Effect of one dimensional quantum structures on the thermoelectric figure of merit

Recently it was shown theoretically that the thermoelectric properties of certain materials can be enhanced very much by preparing them in the form of one-dimensional conductors or quantum wires. For this it was supposed that the carrier mobility is the same both in quantum wire and in bulk material. Using the model of quasi-one-dimensional cylindrical quantum wire of finite radius with infinite potential confinement, we have calculated the mobility as a function of wire thickness. The carrier scattering both on optical and acoustical phonons is taken into account. It is found that the mobility decreases with wire thickness, decreasing from values greater than to values much smaller than the bulk one. This result changes drastically the conclusion about significant increases in the figure of merit of materials by preparing them in form of quantum wire structures.