By measuring the photoluminescence linewidth of a GaAs quantum well under perpendicular electric fields, we have traced the variation of the effective radius a * of a charged exciton (trion) as a function of electron density. The a * increases sharply above a critical density n s = 2 × 10 14 m −2 , which is consistent with the decrease of the screening length predicted by nonlinear-screening theory. Our analysis shows that the crossover from trions to the two-dimensional electron gas plus hole is generated by Coulomb screening in the high-electron-density regime, eliminating the possible mechanism by the trion localization effect due to the single-electron localization.