NOVELTY - The multilayer substrate structure (100) comprises a first chemical element, a second chemical element, a third chemical element, a thermal matching layer, and an amorphous layer. The first chemical element has a hexagonal close-packed structure at room temperature that transforms to a body-centered cubic structure at alpha - beta phase transition temperature higher than the room temperature. The hexagonal close-packed structure of the first chemical element has a first lattice parameter. The second chemical element has a hexagonal close packed structure.    USE - The multilayer substrate structure is useful for epitaxial growth of group III-V compound semiconductors that are used in 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 multilayer substrate structure: is capable of increasing size or diameter of substrates so that throughput of the device can be improved and manufacturing cost of the device can be reduced; and can be manufactured without lattice mismatch and coefficient of thermal expansion mismatch between the gallium nitride layer and the underlying substrate so that crystalline quality can be effectively enhanced.    DETAILED DESCRIPTION - The multilayer substrate structure (100) comprises a first chemical element, a second chemical element, a third chemical element, a thermal matching layer, and an amorphous layer. The first chemical element has a hexagonal close-packed structure at room temperature that transforms to a body-centered cubic structure at alpha - beta phase transition temperature higher than the room temperature. The hexagonal close-packed structure of the first chemical element has a first lattice parameter. The second chemical element has a hexagonal close packed structure at room temperature with similar chemical properties to the first chemical element. The hexagonal close-packed structure of the second chemical element has a second lattice parameter. 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. A lattice constant of the alloy is equal to a lattice constant of a member of group III-V compound semiconductors. A linear relation exists between the first, second and third chemical elements and their associated lattice parameters at constant temperature to allow the lattice constant of the alloy to be equal to that of the 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 in terms of atomic percentage of the first chemical element to the second chemical element is 99-1%. The third chemical element has similar crystal structures and similar chemical properties to the first and second chemical elements. The third chemical element is miscible with the first and second chemical elements to form the alloy. A coefficient of thermal expansion of the thermal matching layer is approximately equal to that of a member of group III-V compound semiconductor. The amorphous layer is arranged between the thermal matching layer and a lattice matching layer (106). INDEPENDENT CLAIMS are included for:    (1) a method of fabricating a multilayer substrate;    (2) a method of depositing a film on a substrate; and    (3) a system for depositing a film on a substrate.    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)