The interband and intersubband transitions in amorphous Si/SiO$- 2$/ multiple quantum well structures, nonlinear effects, and relations between nonlinearity and electron recombination channels have been investigated. Three types of radiative transitions have been observed: subband-to-subband recombination, recombination between subbands of the well and the impurity states in the barrier layers, and the recombination related to impurity states in the barrier layers. A relaxation of excited carriers between the subbands within the conduction and valence bands has been found that allows one to observe hot luminescence caused by higher subbands of the quantum well. The dependencies of the luminescence intensity on the excitation intensity show that the recombination rate is dependent on the concentration of excited carriers. Intersubband absorption has been observed for the first time in undoped amorphous multiple quantum well structures under interband excitation. The transitions take place between the first and second subband of the conduction band involving nonequilibrium electrons excited in the first subband with optical pumping. The dispersive nonlinearity has been investigated in the Fabry-Perot formed by the top interface of the structure and the substrate. The refractive index changes obtained from intensity dependent reflection spectra depend on the excitation intensity in nonlinear manner and can be described by the model of saturating nonlinearity for lower pump intensity. The nonlinear refractive index reveals resonant behavior associated with the subband structure of the QWs.
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