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liesandcake
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Homework Statement
You are to design a coating to enhance the detection efficiency of a silicon detector (n=3.42 at [tex]\lambda[/tex]=351nm)
(a) Is the coting a reflection or antireflection coating?
(b) Should you use a higher or lower index material for the coating? Specify a material to use.
(c) Provide a prescription for the coating you chose for normal incident light at 351nm.
(d) Provide a prescription for the coating you chose for a 45 degree incident light at 351nm.
(e) How would you make the coating more effective for a wider range of wavelengths?
Homework Equations
[tex]e =\frac{\gamma _{rec}}{\gamma _{inc}}[/tex]
[tex]\lambda_\theta = \frac{\lambda_o}{n}\sqrt{n^2 - \sin{\theta}^2}[/tex]
[tex]n_1 t_1 = \frac{\lambda}{4}[/tex]
The Attempt at a Solution
- I'm having trouble deciding what material to use, and which equations will allow me to specify a narrow bandpass at [tex]\lambda = 351nm[/tex].
- So far I have defined "enhance the detection efficiency" as the number of recorded rays divided by the number of incident rays. AKA the amount of incoming rays which are actually absorbed by the detector.
- From my textbook I have deciphered that it is better to use three layers at thickness [tex]\mbox{$\frac{\lambda}{4}$}[/tex] to ensure that there is reflection
- I also believe I want an index of refraction somewhere around the square root of the index of the detector, which would be [tex]\sqrt{3.42} = 1.85[/tex]. I'm unsure if this applies to all layers, or if the index needs to vary. I read that it is good to have a high-index material (~3) matched with a low index material (~1.7) to create the most narrow passband.
- I have found Yttrium Oxide and Silicon Monoxide which I believe have appropriate indices of refraction (n=1.85 and 1.86, respectively) but I have no idea how they would be combined to only allow one wavelength through.
- I think my main issue is that I lack a core understanding of how these thin films work, and a convenient equation that relates the indices/thicknesses to wavelengths so I can see a nice passband.