《A model for the field and temperature dependence of Shockley-Read-Hall lifetimes in silicon》.pdf

A Mo del for the Field and Temp erature Dep endence of Sho ckleyReadHall Lifetimes in Silicon A Schenk Abstract We derive a simple analytical mo del for the eld and temp erature dep endence of Sho ckleyReadHall lifetimes in silicon from a microscopic level where the capture of carriers at recombination centers is assumed to b e a multiphonon pro cess Strong electric elds as often present in mo dern devices cause trap assisted tunneling ie the multiphonon recombination path is no longer purely vertical in a band diagram but has a horizontal branch at an eective energy which is given by the maximum of the transition probability Applying reasonable approximations we calculate this eective recombination path as a function of eld strength and temp erature Field enhancement factors of the inverse carrier lifetimes are then presented that require no integration iteration or higher mathematical functions The anisotropy and multivalley nature of the silicon conduction band is carefully taken into account We discuss all approximations and physical eects by means of the gold acceptor level The mo del is able to describ e the prebreakdown b ehaviour of trap tunneling leakage and is suitable for the implementation into simulation packages Published in SolidState Electronics vol Notation Ai Ai Airy function and its derivative c x c x electron and hole capture rates cm s n p E energy eV Eact F E activation energy for