TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Method: The method further involves precisely controlling and incrementally adjusting the mole fraction of each of In, Ga, and Al to form the continuously-graded interlayer. In the method, forming the graded interlayer involves picking an interlayer composed of InGaAlAs; identifying the set of compositions (C1); identifying a lattice constant for one side of the graded interlayer that matches the middle subcell and a lattice constant for an opposing side of the interlayer that matches the bottom subcell; identifying the subset of compositions (C1), where the subset of compositions have lattice constants ranging from the identified lattice constant that matches the middle subcell to the identified lattice constant that matches the bottom subcell; and selecting a composition for each sublayer of several sublayers from the subset of compositions. The step of identifying the set of compositions (C1) involves identifying using a computer program. The subset of compositions have lattice constants ranging from the identified lattice constant that matches the middle subcell to the identified lattice constant that matches the bottom subcell comprises identifying using a computer program. The step of forming the graded interlayer further involves providing a metal organic chemical vapor deposition (MOCVD) system configured to independently control the flow of source gases for gallium, indium, aluminum, and arsenic; and selecting a reaction time and temperature and a flow rate for each source gas to form the continuously-graded interlayer disposed on the bottom subcell.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The source gas for indium is trimethylindium (InMe3), the source gas for gallium is trimethylgallium (GaMe3), the source gas for arsenic is arsine (AsH3), and the source gas for aluminum in trimethylaluminium (Al2Me6). The middle subcell is composed of gallium indium phosphide (GaInP), gallium arsenide (GaAs), gallium indium arsenide (GaInAs), gallium arsenide antimonide (GaAsSb), or gallium indium arsenide nitride (GaInAsN) emitter region and GaAs, GaInAs, GaAsSb, or GaInAsN base region; or indium gallium phosphide InGaP emitter layer and GaAs or an In0.015GaAs base layer; or InGaAs base and emitter regions. The graded interlayer is a continuously-graded interlayer. The interlayer is a step-graded interlayer comprising several sublayers.