Modeling thermionic emission-limited current voltage curves of metal/organic/metal devices

Transcription

1 phys. stat. sol. (a) 201, No. 1, (2004) / DOI /pssa Modeling thermionic emission-limited current voltage curves of metal/organic/metal devices I. Thurzo *, H. Méndez, and D. R. T. Zahn Institut für Physik, TU-Chemnitz, Reichenhainer Str. 70, Chemnitz, Germany Received 1 August 2003, revised 27 October 2003, accepted 30 October 2003 Published online 11 December 2003 PACS Le, Ns, Ph, z, Jb Steady-state current-voltage (IV) characteristics of metal/organics/metal devices are modelled on the basis of thermionic emission into two back-to-back connected diodes separated by a series bulk resistance. It is shown that the analysis of the IV curves cannot be split in two independent branches corresponding to opposite polarities of the applied bias. At low biases both metal/organic barriers influence the current, whereas at elevated biases the (saturation) current is limited by the non-injecting diode experiencing reverse bias, along with the bulk resistance. Conditions are simulated when the thermal activation energy (barrier height of the metal/organic contact and/or that of bulk conductivity) can be deduced from IV data taken at different temperatures. The model calculations are also helpful for envisaging the potential distribution across the three zones (barrier 1 /bulk/barrier 2 ) at different biases. Experimental data on IV characteristics of Ag/Dimethyl-PTCDI/n-GaAs (sulphur-passivated) recorded at different temperatures are treated within the framework of the model. 1 Introduction Achieving a relatively low and stable threshold voltage for organic light-emitting diodes (OLEDs) is a permanent challenge to those who are working both, theoretically and experimentally, in the field of physics of charge injection and recombination in either single- or multi-layer devices. In their article [1], which is a comprehensive review, Brütting et al. summarized a great deal of what has been done in this field. The most substantial approaches to charge injection can be divided to a few categories: Fowler- Nordheim tunneling [1], Richardson-Schottky thermionic emission overcoming the metal/organic barrier [2, 4] and injection to the transport band via a Gaussian distribution of metal/organic interface states [5 7]. It is often the case that only a single type of charge carrier (electron or hole) is injected and transported through organic single-layer devices. With rectification present, it is usual practice concentrating on the processes taking place at the injecting electrode under forward bias. Examples of successful description of forward current-voltage (I V) characteristics of single-layer devices are found in the papers by Brütting et al. [2] on PPV and by Baldo and Forrest on Alq 3 [7], the success being restricted to biases above 1 V. Actually the possible role of the extracting contact has been ignored in relevant studies. In what follows the thermionic emission model of a Schottky barrier and a series resistance used by Brütting et al. [2] will be extended towards an alternative back-to-back Schottky diode system (metal/organic/metal), the two diodes being separated from one another by the resistance of the undoped bulk material. The aim of the modeling is to emphasize the role of extracting contact when treating the I V curves as a whole, being aware of the fact, that such an approach might apply rather to good- * Corresponding author: ilja.thurzo@physik.tu-chemnitz.de, Phone: , Fax:

2 phys. stat. sol. (a) 201, No. 1 (2004) / ordered organic thin films than to the case of strong energetic disorder and thus, strong localization of charge carriers in amorphous organic thin film, reviewed recently by Scott [3]. Simulated IV curves as a function of temperature T will be presented, in order to illustrate the potential of such experiments for yielding the metal/organic barrier heights and/or the thermal activation energy of the specific resistivity of the organic material. The latter option is mediated by the transition from injection-limited to bulk-limited currents. Finally, experimental current voltage curves of Ag/Dimethyl- PTCDI/n-GaAs, taken at different temperatures, are treated in terms of the interplay between the injecting and extracting barriers. 2 Back-to-back diode model calculations Prior to explaining the equivalent electrical circuit, the formula describing the current I through a Schottky barrier as a function of bias [8] is adopted: * 2 φb qu I = A T exp exp 1, nkt kt (1) where A * is Richardson s constant (in AK 2 ), φ b is the barrier height defined as the energy offset between the Fermi level of metal and the transport band of the semiconductor. Further parameters include Boltzmann s constant k = JK 1, electronic charge q = C, the applied voltage U (potential of the anode) and temperature T. For convenience the symbol K = A * T 2 exp ( φ b /kt) for the emission capability of the metal electrode and a = q/kt are introduced. The ideality factor is set to n = 1, since the latter is not a physical quantity. Before proceeding further, it is necessary to explain why the Schottky effect of lowering the barrier height is ignored, as well as corrections for the electric field dependence of mobility µ(f) [3]. Firstly, it is generally not justified to introduce a unique electric field intensity as F = U/d, d being the thickness of the thin film, while having several space charge regions throughout the film. Secondly, as will be shown further, Eq. (1) makes it possible to obtain the current I through a Schottky barrier as a function of a single variable U, thereby mediating a closed analytical solution for I(U) without the knowledge of the doping level. An inspection of the electrical circuit in Fig. 1 shows two diodes D 1, D 2, respectively, separated by the equivalent resistance R x of the bulk. The direction of the steady-state (positive) current I corresponds to a positive applied external bias which is divided among the three circuit elements (zones). The division is expressed through a set of equations: ( ) I = K1 exp au1 1, (2) I U 2 =, (3) Rx ( ) I = K2 1 exp au3, (4) U = U + U + U (5) x I D 1 R x D 2 U 1 U 2 U 3 Fig. 1 Simplified equivalent circuit of a metal/organic/metal device operating in thermionic emission mode. The direction of the current I corresponds to > 0.

3 164 I. Thurzo et al.: Thermionic emission-limited current voltage curves of MOM devices K 1 = A R x =10 6 Ω T=300K Fig. 2 Calculated current-voltage characteristics of a metal 1 /organic/metal 2 system, the symbols K i (i = 1, 2) denote the saturation currents of the two Schottky diodes. Enclosed are all the fixed parameters, the free parameter being the saturation current K K 2 /A: After defining another symbol b = K 1 /K 2, Eq. (5) reads ( ) ( ( )) Ux = U1 + K1Rx exp au1 1 a ln 1 + b 1 exp au 1. 1 { } To find U 1 and then I by means of Eq. (2), Eq. (6) has been solved by iteration. Note that in the case of the real solution ( > 0) the iteration should start at U 1 satisfying the condition 1 1+ b U1 < a ln. b (7) A few general features of the resulting I versus characteristics emerge from an inspection of Fig. 2, the curves corresponding to a unique temperature T = 300 K. Firstly, at higher negative biases the saturation current is limited by the emission capability of the reverse biased diode D 1 (K 1 ). As expected, just the opposite is true for positive biases, unless a further increase in emission (saturation) current K 2 is counteracted by the series resistance R x = 10 6 Ω. If dealing with a relatively low R x, the injecting contact is, unlike the currently accepted concept, not the one limiting the current at biases in excess of a few kt/q. Secondly, at biases below the latter limit the analysis of the net current should comprise all the elements (zones) involved. Now, the question whether an asymmetry in IV curves at the two polarities (which is much smaller than that corresponding to the difference in the work functions of the two metals applied to the organic layer) is an argument against the concept of thermionic emission, or not, is discussed. With reference to Fig. 3, showing the impact of the series resistance R x on the asymmetry of simulated I curves, the (6) R x /Ω: K 1 = A K 2 = A T = 300 K Fig. 3 A transition from asymmetrical to a fairly symmetrical I behavior is observed for higher series resistances R x. The distortion of the I curve belonging to R x = 10 9 Ω is due to the inaccuracy of the iteration procedure used.

4 phys. stat. sol. (a) 201, No. 1 (2004) / φ 10-6 T/K: b > E R 0 =3x10 3 Ω E = 0.15 ev φ b =0.3eV A * =1.2x AK Fig. 4 A set of simulated I curves of a metal/organics/metal device taken for different temperatures at 10 K steps corresponds to the case of identical barrier heights φ b. The quantity E is the thermal activation energy of conductivity expressed as σ(t) = σ 0 exp ( E/kT). answer is that it is not. Fairly symmetrical I curves are obtained in the case of bulk-limited currents, without any clear tendency to reach saturation at ultimate biases. To shed more light on the mechanism of charge transfer, I V measurements at different temperatures are mandatory, as exemplified further. 3 Temperature dependence of IV curves As already mentioned above, it should be distinguished between thermionic emission- and bulk-limited currents. Since generally the two cases lead to a different temperature dependence of IV curves, a proper analysis should not only help to identify the dominant mechanism of the transport for each temperature range, but also to extract correctly either the barrier heights at the interfaces, or electrical conductivity of the organic material. Denoting the thermal activation energy of the specific conductivity σ(t) by E, the equivalent series resistance is expressed as R x E = R0 exp, kt (8) R 0 being a constant containing the preexponential factor σ 0 in conductivity and geometry of the organic thin film. A more rigorous treatment should admit nonlinearity of R x (U 2 ) with bias, however, for the moment the interest is devoted mainly to I(T, ) at a selected. The physically more correct approach -26 ln(t -2 I/K -2 A) δe HT =0.13eV R 0 =3kΩ E = 0.15 ev φ b =0.3eV A * =1.2x AK -2 : δe LT =0.30eV 2.0x x x x10 20 (kt) -1 /J -1 Fig. 5 Arrhenius plots derived from the data of Fig. 4 for 0.1 V and 0.5 V, respectively, are shown. In the case of = 0.1 V there is a deviation of the slope at higher temperatures (δe HT = 0.13 ev) from that of δe LT = 0.3 ev at low temperatures. The deviation is an indication of the barrier-to bulk-limited current transition.

5 166 I. Thurzo et al.: Thermionic emission-limited current voltage curves of MOM devices 10-3 T/K: φ < E 10-4 b 350 Fig. 6 Temperature dependence of I characteristics for the case φ b < E is shown R 0 =0.1Ω E =0.3eV φ b =0.15eV A * = 1.2x AK would admit a space-charge limited current density J flowing through the neutral zone of thickness d i between the barriers: 2 9εεµ 0 U2 J =. (9) 3 8d i The symbols ε 0 and ε correspond to the permittivity of vacuum and the dielectric constant of the organic material, respectively. Then the equivalent resistor (per unit area) would read R 3 = U2 8di xs. J = 9εεµ 0 U (10) 2 Nevertheless, as long as d i remains unknown, there is no unique solution to the set of equations presented above. The issue of the spatial profile of the potential will be discussed later in this paper. The analysis of the temperature dependent currents I(T, ) begins with the case φ b > E (Fig. 4), taking the same barrier height φ b for both diodes. Then the data was processed via Arrhenius plot representation as ln (T 2 I) versus (kt) 1 to comply with the temperature dependence of the saturation current limited by the barrier height see Fig. 5. Selecting = 0.1 V, this is correct for the low-temperature ev : ln(t -2 I/K -2 A) δe HT =0.22eV =-0.1V R 0 =0.1Ω E =0.3eV φ b =0.15eV δe LT = ev A * = 1.2x AK ev 2.0x x x x10 20 (kt) -1 /J -1 Fig. 7 Arrhenius plots derived from the data of Fig. 6 for 0.1 V and 0.5 V, respectively, are shown. At low temperatures the current is always limited by the bulk resistance R x = R 0 exp ( E/kT). The slope δe LT = ev corresponds to 0.3 ev in a ln (I) versus (kt) 1 representation. In the case of = 0.5 V the current is barrier-limited at high temperatures.

6 phys. stat. sol. (a) 201, No. 1 (2004) / U 1 U 2 (IR x ) U 3 1x 8x 6x Fig. 8 The applied potential is shared by the three zones (cf. Fig. 1). For the given set of parameters the potential drop U 2 across R x dominates at 0.2 V. U i K 1 = A K 2 = A R x =10 6 Ω T = 300 K x 2x 0-2x region (squares), at elevated temperatures the current is limited by the series resistance R x (T) cf. Eq. (8). The corresponding thermal energy δe = 0.13 ev is lower than the input value of E = 0.15 ev. The choice of E means that once the electron has been injected to the transport band of such an energy width, it migrates within this band via thermally assisted hopping. Here is not considered temperature dependence of the (T/T 0 ) n type familiar with crystalline semiconductors at low temperatures (T 0 and n being constants). Hence the correct value of the activation energy of the high-temperature branch of conductivity should be obtained if using ln (I) versus (kt) 1 format for the Arrhenius plot. Considering = 0.5 V, a bias that corresponds to reaching saturation of the current, the emission capability of the D 1 (K 1 ) is limiting the current in the whole temperature region (200 K 350 K, circles). The question arises, whether the thermal activation of the conductivity is due to either the temperature dependent mobility of charge carriers or due to changes of the number of free charge carriers with temperature. The latter contribution to the charge transport, induced by ionization of deep traps at elevated temperatures, cannot be excluded. When including this contribution, inevitably is needed an expression for the temperature as well as bias dependence of occupancy of traps. The reasoning based on the temperature dependent mobility of injected charge carriers within an energy band of shallow localized states is more convincing here. The IV behavior of the same system while keeping constant all the parameters but R 0, and interchanging the values for E and φ b (φ b < E), respectively, is explored in Fig. 6. The related Arrhenius plots belonging to biases 0.1 V and 0.5 ev, respectively, are plotted in Fig. 7. The case of = 0.1 V (squares) is a nice illustration of the complexity of the current response at low biases, the energy δe HT observed at higher temperatures lying somewhere between φ b and E. On the other hand, the lowtemperature limit δe LT is a correct transform of E to the ln (T 2 I) versus (kt) 1 format. Before turning to experimental data, a comment on the potential distribution throughout the metal/organic/metal structure is added. From the model presented above is possible to assess the potential distribution among the three zones (Fig. 8), without specifying the spatial profile of the potential. The latter is usually obtained from electro absorption data, as documented for both electrochemical light emitting diodes (LECs) [9, 10] and OLEDs [11, 12]. Those interested in the specific conductivity σ(t) = σ 0 exp ( E/kT) of the organic have to search for a bias such that U 2 U 1, U 3, and try the approximation σ 0 d E exp, RS kt 0 (11) assuming S to be the area of the contact and d (width of zone 2) being not much smaller than the thickness of the organic thin film.

7 168 I. Thurzo et al.: Thermionic emission-limited current voltage curves of MOM devices -2-4 T/K: 350 Ag/PTCDI(200nm)/n-GaAs Fig. 9 A set of measured I characteristics of an Ag/Dimethyl-PTCDI/n-GaAs diode measured at 10 K steps in high vacuum is shown. -6 log 10 () Experiment N, N -dimethyl 3, 4, 9, 10 perylenetetracarboxylic diimide (Dimethyl-PTCDI) modified Ag/Dimethyl-PTCDI/n-GaAs diodes were prepared by means of organic molecular beam deposition in ultra high vacuum of the organic material on heavily doped (n cm 3 ), sulphur-passivated n-gaas wafers, the nominal thickness of PTCDI amounting to 200 nm. Details about preparation of such diodes have already been published [14]. The top Ag contacts were evaporated in situ through a shadow mask, the diameter of the circular contacts being 0.5 mm, the applied bias corresponds to this electrode. The ohmic back contact to the GaAs wafer consists of an In-Ga alloy. The IV measurements were conducted in a cryostat under high vacuum >10 4 mbar (HV) conditions at temperatures ranging from 100 K to 350 K. A HP4140B picoammeter was used to record the IV curves. I(T) characteristics of the Ag/Dimethyl-PTCDI/n-GaAs diodes, taken at 10 K steps within the temperature interval from180 K to 350 K, are plotted in Fig. 9. Rectification is observed throughout the whole temperature interval, positive biases corresponding to forward currents. For the sake of assessing the thermal activation of both reverse and forward currents, two sets of I(T) values for equal to 0.3 V and 0.3 V, respectively, were considered. It was chosen negative bias with regard to the possible formation of an inversion layer at higher negative biases, the positive bias value is safe with respect to the undesired excess heating of the PTCDI/n-GaAs junction by ultimate forward currents ev Ag/PTCDI(200 nm)/n-gaas =-0.3V ev 2.0x x x x x10 20 (kt) -1 /J -1 Fig. 10 A semilogarithmic plot of the current I versus (kt) 1 corresponding to the Ag electrode biased at = 0.3 V. The asymptotic thermal activation energies were determined from the two slopes recalculated as ln (I) versus (kt) 1.

8 phys. stat. sol. (a) 201, No. 1 (2004) / Ag/PTCDI(200 nm)/n-gaas data linear fit =0.3V 0.29 ev Fig. 11 A semilogarithmic plot of the current I versus (kt) 1 corresponding to the Ag electrode biased at = 0.3 V. Now a unique slope of the ln (I) versus (kt) 1 dependence has been taken in order to assess the thermal activation energy of the current as δe 0.29 ev. The latter may correspond to the position of the LUMO of Dimethyl-PTCDI with respect to the Fermi level of Ag. 2.0x x x x x10 20 (kt) -1 After replotting the I(T, ) data that belongs to = 0.3 V in a semi-logarithmic I versus (kt) 1 format (Fig. 10), there are two distinct branches characterized by the two thermal activation energies of 0.30 ev ± 0.02 ev at low temperatures and 0.65 ± 0.02 ev at temperatures above the room temperature, respectively. When trying to take the quantity IT 2 for the Y-axis, slightly lower values are obtained, the difference is still falling within the experimental error, as proved in the previous section. The situation has changed drastically after going to = 0.3 V, as evident from Fig. 11. Now there are only small deviations from the unique slope corresponding to the forward current thermally activated by 0.29 ev ± 0.02 ev. A tentative explanation is provided, based on the model outlined above. The Dimethyl-PTCDI layer is supposed to be an electron transporting material, i. e. both the Ag and n-gaas electrodes act as cathodes when interfaced with Dimethyl-PTCDI. Applying a negative ( forward ) potential to the Ag electrode, it is injecting electrons while the polarity of the n-gaas electrode is consistent with having a Dimethyl-PTCDI/n-GaAs diode under reverse bias. As a matter of fact, the thermal energy of 0.65 ev from Fig. 10 is consistent with the range of barrier heights of the sulphur-passivated n-gaas (from our laboratory) with respect to the Fermi level of the system, the barrier limiting the net current at = 0.3 V at elevated temperatures. After the bias reversal ( = 0.3 V) the Ag/Dimethyl-PTCDI diode experiences a reverse bias, now the barrier height φ b 0.3 ev of the latter diode is limiting the current in the entire temperature interval explored. The energy offset φ b may correspond to that of the transport band (LUMO) of Dimethyl-PTCDI with respect to the Fermi level of Ag. One cannot exclude a situation when the series bulk resistance R x of PTCDI is limiting the current at a subinterval of temperatures under > 0, provided the Fermi level position in the bulk is the same as that at the Ag/Dimethyl-PTCDI interface. This is true, of course, if the bulk conductivity of Dimethyl-PTCDI is correctly expressed as σ = σ 0 exp ( (LUMO E F )/kt), σ 0 being essentially independent of temperature. Apart from this issue, there is a need to explain the I(T) behavior under < 0 at low temperatures. Bearing in mind that the conduction band E c in the bulk of the heavily doped n-gaas is almost in coincidence with the Fermi level E F, tunneling of electrons from the LUMO of PTCDI through the narrow barrier (depletion layer) of n-gaas directly to E c is likely the charge transport mechanism at low temperatures. Then the only barrier to the charge transport is the thermal energy of 0.3 ev which is necessary to raise an electron from Ag to the LUMO of Dimethyl-PTCDI. The gradual increase of the thermal energy with temperature at < 0 may remind the qualitatively similar results reported by van Woudenbergh et al. [13] for hole injection in poly-dialkoxy-p-phenylene vinylene. They explained the behavior in terms of a hopping transport through a Gaussian distribution of localized states induced by the disorder in the material with an extremely low mobility of charge carriers (µ cm 2 s). The perylene derivatives such as PTCDA and PTCDI are known as well-ordered materials with discotic structure, exhibiting electron mobility close to 10 2 cm 2 s at ambient tempera-

9 170 I. Thurzo et al.: Thermionic emission-limited current voltage curves of MOM devices ture. In addition, the slope of the low-temperature asymptote matches the unique slope of the equivalent plot obtained for positive. It remains, of course, to be mentioned the source of the unintentionally introduced dopants at the top Ag/PTCDI interface. One is likely to be dealing with contamination, taking place in the course of the transfer of the samples from the UHV chamber to the HV cryostat, during which step the sample had been exposed to air. 5 Conclusion The simplified model of two back-to-back connected diodes separated from one another by a series resistance has confirmed the importance of the charge extracting contact of a single-layer metal/ organics/metal device when analyzing IV behavior. Mainly at biases of a few kt/q the system is to be treated as a whole. For obtaining the potential distribution among the three zones, only the case of Richardson Schottky thermionic emission has been considered, yet there is little doubt that a similar conclusion would apply to the case of Fowler-Nordheim tunneling also. Dealing with thick enough organic films, it should be possible to find bias and temperature such that the current is bulk limited (bulk traps included if present). To identify this situation it is useful to apply two metals with different barrier heights and check whether there is a symmetry of the IV branches at opposite polarities of the bias. Then after neglecting the potential drop across the two barriers, temperature dependence of the specific conductivity of the organic material can be deduced from IV measurements at different temperatures. In cases of asymmetrical IV branches there is a chance to assess both barrier heights involved, as exemplified experimentally. References [1] W. Brütting, S. Berleb, and A. G. Mückl, Org. Electron. 2, 1 (2001). [2] W. Brütting, M. Meier, M. Herold, S. Karg, and M. Schwoerer, Chem. Phys. 227, 243 (1998). [3] J. C. Scott, J. Vac. Sci. Technol. A 21, 521 (2003). [4] J. C. Scott and G. G. Malliaras, Chem. Phys. Lett. 229, 115 (1999). [5] H. Bässler, phys. stat. sol. (a) 175, 15 (1993). [6] V. I. Arkhipov, E. V. Emelianova, Y. H. Tak, and H. Bässler, J. Appl. Phys. 84, 848 (1998). [7] M. A. Baldo and S. Forrest, Phys. Rev. B 64, (2001). [8] S. M. Sze, Physics of Semiconductor Devices (John Wiley & Sons, New York, 1981). [9] J. C. demello, J. J. M. Hals, S. C. Graham, N. Tessler, and R. H. Friend, Phys. Rev. Lett. 85, 421 (2000). [10] J. Gao, A. J. Heeger, I. H. Campbell, and D. L. Smith, Phys. Rev. B 59, R2482 (1999). [11] S. J. Martin, G. L. B. Verschoor, M. A. Webster, and A. B. Walker, Org. Electron. 3, 129 (2002). [12] B. Ruhstaller, S. A. Carter, S. Barth, H. Riel, W. Riess, and J. C. Scott, J. Appl. Phys. 89, 4575 (2001). [13] T. van Woudenbergh, P. W. M. Blom, M. C. J. M. Vissenberg, and J. N. Huiberts, Appl. Phys. Lett. 79, 1697 (2001). [14] D. R. T. Zahn, T. U. Kampen, and H. Mendéz, Appl. Surf. Sci , 423 (2003).