Current crowding

Although it may be intended that current should be shared between 106 emitters, in practice there is huge current crowding so that emission occurs from only a few of them, perhaps 1 or 10 in 105. This has two severe consequences. First, the emission site density is much lower than might be expected from the nanotube density. Second, the operating emitters can easily exceed their maximum currents and burn out, passing the emission onto those with the next highest p value, and so on. This leads to unstable emission behavior [27]. 

Due to the lack of a shallow acceptor level in 4H-SiC and a relatively low hole mobility, the intrinsic base resistance of a 4H-SiC BJT is very high for example, a base epilayer sheet resistance of 46 kQ per square was reported for a 4H-SiC BJT in [6]. The high intrinsic base resistance in 4H-SiC BJTs results in a very severe emitter current crowding effect [7], which limits most of the current flow to within 1 jum from the edge of the emitter regions [8]. This indicates that tight cell pitches are necessary to achieve a low specific on-resistance, as shown in Figure 6.2(a) [6]. 

It cannot be emphasized enough that the determination of the contact resistance is not a trivial matter. First, a decision about what measuring structure must be made (four terminal Kelvin, sheet end or other structures) and what correction factors for the current crowding will have to be used. Then extreme care should be taken such that no over etching of the contact down into the silicon occurs and that the correct contact size is... 

AIGalnP LEDs, (b) Current crowding in a mesa-structured GaN-based LED grown on an insulating substrate, (c) Lateral injection geometry. The corresponding equivalent circuits are shown as well. 

A device structure with a lateral current-injection scheme is shown in Fig. 1.13(c). The current is transported laterally in both the n-type and p-type cladding layers. Light is generated in the region between the contacts where the extraction is not hindered by contacts. If the n-type sheet resistance Qn / tn is much lower than the p-type sheet resistance op/ip, the current prefers to flow laterally in the low-resistance n-layer rather than the p-layer. As a result, the junction current crowds near the p-type contact. 

Guo X., Schubert E. F. Current crowding and optical saturation effects in GalnN/... 

This chapter also introduces computer simulations, specifically capacitive computer models, as a method for visualizing the current-distribution pattern. The simulation shows uniform current distribution despite prominent electrode topologies. A dissolution study performed with gold electrodes confirms that the current distribution is uniform during normal usage, but exhibits severe current crowding when charge injection is increased above the safe limit. 

Fig. 18 Resistive models reflect the current-crowding pattern that occurs in hydrolysis regime or with DC bias [30]...

The geometric shape of the electrode influences the current distribution too. Only a hemispherical metal electrode on the surface of a flat insulator of infinite extent (Fig. 4.3) has exactly uniform primary current distribution across the surface [11]. This was the type of electrode used by Brummer and Turner to estimate the maximum surface redox limits for platinum, considering the size of their electrode carrier [4-6]. Nonspherical electrodes may be operating irreversibly even when established safe stimulation parameters are used [14], With the addition of microstructures (micro-post structures) on the electrode surface, current crowding tends to occur near the sharp convex corners. The increased current density at these sites leads to higher irrecoverable charge loss and more corrosion [10]. 

The literary academic market is currently crowded with a range of approaches which seek to understand literary and cultural production outside the analytical frame of the nation state. There are a range of relatively new brands (postcolonialism, diaspora studies, transnationalism, world literature) which in turn draw on and reconfigure older traditions (world-systems theory, area studies, women s and ethnic studies, third world studies. 

Yeh, E.C.C. Choi, W.J. Tu, K.N. Current-crowding-induced electromigration failure in flip chip solder joints. Appl. Phys. Lett. 2002, 80, 580-582. 

---