Two-band random matrices

Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of spectra are directly reconstructed from the recurrence equation for orthogonal polynomials associated with a given random matrix ensemble. It is established that an eigenvalue gap does not affect the local eigenvalue correlations which follow the universal sine and the universal multicritical laws in the bulk and soft-edge scaling limits, respectively. By contrast, global smoothed eigenvalue correlations do reflect the presence of a gap, and are shown to satisfy a new universal law exhibiting a sharp dependence on the odd/even dimension of random matrices whose spectra are bounded. In the case of unbounded spectrum, the corresponding universal `density-density' correlator is conjectured to be generic for chaotic systems with a forbidden gap and broken time reversal symmetry.Comment: 12 pages (latex), references added, discussion enlarge

Glassy Random Matrix Models

This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. Here I present evidence for the presence of multiple solutions both analytically and numerically. As an example I discuss the double well matrix model with potential $V(M)= -{\mu \over 2}M^2+{g \over 4}M^4$ where $M$ is a random $N\times N$ matrix (the $M^4$ matrix model) as well as the Gaussian Penner model with $V(M)={\mu\over 2}M^2-t \ln M$. First I study what these multiple solutions are in the large $N$ limit using the recurrence coefficient of the orthogonal polynomials. Second I discuss these solutions at the non-perturbative level to bring out some differences between the multiple solutions. I also present the two-point density-density correlation functions which further characterizes these models in a new university class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.Comment: 25 pages, Latex, 7 Figures, to appear in PR

Epitaxial growth of heavily P-doped Si films at 450 °C by alternately supplied PH3 and SiH4

Epitaxial growth of heavily P-doped Si films at 450 °C by alternately supplied PH3 and SiH4 has been investigated using an ultraclean low-pressure chemical vapor deposition (CVD) system. By exposing the Si(100) surface to PH3 at a partial pressure of 0.26Pa at 450-750°C, two or three atomic-layers of P are adsorbed. Thermal desorption of P occurs at 650°C and only slightly at 450°C. By alternately supplied PH3 at 300-450°C and SiH4 at 450°C, epitaxial growth of heavily P-doped Si films of average P concentrations of ~1021cm-3 are achieved. In the case of 4 cycles of alternately supplied PH3 and SiH4 at 450°C, 26nm-thick P-doped epitaxial Si film, with the average P concentration of 6xl020cm-3 is formed. It is found that about 60 % of P is electrically active even in the heavily P-doped epitaxial Si film and the resistivity is as low as ∼30Ω.cm. By annealing the film at 550°C and above, it is found that the carrier concentration decreases and the resistivity increases. It is suggested that very low-resistive epitaxial Si film is formed by alternately supplied PH3 and SiH4 only at a very low-temperature such as 450°C