Sublinear behavior of photoconductivity with light intensity in the fullerenes

Solid State Communications,

Vol. 94, No. 2, pp. 141-145, 1995 Elsevier Science Ltd Printed in Great Britain. 0038-1098195 $9.50 + .OO

0038-1098(94)00891-4

SUBLINEAR

BEHAVIOR OF PHOTOCONDUCTIVITY IN THE FULLERENES

WITH LIGHT INTENSITY

A. Hamed, R. Escalante and P.H. Hor Department of Physics and Texas Center for Superconductivity at the University of Houston, Houston, Texas 77204-5932, USA (Received 15 September 1994; accepted 21 November 1994 by E.E. Mendez)

We measure the photoconductivity up and the light intensity dependence of ap as a function of temperature for CT0films. We compare the results with those from previous similar measurements on Cm films. Interpretation of the results in terms of a conduction band tail of gap states, assumed to originate from disorder in the electronic potential, suggests that this disorder decreases with decreasing temperature below 380K for CTo, and below 260K for Cho. Keywords: A. fullerenes, D. electronic states (localized), D. photoconductivity and photovoltaics. possible phase transitions for solid CTo. At high enough temperatures, one might expect a free-rotator THE EXISTENCE of an orientational and structural phase to exist, similar to that of Cm above 260 K. phase transition at 260K in Ceo, the most stable Upon lowering the temperature, the first transition member of the fullerene family [l], has been well would occur when the five-fold axis of the CT0 documented [2-61. Above 260 K, the quasi-spherical molecules is locked along specific crystal directions, 60-carbon atom Cbo shells experience high frequency and a second transition at lower temperatures would nearly uncorrelated rotations while sitting at the sites result from the ceasing of free rotations about the fiveof an Fmjm f.c.c. lattice and almost complete orientafold axis. Indeed, this picture seems to be confirmed tional disorder exists in the solid. Below 260 K, the CeO by a number of studies [7-121, with measured transiunits are no longer symmetry equivalent because of tion temperatures of about 340 K and 280 K for the orientational ordering, leading to a simple-cubic Pa3 high and low temperature transition points, respecstructure. The molecules, however, continue to jump tively. Below 280 K, rotational jumps around the long between a limited number of nearly-degenerate orienmolecular axis seem to persist through motion in a tations separated by energy barriers of 250-300 meV. multiwell potential down to about [7,8] 180 K. EvenAs the temperature is decreased below 260K, the tually, all molecular rotations are frozen at low population of the higher energy misoriented states enough temperatures [7,8]. decreases, and, thus, so does the amount of orientaAn interesting question is how the orientational tional disorder in the solid. Put differently, the disorder in the fullerenes affects the amount of number of molecular jumps per unit time between disorder in the electronic potential. Solids with a the ground and the misoriented states in the solid significant degree of disorder in the electronic potendecreases with decreasing temperature below 260 K, tial develop tails of localized electronic states that as less thermal energy is available. For cooling rates extend into the gap from the conduction and/or 0.01-0.1 Kmin-’ a glassy transition is observed at valence bands [13]. The density of tail states g(e) about 90 K, corresponding to the freezing in of the decays exponentially into the gap, g(c) = go exp(-e/Eo), where the energy E is measured from orientational states. The next most abundant member of the fullerenes the corresponding band edge and the characteristic is CTo. These molecules, with a lower DQ symmetry energy E. = Eoc for the conduction band and and an elongated “rugby-ball” shape, suggest two E. = Eov for the valence band give the width of the 1. INTRODUCTION

141

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PHOTOCONDUCTIVITY

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tail. Exponential tails in the density of gap states can, quite generally, originate from structural, topological and compositional disorder on one hand, or thermal disorder on the other. Measuring the optical absorption coefficient a(hv) for photon energies hv below the optical gap eg, will then also yield an exponential or Urbach tail o(hv) = aoexp[-(hves)/U] resulting from the convolution of the conduction and valence band tails. For those crystalline solids that exhibit an Urbach tail, the value of the characteristic energy U is typically a few meV, though values of 30meV can be observed in heavily doped semiconductors [14]. In amorphous solids, on the other hand, U is signilicantly larger. In hydrogenated amorphous silicon, for example, U is in the range 50- 110 meV, depending on the particular sample [13,15]. Measurements of the absorption coefficient in Cho films have revealed the existence of an Urbach tail with characteristic energy [16] U = 60 meV, a surprisingly large value for a crystalline solid. Is this wide tail due to a large amount of static disorder, such as defective molecules and solvent residues, or, more interestingly, is it the result of thermal disorder and is related to the dynamics of molecular motion. In the latter case, U is expected to change strongly with temperature, and the fullerenes would offer a useful system to study localization of electronic states by thermal disorder, because of their orientational phase and glassy transitions. In this work we use photoconductivity as a probe of changes in the density of gap states with varying temperature in CT0 films. Several studies on the photoconductivity of fullerene thin films have been reported previously [17-293. Here, we measure the temperature dependence in the range lOO-500K of the photoconductivity ob and of y in [UP= br”,]

(1)

where F is the light intensity and b is a temperature dependent coefficient. We compare the results with those of similar measurements reported earlier on Cho films [30]. And, as done in [30] for Ceo, we relate y to the magnitude of a conduction band tail and the amount of disorder in the electronic potential. CT0 polycrystalline films were prepared by sublimation at 520°C of 99% pure CT0powder onto sapphire substrates held at 200°C during deposition in a vacuum of lO-6 Torr. Coplanar conductance measurements were carried in situ using pre-evaporated Ag electrodes having a width of 4mm and a gap of 1 mm. Applied field of up to 8 x lo2 Vcm-’ yielded ohmic behavior. The films were illuminated through a vacuum fused silica window using the white light from a quartztungsten-halogen projector lamp. Light intensities were

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IN FULLERENES

Vol. 94, No. 2

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Fig. 1, Temperature dependence of the in situ photoconductivity op of a 0.7 pm thick CT0 polycrystalline fi~mmwrn~s~red using white light of intensity

adjusted between 1 and lo2 mWcm2 using neutral density filters. Results are presented for a representative CT0 film 0.7pm thick. Figure 1 presents op vs inverse absolute temperature between 450 and lOOK, with data points obtained on cooling at a rate of 3 K mint. A straight line is obtained from 450K down to 180K. A transition region between 180 and 160 K is followed by another straight line segment from 160K down to lOOK. The same curve was obtained on heating, and no hysteresis effects were observed. To obtain the light intensity dependence of apt the sample temperature was first stabilized at a given value for several minutes and then up obtained for various light intensities in the range l-102mWcm~2. The photo~onductivity op is obtained from crp = Ui/ - odd, where nil is the conductivity during illumination, and ad is the dark conductivity. Plotting loglo (g,) vs light intensity yielded a good straight line at all temperatures, and thus the slope of this line gives 7 in a,, = bFy. Figure 2 shows, as an example, up vs F obtained at 300K. Figure 3(a) gives the temperature dependence of y for our CT0film between 100 and 500 K. For comparison, Fig. 3(b) presents the results from [30] of similar measurements of y on a Cm film. Notice that for both fullerene films, ‘TV exhibits a sublinear dependence (y < 1) on light intensity. As seen in Fig. 3(a), y increases for the CT0 film with decreasing temperature from 500 K to about 400 K, then, at about 360 K the value of y begins to slowly decrease over an extended temperature range that ends at 180K, from where y increases again with decreasing temperature. In the

Vol. 94, No. 2 PHOTOCONDUCTIVITY

WITH LIGHT INTENSITY

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IN FULLERENES

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Fig. 2. Phot~onducti~ty op vs light intensity F at room temperature. Dashed hne is only a guide to the eye. case of the Cm film in Fig. 3(b), a steeper increase of y with decreasing temperature takes place between 500 IS and 260 K. This temperature marks the onset of a pronounced decrease in y that extends down to 180K from where again y increases quickly with falling temperature. The value and temperature dependence of y are, quite generally, determined by the dist~bution and properties of gap states. In an n-type se~conductor where the electron quasi-Fermi level sweeps through a uniform trap distribution, for example, one expects [31] y = 1 and a number of photocarriers insensitive to temperature. If the Fermi level remains beiow a uniform trap distribution [31], one obtains y = 0.5 and an exponential dependence of gp on temperature. However, it is possible for y (and (ip) to have considerable structure as a function of temperature. A temperature dependence of y can be observed if, with changing temperature and light intensity, the electron and hole demarcation levels in the semiconductor sweep through regions in the gap containing various types of states with different energy distributions and capture cross sections. One example is the phenomenon of quenching of the photoconductivity, characterized by y > 1 and a minimum in ap in a narrow temperature region [32]. Thus, even in a semiconductor having a fixed temperature independent gap density of states, y and ap can exhibit considerable structure as a function of temperature. However, the fact that the behavior of y changes dramatica~Iy near the phase transition points of 340K and 260K in CT0 and C&, respectively, makes

(K)

‘-Oj--0.8

-

0.6

-

0.4

-

0.2

-

ii

o.oi too

200

300

400

500

T (K) Fig. 3. (a) Temperature dependence of the exponent y for the CT,, film. The dashed lines are fits of equation (2) in the text to data points in the temperature ranges 500-400 K and 180-100 K, with values of the parameter To as indicated. (b) Temperature dependence of the exponent y for a Ca film (from [30]).

it piausible to believe that such change in behavior is associated with changes in the density of gap states in these semiconductors. In what folfows, we relate y to the width of a conduction band tail of states. We notice, first of all, that the value of y lies between 0.5 and 1.0 throughout the temperature range explored for CTO,and throughout most of this range for Cm (a transition to a regime with 7 < 0.5 is observed above 370K for Cm). To explain 0.5 < y < 1.0 over several orders of magnitude in light intensity, one must assume [32] a quasi-Fermi

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PHOTOCONDUCTIVITY

WITH LIGHT INTENSITY

level sweeping through an exponential density of trapping states, g(e) = go exp(-e/krs), where e is measured from the band edge, and go and TO are the parameters defining the tail. Measurements of carrier type in C& films under illumination indicate electrons to be the majority carriers [25,28] and thus Ref. 30 focused on the electron quasi-Fermi level and the conduction band tail. We do the same here for C,,,. Then, in the range of light intensities for which the number of trapped carriers exceeds the number of free carriers, and for T < TO,one obtains [32] equation (1) with y given by Ir = 7b/(T + To)1

(2)

IN FULLERENES

Vol. 94, No. 2

existence of an orientational glassy transition freezes molecular rotations. The model leading to equation (2) for y, also gives a coefficient b in equation (1) that is strongly dependent on temperature [30,32] and is a function of go and material parameters such as the electron cross sections,, of the defect centers. Because of the latitude allowed in choosing parameters like go and s,, whose physically acceptable values can change over several orders of magnitude, one can easily fit equation (1) to the temperature dependence of up observed in Fig. 1, but this procedure provides little additional information on the vaiue and temperature dependence of TO. In summary, we have measured the temperature dependence of y in cp = bl”. The value of this exponent decreases with decreasing temperature below the phase transition point T, that separates the high temperature rotor phase above T, from the partially ordered state below this transition point. Similar results have been reported for C6s. Interpretation of the results in terms of a conduction band tail of electronic gap states, assumed to originate from disorder in the electronic potential, suggests that this disorder decreases with decreasing temperature in a certain temperature range below T, in the fullerenes.

and a coefficient b that changes strongly, almost exponentially, with temperature [30,32] and is discussed in more detail later. Equation (2) predicts that y should increase with decreasing T for fixed TO. In [30], equation (2) was fitted to the data reproduced in Fig. 3(b) in the two temperature ranges 340-260 K and 200- 140 K, extracting the values kTO = 47 and 34meV for each range, respectively. According to equation (2), as also pointed out in [30], the only way for y to decrease with temperature, as observed below 260K for C&, is for TO to decrease with decreasing temperature. We offer here a similar explanation for the decrease of y observed in the CT0 film below 380K. Fitting equaAcknowledgements - This work was funded in part by tion (2) to the data points in the temperature ranges the NSF Low Temperature Physics Program grant 500-400 IS and 180-100 K in Fig. 3(a), the values of No. DMR 9122043, ARPA grant No. MDA 972-90-J1001, and the State of Texas through the Texas Center kTO = 110 and 37 meV are obtained, respectively, for for Superconductivity at the University of Houston. the CT0film, consistent with the alleged decrease of TO in the intermediate region 400-2OOK The above changes of TO in ChO and CT0 are significant. For REFERENCES comparison, we mention here that in a typical film 1. W. Kratschmer, L.D. Lamb, K. Fostiropoulos of undoped hydrogenated amorphous silicon, the & D.R. HufTman, Nature 347,354 (1990). characteristic energy of the valence band tail changes 2. P.A. Heiney, J.E. Fischer, A.R. McGhie, W.J. from [33] 65 to 60meV, and that of the conduction Romanow, A.M. Denenstein, J.P. McCauley, band tail from 133160 to 3OmeV, in the temperature Jr., A.B. Smith III & D.E. Cox, Phys. Rev. Lett. 66,2911 (1991). range from 600 to 300K. 3. R.A. Sachidanandam & A.B. Harris, Phys. Rev. Thus, if we interpret To as a measure of the Lett. 67, 1467 (1991). amount of disorder in the electronic potential, our 4. D.A. Neumann, J.R.D. Copley, R.L. Cappelletti, results suggest that this disorder decreases with W.A. Kamitakahara, R.M. Lindstrom, KM. decreasing temperature below the orientational Creegan, D.M. Cox, W.J. Romanow, N. phase transition points of 380K and 260 K in C70 Caustel, J.P. McCauley, Jr., N.C. Maliszewskyj, and C6@,respectively. As the amount of orientational J.E. Fischer & A.B. Smith III, Phys. Rev. Lett. 67, 3808 (1991). disorder in the fullerenes decreases, with less mol5. W.I.F. David, R.M. Ibberson, T.J.S. Dennis, ecules in higher energy “misoriente~’ states and less J.P. Hare & K. Prassides, Europhys. Lett. 18, transitions between the ground and excited states, so 219 (1991); 18,735 (1992). does the disorder in the potentiai as seen by the 6. R. Tycko, G. Dabbagh, R.M. Fleming, R.C. electrons in these fullerenes. At a low enough temHaddon, A.V. Makhija & SM. Zahurak, Phys. perature, TO is expected to become again temperature Rev. Lett. 67, 1886 (1991). independent, as the static disorder from impurities 7. K. Mizoguchi, Y. Maniwa & K. Kume, Materials Science and Engineering B19, 146 (1993). and imperfections becomes dominant, or as the

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