Light detectors for different jobs are made from different crystals…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Light detectors for different jobs are made from different crystals. Take . The band gap is eV for silicon, eV for germanium and eV for diamond. Find the longest wavelength of light that can lift an electron across the gap in each crystal. Say which of the three can respond to visible light, which runs from nm to nm.
Need a reminder? The key ideaShow
A photon of wavelength has energy , with . It lifts an electron across a gap if , so . The share of electrons that heat lifts across goes as , with .
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. and the three gaps.
Plan. The photon energy must be at least . At the limit , so .
Step 1. Silicon. nm.
Step 2. Germanium. nm.
Step 3. Diamond. nm.
Answer: nm, nm and nm. Silicon and germanium respond to all visible light, because nm is below both cut-offs. Diamond responds only to ultraviolet light, so visible light passes through it.
Check. A smaller gap gives a longer cut-off. The order eV matches the order nm.
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