中国物理B ›› 2005, Vol. 14 ›› Issue (1): 208-211.doi: 10.1088/1009-1963/14/1/038

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇    下一篇

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

白尔隽1, 舒启清2   

  1. (1)Institute of Applied Nuclear Technology, Shenzhen University,Shenzhen, 518060, China; (2)School of Science, Shenzhen University,Shenzhen,518060, China
  • 收稿日期:2003-10-15 修回日期:2004-07-20 出版日期:2005-01-20 发布日期:2005-01-20
  • 基金资助:
    Project supported by the Shenzhen Research and Development Programme on Science and Technology

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   

  1. a Institute of Applied Nuclear Technology, Shenzhen University, Shenzhen 518060, China; b School of Science, Shenzhen University, Shenzhen 518060, China
  • Received:2003-10-15 Revised:2004-07-20 Online:2005-01-20 Published:2005-01-20
  • Supported by:
    Project supported by the Shenzhen Research and Development Programme on Science and Technology

摘要: 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_{\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 energy of the tunnelling electron is equal to $E_{\rm c}$/2, i.e.~as $l_{\rm c} =\mathchar'26\mkern-10mu\lambda _{\rm DB}$, $\mathchar'26\mkern-10mu\lambda_{\rm DB} $ is de Broglie wave length of the electron.

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.

Key words: associated delta potential barrier, tunnelling phase times, tunnelling dwell times charac-teristic length, characteristic energy

中图分类号: 

  • 7340G