The transient emission current densities from flat band semiconductors and the stationary emission from graded electron affinity devices are computed by a combined semi-classical transport+ transmission coefficient method. A rapid sequence of sharp current overshoots can be obtained in the first case for a wide range of built-up speeds of the external field. Their amplitudes and frequencies are field dependent and can be diminished by previous "heating" of the electronic system. In the second case, low field saturation and temperature assisted emission enhancement were found as expected. Several practical conclusions are drawn.