- Email: [email protected]
Laser pulse induced transient photoconductivity of C70 single crystal
0022-3697(95)00149-2
Pergamon
LASER
PULSE
EUGENE
J Phys. Chem Sohds Vol 57. No. 4, pp, 483-494. 1996 Copyright 0 1996 Elwier Science Ltd Printed in Great Britain. All rights reserved 0022-3697196 %15.00 + 0.00
INDUCED TRANSIENT PHOTOCONDUCTIVITY CT0 SINGLE CRYSTAL
OF
FRANKEVICHT, YUSEI MARUYAMAS and HIRONORI OGATAS t The Institute for Energy Problems of Chemical Physics RAS, Moscow 334, Russia $ The Institute for Molecular Science, Okazaki 444, Japan (Received 3 April 1995; accepted 16 May 1995)
Abstract-The transient photoconductivity of CT0single crystal excited by 800ns pulsed N2 laser pulse was studied. The mobility of positive and negative free charge carriers was determined (xl cm2/Vs) which is found to be similar to that determined for Cm single crystal. Trapping of free carriers in C,e was revealed to be much faster than in C, leaving for the lifetime of free carriers only 16 ns. Dark charge injection was shown to occur from gold or aluminum electrodes, and excitation in these conditions resulted in delayed generation of the photocurrent within the time domain of microseconds. This phenomenon was shown to be connected with triplet excitons which detrap injected electrons or holes just producing photoenhanced current. Triplet exciton annihilation may follow. Studying the decay of transient photocurrent within hundreds of microseconds time domajn has permitted us to characterize the trapping sites as being 0.1 eV deep and having a size of about 25 A. The trapping sites are speculated to be caused by structural imperfections which cause local increase of rr-electron density and polarizability. A prominent electrical field effect (of PooleFrenkel type) was revealed on the thermal detrapping rate that appears to be a rare example of the electrical field effect on the neutral trapping sites. Keywords: A. fullerenes, D. defects, D. transport properties, D. electrical properties.
1. INTRODUCTION Studying the transient photocoductivity of fullerene solids permits us to understand the mechanism of generation, transport and trapping of charge carriers in this important new type of carbon-cluster materials. Working with single crystals of C6e and CT0 rather than with thin films may provide researchers with knowledge of the role played by the crystalline structure in the dynamics of photophysical processes. and properties of However, photoconductivity charge carriers were investigated mainly on the thin films and crystals of C& [l-5]. It was shown that generation of charges requires light with wavelength shorter than 620 nm, though the detailed mechanism of ionization of initially produced excited state or dissociation of electron-hole pair remains to be studied. Only one work was devoted to the steady state photoconductivity investigation of C,e thin films [6]. In our previous work [7,8] we studied the transport of charge carriers in C6s single crystals making use of the time-of-flight technique. It was discovered that the mobility value for positive and negative charge carriers is typical for molecular crystals (about 1 cm2/V s) and is almost temperature independent in the broad temperature range except at the phase transition temperature where a change of the character of molecular rotation takes place. It was also shown that the
density of trapping sites in the crystals obtained by gas-phase growing (helium gas) is rather low, thus permitting charge carriers to be free for as long as 1~s. To our knowledge there have been no works devoted to detailed investigation of photoconductivity of C,a single crystals up to now. We hope that such a study may provide additional information on the carrier transport and on the role played by structural defects. The ellipsoidal shape of CT0 molecules permits foreseeing that the packing of molecules in the crystal will be not so perfect as it takes place for truncated icosahedral CM molecules. The present work is devoted to studying the transient photoconductivity of CT0 single crystals which appears as a result of the 800 ps pulse excitation. The mobilities of positive and negative free charge carriers were determined being similar to those previously determined for Cso single crystal. Trapping of free charges in C,s was revealed to be much faster than in C6e single crystal leaving for lifetime of free carriers only about 16 ns. Dark charge injection was shown to occur from gold or aluminum electrodes, and excitation in these conditions resulted in delayed generation of the photocurrent within the time domain of microseconds. It is shown to be connected with triplet excitons which detrap injected electrons or holes just producing photoenhanced current. Triplet exciton 483
E. FRANKEVICH
484
annihilation may be followed. Studying the decay of transient photocurrent within hundreds of microseconds time domain has permitted us to characterize the trapping sites as being 0.1 eV deep and having a size of about 25 A. The trapping sites are speculated to be caused by structural imperfections which cause the local increases of r-electron density and polarizability. A prominent electrical field effect (of Poole-Frenkel type) was revealed on the thermal detrapping rate that appears to be a rare example of the electrical field effect on the neutral trapping sites.
2. ~XP~IMENTAL
Gas-phase grown single crystab of C7s were used in the experiments. Intensively purified C7e powder was sublimed in a vacuum and the collected sublimate was sealed in a quartz tube with helium gas (about IOTorr). The tube was set in a horizontal electric furnace in which the tem~rature gradient was adjusted to keep a little lower temperature at the middle part of the horizontal tube. By this way millimeter-size C,e single crystals were obtained at the lower temperature zone of the tube. The technique was the same as that of growing C& single crystals used by us for mobility measurements previously [S]. A specimen for measurements was constructed as follows. A freshly grown single crystal was pasted in front of a round hole of 0.2-0.5 mm dia. of aluminium plate, 0.3 mm thick. The open external surface of the crystal, normal to the c-axis of the crystal, was illuminated through the hole. The back side of the crystal was cut by a sharp blade so that a thickness of 3060 pm remained. A metal electrode was pasted on the back surface. The front (illuminated) surface of the crystal remained open in one set of experiments, or 0 was covered by 200 A Au or Al by vacuum-deposition. We have been forced to use samples with open surfaces to prevent the appearance of any spurious signals originated from the materials which cover the surface such as IT0 electrode or similar ones. As the intrinsic transient current going through C7e crystal was rather small these spurious signals made the measurements difficult to perform. For the case of the open-surface of the crystal, an electrical field strength within the crystal being proportional to the voltage difference between the front electrode with the hole and the back electrode, was not known precisely. However, it was possible to estimate it performing the time-of-flight experiment with a crystal with known mobility of carriers (C,,). Such a calibration showed that the field strength is about three times lower than that calculated by dividing the voltage difference on the crystal thickness.
et al.
The sample was mounted to the cryostat holder (Air Products and Chemicals, Inc.), and was kept in vacuum at 5 x 10w6Torr during measurements and storage. Excitation light was generated by an Nz laser (LNlOOO, PRA Inc.) which provided light at the wavelength of 337 nm which is strongly absorbed by Cl0 crystal. The light pulses had a duration of 800 ps; maximum pulse energy was 1.1mJ. Tektronix 7834 storage oscilloscope with 7A26 amplifier, both channels of which were connected in series, was used for measurements of transient signals. The photocurrent flowed through the circuit containing the high voltage power supply, the sample, and the input resistance of the amplifier. Time resolution of the amplifier with 1000 resistance at the inputs of both channels was better than 10 ns. We have used mainly an integration regime for measurements of transient currents at short time domains (from 1Ons to 50~s). Input time constant in this regime was measured to be from 80 to 235 ps depending on the input resistance of the first channel (from 0.5 to 2 MSI). Single shot of the laser directed on the hole in the front electrode gave a signal which was displayed at the screen, photographed and analyzed. Thirteen samples of CT0 crystals grown in the same nominal conditions but in different weeks were used for experiments, all showing consistent results.
3. RESULTS AND DISCUSSION
3.1. ~~~~tes with open front swface: ~~h~~~tyof carriers and trapping By using the sandwich type sample and the excitation of the sample by strongly absorbed light one can expect in the simplest case the current response of the sample will have the form:
or a voltage response in the integration regime: u(t) =
!!!$ql
_ e-‘/n).
Here no is the total amount of charge carriers generated by a light pulse, p is the mobility of carriers, d is the thickness of the crystal, 71 is the life time of free carriers before a deep trapping occurs, and Y is the voltage difference. If the lifetime is long enough, some carriers can reach the back part of the crystal and the t value will be limited by the transit time, ttran = d*/,u V, from which the value of mobility p may be determined. Three types of transient voltage curves u(t) were obtained on different samples of C7e with open-
Transient
photoconductivity
of C,, single crystal
Fig. 1. Pictures of integrated transient photocurrent U(Z), obtained on the samples of C,s single crystal of type (ii) (curves A to D) :and type (iii) (curves E to G). Crystal thickness of type (ii) is 42 f 5 brn; of type (iii) is 52 f 5 pm. Curve A: vol ‘tage v= : 1100 V, holes are moving; B: V = + 1000 V; C: V = - 100 V, electrons are moving; D: V = - 1000 V; E: V = -- 300 14; F: v= : - 1000 V; G: V = 400 V. Intensity of the light is about 10’” photon/cm’ per pulse. Sweeping rateis 50 ns’div. (for ct wves A and B); 200ns/div. (for curves C and D); tOOns!div. (for curves E to G). Room temperature.
E. FRANKEVICH
486
surface specimens dependin paration technique.
on the specimen pre-
(i) The first one gives curves of the shape well described by eqn (2) with rt = 16 ns, the shape being independent on voltage. (ii) Typical curves of the second type obtained for transient integrated current (or voltage) u(t) are shown in Fig. 1 for drifting of holes (curves A and B) and electrons (curves C and D). A feature of the curves consists in the dependence of the shape of the curve on voltage. At low voltage (Y = 100 V) curves A and C may be well approximated by eqn (2), giving a value of r1 = Sons both for electrons and holes. At high voltage (V = iOO0V) curves approach to a step with a level off point at ttran = 107 ns for electrons and ttran= 71 ns for holes. (iii) Still another behavior was noticed which is shown in Fig. 1, curves E to G. At low voltages the curves u(t) did not level off at least to times t<2ps; higher voltages decreased the slope of the curve at high t, and the highest voltage used (Y = 1000 V) made the curve to be flat at t& 1OOns. In all the cases (i) to (iii) lowering the temperature below 270 K caused all the curves to look like ones of type (i). Curves of type (ii) and (iii) could be obtained on the freshly prepared crystals. Storage of crystals at room temperature in vacuum for more than one week resulted in the appearance of transient curves of type (i) only. Features of all the curves obtained may be understood by using the model with trapping of free charge carriers when they are drifting from the near surface part of the crystal to the back electrode. For the curves of type (i) it is just a fast trapping by deep traps which permits free carriers to have the lifetime rt = 16 ns which is not long enough for reaching the back electrode. On the curves B and D in Fig. 1 one can see the flat portion of the curve after reaching a level off point. To determine the transit time tt, we have used the value of t1j2 taken at the point where u(t) has l/2 of its maximum value. From eqn (2) at I = ttranit follows that: Itran = -7-t Iog(2e-“‘2’” - 1)
(3)
and values of ttrm = 71 and 107 ns were obtained for transport of electrons and holes, respectively, measured on the same sample. It gives directly the ratio of mobilities of holes and electrons &p, = 1.5 (&lo%). The absolute values of mobility may be estimated only because of uncertainty with the geometry of the electrical field in an open surface sample. Within the factor of 2 an estimate gives the holes ph = 1 cm*/V s.
et al.
Although the behavior of the curves u( t ) of type (iii) cannot be understood in the framework of the above model with drifting of free charge carriers and deep trapping, it can easily be rationalized by assuming the trapping by shallow traps which give for trapped charges a chance to get free during the observation time (up to 1000 ns). The lifetime of charge carriers in the traps r2 must be introduced, and the formula (4) may be obtained well describing the behavior of carriers with free transport, trapping, and detrapping:
valid for t 6 ttran. Gradual decrease of the slope of u(t) curves at higher t with increasing voltage V corresponds to a smaller part of carriers accumulated in traps at higher voltage, and to about none of them being trapped for the curve at V = IOOOV(the curve F in Fig. 1). Computer fitting of the curves like those shown in Fig. 1 (curves E and G) by eqn (4) gives the following values of parameters: rt = 90ns, ~z = 250 ns, and ttra,,(1000 V) = 105 ns. The latter value gives the same estimation of the electron mobility as made above. Thus, the main result from studying the transient photoconductivity in C,e single crystals consists in estimation of lifetimes and mobility of carriers at room temperature. While the mobility and the ratio of mobilities remain typical for molecular crystals, the lifetime of free carriers is rather short, from 16 to 90ns. The density of trapping sites N,, may be estimated using known value of mobility p * I cm’/Vs and assuming the trapping radius to be around R,, = 10 A. Then the trapping rate constant may be estimated as: k,, = hpkTR,,/e
= 2.5 x low8 cm3/s.
And for an estimation of the trapping site density we will get: N,, = l/rtktr = 4.4 x lOI to25 x lOI cm-‘. It should be noted that the value of N,, obtained is about two orders of magnitude higher than that in similar crystals of Cso [8]. Another important thing concerns non-permanent existence of properties of types (ii) and (iii). It looks like there exists slow transformation of properties of trapping sites and of their amount in the crystal, more stable being the properties of type (i), i.e. deep traps which give the shortest lifetime for free carriers. Such a behavior may be understood if one may imagine that traps are of a structural nature and they are able to evolute, possibly
Transient photoconductivity
Y---F-
of C&, single crystal
487
“YE
Fig. 2. Pictures ofintegrated transient photocurrent u(l) for C7e sample with a gold front electrode. Thickness of the sample is 42 f 5 pm. Light intensity is 2 x 10” photon~~* per pulse. Curves A to E are taken at different voltages: +700, +500, -t-400, i-200 and i-100 V respectively. Sweeping rate is 5 ps/div. Curves u(t) F to H are recorded on the sample 45 f 5 pm thick, with Al front electrode, at light intensity 2 x lOI4 photon/cm2 per pulse at V = -500V at different sweeping rates: 100,500 and 2&div., respectively. Room temperature.
488
E. FRANKEVICH IO2
et al.
r
101_Lkl
Voltage. V
Time, ps
Fig. 3. Dependence of the amplitude of u(t) at t = 50@son voltage V. Au front electrode. Holes are moving; room temperature. Experimental points are taken from the curves A to E in Fig. 2. Fitting of the points with power
Fig. 4. Time dependence of the amplitude u(t). Experimental points are taken from the curve A in Fig. 2. Fitting of the dependence with a power function is shown.
function is shown.
by migration, transformation or clustering. In the last part of the present work we will return to this question after discussing additional information on deep traps responsible for the tail of transient photoconductivity in the time domain of hundreds ,US. 3.2. Samples with the front surface covered by semitransparent metal layer: delayed generation of free charge carriers Metal (Au or Al) on the front surface of the crystal deposited by vacuum evaporation changes the photoresponse of the sample dramatically. The magnitude of the photocurrent becomes greater about 1000 times as compared with the open surface crystal case, and the transient photoconductivity becomes much more delayed, maximum of integrated photocurrent can be seen now at a t of about a few tens of microseconds. Figure 2 shows a set of transient integrated signals p(t) obtained at different sweeping rates and voltages. Inversion of the sign of the voltage leads to exactly the same signal in the case of Au electrode, however for the sample with Al front electrode the magnitude of .g
the electron current was 5 times higher than that of the hole current. Figure 3 gives the dependence of the amplitudes of u(t) taken after 50~s on the voltage: superlinear u 0: V’.* behavior is evident. Similar behavior for other polarities of the voltage was recorded. Figure 4 gives the plot of log u vs log t: the function u 0: t0,28is seen to fit the dependence. Figure 5 represents a plot of the amplitude of u(t) at t = to = 10 ps as a function of excitation intensity Z in the loglog scale. The light intensity was varied by controlling the focusing of the laser beam by a quartz lens. Temperature dependence of u( t = 10 ps) is not very sharp: the amplitude decreases steadily with lowering T (Fig. 6). The activation energy determined from the slope of the solid line in Fig. 6 has the value Etotal = 0.034 eV. The dependence of z4(t ) on intensity is most striking: it is very weak and obeys to the same law exactly as the dependence of u on t does (!); u cx t0.28and u 0: Z”.28. Such a coincidence is a key to decipher the mechanism of photoconductivity studied, as it means that parameters expressing time and intensity in the equation describing the kinetics of transient photoconductivity
103
,ol
g
d
u,
2 r;
r I
a
0
!!
z 4
3 a
”
s IO01Light intensity,
10
100
IO00
1014photon/cm* per pulse
Fig. 5. Dependence of the amplitude u( t ) at t = 10 ps on the light intensity at different polarity of the voltage. The same sample as in Fig. 3 is issued. Fitting of the dependence with a ^ . . . power lunctlon IS shown.
3.5
4
4.5
5
5.5
6
6.5
l/T, 10e3K’ Fig. 6. Temperature dependence of the amplitude u(t) at t = 2Ops, V = -500V. Sample with Al front electrode, thickness is 45 f 5 pm.
Transient photoconductivity of C,, single crystal occupy equivalent positions. There is no broad choice for such equations. We consider the results presented here as evidence of realization of the next model: metal on the surface of the crystal injects thermally charged carriers into the crystal which occupy trapping sites within the Debye length of the crystal near the surface. In the dark the electric field will induce the current which may be space charge limited or injection limited. The total charge injected inside the crystal depends on the work function of the metal at zero voltage but at higher voltages it may be as high as the electrical capacity of the sample permits. The light cannot increase the total amount of charges within the crystal. However, the ratio of free to trapped charge can change significantly as a result of detrapping by absorption of photons or by reaction of trapped charge with excitons. The observation of an approximately quadratic voltage dependence of u (t = 50 ps) (Fig. 3) is in line with such a mechanism. The photocurrent which appears due to detrapping of injected space charge is called photoenhanced current, and we believe it reveals itself in our experiments. The mediators which transfer excitation energy to trapped charges are presumably triplet excitons. Absorption of light by fullerenes is known to produce singlet excited states which give triplet excitons by intersystern crossing with quantum yields of about unity [9]. This is a sequence of dipole-forbiddeness of St-S0 radiative transition [lo, 111. For highly absorptive light of 337 nm the region of excitation in the crystal penetrates to about 1/E NN10e5 cm from the electrode. High density of triplet excitons is produced initially which may be estimated from the known light intensity I N 2 x lOI photon/cm* pulse as: nT N IE c5 2
489
Here T and St are triplet and singlet excitons, respectively, and Ss is the ground state. As it is known from the theory [ 121the dependence of the photoenhanced current i,,hen on the density of exciting agents nr may in general be expressed as: (7)
&hen 0: @T)'
where r < 1 and depends on the energy distribution of trapped charges. The integral of the current measured in our experiments,
may give the result which depends equally on nt and t in the case of r = 1 only. The case with r = 1 implies that all the filled traps are deep in the sense that their thermal escape frequency is lower than that induced by reaction with triplet excitons. At r = 1 the solution of eqn (8) gives: u(t) cc $og(l
+ yn{t).
(9)
(a)
(t/S+l),tinns
x lOI 1/cm3.
At such a high density main channel of quenching of triplet excitons is their mutual annihilation (at least within the time interval shorter than the diffusion time to to the electrode, the latter presumably being able to quench excitons, tD = l/e’D x lops, where D is triplet exciton diffusion coefficient taken as D a lo-’ cm2/s).
So, at t < tD the density nr of triplet excitons will obey the law: nr =n;
I
I
I
1
2000
3ooo
4ooa
5ooo
1 + tf5.tin ns
1
where y is the annihilation rate constant for the process T+T=St+Sa.
I
1000
(6)
Fig. 7. The experimental dependencies of the amplitude of the transient signal u( 1) fitted by logarithmic function of 1 + Ft. The best fit gives a fitting parameter F = 2 x 10s l/s. Curves A, B, and C are taken over different time domains at the light intensity I0 = 2 x lOI photon/cm’ per pulse. The same sample with Al front electrode as in Fig. 2.
490
E. FRANKEVICH
This is exactly what is required to account for experimental results (Figs 4 and 5), concerning dependencies ofuon tand1. Figures 7 (a, b and c) show the plots of the experimental dependencies of the transient signal u measured over different time domains (see Fig. 2) at intensity I = I0 = 2 x lOI photon/cm’ per pulse on the value of (1 + Ft) where F is a fitting parameter. One can see a good fitting to occur at F = l/5 ns-‘. Figure 8 shows a replot of Fig. 5 aimed at the demonstration of the logarithmic dependence of the amplitude u(t) at t = to = 10 ps on the light intensity, included in the value of (1 + Fl I) where F, is a fitting parameter. The value of F, = 2 x lo-l3 (photon/cm2 per pulse) -I is chosen for the plots. The meaning of the value of p = 0.28 in the formulas (u(t) 0: tP and u(t = 10~s) 0: Zp determined earlier from plots shown in Figs 4 and 5) becomes clear now if we take into account that the function f = log( 1 + X) may be represented asf cx x0.‘* at .Yof about x x IO2 and asf c( x0.” at x E 103. In our case the role of x is played by yn!& = TIEtO (see eqn 9). Curves shown in Fig. 7 are taken at intensities I0 ten times higher than those used in the cases shown in Figs 4 and 5. So, fitting of plots u vs. t by a power function gives for the former u 0: t0.15 in accordance with mathematics. The fitting parameter F in Fig. 7 can permit a rough estimate of the annihilation rate constant y: l+Fr=l+yn;r=l+yZtr y = F/Z6 x IO-” cm3/s.
-Amplitude at V=+5OOV 6 AmtGtude at V=-SOOV
I
(l+F,),
IO
100
1000
light intensity I in units 10’) photon/cm2 per pulse
Fig. 8. The experimental dependence of the amplitude of the transient signal u at t = 101s on the light intensity I, fitted by logarithmic function of 1 + F, I. The fits shown in the figure by the solid line give the v&e for the fitting parameter Fj = 2 x lo-l3 (photon/cm2 per pulse)-’ (or F, = 2 in r&iprocal units 6f I used in tie plbt). The a‘bsoluie values of the light intensity are known with the accuracy of an order of magnitude only. The same data as those used in Fig. 5 are plotted.
et al.
The estimation is made assuming the quantum yield of triplet excitons to be equal to unity and extinction of 337 nm light in fullerenes to be E = lo5 cm-‘. Triplet exciton annihilation rate constant given here has a roughly estimated but a reasonable value being typical for molecular crystals and corresponding to diffusion coefficient D of triplet excitons D = y/47rR x 1O--5 cm2/s, where R = 7A is taken for a reaction radius. Thus we came to the conclusion that the reaction of the next type takes place: T+
b/2
=
so
+
D;,,,
612
=
neutral trapping site + e.
(10)
Here D,i2 stands for a filled trap which is a doublet state and has a spin l/2 fi. It is known that the rate of reactions of this type may be sensitive to an external magnetic field and resonant microwave field [13, 141. This is because of evolution of the total electronic spin of the intermediate doublet-quadruplet mixed pair induced by magnetic interaction in the triplet exciton and an interference of the external magnetic field with this interaction. If they are magnetic field sensitive indeed, it opens a possibility of studying the dynamics and electronic structure of triplet excitons in fullerenes using reaction yield detected magnetic resonance (RYDMR) technique by monitoring the photoenhanced current [14]. It is worth mentioning that similar crystals of CU covered with Au evaporated electrode did not show the photoenhanced current, though one may expect there is an equally high yield of triplet excitons in both cases. It is a much lower density of trapping sites in the case of CeO that can explain the difference; triplet excitons have no charged trapping sites to react with. It may be added that one can not very often see the log-response of the signal to intensity in other materials and the effect may be useful in some respect when a response which must be almost insensitive to a prominent change of the intensity of the light is needed. The results obtained in the present work are worth comparing with those obtained in [6]. The latter work was done on sublimed CT0 films, 2000A thick, sandwiched between Al (front) and Ag electrodes. The authors found the photoconductivity of CT0 samples to be about two orders of magnitude higher than that of CeO samples. They assume that the generation of electrons and holes under the action of light is the cause for the photocurrent, and the bimolecular recombination of charge carriers takes place in the bulk of the sample. The reason for such a claim was a sublinear dependence of the photocurrent on the light
Transient photoconductivity intensity.
No plots
of the photocurrent
vs. voltage
were shown. Our time resolved results obtained present
work indicate
in the
that higher photoconductivity
with charge injection from the electrode and participation of triplet excitons in photoenhancement of the injected current. Apparently this might be the case for the films of CT0 studied in [6] also. of CT0 samples
with Al electrode is connected
3.3. The tail part of transient photocurrent: studying the properties of trapping sites The tail part of the transient photocurrent within the time domain of hundreds of ,us cannot be seen when using low input impedance of the amplifier as the signal is too small to be measured. Although the sensitivity at high input resistance R > 100 kf2 is high enough, other difficulties appear. At high R we have integration
of the current
about RC-value,
within the time domain
region where the generation triplet excitons
of free charge carriers by
is still essential.
of the curve may be observed general contains
The pure decay part
later. The decay part in
at least two exponents:
being the discharge
of the integrated
other may belong to the detrapping no integration
of
then one can observe an intermediate
one of them
current
and the
process.
There is
at t > RC and the current
regime is
operative. We have noticed that after the curve u(t) reached its
of CT0single crystal
491
maximum value the decay of the signal followed the exponential law with a time constant which was much higher than the RC value of the input circuit of the preamplifier. This was a clear indication of a long lasting detrapping process going on the background of the decay of integrated signal accumulated during earlier stages of transient photoconductivity. It was impossible, however, to separate these two processes as the decrease of RC led to equal decrease of the tail. So we were forced to measure the properties of the current, which appears to be caused by thermal detrapping of charge carriers, on the background of the RC decay. The best experimentally measured parameter, which gives the normalized value of the amplitude B of the tail, is the halfwidth of the decaying part of the transient signal. As it was said the decaying part is the sum of two exponents: u( t ) = Ae-‘iRC + Be-“‘. Below we will find out the connection
(11)
of the halfwidth
t112with the amplitude B of the part of the decaying current connected with detrapping. Let us put t = 0 at the beginning of decaying part near the maximum of the experimental curve u(t). Any change of the amplitude B of the tail will lead to a change of the halfwidth t112determined as follows: a(tt/z)
= (A + R)/2.
Fig. 9. Picture of the decaying part of the transient signal. The sample with Al front electrode; electrons are moving; thickness is 45 i 5 pm; input resistance is 0.5 MR; sweeping rate is 50 &div.; room temperature. Curves are taken at different voltages, from top to bottom, respectively: -200, -400, -700, -900V.
E. FRANKEWCH
AiB A B A B
Sum -100.5~s -246 ps y -1 3.484*eA(-0.~99466x) R= 1 y =2l*e”(-0.00408t6x) R=l
et al.
t.3.102z
l.2.102.
_$ 1.1.102~ c I5 1.102 L % 2 7 z
1.
9.10’ -
3
8.10’ 7.10’ -I: 6.10’1 140
I
i I 200
I 300
I 250
Temperature, Time, gs Fig. 10. The decaying curves a(t) which show the rest&s of the computer decomposition of the ex~rimentaIly obtained decay curve (A + B) into two exponents A and B. Curve (A f B) is taken at room temperature, V = -5OOV, on the sample of CT0single crystal with AI covered front surface as in Fig. 9.
If the condition t = tlf2, and
T >
RC is met, then e-lJT x 1 at
tt12 = -RClog[(l
- B/A)I2].
(12)
or Atliz = RC(B/A)
(13)
For B < A it gives simply: t1/2 = (0.69 + B/A)RC
where Atijz is the halfwidth added due to presence of the tail originated from detrapping. We have studied the decay part of the transient electron current on the same samples as in Section 3.2; with the front electrode in the form of evaporated Al. The typical picture of the transient curve is shown in Fig. 9. The shape of the decay was carefully studied and its appearance in the u vs. t plot is shown in Fig. 10, curve (A + B). The two exponents A and B of the decay curve were extracted by computer analysis and the time constants and amplitudes for each of them were calculated to be RC = 100.5 ns and r = 246ns;
2
I 350
K
Fig. 11.Temperature dependence of the total halfwidth tt/2 of the decay curve. The limiting value of f,/r = 70 ns is seen to be reached at low enough temperature. V = -SOOV, the same sample is in Fig. 9.
A = 39% and B = 61% of the total amplitude at room temperature and I’ = -500V. A help for such an extraction came from the low temperature experiment. It was measured that the change of tl12 stops at T~210 K corresponding to disappearance of the measurable detrapping of carriers. All the exponents of the decay part of the signal and positions of t1/2at room temperature and at low temperature are shown in Fig. 10. In order to study the properties of the tail connected with detrapping of charge carriers we measured the dependence of t1/2 on the temperature and voltage. The value of AtlIz was considered as the parameter directly proportional to the amplitude B [see eqns (12) and (t3)]. Figure 11 shows the plot of tlj2 vs. T. It is seen that the tail connected with detrapping disappears at low temperature, and only RC-decay remains, RC = 1OOns (or t1/2 = 70ns). Figure 12 shows the plot of logAt,/, vs. l/T which permits obtaining the value of the activation energy w s,.td= 0.1 eV in the conditions when the voltage I’ = SOOVis applied.
1.3.102 4.5.100
II
g 1.2.102
k Total
halfwidth 9 Low T limiting value
I
4.100
4 .z 3.5.100 3 % .z 3.100 “, B 2.5.100 d 2.100
6.10’L 3
4
3.5 l/T,
4.5
5
IO-3 K-1
Fig. 12. Temperature dependence of the change of the halfwidth Artlz in the log vs. ij7’scale. The same data as in Fig. 1I are plotted.
1000 Voltage,
V
Fig. 13. Dependence of the total halfwidth tllz of the decay curve on the voltage. The same sample as in Fig. 9; at room temperature. The squared point at V = 0 is shown as a limit of tt/z obtained from the low temperature experiment: T = 200 K, V = -500V for this point.
Transient photoconductivity
External electrical field was revealed to have a prominent effect on the value of tl/2 also. The results are shown in Fig. 13 where the change of the total halfwidth caused by voltage can be seen. As far as the value of tl12 is connected with the ratio of amplitudes A and B only, an ordinary action of the voltage on the absolute value of transient current does not interfere with the effect under study. The field is shown to act on the ratio of B and A only. As the effect was revealed on samples of the type (i) (see Section 3.1 of the present paper) which showed fast trapping of all the charges produced, one could not expect that the amount of the charges trapped would depend on the voltage. Moreover the sign of the effect of electrical field is opposite to that which could be expected if the samples of the type (iii) were used. In order to rationalize the results obtained we have to admit that the tail originates from charge carriers detrapped from traps which were filled during the movement of free charge carriers, and they become excited by triplet excitons from the trapped charge reservoir near the front electrode. It remains unknown whether the traps are distributed in energy or occupy a narrow energy interval. An activation energy determined from temperature dependence of the tail has the value of 0.1 eV which is not very deep trapping. Let us consider the kinetics of the detrapping process. The kinetics of the tail are covered by trapping, detrapping, and retrapping: dn s=
Nv-k,N,,n-kzn
dN - = -Nu + k, Ntrn.
of CT0single crystal
493
potential barrier that keeps the charge localized. What is studied usually and called the Poole-Frenkel effect [ 151is the lowering of the Coulomb field which attracts a trapped charge and the charge of other sign that the trap had before the trapping occurred. Evidently this is not the case for fullerene, as one cannot expect charged trapping sites in these crystals. It is expected [16] that if the carrier is trapped in an otherwise neutral site, then an external field should have a negligible detrapping effect. In our case, however, one can imagine that the geometrical size of the trap is much bigger than that which was previously studied in other materials. The results obtained here may be explained if the traps are originated from a polarization and, due to high polarizability of fullerene molecules, the potential well of the charge which finds itself surrounded by the increased local density of CT0molecules in the crystal defect site, may be quite broad. As far as the polarization energy P gained by a trapped carrier from interaction with polarizable molecules if P(a) = - Ce2a/2r4, where cy is the polarizability of the molecule, a small change of the distance r between molecules at a defect site makes a well at least of one or two molecular diameters broad (15-20 A). In order to estimate the size 6 of the trapping site we used a simple model in which the external field decreases the height of the potential barrier W by A W = Ee6, where e is the electron charge and E = V/d. The comparison of the action of the temperature and field to produce equal changes of tlj2 leads to evaluate the size of the trap 5. Assuming that F(E) = exp(Ee6/kT) one may obtain:
dt
Here n is the density of free carriers; the current measured is proportional to n; N is the density of filled traps; k, is a rate constant of trapping of free carriers by traps with density N,,; k2 is the rate of other processes removing carriers out of play; Y is the trap escape frequency. The solution gives: n = N,,veC”‘/(kl
N,, + k2)
[W - (E + AE)eb] = W - AEe6 T T+AT
(16)
Here E is the electrical field strength used during the measurements of the effect of temperature on lo*-
(15)
where r = k2/(klNtr + k2) and v = v,,exp(-W/kT) F( V/d), F( V/d) stands for the function responsible for the field dependence of the escape frequency, which is proportional to B or to the value of At,,2 measured experimentally; the value of vr has the meaning of l/r used in eqn (11) and also measured experimentally (T = 246 ns at room temperature). In addition to thermal and triplet exciton induced detrapping, detrapping assisted by an external electrical field seems to occur in C70 crystals. It is well known that electrical field can assist in escaping of charge from traps by lowering the height of the
% Pi 2
4
IO'0
200
400
600
I
I
800
1000
Voltage, V Fig. 14. Voltage dependence of the change of the halfwidth Ar,,z in the log vs. V scale. The slope of the solid line gives the parameter 6 in the framework of the model used to account for the effect of electrical field on the detrapping rate. The same data as in Fig. 13 Ire plotted.
E. FRANKEVICH et al.
494
tl12 (E = V/d= 500145 x 10m4M lo5 V/cm); AE and AT are the field and temperature enlargements which cause equal changes of the detrapping rate. We have measured that AE = 3.1 x lo4 V/cm and AT = 25 K at T=295 K. Then knowing that Wfsld = W-E&?= 0.1eV, the size of the trapping site may be calculated:
&aT
Wiield x 2.5x lo-‘cm
AE~(T+AT)
(*lo%)
(17)
sites which are presumably structural defects causing local increase of r-electron density and polar&ability. work was partly sup~rt~ by a Grant-in-Aid for Scientific Research for New Program (06 NP 0301) and also for Fullerene Priority Area (05233104) from the Ministry of Education, Science and Culture. ELF acknowledges the hospitality of the Institute for Molecular Science during his stay in Japan. Acknowfedgeme~tts-This
and W a 0.12eV. Approximately the same value of the parameter S may be obtained from the slope of the solid line in the plot of log At,,2 vs. V in Fig. 14. Thus, having done the estimation of the size S to be about 25 A one may speculate that traps presented in CT0 single crystal are just of structural nature caused by non-perfect packing of ellipsoidal CT0 molecules. Such kinds of defects cannot be assumed to be common in C6e crystals. Three C,,, molecules touching each other by sharper sides may be considered as candidates for such a trapping site. Calculations of electronic properties of such a defect are worth performing.
REFERENCES I. Lee C. H., Yu G., 2.
3.
4. 5.
6.
7. 4. SUMMARY
In conclusion, the present work has shown the features in which the properties of C,, and CT0crystals differ from each other. The dominant differences are connected with high density of trapping sites in C70 crystals. It is the high density of trapped charges injected from electrode which determines the participation of triplet excitons in the generation of the photocurrent. Electronic properties of the trapping sites were studied by making use of the dependence of the detrapping rate on temperature and electrical field strength. Electrical field assisted detrapping permitted to estimate the size of traps in the framework of a simple model and make the conjecture about the nature of trapping
8. 9.
10.
11. 12. 13. 14.
15.
16.
Kraabel B., Moses D and Srdanov
V. I., Phys. Rev. E 49, 10572 (1994). Dick D., Wei X., Jeglinski S., Benner R. E., Vardeny Z. V., Moses D., Srdanov V. I. and Wudl F., Phys. Rev. Lett. 73,276O (1994). Kaiser M., Reichenbach J., Byrne H. J., Anders J., Maser W., Roth S., Zahab A. and Bemier P., Solid State Comm. 81,261 (1992). Lof R. J., Veenendaal M. A., Jonkman H. T. and Sawatzky G. A., Phys. Rev. Lett. 68,3924 (1992). Arai T., Murakami Y., Suematsu H., Kikuchi K., Achiba Y. and fkemoto I., Solid State Comm. 84, 827 (1992). Hosoya M., Ichimura K., Wang 2. H.. Dresselhaus G., Dresselhaus M. S. and Eklund P. C., Phys. Rev. B. 49, 4981 (1994). Frankevich E. L., Maruyama Y., Ogata H., Achiba Y. and Kikucbi K., Solid State Comm. 88, 177 (1993). Frankevich E. L., Maruyama Y. and Ogata H., Chem. Phys. Lett. 214,39 (1993). Wasielewski M. R., O’Neil M. P., Lykke K. R., Pelhn M. J. and Gruen D. M.. J. Am. Chem. Sot. 133.2774 (1991). Lee M., Song O.-K., Seo J.-C., Kim D., Suh Y. D., Jin S. M. and Kim S. K.. Chem. Phvs. Lett. 196.325 (19921. Arbogast J. W. and Foote C. S.; J. Am. Chem. Sk. 113, 8886-9 (1991). Bauser H. and RufH. H., Phyz Stat. Sol. 32,135(1969). Em V. and Merryfield R. E., P&s. Rev. Lett. 21, 609 (1968). Buchachenko A. L. and Frankevich E. L., Chemical Generation and Reception of Radio- and Microwaves. VCH, New York (1994). Simmons __ J. G., ._ Phys. Rev. 155,657 (1967). Pope M. and Swenberg C., Dectronic Properties qf Organic Crystals, pp. 267, 708. CIarendon Press, Oxford and New York (1982).
Pergamon
LASER
PULSE
EUGENE
J Phys. Chem Sohds Vol 57. No. 4, pp, 483-494. 1996 Copyright 0 1996 Elwier Science Ltd Printed in Great Britain. All rights reserved 0022-3697196 %15.00 + 0.00
INDUCED TRANSIENT PHOTOCONDUCTIVITY CT0 SINGLE CRYSTAL
OF
FRANKEVICHT, YUSEI MARUYAMAS and HIRONORI OGATAS t The Institute for Energy Problems of Chemical Physics RAS, Moscow 334, Russia $ The Institute for Molecular Science, Okazaki 444, Japan (Received 3 April 1995; accepted 16 May 1995)
Abstract-The transient photoconductivity of CT0single crystal excited by 800ns pulsed N2 laser pulse was studied. The mobility of positive and negative free charge carriers was determined (xl cm2/Vs) which is found to be similar to that determined for Cm single crystal. Trapping of free carriers in C,e was revealed to be much faster than in C, leaving for the lifetime of free carriers only 16 ns. Dark charge injection was shown to occur from gold or aluminum electrodes, and excitation in these conditions resulted in delayed generation of the photocurrent within the time domain of microseconds. This phenomenon was shown to be connected with triplet excitons which detrap injected electrons or holes just producing photoenhanced current. Triplet exciton annihilation may follow. Studying the decay of transient photocurrent within hundreds of microseconds time domajn has permitted us to characterize the trapping sites as being 0.1 eV deep and having a size of about 25 A. The trapping sites are speculated to be caused by structural imperfections which cause local increase of rr-electron density and polarizability. A prominent electrical field effect (of PooleFrenkel type) was revealed on the thermal detrapping rate that appears to be a rare example of the electrical field effect on the neutral trapping sites. Keywords: A. fullerenes, D. defects, D. transport properties, D. electrical properties.
1. INTRODUCTION Studying the transient photocoductivity of fullerene solids permits us to understand the mechanism of generation, transport and trapping of charge carriers in this important new type of carbon-cluster materials. Working with single crystals of C6e and CT0 rather than with thin films may provide researchers with knowledge of the role played by the crystalline structure in the dynamics of photophysical processes. and properties of However, photoconductivity charge carriers were investigated mainly on the thin films and crystals of C& [l-5]. It was shown that generation of charges requires light with wavelength shorter than 620 nm, though the detailed mechanism of ionization of initially produced excited state or dissociation of electron-hole pair remains to be studied. Only one work was devoted to the steady state photoconductivity investigation of C,e thin films [6]. In our previous work [7,8] we studied the transport of charge carriers in C6s single crystals making use of the time-of-flight technique. It was discovered that the mobility value for positive and negative charge carriers is typical for molecular crystals (about 1 cm2/V s) and is almost temperature independent in the broad temperature range except at the phase transition temperature where a change of the character of molecular rotation takes place. It was also shown that the
density of trapping sites in the crystals obtained by gas-phase growing (helium gas) is rather low, thus permitting charge carriers to be free for as long as 1~s. To our knowledge there have been no works devoted to detailed investigation of photoconductivity of C,a single crystals up to now. We hope that such a study may provide additional information on the carrier transport and on the role played by structural defects. The ellipsoidal shape of CT0 molecules permits foreseeing that the packing of molecules in the crystal will be not so perfect as it takes place for truncated icosahedral CM molecules. The present work is devoted to studying the transient photoconductivity of CT0 single crystals which appears as a result of the 800 ps pulse excitation. The mobilities of positive and negative free charge carriers were determined being similar to those previously determined for Cso single crystal. Trapping of free charges in C,s was revealed to be much faster than in C6e single crystal leaving for lifetime of free carriers only about 16 ns. Dark charge injection was shown to occur from gold or aluminum electrodes, and excitation in these conditions resulted in delayed generation of the photocurrent within the time domain of microseconds. It is shown to be connected with triplet excitons which detrap injected electrons or holes just producing photoenhanced current. Triplet exciton 483
E. FRANKEVICH
484
annihilation may be followed. Studying the decay of transient photocurrent within hundreds of microseconds time domain has permitted us to characterize the trapping sites as being 0.1 eV deep and having a size of about 25 A. The trapping sites are speculated to be caused by structural imperfections which cause the local increases of r-electron density and polarizability. A prominent electrical field effect (of Poole-Frenkel type) was revealed on the thermal detrapping rate that appears to be a rare example of the electrical field effect on the neutral trapping sites.
2. ~XP~IMENTAL
Gas-phase grown single crystab of C7s were used in the experiments. Intensively purified C7e powder was sublimed in a vacuum and the collected sublimate was sealed in a quartz tube with helium gas (about IOTorr). The tube was set in a horizontal electric furnace in which the tem~rature gradient was adjusted to keep a little lower temperature at the middle part of the horizontal tube. By this way millimeter-size C,e single crystals were obtained at the lower temperature zone of the tube. The technique was the same as that of growing C& single crystals used by us for mobility measurements previously [S]. A specimen for measurements was constructed as follows. A freshly grown single crystal was pasted in front of a round hole of 0.2-0.5 mm dia. of aluminium plate, 0.3 mm thick. The open external surface of the crystal, normal to the c-axis of the crystal, was illuminated through the hole. The back side of the crystal was cut by a sharp blade so that a thickness of 3060 pm remained. A metal electrode was pasted on the back surface. The front (illuminated) surface of the crystal remained open in one set of experiments, or 0 was covered by 200 A Au or Al by vacuum-deposition. We have been forced to use samples with open surfaces to prevent the appearance of any spurious signals originated from the materials which cover the surface such as IT0 electrode or similar ones. As the intrinsic transient current going through C7e crystal was rather small these spurious signals made the measurements difficult to perform. For the case of the open-surface of the crystal, an electrical field strength within the crystal being proportional to the voltage difference between the front electrode with the hole and the back electrode, was not known precisely. However, it was possible to estimate it performing the time-of-flight experiment with a crystal with known mobility of carriers (C,,). Such a calibration showed that the field strength is about three times lower than that calculated by dividing the voltage difference on the crystal thickness.
et al.
The sample was mounted to the cryostat holder (Air Products and Chemicals, Inc.), and was kept in vacuum at 5 x 10w6Torr during measurements and storage. Excitation light was generated by an Nz laser (LNlOOO, PRA Inc.) which provided light at the wavelength of 337 nm which is strongly absorbed by Cl0 crystal. The light pulses had a duration of 800 ps; maximum pulse energy was 1.1mJ. Tektronix 7834 storage oscilloscope with 7A26 amplifier, both channels of which were connected in series, was used for measurements of transient signals. The photocurrent flowed through the circuit containing the high voltage power supply, the sample, and the input resistance of the amplifier. Time resolution of the amplifier with 1000 resistance at the inputs of both channels was better than 10 ns. We have used mainly an integration regime for measurements of transient currents at short time domains (from 1Ons to 50~s). Input time constant in this regime was measured to be from 80 to 235 ps depending on the input resistance of the first channel (from 0.5 to 2 MSI). Single shot of the laser directed on the hole in the front electrode gave a signal which was displayed at the screen, photographed and analyzed. Thirteen samples of CT0 crystals grown in the same nominal conditions but in different weeks were used for experiments, all showing consistent results.
3. RESULTS AND DISCUSSION
3.1. ~~~~tes with open front swface: ~~h~~~tyof carriers and trapping By using the sandwich type sample and the excitation of the sample by strongly absorbed light one can expect in the simplest case the current response of the sample will have the form:
or a voltage response in the integration regime: u(t) =
!!!$ql
_ e-‘/n).
Here no is the total amount of charge carriers generated by a light pulse, p is the mobility of carriers, d is the thickness of the crystal, 71 is the life time of free carriers before a deep trapping occurs, and Y is the voltage difference. If the lifetime is long enough, some carriers can reach the back part of the crystal and the t value will be limited by the transit time, ttran = d*/,u V, from which the value of mobility p may be determined. Three types of transient voltage curves u(t) were obtained on different samples of C7e with open-
Transient
photoconductivity
of C,, single crystal
Fig. 1. Pictures of integrated transient photocurrent U(Z), obtained on the samples of C,s single crystal of type (ii) (curves A to D) :and type (iii) (curves E to G). Crystal thickness of type (ii) is 42 f 5 brn; of type (iii) is 52 f 5 pm. Curve A: vol ‘tage v= : 1100 V, holes are moving; B: V = + 1000 V; C: V = - 100 V, electrons are moving; D: V = - 1000 V; E: V = -- 300 14; F: v= : - 1000 V; G: V = 400 V. Intensity of the light is about 10’” photon/cm’ per pulse. Sweeping rateis 50 ns’div. (for ct wves A and B); 200ns/div. (for curves C and D); tOOns!div. (for curves E to G). Room temperature.
E. FRANKEVICH
486
surface specimens dependin paration technique.
on the specimen pre-
(i) The first one gives curves of the shape well described by eqn (2) with rt = 16 ns, the shape being independent on voltage. (ii) Typical curves of the second type obtained for transient integrated current (or voltage) u(t) are shown in Fig. 1 for drifting of holes (curves A and B) and electrons (curves C and D). A feature of the curves consists in the dependence of the shape of the curve on voltage. At low voltage (Y = 100 V) curves A and C may be well approximated by eqn (2), giving a value of r1 = Sons both for electrons and holes. At high voltage (V = iOO0V) curves approach to a step with a level off point at ttran = 107 ns for electrons and ttran= 71 ns for holes. (iii) Still another behavior was noticed which is shown in Fig. 1, curves E to G. At low voltages the curves u(t) did not level off at least to times t<2ps; higher voltages decreased the slope of the curve at high t, and the highest voltage used (Y = 1000 V) made the curve to be flat at t& 1OOns. In all the cases (i) to (iii) lowering the temperature below 270 K caused all the curves to look like ones of type (i). Curves of type (ii) and (iii) could be obtained on the freshly prepared crystals. Storage of crystals at room temperature in vacuum for more than one week resulted in the appearance of transient curves of type (i) only. Features of all the curves obtained may be understood by using the model with trapping of free charge carriers when they are drifting from the near surface part of the crystal to the back electrode. For the curves of type (i) it is just a fast trapping by deep traps which permits free carriers to have the lifetime rt = 16 ns which is not long enough for reaching the back electrode. On the curves B and D in Fig. 1 one can see the flat portion of the curve after reaching a level off point. To determine the transit time tt, we have used the value of t1j2 taken at the point where u(t) has l/2 of its maximum value. From eqn (2) at I = ttranit follows that: Itran = -7-t Iog(2e-“‘2’” - 1)
(3)
and values of ttrm = 71 and 107 ns were obtained for transport of electrons and holes, respectively, measured on the same sample. It gives directly the ratio of mobilities of holes and electrons &p, = 1.5 (&lo%). The absolute values of mobility may be estimated only because of uncertainty with the geometry of the electrical field in an open surface sample. Within the factor of 2 an estimate gives the holes ph = 1 cm*/V s.
et al.
Although the behavior of the curves u( t ) of type (iii) cannot be understood in the framework of the above model with drifting of free charge carriers and deep trapping, it can easily be rationalized by assuming the trapping by shallow traps which give for trapped charges a chance to get free during the observation time (up to 1000 ns). The lifetime of charge carriers in the traps r2 must be introduced, and the formula (4) may be obtained well describing the behavior of carriers with free transport, trapping, and detrapping:
valid for t 6 ttran. Gradual decrease of the slope of u(t) curves at higher t with increasing voltage V corresponds to a smaller part of carriers accumulated in traps at higher voltage, and to about none of them being trapped for the curve at V = IOOOV(the curve F in Fig. 1). Computer fitting of the curves like those shown in Fig. 1 (curves E and G) by eqn (4) gives the following values of parameters: rt = 90ns, ~z = 250 ns, and ttra,,(1000 V) = 105 ns. The latter value gives the same estimation of the electron mobility as made above. Thus, the main result from studying the transient photoconductivity in C,e single crystals consists in estimation of lifetimes and mobility of carriers at room temperature. While the mobility and the ratio of mobilities remain typical for molecular crystals, the lifetime of free carriers is rather short, from 16 to 90ns. The density of trapping sites N,, may be estimated using known value of mobility p * I cm’/Vs and assuming the trapping radius to be around R,, = 10 A. Then the trapping rate constant may be estimated as: k,, = hpkTR,,/e
= 2.5 x low8 cm3/s.
And for an estimation of the trapping site density we will get: N,, = l/rtktr = 4.4 x lOI to25 x lOI cm-‘. It should be noted that the value of N,, obtained is about two orders of magnitude higher than that in similar crystals of Cso [8]. Another important thing concerns non-permanent existence of properties of types (ii) and (iii). It looks like there exists slow transformation of properties of trapping sites and of their amount in the crystal, more stable being the properties of type (i), i.e. deep traps which give the shortest lifetime for free carriers. Such a behavior may be understood if one may imagine that traps are of a structural nature and they are able to evolute, possibly
Transient photoconductivity
Y---F-
of C&, single crystal
487
“YE
Fig. 2. Pictures ofintegrated transient photocurrent u(l) for C7e sample with a gold front electrode. Thickness of the sample is 42 f 5 pm. Light intensity is 2 x 10” photon~~* per pulse. Curves A to E are taken at different voltages: +700, +500, -t-400, i-200 and i-100 V respectively. Sweeping rate is 5 ps/div. Curves u(t) F to H are recorded on the sample 45 f 5 pm thick, with Al front electrode, at light intensity 2 x lOI4 photon/cm2 per pulse at V = -500V at different sweeping rates: 100,500 and 2&div., respectively. Room temperature.
488
E. FRANKEVICH IO2
et al.
r
101_Lkl
Voltage. V
Time, ps
Fig. 3. Dependence of the amplitude of u(t) at t = 50@son voltage V. Au front electrode. Holes are moving; room temperature. Experimental points are taken from the curves A to E in Fig. 2. Fitting of the points with power
Fig. 4. Time dependence of the amplitude u(t). Experimental points are taken from the curve A in Fig. 2. Fitting of the dependence with a power function is shown.
function is shown.
by migration, transformation or clustering. In the last part of the present work we will return to this question after discussing additional information on deep traps responsible for the tail of transient photoconductivity in the time domain of hundreds ,US. 3.2. Samples with the front surface covered by semitransparent metal layer: delayed generation of free charge carriers Metal (Au or Al) on the front surface of the crystal deposited by vacuum evaporation changes the photoresponse of the sample dramatically. The magnitude of the photocurrent becomes greater about 1000 times as compared with the open surface crystal case, and the transient photoconductivity becomes much more delayed, maximum of integrated photocurrent can be seen now at a t of about a few tens of microseconds. Figure 2 shows a set of transient integrated signals p(t) obtained at different sweeping rates and voltages. Inversion of the sign of the voltage leads to exactly the same signal in the case of Au electrode, however for the sample with Al front electrode the magnitude of .g
the electron current was 5 times higher than that of the hole current. Figure 3 gives the dependence of the amplitudes of u(t) taken after 50~s on the voltage: superlinear u 0: V’.* behavior is evident. Similar behavior for other polarities of the voltage was recorded. Figure 4 gives the plot of log u vs log t: the function u 0: t0,28is seen to fit the dependence. Figure 5 represents a plot of the amplitude of u(t) at t = to = 10 ps as a function of excitation intensity Z in the loglog scale. The light intensity was varied by controlling the focusing of the laser beam by a quartz lens. Temperature dependence of u( t = 10 ps) is not very sharp: the amplitude decreases steadily with lowering T (Fig. 6). The activation energy determined from the slope of the solid line in Fig. 6 has the value Etotal = 0.034 eV. The dependence of z4(t ) on intensity is most striking: it is very weak and obeys to the same law exactly as the dependence of u on t does (!); u cx t0.28and u 0: Z”.28. Such a coincidence is a key to decipher the mechanism of photoconductivity studied, as it means that parameters expressing time and intensity in the equation describing the kinetics of transient photoconductivity
103
,ol
g
d
u,
2 r;
r I
a
0
!!
z 4
3 a
”
s IO01Light intensity,
10
100
IO00
1014photon/cm* per pulse
Fig. 5. Dependence of the amplitude u( t ) at t = 10 ps on the light intensity at different polarity of the voltage. The same sample as in Fig. 3 is issued. Fitting of the dependence with a ^ . . . power lunctlon IS shown.
3.5
4
4.5
5
5.5
6
6.5
l/T, 10e3K’ Fig. 6. Temperature dependence of the amplitude u(t) at t = 2Ops, V = -500V. Sample with Al front electrode, thickness is 45 f 5 pm.
Transient photoconductivity of C,, single crystal occupy equivalent positions. There is no broad choice for such equations. We consider the results presented here as evidence of realization of the next model: metal on the surface of the crystal injects thermally charged carriers into the crystal which occupy trapping sites within the Debye length of the crystal near the surface. In the dark the electric field will induce the current which may be space charge limited or injection limited. The total charge injected inside the crystal depends on the work function of the metal at zero voltage but at higher voltages it may be as high as the electrical capacity of the sample permits. The light cannot increase the total amount of charges within the crystal. However, the ratio of free to trapped charge can change significantly as a result of detrapping by absorption of photons or by reaction of trapped charge with excitons. The observation of an approximately quadratic voltage dependence of u (t = 50 ps) (Fig. 3) is in line with such a mechanism. The photocurrent which appears due to detrapping of injected space charge is called photoenhanced current, and we believe it reveals itself in our experiments. The mediators which transfer excitation energy to trapped charges are presumably triplet excitons. Absorption of light by fullerenes is known to produce singlet excited states which give triplet excitons by intersystern crossing with quantum yields of about unity [9]. This is a sequence of dipole-forbiddeness of St-S0 radiative transition [lo, 111. For highly absorptive light of 337 nm the region of excitation in the crystal penetrates to about 1/E NN10e5 cm from the electrode. High density of triplet excitons is produced initially which may be estimated from the known light intensity I N 2 x lOI photon/cm* pulse as: nT N IE c5 2
489
Here T and St are triplet and singlet excitons, respectively, and Ss is the ground state. As it is known from the theory [ 121the dependence of the photoenhanced current i,,hen on the density of exciting agents nr may in general be expressed as: (7)
&hen 0: @T)'
where r < 1 and depends on the energy distribution of trapped charges. The integral of the current measured in our experiments,
may give the result which depends equally on nt and t in the case of r = 1 only. The case with r = 1 implies that all the filled traps are deep in the sense that their thermal escape frequency is lower than that induced by reaction with triplet excitons. At r = 1 the solution of eqn (8) gives: u(t) cc $og(l
+ yn{t).
(9)
(a)
(t/S+l),tinns
x lOI 1/cm3.
At such a high density main channel of quenching of triplet excitons is their mutual annihilation (at least within the time interval shorter than the diffusion time to to the electrode, the latter presumably being able to quench excitons, tD = l/e’D x lops, where D is triplet exciton diffusion coefficient taken as D a lo-’ cm2/s).
So, at t < tD the density nr of triplet excitons will obey the law: nr =n;
I
I
I
1
2000
3ooo
4ooa
5ooo
1 + tf5.tin ns
1
where y is the annihilation rate constant for the process T+T=St+Sa.
I
1000
(6)
Fig. 7. The experimental dependencies of the amplitude of the transient signal u( 1) fitted by logarithmic function of 1 + Ft. The best fit gives a fitting parameter F = 2 x 10s l/s. Curves A, B, and C are taken over different time domains at the light intensity I0 = 2 x lOI photon/cm’ per pulse. The same sample with Al front electrode as in Fig. 2.
490
E. FRANKEVICH
This is exactly what is required to account for experimental results (Figs 4 and 5), concerning dependencies ofuon tand1. Figures 7 (a, b and c) show the plots of the experimental dependencies of the transient signal u measured over different time domains (see Fig. 2) at intensity I = I0 = 2 x lOI photon/cm’ per pulse on the value of (1 + Ft) where F is a fitting parameter. One can see a good fitting to occur at F = l/5 ns-‘. Figure 8 shows a replot of Fig. 5 aimed at the demonstration of the logarithmic dependence of the amplitude u(t) at t = to = 10 ps on the light intensity, included in the value of (1 + Fl I) where F, is a fitting parameter. The value of F, = 2 x lo-l3 (photon/cm2 per pulse) -I is chosen for the plots. The meaning of the value of p = 0.28 in the formulas (u(t) 0: tP and u(t = 10~s) 0: Zp determined earlier from plots shown in Figs 4 and 5) becomes clear now if we take into account that the function f = log( 1 + X) may be represented asf cx x0.‘* at .Yof about x x IO2 and asf c( x0.” at x E 103. In our case the role of x is played by yn!& = TIEtO (see eqn 9). Curves shown in Fig. 7 are taken at intensities I0 ten times higher than those used in the cases shown in Figs 4 and 5. So, fitting of plots u vs. t by a power function gives for the former u 0: t0.15 in accordance with mathematics. The fitting parameter F in Fig. 7 can permit a rough estimate of the annihilation rate constant y: l+Fr=l+yn;r=l+yZtr y = F/Z6 x IO-” cm3/s.
-Amplitude at V=+5OOV 6 AmtGtude at V=-SOOV
I
(l+F,),
IO
100
1000
light intensity I in units 10’) photon/cm2 per pulse
Fig. 8. The experimental dependence of the amplitude of the transient signal u at t = 101s on the light intensity I, fitted by logarithmic function of 1 + F, I. The fits shown in the figure by the solid line give the v&e for the fitting parameter Fj = 2 x lo-l3 (photon/cm2 per pulse)-’ (or F, = 2 in r&iprocal units 6f I used in tie plbt). The a‘bsoluie values of the light intensity are known with the accuracy of an order of magnitude only. The same data as those used in Fig. 5 are plotted.
et al.
The estimation is made assuming the quantum yield of triplet excitons to be equal to unity and extinction of 337 nm light in fullerenes to be E = lo5 cm-‘. Triplet exciton annihilation rate constant given here has a roughly estimated but a reasonable value being typical for molecular crystals and corresponding to diffusion coefficient D of triplet excitons D = y/47rR x 1O--5 cm2/s, where R = 7A is taken for a reaction radius. Thus we came to the conclusion that the reaction of the next type takes place: T+
b/2
=
so
+
D;,,,
612
=
neutral trapping site + e.
(10)
Here D,i2 stands for a filled trap which is a doublet state and has a spin l/2 fi. It is known that the rate of reactions of this type may be sensitive to an external magnetic field and resonant microwave field [13, 141. This is because of evolution of the total electronic spin of the intermediate doublet-quadruplet mixed pair induced by magnetic interaction in the triplet exciton and an interference of the external magnetic field with this interaction. If they are magnetic field sensitive indeed, it opens a possibility of studying the dynamics and electronic structure of triplet excitons in fullerenes using reaction yield detected magnetic resonance (RYDMR) technique by monitoring the photoenhanced current [14]. It is worth mentioning that similar crystals of CU covered with Au evaporated electrode did not show the photoenhanced current, though one may expect there is an equally high yield of triplet excitons in both cases. It is a much lower density of trapping sites in the case of CeO that can explain the difference; triplet excitons have no charged trapping sites to react with. It may be added that one can not very often see the log-response of the signal to intensity in other materials and the effect may be useful in some respect when a response which must be almost insensitive to a prominent change of the intensity of the light is needed. The results obtained in the present work are worth comparing with those obtained in [6]. The latter work was done on sublimed CT0 films, 2000A thick, sandwiched between Al (front) and Ag electrodes. The authors found the photoconductivity of CT0 samples to be about two orders of magnitude higher than that of CeO samples. They assume that the generation of electrons and holes under the action of light is the cause for the photocurrent, and the bimolecular recombination of charge carriers takes place in the bulk of the sample. The reason for such a claim was a sublinear dependence of the photocurrent on the light
Transient photoconductivity intensity.
No plots
of the photocurrent
vs. voltage
were shown. Our time resolved results obtained present
work indicate
in the
that higher photoconductivity
with charge injection from the electrode and participation of triplet excitons in photoenhancement of the injected current. Apparently this might be the case for the films of CT0 studied in [6] also. of CT0 samples
with Al electrode is connected
3.3. The tail part of transient photocurrent: studying the properties of trapping sites The tail part of the transient photocurrent within the time domain of hundreds of ,us cannot be seen when using low input impedance of the amplifier as the signal is too small to be measured. Although the sensitivity at high input resistance R > 100 kf2 is high enough, other difficulties appear. At high R we have integration
of the current
about RC-value,
within the time domain
region where the generation triplet excitons
of free charge carriers by
is still essential.
of the curve may be observed general contains
The pure decay part
later. The decay part in
at least two exponents:
being the discharge
of the integrated
other may belong to the detrapping no integration
of
then one can observe an intermediate
one of them
current
and the
process.
There is
at t > RC and the current
regime is
operative. We have noticed that after the curve u(t) reached its
of CT0single crystal
491
maximum value the decay of the signal followed the exponential law with a time constant which was much higher than the RC value of the input circuit of the preamplifier. This was a clear indication of a long lasting detrapping process going on the background of the decay of integrated signal accumulated during earlier stages of transient photoconductivity. It was impossible, however, to separate these two processes as the decrease of RC led to equal decrease of the tail. So we were forced to measure the properties of the current, which appears to be caused by thermal detrapping of charge carriers, on the background of the RC decay. The best experimentally measured parameter, which gives the normalized value of the amplitude B of the tail, is the halfwidth of the decaying part of the transient signal. As it was said the decaying part is the sum of two exponents: u( t ) = Ae-‘iRC + Be-“‘. Below we will find out the connection
(11)
of the halfwidth
t112with the amplitude B of the part of the decaying current connected with detrapping. Let us put t = 0 at the beginning of decaying part near the maximum of the experimental curve u(t). Any change of the amplitude B of the tail will lead to a change of the halfwidth t112determined as follows: a(tt/z)
= (A + R)/2.
Fig. 9. Picture of the decaying part of the transient signal. The sample with Al front electrode; electrons are moving; thickness is 45 i 5 pm; input resistance is 0.5 MR; sweeping rate is 50 &div.; room temperature. Curves are taken at different voltages, from top to bottom, respectively: -200, -400, -700, -900V.
E. FRANKEWCH
AiB A B A B
Sum -100.5~s -246 ps y -1 3.484*eA(-0.~99466x) R= 1 y =2l*e”(-0.00408t6x) R=l
et al.
t.3.102z
l.2.102.
_$ 1.1.102~ c I5 1.102 L % 2 7 z
1.
9.10’ -
3
8.10’ 7.10’ -I: 6.10’1 140
I
i I 200
I 300
I 250
Temperature, Time, gs Fig. 10. The decaying curves a(t) which show the rest&s of the computer decomposition of the ex~rimentaIly obtained decay curve (A + B) into two exponents A and B. Curve (A f B) is taken at room temperature, V = -5OOV, on the sample of CT0single crystal with AI covered front surface as in Fig. 9.
If the condition t = tlf2, and
T >
RC is met, then e-lJT x 1 at
tt12 = -RClog[(l
- B/A)I2].
(12)
or Atliz = RC(B/A)
(13)
For B < A it gives simply: t1/2 = (0.69 + B/A)RC
where Atijz is the halfwidth added due to presence of the tail originated from detrapping. We have studied the decay part of the transient electron current on the same samples as in Section 3.2; with the front electrode in the form of evaporated Al. The typical picture of the transient curve is shown in Fig. 9. The shape of the decay was carefully studied and its appearance in the u vs. t plot is shown in Fig. 10, curve (A + B). The two exponents A and B of the decay curve were extracted by computer analysis and the time constants and amplitudes for each of them were calculated to be RC = 100.5 ns and r = 246ns;
2
I 350
K
Fig. 11.Temperature dependence of the total halfwidth tt/2 of the decay curve. The limiting value of f,/r = 70 ns is seen to be reached at low enough temperature. V = -SOOV, the same sample is in Fig. 9.
A = 39% and B = 61% of the total amplitude at room temperature and I’ = -500V. A help for such an extraction came from the low temperature experiment. It was measured that the change of tl12 stops at T~210 K corresponding to disappearance of the measurable detrapping of carriers. All the exponents of the decay part of the signal and positions of t1/2at room temperature and at low temperature are shown in Fig. 10. In order to study the properties of the tail connected with detrapping of charge carriers we measured the dependence of t1/2 on the temperature and voltage. The value of AtlIz was considered as the parameter directly proportional to the amplitude B [see eqns (12) and (t3)]. Figure 11 shows the plot of tlj2 vs. T. It is seen that the tail connected with detrapping disappears at low temperature, and only RC-decay remains, RC = 1OOns (or t1/2 = 70ns). Figure 12 shows the plot of logAt,/, vs. l/T which permits obtaining the value of the activation energy w s,.td= 0.1 eV in the conditions when the voltage I’ = SOOVis applied.
1.3.102 4.5.100
II
g 1.2.102
k Total
halfwidth 9 Low T limiting value
I
4.100
4 .z 3.5.100 3 % .z 3.100 “, B 2.5.100 d 2.100
6.10’L 3
4
3.5 l/T,
4.5
5
IO-3 K-1
Fig. 12. Temperature dependence of the change of the halfwidth Artlz in the log vs. ij7’scale. The same data as in Fig. 1I are plotted.
1000 Voltage,
V
Fig. 13. Dependence of the total halfwidth tllz of the decay curve on the voltage. The same sample as in Fig. 9; at room temperature. The squared point at V = 0 is shown as a limit of tt/z obtained from the low temperature experiment: T = 200 K, V = -500V for this point.
Transient photoconductivity
External electrical field was revealed to have a prominent effect on the value of tl/2 also. The results are shown in Fig. 13 where the change of the total halfwidth caused by voltage can be seen. As far as the value of tl12 is connected with the ratio of amplitudes A and B only, an ordinary action of the voltage on the absolute value of transient current does not interfere with the effect under study. The field is shown to act on the ratio of B and A only. As the effect was revealed on samples of the type (i) (see Section 3.1 of the present paper) which showed fast trapping of all the charges produced, one could not expect that the amount of the charges trapped would depend on the voltage. Moreover the sign of the effect of electrical field is opposite to that which could be expected if the samples of the type (iii) were used. In order to rationalize the results obtained we have to admit that the tail originates from charge carriers detrapped from traps which were filled during the movement of free charge carriers, and they become excited by triplet excitons from the trapped charge reservoir near the front electrode. It remains unknown whether the traps are distributed in energy or occupy a narrow energy interval. An activation energy determined from temperature dependence of the tail has the value of 0.1 eV which is not very deep trapping. Let us consider the kinetics of the detrapping process. The kinetics of the tail are covered by trapping, detrapping, and retrapping: dn s=
Nv-k,N,,n-kzn
dN - = -Nu + k, Ntrn.
of CT0single crystal
493
potential barrier that keeps the charge localized. What is studied usually and called the Poole-Frenkel effect [ 151is the lowering of the Coulomb field which attracts a trapped charge and the charge of other sign that the trap had before the trapping occurred. Evidently this is not the case for fullerene, as one cannot expect charged trapping sites in these crystals. It is expected [16] that if the carrier is trapped in an otherwise neutral site, then an external field should have a negligible detrapping effect. In our case, however, one can imagine that the geometrical size of the trap is much bigger than that which was previously studied in other materials. The results obtained here may be explained if the traps are originated from a polarization and, due to high polarizability of fullerene molecules, the potential well of the charge which finds itself surrounded by the increased local density of CT0molecules in the crystal defect site, may be quite broad. As far as the polarization energy P gained by a trapped carrier from interaction with polarizable molecules if P(a) = - Ce2a/2r4, where cy is the polarizability of the molecule, a small change of the distance r between molecules at a defect site makes a well at least of one or two molecular diameters broad (15-20 A). In order to estimate the size 6 of the trapping site we used a simple model in which the external field decreases the height of the potential barrier W by A W = Ee6, where e is the electron charge and E = V/d. The comparison of the action of the temperature and field to produce equal changes of tlj2 leads to evaluate the size of the trap 5. Assuming that F(E) = exp(Ee6/kT) one may obtain:
dt
Here n is the density of free carriers; the current measured is proportional to n; N is the density of filled traps; k, is a rate constant of trapping of free carriers by traps with density N,,; k2 is the rate of other processes removing carriers out of play; Y is the trap escape frequency. The solution gives: n = N,,veC”‘/(kl
N,, + k2)
[W - (E + AE)eb] = W - AEe6 T T+AT
(16)
Here E is the electrical field strength used during the measurements of the effect of temperature on lo*-
(15)
where r = k2/(klNtr + k2) and v = v,,exp(-W/kT) F( V/d), F( V/d) stands for the function responsible for the field dependence of the escape frequency, which is proportional to B or to the value of At,,2 measured experimentally; the value of vr has the meaning of l/r used in eqn (11) and also measured experimentally (T = 246 ns at room temperature). In addition to thermal and triplet exciton induced detrapping, detrapping assisted by an external electrical field seems to occur in C70 crystals. It is well known that electrical field can assist in escaping of charge from traps by lowering the height of the
% Pi 2
4
IO'0
200
400
600
I
I
800
1000
Voltage, V Fig. 14. Voltage dependence of the change of the halfwidth Ar,,z in the log vs. V scale. The slope of the solid line gives the parameter 6 in the framework of the model used to account for the effect of electrical field on the detrapping rate. The same data as in Fig. 13 Ire plotted.
E. FRANKEVICH et al.
494
tl12 (E = V/d= 500145 x 10m4M lo5 V/cm); AE and AT are the field and temperature enlargements which cause equal changes of the detrapping rate. We have measured that AE = 3.1 x lo4 V/cm and AT = 25 K at T=295 K. Then knowing that Wfsld = W-E&?= 0.1eV, the size of the trapping site may be calculated:
&aT
Wiield x 2.5x lo-‘cm
AE~(T+AT)
(*lo%)
(17)
sites which are presumably structural defects causing local increase of r-electron density and polar&ability. work was partly sup~rt~ by a Grant-in-Aid for Scientific Research for New Program (06 NP 0301) and also for Fullerene Priority Area (05233104) from the Ministry of Education, Science and Culture. ELF acknowledges the hospitality of the Institute for Molecular Science during his stay in Japan. Acknowfedgeme~tts-This
and W a 0.12eV. Approximately the same value of the parameter S may be obtained from the slope of the solid line in the plot of log At,,2 vs. V in Fig. 14. Thus, having done the estimation of the size S to be about 25 A one may speculate that traps presented in CT0 single crystal are just of structural nature caused by non-perfect packing of ellipsoidal CT0 molecules. Such kinds of defects cannot be assumed to be common in C6e crystals. Three C,,, molecules touching each other by sharper sides may be considered as candidates for such a trapping site. Calculations of electronic properties of such a defect are worth performing.
REFERENCES I. Lee C. H., Yu G., 2.
3.
4. 5.
6.
7. 4. SUMMARY
In conclusion, the present work has shown the features in which the properties of C,, and CT0crystals differ from each other. The dominant differences are connected with high density of trapping sites in C70 crystals. It is the high density of trapped charges injected from electrode which determines the participation of triplet excitons in the generation of the photocurrent. Electronic properties of the trapping sites were studied by making use of the dependence of the detrapping rate on temperature and electrical field strength. Electrical field assisted detrapping permitted to estimate the size of traps in the framework of a simple model and make the conjecture about the nature of trapping
8. 9.
10.
11. 12. 13. 14.
15.
16.
Kraabel B., Moses D and Srdanov
V. I., Phys. Rev. E 49, 10572 (1994). Dick D., Wei X., Jeglinski S., Benner R. E., Vardeny Z. V., Moses D., Srdanov V. I. and Wudl F., Phys. Rev. Lett. 73,276O (1994). Kaiser M., Reichenbach J., Byrne H. J., Anders J., Maser W., Roth S., Zahab A. and Bemier P., Solid State Comm. 81,261 (1992). Lof R. J., Veenendaal M. A., Jonkman H. T. and Sawatzky G. A., Phys. Rev. Lett. 68,3924 (1992). Arai T., Murakami Y., Suematsu H., Kikuchi K., Achiba Y. and fkemoto I., Solid State Comm. 84, 827 (1992). Hosoya M., Ichimura K., Wang 2. H.. Dresselhaus G., Dresselhaus M. S. and Eklund P. C., Phys. Rev. B. 49, 4981 (1994). Frankevich E. L., Maruyama Y., Ogata H., Achiba Y. and Kikucbi K., Solid State Comm. 88, 177 (1993). Frankevich E. L., Maruyama Y. and Ogata H., Chem. Phys. Lett. 214,39 (1993). Wasielewski M. R., O’Neil M. P., Lykke K. R., Pelhn M. J. and Gruen D. M.. J. Am. Chem. Sot. 133.2774 (1991). Lee M., Song O.-K., Seo J.-C., Kim D., Suh Y. D., Jin S. M. and Kim S. K.. Chem. Phvs. Lett. 196.325 (19921. Arbogast J. W. and Foote C. S.; J. Am. Chem. Sk. 113, 8886-9 (1991). Bauser H. and RufH. H., Phyz Stat. Sol. 32,135(1969). Em V. and Merryfield R. E., P&s. Rev. Lett. 21, 609 (1968). Buchachenko A. L. and Frankevich E. L., Chemical Generation and Reception of Radio- and Microwaves. VCH, New York (1994). Simmons __ J. G., ._ Phys. Rev. 155,657 (1967). Pope M. and Swenberg C., Dectronic Properties qf Organic Crystals, pp. 267, 708. CIarendon Press, Oxford and New York (1982).