QB_PH_SEC6_024: Lasers and Quantum Optics

A semiconductor diode laser emits coherent light at wavelength $\lambda = 827\text{ nm}$. What is the direct bandgap energy $E_g$ (in eV) of the active semiconductor material? Take $h c = 1240\text{ eV}\cdot\text{nm}$. (Give your answer to one decimal place)

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Semiconductor Laser Emission Principle**: Lasing occurs via stimulated recombination of injected electrons from the conduction band edge to holes at the valence band edge: $h\nu = E_g \implies \lambda = \frac{h c}{E_g}$ 2. **Bandgap Evaluation**: $E_g = \frac{h c}{\lambda} = \frac{1240\text{ eV}\cdot\text{nm}}{827\text{ nm}} = 1.49939\text{ eV} \approx 1.5\text{ eV}$ 3. **Official Value**: 1.5 eV.