nanotechnology / apl98(84505)05

w = − p L VDS − Vbi VGS + −1 VGS − 2 VDS − Vbi 2 .

4

An additional phenomenological parameter had to be introduced. Instead of the saturation current, second line of Eq.3 , one has the electron current that is injected at the Mg drain. Its linear dependence on VDS and the parallel shifts with VGS and VGS can be described by

with Gn /w being the channel conductance. With expressions4 and 5 , a rather good piecewise description of the output characteristics is achieved, as shown by the symbols in Fig. 14 a . The built in potential has been estimated from the simulated current-voltage characteristics to be Vbi =−1.0 Vwhere the current vanishes . This value is slightly lower than the input value Vbi =−1.365 V, according to the work functions used. This difference may be due to the small potential drop at the Au accumulation contact. The phenomenological parameter =0.952 deviates only slightly from the ideal value, =1. The other adjusted parameters are the following: p = 1.08¯1.19 10−4 cm2 /V s increasing with the gate-source voltage , VGS =−7.57 V, and the conductance Gn /w=6.3 10−9 S/cm. The extracted hole mobility reproduces well the input value p =1.2 10−4 cm2 /V s. From VGS, we obtain Qif =−10.9 1011 e cm−2 for the interface charge, which is only slightly higher than the input value, Qif =−8 1011 e cm−2. Finally, the n channel conductance has to be considered. This current will be limited by the resistance of the depletion layer between the n channel and the Mg drain, as analyzed in Sec. IV B. Therefore, it

should be described as Gn /w= d/ldep =e nndepld/ldep, where ndepl is the electron concentration in the depletion layer and

ldep its length. Together with the electron mobility, these are three unknown parameters that cannot be determined from the extracted conductance. However, we can check whether the conclusion on the predominance of the tiny depletion region for the entire electron current is appropriate: Estimat-

ing ndepl 1014 cm−3 and ldep 100 nm from the simulated proÞles Fig. 8 and using the input electron mobility n =1.2 10−3 cm2 /V s, we obtain Gn /w 5.8 10−9 S/cm,

which coincides well with the value extracted from the current-voltage characteristics and conÞrms the explanation for the linear dependence of this current on VDS.

Next, we consider the case of Mg as source, with the n-channel transistor characteristics for lower VDS and the hole current injected at the Au source for larger VDS, with the latter having a quadratic dependence on VDS, shifted with VGS Fig. 14 b . Application of the modiÞed Shockley equation 4 to the electron current must be considered as highly questionable because in the derivation of the Shockley equation one supposes at least the source contact to be Ohmic,

whereas in the case considered here the Mg source is clearly non-ohmic. Indeed, by replacing VDS →−VDS ,VGS → −VGS ,Vbi →−Vbi, and p → n =1.2 10−3 cm2 /V s, in Eq.4 , one obtains currents much larger than those simulatedsymbols in Fig. 14 b for VDS =20, 30 and 40 V . Moreover, for the transition into saturation, Eq. 4 leads to a quadratic gate-voltage dependence, whereas the simulations yield an almost linear dependence. Nevertheless, describing the simulated current-voltage characteristic with this equation could be possible by introducing a lower and gate-voltage-

dependent effective mobility n,eff VGS . But in this way one obtains an apparent dependence of the mobility on the con-

tact, which is in contradiction to the reality of an unchanged higher mobility, and a gate-voltage-dependent reduction of the current due to the Schottky contact for the n channel at the source.

For the source at the Mg contact, the hole current injected at the Au drain for larger VDS can be expressed as

which describes both the quadratic voltage dependence and the shift with VGS as seen in Fig. 14 b . The constant V0 =−4 V is not directly connected with Qif in contrast to the corresponding constant VGS in Eq. 5 . The reason has been explained above: Because of the larger electron mobility, the drain-induced p channel only begins to dominate at higher drain-source voltages when the n channel almost disappears. The other constant is B=1.02 10−14 A V−2 m−1. Hole injection at the Au drain, which yields excess holes, and the quadratic voltage dependence suggest SCLC. Then the constant in Eq. 6 will be given by the common expressions,

Here in the second equation the bimolecular recombination rate deÞned in 2 has been inserted. Thus one can determine the geometric mean value of the mobilities n p 1/2 =113 cm2 /V s from the adapted value B; whereas from the input parameters we have n p 1/2 =3.8 10−4 cm2 /V s, i.e. a value more than Þve orders of magnitude lower. In order to explain this discrepancy, the current-voltage characteristics have also been simulated for a diode, with a structure similar to that of a transistor Fig. 3 but without gate oxide and

gate. In this case, Eq. 6 with VGS =0 and V0 =Vbi Þts the simulated current with B=3.12 10−20 A V−2 m−1. Using this value for B with Eq. 7 , we obtain n p 1/2 =3.5

10−4 cm2 /V s, in good agreement with the input mobilities. Actually, Eqs. 6 and 7 are analytical approximations including the one-dimensional solution of the Poisson equation. Therefore they are appropriate for the diode. But in the FET, the the perpendicular Þeld is much larger than the longitudinal one roughly L/dox 105 in our structure , because of the applied gate voltage. It creates the extremely thin accumulation layer, and the excess charge in the hole injection at the Au drain is also conÞned in this thin region. For this

inherent 2D case, an analytical approximation is not possible and the numerical solution can only be obtained with the simulation. Thus it can be concluded that space-charge limitation in an accumulation layer leads to currents that are orders of magnitude larger than those in a diode, but surprisingly, the quadratic voltage dependence is preserved.

VI. CONCLUSIONS

Numerical two-dimensional simulations for a singlelayer model system Fig. 3 yield current-voltage characteristics that exhibit the same attributes of ambipolar operation as those observed experimentally in a double-layer structure with an electron-injecting top contact Fig. 1 b : For Au as source and a negative gate voltage, typical p-channel characteristics are observed for lower negative drain-source voltages with an abrupt steep increase of the drain current at some drain voltage due to electron injection at the Mg drain. With increasingly negative gate voltage, the onset of this current is shifted to more negative drain voltages and the current exhibits an almost linear drain-voltage dependence. For Mg as source and a positive gate voltage, in addition to the n-channel formation at lower drain-source voltages, there is also an additional current for larger drain-source voltages due to hole injection at the Au drain. The n-channel current increases in saturation almost linearly with the gate-source voltage, in contrast to the normal quadratic dependence. The hole current injected at the Au drain depends quadratically on the drain voltage. Owing to the lower hole mobility, this current increase starts to predominate at an even larger drain voltage than that at the transition of the electron current into saturation. This is in contrast to the case of the Au source, where the additional electron currents begins to predominate at roughly the transition of the hole current into saturation. Hence, the two onsets cannot be described by the same threshold voltage.

A detailed understanding of the features described can be obtained from quantitative simulations of the internal proÞles of the potential and the two charge-carrier concentrations. The normal p-channel characteristics for the Au source and the quadratic drain voltage dependence of the hole current injected at Au as drain for larger voltages are connected with the hole accumulation at this contact. As the electron density at the Mg contact is much lower than in the n channel, a depletion zone arises between the contact and the channel. This leads, for Mg as source, to lower currents than expected from the mobility, to the nonquadratic gate voltage dependence, and, for Mg as drain, to the linear drain voltage dependence for higher voltages. Because of the larger electron mobility, the Mg-drain-injected current begins to predominate practically at the drain voltage at which the n channel is formed, whereas the hole current injected at Au as drain becomes visible in the current characteristics only at higher voltages. For larger drain voltages, when both channels coexist, recombination occurs near the position at which n= p, with a shift from drain to source with increasing drain voltage. This shift is more pronounced for the Mg drain, as the electrons injected there have the larger mobility. For the same reason, recombination in both cases is larger near the

Au contact. In the 30 nm layer considered, the concentrations in both channels decrease almost two orders of magnitude towards the outer surface, but they are still larger than n= p, and hence the recombination is almost constant across the layer.

Variation of the doping, the Mg-contact work function, mobilities, recombination, and interface charges conÞrm this interpretation of the device operation. In particular, for a pronounced ambipolar behavior, an appropriate combination of the ratio of the mobilities and of the barrier of the electroninjecting contact is important.

Direct parameter extraction is restricted to the mobility of holes from the p channel with Au as source, as in this case accumulation exists, and to an interface charge leading to a ßatband voltage shift connected with a shift of the onset of the electron current injected at the drain. As there are too many parameters that determine the depletion zone near Mg, they cannot be derived from the current characteristics. Although the hole current injected at the Au drain is spacecharge limited with a quadratic drain voltage dependence, its value deviates drastically from that given by the standard SCLC expression because of the conÞnement by the perpendicular Þeld, which is much stronger than the Þeld in the direction of the current.

Finally, a few preliminary results of the simulation for the heterolayer structure Fig. 1 b are summarized: i For Mg prepared as top contact, one obtains larger electron currents; an effect we have already described in another context.27 ii Although the hole channel occurs at the interface to the oxide, one has two electron channels owing to the Mg top contact: one at the interface to the oxide and the second in the Òelectron conductingÓ P13 layer at the interface to pentacene. However, the main electron channel is the one at the interface to the oxide in the pentacene layer, unless the electron mobility of the Òelectron-transport layerÓ is several orders of magnitude larger than that one in pentacene. iii Improved electron injection due to the larger afÞnity of the second layer reduced barrier is achieved, however, as at the same time the barrier at the heterojunction to pentacene increases, an optimum is expected, similar as in recently demonstrated results on polymer-modiÞed anodes in lightemitting diodes.34

ACKNOWLEDGMENTS

This work is Þnancially supported within the EU-IST- FET program under project IST-33057 ILO and by the Deutsche Forschungsgemeinschaft.

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