= 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>.https://www.kapitza.ras.ru/~glazkov/students/Nobel-akasaki-lecture.pdf[§2, printed pp. 8–10: direct/indirect gaps and nitride composition range]{ref}
For an emitted <photon>, with <frequency> $\nu$ and vacuum <wavelength> $\lambda$,
$$
E_\gamma=h\nu=\frac{hc}{\lambda},\qquad
\lambda=\frac{hc}{E_\gamma},
$$
where $h$ is the <Planck constant> and $c$ the vacuum <speed of light>. Multiplying <energy> by <wavelength> gives $hc=1239.841984\,\mathrm{eV\,nm}$. 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.<Candela-class high-brightness InGaN⁄AlGaN double-heterostructure blue-light-emitting diodes by Shuji Nakamura and others>[p. 1688, Fig. 2 discussion: Zn-related emission]{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 $V_f=V_j+IR_s$, whereas an optical transition does not acquire an extra <energy> $qIR_s$ merely because the contact drop increases. Consequently, extracting a <band gap> from one terminal-voltage reading is not justified.
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