Binding Energy of the hydrogenic acceptor state in Silicon?

[HunterDX77M]

Homework Statement

Find the theoretical binding energy of the hydrogenic acceptor state in Si (eg, as produced by Aluminum impurities), using hole mass 0.39 and permittivity 11.8.

Homework Equations

<br /> E_b = \frac{k_c e^2}{2a_0} \\<br /> a_0 = \frac{\hbar ^2}{mk_c e^2}<br />

The Attempt at a Solution

When we discussed binding energy in my class, these were the two equations that my professor gave. But looking at them now, I don't think they are right. For one thing, they don't take the permittivity into account and for another, a₀ seems to cancel out several variables in E_b. I've searched around for some time trying to find the equation(s) that would make more sense for this type of problem, but have so far had nothing but dead ends. Is anyone familiar with the equations for a problem like this?

 

[ehild]

Homework Statement

Find the theoretical binding energy of the hydrogenic acceptor state in Si (eg, as produced by Aluminum impurities), using hole mass 0.39 and permittivity 11.8.

Homework Equations

<br /> E_b = \frac{k_c e^2}{2a_0} \\<br /> a_0 = \frac{\hbar ^2}{mk_c e^2}<br />

The Attempt at a Solution

When we discussed binding energy in my class, these were the two equations that my professor gave. But looking at them now, I don't think they are right. For one thing, they don't take the permittivity into account and for another, a₀ seems to cancel out several variables in E_b. I've searched around for some time trying to find the equation(s) that would make more sense for this type of problem, but have so far had nothing but dead ends. Is anyone familiar with the equations for a problem like this?

ke means 1/(4∏ε) in a medium of permittivity ε.

No variables cancel if you plug in the expression for ao into the formula for the energy.

ehild

 

[HunterDX77M]

ke means 1/(4∏ε) in a medium of permittivity ε.

Oh, yeah. How could I forget about that? That's pretty basic. :-/

No variables cancel if you plug in the expression for ao into the formula for the energy.

This is probably why it's a bad idea for me to do homework without sleeping for the majority of the day.

Thanks for your help! :)