QB_PH_SEC8_016: Semiconductor Devices & Diodes

What is the minimum bandgap energy $E_g$ (in eV) required for a semiconductor to emit red light of wavelength $\lambda = 620\text{ nm}$ in a Light Emitting Diode (LED)? Take $h c = 1240\text{ eV}\cdot\text{nm}$. (Give your answer to one decimal place)

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Spontaneous Radiative Recombination**: In an LED, injected excess electrons and holes recombine radiatively across the direct bandgap energy $E_g$, emitting photons of energy: $h\nu = \frac{h c}{\lambda} \approx E_g$ 2. **Numerical Evaluation**: - $h c = 1240\text{ eV}\cdot\text{nm}$ - Peak emission wavelength: $\lambda = 620\text{ nm}$ $E_g = \frac{1240\text{ eV}\cdot\text{nm}}{620\text{ nm}} = 2.0\text{ eV}$ 3. **Official Value**: 2.0 eV.