Quantum dots’ repulsion helps determine lasing characteristics, Sandia researchers find

In the children’s pastime of connect-the-dots, images form as dots are linked.

But quantum-sized dots, which are only a few thousand atoms in size compared with the trillions of atoms in a pencil dot, are far less amiable about being linked and in fact repel each other, scientists using novel probes developed at Sandia have found.

Quantifying this repulsion may be key in turning assemblages of dots into the world’s most effective solid-state lasers, says Sandia principal investigator Jerry Floro of Nanostructure and Semiconductor Physics Dept. 1112.

"We developed probes that uncovered a repulsion effect between quantum dots. This effect may completely govern the way they organize themselves. Understanding this self-organization is critical if we are to control dot characteristics for lasing devices," says Jerry.

The probes, one of which was just patented, have made unique real-time measurements of atoms clustering to form relatively large three-dimensional dots, called islands. Also observed for the first time is the role of mutual repulsion in causing dot shapes to change as they grow, and how dots self-organize dynamically under strain during growth.

Understanding these factors is an important step in basic science because the smaller the dot, the shorter the emission wavelengths; the more tightly the dots are packed, the more intense the beam; and the more uniform their size, the more uniform the frequencies.

The ongoing work, details of which have been published in a series of articles in Physical Review Letters, was the subject of an invited talk by Jerry, "Formation of Quantum Dots," at the Gordon Conference on Thin Film and Crystal Growth Mechanisms, in Plymouth, N.H., in late June. Work was done in collaboration with researchers now at Brown University and the University of Illinois at Urbana-Champaign.

Quantum dots form when very thin semiconductor films "buckle" under stress. Stress arises when films have lattice structures slightly different in size from those of the material upon which the films are grown.

Just a few percent difference in lattice size creates stresses (or pressures) in the film that are ten times larger than those present in the deepest oceans of Earth.

These huge pressures, as new layers are deposited, force the initially flat film to separate into dots and then pop up into the third dimension to relieve stress, rather than continue to grow against resistance in two dimensions. This extra dimension, combined with the extremely small size of the dots, gives them different properties from when the material was in its original flat film shape.

Semiconductor quantum dots have the potential to produce laser light output at wavelengths where, in a manner of speaking, no flat film has gone before, depending on the size of the dots. But while crude collections of quantum dots have been grown and set lasing, knowledge of the conditions needed to influence the dots so that they form more regularly in size, shape, and pattern — thus improving control of their lasing frequency and intensity — has been only a dream.

Techniques of physical etching — even nanolithography — can’t be used to make them, because the dots are so small that they do not manifest the continuous nature of a solid. "People have made crude devices," says Jerry. "But to make them reliably, we need to understand the ground rules."

The collaboration between Sandia and Brown University makes use of optical and stress measurements to observe dot formation as it happens on silicon germanium.

Stress in the film causes the substrate to bend, which the researchers measure by bouncing laser beams off the sample. When the dots form and change shape, the stress changes and so does the amount of bend in the substrate. So, mapping the substrate as it bends reveals when dots first form and how their shapes evolve.

"Tiny dots cause detectable bending in a substrate that is ten thousand times thicker than the dots themselves," Jerry says.

The conventional laboratory approach, by contrast, has been to artificially stutter dot formation into separate time intervals and bring intermediate results to powerful microscopes to observe formations at each stage.

As more film layers are deposited, the dots grow closer and closer, and, because they repel each other, they are forced to become more uniform in size, line up in orderly fashion, and change their shape. Some dots are even "eaten" by their neighbors in an attempt to reduce the overcrowding, a process known as coarsening.

But how does one "see" dots so small? The researchers were clever and used bigger dots, called islands, thousands rather than hundreds of angstroms in size, made of silicon germanium, because the larger ones could be more easily examined. The researchers earlier showed that larger semiconductor entities in groups interact the same way as smaller semiconductor entities.

According to Dennis Deppe, an electrical engineering professor at the University of Texas at Austin working in the field but unconnected with the Sandia-Brown effort, "Many of the same basic growth phenomena are seen in different material systems. So it is possible to learn some important physical principles concerning nucleation and dot formation in one semiconductor system [and have some of them] carry over to another."

"We directly measure the kinetics of nucleation, coarsening, self-organization, and phase transformations within growing island arrays," says Jerry. "All these processes are explained within a unified model that works with ensembles of islands rather than individual islands in isolation."

In terms of actual formation, the process characteristically went like this: ten atomic layers of film would form smoothly. As more layers were deposited, the film broke up into tiny pyramid-shaped islands. With more layers, the pyramids self-organized and coarsened, and then became dome-shaped islands.

But there’s more. The researchers, not content with one novel tool to examine dots, realized they had another.

Jerry, along with Bob Hwang (8721), Ray Twesten at the University of Illinois at Urbana-Champaign, and Eric Chason and Ben Freund of Brown University, made measurements that treat dots as the originators of light-interference patterns. Since light’s direction and intensity varies depending on the size, shape, and spacing of the islands, the results offer information in realtime to determine what is happening to the tiny islands as temperatures, material compositions, and stresses change.

"We realized that if we could produce islands more than 1,000 angstroms across, the spacing between islands was like that of a diffraction grating," says Jerry. "Combined with our real-time stress observations, this allowed us to measure stress, shape, and size simultaneously instead of having to stop the process, take the dots out, and measure them. A key ingredient was our ability to show that the basic physics of the large islands mimics that of the much smaller dots."

Observing the process of dots going from one shape to another to relieve stress provided deep insight into the physics governing island formation. "It showed us what controls dot evolution, and how process conditions like temperature and strain enhance or suppress dots."

Silicon germanium is not a good laser emitter, but it is simple enough to derive the applicable physics. "We next need to find out next how much of the physics learned in silicon germanium will apply to real laser materials like indium gallium arsenide," says Jerry. "If we can understand the physics, we can make better quantum dots."

The DOE Office of Basic Energy Sciences, Division of Materials Sciences, funds the work.