A new and simple theoretical model is developed for ambipolar transport in compensated N-semi-insulating (SI)-N or P-SI-P diodes and is validated with exact J-V-a characteristics obtained through numerical modelisation. The electrical parameters used correspond to SI GaAs layers, but these results are valid for other compounds such as SI InP and InGaP. A relation between the bulk non-equilibrium excess carrier concentrations, valid for low and intermediate applied voltage, is first established. For a deep donor (N-t) compensating a residual shallow acceptor (N-A): (n - n(e)) approximate to tau(nt)/tau(pt) (N-1-N-A/N-A) (p - p(e)), where n(e) and p(e) are the thermal equilibrium free carrier densities in the SI layer, r,,,, TP, and ril, pl, are the familiar Shockley-Read-Hall (SRH) parameters of the deep trap. This relation represents an extension of the well known quasi space charge neutrality condition: (n - n,) - 5 (p - p,) valid for extrinsic semiconductors. We show then that a linear J-V-a relationship is observed in N-SI-N diodes when M-t(= N-A/(N-1-N-A) tau(nt)/tau(pt) p(1t)/n(1t)) < 1 and in P-SI-P diodes when: M-t > 1. The quasi totality of the applied voltage V, is lost across the SI layer and the electric field is constant (E approximate to V-a/L-S1). M-t < 1 characterizes a SI(N-) layer where a strong hole depletion (p approximate to 0) across the SI bulk is associated to an "ohmic" electron current where n is constant but such that n < n(e), M-t > 1 characterizes a SI(P-) layer where forn approximate to 0, p < p(e). On the other hand, the J-V-a characteristics of N-SI(P-)-N diodes and P-SI(N-)-P diodes show a saturation effect. Most of the applied voltage is now lost across the reverse biased contact and the electric field is low across the SI layer. For Mt values close to 1, we switch from a linear to a saturation regime. Equivalent relations are given for a deep acceptor compensating a shallow donor. We present results for short SI layers having lengths L-S1 in the micrometer range and of the order or inferior to the ambipolar diffusion length L-Da, such layer are used as insulating layers in buried heterostructures for diode laser technology, as well as for long SI layers, L-SI >> L-Da, as used in radiation detectors technology. (C) 2008 Elsevier Ltd. All rights reserved.