Influence of surface traps on space-charge limited current

We analyze the effect of surface traps on unipolar space charge limited current and find that they have a profound influence on the I-V curves. By performing calculations that account for the presence of these traps, we can reproduce experimental observations not captured by the conventional theory that only considers the presence of traps in the bulk of the material. Through the use of realistic material parameters, we show that the effects discussed have clear experimental relevance. Space charge limited transport occurs in undoped, wide- gap semiconductors in which the density of charge carriers at equilibrium is vanishingly small. In these materials, the cur- rent is carried by charge injected from the contacts, whose density is determined limited by electrostatics. Space charge limited current SCLC is relevant for the operation of electronic devices e.g., organic light emitting diodes and is routinely used in the characterization of semiconductors to estimate parameters such as the mobility of charge carriers, the density of trap states, and their energy depth. 1-5 The description of SCLC relies on a simple phenomeno- logical theory first developed in the 1950s and extended later to include model specific details. 6,7 These extensions have led to predictions of SCLC I-V characteristics that resemble rather closely what is actually measured. In practice, how- ever, the comparison between space charge limited current SCLC measurements and theory is not very satisfactory in many cases, especially for experiments performed on high- quality materials with a low density of defects. First, an in- dependent validation of specific assumptions adopted in the analysis of SCLC I-V curves is almost always impossible, which causes ambiguities in the interpretation of the experi- ments. Even when the theoretically predicted I-V character- istics exhibit a behavior close to that observed experimen- tally, a sufficiently detailed analysis often reveals inconsistencies. 8 Second, SCLC I-V curves measured on nominally identical samples often exhibit significant differences, 3 which makes it inappropriate to compare ex- perimental data with theoretical predictions that are critically sensitive to the assumptions on which models rely. This cur- rent situation suggests that some important aspects of the physics of space charge limited transport are being over- looked. In this context, and motivated by recent experimental work on high-quality organic single crystals, we investigate the effect of deep traps at the surface of the semiconducting material, underneath the electrical contacts used to inject charge carriers. We show that these surface traps are an es- sential ingredient for the proper understanding of SCLC I-V curves, which has been neglected until now. In particular, surface traps cause a large change in the electrostatic profile throughout the bulk of the material, profoundly affecting the behavior of SCLC. Calculations accounting for the presence of surface traps enable us to reproduce experimental obser- vations that are not captured by the conventional theory, such as orders-of-magnitude asymmetries in the I-V curves. These calculations, which do not require any detailed, model- specific assumption, further illustrate how the combined ef- fect of surface and bulk traps also results in features in the I-V curves that have been so far attributed to different physi- cal mechanisms. In this way, our work provides the correct framework for the interpretation of SCLC measurements and may explain inconsistencies often found in the analysis of past experimental results. To understand how the effect of surface traps is taken into account in our calculations, we first briefly review the main aspects of the conventional theory of unipolar SCLC. 6 The theory relies on the simultaneous solution of the Poisson and the continuity equation, dEx dx = ensx 1