Identity between spreading and noise diffusion coefficients for hot carriers in semiconductors

It is proved that the three diffusion coefficients, related to noise, spreading of a bunch of carriers, and gradient of concentration, are identical. This demonstrates in the hot carrier regime the validity of the relation kTn(E)/q=D (E)(dvd(E)/dE)−1 which is an extension of the Ohmic Einstein relation (Tn is the noise temperature, D is the diffusion coefficient, vd is the drift velocity). Therefore the noise and time-of-flight techniques appear as being two ways which are quite different, leading to the same diffusion coefficient.