Transit pulse dispersion in PVK

~

Solid State Co~unications, Voi.34, pp.75-78. Pergamon Press Ltd. 1980. Printed in Great Britain.

TRANSIT PULSE DISPERSION IN PVK A.R. Birkbeck

College, (Received

Tahmasbi and J.

(University 4th

Hirsch

of London),

February

L o n d o n WC1E 7HX

1980 by R.A. Cowley)

Time-of-flight measurement show that the hole hopping mobility in polyvinylcarbazole layers is independent of thickness b e t w e e n 3 a n d 8 0 pm. Long-tailed transit current profiles with "knees" are observed at all thicknesses a n d down t o - 8 0 ° C , b u t s c a l e o n l y s u p e r f i c i a l l y with transit time. The discrete mobility is reconciled with the transit pulse dispersion by reference to Marshall's computer model of trap-controlled transport.

1.

Introduction

In amorphous solids, the injection of excess carriers at one surface by a short excitation pulse, under a constant drift field, commonly results In transit current profiles of "dispersive" shape ] . These may, o r may n o t , e x h i b i t a "knee" marking the transit tlme. If such a profile is plotted in the form log(current,I)/log(time,t), two straight-line regions are disclosed. The intercept of these is taken to signal the transit t i m e , e v e n when no k n e e i s o b s e r v a b l e , but it does not correspond exactly to the position of the knee when present. At a given temperature, the long-tailed pulses seem to scale with transit time. Ocasionally, similar behaviour has been observed in low-mobility c r y s t a l s 2. I n some c a s e s , the mobility deduced from log I/log ~ plots appears to depend not only on temperature and drift field, but also on sample thickness in a way suggesting that it decreases as the average time spent by carriers in transit increases. Such a "mobility" is meaningless as a parameter describing a material property.

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Fig. I.

Poly-n-vlnyl carbazole (PVK) i s a m a t e r i a l exhibiting the dispersive form of current transits. An e x a m p l e i s s h o w n i n f i g . 1 . It Is well established that hole transport in this a m o r p h o u s p o l y m e r t a k e s p l a c e b y h o p p i n g 3. On the other hand, the mobility is strongly fielddependent in a way unexpected in hopplng transport, and the mobility activation energy is also unexpectedly high. Recently, one of us suggested that the hopping mobility is in fact controlled by charged traps of discrete depth which is related to the relative permittivity and its temperature dependence ~ . Subsequently, we p r e s e n t e d strong experimental evidence to support this interpretation s . However, the conclusions drawn in both papers hinge on the tacit assumption that the mobility and lts field dependence are genuine material properties. Tentative evidence for this assumption came from sanples whose thickness varied over only a limited range.

Typical hole transit current pulse

at room temperature.

PVK layer 10.5 pm

thick, bombarding dose 0.8 pJ cm -2, drift field ]90 kV cm -I.

; vertical division =

I nA cm -2, I horizontal division = 20 ms.

2.

Experiments

and Results

We now p r e s e n t the results of mobility measurements, under space-charge free conditions, uslng electron b e a n e x c i t a t i o n G, o n s a m p l e s c a s t f r o m BASF L u v t c a n r a n g i n g i n thickness f r o m 3 t o 8 0 ~m. Increased attention paid to purification s and to the thorough removal of residual solvent was effective in reducing the concentration of range-l~iting d e e p t r a p s 7. Every value of transit time was deduced directly from a knee in the transit pulse. The r e s u l t s , at two temperatures, are

75

76

TRANSIT PULSE DISPERSION IN PVK

shown in fig. 2. They clearly demonstrate that the mobility is independent of thickness, but dependent on drift field. Over the entire thickness range, the shape of the transit pulses when normalized to transit time remained superficially similar. 164

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Vol. 34, No. 2

curves merely intersect at a point, and ment with the theory seems fortuitous. over, the temperature of 52°C in fig. 2 chosen because it lies in the middle of range in which the transits are said to

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thickness and drift field at 22°C and 52°C. The vertical bars indicate standard deviation of mean. In fact, scaling is imperfect, as can be seen in fig. 3 w h e r e we h a v e p l o t t e d s 1 and s2, the magnitudes of the slopes (both negative) of log f/log tduring and after transit, against drift field (F) at room temperature, for four samples spanning a thickness range 10'1. Between the thickest sample at minimum F and the thinnest a t m a x i m u m F, t h e t r a n s i t time varies by 4x104:1. We n o t e t h a t s 1 r e m a i n s almost constant but that s 2 changes throughout the range of F. Fig. 4 shows the variation of s] and s 2 with reciprocal temperature (for a reason to be explained later) at constant b' = 0 . 2 MV/cm. When p l o t t e d , instead, in the form ~i = l-s1 and ~f = s2-1 against linear temperature for comparison with fig 2 of ref. ( 8 ) , we f i n d t h e results in remarkably good agreement with each other. H o w e v e r , we c a n n o t a g r e e w i t h P f i s t e r and Grlffiths's conclusion s that Scher and Montroll's result 9 az = af applies t o PVK e v e n over a limited temperature range; t h e two

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It is noteworthy that, out of about 100 samples studied, 5 exhibited humped profiles during transit, the humps showing a tendency to increase in height with increasing temperature. The hole mobility in such samples is the same as in the larger group. Humps h a v e o f t e n b e e n reported in the literature, and sometimes attributed to space charge, but under spacecharge free conditions as in this work they can only be due to persistent release from surface states of some kind We h a v e b e e n u n a b l e t o isolate the exact cause of the effect: probing with an electron beam as in ref. (10) failed to disclose any trap-rich layer of significant thickness, and hole injection from the alumznium e l e c t r o d e s used here is most unlikely. However, the results presented in figs. 3 and 4 a r e f o r s a m p l e s w h i c h do n o t s h o w h u m p e d profiles at any temperature

77

TRANSIT PULSE DISPERSION IN PVK

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Discussion

The invariance of the mobility with thickness confirms our interpretation of its field dependence 4'5. We a r e , therefore, confident that the mobility is controlled by traps of essentially discrete depth. The problem is to reconcile this conclusion with the dispersive shape of the transit profiles. In conventional, coherent, shallow-trap controlled transport, a substantial current tail after transit can only be due to delayed release of carriers; either from deeper bulk traps filled during transit, or from traps located near the excited surface as discussed above. A profile such as fig. 1 shows that carrier loss during transit cannot possibly account for the charge collected after transit (we discuss deep bulk trapping in a separate paperll). Without humps in the profiles, surface release would appear to be absent. It seems most unlikely that both effects are present but consistently combine in such a way as to produce a slope s 1 almost independent of field and invariant from sample to sample (fig. 3), and only weakly dependent on temperature (fig. 4a). We t h e r e f o r e dtsmi•• delayed release as insignificant in this work, but wish to emphasize that, when such a mechanism plays a rSle, its effect on sl as well as s 2 must be taken into account 12'13 We h a v e t r i e d to reconcile our results with recent theories of dispersive multiple trapping tran•port 14'15.1 but failed to do so. However, M a r s h a l l 16 h a s s h o w n , b y c o m p u t e r simulation, that a ~rap-controlled mobility is compatible

Slopes

(a) s I and (b) s 2 as func--

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temperature.

Drift

field 0.8 MV cm -I.

Solid circles repre-

sent polnts taken from fig. 2 of ref. 8 and adjusted to 0.8 MV cm -I using fig. of this paper,

3

sl(M) and s2(M) are lines

predicted by Marshall's computer model 16 for 30 trapping events per transit at the spread of trap energies 6e stated. with a dispersive pulse shape if quite a small amount of Gaussian trap level broadening i• allowed for. This model applies to trap-controlled bar~ transport in which pulse broadening would he negligible in the absence of trapping. In hopping transport, some spread in hopping time• would be expected 1, although it t• now a c c e p t e d that this is insufficient to account fully for the observed dispersion~'ls'~ S i n c e i n PVK t h e t r a p p e d / f r e e time ratio 4 i• of the order 104 , we may assume that in any case the spread in trap release rates predominates, and that Marshall's m o d e l 16 i s a p p l i c a b l e . Qualitatively, the model can explain all the feature• observed, including the loss of the transit knee at low temperatures. Quantitatively the fit is not very good. Thi• may partly be due to the fact that the model computations were made as•uming 30 trapping events per transit, whereas in our experiment• the shortest transit times may correspond to as few as 10 event• ~. In the model, only one parameter describes the dispersion, viz.6E/kT where dE = ~ × s t a n d a r d deviation of the trap

TRANSIT PULSE DISPERSION IN PVK

78

depths. The loss of the knee at =190 K corresponds to ~/kT= 3 i.e. 6E ~ 5 0 meV. The predicted slopes st(M) and s2(M) vary approximately exponentially with 6£/kT. By p l o t t l n g the experimental values of sl against log(i/T), a reasonable fit of aI(M) to the rather scattered experimental points in fig. 4a xs obtained w i t h ~E ~ 3 5 meV. In the case of s2, the agreement is poor (fig. 4b). The measured s2 correspond to values o f 6E s h i f t i n g from 35 to 65 ~eV as the temperature is lowered.

The variation of S2 with field (fig. 3) is also much stronger than predicted by 16. A similar discrepancy has been noted by Marshall for the case of hole transport in Se.

Vol. 34, No. 2

I n PVK, t h i s c a n p e r h a p s b e u n d e r s t o o d by reference to the Poole-Frenkel model used to describe the escape of carriers from the large Coulomb centres ~ . This description becomes increasingly unsatisfactory as the field is decreased and escape in directions other than the forward one begins to compete. The trap depth then becomes less well defined, i.e. 6£ increases. In summary, agreement between Marshall's model and our observations is only r o u g h ; b u t w i t h ~ c = 5 0 meV t h e m o d e l g i v e s a better account of the observations than any other to date. Acknowledgement - The authors Dr. J.M. Marshall for helpful

wish to thank discussions 2°

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

PFISTER G. and SCHER H., Advances in Physics 27, 747 (1978) - a review article. MARSHALL J.M., J. Phys. C I0, 1283 (1977). GILL W.D. in MORT J. and PAI D.M. (Eds.), Photoconduetlvity and Related Processes, p. 303. Elsevier Co., Amsterdam (1976) - a review article HIRSCH J., J. Phys. C 1_22, 321 (1979). TAI~MASBI A.R., HIRSCH J. and KOLENDOWICZ J.Z., Sol. State Commun. 29_, 847 (1979). SPEAR W.E., Proc. Phys. Soc. (London) B 7__00,669 (1957). REUCROFT P.J. and TAKAHASHI K., J. Non-tryst Sollds I__7, 71 (1975). PFISTER G. and GRIFFITHS C.H., Phys. Rev. Letts. 40, 659 (1978). SCHER H. and MONTROLL E.W., Phys. Rev. B 12, 2455 (1975). GODSON S.M. and HIRSCH J. in SPEAR W.E. (Ed.) Amorphous and Liquid Semiconductors, 7th Intl. Conf. p.770, Univ. of Edinburgh (1977). HIRSCH J. and TAHMASBI A.R., following paper. SILVER M., DY K.S. and HUANG I.L., Phys. Rev. Letts 27, 21 (1971). HIRSCH J., Phys. status solidi (a) 25, 575 (1974). SCHMIDLIN F,W., Phys. Rev. B 16, 2362 (1977). NOOLANDI J., Phys. Rev. B 16, 4466, 4474 (1977). MARSHALL J.M., Phil. Mag. 36, 959 (1977). POLLAK M. in SPEAR W.E. (Ed.) Amorphous and Liquid Semiconductors, 7th Intl. Conf. p. 219, Univ. of Edinburgh (19771. SILVER M., ibld p. 214. MARSHALL J.M., Phll Mag. 38, 335 (1978). Dr. Marshall has kindly supplled us with modified values for the slopes resultlng from a recently improved approximation to the Gausslan function. Our general conclusions are unaffected, but the best fit of s~(M) now corresponds to ~50 meV. The fit of s2(~) is improved and corresponds to =75 meV.