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Dispersive carrier transport in partially oriented p-quaterphenyl layers
Thin Solid Films, 76 (1981) 329-333 ELECTRONICSAND OPTICS
329
DISPERSIVE C A R R I E R TRANSPORT IN P A R T I A L L Y ORIENTED p- Q U A T E R P H E N Y L LAYERS w. MYCIELSKI,S. KANIAAND A. LIPII~ISKI Technical University of Lbd~, Institute of Physics, ul. Wblczanska 219, 93-005 Lbdk (Poland)
(ReceivedJuly 21, 1980;acceptedAugust 15, 1980)
Charge carrier transport in partially oriented p-quaterphenyl films was investigated using the transient current technique. In contrast to completely oriented layers, all current pulses in textured p-quaterphenyl films were highly dispersive and their representation on a double logarithmic scale may be described by two straight lines (with slopes - ( l - a ) and - ( l + a ) , where a ~ 0.65). This indicates the possibility that the results can be interpreted in terms of the Scher-Montroll model of dispersive transport in disordered systems.
1. INTRODUCTION Recently we have reported results of drift mobility experiments on oriented pquaterphenyl layers 1' 2. It was observed that hole and electron mobilities decrease with increasing electric field approximately as E - 1. These results were obtained for p-quaterphenyl layers deposited onto substrates at relatively high temperatures (~420 K) and very low deposition rates (below 25 A s-t). The crystal structure of such layers was very good t. In the present paper we report the results of studies of transport phenomena in textured p-quaterphenyl layers. The shape of transient currents in such layers is not interpretable on the basis of the "classical" time-offlight method 3 and we try to explain these results in terms of a dispersive transport model first described by Scher and Montroll 4 and later developed by Pfister and Scher 5. 2. BASICASSUMPTIONSOF THE MODEL Extensive iJ~vestigation of electronic transport in disordered solids has shown that the interpretation of experimental data is very difficult. Anomalous transport properties have been observed particularly in electrophotographic materials such as As2Se3, selenium and poly-(N-vinylocarbazole) films (for a review see refs. 4 and 5). Anomalous properties are demonstrated, first of all, by a long tail in the transient current pulse without a characteristic cusp related to the transit time t t (Fig. l(a)). According to Scher and Montroll (SM)4, such a result is caused by a wide distribution of the event times in stochastic hopping conduction. Scher and 0040-6090/81/0000-0000/$02.50
© ElsevierSequoia/Printedin the Netherlands
330
W. MYCIELSKI, S. KANIA, A. LIPI/~ISKI
Montroll assumed that the distribution£unction ~,(t) can be described by the slowly varying power dependence ~9(t) oct -tl +~) where ~ is a constant (0 < ~ < 1). This time dependence of ~,(t) leads to a non-gaussian time development of the packet of carriers injected into the sample and, in consequence, to the highly dispersive type of current pulse shown in Fig. l(a). Scher and Montroll have used the theory of continuous time random walk (CTRW) to calculate the time dependence of the current. The general results of their calculation are summarized in the following relations 4, 5. ( t - t 1 2) i(t) oc [ t _ t I +,,
t <: t t t > t,
These results are shown in Fig. l(b), in which log i v e r s u s log t is plotted. As can be seen from this figure, the SM model provides new possibilities for the interpretation of electronic transport mechanisms, although the transit time t t determined in this way has not such a simple interpretation as has that obtained from non-dispersive pulses.
A
ta~
t
(b)
log t
Fig. 1. (a) An example of a dispersive transient current pulse and (b) its log log representation.
Non-gaussian transport in disordered solids may also be discussed in terms of a multiple-trapping model. Noolandi 6' v and Schmidlin 8 have made a comparison of the SM model" and multiple-trapping models and demonstrated their formal equivalence. In addition to the aforementioned analytical studies, a numerical simulation represents another approach to the investigation of the dispersive transient transport in disordered systems 9-11. An important point of these studies has been the discussion of the influence of surface trapping on the transient current shape 9. 3. EXPERIMENTAL DETAILS AND RESULTS Thin films of p-quaterphenyl were prepared by vacuum evaporation at a pressure of the order of 10 -5 Torr. For electrical measurements these films (thickness 2-7 ~tm) were sandwiched between gold (bottom) and aluminium (top) electrodes. The details of the deposition technique for p-quaterphenyl layers have been given elsewhere 1. Contrary to the conditions described previously for growing oriented layers, we employed a substrate temperature of 390-430 K and a deposition rate greater than 40 A s-1. The p-quaterphenyl layers obtained in this way were partially oriented (textured), as can be seen from Fig. 2. For such layers we measured
DISPERSIVE CARRIER TRANSPORT IN p-QUATERPHENYL LAYERS
331
the carrier drift mobility because of our interest in the relation between the structure of organic layers and their transport phenomena. The drift mobility was investigated using the time-of-flight technique described elsewhere12.
Fig. 2. An electron diffraction pattern from thin partially oriented p-quaterphenyl layers.
In the case of partially oriented p-quaterphenyl films all current pulses were highly dispersive. Figure 3 shows a typical current-time profile for such layers in comparison with the profile for completely oriented layers 1. Figure 4 gives an example of the log/-log t representation of the dispersive current pulse. According to the SM model the sum of the slopes for times shorter and longer than tt is approximately - 2 and the value of a is about 0.65.
\
~ , ~ m m--~=-,
(a)
(b)
Fig. 3. Typical transient currents in (a) partially oriented and (b) completely oriented p-quaterphenyl layers. The thicknesses of the samples were (a) 4.0 ttm and (b) 4.2 rtm, the applied voltage was 36 V, the vertical scale is 10 - s A div- 1 and the horizontal scale is 10 -4 s div- 1.
4. DISCUSSION These experimental data constitute an example in which the transition from non-dispersive (or weakly dispersive) to completely dispersive transport can be observed as a function of increasing disorder in thin p-quaterphenyl layers. In a
332
W. MYCIELSKI, S. KANIA, A. LIPII~ISKI
previous paper I we have shown that charge carriers in oriented layers are transported via hopping between localized states situated near the Fermi level. The width of such an "impurity band" was found to be about 0.025 eV *. In accordance with Pollak's suggestion 14 we suppose that a small energetic spread of the hopping states leads to non-dispersive transport and the transit time is well defined by the shape of the transient current pulse. The situation is quite different in partially oriented layers. In this case an anomalous dispersion of the transient times is due probably to a greater bandwidth of the localized states and/or due to the existence of deep traps caused by intergrain barriers or other structural imperfections. This situation is similar to the trap-controlled hopping described by Pfister and Scher 5 and observed earlier in doped polymers by Pfister et al. 15
10 7
10-s
0.01
0.1
1 t (ms)
---
Fig. 4. A log/--log t representation of the dispersive current pulse of Fig. 3(a).
As can be seen from Figs. 3 and 4, the characteristic transit time t t for partially oriented layers is a little shorter than that for oriented layers (the thicknesses of the samples and the applied voltages in both cases were similar). That is, the drift velocities of the f a s t e s t carriers in dispersive and non-dispersive transport are also similar and the dispersion is a result of carrier immobilization due to deep traps inside the partially disordered p-quaterphenyl layers. Although our work on dispersive transport is still at an early stage we suggest that the results presented here and other anomalous transport properties of low molecular weight organic layers may be explained on the basis of the SM model and its modifications. ACKNOWLEDGMENTS
This work was carried out under Research Project MR I-5-9.05.
* This value was found to be the activation energy of the drift mobility according to the well-known M o t t - D a v i s hopping model 13. In the case of partially oriented layers the drift mobility and its activation energy were not calculated because of the limitations of the concept of mobility in the treatment of the dispersive type of transport.
DISPERSIVE CARRIER TRANSPORT IN p-QUATERPHENYL LAYERS
333
REFERENCES 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15
S. Kania, W. Mycielski and A. Lipifiski, Thin Solid Films, 61 (1979) 229. S. Kania, A. Lipifiski and W. Mycielski, Phys. Status Solidi A, 53 (1979) K223. W.E. Spear, J. Non-Cryst. Solids, 1 (1969) 197. H. Scher and E. W. Montroll, Phys. Rev. B, 12 (1975) 2455. G. Pfister and H. Scher, Adv. Phys., 27 (1978) 747. J. Noolandi, SolidState Commun., 24 (1977) 477. J. Noolandi, Phys. Rev. B, 16(1977)4474. F.W. Schmidlin, Phys. Rev. B, 16 (1977) 2362. M. Silver, K. S. Dy and I. L. Huang, J. Non-Cryst. Solids, ~ 1 0 (1972) 773. M. Silver and L. Cohen, Phys. Rev. B, 15 (1977) 3276. M. Kr61, M. Inglot-Siemaszko and A. Szymafiski, Proc. 2nd Conf. on Electrical and Related Properties of Organic Solids, September 18-23 1978, Karpacz, Poland, Wroctaw Technical University, Wroctaw, 1978, p. 211. W. Mycielski and A. Lipifiski, Thin Solid Films, 48 (1978) 133. N.F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, Oxford University Press: Clarendon Press, Oxford, 1971. M. pollak, Postcpy Fiz., 28 (1977) 547. G. Pfister, S. Grammatica and J. Mort, Phys. Rev. Lett., 37 (1976) 1360.
329
DISPERSIVE C A R R I E R TRANSPORT IN P A R T I A L L Y ORIENTED p- Q U A T E R P H E N Y L LAYERS w. MYCIELSKI,S. KANIAAND A. LIPII~ISKI Technical University of Lbd~, Institute of Physics, ul. Wblczanska 219, 93-005 Lbdk (Poland)
(ReceivedJuly 21, 1980;acceptedAugust 15, 1980)
Charge carrier transport in partially oriented p-quaterphenyl films was investigated using the transient current technique. In contrast to completely oriented layers, all current pulses in textured p-quaterphenyl films were highly dispersive and their representation on a double logarithmic scale may be described by two straight lines (with slopes - ( l - a ) and - ( l + a ) , where a ~ 0.65). This indicates the possibility that the results can be interpreted in terms of the Scher-Montroll model of dispersive transport in disordered systems.
1. INTRODUCTION Recently we have reported results of drift mobility experiments on oriented pquaterphenyl layers 1' 2. It was observed that hole and electron mobilities decrease with increasing electric field approximately as E - 1. These results were obtained for p-quaterphenyl layers deposited onto substrates at relatively high temperatures (~420 K) and very low deposition rates (below 25 A s-t). The crystal structure of such layers was very good t. In the present paper we report the results of studies of transport phenomena in textured p-quaterphenyl layers. The shape of transient currents in such layers is not interpretable on the basis of the "classical" time-offlight method 3 and we try to explain these results in terms of a dispersive transport model first described by Scher and Montroll 4 and later developed by Pfister and Scher 5. 2. BASICASSUMPTIONSOF THE MODEL Extensive iJ~vestigation of electronic transport in disordered solids has shown that the interpretation of experimental data is very difficult. Anomalous transport properties have been observed particularly in electrophotographic materials such as As2Se3, selenium and poly-(N-vinylocarbazole) films (for a review see refs. 4 and 5). Anomalous properties are demonstrated, first of all, by a long tail in the transient current pulse without a characteristic cusp related to the transit time t t (Fig. l(a)). According to Scher and Montroll (SM)4, such a result is caused by a wide distribution of the event times in stochastic hopping conduction. Scher and 0040-6090/81/0000-0000/$02.50
© ElsevierSequoia/Printedin the Netherlands
330
W. MYCIELSKI, S. KANIA, A. LIPI/~ISKI
Montroll assumed that the distribution£unction ~,(t) can be described by the slowly varying power dependence ~9(t) oct -tl +~) where ~ is a constant (0 < ~ < 1). This time dependence of ~,(t) leads to a non-gaussian time development of the packet of carriers injected into the sample and, in consequence, to the highly dispersive type of current pulse shown in Fig. l(a). Scher and Montroll have used the theory of continuous time random walk (CTRW) to calculate the time dependence of the current. The general results of their calculation are summarized in the following relations 4, 5. ( t - t 1 2) i(t) oc [ t _ t I +,,
t <: t t t > t,
These results are shown in Fig. l(b), in which log i v e r s u s log t is plotted. As can be seen from this figure, the SM model provides new possibilities for the interpretation of electronic transport mechanisms, although the transit time t t determined in this way has not such a simple interpretation as has that obtained from non-dispersive pulses.
A
ta~
t
(b)
log t
Fig. 1. (a) An example of a dispersive transient current pulse and (b) its log log representation.
Non-gaussian transport in disordered solids may also be discussed in terms of a multiple-trapping model. Noolandi 6' v and Schmidlin 8 have made a comparison of the SM model" and multiple-trapping models and demonstrated their formal equivalence. In addition to the aforementioned analytical studies, a numerical simulation represents another approach to the investigation of the dispersive transient transport in disordered systems 9-11. An important point of these studies has been the discussion of the influence of surface trapping on the transient current shape 9. 3. EXPERIMENTAL DETAILS AND RESULTS Thin films of p-quaterphenyl were prepared by vacuum evaporation at a pressure of the order of 10 -5 Torr. For electrical measurements these films (thickness 2-7 ~tm) were sandwiched between gold (bottom) and aluminium (top) electrodes. The details of the deposition technique for p-quaterphenyl layers have been given elsewhere 1. Contrary to the conditions described previously for growing oriented layers, we employed a substrate temperature of 390-430 K and a deposition rate greater than 40 A s-1. The p-quaterphenyl layers obtained in this way were partially oriented (textured), as can be seen from Fig. 2. For such layers we measured
DISPERSIVE CARRIER TRANSPORT IN p-QUATERPHENYL LAYERS
331
the carrier drift mobility because of our interest in the relation between the structure of organic layers and their transport phenomena. The drift mobility was investigated using the time-of-flight technique described elsewhere12.
Fig. 2. An electron diffraction pattern from thin partially oriented p-quaterphenyl layers.
In the case of partially oriented p-quaterphenyl films all current pulses were highly dispersive. Figure 3 shows a typical current-time profile for such layers in comparison with the profile for completely oriented layers 1. Figure 4 gives an example of the log/-log t representation of the dispersive current pulse. According to the SM model the sum of the slopes for times shorter and longer than tt is approximately - 2 and the value of a is about 0.65.
\
~ , ~ m m--~=-,
(a)
(b)
Fig. 3. Typical transient currents in (a) partially oriented and (b) completely oriented p-quaterphenyl layers. The thicknesses of the samples were (a) 4.0 ttm and (b) 4.2 rtm, the applied voltage was 36 V, the vertical scale is 10 - s A div- 1 and the horizontal scale is 10 -4 s div- 1.
4. DISCUSSION These experimental data constitute an example in which the transition from non-dispersive (or weakly dispersive) to completely dispersive transport can be observed as a function of increasing disorder in thin p-quaterphenyl layers. In a
332
W. MYCIELSKI, S. KANIA, A. LIPII~ISKI
previous paper I we have shown that charge carriers in oriented layers are transported via hopping between localized states situated near the Fermi level. The width of such an "impurity band" was found to be about 0.025 eV *. In accordance with Pollak's suggestion 14 we suppose that a small energetic spread of the hopping states leads to non-dispersive transport and the transit time is well defined by the shape of the transient current pulse. The situation is quite different in partially oriented layers. In this case an anomalous dispersion of the transient times is due probably to a greater bandwidth of the localized states and/or due to the existence of deep traps caused by intergrain barriers or other structural imperfections. This situation is similar to the trap-controlled hopping described by Pfister and Scher 5 and observed earlier in doped polymers by Pfister et al. 15
10 7
10-s
0.01
0.1
1 t (ms)
---
Fig. 4. A log/--log t representation of the dispersive current pulse of Fig. 3(a).
As can be seen from Figs. 3 and 4, the characteristic transit time t t for partially oriented layers is a little shorter than that for oriented layers (the thicknesses of the samples and the applied voltages in both cases were similar). That is, the drift velocities of the f a s t e s t carriers in dispersive and non-dispersive transport are also similar and the dispersion is a result of carrier immobilization due to deep traps inside the partially disordered p-quaterphenyl layers. Although our work on dispersive transport is still at an early stage we suggest that the results presented here and other anomalous transport properties of low molecular weight organic layers may be explained on the basis of the SM model and its modifications. ACKNOWLEDGMENTS
This work was carried out under Research Project MR I-5-9.05.
* This value was found to be the activation energy of the drift mobility according to the well-known M o t t - D a v i s hopping model 13. In the case of partially oriented layers the drift mobility and its activation energy were not calculated because of the limitations of the concept of mobility in the treatment of the dispersive type of transport.
DISPERSIVE CARRIER TRANSPORT IN p-QUATERPHENYL LAYERS
333
REFERENCES 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15
S. Kania, W. Mycielski and A. Lipifiski, Thin Solid Films, 61 (1979) 229. S. Kania, A. Lipifiski and W. Mycielski, Phys. Status Solidi A, 53 (1979) K223. W.E. Spear, J. Non-Cryst. Solids, 1 (1969) 197. H. Scher and E. W. Montroll, Phys. Rev. B, 12 (1975) 2455. G. Pfister and H. Scher, Adv. Phys., 27 (1978) 747. J. Noolandi, SolidState Commun., 24 (1977) 477. J. Noolandi, Phys. Rev. B, 16(1977)4474. F.W. Schmidlin, Phys. Rev. B, 16 (1977) 2362. M. Silver, K. S. Dy and I. L. Huang, J. Non-Cryst. Solids, ~ 1 0 (1972) 773. M. Silver and L. Cohen, Phys. Rev. B, 15 (1977) 3276. M. Kr61, M. Inglot-Siemaszko and A. Szymafiski, Proc. 2nd Conf. on Electrical and Related Properties of Organic Solids, September 18-23 1978, Karpacz, Poland, Wroctaw Technical University, Wroctaw, 1978, p. 211. W. Mycielski and A. Lipifiski, Thin Solid Films, 48 (1978) 133. N.F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, Oxford University Press: Clarendon Press, Oxford, 1971. M. pollak, Postcpy Fiz., 28 (1977) 547. G. Pfister, S. Grammatica and J. Mort, Phys. Rev. Lett., 37 (1976) 1360.