Question

Density of states for electrons in a quantum well:

Consider a quantum well with infinite energy barriers at z = 0 and z = 5nm. Assume no boundaries in the x and y-directions.

(Effective mass of electron = 9.11 * 10^-31 kg)

(a) Find three quantized energy levels (from the lowest to the third) due to the confinement in the z-direction.

(b) Calculate and plot all the critical points and values. Your plot should include all three energy levels calculated in (a)

Answer 1

Hi,

the quantum well is such kind of system,where a particle is confined in that . that means it's bound in between two walls.

Here as you can notice that,only in z-direction,the particle is confined. So,the quantum well behaves like a one dimensional potential box.(you can more in your text book).

The momentum of the particle is quantized,is calculated to be as

where,n is an integer

l=length of the box

So,

Ground state(lowest energy)

put n=1,we'll get

put n=2, we'll get first excited state

put n=3,we'll get second excited state

here given l=5nm

and m is given.use this formula to calculate.

b)I do't understand that critical values,pls provide that in the comment section. I'll do that.