A solar cell stack having a first semiconductor solar cell that has a p-n junction of a first material with a first lattice constant, and having a second semiconductor solar cell that has a p-n junction of a second material with a second lattice constant. The first lattice constant is smaller than the second lattice constant. The solar cell stack has a metamorphic buffer that includes a sequence of a first, lower AlInGaAs or AlInGaP layer and a second, center AlInGaAs or AlInGaP layer, and a third, upper AlInGaAs or AlInGaP layer, and the metamorphic buffer is formed between the first semiconductor solar cell and the second semiconductor solar cell. The lattice constant in the metamorphic buffer changes along the thickness dimension of the metamorphic buffer, and the lattice constant and the In content increase and the Al content decreases between at least two layers of the metamorphic buffer.