anderson - PHZ 5156 Final project Anderson model This...

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PHZ 5156 Final project Anderson model This problem is a simple but very powerful model for impurity states in a semi- conductor. As impurities (i.e. dopants) increase in concentration, the can form an impurity band . In principle the impurity band might be metallic, but disorder can result in localized states at the Fermi level and the system is semiconducting. In other words, disorder can result in trapped electrons that only conduct due to thermally-activated hopping processes. The simplest model is due to Anderson. The Hamiltonian can be represented by a matrix with diagonal elements ˆ H j,j = ± j and off-diagonal elements for neighboring sites ˆ H j,j + m = I The sites themselves represent impurity ions. The diagonal elements of ˆ H represent the energy of placing an electron on an impurity. The off-diagonal elements that con- nect neighboring sites represent the overlap between neighboring states and permit electrons to hop from site to site. The key element of this simple model is that the diagonal site energies
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This note was uploaded on 08/08/2011 for the course PHZ 5156 taught by Professor Johnson,m during the Fall '08 term at University of Central Florida.

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anderson - PHZ 5156 Final project Anderson model This...

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