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Research in my group is in the general area of optical properties of solids. We do experimental work, but we emphasize the connection to theory. We use a variety of experimental techniques, including Raman spectroscopy and spectroscopic ellipsometry. We have recently applied these techniques to the study of semiconductors, fullerenes, and carbon nanotubes. For a list of recent publications click here.
For several years we have concentrated on understanding the vibrational structure of fullerenes. These are caged carbon molecules which owe their names to the dome-like structures characteristic of the architectural work of Buckminster-Fuller. The most beautiful fullerene is C60, which has the shape of a truncated icosahedron (soccer ball). It was discovered in 1985, and three of its discoverers (Kroto, Curl, and Smalley) received the Nobel Prize in Chemistry. Five years later Krätschmer and Huffman (the latter a Professor of Physics at an otherwise unremarkable university south of Phoenix) discovered a procedure to make large quantities of C60 and C70, and this lead to an explosion of research on these materials.
The unique symmetry of the C60 molecule has profound spectroscopic implications, which we have studied in detail both experimentally (using Raman spectroscopy) and theoretically, in collaboration with Prof. John B. Page. Our work has led to what we believe is the most detailed and accurate picture of the molecular vibrations in C60. You can see live movies showing these vibrations here. This detailed knowledge is extremely useful for the characterization of new fullerene materials. For example, Page and collaborators have recently shown that using the Raman spectrum of C60 as a starting point, they can predict the Raman spectrum of fullerene-polymers and discriminate among several proposed structures.
The electronic structure of materials can also be probed with Raman spectroscopy by using the Resonance Raman Scattering technique, which uses tunable lasers to determine Raman intensities as a function of the laser photon wavelength. We have recently demonstrated that this approach is ideally suited to study the electronic structure of carbon nanotubes, and we have an ongoing effort in this field.
We collaborate with the group of Prof. John Kouvetakis (Dept. of Chemistry and Biochemistry), which specializes on developing new molecular precursors for the growth of semiconductor materials. This allows them to grow semiconductor materials that are impossible to synthesize by conventional means. Our most recent interaction focuses on the characterization of alloy semiconductors containing the element tin (Sn). Together with C, Si, and Ge, Sn belongs to the group IV in the periodic table, and alloys of Sn and Ge are expected to have properties similar to the well-known alloys of Ge and Si, which play a significant role in modern microelectronic devices.
Atoms in a solid are never at rest. (Not even when the temperature approaches the absolute zero). They vibrate about their equilibrium positions, and these vibrations can be described theoretically from a knowledge of the interatomic potential energy. Since the displacements from equilibrium are small (even when the solid is about to melt they rarely exceed one tenth of the interatomic spacing), it makes sense to expand the potential in a Taylor series in these displacements. The constant term in the series is irrelevant for the dynamics (there are colorful New Age websites describing the great benefits of having "positive energy", but you know from elementary physics that when it comes to motion a constant energy can always be added arbitrarily with no adverse health effects). The terms linear in the displacements vanish because the forces are zero at the equilibrium position. Therefore, the first non-trivial terms in the series are those quadratic in the displacements. In the so-called "harmonic approximation" the series is truncated at this point and all higher-order terms are neglected. All physical effects which require these higher-order terms for their explanation are said to be due to "anharmonicity."
The vibrational frequencies calculated within the harmonic approximation are in excellent agreement with experiment in all semiconductors. Moreover, the calculations can be performed from "first principles" (with no experimental input), by cleverly applying the rules of quantum mechanics to the lattice of atoms. The density functional theory underlying this type of calculations earned Walter Kohn the 1998 Nobel Prize in Chemistry. Even though the harmonic approximation is so good, in real life there are measurable deviations from its predictions. In a harmonic world there is no thermal expansion, the vibrational frequencies are independent of any applied stress, and any particular vibration, once started, would last forever. Deviations from these predictions can be easily measured in the laboratory, as seen in the graph below.
One of the constant themes of our research in this field is the search for a "scaling" behavior in the properties of group-IV semiconductor alloys. This possibility is suggested by the strong similarities between the electronic properties of Si, Ge and Sn. We have already discovered intriguing correlations. For example, we have shown that the compositional dependence of Raman peak frequencies in Ge-Sn alloys can be predicted from the known compositional dependence of the corresponding frequencies in Ge-Si alloys. We have also discovered a related behavior in the electronic properties. The compositional dependence of optical transition energies in alloy semiconductors can be described quite often with a simple quadratic polynomial. The coefficient of the quadratic term is known as the "bowing" parameter. We have found that bowing parameters in Ge-Sn and Ge-Si alloys are also related by scaling relationships.
More recently, we have extended our work to ternary alloys of Si-Ge-Sn, which have been synthesized at ASU for the first time.
Sn-containing alloys have a great potential for applications. We are members of a team exploring the possibility of developing lasers based on these materials.
The left panel shows the real-time displacement of the phonon coordinate corresponding to the low-energy E2 mode in ZnO. These coherent phonon oscillations were generated via impulsive Raman scattering. The right panel shows a phase-corrected Fourier transform that corresponds to the spontaneous Raman spectrum. Notice how longer lifetimes on the left correspond to narrower widths on the right. This work was done in collaboration with Prof. R. Merlin (U. of Michigan). The time-domain data was collected by Cynthia Aku-Leh.
Our interest in anharmonic effects is twofold: on the one hand, we would like to find out if theory can come up with predictions for the third- and higher order terms in the expansion of the interatomic potential that are as good as the calculated quadratic terms. On the other hand, we would like to exploit anharmonicity to characterize stress fields in semiconductors by measuring the changes in vibrational modes induced by the anharmonic terms. This characterization is very important for the semiconductor industry. Semiconductor devices are very complicated structures with layers upon layers of different materials that exert large stresses on each other. These stresses can significantly enhance or degrade the device performance and must be characterized in detail.
The technique of choice for our studies of anharmonicity is laser Raman spectroscopy, the inelastic scattering of light by optical vibrations (phonons). We test the accuracy of the calculated anharmonic potential terms by studying how the anharmonic self-energy shift, broadens, and distorts the spectral lineshape of Raman-active phonons. These measurements are not easy because the Raman peaks in the materials of interest to us have a width comparable to the spectral resolution of most Raman instruments. We take advantage of unique ultra-high resolution Raman monochromators at ASU.
Very recently, we have begun to carry out these studies in suspended individual carbon nanotubes, where the one-dimensional nature of system has a profound impact on the anharmonic behavior.
