Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

A New Experimental Approach to Evaluate Plasma-induced Damage in Microcantilever

Plasma  etching,  during  micro-fabrication  processing  is  indispensable  for  fabricating  MEMS  structures.  During  the plasma  processes,  two  major matters,  charged  ions  and  vacuum–ultraviolet  (VUV)  irradiation  damage,  take  charge  of reliability  degradation.  The  charged  ions  induce  unwanted  sidewall  etching,  generally  called  as  “notching”,  which causes  degradation  in  brittle  strength.  Furthermore,  the  VUV  irradiation  gives  rise  to  crystal  defects  on  the  etching surface.  To  overcome  the  problem,  neutral  beam  etching  (NBE),  which  use  neutral  particles  without  the  VUV irradiation,  has  been  developed.  In  order  to  evaluate  the  effect  of  the  NBE  quantitatively,  we  measured  the  resonance property of a micro-cantilever before and after NBE treatment. The thickness of damage layer (δ) times the imaginary part  of  the  complex  Young's  modulus  (Eds)  were  then  compared,  which  is  a  parameter  of  surface  damage.  Although plasma processes  make the initial surface of cantilevers damaged during their fabrication, the removal of that damage by NBE was confirmed as the reduction in δEds. NBE will realize a damage-free surface for microstructures