The electrons produced by cathode emission in a plane diode generate ions by collisions with background gas atoms. Poisson's equation is solved numerically in the steady state for non-relativistic particle motion assuming that, at the cathode surface, there is zero field and an abundant supply of zero-energy electrons. A suitable choice of non-dimensional variables enables the interelectrode potential distribution, space charge distribution and electron current density to be presented quite generally as a function of the gas filling parameters. The calculations are carried out for anode potentials up to 30 kV and for diode currents up to 1.7 times the Child-Langmuir vacuum limit. Depletion of neutral particles defines two modes of diode operation to which these calculations are applicable. The first is the pulsed mode on a time scale over which the neutral depletion is negligible and the second mode is the final steady state in which the ion flux is balanced by an opposing self-diffusion flux of neutral particles. Finally, the calculations are applied to diodes with a xenon gas filling and it is shown that the above currents can be generated with less than 1% gas scattering of the electron beam.