Steady-state and transient forward current-voltage I-V characteristics have been measured in 5.5 kV p(+)-n-n(+) 4H-SiC rectifier diodes up to a current density j approximate to 5.5 x 10(4) A/cm(2). The steady-state data are compared with calculations in the framework of a model, in which the emitter injection coefficient decreases with increasing current density. To compare correctly the experimental and theoretical results, the lifetime of minority carriers for high injection level, T-ph, has been estimated from transient characteristics; At low injection level, the hole diffusion length L-pl has been measured by photoresponse technique, For a low-doped n-base, the hole diffusion lengths are L-pl approximate to 2 pm and L-ph approximate to 6-10 mu m at low and high injection levels respectively. Hole lifetimes for low and high injection levels are tau(pl) approximate to 15 ns and tau(ph) approximate to 140-400 ns, The calculated and experimental results agree well within the wide range of current densities 10 A/cm(2) < j < 4 x 10(3) A/cm(2). At j > 5 kA/cm(2), the experimental values of residual voltage drop V is lower than the calculated ones. In the range of current densities 5 x 10(3) A/cm(2) < j < 2 x 10(4) A/cm(2), the minimal value of differential resistance R-d = dV/dj is 1.5 x 10(-4) Omega cm(2). At j > 25 kA/cm(2), R-d increases with increasing current density manifesting the contribution of other nonlinear mechanisms to the formation steady-state current-voltage characteristic. The possible role of Auger recombination Is also discussed.