Electron tunnelling phase time and dwell time through an associated delta potential barrier
Bai Er-Juan (白尔隽)a, Shu Qi-Qing (舒启清)b
a Institute of Applied Nuclear Technology, Shenzhen University, Shenzhen 518060, China; b School of Science, Shenzhen University, Shenzhen 518060, China
Abstract The electron tunnelling phase time $\tau^{\rm p}$ and dwell 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_{\rm e}\xi $ and the characteristic energy $E_{\rm c}=m_{\rm e}\xi^{2}/\hbar^{2}$ of the delta barrier, where $m_{\rm e}$ 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 energy of the tunnelling electron is equal to $E_{\rm c}$/2, i.e. as $l_{\rm c} =\lambda _{\rm DB}$, $\lambda_{\rm DB} $ is de Broglie wave length of the electron.
Received: 15 October 2003
Revised: 20 July 2004
Accepted manuscript online:
Fund: Project supported by the Shenzhen Research and Development Programme on Science and Technology
Cite this article:
Bai Er-Juan (白尔隽), Shu Qi-Qing (舒启清) Electron tunnelling phase time and dwell time through an associated delta potential barrier 2005 Chinese Physics 14 208
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