Inversion Layer Formation in Organic Field-effect Transistors

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Inversion layer formation in organic field-effect devices

Th. Lindner and G. Paascha

Leibniz Institute for Solid State and Materials Research IFW Dresden, PF 270116, D-01171 Dresden,Germany

Received 20 April 2007; accepted 17 July 2007; published online 14 September 2007

One of the challenges for polymer electronics is the realization of complementary

metal-oxide-semiconductor circuits, requiring both n- and p-channel transistors on the chip. The

difficulty to create both accumulation and inversion layers in the same material has been attributedto obstacles to the synthesis of metallic source/drain contacts for efficient injection of both electrons

and holes, and also to the fact that the electron and hole mobilities differ often by several orders

of magnitude. Although the formation of inversion layers has been well understood in

microelectronics, it has to be studied anew for organics, since the mobility and the intrinsic density

are many orders of magnitude lower. An analytical estimate of the relation between relevant

characteristic times reveals the peculiarities occurring in the organics. Detailed insight is obtained

from a numerical simulation study for metal-oxide-semiconductor capacitors and transistors of

different design. In simulated quasistatic capacitance-voltage characteristics hysteresis effects

are obtained due to the inversion layer formation process. This mechanism can be understood

by inspecting the internal density profiles obtained by the simulation. In addition, capaci-

tance-frequency characteristics are simulated and analyzed in more detail with equivalent circuit

models that describe the simulated characteristics well. Here, the relaxation times characterizing the

transition between the maximum capacitance and the geometrical capacitance are determined by

resistances and capacitances of sublayers, which can be ascribed different regions as oxide, bulk,

depletion, accumulation, or inversion. Both the design and the source/drain contact properties

influence the characteristics significantly. 2007 American Institute of Physics.

DOI: 10.1063/1.2776235

I. INTRODUCTION

There has been an increasing interest in organic electron-

ics in recent years. Organic field-effect transistors FETs areparticularly attractive for low-cost and low-performance ap-

plications, such as organic displays,1

organic complementary

circuits,25 and all-polymer integrated circuits.68 One of the

challenges for polymer electronics is the realization of

complementary metal-oxide-semiconductor CMOS circuitsrequiring both n- and p-channel transistors on the chip. Ad-

vantages of digital circuits using complementary logic in-

clude lower power dissipation, more robust operation, better

noise margins, and ease of circuit design. This counts, of

course, also for organic-based electronics.

Organic semiconductors are usually unintentionally

p-doped, i.e., application of a negative gate voltage in or-

ganic thin-film transistors TFTs results in the formation ofa hole accumulation layer at the semiconductor-insulator in-

terface forming the current channel. For the reversed polar-ity, an inversion layer of electrons should appear, but this is

usually not observed. This has been attributed, on the one

hand, to the difficulty in engineering the metallic source/

drain contacts for efficient injection of both electrons and

holes,9

and on the other hand, to the fact that in the past

reported electron mobilities are usually several orders of

magnitude lower than those of the holes. But, good ohmic

contacts for the injection of both holes and electrons into the

same material are possible, e.g., by bilayer source/drain con-

tacts. Also, a high work function, nonoxidizing metal goldas source/drain contact material can give good performance

for both p- and n-channel transistors.5

The low electron mo-

bility values can be caused by charge trapping in the semi-conductor or at the semiconductor-insulator interface. In the

second case, extrinsic impurities are important. Indeed, cur-

rent limiting trap states can be avoided by improved techno-

logical processing. Thus, the data presented in Ref. 10 pro-

vide evidence that silanol groups present at the commonly

used SiO2 dielectric interface can quench n-channel activity

of organic semiconductors.

Both p- and n-channel operation in a single organic

field-effect transistor is realized in so-called ambipolar or-

ganic TFTs. The first report on ambipolar operation was for a

device employing a heterostructure with two separate or-

ganic semiconductors as active layers; one electron- and one

hole-conducting material.11

In this structure, identical Auelectrodes as source and drain contacts are used, leading to a

limitation of electron injection. In another ambipolar hetero-

structure organic FET with two active organic semiconductor

layers, source and drain electrodes of Au and Mg,

respectively,12,13

are used to optimize hole and n-electron

injection. In order to achieve n- and p-channel conduction, as

well as efficient injection of both types of carriers in the

same material, a single layer device based on an interpen-

etrating network of two materials as active layer was

realized.14

Even single layer devices with an active layer

aCorresponding author. Electronic mail: [email protected]. URL:

http://www.ifw-dresden.de/institutes/itf/members/paasch

JOURNAL OF APPLIED PHYSICS 102, 054514 2007

0021-8979/2007/1025 /054514/12/$23.00 2007 American Institute of Physics102, 054514-1

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consisting of a single organic material were realized, which

are capable of operating in both p- and n-channel

regimes.4,10,14

In view of the experimental progress in realizing

single layer organic TFTs with both p-accumulation and

n-inversion channels, it is worth to consider the conditions

for the inversion layer formation theoretically by numerical

simulation. Here, the interplay of different influencing fac-

tors will be demonstrated, such as the width of the gap morecommon are at present organic wide gap materials, but

smaller gaps as 1.5 eV Ref. 15 or even below 1 eV Refs.16 and 17 are known, different geometries of TFTs andmetal-oxide-semiconductor MOS capacitors, material prop-erties of contacts and the organic layer, and measuring con-

ditions.

II. DEVICE SIMULATION AND MATERIALPARAMETERS

Simulations using the drift-diffusion model DDM werecarried out for both MOS capacitors and TFTs with an or-

ganic semiconductor as an active layer. In the present inves-tigation, the two-dimensional 2D device simulation pro-gram ISE-TCAD

18is used. The applicability of the DDM to

organic materials has been discussed in Refs. 1921. Suc-

cessful simulations of organic light-emitting diodes19,2224

and field-effect devices2529

have been performed. The pro-

gram solves simultaneously the Poisson equation for the

electrical potential and the continuity equations for the

hole p and electron n densities. Here we mentionshortly

19,20that the Poisson equation and the continuity equa-

tions are of course of general validity. The current density as

composed of drift and diffusion contributions as used in the

DDM is also valid for transport in the organics. In the

nondegenerate limit the hole p and electron n den-sities are connected with the hole and electron quasi-

Fermi potentials Fp

and Fn

by p = ni expeFp

/kBTand n = ni expeFn/kBT. The intrinsic density ni=NVNC expEg/ 2kBT is connected with the gap energyEg and the effective densities of states NV and NC. For a

molecular material one has to use the molecular or monomer

density instead of the effective density of states.19

For a

polymer with a Gaussian or exponential density of trans-port states it has been shown in Ref. 21 that the nondegen-

erate approximation results in a surprising good approxima-

tion for the accumulation charge per unit area, which is just

the quantity that determines the current in the transistorchannel. There remains only a small error in the flatband

voltage, which can be corrected afterwards if needed. Details

of the simulation method are summarized in Refs. 2729.

The simulated device structures are shown in Fig. 1. The

MOS capacitor has a thickness of the organic layer of dorgcap

=150 nm Fig. 1a, which is larger than the depletionlength for the chosen doping. In the case of the frequency

response also a layer thickness dorgcap =50 nm less than the

depletion length is chosen. For the thin-film transistor Figs.1b and 1c an organic layer thickness of dorg

tft =50 nm is

chosen, since a thickness less than the depletion layer length

is essential for the TFT operation.20

TFTs with either source

and drain as top contacts TOC Fig. 1b or bottom con-tacts BOC Fig. 1c are considered. The channel length isL = 1 m, the source and drain contact lengths are 1 m. In

the simulations the device width is always w = 1 m and the

insulator thickness dox =50 nm. The gate contact area is in

all cases 3 m1 m. The gate contact material is char-

acterized solely by its work function. Here we have chosen

G = 4.05 eV for both devices, which corresponds to the us-

age of n+-poly-Si as contact material. The metal work func-

tions of the bulk contact B and of the source/drain contacts

S/D, respectively, are varied in order to describe either a

neutral ohmic contact for holes or an accumulation contact

for either holes or electrons.

The following material parameters are used: The dielec-tric constant of the insulator is ox =3.9 SiO2. For the bandgap Eg of the organic semiconductor three different values

are used: 2.0, 1.2, and 0.8 eV. The larger value is typical for

the material used at present but low-band-gap organics have

been reported also.1517

Further parameters of the organic

material are chosen as follows; dielectric constant =3.24;

electron affinity =3.0 eV; minority carrier life time n= 105 s for electrons and p = 310

6 s for holes Si valueshave been used due to the lack of reliable data for organics;

one estimate ofn = 104 s has been given only for electrons

in poly-phenylenevinylene in Ref. 30; the relevant relaxation

time for inversion layer formation Eq. 3 is much stronger

FIG. 1. a Simulated MOS structure, b top contact TOC field-effectthin-film transistor, and c bottom contact BOC field-effect thin-filmtransistor.

054514-2 Th. Lindner and G. Paasch J. Appl. Phys. 102, 054514 2007



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influenced by the uncertainty concerning the intrinsic den-

sity; mobilities n =p = 103 cm2 /V s; and effective den-

sity of states NC=NV= 1021 cm3 monomer density. As a

basic doping concentration a value of NA = 1017 cm3 is cho-

sen modeling the usually occurring unintentional p doping.

Quasistatic capacitance-voltage C V characteristicswere simulated as follows. At first, a gate-bulk voltage gate-source voltage of VGBVGS = +20 V is applied and held

fixed over a waiting time of 100 s and then the voltage ischanged linearly in time with a ramp rate of R =0.1 V/s up

to VGBVGS =20 V. After a further waiting time of 100 sthe back sweep starts with the same ramp rate. The voltage

applied to the gate electrode of the device changes with time

R = dVGB/dt. By simulation the resulting charging currentflowing to the gate electrode IG is obtained, which is con-

nected to the charge at the gate electrode QG by IG= dQG/dt. Finally, the capacitance can be calculated after-

wards using one of the two relations: CVGB = IGVGB/Ror CVGB = dQGVGB/dVGB.

For the frequency response the dependency of the ca-

pacitance on the frequency of an applied high-frequency hf

signal capacitance-frequency Cf characteristics for agiven gate-bulk voltage is simulated as follows: At first, the

gate-bulk voltage of VGB = +10 V and VGB =10 V, respec-

tively, is applied successively in steps of 1 V and then held

fixed while the simulation of the Cf curve is performed.

III. VOLTAGE SWEEP, TRANSPORT, AND CARRIERGENERATION

For silicon electronics, the different processes determin-

ing inversion layer formation have been analyzed in Refs.

3133. For temperatures below 410 K generation recom-

bination is dominant; for higher temperatures diffusion be-comes dominant in these devices a bulk region is present.Thereby, generation recombination through traps in the junc-

tion region is much more effective than through surface

states, since only trap levels near midgap and close to the

Fermi level contribute significantly. The minority carrier re-

sponse time is then determined by generation see Eq. 3below. For minority carriers in silicon at room temperaturethe response time is typically 0.01 1 s, i.e., they respond to

a maximum frequency of 100 Hz. The fact that silicon tran-

sistors operate also at GHz frequencies is due to a third

mechanism: In the conventional transistor structure minority

carriers can be injected easily from the source and drain re-

gions, which are doped oppositely to the substrate and whichare in close contact to the channel region.

In organic electronics based on large band-gap organic

materials, the generation process is very inefficient. More-

over, another device structure is used, usually the thin-film

design with bottom or top source/drain contacts. In addition,

the usual MOSFET has a back contact which is missing in

the TFT, but is present in capacitors used for C V and C

f measurements. Thus, for organic electronics there is a

need to consider anew the processes determining inversion.

For a qualitative understanding of C V and Cf char-

acteristics, it is useful to discuss the relevant time constants

characterizing the measuring process, transport, and genera-

tion of minority carriers. The quasistatic measurements are

carried out with a ramp rate R, which is determined by the

measuring equipment developed especially for Si devices.

Thus a range of R =0.1, .. . ,1 V/ s is typical.25

For a ramprate of R = 0.1 V / s the characteristic time constant is

meas =1 V

R= 10 s. 1a

In contrast, dynamic measurements are usually carried out at

a fixed frequency f and thus

meas = f1 . 1b

In the case of impedance measurement a large frequency

range is accessible f= 103 , . . . , 1 07 Hz, meas= 103 , . . . , 1 07 s.

Transport is characterized by the dielectric relaxation

time for the carrier species j,

d,j =0

j, 2

where j = enjj is the electrical conductivity of the respec-

tive species with concentration nj and mobility j. The car-

riers can follow the external signal for d,jmeas or equiva-lently njj0/emeas. For an unintentionally p-dopedpolymer nj =p = 10

17 cm3 with a relatively high mobilityas required in a transistor, say j =p = 10

3 cm2 V1 s1,

one has =3 as typical value for majority carriers d,p 108 s and this condition is fulfilled not only for the qua-

sistatic regime according to Eq. 1a and 1b, but also forthe frequency response up to f 107 Hz compare Fig. 2.Under this condition the p-accumulation layer can be formed

if the contacts are ohmic for holes for large negative gate-bulk and gate-source voltages, respectively. Since the semi-

conductor capacitance increases strongly in accumulation,

one measures then the oxide capacitance see Figs. 3 and 6because both are in series.

It must be mentioned here that the response time of the

carriers depends on the actual concentration nj, which varies

within the MOS device by orders of magnitude. Therefore,

the carrier response time is locally different within the device

depending on the variation of the carrier concentration nj.

FIG. 2. Relaxation times as function of the gap energy: Measurement

dashed Eq. 1a and 1b, dielectric of minority carriers dash-dotted Eq.2, dielectric of majority carriers dotted Eq. 2, generation of inversioncharge of minority carriers solid Eq. 3. A doping concentration of Ndop=NA = 10

17 cm3 is supposed.




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Regions with a low carrier concentration are most limiting.

Such inhomogeneities and the influence of the oxide capaci-

tance can be described by equivalent circuit models as dem-

onstrated below.

The run of the C V curve between accumulation and

depletion is determined by the depletion length in the semi-

conductor. If it is small, i.e., if there are many charge carriers

high doping, the capacitance decreases gradually. On theother hand, if there are only few carriers, the depletion zone

increases very fast with increasing voltage and the capaci-

tance drops down in a narrow voltage range near the flatband

voltage.

There are several mechanisms which are able to supply

minority carriers to change the charge in the inversion

layer.31

Generation of minority carriers by light is not con-

sidered here. Then one has in the MOS capacitor two mecha-

nisms. Generation of minority carriers is determined by the

relaxation time25,31

inv =1

2Ndop

ni

np. 3

Here n and p are the minority charge carrier lifetimes of

electrons and holes, respectively, Ndop is the concentration

of ionized dopants, and the intrinsic density

niexpEg/ 2kBT decreases exponentially with increasinggap energy Eg. The other mechanism is generation/injection

of minority carriers at the bulk contact followed by diffusion

through the bulk region of the semiconductor and drift

through the depletion layer. For p material with concentra-

tion NA of ionized acceptors the bulk minority density is n

= ni2/NA, and the corresponding dielectric relaxation time

d,nni2. The relations between the relaxation times deter-

mine what happens during the measurement. Minority carrier

current and generation of minority carriers act in parallel in

the formation of the inversion layer; in this case, the faster

process is determinative. As demonstrated in Fig. 2 param-eters according to the preceding section, this is the genera-

tion process for a gap 0.75 eV. However, for a gap

Eg1.25 eV, the measurement is faster and there is no in-

version layer formation. On the other hand, for very low gap

Eg0.75 eV one has d,ninvmeas; the inversionlayer is formed by the minority carrier current even without

generation. For somewhat larger gap, generation dominates

and at about Eg = 1.25 eV measuring is as fast as generation.

Then, the formation of the inversion layer is slowed down.

And since recombination for the back voltage sweep is fast,one has in this region a hysteresis, for an even larger gap

inversion layer generation is too slow and only depletion is

obtained. Corresponding simulated dependencies will be dis-

cussed in the next section.

IV. FORMATION OF THE INVERSION LAYERIN ORGANICS WITH DIFFERENT GAP WIDTH

A. MOS capacitor

The conditions for the formation of an inversion layer

have been discussed in Sec. III. Determinative are the relax-

ation times for generation of minority charge carriers inv 3Refs. 25 and 31 and the dielectric relaxation time for mi-nority carriers electrons for p material d,n =0NA/eni

2,both compared to the characteristic time of the measurement

1a and 1b. Depending on the width of the gap of the usedsemiconductor material, different C V characteristics are

expected as discussed in connection with Fig. 2. Now in Fig.

3 an example will be presented for different gap widths Eg=2.0, 1.2, 0.8 eV and the same affinity. We have chosenbulk p doping with completely ionized acceptors of the con-

centration 1017 cm3; the bulk Fermi energy lies 0.238 eV

above the valence band edge. To ensure similar conditions at

the bulk contact, the work function of the metallic contact

was chosen such that it is aligned with the valence bandedge. Thus, its value changes with the band gap but there is

always a hole accumulation ohmic contact. The work func-tion of the gate contact material is G =4.05 eV. Then, for

the chosen three values of the gap the flatband voltages are

0.712, +0.088, +0.488 V. This shift is clearly visible in

Fig. 3 at the transition into the oxide capacitance where thecurvature changes. For a large band gap of 2 eV, as dis-cussed in Sec. III, transport of minority carriers is negligible,

and compared to the ramp rate generation of minority carri-

ers is too slow for the formation of the inversion layer. In-

deed, there is only a transition of the C V characteristic

from the oxide capacitance at negative voltages accumula-

tion to the geometrical capacitance at positive voltages. Thevalue of the latter corresponds to a fully depleted organic

layer. Since the gate electric field cannot be screened by an

inversion layer, the width of the depletion in the semiconduc-

tor increases until the whole layer is depleted. In contrast, in

the case of a small band gap of 0.8 eV, the time for the

formation of the inversion layer is small compared to the

measuring period and a usual quasistatic C V characteristics

is obtained. Especially in this case one gets the same behav-

ior even without including any recombination process in the

calculation Shockley-Hall-Read SHR is normally used asdiscussed above. Evidently, due to the small band gap the

charge carrier concentration in the material is high enough

FIG. 3. Simulated quasistatic C V characteristics of the MOS structure

Fig. 1a ramp rate 0.1 V/ s for different values of the band gap. Thework function of the bulk contact material is always aligned with the maxi-

mum of the valence band, so its absolute value changes with the band gap

ohmic contact, accumulation contact. Work function of the gate contactmaterial 4.05 eV, doping NA =10

17 cm3, contact area 3 m1 m.




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for a minority carrier current from the bulk to the interface.

But for a larger band gap Eg1 eV, compare Fig. 2 thebulk minority carrier concentration is too low and the inver-

sion charges can be created only by generation. In case of the

medium band gap of 1.2 eV, during the measuring period

inversion is formed slowly and thus with increasing positive

voltages the capacitance increases gradually until the oxide

capacitance is reached. In contrast to the formation, the re-

duction of the inversion layer takes place rather fast and the

characteristics for the sweep direction from positive to nega-

tive voltages is identical with the common quasistatic char-acteristics. The sharp increase of the capacitance from VGB= + 20 V to VGB = + 18 V is discussed below.

The reason for this hysteresis is a recombination rate

considerably higher than the generation rate for the forma-

tion of the inversion layer. This is demonstrated in Fig. 4,

where profiles of a current densities, b carrier concentra-tions, and c recombination rate are shown along the middleof the MOS capacitor. The bulk contact is at y = 0 m, the

interface at y =0.15 m, and the gate contact at y =0.2 m.

All profiles correspond to an applied gate voltage of VGB= +5 V, i.e., in the range of hysteresis Fig. 3, Eg =1.2 V.In Fig. 4a the current densities for electron-, hole-, and

displacement currents are depicted. They are different for the

two sweep directions. Of course, in the oxide there is only a

displacement current density. Since the reduction of the in-

version layer takes place much faster accordingly a fasterchange of the electric field across the oxide occurs this den-sity has to be larger for the sweep from positive to negative

voltages. For this sweep direction the displacement current is

zero in the semiconductor apart from the decrease in a nar-

row region immediately at the interface. However, for theopposite sweep direction, the displacement current density is

at first 2109 A/cm2 and drops down to zero in the middle

of the semiconductor layer with approaching the bulk con-

tact. Since inversion builds up slowly, the depletion zone

extends at first deep into the semiconductor, with gradually

increasing inversion layer formation; its width decreases un-

til the inversion layer is completely formed. Finally, the

width of the depletion zone reaches a value, which is con-

nected with the surface potential at inversion this is theusual maximum depletion layer width, but if there is no in-

version layer the depletion zone has, of course, a larger

width. In case of a completely depleted semiconductor layerthe displacement current density would not drop down tozero up to the bulk contact. The electron current is prominent

only near the oxide interface, where electrons are generated

or where they recombine compare with Fig. 4c. Directlyat the interface this current drops down to zero and is not

relevant in the bulk p-type semiconductor. Toward the inter-

face the hole current decreases, corresponding to the rise of

the electron current, and is of course zero directly at the

oxide interface. The sum of both is called conduction cur-

rent. In the bulk material it is solely given by the hole current

and it is different for both sweep directions at the bulk con-

tact. These two values of the hole current density, or equiva-

lently, the difference of the total current densitiesj

tot=j

n+jp +jdisplace at the gate and the bulk contact results in thecorresponding currents and capacitances of the C V charac-

teristic, respectively, at VGB = +5 V for both sweep direc-

tions. In Fig. 4b the electron and hole densities are de-picted. They differ substantially for both voltage sweep

directions note the logarithmic scale. For the sweep fromnegative to positive voltages the semiconducting layer be-

comes at first partially depleted, since the generation of in-

version charges is very slow. This results in much lower

charge carrier concentrations and stronger band bendingthan for the opposite sweep. The recombination and genera-

tion rate is determined by the deviation of the carrier densi-

ties from equilibrium. The rate is largest at the positionwhere both carrier concentrations are equal. As these densi-

ties are different for the two sweep directions, the generation

rate for the creation of inversion charges and the recombina-

tion rate for their reduction are different. This is explicitly

shown in Fig. 4c. Even though the generation of carriersoccurs in a broader region of the semiconductor, its rate is

significantly lower than the recombination rate. This explains

the observed hysteresis in Fig. 3. The maximum recombina-

tion rate is at the position where electron- and hole-charge

densities, as well as the current densities, are equal.

Now we consider in more detail the capacitance at VGB= +20 V for the medium band gap ofEg = 1.2 V. As already

FIG. 4. Profiles of the a current densities, b charge carrier densities, andc recombination/generation rate in the middle of the MOS capacitor fromthe bulk contact y =0 to the gate y =0.2 m for the CV characteristics

with Eg =1.2 eV in Fig. 3 at VGB = + 5 V .




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discussed in connection with Fig. 4b inversion builds up

slowly, a depletion zone extends at first deep into the semi-conductor, and with gradually increasing inversion layer for-

mation its width decreases until the inversion layer is com-

pletely formed leading to the gradual increase of the

capacitance for the sweep direction from negative to positive

gate voltages. However, the formation of this deep depletion

zone takes place very fast while its following reduction is a

slow process. Due to the low carrier densities in that region

the dielectric relaxation time is very large and therefore the

redistribution to equilibrium especially of the electrons isvery slow, in addition to the slow carrier generation. In Fig.

5 carrier density profiles are depicted from the bulk contact

to the insulator interface in the middle of the MOS capacitor

at VGB = + 20 V. It is clearly visible that the charge densitydistribution at the end of the voltage sweep from negative to

positive gate voltage dashed lines, before waiting time isfar away from equilibrium solid lines, even though the ox-ide capacitance is nearly reached in the C V characteristics

at this point compare Fig. 3. Solely direct at the interfacethe electron density is equal to the equilibrium value. Also,

after the waiting time here 100 s, before starting the backvoltage sweep dotted lines, equilibrium is not completelyreached; carrier generation still takes place. This causes the

C V curve for the back sweep from positive to negative

voltage to start with a value below the oxide capacitance.

Until equilibrium is reached, there is no effective recombi-

nation because there are less charge carriers than in equilib-rium that results in a reduced hole current from bulk contactto the recombination zone connected with a lower capaci-

tance. Simulation shows that this behavior at VGB =+20 V is

still present for a longer waiting time of 500 s, i.e., a fairly

long time is necessary to reach the equilibrium charge carrier

distribution, because in approaching equilibrium the genera-

tion rate will decrease.

B. Thin-film top contact transistor

Similarly, as in the capacitor Fig. 1a one can alsoobtain quasistatic C V characteristics for the TOC transistor

structure Fig. 1b if source and drain are set to zero volt-age while the voltage ramp is applied to the gate. The result-

ing characteristics are depicted in Fig. 6, again for three dif-

ferent gap widths. Compared to the capacitor only the device

structure is changed, since in contrast to the bulk contact in

the capacitor the source and drain contacts are separated by

the channel. In addition, the organic layer is only 50 nm

thick. All other parameters are the same as for the quasistatic

C V characteristics of the capacitor Fig. 3. As visible fromFig. 6, the qualitative dependencies remain the same. The

oxide capacitance which is equal for both device structuresis obtained for sufficiently large negative gate voltages. The

flatband voltage depends on the gap width for the same rea-

son as explained for the capacitor in Sec. IV A. Again, the

appearance of inversion for sufficiently large positive gate

voltages depends on the gap width. For a small gap, inver-

sion charges can be generated fast enough and a usual qua-

sistatic characteristic is obtained. In case of the large band

gap the inversion layer is not formed, and for positive volt-

ages there is only a transition of the C V characteristics to

the geometrical capacitance. In the TOC structure its value

must be determined numerically. But a good estimate is ob-

tained if one considers, besides the smaller organic layer

thickness, only the area of source and drain as contact area,i.e., 2 1 m1 m. With the common analytic expres-sions a value of 0.626 fF is then obtained for the geometrical

capacitance compared to a simulated value of 0.656 fF ex-

tracted from Fig. 6. Of course, for the value of the oxide

capacitance the whole device area of 3 m1 m must be

considered because the accumulation layer formed at the in-

terface to the insulator extends over the whole length of the

device. Finally, for a medium gap width hysteresis arises. For

both sweep directions the increase of the capacitance is much

slower than in the capacitor. Because of the much thinner

organic layer the carrier generation zone cannot expand as

much as in the capacitor. Therefore, in this transistor struc-

FIG. 5. Hole and electron densities in the middle of the MOS capacitor from

the bulk contact y =0 to the insulator interface y =0.15 m at an appliedvoltage ofVGB = +20 V. Compared are density profiles before dashed lineand after dotted line the waiting time of 100 s at VGB = +20 V with equi-librium distribution solid line.

FIG. 6. Simulated quasistatic C V characteristics of the TOC transistor

Fig. 1b ramp rate 0.1 V /s for different values of the band gap. Thework function of the source- and drain-contact material is always aligned

with the maximum of the valence band, so its absolute value changes with

the band gap ohmic contact, accumulation contact. The gate contact area is3 m1 m and 1 m1 m for source and drain. Other parameters

as in Fig. 3.




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ture generation is lower and the reduction of the deep deple-

tion zone which is formed because the generation of inver-sion charges is too slow takes much more time.

V. QUASISTATIC CV CURVES FOR TFTS WITH WIDE

GAP ORGANICS AND WITH DIFFERENT SOURCE/DRAIN WORK FUNCTIONS

In most organic materials generation of carriers is too

inefficient due to the large gap, even at low frequencies. To

obtain both accumulation and inversion in a thin-film tran-

sistor with such material, it is necessary to inject both types

of carriers via source and drain. This can be achieved either

by using different contact materials or by contacts which

allow for efficient injection of both carrier types for some

reason both have been realized in ambipolar transistors; seeSec. I. This is in contrast to a conventional transistor struc-ture, which is usually a 4-terminal device. There, the bulk

contact is ohmic for majority carriers and allows for injectionto obtain accumulation. Source and drain are doped oppo-

sitely to the substrate and allow therefore injection of minor-

ity carriers. But in a thin-film structure the bulk contact is

missing.

In the preceding Sec. IV the work function of the bulk

contact or of the source/drain contacts was chosen such that

it is aligned with the valence band edge. Thus, with the cho-

sen p doping, these contacts are hole accumulation ohmiccontacts. In this case inversion at the interface of the organic

layer with the oxide could not be achieved for the wide gap

organic material. In this section it is demonstrated how dif-

ferent choices of the materials for source and drain influence

the channel formation of TOC and BOC transistors. We con-

sider the cases when the contact work function is as before

aligned with the valence band = 5 eV, hole injecting con-tact or with the conduction band = 3 eV, electron inject-ing contact. Quasistatic C V characteristics ramp rate0.1 V/s are shown for the TOC transistor in Fig. 7a andfor the BOC transistor in Fig. 7b. The work functions of thesource/drain contacts are chosen as indicated in the figure. If

the work functions for source and drain are the same, one

obtains for the larger lower work function accumulationinversion for larger negative positive gate-source voltageand hence the capacitance approaches the oxide capacitance,

whereas for larger positive negative gate-source voltage thegeometric capacitance is approached, which is different forthe TOC and BOC structures. Due to the used p doping the

transition from accumulation to depletion is different from

the transition from inversion to depletion. On the other hand,

for different work functions for source and drain one has

good inversion charge injection from one contact and good

accumulation charge injection from the other contact. There-

fore, both inversion and accumulation do occur. Thus, the

oxide capacitance value is reached for negative and positive

gate-source voltages as well. Such a structure has been ex-

ploited in ambipolar TFTs, but the disadvantage of such de-

vices is that they do not really have an off-state.

VI. FREQUENCY RESPONSE OF MOS CAPACITORS

The frequency response is characterized by the complex

frequency dependent impedance Z, or alternatively the ad-

mittance Y, the dielectric function , or the modulus M ,

which are connected among each other by

Z =dVGS

dI= Z + iZ = Y1 = iC+ G1 , 4

= + i =Y

iCgeo= M 1 . 5

Since real and imaginary parts of each quantity are not inde-

pendent, one of them contains the full information. However,

due to the different asymptotic dependencies, usually one

quantity gives at best an immediate insight. For a capacitive

device this is of course the capacitance C. Nevertheless, di-rect information on relaxation times can be better seen from

the imaginary part of the dielectric function.

In the following, examples for the simulated frequency

response are analyzed for MOS capacitors with the structure

shown in Fig. 1a. The gap width of the organic semicon-ductor is 2 eV. Inspection of internal density profiles allows

one to understand the rather different dependencies obtained

for capacitors with thickness of the organic layer smaller or

larger than the depletion length. Moreover, lumped equiva-

lent circuit models will be discussed, which are suitable to

analyze measured data and the elements of which are

uniquely assigned to sublayers of the organic layer.

FIG. 7. Quasistatic C V characteristics ramp rate 0.1 V/ s for the aTOC and b BOC transistors. The work functions of the source/drain con-tacts are chosen as indicated.




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As mentioned above, a p-doped organic semiconductor

is considered NA = 1017 cm3 for dorg =50 nm and NA = 51017 cm3 for dorg =150 nm. With such a doping a hole-accumulation bulk contact is usually chosen we use in thesimulation the bulk contact work function B =5.0 eV andthe notation p-accumulation inversion refers to the chargeat the interface when a negative positive gate-bulk voltageis applied. However, being interested in an n channel in the p

material one could also consider the influence of a bulk con-

tact with electron accumulation; thus we consider also a bulk

contact work function of B =3.0 eV, but the notations

p-accumulation and inversion will be used as defined be-fore. Thin-film MOS capacitors are considered with a thick-

ness of the organic layer of dorg =50 nm 150 nm, which issmaller larger than the depletion length for the chosen dop-ing. The capacitance of the semiconductor layer is Corg=0orgA/dorg and the oxide capacitance is Cox =0oxA/dox= 2.07 fF. Thus the geometrical capacitance is for the thinner

organic layer Cgeo= Cox1 + Corg

1 1 =0.95 fF and 0.45 fF forthe thicker layer. It should be noticed that in the inversion

regime charge carrier generation/recombination is negligible

in the considered frequency range due to the large band gap

as mentioned before.

In Fig. 8 the Cf characteristics are shown for the MOS

capacitor with the thinner organic layer. Figure 8a is for apositive gate-bulk voltage of VGB = +10 V, i.e., inversion of

the p-type material at the interface to the oxide and Fig. 8bfor a negative gate-bulk voltage of VGB =10 V, leading to

hole accumulation at the interface to the oxide. At first the

situation will be analyzed for the positive gate-bulk voltage.

Here, for the hole injection bulk contact with the larger work

function the geometrical capacitance is obtained for the

whole frequency range. On the other hand, for the low work

function bulk contact one has a clear transition between the

oxide capacitance at low frequencies and the geometrical ca-

pacitance at high frequencies with a transition frequency of

2105 Hz marking the maximum of in Fig. 8a. In ad-dition, at higher frequencies there is a plateau of the capaci-

tance, which is 1.04 fF slightly larger than the geometrical

capacitance and the final transition to the latter is flattened

and occurs at about 5107

Hz. In

a hint for a secondmaximum is visible also. The reason for these dependencies

becomes clear from the simulated concentration profiles de-

picted in Fig. 9a. For the larger bulk contact work functionthe electron density is so small there, that in the thin layer,

inversion is not achieved at the interface to the oxide. Apart

from a tiny region near the hole injecting bulk contact both

concentrations are negligibly small, the layer is depleted, and

hence only the geometrical capacitance occurs. But for the

lower work function one has at the bulk contact and at the

interface to the oxide a high electron concentration, the mini-

mum in between is n 21015 cm3, and the whole layer isflooded by minority carriers. Disregarding first the transition

FIG. 8. Cf characteristics for the MOS capacitor according to Fig. 1awith a reduced organic layer thickness of dorg =50 nm for a positive gate-

bulk voltage of VGB = + 1 0 V a and a negative gate-bulk voltage of VGB=10 V b. For the work function of the bulk contact material two differ-ent values are used: B =3 eV and B =5 eV. The curves with open sym-

bols are for the equivalent circuit models. In a also the imaginary part ofthe dielectric function is shown for B =3 eV.

FIG. 9. Electron n and hole concentration profiles from the bulk contacty = 0 to the interface to the oxide y =0.05 m for the Cf characteristicsof Fig. 8 of the MOS capacitor with a reduced organic layer thickness of

dorg = 50 nm for a positive gate-bulk voltage ofVGB = + 1 0 V a and a nega-tive gate-bulk voltage ofVGB =10 V b. For the work function of the bulkcontact material two different values are used: B =3 eV and B =5 eV.




9/12

at higher frequency, this situation can be modeled see Ap-pendix by an equivalent circuit with the oxide capacitancein series with a parallel connection of the capacitance of the

organic layer and its resistance Rn with an averaged elec-tron concentration model 1, Eq. A1 with only one R Cterm. This leads to the capacitance

C= Cox1 + 2Rn

2CorgCorg + Cox

1 +

2Rn

2

C

org +C

ox

2= Cox

1 + 212

1 +

2

22 , 6

1 = RnCorg, 2 = RnCorg + Cox , 7

describing the transition from the oxide capacitance to the

geometrical capacitance, and the inflection point is deter-

mined by the relaxation time 2 and not simply by the dielec-

tric relaxation time 1 of the minority carriers. The simulated

capacitance is well described by this simple dependency as

visible in Fig. 8a with Rn =1.58108 as the only param-

eter. From this value and the chosen mobility, one obtains the

averaged electron density as n =6.61015 cm3, which is

close to the simulated minimum. Using the full Eq. A1model 2 the whole frequency dependence of the capaci-tance is described well including the low plateau and the

transition at higher frequency. From the two capacitances

and resistances obtained from the nonlinear fit and using themobility as used in the simulation one obtains for the thick-ness and the averagedelectron concentration in the inversion

layer d2 8 nm and n2 1.21018 cm3 and for the re-

maining part of the organic layer d1 41 nm and n1 5.21015 cm3. Values close to these ones are obtained already

from the three capacitances and two transition frequencies

extracted from Fig. 8a and Eqs. A2 and A3. It is re-markable that the simple model A1 with only two R Cterms results in such good description, although the electron

density is strongly inhomogeneous as seen in Fig. 9a.Moreover, though the large inversion capacitance is not vis-ible directly since it is larger than the oxide capacitance itdetermines the higher transition and can therefore be de-

tected.

The situation is almost analog for the negative gate-bulk

voltage of VGB =10 V Fig. 8b. Now for the electroninjection bulk contact with the lower work function the geo-

metrical capacitance is obtained for the whole frequency

range. For the hole injecting bulk contact with the higher

work function one has the transition between the oxide ca-

pacitance at low frequencies and the geometrical capacitance

at high frequencies, but with a higher transition frequency.

Thus, it is close to the second, higher transition frequencyand instead of the low plateau in the capacitance one has

only a smeared out transition. Indeed, simulated concentra-

tions Fig. 9b show that for the smaller bulk contact workfunction the whole layer is almost depleted from both elec-

trons and holes, apart from a narrow region near the bulk

contact with high electron concentration. On the otherhand, for the larger work function one has at the bulk contact

and at the interface to the oxide a high hole concentration,

the minimum in between is p 1.11017 cm3, larger thanfor electrons in the former case due to the doping. Again,

already model 1 Eq. 6 describes the simulations well, ofcourse with Rn replaced by Rp. The chosen value of 5.42

10

6

is smaller corresponding to an averaged hole con-centration of p =1.91017 cm3, again close to the simu-

lated minimum. With the full Eq. A1 model 2 the wholefrequency dependence of the capacitance is described well

including the smeared out transition. From the two capaci-

tances and resistances obtained from the nonlinear fit andusing the mobility as used in the simulation one obtains forthe thickness and the averaged hole concentration in the ac-

cumulation layer d2 8.5 nm and p2 1.91018 cm3, and

for the remaining bulk part of the organic layer d1 41 nmand p1 1.510

17 cm3 close to the doping level of1017 cm3.

The capacitance-frequency dependency is quite different

for the thicker layer Fig. 10. Here the oxide capacitance isreached as maximum capacitance at low frequencies only for

the negative gate-bulk voltage and the hole injecting large

work function bulk contact. For the electron injecting holeblocking low work function contact the maximum capaci-tance is much lower and the same is the case for inversion

for both types of contacts. The transition frequencies are near

together for the four cases, however slightly larger when the

maximum capacitance is lower. For an understanding one

can inspect at first the simulated profiles of holes in Fig. 11

for the curves from Fig. 10. The electron concentration is

negligibly small, except for a 2-nm accumulation layer at the

low work function bulk contact. It is clearly seen that in the

FIG. 10. Cf characteristics for the MOS capacitor according to Fig. 1awith layer thickness of dorg =150 nm for a positive gate-bulk voltage of

VGB = + 1 0 V a and a negative gate-bulk voltage of VGB =10 V b. Forthe work function of the bulk contact material two different values are used:

B =3 eV and B =5 eV. The curves with open symbols are for the equiva-

lent circuit models.




10/12

middle of the layer one has bulk concentrations since the

layer thickness is larger than the depletion length. Thus, in

all cases one has a bulk region with the hole concentrationgiven by the doping level and a negligible electron concen-

tration. But for the low work function contact one has a

depletion zone of holes of a width ddepl = 39 nm. In inversion

and for the hole injecting contact there is a depletion zone

near the interface to the oxide with ddepl= 32 nm, and for the

electron injecting contact there are depletion zones on both

sides of the layer, the total width of which is ddepl=49 nm.

Thus, the model A1 can be simplified by setting the resis-tance of the depletion layer as very large. Then one can de-

scribe the system by an equivalent circuit model, which is a

series connection of the oxide capacitance with the capaci-

tance Cdep of the respective depletion layer and with a paral-

lel connection of the bulk capacitance Cbulk and resistanceRp,bulk, the latter with the bulk hole concentration and a

length dbulk= dorg ddepl. The total capacitance is then given

by

C= Cins1 + 212

1 + 222

, 8

Cins =CoxCdep

Cox + Cdep, 9

1 = Rp,bulkCbulk, 2 = Rp,bulkCbulk+ Cins. 10

The maximum capacitance is reduced to Cins and the transi-

tion frequency is determined by 2, which explains the

slightly different values visible in Fig. 10. The model depen-

dency is shown also in Fig. 10. Thereby ddepl is chosen to fit

the maximum capacitance; the values for accumulation with

electron injection bulk contact, inversion with hole contact,

and electron contact are 38, 32, and 45 nm, almost the same

as obtained directly in the simulation. From the value of

Rp,bulk needed to fit the transition frequency one obtains for

the bulk hole concentration values between 4.21017 cm3

and 5.31017 cm3 near the simulation input of 5

1017 cm3.

Thus, the frequency response of thin organic capacitors

can be rather different depending on doping, thickness, and

type of the bulk contact. However, it can be modeled rather

simply by appropriately specifying the equivalent circuit

model A1.

VII. CONCLUSIONS

In the usually unintentionally p-doped organics used in

TFTs with high work function metal contacts as source and

drain, a p-accumulation channel is formed as the on state for

negative gate voltage. For using the advantages of CMOS

circuitry, and also inversion, that means n-channel formation

is needed. Since the organic TFTs differ from the usual

MOSFETs by the missing back contact and usage of metals

for source and drain contacts, and since the organics for the

active layer are until now usually wide gap materials and

have a low mobility, inversion layer formation has been ana-

lyzed for organic field-effect devices. This work is intended

partly also to stimulate experimental investigations on the

inversion layer formation in organic TFTs and MOS struc-tures. So far, only steady-state measurements have been re-

ported on the ambipolar devices, where an inversion channel

is formed.

A general insight is obtained comparing relaxation times.

For the chosen characteristic mobility values for very lowgap Eg0.75 eV one has d,ninvmeas, the inversionlayer is formed by the minority carrier current without gen-

eration. For somewhat larger gap, generation dominates

compared with minority carrier current, the formation of the

inversion layer is slowed down, and since recombination for

the back voltage sweep is fast, one has in this region a hys-

teresis. For a gap Eg1.25 eV, the measurement is faster

and there is no inversion layer formation.More details are obtained from the numerical simula-

tions taking into account the geometry of MOS capacitors

and TFTs and the type of contacts. For the MOS capacitors

with different gap widths Eg =2.0, 1.2, and 0.8 eV of the

organics and a hole injecting bulk contact, the qualitative

expectations are confirmed. For a large band gap transport of

minority carriers is negligible, and compared to the ramp rate

generation of minority carriers is too slow for the formation

of the inversion layer and the layer becomes fully depleted

for larger positive gate voltage; whereas for small band gap a

usual quasistatic C V characteristic is obtained indeed with-

out generation of minority carriers. In case of the medium

FIG. 11. Hole concentration profiles from the bulk contact y =0 to theinterface to the oxide y =0.15 m for the Cf characteristics of Fig. 10 ofthe MOS capacitor with the organic layer thickness of dorg =150 nm for a

positive gate-bulk voltage ofVGB = + 1 0 V a and a negative gate-bulk volt-age of VGB =10 V b. For the work function of the bulk contact materialtwo different values are used: B =3 eV and B =5 eV.




11/12

band gap, during the measuring period inversion is formed

slowly, whereas the reduction of the inversion layer takes

place rather fast and the characteristics for the sweep direc-

tion from positive to negative voltages are identical with the

common quasistatic characteristics. Simulated profiles of

current densities, concentrations, and recombination support

this interpretation in detail and also a peculiar dependency

occurring when changing the sweep direction at larger posi-

tive voltage.The qualitative dependencies and the influence of the

gap width remain the same for quasistatic C V characteris-

tics of a top contact transistor source/drain at zero voltagewhile the voltage ramp is applied to the gate. Quantitative

differences occur only due to the different geometry and

layer thickness.

For TOC and BOC TFTs with a wide gap organic layer

accumulation and inversion are possible if the source and

drain contacts are from different materials, one hole injecting

and the other one electron injecting. Such structures have

been used in ambipolar TFTs, but the disadvantage of such

devices is that they do not really have an off state.

The simulations show that the frequency response of thinorganic MOS capacitors can be rather different depending on

doping, thickness, and type of the bulk contact. Of special

importance is whether the layer thickness is smaller or larger

than the depletion length. However, it can be modeled rather

simply by appropriately specifying the equivalent circuit

model. Thus, the relaxation times characterizing the transi-

tion between the maximum capacitance and the geometrical

capacitance contain resistances and capacitances of sublay-

ers, which can be assigned to different regions as oxide,

bulk, depletion, accumulation, or inversion, depending on

layer thickness, doping, type of bulk contact, and sign of

applied voltage.

APPENDIX

In the frequency range of interest generation/

recombination is negligible for wide gap materials. Then, the

impedance of the MOS capacitor is given approximately by

Z = Rlead +Rox

1 + iRoxCox+

1

A

0

dorg 1

x + i0orgdx

with the integration perpendicular to the organic layer. The

specific conductivity is = epp + enn. It is often sufficient

to replace the integral by a series connection of two parallel

R C terms. Supposing Rox to be large and Rlead negligible

which is in experiment not always the case one has

Z 1

iCox+

R1

1 + iR1C1+

R2

1 + iR2C2. A1

How the two capacitances and resistances should be assigned

to regions in the organic layer depends on the bulk contact

and the applied voltage. Formally, one has in this system the

following four relaxation times:

1 = R1C1, 2 = R2C2, 1,ox = R1Cox, 2,ox = R2Cox.

Actually, a closer inspection shows that one has only two

resonance frequencies. The relaxation time for the lower fre-

quency is given by

low = 1 + 2 + 1,ox + 2,ox = R1C1 + Cox + R2C2

+ Cox

R1C1 + Cox for R1

R2, A2

and that one for the higher frequency is determined by

1

high=

low

12 + 12,ox + 21,ox

=1

R1C11 Cgeo

C1 + 1

R2C21 Cgeo

C2

1

R2C21 Cgeo

C2 for R1R2. A3

Remarkably, in both cases the corresponding simple R Cproduct is only an approximation.

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Inversion Layer Formation in Organic Field-effect Transistors

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