Deep level transient spectroscopy (DLTS) study of defects introduced in antimony doped Ge by 2 MeV proton irradiation

Deep level transient spectroscopy (DLTS) and Laplace-DLTS have been used to investigate the defects created in Sb doped Ge after irradiation with 2 MeV protons having a fluence of 1×10¹³ protons/cm². The results show that proton irradiation resulted in primary hole traps at E_V +0.15 and E_V +0.30 eV and electron traps at E_C ?0.38, E_C ?0.32, E_C ?0.31, E_C ?0.22, E_C ?0.20, E_C ?0.17, E_C ?0.15 and E_C ?0.04 eV. Defects observed in this study are compared with those introduced in similar samples after MeV electron irradiation reported earlier. E_C ?0.31, E_C ?0.17 and E_C ?0.04, and E_V +0.15 eV were not observed previously in similar samples after high energy irradiation. Results from this study suggest that although similar defects are introduced by electron and proton irradiation, traps introduced by the latter are dose dependent.     

A note on a nonlinear functional equation and its application

This paper treats the following type of nonlinear functional equations

     

Bounds for a constrained optimal stopping problem

In this short letter, we present an explicit upper bound for the optimal value of a bidimensional optimal stopping problem over stopping times τ subject to a constraint , where x(.) is a geometric Brownian motion coupled with an arbitrary diffusion process y(.), θ(., .) and c(.) are given positive, continuous functions and β > 0 is a fixed constant. The present result is derived from a corresponding Lagrangian dual problem, and using a recent result of Makasu (Seq Anal 27:435–440, 2008). Examples are given to illustrate our main result. Partial results of this note were obtained when the author was holding a postdoc grant PRO12/1003 at the Mathematics Institute, University of Oslo, Norway.