Thin Film Electron Interferometry

Abstract

Electron transport through thin overlayers of tin grown on a silicon substrate, and stacking-fault contrast in topographic and conductivity images of Si (111) – 7 × 7 are investigated. Resonances that depend on structural integrity of the overlayer are observed in the conductivity images, and are interpreted as consequences of electron standing-wave formation within the overlayer. The experimental spectra are analyzed using a one-dimensional model which has scattering potentials located at the sample surface and at the overlayer-substrate interface. The agreement between experiment and theory demonstrates that electron-standing wave spectra, in conjunction with bias-dependent topographic and conductivity images, are useful for probing details of buried interfaces formed by surface reconstruction and in heteroepitaxial growth.

Generalized Weierstrass-Enneper Inducing, Conformal Immersions, and Gravity

“…This is stated e.g. in [18,51] and verified in [9] and below in Section 4 (it is also implicit in [8,10]). This means that (2.33) is automatically true and hence there are no a priori restrictions on ψ i , p imposed by the fit above, beyond the condition detψ = 1/2p.…”

“…and as in (2.36) for h √ g = 1 we have T zz = D zf . Such formulas also arise in [18,19,20,42,43,44,45,51] (cf. [9]) and we will look at this below.…”

“…We go next to [35,36,49,50] involving conformal immersions and will sketch some of the results (cf. also [8,9,18,19,20,21,24,25,38,39,42,43,44,45,46,47,48,51,53,55,56]). Consider an oriented 2-D surface immersed in R n , realized as a conformal immersion of a Riemann surface S, i.e.…”

“…This is accomplished in a conformal gauge for the induced metric (∼ Hzz). The mathematics however, involving the Kaehler function f of (2.23), then leads to formulas similar to those of Liouville-Beltrami intrinsic gravity a la [9,18,19,20,38,39,42,43,44,45,51] for example (e.g. formulas such as (2.33), (2.39), (2.40), etc.).…”

“…We recall also some results from [18,51] (we write here T for T zz at times). The presentation in [18,51] is somewhat abbreviated and unclear at times and we give here an enhanced treatment of this material with proofs in order to utilize some of the results later and also to make propaganda for these matters. We are led to consider the subject as follows.…”