,Electron tunnelling phase time and dwell time through an associated delta potential barrier

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The electron tunnelling phase time τp and dwell time τD through an associated delta potential barrier U(x) = ξδ(x)are calculated and both are in the order of 10-17 - 10-16s. The results show that the dependence of the phase time on the delta barrier parameter ξ can be described by the characteristic length lc = h2/meξ and the characteristic energy Ec = meξ2/H2 of the delta barrier, where me is the electron mass, Ic and Ec are assumed to be the effective width and height of the delta barrier with lcEc= ξ, respectively. It is found that τD reaches its maximum and τD = τP as the energy of the tunnelling electron is equal to Ec/2, i.e. as lc = λDB, λDB is de Broglie wave length of the electron.
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