2026 MATSE 413 Homework 12

Please clearly indicate your answer to aid in grading. You are welcome to use any math software you like (or none at all). If you use software and do not show your work, you cannot receive partial credit. If you show your work either by writing down your equations or by taking a screenshot of your program, you will be eligible to receive partial credit. If you use Python or similar, please comment your code if you wish to receive partial credit. Remember: if your answer does not have Si-based units, you will receive zero points! Note: in this class, I generally expect that you can look up constants like the mass of the electron or the speed of light.

Consider copper.

Calculate the conductivity of copper using its index of refraction n=0.14 and its damping constant k=3.35 at λ=600 nm. (2 points)

Compare your result from part a with the conductivity you calculated in Homework 10 and the experimental value (5.96×107 S/m). The value you got from part a will be different by orders of magnitude (make sure you are comparing values using the same units). Why is this? (4 points)

Consider the dielectric function shown in the dashed black lines below. Panel a shows the real part of the permittivity, while panel b shows the imaginary part. The blue lines are not used for this problem.

At a wavelength of 0.6mm, will this material be reflective or transparent? Explain how you know. (2 points)

At a wavelength of 0.3mm, will this material be reflective or transparent? Explain how you know. (2 points)

At what wavelength is the loss in the material the highest? At what wavelength is the loss in the material the lowest? Explain how you know. (3 points)

Consider the wavelength range between 0.25-0.35 mm. Is the permittivity dominated by free electrons or by another effect (bound electrons, interband, or intraband transitions)? You do not need to identify the other effect. Explain how you know (3 points).

Consider the wavelength range between 0.5-0.7mm. Is the permittivity dominated by free electrons or by another effect (bound electrons, interband, or intraband transitions)? You do not need to identify the other effect. Explain how you know (3 points).

Estimate what the plasma wavelength for this material would be if only free electrons contributed to the permittivity. Give your answer in microns. (3 points)

The intensity of light transmitted by a gold film has an intensity 15% of the incoming light. What is the thickness of the gold film? Give your answer in nm. Assume λ=589 nm and k=3.2. (3 points)

Tauc plots for a material in its as deposited state (black squares) and annealed at various temperatures (colored symbols) are shown below.

Is this material a direct or indirect gap semiconductor? (2 points)

What are the band gaps of the five different samples? Give your answer in eV. (2 points)

Does the material quality improve or degrade with annealing? Explain your answer. (3 points)