Junction layer analysis in one-dimensional steady-state Euler–Poisson equations

We study the quasi-neutral limit in one-dimensional steady-state Euler–Poisson equations with junction layers. Typically, the junction layer phenomenon occurs in a ballistic diode of a semiconductor device where the doping profile is a discontinuous function. We derive the junction layer equations and prove the existence of their solutions which decay exponentially. Finally, we justify the quasi-neutral limit with junction layers by giving uniform error estimates.