# Semiconductor Sub-band Occupancy

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1. Apr 25, 2015

### Matt atkinson

1. The problem statement, all variables and given/known data
a) A quantum well contains electrons at a sheet carrier density of $n_s =2 \times 10^{16}m^{-2}$. The electron effective mass is $0.1m_e^*$. Calculate the Fermi energy of the carrier distribution in the well. You may assume the spacings between sub-bands in the quantum well is very much greater than the Fermi energy.
b) If instead the spacing between the lowest two sub-bands is $25meV$, deduce the resultant occupancy in meV of each of the two sub-bands.

2. Relevant equations
For a) I used
$$\varepsilon_F=\frac{\hbar^2\pi}{m_e^*}n_s$$
which was derived from the 2D density of states.
3. The attempt at a solution
So I understand part a), but part b) has me confused.
I interpreted the problem as shown in the image below.
I assume the thing that I need to find is the energies I denoted as $\Delta E_{1_o}$ and $\Delta E_{2_o}$, and when I asked my lecturer about the question he said to look at it as a geometry problem but I just cant see, would I literally just need to calculate the energys $E_1$ and $E_2$ and use that and the fermi energy to determine the width?

Using;
$$25meV=\frac{\hbar^2\pi^2}{2m_e^*d^2}\left( 2^2-1^2 \right)$$

I found the QW width and then used the following relations to get the occupancy;
$$\Delta E_{1_o}=\varepsilon_F -E_1$$
$$\Delta E_{2_o}=\varepsilon_F -E_2$$

Last edited: Apr 25, 2015
2. Apr 30, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?