Gonzálezet al.Reply:
T. González, C. González, J. Mateos, D. Pardo, L. Reggiani, O. M. Bulashenko, J. M. Rubí
1999
Physical Review Letters
González et al. Reply: In a recent Letter [1] we reported the results of a Monte Carlo simulation of shot-noise suppression associated with long-range Coulomb interaction in nondegenerate diffusive conductors. In the case of a 3D momentum space, and for elastic scattering characterized by an energy-independent scattering time t, within numerical uncertainty the suppression factor g was found to be about 1͞3 under the following asymptotic conditions: (i) qU ¿ k B T, applied voltage much larger
more »
... an the thermal value; (ii) L ¿ ᐉ, L Dc , length of the conductor much greater than both the elastic mean free path (diffusive transport regime) and the Debye length (strong spacecharge effects). Once these conditions are fulfilled, the 1͞3 suppression exhibits several universal properties [2], namely, it is independent of material parameters, applied voltage, value of the scattering time, screening length, and carrier injective statistics. In view of the repeated appearance of the 1͞3 suppression factor in diffusive conductors under different physical conditions [3], in [1] we briefly speculated about the possibility that this result could be a universal phenomenon originating from some unifying concept. However, we were not sustaining the universality of the 1͞3 reduction in nondegenerate conductors found in our simulations. Indeed, as already stressed by Landauer [4], such a universality is spoiled by the fact that for a 2D momentum space we found g ഠ 1͞2. In any case, for a given dimensionality the above mentioned universal properties of the suppression factor still apply. Recently, our Monte Carlo results have been analytically interpreted by Beenakker [5] on the basis of a Boltzmann-Langevin approach applied to the case of space-charge limited current conditions within a drift-diffusion current modeling. A satisfactory agreement between analytical and numerical calculations has been obtained, even if the diffusion current has been neglected in the analytical derivations. Here the 1͞3 and 1͞2 reductions are found approximately to occur, and the following argument against the universality is also provided. Even if for a given dimensionality there is no dependence on material parameters, shot-noise suppression does depend on the energy dependence of the scattering time. In particular, for a 3D momentum space and for t͑´͒~´2 1͞2 , a value of g 0.407 is predicted. This value is slightly above the 1͞3 suppression factor obtained for an energy-independent t. In his Comment, Nagaev [6] provides a similar argument to demonstrate that the 1͞3 suppression is nonuniversal. By means of the Boltzmann-Langevin equation, he shows that, for the specific dependence t͑´͒~´2 3͞2 , the fluctuations of the distribution function averaged over momentum directions are not affected by the fluctuations of the self-consistent electric field. As a result, Coulomb interaction does not suppress shot noise (i.e., g 1). We have performed Monte Carlo simulations with energy-dependent scattering times which, within the uncertainty of the calculations, confirm both Beenakker [5] and Nagaev [6] analytical predictions. Under far-from-
doi:10.1103/physrevlett.83.1268
fatcat:bphi34rgobe7rb2ldutoe7qfki