Trap-Filled-Limit

If the traps are deep, an analytical expression for J cannot be obtained. However numerical solutions can be obtained easily [38], In this case most of the injected carriers remain trapped and the current by injection remains small until all the traps are filled. As the traps are nearly filled the SCLC begins to flow. It increases rapidly and as the trap-filled limit is reached, it follows the trap-free V2 law. In this case trap-filled limit voltage Vtel and Vq are equal. Recent work [41] on the approach to trap-filled limit will be discussed later. 

S.C. Jain, A.K. Kapoor, W. Geens, J. Poortmans, R. Mertens, M. Willander, Trap filled limit of conducting organic materials, J. Appl. Phys. 92 (2002) 3752-3754. 

Figure 65 Unipolar (electron) current vs. electric field for a 0.1 cm-thick naphthalene single crystal provided with silver electrodes. Several different regimes can be distinguished (i) the low-field linear increase of the current (Ohmic regime) (ii) the SCLC in the presence of shallow traps (AE < kT) (iii) the trap-filled limit at FTFl and (iv) the SCLC with filled traps (no trapping). Adapted from Ref. 350a.

Figure 147 The relative cascade-like pattern of the increase of triplet exciton monomolecular decay rate constant (/ = t 1) as a function of charge-injecting voltage in anthracene crystal. Consecutive trap-filled limits are indicated by C/TFL (1), /TFL(2) and C/TFL (3). Dotted line indicates the averaged (linear) dependence of A/ // 0 as resulted from the standard interpretation assuming a continuous increase in the charge density proportional to the injecting voltage [334]. Adapted from Ref. 240.

In practice, the trap-filled limit is difficult to observe as it is often preceded by electrical breakdown of the sample. The transition from the linear to square law (Child s Law) dependence of current on voltage is usually not sharply defined. Thus samples may display an intermediate power law over a considerable voltage range. This, and the uncertainty of the trapping factor, render the measurement of current-voltage characteristics unsuitable for tire determination of carrier mobility. 

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