  We investigate the quality (Q) factor and the mode dispersion of
single-defect nanocavities based on a triangular-lattice GaAs photonic-crystal
(PC) membrane, which contain InAs quantum dots (QDs) as a broadband emitter. To
obtain a high Q factor for the dipole mode, we modulate the radii and positions
of the air holes surrounding the nanocavity while keeping six-fold symmetry. A
maximum Q of 17,000 is experimentally demonstrated with a mode volume of
V=0.39(lambda/n)^3. We obtain a Q/V of 44,000(n/lambda)^3, one of the highest
values ever reported with QD-embedded PC nanocavities. We also observe ten
cavity modes within the first photonic bandgap for the modulated structure.
Their dispersion and polarization properties agree well with the numerical
results.
