Theoretical and numerical investigations of carriers transport in N-Semi-Insulating (SI)-N and P-SI-P diodes is extended to the case of extrinsic (N type) or SI samples with Gunn like electric field dependent mobilities The results obtained in a preceding publication 111 are valid as long as the bulk electric field does not increase above a threshold field E-th associated with the beginning of negative electron differential mobility values mu(n diff) = (dv(n)/dE) < 0 v(n) being the electron drift velocity Convergence and stability problems occur only for the steady state numerical simulation in long N+-N-N+ or N+-SI(N-)-N+ diodes SI(N-) characterizes a SI layer which keeps under applied bias a free electron concentration close to its thermal equilibrium value up to the beginning of electron space charge injection A systematic study has been made by varying the contact boundary properties flat band metallic N+ or P+ the length of the sample and the electric parameters of the deep compensating trap of the SI layers We show that these steady state numerical instabilities are related to the existence of multiple current-voltage solutions when numerical modelisation is made using the drift-diffusion model (C) 2010 Elsevier Ltd All rights reserved