Steve Simon

Abstract:

We experimentally determine the density dependence of the transport lifetime (τ t) obtained from low-field Hall measurements and the quantum lifetime (τ q) derived from analysis of the amplitude of Shubnikov-de Haas oscillations in a tunable high mobility two-dimensional electron gas (2DEG) in a Al 0.06Ga 0.94N/GaN heterostructure. Using an insulated gate structure, we are able to tune the 2DEG density from 2 × 10 11 to 2 × 10 12 cm -2, and thus, monitor the evolution of the scattering times in a single sample at T=0.3 K in a previously unexplored density regime. The transport lifetime τ t is a strong function of electron density, increasing from ∼2.7 ps at n e=2 × 10 11 cm -2 to ∼11 ps at n e= 1.75 × 10 12cm -2. Conversely, we find that the quantum scattering time τ q is relatively insensitive to changes in electron density over this range. The data suggest that dislocation scattering accounts for the density dependence of τ q as well as τ t in our low-density sample. © 2004 American Institute of Physics.

Abstract:

The dramatic appearance of luminescence rings with radius of several hundred microns in quantum well structures can be understood through a fairly simple nonlinear model of the diffusion and recombination of electrons and holes in a driven nonequilibrium system. The ring corresponds to the boundary between a positive hole gas and a negative electron gas in steady state. While this basic effect is now well understood, we discuss several other experimental results which cannot be explained by this simple model.

Abstract:

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theory to multivariate analysis.