Point Defect Thermodynamics: Macro- vs. Nanocrystals

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Abstract
Point defect themodynamics is considered for macro- and nanocrystals. The first part reviews − for the equilibrium case − the way in which ionic and electronic carrier concentrations can be calculated in bulk and boundaries of macroscopic crystals as a function of the decisive control parameters. The includes pure and impure materials, complete and partial equilibria as well as different levels of concentrations (dilute case, interactions). In the second part trivial and non-trivial effects are discussed, occurring if the crystal size is continuously decreased towards and below the nano-range. Not only become core disorder and space charge effects increasingly important, but also will there be two characteristic scales defining mesoscopic effects. One is the Debye-length, the other the scale that characterises the transition from crystal chemistry to cluster chemistry. The situation is more complicated if pronounced elastic effects of long range are important. Simple estimates are given for a variety of simplified cases. The phenomena are discussed in terms of transport properties. The treatment includes boundary phase transitions and the effect of ionic heterostructures. Experimental examples are discussed which underline the conclusions.