Transmission over a step semiconductor heterojuction

[John Loven]

I have calculated the electron transmission function T(E) over a potential step using T-matrices. I model a semiconductor heterojunction, which requires different effective electron masses on either side of the step.

We have 2 boundary conditions at the step at x = x0:

Y1(x0) = Y2(x0)
1/m1*d/dxY1(x0) = 1/m2*d/dxY2(x0)

Note that the second boundary condition is not the standard one, since we have to account for the different masses, in order to have current conservation.

When plotting T(E) it only approaches unity for increasing E, if the masses are equal. If they are not equal T(E) approaches a value less than unity.I'm just wondering if this result is correct? Is there always some reflection at a heterojunction with different effective electron masses, even for very large energies?

Thanks,

John

 

[mfb]

I never worked with models where the electron mass changes as function of position, but the result does not surprise me.