Single barrier with impurity as a 1D resonant tunneling model

[MBungle]

Friends,
I am trying to consider an impurity which can be viewed as a 1D resonant-tunnelling problem.
I gather that the transmission coefficients TL and TR will decay exponentially from the impurity to the edges of the barrier. However, I am unsure how to predict how the peak & area of T(E) depend on the location of the impurity in the barrier...Davies on p.203, 5.16 reveals that the resonant tunneling is most effective when the impurity is placed in the center, but I am unsure why.
Thanks for any help.
M.Bungle

 

[BigJDubs]

The resonance peak in T(E) is a result of constructive interference of the waves that travel through the barrier and are reflected by the impurity. The peak will be more pronounced when the impurity is located at the center because the transmission coefficients TL and TR will have the same magnitude and phase, allowing for constructive interference of the waves from both sides. As the impurity moves away from the center, the magnitude and/or phase difference between TL and TR will increase, resulting in lower interference and a weaker peak.