By using Laplace transformation, the solution of the system of differential equations, describing the transport of added current carriers in a homogeneous semiconductor, can be found to a high degree of approximation for the small signal case and for sufficient small concentrations of added carriers.
For times, much larger than the relaxation time, the obtained result agrees with the one derived by Keilson in another way. During relaxation the part of the flow which eventually provides the establishment o1 a strict overall and an approximate local charge neutrality can be given in function of a diffusion coefficient and a mobility which differ from those needed for the description of the other part. This last part is the only one which is not negligible after relaxation.
By using the same method, an approximate value can be calculated for the small local space charge occuring during the transport of the added current carriers and the physical interpretation o1 the result is straightforward.
At last it can be shown that the polarizability of each injected pair "electron-hole'" calculated by K e i 1 s o n for a static field, becomes complex for an alternating field and this corresponds to the relaxation in the reorientation of the local space charge.