Isaak D. Mayergoyz - US grants

9314084 Goldsman We are developing a new approach to device simulation by direct, self-consistent solution of the Poisson equation and the Boltzmann transport equation (BTE). The method will quickly calculate the momentum distribution function for a semiconductor device. To solve the BTE, the distribution function will be expressed as a quasi-infinite spherical harmonic (SH) expansion, with unknown coefficients that depend on energy and position. To find the coefficients, a system of arbitrarily high-order equations will be obtained by projecting the BTE onto the SH basis. The system will then be solved numerically to yield the coefficients and thereby the device distribution function. ***

This proposal concerns new improvements that have the potential to achieve significant speed-up for the fast multipole method (FMM) for use in solving the Helmholtz and other problems used to model phenomena encountered in electromagnetics, acoustics, biology etc. Solving larger problems holds promise for better design on the one hand, and elucidation of new physics/biology on the other. Discretizations of the partial differential equations arising from these equations yield large systems of equations for which both direct and iterative solution techniques are expensive.

The introduction by Rokhlin & Greengard of the FMM generated tremendous interest in the scientific computing community, as it demonstrated a way to generate structure and achieve fast solution of equations without relying on the discretization. Despite its promise, the algorithm has not achieved widespread implementation for many practically important problems that could use the promised speedups. Some researchers have reported that the approximate integrals both make implementation difficult, and in practice they have been shown to introduce stability problems. We have recently derived exact expressions for the translation and rotation of multipole solutions of the Helmholtz equation, which enable fast computation via simple recursions. Further we have obtained very promising results on the properties of the translation operators that enable creation of very tight error bounds. Our translations have the same asymptotic complexity as the standard integral expressions, but with much smaller coefficients. We have also found that the translation operator can be decomposed into the product of sparse recurrence matrices and this can be the basis for a T(p2) algorithm, which we propose to pursue. Based on these expressions, we will develop software for solution of different problems using the FMM. To be useful in pushing ahead the information technology revolution our software will be well documented and published in accessible peer reviewed forums. Such availability will act to improve adoption by large numbers of practitioners.

"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)"

Currently plasmon resonances are mostly studied numerically or experimentally by using a ?trial-anderror?
approach, i.e., by probing nanoparticles with radiation of various frequencies and polarizations.
The goal of this project is to advance novel techniques for the direct analysis of plasmon resonance
frequencies and plasmon modes in nanoparticles by treating plasmon resonances as an eigen value
problem. The main emphasis of the research work on this project will be the development of novel
boundary integral equation techniques for the time-domain analysis of plasmon resonances, finding the
conditions for efficient coupling of incident radiation to specific plasmon modes, and the study of
general physical properties of plasmon resonances. It is expected that new powerful software tools will
be developed for the design of promising engineering nanostructures. It is also intended to explore the
device applications of plasmon resonances in semiconductor nanoparticles where these resonances can
be controlled through optical manipulation of the conduction electron density. This controllability is
especially promising for the development of all-optical nanotransistors. Furthermore, the research
activities on this project will include the study of applications of plasmon resonances in both thermally
assisted and all-optical magnetic recording as well as the elucidation of the electromagnetic mechanism
of surface enhanced Raman scattering (SERS).

It is known that spin-polarized current injection may fully compensate for energy dissipation due to damping and result in undamped magnetization precessions in nanomagnets. The frequencies of these undamped magnetization precessions are controlled by injected spin-polarized currents. These microwave spin-torque oscillators have unique properties such as nanoscale dimensions, radiation hardness, wide bandwidth of phase-locking and rapid frequency tuning. For this reason, the microwave spin-torque oscillators have been the focus of considerable experimental and theoretical research lately.

Intellectual Merit:
Currently spin-torque oscillators are mostly studied by using the classical spin-wave theory. This spin-wave approach is efficient only for near to generation threshold conditions. The goal of this project is to develop the analysis of microwave spin-torque oscillators based on the nonlinear dynamic system theory and applicable for both near and far from generation threshold conditions. The main objectives of the research work on this project will be 1) stability study of spin-torque nano-oscillators (STNO) with respect to thermally generated spatially non-uniform (spin-wave like) perturbations, 2) noise and spectral density analysis of STNOs by using randomly perturbed magnetization dynamics equations and the theory of stochastic processes on graphs, 3) noise analysis of STNOs by using Poisson-noise perturbations of Landua-Lifshitz-Slonczewski equations, and 4) the study of phase-locking of STNOs in the context of the bifurcation theory. Theoretical results and predictions will be verified through their comparison with numerical simulations and experiments.

Broader Impact:
Nanoscience and nanotechnology promise to have a continuing and long-term impact on the US and world economies, and are anticipated to be engines of growth in the near future. The proposed research has potentially transformative technological applications in the area of nano-spintronics. This research will directly support two graduate students, and will also involve undergraduate students via the ECE Department?s MERIT and GEMSTONE programs. They will add to the nation?s pool of talent in this important emerging area of technology. This research will also have a strong international collaboration component and it will serve as a vehicle to expand and strengthen the existing scientific collaborations with Italian colleagues, Drs. G. Bertotti and C. Serpico, as well as with their students.