Concept:The threshold wavelength for band-to-band carrier generation is given by \( \lambda_{\text{max}} = \frac{h c}{E_g} \).
Formula:$$\lambda_{\text{max}} = \frac{h c}{E_g} = \frac{1240\text{ eV}\cdot\text{nm}}{0.70\text{ eV}} \approx 1771.4\text{ nm} \approx 1771\text{ nm}$$
Solution:- Given: \( E_g = 0.70\text{ eV} \) and \( h c \approx 1240\text{ eV}\cdot\text{nm} \).
- Cutoff wavelength: \( \lambda_{\text{max}} = \frac{1240}{0.70} \approx 1771\text{ nm} \) (short-wave infrared).
- Germanium absorbs photons across the visible spectrum and into the infrared up to \( 1771\text{ nm} \).
Why other options are incorrect:- Option B: 1127 nm is the threshold cutoff wavelength for Silicon.
- Option C: 550 nm is in the visible green spectrum, corresponding to \( E_g = 2.25\text{ eV} \).
- Option D: 3500 nm corresponds to \( E_g = 0.35\text{ eV} \).
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