we Journal of JET v°iume 8 (2015) p.p. 17-30 Issue 2, October 2015 Typology of article 1.01 Technology www.fe.um.si/en/jet.html THE INVERTED DISTORTED PARABOLA-LIKE SHAPE OF THE BIAS-DEPENDENT ELECTRIC FIELD AT AN ELECTRON-INJECTING METAL/ORGANIC INTERFACE DEDUCED USING THE CURRENT-VOLTAGE METHOD OBRNJENA, DEFORMIRANI PARABOLI PODOBNA ODVISNOST ELEKTRIČNEGA POLJA OD PRITISNJENE NAPETOSTI NA VMESNI PLOSKVI KOVINA/ORGANSKI POLPREVODNIK IZPELJANA Z UPORABO METODE TOKOVNE KARAKTERISTIKE Matjaž KoželjR Bruno Cvikl1 Keywords: Metal-organic interface, Electric field, Bias-dependent interfacial field, Current density modelling, Effective electron mobility, Organic semiconductors Abstract Using the recently derived expression for the traditional Mott-Gurney charge-drift model extended by the non-zero electric field at the charge-injecting interface E.nt, the published dependence of the R Corresponding author: Matjaž Koželj, MSc, Tel.: +386 1 588 5277, Fax: +386 1 588 5376, Mailing address: Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia E-mail address: matjaz.kozelj@ijs.si 1 Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia, and University of Maribor, Faculty of Energy Technology, Hočevarjev trg 1, 8270 Krško, Slovenia JET 17 Matjaž Koželj, Bruno Cvikl JET Vol. 8 (2015) Issue 2 current density on the applied electric field j-Ea for two good-ohmic-contact, electron-only, metal/ organic structures is analysed. It is argued that the Mott-Gurney law with the well-known empirical exponential bias-dependent mobility included, in spite of a very good fit to the j-Ea measurements, represents an unsatisfactory method for data analyses. It is shown that the internal electric field at the electron-injecting interface is strongly bias dependent, and in such a way is coupled to the electron current within the organic bulk. The bias dependence of the interfacial field resembles an inverted, distorted, parabola-like-shaped curve, the maximum of which is organic-material dependent. Beyond the maximum, which occurs at high values of the externally applied electric field Ea, the interfacial electric field E exhibits a rapid decrease towards zero, and only at this limit can the traditional Mott-Gurney law be applied. In contrast to the present notion, it is found that the (large) electron effective mobility for the two samples investigated does not change with the bias, but it is the total effective mobility (its product with the specific non-linear algebraic function of Ea) that is bias dependent. The effective mobility may be uniquely determined, providing the applied electric field spans a sufficiently wide Ea interval. It is argued that an appropriate width of this interval may be tested by the judicious application of the derived expression in the limit E ® 0. The Alq3 bias-dependent interfacial electric field at the electron injecting cathode/organic junction results in a non-linear response of the corresponding free electron density, nfree(L=200 nm), at this site. The possibility for an investigation of the electric field at the charge-injecting metal/organic interface using the j-V method is therefore outlined. Povzetek V prispevku je analizirana odvisnost tokovne gostote od pritisnjenega električnega polja j-Ea za primer dveh struktur kovina/organski polprevodnik, katerih značilnost so dobri ohmski kontakti in elektronsko prevajanje toka, pri čemer smo uporabili nedavno izpeljano enačbo za konvencionalni Mott-Gurney model dopolnjen z od nič različnim električnim poljem na vmesni ploskvi. Dokazano je, da Mott-Gurneyev zakon z vključeno empirično eksponentno odvisnostjo, kljub dobrem ujemanju z j-Ea meritvami, ne predstavlja zadovoljivo metodo za analizo podatkov. Pokazali smo, da je električno polje na vmesni ploskvi, na kateri poteka vbrizgavanje elektronov, močno odvisno od pri-tisnjene napetosti in tako povezano z elektronskim tokom skozi organski polprevodnik. Odvisnost električnega polja od pritisnjene napetosti je podobna obrnjeni, deformirani paraboli podobni krivulji, katere maksimum je odvisen od vrste organskega materiala. Konvencionalni Mott-Gurneyev zakon je možno uporabiti v limiti, ko električno polje na vmesni ploskvi, E , preseže maksimum in se potem hitro zmanjša do nule, kar se zgodi pri visokih vrednostih pritisnjene napetosti. Za razliko od trenutno veljavne razlage smo ugotovili, da se (velika) efektivna elektronska mobilnost v dveh raziskanih vzorcih ne spreminja s pritisnjeno napetostjo, pač pa je celotna efektivna mobilnost (produkt efektivne mobilnosti s specifično nelinearno algebraično funkcijo Ea) odvisna od pritisnjene napetosti. Efektivno mobilnost je možno določiti izključno pod pogojem, da se pritisnjeno električno polje spreminja v dovolj širokem intervalu. Dokazano je, da je primernost tega intervala možno preveriti s primerno uporabo izpeljanega izraza v limiti E ® 0. Električno polje na vmesni ploskvi katoda/organski polprevodnik Alq3, na kateri poteka vbrizgavanje elektronov, ki je odvisno od pritisnjene napetosti, ima za posledico nelinearni odziv ustrezne gostote prostih elektronov, nfree(L=200 nm), na tem mestu. Podana je možnost za raziskave električnega polja na vmesni ploskvi kovina/ organski polprevodnik, kjer poteka vbrizgavanje naboja, s pomočjo j-V metode. 18 JET The inverted distorted parabola-like shape of the bias-dependent electric field at an electron-injecting metal/organic interface deduced using the current-voltage method 1 INTRODUCTION An understanding of the intrinsic charge-transport properties is vital to the optimum operation of any electronic device that is based on organic semiconductors. Such devices currently used in practical applications include flat-panel displays, organic solar cells, flexible electronics, solidstate lighting, etc. An important step towards the widespread additional application of organic electronic devices is the continuous striving for a fuller understanding of the numerous factors that are currently limiting their performance. Considerable research has been devoted to uncovering the exact operation mechanisms of such devices and to a precise determination of their electrical and optical properties. In this respect, two important issues that have received a great deal of attention recently are the effects of the organic electron and hole layers on the efficiencies of devices, [1], and the exact role of chemical impurities, [2], which may either hinder or enhance the performance of the device. Both issues are intimately related to an investigation of the intrinsic charge-carrier mobility, [3-5], which is often measured using the current-voltage method, admittance spectroscopy, the time-of-flight method and transient electroluminescence. This work is focused on a determination of the electron mobility within a single organic layer using the current-voltage method. It represents the extension of a related investigation on hole charge carrying, [6], with the aim being to dispense with the charge-density singularity at the charge-injecting metal/organic interface that characterizes the well-known Mott-Gurney law. The Mott-Gurney expression, incorporated with the empirical exponential bias-dependent mobility, [7], is of paramount importance for the charge-carrier mobility determination using the current-voltage method. It has been shown recently, [6], that the existence of a non-zero interfacial electric field at the charge-injecting metal/organic junction causes the extinction of the singularity of the free-charge density that the Mott-Gurney law predicts. The investigation of the published j-V data obtained on two distinct organic structures, characterized by a series of single organic layers that differ in thickness, has shown that the effective hole mobility (to be distinguished from the total hole mobility) is bias independent. It was shown in the literature that the well-known empirical exponential bias-dependent mobility, [7], is an artefact that should be replaced by a derived, nonlinear algebraic expression that depends only on the ratio of the interfacial field to the externally applied electric field [6]. However, assuming a non-zero bias-independent interfacial electric field at the electron-injecting cathode/organic interface, Eint, it is not possible to describe the electron-only current-voltage, j-V, data of the good-ohmic-contact, single-layer organic structures of Yasuda et al., [8]. However, these data have been analysed by the authors in terms of the Mott-Gurney law that includes the empirical exponential bias-dependent mobility, and a very good fit was obtained; see Figs. 4 and 5 of Ref. [8]. In this work, it is shown that the electron-only current density within the two organic structures investigated in Ref. [8] is strongly coupled to the bias-dependent internal electric field existing at the electron-injecting interface. The bias dependence of the interfacial electric field, Ent, is explicitly revealed for the published j-V data [8] for two metal/organic structures. For small applied fields Ea, it is shown that the interfacial electric field of both structures coincides and exhibits a linear increase with an increasing external electric field Ea, a behaviour that is apparently independent of the organic composition. At a certain value of Ea, which is organic-material dependent, the straight line transforms into an inverted distorted parabola-like curve, JET 19 Matjaž Koželj, Bruno Cvikl JET Vol. 8 (2015) Issue 2 rapidly decreasing to a value close to zero. This small value of Eint apparently occurs when the last, the maximum, value of the current density in the j-Vdiagram is reached. If Eint turns out to be negligibly small at the maximum value Eamax of the Ea interval, then the traditional Mott-Gurney limit is attained. The effective mobility within the electron-only, single-layer, metal/organic structure investigated in this work turns out to be bias independent. As shown earlier in [6], apart from the Ea2 term, the additional external bias dependence of the current density is provided by the previously derived, non-linear algebraic function of the argument X(Ea) = E|ntE^, which is ~a implicitly and explicitly dependent on the external electric field. This fact offers an indication that the processes that determine the electron mobility differ from the ones that determine the hole mobility. In this work, it is once again confirmed that the empirical exponential bias-dependent function for the effective mobility is redundant, within the range of the j-V measurements. 2 THEORETICAL OUTLINE It can be easily verified that the drift-current density in a single-layer organic structure is, irrespective of the sign of the charge carriers, described by the expression, [6], . _ ssoMeff E 2 J _ 2L a i 8 2 I 64 4 9 3X_27X (2.1) where Ea is the externally applied electric field, defined as Ea = Va/L, and Va is the applied bias on the anode placed at the origin of the frame of reference (the cathode at x = L is at zero potential), j is the current density through the metal/organic structure, ¡ueff is the effective mobility, £ is the dielectric constant and £0 is the permittivity of free space, [6]. The current density, j, Eq. (2.1) replaces the well-known generalized Mott-Gurney model (in the sense that the empirical, [7], exponential bias-dependent charge mobility is included in the expression) of charged traps in the organic layer for completely empty (or equivalently, completely full) or the stated model, if the non-zero interfacial electric field, Eint, occurring at the charge-injecting metal/organic interface is taken into account. Here, the parameter X denotes the ratio of the non-zero electric field at the charge-injecting interface, Eint, to the externally applied electric field, Ea, X = (2.2) Ea where Eint might be bias dependent The introduction of the interfacial field results in the disappearance of the free-charge-density singularity at the stated interface, a serious shortcoming of the above-mentioned, generalized Mott-Gurney model. Of equal importance is the fact that in Eq. (2.1) the effective mobility |eff is bias independent and the bias dependence is described in terms of the non-linear algebraic expression, which is a function of the parameter A. Evidently, for Eint = 0, Eq. (2.1) reduces to the (original) Mott-Gurney model with a bias-independent effective mobility. In Ref. [6], Eq. (2.1) was tested on the published j-V data obtained on two different sets of single-layer, hole-only, metal/organic structures and good agreements with the measurements were obtained. For holes, it was shown that the interfacial electric field is bias independent and just slightly smaller than the initial value of the externally applied electric field. It was also explicitly shown that the effective mobility of the holes is thickness dependent, 20 JET 8 The inverted distorted parabola-like shape of the bias-dependent electric field at an electron-injecting metal/organic interface deduced using the current-voltage method but bias independent. Furthermore, it was shown that the empirical exponential bias-dependent effective hole mobility is redundant in j-V experiments since it represents merely an approximation of the derived algebraic expression represented by Eq. (2.1). It can be easily shown that the expression for the current density j, i.e., Eq. (2.1), is invariant with respect to the sign of a drifting charge carrier within a single organic layer and is consequently also valid for electrons. Consequently, the spatial dependence of the internal electric field E(x) reads, EX) = E + j-(L-x) V ss0/eff (2.3) and the spatial dependence of the electric potential V(x), taking into account that V(L) = 0, is then: V(x) sso/eff 3j(Ee ) 2 + ^Zo^o Eint + j(Ee ) (L-x ) - Ei3 and the free-electron (number) density no(x) reads: j(Ee , q/oo no(x) ■s0e CE (x ) q Cx E2nt +j1 (L-x ) (2.4) (2.5) ss. 0 Veoo In Eq. (2.5) d denotes the ratio of the free to the total (free and the bound) charge densities [9], d = 'o and the effective mobility [9] is defined as neoo = n d. (nî + nb ) Evidently, in the limit Einl = 0, Eq. (2.1) reduces to: j(Ee) = 9 ^E2 8 L (2.6) the well-known Mott-Gurney expression, which in combination with the empirical exponential bias-dependent mobility of Gil, [7] neoo = no exp ) (2.7) has been in current-voltage, j-V, experiments exclusively used for the determination of the charge mobility. For Eint # 0, the curve evaluated by the combination of Eqs. (2.6) and (2.7) may, within the relevant interval of Ea, coincide with Eq. (2.1), see Ref. [6]. Here, the two parameters Ho and y are determined from the fit to the experimental data, but have no clear physical meaning. However, as pointed out in Ref. [6], the combination of Eqs. (2.6) and (2.7) is incomplete, exhibiting a singularity of the free-charge density at the charge-injecting interface, see Eq. (2.5), and it should be substituted by the corresponding Eq. (2.1). This assertion was already empirically proved for hole charge carriers, [6], and so its extension to the electron current density is the subject of the work presented here. 1 JET 21 Matjaž Koželj, Bruno Cvikl JET Vol. 8 (2015) Issue 2 3 BIAS DEPENDENCE OF THE INTERFACIAL ELECTRIC FIELD Yasuda et al. [8] used the current-voltage method to investigate the electron mobility of six different electron-only, single-layer organic structures characterized by a quasi-ohmic contact. It should be emphasized that all the data were analysed in terms of Eqs. (2.6) and (2.7), since an excellent agreement between the calculated curves and the measurements was obtained, see Figs. 4 and 5 of Ref. [8]. For the purposes of this work, the interval of the externally applied electric field constitutes indispensable information for the application of Eq. (2.1). For two of the six organic structures, i.e., tris-(8-hydroxyquinoline), denoted as Alq3, and 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline, known as the BCP organic material, this information is clearly revealed, see Figure 2 of Ref. [8]. As a result of the excellent agreement between the data and the calculated fit shown in Ref. [8], in this work the data will be represented in terms of Eqs. (2.6), and (2.7) for the following values of the parameters, [8]: /j.0 = 4.7 x 10-13 m2/Vs and y = 6.9 x 104 (m/V)1/2 valid within the interval of the bias 1 V < Va < 20 V for the Alq3 organic, and Ho = 2.3 x 1012 m2/Vs and y = 11.0 x 10-4 (m/V)1/2 valid within the interval of the bias 3 V < Va < 15 V for the BCP structure. In both cases, an average value [8] L = 200 nm was taken as the layer thickness in the calculations. It is clear that because of the considerable disagreement between the two curves shown in Figure 1, the interfacial electric field Eint may not be constant in the experiment of Yasuda et al. [8]. In order to test the hypothesis, the current density of Eq. (2.1) at a given Ea should equal the corresponding data (i.e., using Eqs. (2.6), and (2.7) for convenience) and the parameter X is then deduced as a real root of the expression, Meff 9 - 312+i 81 _ 3 a + sa3 - 2712 8 2 I 64 4 8 ßoexp W ) (3.1) The obtained value of X and the associated value of the interfacial electric field at the electron-injecting interface Eint are presented in Table 1. Using these values in Eq. (2.1), the two curves presented in Figure 1 then coincide to an excellent degree. The deduced bias dependence of Eint for the Alq3 organic (circles) is presented in Figure 2. 9 4 22 JET The inverted distorted parabola-like shape of the bias-dependent electric field at an electron-injecting metal/organic interface deduced using the current-voltage method 2 4 6 8 10 Ea[x 107 V/m] Figure 1: The room-temperature j-Ea data of the electron-only, good-ohmic-contact, Al/Alq3(200 nm) structure are within the complete interval 5 MV/m