Final answer:
We calculated the energy levels of an electron in a quantum well using the formula for infinite potential energy wells. Then, these levels are compared with those for a finite well, highlighting differences due to tunneling effects.
Step-by-step explanation:
To address the question about the energy levels (ΔE1 and ΔE2) of an electron in a GaAs quantum well (QW) bordered by Al0.40Ga0.60As barriers, we initially consider the case of an infinite potential energy (PE) well. For an infinite well, the energy levels are quantized and given by the formula:
ΔEn = (n^2 * π^2 * ħ^2) / (2 * m * d^2)
Here, n is the quantum number (1 for the ground state, 2 for the first excited state, etc.), ħ is the reduced Planck's constant, m is the electron's effective mass in the well, and d is the width of the well.
For ΔE1 (ground state):
n = 1, m = 0.067me, d = 8 nm (0.008 µm)
ΔE1 = (1^2 * π^2 * (ħ^2 / (2 * 0.067 * me)) / (8 nm)^2
For ΔE2 (first excited state):
n = 2, m = 0.067me, d = 8 nm (0.008 µm)
ΔE2 = (2^2 * π^2 * (ħ^2 / (2 * 0.067 * me)) / (8 nm)^2
After calculating the energy levels using the effective mass and the width of the well, we should compare them to the provided finite PE well values (ΔE1=0.050eV and ΔE2=0.197eV). The finite well calculations normally yield lower energy levels because the infinite well assumption implies that the walls are perfectly rigid, which is an idealization. In reality, the finite potential allows for the possibility of tunneling through the barriers, which affects the energy levels.
The comparison between the infinite and finite well models will give us insight into the significance of barrier penetrability on the quantized energy states within quantum wells in semiconductor physics.