NOVELTY - The lattice matching layer (106) comprises a first chemical element, a second chemical element, and a third chemical element. The first chemical element has a hexagonal close-packed structure at room temperature that transforms to a body-centered cubic structure at an alpha - beta phase transition temperature, which is higher than the room temperature. The second chemical element has a hexagonal close-packed structure at room temperature with similar chemical properties to the first chemical element. The second chemical element is miscible with the first chemical element.    USE - The lattice matching layer is useful in a multilayer substrate structure (claimed) that is useful for epitaxial growth of group III-V compound semiconductors such as gallium nitride, gallium arsenide, indium nitride, aluminum nitride and gallium phosphide, where semiconductors are useful in the manufacture of electronic devices such as microwave frequency integrated circuits, LED, laser diodes, solar cells, high-power and high-frequency electronics and opto-electronic devices.    ADVANTAGE - The lattice matching layer improves the throughput and reduces the cost of the epitaxial growth of group III-V compound semiconductors.    DETAILED DESCRIPTION - The lattice matching layer (106) comprises a first chemical element, a second chemical element, and a third chemical element. The first chemical element has a hexagonal close-packed structure at room temperature that transforms to a body-centered cubic structure at an alpha - beta phase transition temperature, which is higher than the room temperature. The second chemical element has a hexagonal close-packed structure at room temperature with similar chemical properties to the first chemical element. The second chemical element is miscible with the first chemical element to form an alloy with the hexagonal close-packed structure at the room temperature. The third chemical element has a hexagonal close-packed structure at the room temperature with similar chemical properties to the first and second chemical elements. The hexagonal close-packed structures of the first, second and third chemical elements have first, second and third lattice parameters. The third chemical element is miscible with the first and second chemical elements to form the alloy. A lattice constant of the alloy is approximately equal to a lattice constant of a member of group III-V compound semiconductors. One of the first and the second chemical elements belongs to group four elements in periodic table. A mole fraction of atomic percentage of the first chemical element to the second chemical element is 1-99%. A linear relation exists between the first, second and third chemical elements and their associated lattice parameters at constant temperature to allow lattice constant of the alloy approximately equal to that of the member of group III-V compound semiconductors. A coefficient of thermal expansion of the alloy along a plane is approximately equal to that of the member of group III-V compound semiconductors along the same plane. The lattice matching layer has a thickness of 5-50 nm. An INDEPENDENT CLAIM is included for a method of fabricating a lattice matching layer.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic cross-sectional view of multilayer substrate structures.    Multilayer substrate structure (100)    Substrate (102)    Epitaxial layer (104)    Lattice matching layer (106)    Amorphous layer. (108)