by a down-ward swing of current to a level below that existing before the increase in field. Following this the background steady current with uscillations superimposed rises to s 9-7 i94 OSCILLATIONS IN POLYETHYLENE a peak and then decays slightly to leave a regular oscillating pattern. The fact that the oscillations begin invariably by a downward swing of current is important for our later discussion of the mechanism. The amplitudes' of oscillations were not markedly dependent on iodine concen- tration but were always greatest after a field change and then (as in fig.1) decreased somewhat with time. Sometimes as Swan also found the oscillations were modu- lated in a slow way and sometimes there were simultaneous oscillations of slightly different frequency which distorted the sinusoidal form. Occasionally as in fig. 2 there would be a gradual transition from one frequency to a slightly different one reflecting presumably some slow change in conditions within the sample. tirne FIG,2.-Oscillations showing the slow transition from one frequency to another. Note also that there is initially some distortion of the wave due to the presence of other frequencies. Polyethylene film 127 pm thick. Iodine concentration 5 g in 1 1. of 1 M KI solution at 30T. Field 5.51 x lo7 V m-l.As fig. 3 shows the threshold field Et varied inversely as the sample thickness tl and also increased as the iodine concentration decreased. The dry system for which the iodine concentration was low but not precisely determined produced a result in agreement with the others. The characteristics if extrapolated converge to a limiting value Etz2.2x 10 'V m-1 for infinite thickness. It is interesting to note that if two films were put together as a single composite film of double thickness the oscillations were characteristic of a single film of double thickness for both wet and dry systems. 0 2 4 6 8 101214 d-l /m-'x lo3 Frc;. 3.-Variation of threshold field Et with reciprocal thickness and with iodine concentration at a temperature of 30°C.Concentration of iodinc (gin 1 1. of 1 M KI solution) U,25 ; 0, 10; A 5 ; a,1; x dry system. The frequency of oscillationfwas found to be a maximuin at E and to decrease as the field was raised above that value as Swan also found. Ultimately at a sufficiently high field oscillations become uncertain and periodicity was lost. By interpreting (arbitrarily at this stage)f-' as a transit time z of a disturbance across the film the mobility of the disturbance may be written as d/(sE)where E is the average applied field (E 3 &). The results for a range of fields and film thicknesses at ;Iconstant G. T. JONES AND T. J. LEWIS concentration lie on a universal curve (fig. 4) p decreasing with increasing E. Even the result for the double film (76f76) pm fits well on the curve.Arrhenius plots of the frequency against reciprocal temperature produced an activation energy of 1.2 eV in remarkable agreement with Swan.4 Oscillations could be obtained even when the * l6k \ I \ -I2 8- 4-'0 3 4 5 6 7 8 9 10 E/V m-I x lo7 FIG.4.-Mobility p determined from frequency of oscillations as a function of field E showing independence of thickness d. Iodine concentration 10 g/l. 1M KI at 30°C. x 178 pm 0(76+76) pm; 0 127pm; 76pm. temperature was low enough to freeze the electrodes. The period of oscillation decreased or the mobility p increased with increasing iodine concentration as shown in fig. 5 but the indication is that a limiting value might be reached ultimately. 30t I I I I 01 ' 0.I 1.0 10 100 iodine concentration/g 1.-l 1 M KI FIG.5.-Effective mobility 1-1 determined from f as a function of iodine concentration for a 127 pm sample at 30°C.0,4.7 x lo7V n1-l ; x 5.5 x lo' V m-' ; @ 7.9 x lo7V m-I ; .,dry system at 5.5 x 10' V m-'. The background static current has several interesting features which are related to the oscillations. Some (current field) characteristics are shown in fig. 6. The current first varies supralinearly with the field and then approaches a saturation value which for most samples begins to set in at a field just above 2x lo7 V m-l. Sub-sequently at the threshold field for oscillations E, there is a rapid increase in current and thereafter a variation with field which is less than linear.Again these results are very similar to those of Swan and illustrate how reproducible are the conductivity characteristics of iodine doped polyethylene in contrast to the poor reproducibility of such characteristics for natural polyethylene. The combination of oscillatory current the particular form of (current field) f 96 OSCILLATIONS IN POLYETHYLENE 4 3 m 2 X N E s2 x Y .m 3 a U s t: 21 L I I I I 1 0 2 4 6 8 applied field/\(' m-I x lo7 FIG. &-Static current-field characteristics showing the rapid increase of current above a quasi- saturation value as the threshold field Et is exceeded. Film thickness 127 pm temperature 30°C. Iodine concentration (g in 1 1. of 1 M KI solution) (a),I ; (B) 10 ; (c) 50..-. c1 .-x 0 I field E distance from injecting clcctrode (4 (6) V (4 FIG.7.-Characteristics associated with the onset of space charge domain propagation. (a)(Velocity field) characteristic with negative slope above the critical field Ec ; (6) field distribution in solid for various current ratios J/Jc (Jc = ywc where n is the carrier density) (c) general form of (current average field) characteristic deduced from (6). G. T. JONES AND T. J. LEWIS 197 characteristic and an apparent mobility which decreases with increasing field (fig. 4) supports a thesis that space charge domains are propagating in the films above the onset field Et. It is therefore worthwhile to review briefly the salient features of space charge domain propagation as developed for conventional semiconductor^.^* The essential requirement is that the mobile charge carrier concerned should have a (velocity field) characteristic with negative slope over the range of fields of interest (fig.7a). Assuming this velocity characteristic a uniform carrier concentration n in the bulk and an efficient carrier injecting electrode it has been shown that ' the field distribution will be as in fig. 7b. For current density J -cJ where J = qmc is the current corresponding to Ec and q is the charge of the carrier the field approaches a limit E < E which extends over most of the sample. For J > J, the field increases monotonically with distance from the injecting electrode. The (current field) characteristic may also be found and has the form shown in fig.7c the marked upturn in current coming when the ratio J/Jcis such that there is a rapid increase in field away from the carrier injecting electrode. In the negative slope regime (fig. 7a) space charge may accumulate locally and then propagate as a domain.5* When such an accumulation domain propagates the field ahead of it E, will tend to increase and that behind Eb to decrease (fig. 7a). If u < vb then accumulation continues but when zt > q,,any accumulation is dissipated. Thus depending on the field distribu- tion and notably on the operating mean bias field E so domains might propagate fully across the sample or first grow and then decline part way across or if the bias field were high enough (or low enough) so that operation moved outside the negative regime in fig.7a not be generated at all. This model thus suggests why there will be a critical field for the onset of oscilla-tions and why at much higher fields they will die out. It also provides a (current field) characteristic generally in agreement with experiment. MOBILITY MEASUREMENTS A central feature of the space charge domain theory is a negative differential (velocity field) or (mobility field) characteristic. Thus most convincing for our present argument is that we have been able to demonstrate directly the existence of a negative differential mobility coefficient by extending the method outlined by Davie~,~ Wintle and others to high fields. The experiment utilises essentially the same rime time time (4 (b) (4 FIG.8.-Typical results for Y and IdV/dtI as functions of time for a 76 pm thick sample containing 10 g iodinell.of 1 M KI solution at 23°C; -V,--IdV/dtI. (a)0.79 x lo7V m-l (b)3.9 x lo7 V m-' (c)7.9 x lo' V m-l. In (c) it should be noted how IdV/dtJ increases as Vdecreases with time which is indicative of the negative differential (mobility field) relationship. arrangement as for our other measurements reported above except that the constant voltage applied to the electrodes is replaced by a fixed charge placed on the high voltage electrode at an initial time and of sufficient magnitude to raise the field in the OSCILLATTONS IN POLYETHYLENE sample to the value required for the experiment. The electrode is then isolated so that charge can decay only through the sample and the electrode potential Y falls according to the mobility of carriers in the sample.The rate of fall is determined by monitoring the potential of the electrode using a rotating vane field-mill electrostatic voltmeter exposed to the field of the electrode and differentiating the output electronic- ally. t 000 0 2 4 6 002468 E/V m-I x lo7 EIVm-‘ x107 (4 (b) FIG.9.-Apparent mobility p’ from potential decay curves. (a)Iodine concentration 10 g per litre KI solution at 30°C. Film thickness in pm shown on curves. (b) Film thickness 76 pm,temperature 23°C. Concentration of iodine in g per litre KI solution shown on curves. It is possible to show that the apparent carrier mobility p’ is given by 2d Id V/dt 1 p‘ = (2a+l)p = v2 9 t=O where p is the true mobility Q = d2qn,/&V, q is the charge n is the concentration of thermally generated carriers and E is the permittivity.V and IdV/dtI are to be evaluated at time t = 0. In fig. 8 typical results for the decay of Y and Id V/dtI with time are shown at a low a critical and at a high field where the negative differential mobility-field characteristic holds good (see fig. 4). Determining values of Y and jdV/dtI at t = 0 from these it was possible to construct the apparent (mobility field) curves shown in fig. 9. It is seen that p’ reaches a maximum in the range 2-3 x lo7 V m-1 for all the con- ditions chosen and significantly exhibits a negative slope above this range.The onset of the latter regime coincides with the field range in which oscillations are found and for which there is also a negative slope of the mobility curve (fig. 4) derived from these oscillations. Our values of p’are in quite reasonable accord with those reported by Davies lo on iodine-doped polyethylene at low fields. The mobility p estimated from the period of oscillations (fig.4) is less than p’ (fig. 9) and it is very likely that the G. T. JONES AND T. J. LEWlS I99 difference is accounted for by the factor (2a+ 1) in eqn (1). From the daia of fig. 4 and 9a and the expression for 0 it is possible to determine n, assuming that the permittivity E of the film is known. We have taken E to be the value for undoped polyethylene which direct measurement of the permittivity of the filins in situ sup gested was appropriate.Values of n are shown in the table immediately below. ESTIMATES OF THERMALLY-GENERATED CARRIER DENSLTIES flt BASED ON MOBILITIES El AND p' (IODINE 10 g PER LITRE I M K1 SOLUTION AT 30°C) d=76pmE&'rn-':< 107 rlt/n1-3x 1020 E d = 127~111 nt TJ d= 178pm nt 5.25 2.8 4.5 I .4 3.5 0.7 6.0 2.7 5.O 1.7 4.0 0.9 7.0 3.0 6.0 1.9 5.0 I .3 7.0 1.8 6.0 1.3 8.0 1.8 7.0 1.3 The value of n remains sensibly constant for any given sample at a value of about lo2*m-3 in close agreement with trap densities estimated by Davies.lo Choosing a value of n, it is possible to calculate the contribution to the static current density from such carriers. For a 127 pm sample at a field of 4.5 x lo7V m-l and assuming a value of mobility from fig.4 we find a current density of 8 x A rr2. This is less than the measured value from fig. 6 (-1.5 x A m-2) but in view of the various possible inaccuracies is surprisingly close and suggests that a major part of the static current characteristic comes from thermally generated carriers. We should note that the onset of the peak in p' (fig. 9) coincides with the plateau region of the current-field curves (fig. 6) and also with the extrapolated threshold field Et (fig. 3). Although the magnitude of the peaks (fig. 9b) increases with iodine concentration the position of the peaks on the field axis is not so affected in agreement with the fact that the limiting Et in fig. 3 is also independent of concentration.The situation appears to be similar for the KI solution alone in fig. 9b but there will be some free iodine in this case also. Since the essential action of the iodine is likely to depend on its electronegativity and strong acceptor action it is important to try other similarly active dopants. In fact using sulphuric acid in water in a ratio 1 part in 5 in place of the iodine-KI solution produced similar although less repeatable oscillation phenomena and a (current field) curve with all the characteristic features of fig. 6 but at a lower level of current. The calculated mobility (p-10-13 m2 V-' s-l ) w as in agreement with that for the dry iodine samples (see fig. 5) i.e. those of lowest iodine concentration. DISCUSSION The direct evidence of a negative differential coefficient for mobility adds consider- able weight to the argument that the current oscillations are associated with domain f~rmation.~.There may also be significance in the fact that a second general condition for the onset of domain formation namely that the product of carrier density and specimen length should exceed a certain minimum,6 is also obeyed for the present system. There is more than one derivation of this condition but the general result for conventional semiconductors is that the product should be in the range 10l5 to 10l6 m-2. In our case if we choose values from the table we find the product to be practically constant at 2 x 1016m-2. We can see also from this condition why oscillations might not be possible in thin specimens (d = 50 pm) unless the iodine concentration was very large.OSCILLATIONS IN POLYETHYLENE It is now necessary to consider in more detail the action of iodine (or sulphuric acid) and the nature of the carrier whose motion could give rise to the behaviour illustrated in fig. 4 or 9. The iodination action in polyethylene may be twofold. First the strong electronegativity of iodine will create donor-acceptor complexes with the polymer and the evidence is that this occurs in association with the terminal double bond vinyl groups. Electron transfer to the iodine releases vacancies (“ holes ”) into the polymer chain which then become mobile in the crystalline region of the polymer structure since in the close-packed crystallite hole transfer between chains is also possible.* 2* Secondly neutral iodine as associated complexes 1 might be able to link polymer molecules across the amorphous gap between crystal- lites. Electron transfer along an I, chain could occur readily. Thus composite conduction pathways are opened up which unlike those in conventional semiconduct- ors may be localised and devious.2 Vacancies will have an effective mobility which takes account of both drift through the polymer crystallite lattice and trapping at iodine sites with an associated activation energy Wn2 Thus where y is the lattice mobility and 13 is a factor involving the trapping site density which will probably depend on the density of iodine at low concentrations and on the density of vinyl end groups at higher saturation concentrations of iodine.Eqn (2) is similar to that used by Davies * and W may be assigned the value 1.2eV estimated from the temperature dependence of the frequency of oscillations as well as the static current. The lattice mobility p1 can be represented by a relaxation time approxima- tion y1 = z/m:kwhere z is the relaxation time for collisions within the polymer crystal- lites themselves and m* is an effective mass for the carrier moving in an appropriate energy band ofthe crystallite structure. If as the field increases the carrier moment- um increases m* could increase markedly particularly if it is moving in a narrow band. Thus p1 could exhibit the necessary decrease with increasing field. At fields below the critical value Et we find according to fig.9 that p’,and therefore p increases rather than decreases with field. This might be explained by the counter influence of afield lowering of the activation barrier W. Much more work is required to confirm these ideas conclusively but it is certainly plausible that a decrease in effective mass of holes in the polymer chain is responsible for the mobility character- istic and thus for the current oscillations. The role of the electrodes has not been questioned so far but it has been implicit according to the model that the cathode and anode are ready hole and electron acceptors respectively. Diffusion experiments by Taylor and Lewis have indicated that it is certainly necessary to have iodine at the cathode interface for electron injection there but that under steady state conditions the current is bulk rather than injection limited.The experiments with double films either in the wet or the dry arrangement also lead to the conclusion that interfaces do not play a crucial role in the oscillatory process. It will be important to establish whether the phenomena observed with the poly- ethylene system may also be found with other long chain organic structures provided vacancies can be introduced into the chain. Negative differential mobility for carriers moving in narrow energy bands in organic crystals or even for movement along extended chain molecules might be a more common property than hitherto expected and overlooked in the past because of the need to operate at high electric fields and with low currents.Oscillatory currents have been observed in other organic polymers for example by Swaroop and Predecki l4 in dry polyethylene terephthalate and polystyrene as well G. T. JONES AND T. J. LEWIS 20 1 as polyethylene fhs withcut iodine doping. The likelihood in many such cases is simply that a relaxation breakdown phenomenon is being observed l5 especially since fields greater than 10' V m-l are required. Recently Toureille Reboul and Caillon have reported observations of oscillatory current phenomena in the form of regularly spaced peaks in the same three polymers. They find that oscillations coincide with the onset of a negative differential resistance which disappears along with the oscillations at higher fields.From the period of oscillations they estimate a carrier mobility of 10-13 m2 V-1 s-l for polyethylene which since their sample is undoped is much greater than ours would be in similar circumstances. The niodel they propose is that above a threshold field the injection capacity of an electrode increases markedly so that excess charge is momentarily injected into the film. While it propagates this charge serves to lower the field at the electrode and so interrupts the injection. Injection thereby becomes intermittent and the current fluctuates in a quasi-regular manner. Further work is required to confirm whether this phenomena differs fundamentally from that found for the iodine-doped system but it is encouraging that the subject is receiving continued attention.The authors thank Dr. D. M. Taylor and Mr. M. G. Jones for much help especially in earlier stages of this work. Many thanks are also due to Dr. F. J. Smith and the Monsanto Chemical Company for the supply of polyethylene samples and helpful discussions. One of us G. T. Jones is grateful for the award of a Science Research Council Research Studentship. D. W. Swan J. Appl. Phys. 1967,38 5051. T. J. Lewis and D. M. Taylor J. Phys. D Appl. Phys. 1972,5,1664. V. A. Marikhin A. I. Slutsker and A. A. Yastrebinskii Sou. Phys.-Solid State 1965 7 352. 4D.W. Swan J. Appl. Phys. 1967,38 5058. D. E. McCumber and A. G. Chynoweth Trans. I.E.E.E. Electron Deaices 1966 13 4. P. H. Butcher Rep. Prog. Phys. 1967 30 97. 'D. K. Davies Static Electrification I.P.P.S.Conference 1967 Ser. No. 4 29. 'H. J. Wintle J. Appl. Phys. 1970 41 4004. K. Keiji Kanazawa I. P. Batra and H. J. Wintle J. Appl. Phys. 1972 43 719. lo D. K. Davies J. Phys. D. Appl. Phys. 1972 5 162. I' D. K. Davies and P. J. Lock J. Electrocheiti. SOC. 1973 120 266. R. J. Fleming Trans.Furuduy SOC.,1970 66,3090. I3 E. A. Liberman and V. P. Topaly Biochim. Biophys. Actrr 1968 163 125. l4 N. Swaroop and P. Predecki J. Appl. Phys. 1971 42,863. N. Swaroop P. Predecki and J. P. Allen J. Appl. Phys. 1973 44 1943. l6 A. Toureille J. P. Reboul and P. Caillon Comnpt. Rend. 1974 278 849.