Current crowding (also current crowding effect, or CCE) is a nonhomogenous distribution of current density through a conductor or semiconductor, especially at the vicinity of the contacts and over the PN junctions.
Current crowding is one of the limiting factors of efficiency of light emitting diodes. Materials with low mobility of charge carriers, e.g. AlGaInP, are especially prone to current crowding phenomena. It is a dominant loss mechanism in some LEDs, where the current densities especially around the P-side contacts reach the part of the emission characteristics with lower brightness/current efficiency. 
Current crowding can lead to localized overheating and formation of thermal hot spots, in catastrophic cases leading to thermal runaway. Nonhomogenous distribution of current also aggravates electromigration effects and formation of voids (see e.g. Kirkendall effect). Formation of voids causes localized nonhomogeneity of current density, and the increased resistance around the void causes further localized temperature rise, which in turn accelerates the formation of the void. Conversely, localized lowering of current density may lead to deposition of the migrated atoms, leading to further lowering of current density and further deposition of material and formation of hillocks, which may cause short circuits. 
Current crowding occurs especially at the areas of localized lowered resistance, or in areas where the field strength is concentrated (e.g. at the edges of layers).