Crystal Orientation Lattice Matching Optimized in Sapphire Substrate Epitaxy

Sapphire has a stable corundum structure. Although it is fundamentally trigonal (rhombohedral), it is typically treated as hexagonal in industrial applications. Accurately defining the crystal plane orientation of the substrate is critical during epitaxial growth.

With the development of X-ray diffraction technology, the Miller index has become the standard method for defining crystal plane orientation. Even so, the industry widely continues to use traditional terms derived from crystal habits, such as a-plane, c-plane, m-plane and r-plane. Because some of these terms — including r-plane {01-12} and R-plane {10-14} — are ambiguous in capitalization or definition, technical documents should always pair the habit name with the corresponding Miller index to ensure process parameters are communicated accurately.

The central challenge in epitaxial growth is the lattice mismatch between substrate and film. The lattice mismatch rate is a key metric for gauging how well the two align, calculated as (|a_f - a_s|) / [(a_f + a_s) / 2], where a_f and a_s are the lattice constants of the film and substrate respectively. The smaller the value, the better the lattice match and the lower the probability of lattice distortion in the film.

Consider the deposition of a GaN film on c-plane sapphire. Although GaN grows along the c-axis, its a-axis sits at a 30-degree rotation relative to sapphire's a-axis. When calculating lattice matching, sapphire's standard a-axis constant cannot be applied directly; the Al-Al atomic arrangement direction must be taken into account instead.

If sapphire's effective lattice constant is taken as 0.2747 nm, its lattice mismatch rate with GaN (a = 0.319 nm) comes out to roughly 14.9 percent. Because epitaxial growth typically occurs at high temperature while devices operate at room temperature, the difference in thermal expansion coefficients between substrate and film must also be assessed. Otherwise, stress generated during cooling can crack the film or degrade its performance.

Lattice mismatch governs the initial registry between film and substrate, while thermal expansion mismatch governs the stress accumulated across the temperature swing from growth to operation. Assessing only one of the two leaves the strain state of the epitaxial layer incompletely characterized.