A theory describing the generation of pure spin currents has been developed for the case of the photoionization of n-type quantum wells with spin-orbit splitting induced by the built-in electric field. It is shown that the optical transitions of electrons from the size-quantization level to the continuum give rise to two competing components of the pure spin current. An important feature of the process under study is an additional degree of freedom acquired by the charge carriers, which could be promising for spintronic applications.