PRL 95, 256405 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending16 DECEMBER 2005

Direct Determination of the Hole Density of States in Undoped and Doped Amorphous OrganicFilms with High Lateral Resolution

O. Tal,1,* Y. Rosenwaks,1,† Y. Preezant,2 N. Tessler,2 C. K. Chan,3 and A. Kahn3

1Department of Physical Electronics, Tel Aviv University, Tel Aviv 69978, Israel2Department of Electrical Engineering, Technion Israel institute of Technology, Haifa 32000, Israel

3Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA(Received 21 August 2005; published 16 December 2005)

0031-9007=

We investigate the density of states (DOS) for hole transport in undoped and doped amorphous organicfilms using high lateral resolution Kelvin probe force microscopy. Measurements are done on field effecttransistors made of N;NI-diphenyl-N, NI-bis(1-naphthyl)-1,10-biphenyl–4,4II-diamine undoped or pdoped with tetrafluoro-tetracyanoquinodimethane. We determine the DOS structure of the undopedmaterial, including an anomalous peak related to interfaces between regions of different surface potential,the DOS doping-induced broadening, and doping-induced sharp peaks on the main DOS distribution.

DOI: 10.1103/PhysRevLett.95.256405 PACS numbers: 71.23.�k, 73.20.At, 73.50.�h, 73.61.�r

The density of states (DOS) for charge-carrier transportin organic molecular films and the impact of electricaldoping on the DOS are of fundamental importance forunderstanding charge transport in organic films. Trans-port in amorphous organic semiconductors is generallydescribed in terms of charge-carrier hopping between dis-ordered localized energy states [1]. The energy disorder isascribed to the different environment of each molecule:Static and dynamic disorder in position and orientationaffect the molecular energy levels through electrostatic[2,3] and steric [4] interactions. This disorder leads to aDOS usually modeled by a Gaussian [2] or exponential [5]distribution. The insertion of dopant molecules, i.e., elec-tron donors or acceptors or optical dopants, further modi-fies this DOS. Dopants are introduced either intentionally,to improve the film conductivity [6], modify charge injec-tion barriers [7], add functionality (e.g., a pn junction [8]),and modify the film optical properties [9], or unintention-ally, as synthesis impurities [10], solution residuals [11],and chemically induced doping [12], which deteriorate theperformance of the organic material. In any case, an accu-rate understanding of the DOS energy distribution and howit is affected by molecular doping is one of the keys toadvancing basic research on, and technological applica-tions of, organic semiconductor films, since many elec-tronic properties of organic semiconductors are closelyrelated to the shape of the DOS [13,14].

The influence of dopants on the DOS distribution hasbeen studied indirectly by assuming a Gaussian DOSdistribution and extracting function parameters from car-rier mobility measurements as a function of dopingconcentration. It was found that the DOS distributionbroadens with increasing doping concentration [6], a ten-dency that was attributed to potential fluctuations causedby the Coulomb field of the randomly distributed dopant[15,16]. However, experimental information on the specificshape of the DOS relevant to carrier transport in organic

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films has been very limited, and the influence of doping onthe DOS has never been explored directly. Lang et al. haveused current-voltage measurements as a function of tem-perature in organic thin film transistors (OTFTs) to extractthe density of gap states in amorphous and single crystalpentacene [17], and Hulea et al. have used an electro-chemically gated transistor to measure a wide energy rangeof the highest occupied molecular orbital (HOMO) DOS inpoly(p-phenylenevinilene) by injection of holes and ion-ized dopants in different concentrations during the mea-surement [18].

In this Letter, we report the direct determination of theDOS around the HOMO level in undoped and dopedamorphous organic thin films using Kelvin probe forcemicroscopy (KPFM) measurements on an OTFT structure.We observe a broadening of the DOS distribution, as wellas sharp doping-induced peaks in the DOS distribution.Exploiting the KPFM nanoscale lateral resolution, an addi-tional peak is observed in the main DOS distribution of theundoped film at specific sites located at interfaces betweenregions of different surface potential, while the doped filmsexhibit a laterally more homogeneous DOS distribution.

The OTFT structure (Fig. 1) consisted of a heavilydoped p-type silicon gate electrode, a thermally grown90 nm silicon oxide gate insulator, and 50 nm thickgold strips evaporated on the oxide to form source anddrain electrodes separated by 16 �m. A thin film (10 nm)of N;NI-diphenyl-N, NI-bis(1-naphthyl)-1,10-biphenyl–4,4II-diamine (�-NPD) was deposited on the substrateby sublimation in an ultrahigh vacuum chamber. Doped�-NPD films were formed by coevaporation of tetrafluoro-tetracyano-quinodimethane (F4-TCNQ) with the hostmolecules [19]. The transistors were transported undernitrogen atmosphere to a nitrogen glove box (<2 ppmH2O) in which the KPFM (Autoprobe CP—Veeco Inc.with homemade Kelvin probe electronics) is located. Asemiconductor parameter analyzer (HP 4155C) was used

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FIG. 2. (a) Inset: VL profiles measured across an undopedtransistor for VDS � 0 V and VGS ranging from 0 to �16:5 V.(a) VL as a function of VGS � Vt measured on undoped (A) anddoped (B) samples. (b) DOS vs energy relative to � for VGS �Vt for undoped (solid triangles) and doped (solid circles)samples. The solid curves are a fitting of a Gaussian function[Eq. (2); curve A] and an exponential function [Eq. (4); curve B]to given ranges in the undoped sample DOS curve and a fitting ofEq. (3) (curve C) to the doped sample DOS curve.

Gate

α -NPD thin film

Insulator

KPFM tip

Source Drain

FIG. 1. Schematic of the OFET structure and KPFM tip abovethe channel.

PRL 95, 256405 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending16 DECEMBER 2005

to control the gate voltage, with respect to the groundedsource and drain electrodes, and monitor the drain, source,and gate electrode currents. The contact resistance [20,21],leakage current through the gate insulator and to the pe-riphery of the active area, and shifts of the thresholdvoltage [20] due to continuous voltage application werefound to be negligible in these transistor structures.

The OFETs were scanned with the KPFM across rela-tively smooth regions of the organic layer (roughness<1 nm) at different gate potentials. When the gate-sourcevoltage (VGS) is lower than the threshold voltage (Vt),which is defined as the VGS at flat levels condition [22]or zero level shift in thin enough organic films, holes areinjected into the organic film and populate the edge statesof the HOMO, and the molecular energy levels shift towardthe chemical potential (�) energy level. During the mea-surement, � is kept constant by grounding the source anddrain contacts, and the molecular energy levels are shiftedwith respect to � by the gate-induced voltage.

According to numerical calculations [23] conducted fora 10 nm thick organic layer in an OFET structure anddifferent Gaussian DOS distributions, the induced chargeis approximately homogeneously distributed across theorganic film width, and the energy level bending fromthe film surface to the film/gate-insulator interface is neg-ligible for the measured VGS range. We emphasize that thisassumption holds up only to a certain VGS; according to ourcalculations, above this VGS [24], the conducting channel issqueezed toward the gate insulator and the level bending isnot negligible. This behavior has already been reportedelsewhere [22,25]. Under a negligible level bending con-dition, the shift of the energy levels (VL) for differentVGS with respect to the level position at VGS � Vt can bemeasured directly by the KPFM: VL�x� � CPD�x� �CPDt�x�, where CPD�x� is the contact potential differencemeasured between the KPFM tip and the sample at a givenlocation (x) across the transistor, and CPDt�x� is measuredat VGS � Vt. The DOS is then calculated using

g�qVL�x�� � �Cox=dorgq2���dVL�x�=d�VGS � Vt��

�1 � 1�;

(1)

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where Cox is the silicon oxide capacitance per unit area,dorg is the organic film thickness and q is the electroncharge.

The inset in Fig. 2(a) shows the VL measured across anundoped transistor. The potential of the grounded sourceand drain appears as the flat portion at each end of thecurves, and the potential distribution across the organicchannel is seen in between. The curves were measured forVDS � 0 V and VGS ranging from 0 to �16:5 V.Figure 2(a) shows VL measured as described in the insetacross the organic film far from the drain and sourceelectrodes, as a function of VGS � Vt [26] for undoped(curve A) and doped �-NPD (curve B). The doping con-centration is 1:4��0:4� � 1018 cm�3 (0:1% of the totalmolecular density) [27]. Each curve is an average of50 curves measured at different locations on the transistorsto reduce the experimental uncertainty. Measurements ondifferent transistors gave very similar results. The curvesfor both undoped and doped layers show that the change inVL is largest at small jVGSj, then decreases, and finallysaturates as jVGSj increases. During this process, the

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PRL 95, 256405 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending16 DECEMBER 2005

HOMO shifts toward � and holes are injected into avail-able states near �. A low state density results in a largerchange in VL and vice versa; hence, the slope of theVL=�VGS � Vt� curve is inversely proportional to theDOS. It points to an increase in the DOS as � penetratesdeeper into the HOMO state distribution, while the finestructure observed on the curves is a result of finer changesin the DOS. The VL saturation at large enough jVGSjpossibly stems from the onset of large level bending nearthe gate insulator at high charge concentrations or from �pinning at high DOS.

The DOS vs qVL in Fig. 2(b) is obtained for undoped(triangles) and doped (circles) samples by applying Eq. (1)to the data of Fig. 2(a). The energy scale in Fig. 2(b)represents the energy relative to � for VGS � Vt, and thenegative sign denotes values below �. The sharp increasein DOS near the high-energy end of the curves [left side ofFig. 2(b)] should be considered as a measurement artifactthat reflects the termination of the level shift [VL saturationas appears in Fig. 2(a)]. While the DOS of the undopedsample has a single peak around 0:408� 0:005 eV in themeasured energy range, the DOS of the doped sampleexhibits several peaks at �0:356; 0:393; 0:431; 0:456; 0:472;0:518; 0:534; 0:560; 0:850� � 0:005 eV. These peaks im-ply the presence of several doping-induced energy levels.A variety of dopant configurations, i.e., dopant clusterswith various sizes or different configurations of dopantand host molecules, can lead to local shifts in potentialenergy and result in several discrete energy levels, as ismeasured here.

The DOS in the undoped sample can be divided intothree main regions: a tail, a single peak around E �0:408� 0:005 eV, and a region that can be fitted to aGaussian distribution [13] [curve A in Fig. 2(b)]:

gi�E� � �Ni=���������2�p

�� exp����E� Ec�=����2p���2�: (2)

Inserting the total state density Ni � 1:2� 1021 cm�3 for�-NPD (equivalent to one state per molecule), we find aGaussian width (variance) � � 0:10� 0:01 eV centeredat Ec � �0:84� 0:04 eV. This width should be consid-ered with care, since the Gaussian function is fitted to arelatively small range of the measured DOS curve; how-ever, it can serve as a guiding parameter that can be appliedto an analytical expression that describes the influence ofdoping on the DOS [15]:

g�E� � ��Ni � Na�=Ni�gi�E� �Na=Ni�gi�E

e2=�4�""0a� ���������������������������e3F=��""0�

q�; (3)

where gi�E� is given by Eq. (2), Na � 1:4��0:4� �1018 cm�3 is the doping concentration, a � 0:6 nm is thedistance between a dopant and the nearest intrinsic hop-ping site [15], "0 is the dielectric permittivity, " � 3 is therelative dielectric constant of �-NPD [19], and Ec �

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�0:88� 0:04 eV [appeared in gi�E�, Eq. (2)], which isin good agreement with the Ec of curve A. The lateralelectric field (F) between the source and the drain isconsidered equal to zero since the drain-source voltage iszero. Equation (3) yields the curve B in Fig. 2(b) anddescribes well the main DOS distribution of the dopedsample. According to Ref. [15], the second term inEq. (3) expresses the shift of states toward the center ofthe gap due to the presence of dopants; note that its con-tribution in curve B is observed mostly at E � �0:49 eV.Further examination of the measured DOS of the undopedsample reveals a DOS tail at �0:38 � E � 0 eV that canbe fitted to an exponential function [5] [curve C inFig. 2(b)]:

g�E� � �Nt=�kT0�� exp��E=�kT0��; (4)

with a total trap density Nt � 3:4� 1015 cm�3 and aneffective temperature T0 � 1350 K. In the case of thedoped sample, a moderately sloped exponential-like DOStail, which deviates from curve C, appears at �0:31 �E � 0 eV. The observed flattening and rising of theexponential tail due to doping has been previously de-scribed with an analytical model for an exponential DOStail [28]. The described changes point to a DOS broadeningdue to doping, as was also observed indirectly by othermethods [6].

KPFM topographic measurements across various tran-sistor regions show a smooth organic film surface, yetconcomitant CPD measurements show randomly distrib-uted potential fluctuations in both doped and undopedsamples. The inset in Fig. 3(a) shows such fluctuations inVL profile measured across the central region of an un-doped transistor channel at VGS � �0:1 V. The DOS pre-sented in Fig. 3(a) is measured at the center of the potentialdepressions and protrusions (locations a, c, and e in theinset) and at their interfaces (location b, d, and f). Anadditional peak appears at E � 0:408� 0:05 eV on themain DOS distribution measured at these interfaces. Apossible origin for this additional intensity in the statedistribution is the presence of interface states betweenmolecular aggregates with slightly different averaged mo-lecular orientation, leading to differences in the measuredCPD. For the doped sample, DOS distributions measuredat five different locations [Fig. 3(b)] show the same distri-bution of the main peaks with different amplitudes. Theadditional peak seen in the DOS of the undoped film[Fig. 3(a)] may be masked by the dopant-induced changesin the DOS of the doped film. The average lateral separa-tion between the dopants is around 10 nm; this is less thanthe KPFM spatial resolution, estimated to be tens of nano-meters; thus, DOS fluctuations in the vicinity of a specificdopant are most likely not detected, and the different peakamplitudes at different locations may stem from changes inthe relative contributions of the various dopant energies.

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FIG. 3. (a) Inset: VL profile measured across the channel of anundoped transistor. (a) DOS distributions measured at differentlateral locations across the channel marked as a–f in the inset.(b) DOS distributions measured at different lateral locationsacross the channel of doped transistor. Each DOS curve is anaverage of three curves that were measured at the same location.

PRL 95, 256405 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending16 DECEMBER 2005

In conclusion, the KPFM-based method described hereallows the direct determination of the DOS distribution in amolecular film and of the influence of doping on thisdistribution, with a lateral resolution of tens of nanometers.The DOS of the undoped organic film exhibits anexponential-like tail and a more complex structure, includ-ing an additional peak at specific physical locations on thefilm that correspond to interfaces between regions withdifferent surface potential. Doping broadens the DOS andinduces several discrete peaks on the main distribution.DOS distributions measured at different lateral positionson the doped samples have similar shape and peak energiesbut different peak heights. Such sensitive DOS measure-ments provide new information on the effect of doping onthe electronic energy states distribution. This informationis crucial for understanding carrier transport in amorphousorganic semiconductors.

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This research was generously supported by the U.S.–Israel Binational Science Foundation (BSF), GrantNo. 2000-092. The authors thank J. Klafter for fruitfuldiscussions. A. K. also gratefully acknowledges partialsupport of the work by the NSF (DMR-0408589).

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*Electronic address: orent@eng.tau.ac.il†Electronic address: yossir@eng.tau.ac.il

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