  Making use of droplet epitaxy, we systematically controlled the height of
self-assembled GaAs quantum dots by more than one order of magnitude. The
photoluminescence spectra of single quantum dots revealed the strong dependence
of the spectral linewidth on the dot height. Tall dots with a height of ~30 nm
showed broad spectral peaks with an average width as large as ~5 meV, but
shallow dots with a height of ~2 nm showed resolution-limited spectral lines
(<120 micro eV). The measured height dependence of the linewidths is in good
agreement with Stark coefficients calculated for the experimental shape
variation. We attribute the microscopic source of fluctuating electric fields
to the random motion of surface charges at the vacuum-semiconductor interface.
Our results offer guidelines for creating frequency-locked photon sources,
which will serve as key devices for long-distance quantum key distribution.
