Multiple steady state current–voltage characteristics in drift–diffusion modelisation of N type and semi-insulating GaAs Gunn structures

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 [1] 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: μ 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.