How Does Adding a Hydrogen Layer Affect Tunneling Coefficients in STM Analysis?

[erok81]

Homework Statement

In my never ending quest to suck and never be able to do Taylor Expansions, I have another one. I hope one day I'll be able to do these.

I have an unknown material and a scanning tunnel microscope. A layer of hydrogen atoms of radius R are added to the surface. This of course will affect my potential barrier as it changes the work function of my set up.

Call my original tunneling coefficient to be T₀ and my hydrogen layer to be T₁.

With R << 1/α, how does the difference T₀-T₁ modifies. Use a taylor expansion.

Homework Equations

My tunneling probability is given by:

$$T=\frac{16E(U_{0}-E)}{U_{0}^{2}}e^{-4 \alpha L}$$

Where my transmission coefficient is given by:

$$T=\frac{16E(U_{0}-E)}{U_{0}^{2}}$$

The Attempt at a Solution

I hate posting problems like this because I have no idea how to begin.

I know that 1/α Ξ δ where δ is the penetration depth in a potential barrier. And obviously is L>>δ not much of the wave function will survive the barrier. So here R is much less than the penetration depth.

That's about all I have.

 

[erok81]

So...any ideas?

I've tried reading up a bit more on Taylor expansions but still don't quite get how to apply them in this case.