NOVELTY - The method comprises forming an upper first solar subcell on a first substrate having a first band gap, where the substrate is useful for epitaxial growth of semiconductor, forming a middle second solar subcell over the first solar subcell having a second band gap smaller than the first band gap, forming a graded interlayer over the second solar cell using a surfactant, and forming a lower third solar subcell over the graded interlayer having a fourth band gap smaller than the second band gap such that the third subcell is lattice mismatched with respect to the second subcell.    USE - The method is useful for forming an inverted metamorphic multifunction solar cell, which is useful: for concentrator terrestrial power systems and satellites useful in data communications; and as power conversion devices for the on-board power systems.    ADVANTAGE - The method is capable of forming the commercially viable inverted metamorphic multifunction solar cell with improved power and energy conversion characteristics and high performance and efficiency.    DETAILED DESCRIPTION - The method comprises forming an upper first solar subcell on a first substrate having a first band gap, where the substrate is useful for epitaxial growth of semiconductor, forming a middle second solar subcell over the first solar subcell having a second band gap smaller than the first band gap, forming a graded interlayer over the second solar cell using a surfactant, forming a lower third solar subcell over the graded interlayer having a fourth band gap smaller than the second band gap such that the third subcell is lattice mismatched with respect to the second subcell, forming a lattice constant transition material using the surfactant, depositing a contact layer (104) over the third solar subcell for making electrical contact, attaching a surrogate second substrate over the contact layer and removing the first substrate, patterning the contact layer into a grid, etching a trough around the periphery of the solar cell to form a mesa structure on the surrogate second substrate, thinning the surrogate substrate (125) to a predetermined thickness and mounting the solar cell on a support, and removing the surrogate substrate and mounting the solar cell on a support. The graded interlayer has a third band gap greater than the second band gap and 1.5 eV band gap throughout its thickness, is compositionally graded to lattice match the middle subcell on one side and the lower subcell on the other side, and is composed of nine or more steps of layers of semiconductor material with monotonically changing lattice constant and constant band gap. The support is a rigid coverglass. The lattice constant transition material has a lattice constant that changes gradually from the first lattice constant to the second lattice constant. The transition material is composed of (InxGa1-x)yAl1-yAs, where x and y are selected such that the band gap of the transition material remains constant at a band gap energy greater than that of the first subcell and at 1.50 eV. The solar cell is eutectically bonded to the surrogate substrate by an adhesive (124). An INDEPENDENT CLAIM is included for a multifunction solar cell.    DESCRIPTION OF DRAWING(S) - The diagram shows a cross-sectional view of a solar cell.    Buffer layer (102)    Etch stop layer (103)    Contact layer (104)    Adhesive (124)    Surrogate substrate. (125)