= Solution
\b[<GaN> has a substantial band-gap advantage for high-temperature operation.] Its gap is larger than those of <GaAs> and <GaP>, suppressing thermally generated intrinsic carriers through $n_i\propto e^{-E_g/(2kT)}$. A doped junction therefore retains its intended carrier imbalance and can have lower thermally generated leakage over a wider <temperature> range, other factors being equal. The wide gap also supports emission at higher <photon> energies.
This is a materials-based expectation, not a guarantee for every finished device. Dopant activation and compensation, defects, contact stability, heat extraction and nonradiative recombination can set the practical limit. Increasing <temperature> also reduces carrier mobility and can broaden or quench light emission. The relevant advantage is reduced intrinsic excitation; a comparison of operating temperatures needs those other device properties too.
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