Connection between sources formalism and correlation formalism for transport noise: Application to injection diodes

The connection between the sources formalism and the correlation formalism for fluctuations in transport processes is reinvestigated, with special emphasis on terms resulting from the boundary conditions. For fluctuations in vector quantities, like the electric field, the conditions on the tensor Green’s functions, necessary for the surface terms to vanish, are discussed. They are not satisfied for transport in three-dimensional injection diodes, in which transverse diffusion is neglected. A pseudoscalar conversion analysis for the radial Green’s function leads to an extended correlation formalism expression, which yields exact agreement with the sources formalism results.