At first sight it may seem self-evident that epitaxial crystals must grow with their atomic planes parallel to the lattice planes of the substrate crystal. The simplified sketch in Figure 1a shows atoms raining onto a substrate from a molecular beam, and then diffusing to step-edges in a desirably controlled growth process termed step-edge (or ledge) flow. Drawn this way, the conclusion that the planes must lie parallel seems obvious. If, however, the process is heteroepitaxial, and the new lattice (solid circles) differs in spacing or structure from the substrate template (lines), the outcome is less straight-forward. Accommodating the difference of step heights at the interface then requires local tilts amounting to a fraction of one atomic spacing in, say, 25 atoms or perhaps half a degree, depending from one point to the next on details of the neighboring interfacial structure.
In what follows I describe a qualitatively different and newly discovered behavior we term coherent tilt. The coherent tilt process causes the atomic planes of the epilayer to grow at an accurately predictable and reproducible angle with respect to the substrate planes. The tilt axis, tilt angle, and sense of rotation remain precisely fixed over an entire substrate, with the result that the process occurs coherently over the dimensions of a macroscopic sample. Large tilts over 7° have already been produced with the angle predictable from first principles to 0.1° The characteristics of coherent tilt are sketched in Figure 1b.