A four-junction inverted metamorphic solar cell comprising: an upper first solar subcell having a first band gap, wherein the upper first solar subcell is composed of an AlInGaP or InGaP emitter layer and an AlInGaP base layer; a second solar subcell adjacent to said upper first solar subcell and having a second band gap smaller than said first band gap, wherein the second subcell is composed of an InGaP emitter layer and an AlGaAs base layer; a third solar subcell adjacent to said second solar subcell and having a third band gap smaller than said second band gap, wherein the third solar subcell is composed of GaAs or In x Ga 1-x As with 0 < x < 0.01; a graded interlayer adjacent to said third solar subcell, said graded interlayer having a fourth band gap greater than said third band gap; and a lower fourth solar subcell adjacent to said graded interlayer, said lower fourth solar subcell having a fifth band gap smaller than said third band gap such that said lower fourth solar subcell is lattice mismatched with respect to said third solar subcell, wherein the bottom fourth subcell is composed of InGaAs; wherein the graded interlayer is compositionally graded to lattice match the third solar subcell on one side and the lower fourth solar subcell on the other side, and is composed of (In x Ga 1-x) y Al 1-y As with 0 < x < 1, 0 < y < 1, and x and y selected such that the band gap remains constant at a value in a range of 1.42 - 1.6 eV throughout its thickness, subject to the constraints of having the in-plane lattice parameter greater than or equal to that of the third solar subcell and less than or equal to that of the lower fourth solar subcell; wherein the lower fourth solar subcell has a band gap of approximately 1.10 eV, the third solar subcell has a band gap in the range of 1.40 to 1.42 eV, the second solar subcell has a band gap of approximately 1.73 eV and the upper first solar subcell has a band gap of approximately 2.10 eV. an upper first solar subcell having a first band gap, wherein the upper first solar subcell is composed of an AlInGaP or InGaP emitter layer and an AlInGaP base layer; a second solar subcell adjacent to said upper first solar subcell and having a second band gap smaller than said first band gap, wherein the second subcell is composed of an InGaP emitter layer and an AlGaAs base layer; a third solar subcell adjacent to said second solar subcell and having a third band gap smaller than said second band gap, wherein the third solar subcell is composed of GaAs or In x Ga 1-x As with 0 < x < 0.01; a graded interlayer adjacent to said third solar subcell, said graded interlayer having a fourth band gap greater than said third band gap; and a lower fourth solar subcell adjacent to said graded interlayer, said lower fourth solar subcell having a fifth band gap smaller than said third band gap such that said lower fourth solar subcell is lattice mismatched with respect to said third solar subcell, wherein the bottom fourth subcell is composed of InGaAs; wherein the graded interlayer is compositionally graded to lattice match the third solar subcell on one side and the lower fourth solar subcell on the other side, and is composed of (In x Ga 1-x) y Al 1-y As with 0 < x < 1, 0 < y < 1, and x and y selected such that the band gap remains constant at a value in a range of 1.42 - 1.6 eV throughout its thickness, subject to the constraints of having the in-plane lattice parameter greater than or equal to that of the third solar subcell and less than or equal to that of the lower fourth solar subcell; wherein the lower fourth solar subcell has a band gap of approximately 1.10 eV, the third solar subcell has a band gap in the range of 1.40 to 1.42 eV, the second solar subcell has a band gap of approximately 1.73 eV and the upper first solar subcell has a band gap of approximately 2.10 eV.