Trap-limited transport

The departure of the experimental data from the y/Ici,sat versus Vg straight line at low gate biases is generally attributed to a subthreshold regime (like in conventional MISFETs). We note, however, that such an interpretation is at variance with Eq. (14.47), which predicts a positive value for V,. As noted above, another origin of this departure would be a decrease in the mobility at low gate voltages, as in amorphous silicon TFTs [13, 18]. 

An altemative method to estimate the field-effect mobility consists of using the transconductance in the linear regime, given by Eq. (14.32). We note that the 

A crucial element in MTR is the profile of the localized state density as a function of energy, the so-called density of states (DOS). Unfortunately, a direct derivation of the DOS from the variation of the mobility is not straightforward. In two papers published in 1972 and 1976 [116, 117], Spear and Le Comber developed a method based on a simplified description of the accumulation layer, which was assumed to behave like a depletion (Schottky) layer, with a constant density of carrier up to a given thickness 2. This method has been more recently analyzed by Powell [118], who concluded that is was only able to give a rough estimate of the DOS. Nevertheless, we have used this method to estimate the DOS in 6T and DH6T [115] and found an exponential distribution of the form 

q is the total density of traps and Tq is a characteristic temperature that accounts for the slope of the distribution. Results are gathered in Table 14-4. In both materials, a comparable characteristic temperature was found, while the total density of traps was ten times higher in 6T than in DH6T. 

At the same time, we determined the trap-free mobility, that is, the mobility corresponding to a high gate bias, at which all traps are filled. Interestingly, as shown in Table 14-4, we found a similar trap-free mobility in 6T and DH6T, de- 

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On the experimental front, Burrows and Forrest 155] have measured the electric field and thickness dependence of the current and radiance from bilayer devices with various HTLs and Alqs as the ETL. The data were analyzed in temis of trap-limited transport in the Alq t layer, with the assumption that the voltage drop across the HTL is negligible. However, this assumption was challenged by Vestweber and Riess [ I56 and Giebcler et al. 1157], who demonstrated that HTL plays an important role in determining the efficiency of bilayer OLEDs. 

To explain the trap-limited transport it is useful to consider the model of a single trapping level of density, Nj., at energy E. below the conducting states, as illustrated in Fig. 3.10. The drift mobility is the free carrier mobility reduced by the fraction of time that the carrier spends in the traps, so that,... 

Fig. 3.10. Illustration of trap-limited transport of carriers for a discrete or distributed trap level.

With the experimental results in mind we retium to the analysis of the trap-limited transport. The time-dependent decrease in the apparent mobility is obviously consistent with our earlier argument that the average trapping time will increase with the number of trapping events for an exponential band tail. Scher and Montroll (1975) were the first to point out this property of a very broad distribution of release times and to associate the effect with transport in disordered semiconductors. They analyzed the random walk of carriers with such a distribution and... 

This is in accord with the theory of dispersive trap limited transport in ID (13) where it is shown that a time averaged trap limited velocity is given by... 

Recently the concept of trap limited drift velocity providing the explanation for the observed saturation have gained much currency (12,13). This has been shown to be inapplicable in explaining these results (3) and % ould any way require trap limited mobilities to be > 20 m /V/s. This ultra high value finds no explanation in such trap limited transport theories and would indicate that the intrinsic mobility was even higher I... 

Figure 9-28. Trap-limited current (low ills (solid lines) lo the experimental (symbols) l/V characteristics of two typical devices with a 200 nin and 600 nm thick hole-transport layer and Alq3. Inset shows l/V curves for various different Alq3-lhicknesses. Reproduced front Ref. 82. ...

Figures 12-12 and 12-13 document that trap-free SCL-conduction can, in fact, also be observed in the case of electron transport. Data in Figure 12-12 were obtained for a single layer of polystyrene with a CF -substituted vinylquateiphenyl chain copolymer, sandwiched between an ITO anode and a calcium cathode and given that oxidation and reduction potentials of the material majority curriers can only be electrons. Data analysis in terms of Eq. (12.5) yields an electron mobility of 8xl0 ycm2 V 1 s . The rather low value is due to the dilution of the charge carrying moiety. The obvious reason why in this case no trap-limited SCL conduction is observed is that the ClVquatciphenyl. substituent is not susceptible to chemical oxidation.

In the case of material with a significant concentration of localized states, it is possible to assnme that transport of a carrier over any macroscopic distance will involve motion in states confined to a single energy. Here it is necessary to note that a particn-larly important departnre from this limiting situation is (according to Rose [4]) a trap-limited band motion. In this case, transport of carrier via extended states is repeatedly interrnpted by trapping in localized states. The macroscopic drift mobility for such a carrier is reduced from the value for free carriers, by taking into acconnt the proportion of time spent in traps. Under steady-state conditions, we may write... 

The possibility of space charge limited transport was verified by measuring the dependence of the conducting current on film thickness. That this mechanism does make a contribution could, in accordance with the SCLC theory (3JI), follow from the second branch of the Inj-lnV characteristics where n > 2 (Fig. 3). However, in no case do the results obtained confirm the j a/ d n dependence required by the SCLC theory, where d is film thickness, and n - a parameter depending on trap distri-... 

Burrows. P. E. Forrest. S. R. (1994). Electroluminescence from trap-limited current transport in vacuum deposited organic light emitting devices. Applied Physics Letters, vol. 64, no. 17,2285-7. 

Insensitivity to surface/solution conditions. Electrokinetic trapping and transport techniques are compatible only with a limited class of fluids, exhibit extreme sensitivity to surface conditions and are difficult to use with semiconductor substrates such as silicon (as it relies on an insulating substrate). Our technique is much less dependent on these conditions and can be used in a broader class of systems. 

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