Ideality factor in transport theory of Schottky barrier diodes
  A microscopic many-body transport approach for electronic properties of spatially inhomogeneous systems is developed at the fully quantum-mechanical level by means of plane wavelets second quantization representation. It is obtained that current density is determined by the statistically averaged microscopic polarization, dependent on the quantized positions and quantized momenta of charge carriers. Distribution function of electrons includes many-body effects via drift, diffusion and thermionic emission as well as entirely quantum-mechanical tunneling through a Schottky barrier. Dependences of the current versus voltage on the thickness of semiconductor layer, the relaxation times in the neutral region and in the depletion layer, the width of Schottky barrier and the mean free paths are investigated. It is established that ideality factor is a function of applied voltage and depends on a relation between the width of Schottky barrier and depletion layer. The value of at which I-V characteristics acquire an ohmic nature is depended on the parameters of semiconductors. 
A. A. Klyukanov, P. A. Gashin, R. Scurtu
cond-mat.mtrl-sci