Supercomputing Institute Research Bulletin Fall 1997

Quantum Confinement Effects in Silicon Nanocrystals

Silicon is the material of choice for making most electronic devices. In its natural crystalline form, however, silicon has a very low optical radiative efficiency and produces light only outside the visible range. If the optical property of crystalline silicon could be modified to increase the frequency of emitted light, silicon would have even more device applications, such as use in lasers or solar cells. Porous silicon (p-Si) is one such modification. p–Si, which is prepared by etching silicon, emits visible light at room temperature with a greatly enhanced efficiency. This exciting discovery has stimulated growing experimental and theoretical interest in understanding the optical properties of semiconductor structures with reduced dimensions like p–Si. p–Si contains small (with diameters ~20-100Å) isolated crystalline silicon regions called “quantum dots.” Light emission is thought to result from a quantum confinement (QC) effect in these dots. The QC effect occurs because energy spacings of electronic states in confined geometries are larger than those in unconfined geometries. Thus, the QC effect enhances optical efficiency and increases the optical gap from the bulk value of 1.1eV to the visible region (1.5–3 eV). The building blocks of p–Si are formed by truncating bulk silicon and passivating the surface of the dot with hydrogen atoms. A key issue in investigating the optical properties of these dots is to understand their size dependence. Almost all existing theoretical calculations on Si quantum dots have been empirical. This approach postulates the transferability of bulk interaction parameters to the nanocrystalline environment. This may have important effects on the calculated optical gaps, especially since the confinement-induced changes in the optical gaps are not properly taken into account in empirical calculations. Parameter-free or “first principles” calculations, on the other hand, have so far been limited to small systems which usually do not correspond to the sizes of nanoparticles for which the experimental data are available. Serdar Ögüt and Professor James Chelikowsky of the University’s Department of Chemical Engineering and Materials Science and Professor Steven Louie of the University of California at Berkeley have overcome the challenges in theoretical modeling of the optical properties of large Si quantum dots using a new calculational approach which they developed with collaborators Professor Yousef Saad and Andreas Stathopoulos of the University of Minnesota’s Department of Computer Science. To determine the role of quantum confinement with respect to the optical gap of the dot, the researchers perform two steps. First, the energy of the optical excitation is determined without including any interactions between the excited electron and hole. In the second step, the electrostatic interaction energy of the electron and hole is added to this excitation energy to calculate the optical gap. An important piece in the research of Ögüt, Chelikowsky, and Louie was to show from first principles that QC and reduced screening at these nanoscale dimensions result in substantial electron-hole electrostatic interaction energies. From a technical achievement point of view, the calculations of Ögüt, Chelikowsky, and Louie represent a breakthrough in material simulations. The largest quantum dot investigated in their research (Si525H276), as shown below, with ~800 atoms and 27.2 Å in diameter, is the largest quantum system that has been studied using a first principles method. The As shown on the left, the calculated optical gaps are in very good agreement with experimental absorption data from Si quantum dots. This gives further evidence for the role of QC in producing exciting optical properties in nanosize Si particles. At right, Si525H276–the largest quantum dot investigated by this group.

In This Issue: 1997 Research Scholars LCPC Workshop T3E Upgrade Computing Applications in Neuroscience Unraveling Protein Structures Silicon Nanocrystals Research Reports