resistors - PHZ 5156 Final project Random resistor network...

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PHZ 5156 Final project Random resistor network We saw in class that hopping in a disordered semiconductor has a rate given by, Γ i,j = γ i,j exp ( - 2 r ij a ) exp ( - ± ij k B T ) This accounts for the overlap of local wave functions of size a , and also the activated hopping (through phonon emission/adsorption) of carriers between sites with energy difference ± ij . This leads to a resistance between sites i and j , R ij = R 0 ij exp ( ξ ij ) where ξ ij = 2 r ij a + ± ij k B T and R 0 ij = k B T e 2 γ 0 ij . In the random resistor model, we assume that we can treat the problem as a regular network (e.g. a square array) connected by random resistances. Take the distribution F ( ξ 0 ) of the values ξ to given by F ( ξ 0 ) = 1 2 ξ 0 for | ξ 0 | < ξ 0 , and F ( ξ 0 ) = 0 for | ξ 0 | > ξ 0 . Each resistance then is assigned based on the random numbers ξ 0 drawn from the range - ξ 0 to ξ 0 , with R = R 0 e ξ 0 . Begin with an N × N square lattice of nodes with random resistors connecting each node. You can represent in your code the voltage at each node by an array
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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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resistors - PHZ 5156 Final project Random resistor network...

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