<p>In this paper, we investigate a physically relevant hydrodynamic model for a bipolar semiconductor device considering Ohmic conductor boundary conditions and a non-flat doping profile. From proper scaling, when the relaxation time in the bipolar isentropic Euler–Poisson system tends to zero, we can obtain the bipolar drift-diffusion equations. First, we show that the solutions to the initial boundary value problems of the bipolar isentropic Euler–Poisson system and the corresponding drift-diffusion equations converge to their corresponding stationary solutions as the time tends to infinity, respectively. Then, it is shown that the solution for the bipolar isentropic Euler–Poisson equations converges to that of the corresponding bipolar drift-diffusion equations as the relaxation time tends to zero with the initial layer. These results are proven by the decay estimates of solutions, which are derived by energy methods.</p>