Colloidal quantum dots. From scaling laws to biological applications

Over a twenty-year period, condensed matter physicists and physical chemists have elucidated a series of scaling laws which successfully describe the size dependence of solid state properties (1,2). Often the experiments were performed under somewhat exotic conditions, for instance on mass-selected clusters isolated in molecular beams or on quantum dots grown by molecular beam epitaxy and interrogated at low temperatures and in high magnetic fields. As a result, we now have an understanding of how thermodynamic, optical, electrical, and magnetic properties evolve from the atomic to the solid state limit. This area of research is presently undergoing a remarkable transformation. The scaling laws, previously the direct subject of research, now provide a tool for the design of advanced new materials. In the case of colloidal quantum dots, or semiconductor nanocrystals, these new insights are poised to have impact in disciplines remote from solid state physics (3). NANOCRYSTAL AS "SINGLE STRUCTURAL DOMAIN" Industrial processing of semiconductor materials is our most advanced technology, an amazing but also very complicated affair. Because even a few defects or impurities can alter the performance of a device, great effort is extended to ensure precise control of atomic composition at every stage. While very expensive, this is necessary for materials that are comprised of large (order microns) component domains. Using some scaling laws from magnetism and phase transitions as a guide, we can quickly see that it is possible, and indeed perhaps preferable, to prepare extremely high-quality nanometer-size components in more simple ways. One of the most famous size-dependent scaling laws concerns the variation of magnetic proper- ties as a function of the size. Over fifty years ago, Neel provided a theory that successfully describes the size dependence of magnetization reversal (4). In a small magnetic crystal the spins within each unit cell couple to each other, resulting in a single, giant magnetic moment (single magnetic domain). An exter- nal field can be used to align this magnetic moment. If this field is now reversed rapidly, it will take time for the magnetic moment of the crystal to realign. In the simple model of Neel, this time depends exponentially upon the volume of the small crystal. This can be understood if each unit cell of the crystal contributes equally to an energetic barrier (the crystalline anisotropy) that must be overcome thermally. The larger the crystal, the greater the barrier. Interestingly, recent studies of magnetization reversal in individual single domain magnets show that the Neel model provides a qualitatively correct picture, despite many simplifying assumptions (5) (chief among them neglect of the surface). Even more recent work suggests that in extremely small, molecular-size magnets, the magnetic moment changes in a discrete series of steps, corresponding to tunneling of the magnetization (6). How can this scaling law for magnetization reversal teach us anything about processing of na- nometer size materials? Consider what happens in ever-larger magnetic crystals. A sufficiently large