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Photon upconversion (PU) is a process where an electron is excited from the valence band to the conduction band of a wide-gap semiconductor by the sequential absorption of two or more photons via real states. For example, two-step PU can generate additional photocurrent in the so-called intermediate-band solar cells. In this work, we consider two- and three-step processes; we study multi-step PU in a quantum dot (QD)-based single-junction solar cell with a double-heterointerface structure. The solar cell consists of three different absorber layers: Al0.7Ga0.3As, Al0.3Ga0.7As, and GaAs, which form two heterointerfaces. Just beneath each heterointerface, an InAs/GaAs QD layer was inserted. After band-to-band excitation, electrons accumulate at each heterointerface, and then, below-bandgap photons excite a certain fraction of these electrons above the barrier energy. The photoluminescence spectra of the InAs QDs reveal slightly different QD size distributions at the two heterointerfaces. We show that the external quantum efficiency is improved by additional irradiation with below-bandgap infrared photons, which suggests a multi-step PU process that involves the two heterointerfaces. The dependence of the photocurrent on the infrared excitation power density only shows a superlinear behavior when the GaAs layer is excited but the Al0.3Ga0.7As layer is not. These data demonstrate a multi-step PU process that consists of one intraband transition at each of the two heterointerfaces and one interband transition in GaAs. [ABSTRACT FROM AUTHOR]