Quantum mechanics

Learning Goal: I’m working on a electrical engineering multi-part question and need the explanation and answer to help me learn.

2) Consider a heterostructure consisting of three layers ��−���2 −�� The central ���2 layer is
a barrier (insulator). Silicon which is a semiconductor is on the two sides of the central Silicon
dioxide layer. The barrier for electrons in the conduction band of Silicon that tunnel through
the Silicon dioxide to the Silicon on the other side is approximately 3.4 eV. The Silicon dioxide
region is 1.4 nm thick. Assume that the potential energy in both Silicon layers is the same. This
problem is representative of the device physics associated with tunneling through the insulator
in MOSFETs.
(a) Calculate the tunneling probability for electrons to tunnel through the Silicon dioxide as a
function of energy. In the plot, mark all the differences between a quantum barrier and a
classical barrier.
(b) Calculate the tunneling probability for a barrier that is 6 nm thick. All other parameters are
the same as part (a). In a single graph compare the tunneling probability of parts (a) and (b).
How does the tunneling probability change as a function of barrier thickness?
[In drawing plots for parts (a) and (b), focus on representing the data in an easy-to-read manner.
Use logarithmic scales when it is challenging to read values.]