“Sand” represents a “state of matter” to which not much attention has been paid. A sand pile can be formed into different shapes; it can exist in many stable states, almost all of which are not the flat lowest energy state. Thus, sand contains memory; one can write letters in sand. If a heap of sand is perturbed, for instance by adding more sand, by tilting the pile, or by shaking it, the system goes from one metastable state to another. In some sense, this happens by a diffusion process, but this process is very different from the process which relaxes a glass of water to equilibrium after shaking. The diffusion process in sand can stop at any of many states, and the process is a threshold process, where nothing happens before the perturbation reaches a minimum magnitude.

The threshold dynamics of sand is a paradigm of many processes in nature. Earthquakes occur only when the stress somewhere on the crust of the Earth exceeds a critical value, and the earthquake takes the crust from one stable state to another. Economie systems are driven by threshold processes: the individual agents change their behavior only when certain factors reach a certain level. Biological species emerge or die when specifie conditions in the ecology are fulfilled. Neurons in a network fire when the input reaches a threshold level, etc.

During the last decade a powerful new approach for designing semiconductor structures with tailored electronic and optical properties, bandgap engineering, has spawned a new generation of electronic and photonic devices. Central to bandgap engineering is the notion that by spatially varying the composition and the doping of a semiconductor over distances ranging from a few microns down to ~2.5 Å (~1 monolayer), one can tailor the band structure of a material in a nearly arbitrary and continuous way. Thus semiconductor structures with new electronic and optical properties can be custom-designed for specific applications.

The enabling technology which has made bandgap engineering an exciting reality with far reaching implications for science and technology is molecular beam epitaxy (MBE), pioneered by Cho and Arthur in the late 1960s.

In the subsequent decade MBE demonstrated jts ability to create ultra-thin (10–100 Å) layers and atomically abrupt interfaces between two different semiconductors (heterojunctions).

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.