 Blue light-emitting diode

Blue transitions motivate wide-bandgap semiconductors, but a large band gap alone cannot guarantee efficient emission. Gallium nitride has a direct band gap; indium gallium nitride composition tunes the transition energy.^[ref]

For an emitted photon, with frequency $\nu$ and vacuum wavelength $\lambda$,where $h$ is the Planck constant and $c$ the vacuum speed of light. Multiplying energy by wavelength gives $hc=1239.841984\mathrm{eV}\mathrm{nm}$. Thus chosen wavelengths $450\mathrm{nm}$ and $630\mathrm{nm}$ correspond to $2.75520\mathrm{eV}$ and $1.96800\mathrm{eV}$: blue requires more energy per photon than red. A stipulated transition energy $3.40\mathrm{eV}$ instead gives $364.659\mathrm{nm}$, in the ultraviolet. These are conversions, not measured emission lines.

For near-edge emission, $E_{\gamma }\approx E_g$ estimates the photon energy from the emitting material's band gap. Quantum well confinement or impurity transitions can change it. The 1994 blue light-emitting diode used zinc-doped indium gallium nitride, emitting below its near-edge transition.^[ref]

The measured forward terminal electric potential difference $V_f$ is also not fixed by $E_g/q$, where $q$ is the elementary charge. It depends on electric current, temperature, contacts and series electrical resistance. Even the simple Shockley diode equation with series electrical resistance has $V_f=V_j+I{R}_s$, whereas an optical transition does not acquire an extra energy $qI{R}_s$ merely because the contact drop increases. Consequently, extracting a band gap from one terminal-voltage reading is not justified.