www.advmat.dewww.MaterialsViews.com

CO

MM

UN

ICA

Christian Melzer , * Christopher Siol , and Heinz von Seggern

Transit Phenomena in Organic Field-Effect Transistors Through Kelvin-Probe Force Microscopy

TION

A useful tool to investigate the local performance of organic

fi eld-effect transistors (OFETs) is the Kelvin-Probe Force Micro-scope (KPFM) allowing for the local mapping of the electrical potential in the transistor channel. Besides the fact that this technique can be employed to estimate the impact of current limiting contacts on the overall device performance of the OFET, [ 1 , 2 ] it was used to determine the capability of the tran-sistor channel to trap charge carriers [ 3 , 4 ] or to determine the electric fi eld and charge-carrier density dependent fi eld-effect mobility. [ 1 ]

Mostly, the transistor is investigated by KPFM in the on-state at limited lateral electrical fi elds. Thereby, the surface-potential distribution from the source to the drain contact is mapped being determined by the accumulation of excess charge carriers. Using the gradual channel approximation, one can determine the elec-tric fi eld and charge-carrier density dependent mobility as long as the drain current is recorded simultaneously. The reason is that the local surface potential is proportional to the local charge (carrier) density and that the derivative of the local surface poten-tial along the current direction is the electric fi eld. In the off-state of an ideal transistor the channel is depleted, nota bene no transportable carriers are present, and only parasitic currents are determined. Thus, the determination of the carrier mobility in the off-regime of the transistor is likewise not applicable using a combined measurement of current and local surface potential. However, without mobile charge carriers the remaining trapped charge carriers can be still quantifi ed via KPFM. [ 5 ] For example, it was demonstrated that OFET instabilities can be triggered in the saturation or depletion regime initiated by trapping of com-plementary carriers creeping into the transistor channel. [ 4 ]

In the present article, we investigate the charge-transport properties in the sub-threshold regime of pentacene based OFETs by employing dynamic KPFM measurements during the charge reversal from the depleted to the hole dominated device. While the local carrier density and the electric fi eld are determined by the surface potential and its gradient respec-tively, the local current is obtained from the charge-carrier front entering the channel from the source and drain contacts during

© 2013 WILEY-VCH Verlag G

Dr. C. MelzerRuprecht-Karls-Universität HeidelbergCentre for Advanced MaterialsIm Neuenheimer Feld 270, 69120 Heidelberg, Germany E-mail: christian.melzer@kip.uni-heidelberg.de Dr. C. Siol, Prof. Dr. H. von SeggernTechnical University of DarmstadtInstitute for Material ScienceElectronic Materials DivisionPetersenstraße 23, 64287 Darmstadt, Germany

DOI: 10.1002/adma.201300004

Adv. Mater. 2013, DOI: 10.1002/adma.201300004

charge reversal. Thus, no additional current determination is required. The temporal and positional evolution of the charge-carrier front can be followed by KPFM employing a quasi-simultaneous measurement of the surface potential everywhere in the channel. This allows the determination of the charge-carrier mobility for low carrier densities in organic fi eld-effect transistors.

The investigated p-type pentacene OFETs consisted of a p + + -Si substrate with a SiO 2 / PMMA double-layer gate dielec-tric, an evaporated polycrystalline pentacene layer, and Au top contacts ( Figure 1 ). The PMMA layer is used to enable bipolar transport in the transistor channel. [ 4 ] The channel length L was 5 μ m. The threshold voltage and fi eld-effect mobility were estimated from the transfer characteristics to be –11 V and 0.14 cm 2 V − 1 s − 1 at a gate voltage of –25 V to –30 V.

The device operation regimes can be followed by KPFM at a fi xed position within the transistor channel while the source and drain contact potentials U C are swept relative to the grounded gate. [4] Figure 1 shows the surface potential φ versus the applied bias U C . Starting at 20 V the bias is reduced with –2 Vs − 1 . Since the measured surface potential is positive and follows simply the applied bias, a movable, positive car-rier density needs to be present in the channel, fully screening the electric fi eld originating from the gate. The transistor is on. Once one crosses 0 V the surface potential remains close to zero, which indicates a depletion of the transistor channel. The transistor is off. As soon as the bias reaches approximately –23 V the surface potential is further reduced indicating the injection of electrons, which leads to electron conduction if the bias is further decreased. Repeating the procedure at the same position shows that after four repetitions the observed surface potential evolution is almost invariant. Once the bias is again increased from a negatively charged channel, φ again simply follows U C without delay. The electrons redistribute instantane-ously because the conductivity in the channel is large enough. The bias is changed at the source and drain contacts displaced from the measurement position in the channel. In order to observe a change in surface potential at the measurement spot, the bias change at the source and drain contacts needs to be passed to the tip position. This requires time depending on the channel conductivity. For a surface potential approaching zero, less carriers are present in the channel and the conduc-tivity is reduced. As a consequence, the source/ drain potentials cannot propagate to the tip position in time. The surface poten-tial saturates. This happens at approximately –10 to –3 V where the switching from electron to hole accumulation occurs. The charge reversal shows a signature of a temporary depletion of the channel from movable electrons and subsequent injection of holes. The shift of the transition region to negative biases indicates the presence of a remnant negative background

mbH & Co. KGaA, Weinheim 1wileyonlinelibrary.com

www.advmat.dewww.MaterialsViews.com

CO

MM

UN

ICATI

ON

Figure 1 . Measured surface potential φ versus the applied contact poten-tial U C while the gate was grounded. The sweep rate was ± 2 Vs − 1 . For the sweep from + 20 to –30 V the successive traces (fi rst gray then black dashed line) show a negative charging of the transistor channel. After < 10 cycles an invariant dependence of surface potential on the contact bias is observed demonstrated by the successive sweeps (fi rst gray then black dashed line) from –30 to + 20 V. A displacement of the Kelvin probe out of the channel, far away from the contacts, results in a delayed response of the surface potential on the bias change at the contacts (dash dotted line). Insets: Device layout of the OFET in cross-section and top-view.

organic channel

φ/ V

UC / V

0

-10

-20

-30-30 -20 -10 0 10 20

UC

x

z

gate

pentacene (50 nm)

PMMA (110 nm)

Au Au

SiO2(100 nm)

5 µm

S D

charge. Be aware that only at high negative U C a substantial electron contribution to a DC current is measurable since the electron injection from the Au source and drain contacts to pentacene is strongly hampered.

Once we displace the tip to a spot several 10 micrometers away from the contacts outside the channel, the surface-poten-

2 wileyonlinelibrary.com © 2013 WILEY-VCH Verlag

Figure 2 . The time evolution of the surface-potential distribution upon a was obtained by performing bias sweeps at 70 points across the channelevolution in the charge-reversal point from an electron to a hole rich device(left bottom)

tial behavior changes (Figure 1 , dash dotted line). The surface potential saturates at lower bias and the onset of hole injection is shifted to a larger bias. Both phenomena can be explained by a delayed response of the surface potential upon the change in external bias due to an increased transit time of the carrier front. [ 6 ] Once the distance between source and drain contacts and the tip position is increased, the response of the delay line becomes slower. On the one hand, an earlier saturation of the surface potential is observed since the change in the source/ drain potentials cannot be passed in time to the tip position. On the other hand, a delayed arrival of injected holes occurs. If it is true that the observed surface-potential evolution at the charge-reversal point relates to a transit phenomenon, one should in principle be able to image the depletion process of the channel from electrons and the subsequent charging process of the channel with holes. Yet, still a probe technique is performed and the simultaneous determination of the surface potentials at different locations in the channel is not possible. To circum-vent this problem, the reproducibility of the transient experi-ment can be employed. After multiple repetitions of the bias sweep the surface potential evolution at one position of the probe in the channel reaches a steady-state behavior (see Figure 1 ) allowing for quasi-simultaneous measurements with the KPFM. The operation scheme of the employed quasi-simultaneous measurement is depicted in Figure 2 . A bias sweep cycle is per-formed and the potential evolution in the vicinity of the charge-reversal point is record in time. Subsequently, the tip is displaced ∼ 120 nm to the next position, where another bias sweep is performed and the potential evolution of that spot is recorded. Repeating this procedure back and forth, the temporal evolution of the surface potential in the entire transistor channel can be reconstructed.

In Figure 2 the obtained temporal evolution of the surface potential distribution is depicted. At small times and thus low

GmbH & Co. KGaA, Weinheim

bias change of the contacts with a rate of + 2 Vs − 1 (left top). This evolution from U C = + 20 to -30 V and back to + 20 V recording the surface-potential (right). Additionally, the topography of the pentacene transistor is depicted

Adv. Mater. 2013, DOI: 10.1002/adma.201300004

www.advmat.dewww.MaterialsViews.com

CO

MM

UN

ICATIO

N

source and drain potentials the channel potential follows the source/ drain potential and thus, electrons can redistribute fast during the bias change. At approximately –9 V the nega-tive carriers cannot follow the change in bias any longer and the channel depletes from free carriers. Thereafter, holes are entering the channel from the source and drain contacts and it requires about 3 to 4 s until the surface potential follows again U C everywhere in the channel. The behavior can be understood on basis of the transmission-line equations according to Burns [ 6 ] (see Supporting Information). In this model, the charging of the transistor channel by the injection of carriers from con-tacts is described by ∂ t φ ( x , t ) = μ /2 · ∂ x , x φ ( x , t ) 2 where μ is the constant carrier mobility and φ ( x , t ) is the time and space dependent surface potential. In contrast to Burns, who investi-gated the charging of the transistor upon an application of a bias step, the surface-potential evolution during the application of a bias ramp needs to be considered here. Upon the substitution φ ( x , t ) = U C ( t ) · ν ( x , t ) with U C ( t ) = β · t and Y = ( x + L /2)/(2( β μ ) 1/2 · t ) as common variable, the differential equation trans-forms to an ordinary differential equation of second order: 4 ν ( Y ) = 4 Y · ∂ Y ν ( Y ) + ν ( Y )∂ Y , Y ν ( Y ) + (∂ Y ν ( Y )) 2 . Here β is the rate of bias increase and L is the channel length. Considering only the left contact in the time frame between 18.5 s and 21.5 s this equation needs to be solved for the boundary conditions v (0) = 1 and v ( ∞ ) = 0. The solution can only be found numerically but can be approximated to v ( Y ) = 1-2 Y for Y < 1/2 and v ( Y ) = 0 for Y ≥ 1/2. Thus, we obtain for x + L /2 < ( β μ ) 1/2 · t the spatial and time dependent surface potential φ ( x , t ) = β · t - ( β / μ ) 1/2 ( x + L /2). For x + L /2 ≥ ( β μ ) 1/2 · t the surface potential φ ( x , t ) is zero. The time τ required for the carrier front to reach the middle of the channel ( x = 0 μ m) is hence L /(4 β μ ) 1/2 . With L ≈ 5 μ m, τ = 3 s and β = 2 Vs − 1 a carrier mobility of 3.5 × 10 − 9 cm 2 V − 1 s − 1 in the low charge regime is found characterizing the sub-threshold regime of the OFET. The estimated mobility is eight orders of magnitude lower than the mobility in the on-state of the transistor.

According to the transmission-line model, a linear decreasing potential front should enter the transistor channel. This, how-ever, does not refl ect the experimental observation (see Figure 2 ). The surface potential rather follows an S-shaped spatial pro-fi le indicating that the assumption of a constant mobility is wrong, as known from literature. [ 7 , 8 ] This can be seen by esti-mating the carrier mobility with φ ( x , t ) = β · t -( β / μ ) 1/2 ( x + L /2) for the carrier movement at a different charge state or equiva-lently at different surface potential. While a carrier mobility of 3.5 × 10 − 9 cm 2 V − 1 s − 1 was extracted for the onset of the potential front ( φ ≈ –9 V), a mobility of 3.1 × 10 − 8 cm 2 V − 1 s − 1 was found at φ ≈ –4 V ( τ ≈ 1 s) being one order of magnitude higher. Be aware that the use of φ ( x , t ) = β · t -( β / μ ) 1/2 ( x + L /2) is strictly speaking not valid for the temporal evolution of the surface-potential distribution at higher charge states since the boundary condition v ( ∞ ) = 0 does not hold over the entire transit time. Nonetheless, the estimation demonstrates that the carrier mobility cannot be assumed to be constant in the sub-threshold regime.

The electric-fi eld and charge-carrier density dependence of the carrier mobility in the measurement window can be recon-structed since the temporal evolution of the lateral surface-potential distribution was measured (see Figure 3 ). Under the assumption that the trapped negative charges shifting the surface

© 2013 WILEY-VCH Verlag GmAdv. Mater. 2013, DOI: 10.1002/adma.201300004

potential in depletion towards φ 0 ( x ) = –9 V are residual under hole accumulation [ 4 ] one fi nds with p a ( x , t ) = C 0 / q ( φ ( x , t )- φ 0 ( x )) the areal hole density at given position and time. Here C 0 is the areal capacitance of the gate dielectric and q is the positive elementary charge. Likewise, the local electric fi eld F ( x , t ) in plane of the substrate can be estimated by F ( x , t ) = − ∂ x φ ( x , t ). Since source and drain are shortened, the net current through the device is zero and the charging current I ( x , t ) can be cal-culated out of the continuity equation using the device sym-metry: I ( x , t ) = WC 0 ∫

x 0 ∂ t φ ( y , t )∂ y (see Supporting Information). Here, W is the width of the transistor channel and the integra-tion is performed from the middle of the transistor channel at x = 0 μ m towards the contacts, because at x = 0 μ m the total current is zero for all times. With I ( x , t ) = W q μ p a ( x , t ) F ( x , t ) the fi eld-effect mobility in dependence of the prevailing electric fi eld and the areal hole density is obtained. The applicability of the transient technique to estimate the density and electric fi eld dependent carrier mobility is strongly limited by the noise of the measured surface potential which might initiate zero cross-ings of the electric fi eld. In particular, in equipotential regions the noise determines the local electric fi eld and therefore these regions are excluded from the analysis. To reduce the noise, the surface potential was smoothened by averaging φ with the sur-face potential of the next neighbor measurement point. More-over, it is corrected for the potential distribution at t = 24 s to consider the shift of the Fermi level towards the HOMO of pen-tacene once the channel is positively charged. Each obtained triplet of carrier mobility, carrier density, and electric fi eld was further averaged with neighbor triplets within an ellipsoid with main axis of 5 × 10 − 3 V cm − 1 and 2 × 10 11 cm − 2 . The result is depicted in Figure 3 . The carrier mobility reaches values up to 2 × 10 − 8 cm 2 V − 1 s − 1 for a hole density of up to 7 × 10 11 cm − 2 and an electric fi eld smaller than 6 × 10 4 V cm − 1 . For the unfi lled channel a carrier mobility of approximately 10 − 9 cm 2 V − 1 s − 1 is obtained. These values fi t the prediction from the transmission-line approximation. Apparently, the increase in hole mobility is initiated by the increase in hole density but not due to an increase in electric fi eld. The electric fi eld driving the carriers is even reduced for an increased areal carrier density.

Even though the thermal deposition of pentacene results in polycrystalline thin fi lms, there are reports demonstrating that transport models elaborated for amorphous materials fi t to polycrystalline pentacene fi lms as well. [ 8 , 9 ] Yet, for organic fi eld-effect transistors mainly the density dependence of the carrier mobility was considered. The electric-fi eld and carrier-density dependence of the carrier mobility in disordered organic semi-conductors were unifi ed by Pasveer et al. [ 10 ] to the extended Gaussian disorder model (EGDM). The EGDM provides an analytical expression of the carrier mobility being mainly deter-mined by the disorder parameter σ , the intermolecular spacing a , the temperature T and the carrier volume density p , as well as the electric fi eld F . The carrier mobility reads:

μ(p, F ) = μp(p) · μF (F ) (1)

with

μp(p) = μ0 E xp(−c1σ̂ 2 + 1

2

(σ̂ 2 − σ̂

) (2pa3

)δ)

(2)

and

3wileyonlinelibrary.combH & Co. KGaA, Weinheim

www.advmat.dewww.MaterialsViews.com

CO

MM

UN

ICATI

ON

Figure 3 . Since I = W · q · μ · p a · F holds, the carrier mobility in dependence of the prevailing electric fi eld and carrier density can be obtained. (a) From the time evolution of the surface-potential distribution φ , the time evolution of the local charging current I , the time evolution of the electric-fi eld distribu-tion F and the time evolution of the local carrier density p a can be obtained. The minimal and maximal values were: –1.35 × 10 − 12 A < I < 1.23 × 10 − 12 A, –5.2 × 10 4 V cm − 1 < F < 5.9 × 10 4 V cm − 1 , 0 cm − 2 < p a < 10 12 cm − 2 . (b) The resulting electric fi eld and areal carrier density dependent mobility (dots). The colors of the dots represent the experimentally determined mobilities from (a), while the background color represents the solution of an optimal fi t of Equations 1–3 to the data. (c) The projection of the experimentally determined carrier mobility on the mobility vs. areal carrier-density plane (dots) for all fi elds. Since the electric fi eld is small, the obtained carrier mobility does not depend on the electric fi eld. The red line is an optimal fi t of Equations 1–3 to the data.

-2 2 -2 2 -2 2

= W × q × µ × ×

I / A F / Vcm-1 pa / cm-2S

x / µm x / µm x / µm

S SD D D

17

19

21

23

tim

e /

s

min

max

2 4 6

0

1

2

3

4

5

6

elec

tric

fie

ld /

10

4V

cm-1

1.350E-13

3.644E-13

5.938E-13

8.231E-13

1.053E-12

1.282E-12

1.511E-12

1.741E-12

1.970E-12

areal hole density / 1011

cm-2

µ / cm2V-1s-1

2 4 60

1

2

mobil

ity /

10

-8cm

2V

-1s-1

areal hole density / 1011

cm-2

(a)

(b) (c)σ / eV 0.16

a / nm 1.5

µ0 / cm2V-1s-1 1.35×10-5

×10-9

×10-9

×10-9

×10-9

×10-8

×10-8

×10-8

×10-8

×10-8

μF (F ) = E xp

(c2

(σ̂

3/2 − c3) (√

1 + c4( qaF

σ

)2 − 1))

(3)

with σ̂ = σ/(kT ) , c1 = 0.42, c2 = 0.44, c3 = 2.2 and c4 = 0.8. The parameter δ is given by 2/σ̂ 2

(ln

(σ̂ 2 − σ̂

) − ln (ln (4))) .

μ 0 is the mobility at zero electric fi eld and infi nite tempera-ture. Assuming that the carrier-density distribution across the pentacene thin fi lm in the transient experiment is given by the one of a DC-operated OFET one can approximate the rela-tion between surface and volume density of the carrier at the interface of pentacene and PMMA to p ≈ q 2 p a 2 /(2 kT ε ). ε is the dielectric function of the organic semiconductor. Thus, the hole mobility can be calculated in dependence of the prevailing elec-tric fi eld and the areal density of carriers. In Figure 3 b and c the fi t of the model to the experimental data is depicted resulting in a disorder parameter of σ = 0.16 eV, an intermolecular dis-tance of a = 1.5 nm, and μ 0 of 1.35 × 10 − 5 cm 2 V − 1 s − 1 . While the intermolecular distance appears to be in the range known from structural analysis, [ 11 ] the disorder parameter is large even if compared to amorphous materials. [ 10 ] For pentacene based OFETs, values in the range of 0.095 eV and lower have been reported in the on-state of the transistor. [ 9 ] The large disorder parameter cannot be explained by Joule heating increasing locally the temperature or altering the morphology. Irreversible changes in the surface potentials and transistor characteristics have not been observed.

4 wileyonlinelibrary.com © 2013 WILEY-VCH Verlag

The fact that a strong carrier-density dependence of the hole mobility in the lower charge state is observed, contradicts the Gaussian disorder model where a density independent mobility is expected. [ 12 , 13 ] However, a substantial density dependence of μ in the low charge regime has been reported e.g. in poly-crystalline zinc phthalocyanine (ZnPC) thin fi lms and has been explained by additional trap states in the ZnPC energy gap. [ 13 ] In amorphous ZnPC the density dependence was less pronounced. Assuming the Gaussian disorder model, the pres-ence of trap states results in a larger effective disorder param-eter as was demonstrated earlier. [ 14 ] Hence, a trap-state broad-ened, effective disorder parameter at low carrier densities in polycrystalline pentacene fi lms is possible going along with the pronounced carrier-density dependence of the hole mobility. Although the origin of the large σ is not fully unriddled, the EGDM can describe the extracted transient mobilities demon-strating that even in the presented charging experiment, the available electric fi elds pulling at the carrier front are insuffi -cient to trigger a substantial increase in mobility. The increase in the fi eld-effect mobility depends simply on the available car-rier density, even in the low carrier-density regime.

We have investigated the charge reversal of a pentacene based organic fi eld-effect transistor from electron to hole domination. Using the KPFM, we realized a delayed response of the local surface potential in the transistor channel upon a bias change in a dynamic measurement being even more delayed once the

GmbH & Co. KGaA, Weinheim Adv. Mater. 2013, DOI: 10.1002/adma.201300004

www.advmat.dewww.MaterialsViews.com

CO

MM

UN

ICATIO

N

tip position was shifted further away from the contacts indi-cating a transient phenomenon. Since a successive repetition of the dynamic charge reversal ended in a reproducible response of the local surface potential, the surface potential could be determined quasi-simultaneously everywhere in the transistor channel. Thus, the entire time evolution of the surface-poten-tial distribution could be monitored. From such measurements it is possible to access the electric fi eld and charge-carrier den-sity dependency of the sub-threshold mobility of pentacene based organic fi eld-effect transistors. The mobility at low carrier densities was found to be below 2 × 10 − 8 cm 2 V − 1 s − 1 for a hole density below 7 × 10 11 cm − 2 .

Experimental Section The OFETs consisted of a p + + -Si substrate with a dry thermally grown SiO 2 layer of 100 nm. The substrates were cleaned in Deconex PF15 (Borer Chemie AG) and deionized water and transferred to a nitrogen environment. Thereafter, ∼ 110 nm PMMA were deposited via spin-coating out of a 2 wt% tetrahydrofuran solution and cured for 60 min at 110 ° C. 50 nm of pentacene, 230 nm Al contact pads and 50 nm thick Au source and drain contacts were deposited at room temperature with ∼ 2 Å s − 1 by PVD through shadow masks. During Au deposition a 5 μ m thick carbon fi ber (Toho Tenax Europe GmbH) in the shadow mask defi ned the transistor channel. The base pressure was always below 10 − 6 mbar. The channel length L was 5 μ m and the channel width W was 0.5 mm. Current/ voltage (IV)-characteristics were measured using an HP4155A parameter analyzer. KPFM measurements were carried out with a customized Omicron VT AFM atomic force microscope with homebuilt electronics to bias the OFET during the Kelvin measurement under UHV conditions at room temperature. The drain current was monitored in situ via a 200 Ω shunt resistor. The KPFM setup is based on the frequency modulation (FM) method described by Kitamura and Iwatsuki. [ 15 ]

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

© 2013 WILEY-VCH Verlag Adv. Mater. 2013, DOI: 10.1002/adma.201300004

[ 1 ] L. Bürgi , H. Sirringhaus , R. H. Friend , Appl. Phys. Lett. 2002 , 80 , 2913 .

[ 2 ] A. Petrovic , E. Pavlica , G. Bratina , A. Carpentiero , M. Tormen , Synth. Met. 2009 , 159 , 1210 .

[ 3 ] S. G. J. Mathijssen , M. Kemerink , A. Sharma , M. Coelle , P. A. Bobbert , R. A. J. Janssen , D. M. de Leeuw , Adv. Mater. 2008 , 20 , 975 .

[ 4 ] C. Siol , C. Melzer , H. von Seggern , Appl. Phys. Lett. 2008 , 93 , 133303 .

[ 5 ] S. G. J. Mathijssen , M. Cölle , A. J. G. Mank , M. Kemerink , P. A. Bobbert , D. M. de Leeuw , Appl. Phys. Lett. 2007 , 90 , 192104 .

[ 6 ] J. R. Burns , RCA Rev. 1969 , 30 , 15 . [ 7 ] a) H. Bässler , Phys. Stat. Sol. B 1993 , 175 , 15 ; b) H. Bässler ,

A. Köhler , Top. Curr. Chem. 2012 , 312 , 1 . [ 8 ] M. C. J. M. Vissenberg , M. Matters , Phys. Rev. B 1998 , 57 , 12964 . [ 9 ] I. I. Fishchuk , A. K. Kadashchuk , J. Genoe , M. Ullah , H. Sittler ,

T. B. Singh , N. S. Sariciftci , H. Bässler , Phys. Rev. B 2010 , 81 , 045202 . [ 10 ] W. F. Pasveer , J. Cottaar , C. Tanase , R. Coehoorn , P. A. Bobbert ,

P. W. M. Blom , D. M. de Leeuw , M. A. J. Michels , Phys. Rev. Lett. 2005 , 94 , 206601 .

[ 11 ] C. D. Dimitrakopoulos , A. R. Brown , A. Pomp , J. Appl. Phys. 1996 , 80 , 2501 .

[ 12 ] C. Tanase , E. J. Meijer , P. W. M. Blom , D. M. de Leeuw , Phys. Rev. Lett. 2003 , 91 , 216601 .

[ 13 ] R. Schmechel , J. Appl. Phys. 2003 , 93 , 4653 . [ 14 ] a) A. Fleissner , H. Schmid , C. Melzer , H. von Seggern , Appl. Phys.

Lett. 2007 , 91 , 242103 ; b) U. Wolf , H. Bässler , P. M. Borsenberger , W. T. Grünbaum , Chem. Phys. 1997 , 222 , 259 .

[ 15 ] S. Kitamura , M. Iwatsuki , Appl. Phys. Lett. 1998 , 72 , 3154 .

Acknowledgements The authors would like to thank the Bundesministerium für Bildung und Forschung (BMBF) for their fi nancial support through Project No. 01BI564.

Received: January 1, 2013 Revised: March 5, 2013

Published online:

5wileyonlinelibrary.comGmbH & Co. KGaA, Weinheim