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We study semiconductor hyperbolic metamaterials (SHMs) at the quantum limit experimentally using spectroscopic ellipsometry as well as theoretically using a new microscopic theory. The theory is a combination of microscopic density matrix approach for the material response and Green’s function approach for the propagating electric field. Our approach predicts absorptivity of the full multilayer system and for the first time allows the prediction of in-plane and out-of-plane dielectric functions for every individual layer constructing the SHM as well as effective dielectric functions that can be used to describe a homogenized SHM. [ABSTRACT FROM AUTHOR]