S Kania - Charge carrier transport in the tetracene layers with a different structural order - страница 1
ВІСНИК ЛЬВІВ. УН-ТУ
Серія фізична. 2007. Вип.40. С.322-336
VISNYKLVIV UNIV. Ser.Physic. 2007. N40. P.322-336
PACS number(s): 51.50.+v
CHARGE CARRIER TRANSPORT IN THE TETRACENE LAYERS WITH A DIFFERENT STRUCTURAL ORDER
Institute of Physics, Technical University of Lodz, Wolczanska 219,
PL 90-924 Lodz, Poland Center of Mathematics and Physics, Technical University of Lodz, ul. Al. Politechniki 11, PL 90-924 Lodz, Poland e-mail: firstname.lastname@example.org
There were made investigations under drift mobility of electrons and holes in the tetracene layers with different level of structure order (polycrystalline, quasi-amorphous and amorphous). The investigations were made using the Time-Of-Flight (TOF) method with typical set-up controlled by a computer. Obtained current-time pulses let ones to direct determination the time-of-flight and followingly the drift mobility value. The results may suggest that the dominant transport mechanism is the hopping transport through the localized states. Occurrence of such a transport was shown directly for the polycrystalline layers of low-molecular-weigh simple aromatic hydrocarbons . The studies taken off with the assumption of such a mechanism give for electrons the worth for the average distance between localized states to be in the order of 30-39 A and the density of localized states N(EF) from 0,8 to 1,7-10 cm" 3eV-1 and for holes the average distance between localized states a value in the order of 24-36 A and the density of localized states N(EF) from 1,9 to 6,5-1020cm"3eV-1.
Key words: amorphous, quasi-amorphous, polycrystalline tetracene films, electron mobility, hole mobility, carrier transport.
The transport mechanism can be determined when we know: the mobility value, the temperature dependence of the mobility, which ensures the determination of the activation energy for mobility and the character of the mobility dependence due to the change of the density of states.
At this time exists several methods designed for determining the drift mobility. Because the drift mobility is directly dependent on the distribution of the states it is a useful way to perform the studies on the mobility in regard to above aspects.
It would have to seem that the change of the localized states density can be obtained with the change of the structural order. Charge transport in organic molecular materials is dominated by the comparatively weak short-range intermolecular forces what enables a single molecule to preserve its individuality to some extend. The temperature dependence of both hole and electron drift mobility in single crystals of
© Kania S., 2007
simple aromatic hydrocarbons suggests that the band model should be sufficient for the theoretical base of the charge transport at nitrogen temperatures. But under 100 K starts the transition from band to hopping mechanism . And for the majority of the polycrystalline structures of simple aromatic hydrocarbons (such as tetracene, p-terphenyl, p-quaterphenyl and coronene) the hopping transport is supposed to dominate [2-5]. The mean free path of the electron in antracene is estimated to be of the same order as the intermolecular spacing in anthracene, so it might be non realistic to describe charge carrier motion in terms of the band model. In this paper the results of measurements of electron and hole drift mobility in polycrystalline, quasi-amorphous and in amorphous tetracene films are presented.
There are several methods for determining drift mobility in existence now . The main group are the photocurrent measurement methods especially in the case of high ohmic materials. Photo generation process analysis make possible to characterize the density of the states (DOS), the tails of the bands, the lifetimes of recombination, and the values of the energies for activity of the conduction, and the traps energy spectrum.
There is a wide variety of experimental techniques based on photoconductivity. The first group of them can be named as steady-state photoconductivity methods where the focus is on the stationary photocurrent levels which is valuable for materials with widespread practical applications. Here we have two possibilities first (Equilibrium Photoconductivity with Single-Beam and Dual-Beam) with constant illumination which can give us the generation rate, quantum efficiency of the generation process and second possibilities with modulated beam (Modulated Photoconductivity) which is a powerful tool for material analysis enable to estimate the DOS in the whole band gap and the lifetimes for all traps.
The second group of the photoconductivity methods are transient photoconductivity experiments among them time-of-flight (TOF) experiment and interrupted field time-of-flight (IFTOF). This group of methods can give us the dynamical parameters of the material such as the mobility value, the mobility band gap value.
The most useful for investigations of the organic dielectric with lower value of the mobility is the TOF method. The method TOF which apparatus scheme is presented in Fig. 4 can yield independent information on quantum yield of photo generation, the mobility of the charge carriers, and the nature of the charge transport process. Sample is sandwiched between a semi-transparent front electrode and the back drain electrode. Incident strongly absorbed light pulse with microsecond duration impinging through the front electrode produces a thin sheet of charge carriers that migrates through the sample under the influence of the applied electric field. The change of the bias direction allows to investigate separately in the same sample the electron transport or hole transport. The sign of transport depends upon the sign of the applied potential difference and on the sample material. Straightforward interpretation of the transient photocurrents needs non-injecting electrodes and to make a blocking contact between the front electrode and the bulk, because to avoid dark currents and to avoid an immobile space charge. The measuring electrode should allow an effective drainage of the carries that had flown through the layer to the electrode. The sample makes a plate condenser, which can collect a maximal useful charge of a value equal the product of applied voltage and the capacitance. The photo generated charge must be small in order to avoid space charge.
There is an observable difference in the character of transients in different materials. Non-dispersive charge transport was obtained in the inorganic materials and in the organic single crystals. That is in a case essentially with rectangular shape of pulse [1, 10-15], which one can describe as follow:
і (t) = q for t < ttr,
і (t) = 0 for t > ttr,
here: i(t) - the current on the collecting electrode, q - the total photogene rated charge,
tr - transit time related to the mobility by formula:
ttr = — = -F = -77, О vdr Vе v-U
where : L - thickness of the sandwich, vdr - carriers drift velocity, ц - mobility, E -applied field and U - applied potential difference. In the conditions when the Einstein formula:
eD = \\kT (3) is true (here: e - charge of a carrier electron or hole, D - diffusion constant for electron or hole, k=1,38-10-23 J/K), we can write two formulas for non-dispersive transport spread (Дх2)12 of a sheet of charge carriers that has traveled a distance x:
(Ax 2)1/2 = КГ_ Ґ _2_ Y/2
x eE [ Dt J , (4)
(Дх 2)1/2 =(2 Dt )1/2.
The transient photocurrents observed for several amorphous systems (inorganic and organic) showed dispersive phenomena. It is a case of continual monotonicity, the signal permanently decreasing. The transient plotted in the double logarithmic scale; logarithm of current versus the logarithm of the time gives two lines:
і (t)oc ta-1 for t < tr
V ' (5)
І (t)« І (ttr )• tM for t >
with 0<a<1 and p<0, and intersections of the lines give tr - a transit time for the fastest carriers. These features suggest dispersive transport, where the velocity of a sheet of carriers decreases as the packet traverses the sample.
The tetracene samples were obtained by evaporation in vacuum under the pressure of the order of 10-5 Torr on glass plates supplied with Au electrode. For polycrystalline samples the substrate temperature was about 290 K and the growth rate was 10-15 A/s. The quasi-amorphous films were obtained by evaporation in vacuum under the pressure of the order of 10-5 Torr. The substrate temperature was from 170 to 200 K and the evaporation rate was changed in the range 80-110 A/s. The amorphous films were obtained by evaporation in vacuum under the pressure of the order of 10-5 Torr and the substrate temperature were from 140 to 150 K and the evaporation rate was changed in the range 110-150 A/s. X - ray diffraction structural examinations for obtained tetracene layers were made using an automatic diffractometer DAR. Diffraction examinations were made in the 29 range from 5° to 80° with measuring step 0,05°.
Typical Rontgen diffraction patterns for the obtained tetracene films are presented as follow in Fig. 1, 2, 3. In the Fig. 1 one can see the typical reflexes for polycrystalline phase, in the Fig. 2 - typical for quasi-amorphous phase and in the Fig. 3 - typical for the amorphous phase. The glitches in Fig. 1 makes one clear that there is a polycrystalline solid, a long - range order is visible, but the graph presented in the Fig. 3, without jumps is a pattern for a structure of a real amorphous solid.
The semitransparent aluminum electrodes were also evaporated in vacuum on the film of the investigated compound.
Fig. 1. Diffraction pattern (X - ray) for polycrystalline tetracene film. Plot of the intensity of diffraction lines in function of the angle 2©
Fig. 2. Diffraction pattern (X - ray) for tested quasi-amorphous tetracene film. Plot of the intensity of diffraction lines in function of the angle 2©
Fig. 3. Diffraction pattern (X - ray) for tested amorphous tetracene film. Plot of the intensity of diffraction lines in function of the angle 2©
There were made the carrier mobility measurements in the ambient air atmosphere for the films with the different structure using the time - of - flight (TOF) method.
Semitransparent Al electrode
Fig. 4. Schematic diagram of the time of flight (TOF) experimental set-up
Fig. 4 shows a schematic diagram of the equipment used for the time - of - flight measurements. A short light pulse goes through the semitransparent aluminum electrode and then generates a number of electron - hole pairs in a thin interface layer at the electrode - substrate junction. Depending on the polarization of sample the
holes or electrons travel through a sample giving rise to a current signal registered by a current meter. All the system works under computer control which enables to control the measurements and to store the data. The time of flight is found from the current signal. The current pulses were measured with digital oscilloscope DSO 5804 and then via interface they were registered with computer.
In the tetracene layers with different structure the transport of the electrons and holes was examined. In the case of electrons for all of the structures the pulses show detectable changes of slope (kink of the plot) which enables to find the transit time for charge carriers. For the polycrystalline layers the above was obvious, but for the quasi-amorphous and for amorphous ones the occurrence of the Gaussian transport is interesting. Typical current pulse for electron obtained for the quasi-amorphous tetracene films is shown in the Fig. 5.
Fig. 5. Typical current pulse for electrons obtained for the quasi - amorphous tetracene film, thickness L = 17,5 |im, voltage applied to the film U = 14 V, in the air
Typical TOF pulse for amorphous tetracene layer is presented in Fig. 6 and Fig. 6a.
Fig. 6. Original oscilloscope current pulse for electrons obtained in the air for the amorphous tetracene film, thickness L = 19 |im, voltage applied to the film U = 30 V, the insert shows the same diagram digitally processed with the time axis in milliseconds
Fig. 6, a in which the plot current - time pulse is presented, with the scale log i - log t, was made to get an insight into the fact that the time-of- flight is the same independently on the diagram scale format (linear or logarithmic). In this way ones verify if there is Gaussian or dispersive transport here. We have written about it in the introduction. Identical value of the ttr measured as a kink of the plot is clearly seen in the Fig.6.a. to be the same for linear and logarithmic scale. In this way obtained results suggest that our case is a Gaussian packet of the carriers what is a something interesting fact. In that case there are fulfilled conditions in which the formula (2) is valid.
li = L2/ttr -U, (6) where L is the sample thickness, ttr is time of flight and U is the voltage. In order to attain to evaluate the faultiness of the estimation of the time-of-flight, as expressed in the formula (2) one performed a diagram of an inverse time-of-flight 1/ttr upon the voltage applied to the film. The plots of those dependencies for electrons are presented in the Fig. 7, 8.
0 0,2 0,4 0,6 0,8 1 1,2
Fig. 6, a. Current time pulse versus time for electrons in amorphous tetracene layer, digitally processed
There were obtained the following values in the air atmosphere for the electron mobility for polycrystalline films: 7 -10 -4 cm2/Vs [8, 18] in the quasi-amorphous films (see Fig. 7) 3,2-10 -4 cm2/Vs to 9,8-10 -4 cm2/Vs and in the amorphous films (see Fig. 8) the values were similar and were in the range from 3-10 -4 cm2/Vs to 1-10 -3 cm2/Vs. The activation energies for drift electron mobility were similar for all studying films: polycrystalline, quasi-amorphous and amorphous and the values were in the order of
The measurements were made for holes in the tetracene layers with all of the structures too. For holes there were obtained identical shapes of the pulses as for the electrons. The pulses show detectable changes of slope (kink on the plot) which enables to find the transit time for charge carriers what is visible in the Fig. 9 and 10.
Fig. 7. Diagram of an inverse time-of-flight 1/tr for electrons upon the voltage applied to the film, L =17,5 шгі , ue = 9,5 ' 10-4 cm2/V s, in the air
And we can calculate the drift mobility from the expression (6).
10 20 30 40
Fig. 8. Diagram of an inverse time-of-flight 1/ttr for electrons upon the voltage applied to the amorphous film, L =20 urn , ue = 8-10-4 cm2/Vs ,in the air
Typical current pulse for hole obtained for the quasi - amorphous tetracene films is shown in the Fig. 9.
П 7 сна:
□ 1.0 V/C V O.lnSFk t>IU
UlJZ 1 nil J
Uer tykл 11 CHl/'CHt
Probkі tit .do DOO.L. ,E 1П
OSC > > .
HCOSC: dsae , data 2002.08.17 U;32;30
Fig. 9. Typical current pulse for holes obtained for the quasi - amorphous tetracene film, thickness L = 14,5 шп, voltage applied to the film U = 7 V, in the air
Fig. 10. Current hole pulse in the air for amorphous film digitally processed, as an insert is the same pulse in the double logarithmic scale
The inverse time of flight dependencies versus applied voltage for polycrystalline, quasi - amorphous and amorphous layers are shown in the Fig. 11, 12,
The temperature dependence of the drift mobility for holes turned out to be rather weak, in the temperature interval 290-340 K, and the activation energy for mobility was determined to be circa 0,025-0,03 eV [8, 9, 16, 17, 19].
Fig. 11. Diagram of an inverse time-of-flight 1/tr for holes upon the voltage applied to the polycrystalline tetracene film, in the air, L =18,5 шп , uh = 2,59-10-3 cm2/V s
Fig. 12. Diagram of an inverse time-of-flight 1/tr for holes upon the voltage applied to the quasi-amorphous tetracene film, in the air, L =17,5 шп , uh = 2,2-10-3 cm2/Vs
The value for the activation energy of the drift mobility which was of the order kT and low for holes drift mobility, imply as a possibility that the model of hopping transport in narrow band of localized states at Fermi level should be taken into account.
Fig. 13. Diagram of an inverse time-of-flight 1/tr for holes upon the voltage applied to the amorphous tetracene film, in the air, L =20 шп , |xh = 2,5-10-3 cm2/Vs
The wide spread of mobility values for amorphous tetracene layers was observed. The hole mobilities were in the limits 5,4-10 -4 and 2,6-10 -3 cm2/Vs for quasi-amorphous and between 6-10 -4 and 3-10 3 cm2/Vs for amorphous films and in the proximity of the 2,5-10 -3 cm2/Vs for polycrystalline films. Obtained results are very similar. All that concerns as well the mobility value as well energy activation value. It must be marked that the large spread of the mobility values for quasi -amorphous and for amorphous layers were due to the lack of the stability of the electric properties of these layers. In addition, obtained amorphous layers showed a lack of the temperature stability for the electric properties during measurements.
Obtained results for tetracene layers with a different structures are summarized in the Table 1 [8, 9, 16, 17, 18, 19].
order of the layer
7-10 - 4
2,5-10 - 3
3,2-10 - 4 - 9,8-10 -4
5,4-10 - 4 -2,6-10 -
3-10 - 4 - 1-10 - 3
6-10 - 4 - 3,0-10 - 3
Obtained results for electrons and holes concerned either with the magnitude of the mobility or with their temperature dependence character suggest, that in that case we are with the hopping transport. If one assume such a kind of transport through localized states in the proximity of the Fermi level then the drift mobility in the Mott-Davies model should be given by :
ц = (1/6)(eR2/kT)-Vph-exp(-2aR)-exp(-AE/kT), (7) where: R - is the average distance between localized states, e - is electron charge, vph - is the phonon frequency, a - is the decay of the localized state wave function, ДЕ -is the width of the narrow band of localized states taking part in the charge transport. Usually a-1 is assumed to be comparable to the average distance between molecules. The choice of a-1 is burdened with some uncertainty. Using the expression (7) for the carrier mobility and geometric formula for density of states:
N(EF) = (3/4л)(1Я13ДЕ) (8) one can estimate the average distance between the localized states and the density of localized states at the Fermi level. The spread of mobility values for charge carriers (both electrons and holes) might results from structural changes in layers during conducting the observations. Basing on the expressions (7) and (8) one might to estimate average values of the distances for localized states for holes Rh and for electrons Re and to estimate the average density of localized states N(EF) near the Fermi level [8, 18].
Taking into account obtained results, and accepting the commonly used for the organic solid state the worth for a-1 = 12 A [1, 15, 17], we can get the following values for the average distance between the localized states - R and for density of localized states - N(EF). The results are presented in the Table 2.
order of the layer
The average distance between the localized states, R
The density of localized states, N(EF)
39 - 30
(0,83 - 1,67)-1020
39 - 30
(0,82 - 1,69)-1020
Obtained values (see the Tab. 2) can be fully accepted in the case of organic solid state [1, 8, 15, 18]. From the Table 2 outcome that here there is an absent of the simple linear dependence between the mobility of the charge carriers due to the growth of disorder and due to the growth of the localized states density N(EF). However the above dependence should have been expected with hopping transport mechanism assumed here. Likely all what was written above is due to the fact that the measurements were made in the ambient air atmosphere (the measurements in vacuum
were impossible to do) and to the fact that the density of states determined is by a diffusion of the water and O2 molecules to the film. All the more the above can exist, because such molecules can diffuse more easily into the polycrystalline structure.
Despite our assumptions that we were here with a case of the hopping transport, the obtained results do not unambiguously decide that problem. From the pulse shape one can get into conclusion that there is a case of Gaussian transport, and it may suggests after all, that we are here with the transport in a slightly shaped band with the participation of the trap states [4, 6, 15].
Considering the possibility of the band transport in such a case, one can describe the mobility with the formula:
ц = ц0© ,
where Li0 - the band mobility, ш - measured drift mobility and 0 - the parameter dependent on the density of trap states. For the band transport in the room