Low-energy continuous states of electron in heterosrtucture with periodically placed quantum-dot sheets are studied theoretically. The Greens function of electron is governed by the Dyson equation with the self-energy function which is determined the boundary conditions at quantum-dot sheets with weak damping in low-energy region. The parameters of superlattice formed by quantum-dot sheets are determined using of the short-range model of quantum dot. The density of states and spectral dependencies of the anisotropic absorption coefficient under mid-IR transitions from doped quantum dots into miniband states of superlattice strongly depend on dot concentration and on period of sheets. These dependencies can be used for characterization of the multi-layer structure and they determine parameters of different optoelectronic devices exploiting vertical transport of carriers through quantum-dot sheets.
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