Quantum Well Electron Energy

[jendrix]

Homework Statement

For a GaAs with bandgap Eg =1.4eV

Effective electron mass is 0.07*me

d=10nm

Calculate the energy of the ground (lowest) electron level in the conduction band with respect to the bottom of the conduction band.

Homework Equations

Ea =Ec + h^2a^2 / 8*me*d^2

The Attempt at a Solution

As it was with respect to the conduction band bottom I only used the second part of the equation and as it was the lowest level I had a=1

My result

Put it through Wolfram so you can see working

http://i.imgur.com/xRbGy5f.png

However the answer I was given as a solution was

4.36*10^-21 J ( 0.027eV)in the book

where as my result is 8.6*10^-21

Is there something wrong with my method?

Thanks

 

[mark726]

for your post! Your method looks correct, but there may be a discrepancy in the values used for the effective electron mass and the bandgap. Can you double check the values you used and make sure they are accurate? Also, make sure to convert all units to the same system (eV or J) before plugging them into the equation.

Another possibility is that the book may be using a different formula or method to calculate the energy of the ground electron level in the conduction band. It may be helpful to check the book for any additional information or formulas that could be used for this calculation.