Effect of growth rate on the composition fluctuation is investigated in In0.34Ga0.66As0.98N0.02/GaAs single quantum wells (QWs) by photoluminescence (PL), transmission electron microscopy, and admittance spectroscopy. In an InGaAsN layer grown at a normal growth rate, the PL spectra show a low-energy bump at the tail of an InGaAsN emission, suggesting the presence of composition fluctuation. Lowering the growth rate degrades the composition fluctuation by segregating into bimodal phases of an InGaAsN and InGaAs-rich phase. Further lowering the growth rate leads to a three-dimensional growth and enhances the InGaAs-rich phase. The carrier distribution for the InGaAsN layer grown at the normal rate shows a carrier bump at the tail of a strong accumulation peak, suggesting the presence of an electron state below the QW ground state. The admittance spectroscopy shows that the activation energy (32 meV) of this electron state is comparable to the energy separation (30 meV) between the InGaAsN emission and the low-energy bump, and thus it is possible that the composition fluctuation actually induces an electron state closely below the QW ground state.