Multi-Charge Carrier Trapping in Organic Crystals: Quantized Internal Macrotrap Energy Levels

Abstract

Multi-charge carrier capture by each member of a set of discrete spatially extended domains (macrotraps) is considered as a trapping mechanism responsible for the space charge evolution in the high-concentration regime of the charge introduced to organic crystals.

Finite dimension and energy depth limit the number of carriers of the same sign to be captured by such a macrotrap. Due to the Coulombic repulsion within the macrotrap, different discrete energy levels (E_k) are allowed for occupation with increasing number (k = 12, n) of the carriers. These energy levels can be visualized by the cascade-like pattern in the plots illustrating various electronic phenomena related to trapping and detrapping charge carriers. A detailed analysis of two such phenomena is presented: (i) the shortening of the triplet exciton lifetime by thermally-injected electrons as a function of injecting voltage in anthracene, and (ii) the fluorescence quenching by the triplet-exciton injected holes as a function of exciting light intensity in tetracene crystals. The cascade-like plots of these two dependences are interpreted in terms of the discrete energy levels characteristic of multi-charge carrier trapping by macrotraps.

We have proposed a model of multi-charge trapping by spatially extended domains (macrotraps) present in molecular organic crystals. By virtue of the quantization of the charge, the macrotraps energy can have only certain discrete values E,₁, E,₂, E,₃, characteristic for a given macrotrap. Calculations of E (i = 1, 2, 3, n) are presented, using the approximation of a continuous charge distribution and previously determined typical macrotrap parameters obtained from an analysis of SCLC data on anthracene single crystals. The continuous charge data distribution approach reproduces well the energy levels obtained from the exact calculations with discrete charges located according to the symmetry resulting from the number of charges occupying a macrotrap.

We have also proposed a straight-forward method for interpreting the cascadelike pattern behaviour of various characteristics of the electronic processes on the elaborated multi-charge trapping (MCT) model. The model reproduces the principal experimental results illustrated in details by the charge-induced changes of the triplet exciton lifetime in anthracene and total fluorescence quenching in tet-racene crystals. The physical difference between multi-charge trapping and trapping by a set of separate individual traps is emphasized and discussed in terms of the MCT approach. Although the general features of the cascade-like patterns can be explained by either of these two trapping processes, the MCT approach allows to show that the energy spacings corresponding to successive cascade steps (especially at low charge density level) can be an order of magnitude larger than k_B T in contrast to the result from the trapping by separate individual traps differentiated in energy depth (by clustering of successive dimers for example). At high charge density level the energy gaps become comparable and even smaller than k_BT. The experimental ability of detection such small energy spacings also warrants emphasis.

Key Words:

• charge trapping
• molecular solids
• crystal defects
• charge injection
• photoinjection
• exciton-charge carrier interactions.