Organic Zener Diodes: Tunneling across theGap in Organic Semiconductor MaterialsHans Kleemann,*,† Rafael Gutierrez,‡ Frank Lindner,† Stanislav Avdoshenko,‡Pedro D. Manrique,‡ Bjorn Lussem,‡ Gianaurelio Cuniberti,‡,§ and Karl Leo†

† Institut fur Angewandte Photophysik and ‡Institute for Materials Science and Max Bergmann Center forBiomaterials, Technische Universitat Dresden, 01069 Dresden, Germany and §National Center for NanomaterialsTechnology, POSTECH, Pohang 790-784, Republic of Korea

ABSTRACT Organic Zener diodes with a precisely adjustable reverse breakdown from -3 to -15 V without any influence on theforward current-voltage curve are realized. This is accomplished by controlling the width of the charge depletion zone in a pin-diodewith an accuracy of one nanometer independently of the doping concentration and the thickness of the intrinsic layer. The breakdowneffect with its exponential current voltage behavior and a weak temperature dependence is explained by a tunneling mechanismacross the highest occupied molecular orbital-lowest unoccupied molecular orbital gap of neighboring molecules. The experimentaldata are confirmed by a minimal Hamiltonian model approach, including coherent tunneling and incoherent hopping processes aspossible charge transport pathways through the effective device region.

KEYWORDS Organic semiconductors, organic pin-diodes, molecular doping, tunneling, Zener diodes

In the past few years, the physical properties of organicsemiconductors have been studied with considerabledetail. Despite the fact that there is still a limited under-

standing of the relevant microscopic charge transport sce-narios in such systems, various organic electronic devicessuch as efficient organic light-emitting diodes (OLEDs),1,2

organic memory cells,3 organic field-effect transistors,4

vertical triodes,5 and high-frequency diodes6 have beensuccessfully demonstrated.

The main difference between inorganic and organicsemiconductors is that the latter usually do not display (atroom temperature) bandlike transport through delocalizedstates, but rather exhibit hopping of carriers between spa-tially localized states. This can either happen as electrontransport through the lowest unoccupied molecular orbitals(LUMO) or hole transport through the highest occupiedmolecular orbitals (HOMO). Typically, this results in mobili-ties three or more orders of magnitude below those of bandtransport and an entirely different temperature dependence,that is, an increase of mobility with increasing temperature,can be obtained.

In inorganic semiconductors, there are a number of basictransport effects that involve more than one band, forexample, interband (Zener) tunneling or avalanche break-through.7,8 While these effects are now understood in detailfor inorganic semiconductors, they have not been experi-mentally studied in detail for organic semiconductors so far.Because of the structural complexity of organic semiconduc-tors, the theoretical study of their charge transport properties

is also quite challenging, so that theoretical studies areusually limited to structurally ordered systems.9-12 A keyelectronic device based on the Zener effect, the Zener diode,is crucial for basic electrical circuit requirements, such asvoltage- and temperature stabilization and overvoltage pro-tection. An organic Zener diode with an adjustable break-down is still missing. Likewise Zener diodes are key ele-ments for passive matrix memory arrays,13 where Zenerdiodes are essential to prevent parasitic current flow throughnonselected crosspoints. The required parameters for theZener diode are given by the read-, write-, and erase voltagesof the memory.14

In the letter, we investigate the HOMO-LUMO Zenertunneling in an organic semiconductor system by detailedmeasurements of the reverse currents in organic pin-diodes.In particular, we provide evidence for the tunneling natureof the reverse currents by showing a strong influence of theeffective tunnel barrier and a very weak temperature de-pendence. To get a first insight into the possible chargetransport mechanisms, we complement the experimentalinvestigations by an effective low-dimensional model thatis then treated in two limiting physical situations: incoherenthopping transport and coherent tunneling. Our results sug-gest that both mechanisms may exist in the system understudy in dependence of the sign of the applied voltage.

Experimental Section. We address Zener tunneling inthe reverse current regime of organic pin-diodes. The break-through properties of such devices have only been rarelyinvestigated, see, for example, ref 15. The advantage of thepin-diode concept16 is that the geometry and the potentialswithin the semiconductor layers can be controlled veryprecisely, thus allowing the study of the tunneling effects,which sensitively depend on minute variations of these

*To whom correspondence should be addressed. E-mail: Hans.Kleemann@iapp.de.Received for review: 08/17/2010Published on Web: 10/27/2010

pubs.acs.org/NanoLett

© 2010 American Chemical Society 4929 DOI: 10.1021/nl102916n | Nano Lett. 2010, 10, 4929–4934

parameters, in a very controlled manner. Thus, the tunnelingcurrent is independently tunable by two parameters: thethickness of the intrinsic interlayer (IIL) and the dopingconcentration of the electron and hole transport layers (ETL/HTL). Doping changes the charge carrier concentration17 andwidth of depletion regions.18 Furthermore, one obtains abarrier-free transport until the charge carriers reach the IIL.19

In contrast, the IIL acts as an additional depletion layer andthe voltage drop over the pin-junction mainly occurs in thisintrinsic layer.19 A comparative study of organic pn- and pin-junctions comprising doped organic layers would be desir-able. However, as we will show in this letter the typical widthof the native depletion zone in the doped layers is less than3 nm. Therefore, the current in a pn-junction would becaused not only by drift and diffusion but also by a tunnelingmechanism. In this way the backward current should notbe tunable independently of the forward direction.

The structures investigated (see the inset of Figure 1b)consist of three organic layers sandwiched between two alu-minum contacts, which define the active area of 6.38 mm2.

The inner structure of the organic layers follows the pin-concept with a highly p-type doped HTL, a highly n-type dopedETL, and an intrinsic layer in between (see Supporting Informa-tion for details). Figure 1 displays the current-voltage (I-V)characteristics of such a device. In forward direction theexpected diode-like behavior16 is observed. The interlayerthickness does not affect the onset and the slope of the current

rise in forward direction, which appears at 2.3 V. In contrast,there is a significant influence on the reverse current, whichcan be seen in the loss of the rectifying property at a certainvoltage depending on the interlayer thickness. The onset of thereverse breakdown shifts in a controlled manner to highernegative voltages (from -3 to -15 V) by increasing the inter-layer thickness (see Figure 1a); we observe a shift of the reversebreakdown voltage of approximately 1 V by each additionalnanometer of IIL thickness. Current densities of more than 300mA/cm2 in reverse direction can be achieved without limitingreversibility or reproducibility. Obviously, the large reversevoltage region is dominated by a purely exponential rise of thecurrent, which provides a strong hint for a tunneling likemechanism. Also a flat part of the I-V curve can be observedin reverse direction. Since this is more pronounced for thickerinterlayers it is considered to be related to a leakage currents.Hence, a larger field and a larger voltage are needed to be inthe tunneling regime for thicker interlayers. The limitation ofthe transport layers and the injection gives rise to the flatteningof the I-V curve for larger negative voltages.

To further understand these observations, we performcapacitance-voltage (C-V) measurements, allowing thestudy of voltage-dependent effects of charge depletion andaccumulation in the IIL and allow correlating layer thick-nesses to capacitance values. In our devices, the transportlayers have a larger thickness and a better conductivity incomparison to the IIL which is thus the dominating RC-element in the stack. Capacitance frequency (C-f) measure-ments are done to prove independently the capacitancecalculated by the assumption of one dominant RC-circuit (seeSupporting Information). Thus, it is checked that the calcu-lated capacitance at 0 V corresponds to the assumed inter-layer thickness, which means that the IIL is still depletedeven for such thin films and no diffusion of dopants occurs.The C-V curves shown in Figure 1b obey the Mott-Schottkyrule as long as no significant current appears (between 0 and-4 V, see Supporting Information). In the forward voltagedirection thus, a sudden capacitance drop appears indepen-dently of the IIL thickness at 2.3 V, where the geometricalcapacitance dominates the C-V curves since the flat-bandcondition is reached. The small drop of capacitance for asmall forward bias is related to the ETL system of cesiumdoped BPhen. The significant number of trap states in thismaterial that will be filled under forward voltage conditionscauses the drop in capacitance. As one can see, for example,in Figure 3b, this effect does not appear in doped RE68.However, in reverse direction, a weak decrease of thecapacitance is observed as predicted by the Mott-Schottkyrule. This corresponds to a charge depletion at the HTL/IILand ETL/IIL interfaces. Besides this, a drop of the capacitanceis obtained as expected from the I-V curves for certainreverse voltages depending on the IIL thickness caused bya significant injection into the ILL.

To demonstrate the control of the reverse behavior andto discuss the possible relevant charge transport mecha-

FIGURE 1. (a) Current voltage characteristics for different interlayerthicknesses. (b) Capacitance voltage characteristics (measured at 1kHz) of the samples shown in panel a. The inset is a sketch of thedevice structure and the layers are listed as they are evaporated ona cleaned glass substrate (1): Al(100 nm)(2)/MeO-TPD-F4TCNQ[4 wt%](50 nm)(3)/Balq2-NPB[50 wt %](4)/Bphen-Cs(50 nm)(5)/Al(100nm)(6).

© 2010 American Chemical Society 4930 DOI: 10.1021/nl102916n | Nano Lett. 2010, 10, 4929-–4934

nisms, we plot in Figure 2 the reverse current for differenttemperatures and IIL thicknesses. For decreasing ILL thick-ness (from 11 to 5 nm), a purely exponential currentdependence is observed (for reverse voltages larger than -3V), with an increase of the reverse current by nearly 6 ordersof magnitude.

A further strong evidence of tunneling is the observedtemperature dependence. In addition to the exponential be-havior, we find a rather weak influence of the temperature onthe reverse current. In contrast to a typical activation energyof the forward current (Eact

for ) (170 ( 20) meV) for such a pin-device,20 a surprisingly small activation energy of Eact

rev ) (30(10) meV is measured in the reverse direction without anyvoltage dependence (see inset of Figure 2b). This low reverseactivation energy can be interpreted as being related toHOMO-LUMO tunneling processes that become dominant inthis voltage region. The difference between this proposedmechanism and the effect described by Drechsel et al.21 canclearly be seen in the weak interlayer thickness dependenceof the backward current reported by Drechsel. This is mainlydue to a change in the injection conditions for majority chargecarriers at the schottky contact and not related to a tunnelingof minority charge carriers as reported here. Concerning theactivation energy in reverse direction it should be mentionedthat since we cannot neglect the influence of the transportlayers to the temperature dependence the real value of activa-

tion energy remains elusive. However, even if the foundtemperature and interlayer dependences are a strong evidencefor a tunneling mechanism a second effect, the Avalanchebreakdown, could also play a role as a possible transportmechanism. Since we obtain an exponential current-voltagecharacteristic for different interlayer thicknesses and for a largevoltage region just one kind of these two processes is supposedto be dominant. Avalanche and Zener breakdowns are distin-guishable by the field, which needs to be applied to be in thebreakdown region.7,8 Thus, for a certain energy gap of thematerials used for the diode Zener tunneling should appear forlower fields than Avalanche multiplication. Since we do notobtain a second process in the current-voltage curves forhigher voltages, the Zener effect is supposed to be the domi-nant mechanism.

If one assumes a transport mechanism similar to inorganicZener diodes, one can further expect a control of the reversebreakdown by the doping concentration of the transport layers.Figure 3 shows data a for a diode of RE68 designed as ahomojunction; the breakdown voltage can be shifted to highervalues for lower doping concentrations as expected. The reasonis a change of the effective thickness of the intrinsic layer byan additional depletion region at the HTL/IIL and the IIL/ETLinterface. Although the reverse current has a reduced sensitivityto the doping concentration than to the IIL thickness, this allows

FIGURE 2. Current density at a reverse voltage of -5 V for differentinterlayer thicknesses. Device structure as in Figure 1b Temperaturedependence of the current density in reverse direction measuredat -3 V and in the exponential rise of the forward direction at 2.6V. The inset shows the temperature dependence for differentbackward voltages. The devices consist of Al(100 nm)/MeO-TPD-NDP2[4 wt %](50 nm)/Balq2-NPB[50 wt %](7 nm)/Bphen-Cs(50 nm)/Al(100 nm) on a cleaned glass substrate.

FIGURE 3. (a) Current density for different doping concentrationsin the HTL. The devices consist of Al(100 nm)/RE68-NDP2[x wt%](50 nm)/RE68(7 nm)/RE68-NDN1[16 wt %](50 nm)/Al(100 nm)on a cleaned glass substrate. Inset: comparison of different dopandmaterials regarding the I-V performance. The structure consists ofa doped HTL(50 nm), an intrinsic interlayer (Balq2-NPB[50 wt %](7 nm)) and a doped ETL(50 nm). The colors denote (HTL/ETL): Meo-TPD-F4TCNQ[4 wt %]/BPhen-Cs (light green), Meo-TPD-NDP2[4wt%]/BPhen-Cs(magenta),Meo-TPD-NDP2[4wt%]/BPhen-NDN1[16wt %] (dark blue). (b) Capacitance voltage characteristics of thesamples shown in Figure 3a

© 2010 American Chemical Society 4931 DOI: 10.1021/nl102916n | Nano Lett. 2010, 10, 4929-–4934

a second independent approach to control the breakdownvoltage. Furthermore, we also obtain no influence on theforward direction of the diode, which means that neither theseries resistance of the transport layers nor the flat-bandcondition have been significantly changed.

C-V spectroscopy investigations (see Figure 3b) oncemore reveal a Mott-Schottky like behavior for differentdoping concentrations. Obviously, there is an increase of thecapacitance for a decreasing concentration of dopant mol-ecules. Hence, if the thickness of the depletion layer iscalculated from the capacitance, one obtains, for example,8.3 nm for the 4 wt % of dopants and 11.3 nm for the 0.5wt % of dopants (including the IIL thickness of 7 nm). Thismeans that the depletion region thickness is the sum of theIIL and the interface depletion thickness, being sensitive tothe doping concentration. We obtain a similar rule asmentioned before in case of the thickness controlled reversecurrent: the reverse breakdown can be shifted by 1 V or thereverse current can be increased by 1 order of magnitudeby adding one additional nanometer to the thickness of thedepletion layer (IIL plus interface depletion). This dopingcontrolled reverse behavior can also be obtained for variousconcentrations of n-type dopants in ETL without any notice-able difference. Instead of NDN1 one can use cesium as afreely available n-type dopant (see Supporting Information).

Theoretical Modeling. The IIL part of the device is notexpected to have an ordered crystalline structure, but ratherdisplay a high degree of static and dynamic disorder. Sincethe spatial arrangement of the molecular building blocks inthe IIL is not known a priori, a first-principle description ofthe IIL electronic structure as well as of charge migration9-11

in such a system represents a very strong challenge. Hence,to gain a first qualitative insight into the possible chargetransport pathways, we have adopted a minimal modelapproach. Basically, the model consists of an electronicladder with N blocks describing the IIL, each block containingtwo energy levels εj

s(V) whose energetic position is deter-mined not only by the intrinsic electronic structure of amolecular building block but also by the built in field and bythe applied voltage (see inset of Figure 4). The Hamiltonoperator for this tight-binding model can be written as

The levels are denoted by s ) H (highest occupiedmolecular orbital, HOMO) and L (lowest-unoccupied molec-ular orbital, LUMO) and are thus representative of thefrontier orbitals of a given molecular unit. Their energeticposition is assumed to be given by the linear relation: εj

s(V)

) εs - κj + (j/N)eV, where εs is the bare onsite energy of themolecular orbital (assumed to be site-independent for sim-plicity). The local H-L gap ∆H-L ) εH - εL ∼ 3.0 eV is takenfrom the experimental energy diagram profiles. The built-in electric field is modeled as a linear ramp with slope -κ,which is supported by the current experiments as well asby photoelectron spectroscopy measurements in organicpin-diodes.19 The second, third, and fourth summands in eq1 describe different electronic couplings within the ladder:intra-strand nearest-neighbor couplings (second term) aswell as nearest- and next-nearest neighbor interstrand in-teractions (third and fourth terms). If not stated otherwise,we will assume for the sake of simplicity in the calculationstH ) tL ) t0 and tA

H-L and tBH-L ) ηt0, with 0 e η < 1. All

electronic parameters can in principle be obtained frommicroscopic first-principle calculations; this goes howeverbeyond the scope of the present minimal model approach.The last row in eq 1 describes the electronic structure of theR) l (left) and r (right) electrodes and the coupling betweenthem and the ladder. The specific electronic properties ofthe electrodes will not appear explicitly in our treatment;they are considered only as sinks of charges and will beincluded in the calculations via phenomenological param-eters. The electrode-ladder interaction, given by the tkR,sj

matrix elements is in general not limited to the ladder sitesnearest to the electrodes but it can have a longer range. Thiswill qualitatively account for the fact that the real structuralmolecular arrangement in the active region does not ingeneral have a linear chain topology-it is expected to ratherbe a complex network-so that interactions do not neces-sarily have to be confined to the electrodes’ nearest neigh-boring molecular blocks.

H ) ∑s)H,L

∑j

εjs(V)d+dsj + ∑

s)H,L

ts ∑j

(dsj+dsj+1 + hc) +

tAH-L ∑

j

(dHj+dLj+1 + hc) + tB

H-L ∑j

(dHj+dLj+2 + hc) +

∑k,α)l,r

εkαckα+ ckα + ∑

k,α)l,r∑

j,s)H,L

tk,α,j,s(ckα+ dsj + hc) (1)

FIGURE 4. Calculated I-V curves in the (a) hopping and (b) coherenttransport regimes compared with the measured characteristics. Theinset shows a schematic drawing of the two legs electronic ladderused to model charge transport in the device. The basic modelparameters are: (a) t0 )150 meV, tA

H-L ) 50 meV, tBH-L ) 0, Γl

L ) ΓrH

) ΓlH ) Γr

L ) 25 meV, and K ) 0.5, 0.37, and 0.27 eV for N ) 3, 4,and 5; (b) t0 )150 meV, tA

H-L )150 meV, tBH-L )50 meV, Γl

L ) ΓrH ) Γl

H

) ΓrL ) 100 meV, � ) 1.2, and K ) 0.66, 0.6, and 0.55 eV for N ) 6,

7, and 8. For a definition of the model parameters we also refer thereader to the Supporting Information.

© 2010 American Chemical Society 4932 DOI: 10.1021/nl102916n | Nano Lett. 2010, 10, 4929-–4934

The Ansatz for εjs(V) allows to account qualitatively for two

different physical scenarios: with increasing V > 0, the built-in field κ can be progressively counter-acted by the voltage-dependent term (j/N)eV, the energy levels become increas-ingly aligned and the current can dramatically grow due tothe reduction of tunnel barriers between the sites. Fornegative bias, transport is blocked up to a critical bias -V*;the energy scale |eV*| is roughly related to the situationwhere the H-level at a site j and the L-level at site j + 1become nearly resonant (additionally, at least the first siteof the H-strand should move above the left chemical poten-tial in order to have a current flow). Once this happens, anexponential current onset can occur. We have used twodifferent modeling strategies based on two possible differentmicroscopic transport mechanisms: hopping transport (HT)and coherent tunneling (CT). HT seems to be reasonable,since it is expected that the active device region displayssome degree of static and dynamic disorder which maysuppress coherent tunneling pathways over long distances.We have used a reduced density matrix approach22 (for HT)and the Landauer formalism23 to compute the I-V charac-teristics of the model in the CT regime (see the SupportingInformation for details of the calculation).

The results (scaled by an arbitrary factor) are displayedin Figure 4 in comparison with the experiments. It is obviousthat the weak (strong) thickness dependence for positive(negative) voltages can be qualitatively described within bothtransport regimes. Notice, however, the different numberof sites needed in both regimes to account for the experi-mental curves, This is related to the fact that tunnelingprocesses can still be efficient for short lengths, so thatalmost no zero-current gap is obtained. Only with increasinglength tunneling transport is blocked at low bias.

Some basic features of the transport process can besummarized as follows: for positive voltages the onset ofcurrent takes place approximately at the critical bias wherethe first site of the HOMO-strand moves above the leftchemical potential µl (which is kept fixed at µl ) EF while µr

) EF + eV). Under this condition, charge transport can takeplace. A further increase of the bias leads to an increase ofthe current until all the electronic levels along the ladderbecome aligned (the external potential cancels the built-infield κ). This provides the maximum current in this model;for larger positive voltages the misalignment of the levelsdevelops again and negative differential resistance caneventually be obtained. For negative voltages, the currentis almost zero in the case of coherent tunneling, since thisprocess is very sensitive to the presence of energy gaps alongthe ladder. This behavior can be lifted by allowing for long-range interactions between the electrodes and the ladderstates (see eq 7 in the Supporting Information). On thecontrary, hopping transport can also take place in thenegative bias regime with only nearest-neighbor interactions.

Our results suggest that the effective microscopic trans-port mechanism may include both HT and CT contributions,

each of them becoming dominant in different voltage re-gions. This may be the reason for the different slopes in theI(V ) const.,T) versus T-1 plots for positive and negativevoltages (Figure 2). A pure CT model cannot account for aT-dependence; HT contributions can however explain it. Inthe HT regime, a different qualitative behavior for positiveand negative voltages is expected on the basis of a simpleargument: the nearest neighbor intersite hopping rateswithin the ladder include (see eq 4 in the SupportingInformation) thermal factors exp(-(εj+1

s - εjp)/kBT), whenever

εj+1s - εj

p > 0 (s,p ) H,L). For s * p (sites on different strands),one obtains εj+1

s - εjp ) ∆H-L - κ + eV/N; from here it is

obvious that for V > 0 the temperature dependence is mainlydetermined by the gap ∆H-L , kBT (large slope). For negativebias, ∆H-L can be partially compensated by the term -κ -e|V|/N and thus the temperature dependence may be weak-ened. A more accurate quantitative analysis requires asystematic experimental study of the temperature depen-dence, taking also the influence of the transport layers intoaccount.

Conclusions. In this letter, we unambiguously observesignatures of Zener tunneling in a organic molecular semi-conductor. The reverse currents in organic pin-diodes showgeometry, field, and temperature dependence in excellentagreement with this tunneling effect not observed so far insuch systems. The realized pin-Zener diodes have excellentdevice properties and allow important application possibili-ties, for example, to reduce crosstalk in passive matrixarrays. The basic effect of valence- to conduction-leveltunneling could be used in further device concepts, such asdevices employing tunable resonant tunneling. Using aminimal model Hamiltonian, we can describe semiquanti-tatively the measured electrical response. However, bothlimiting cases investigated here, incoherent hopping orcoherent tunneling, can describe the observed experimentalfeatures. It therefore seems appealing to expect that thedominant charge transport mechanism may sensitivelydepend on the sign of the applied bias. A further point to beconsidered is the coupling to dynamical degrees of freedomthat may induce polaron formation, so that the transportprocess will be rather mediated by dressed electrons orholes. We have not taken these issues in our model, whichis only addressing electronic degrees of freedom. Furtherwork in this direction including detailed first-principle elec-tronic structure calculations is thus needed.

Acknowledgment. The authors thank Novaled AG, thefree state of Saxony and EU (EFRE) for financial supportunder project NKOE (12712) and Novaled for providingthe HTL dopant NDP2 and the ETL dopant NDN1. Thiswork was also supported by the Volkswagen Foundationthrough Grant I/78-340, by the cluster of excellence of theFree State of Saxony European Center for EmergingMaterials and Processes Dresden ECEMP/A2, and by WCU(World Class University) program through the KoreaScience and Engineering Foundation funded by the Min-

© 2010 American Chemical Society 4933 DOI: 10.1021/nl102916n | Nano Lett. 2010, 10, 4929-–4934

istry of Education, Science, and Technology (Project No.R31-2008-000-10100-0).

Supporting Information Available. Preparation methods,additional I-V, C-V, C-f, and Mott-Schottky curves for thefree available materials. Furthermore, we present a moredetailed description of the microscopic model applied todescribe the charge transport characteristics in the organicZener diode. This material is available free of charge via theInternet at http://pubs.acs.org.

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