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

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 = h^2/meξ and the characteristic energy Ec=meξ^2/h^2 of the delta barrier, where me is the electron mass, lc and Ec are assumed to be the effective width and height of the delta barrier with lcEc=ξ, respectively. It is found that TD 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.

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

The electron tunnelling phase time $tau ^{rm p}$ anddwell time $tau _{rm D}$ through an associated delta potential barrier $U (x)=xi delta (x)$ are calculated and both are in the order of 10$^{-17} -10^{-16 }$s. The results show that the dependence of the phase time on the delta barrier parameter $xi $can be described by the characteristic length $l_{rm c} =hbar^{2}/m_{e}xi $ and the characteristic energy $E_{rm c}=m_{e}xi^{2}/hbar^{2}$ of the delta barrier, where $m_{e}$ is the electron mass, $l_{rm c}$ and $E_{rm c}$ are assumed to be the effective width and height of the delta barrier with $l_{rm c}E_{rm c}=xi$, respectively. It is found that $tau_{rm D}$ reaches its maximum and $tau _{rm D}=tau ^{rm p}$ as the energyof the tunnelling electron is equal to $E_{rm c}$/2, i.e.~as $l_{rm c} =mathchar'26mkern-10mulambda _{rm DB}$, $mathchar'26mkern-10mulambda_{rm DB} $ is de Broglie wave length of the electron.