The dynamics of In surface segregation during molecular beam epitaxy growth of In.22Ga.78As/GaAs quantum wells (QWs) are studied by temperature-programmed desorption (TPD). The TPD spectra show two In peaks: a low temperature (low-T5) peak and a high temperature (high-T5) peak, which arise from desorption of surface segregated In and dissociation of the underlying InGaAs lattice, respectively. Integration of the low-Ts peak provides quantitative determination of the surface segregated In population ΘIn, as a function of InGaAs layer thickness, incident arsenic dimer flux [(Fi(As2)], InGaAs growth temperature, and GaAs cap thickness. The surface segregated In population ΘIn, is observed to grow with InGaAs thickness, until reaching a temperature-dependent steady state value between 1.0 and 2.0 monolayers after approximately ten monolayers of growth, and then decays during GaAs overlayer growth. The variation of ΘIn with thickness closely mimics the resulting vertical composition profile, which is characterized by an In-depleted bottom interface and segregation of In into the GaAs cap. Based on these results, a sequence of: 1) In predeposition, 2) InGaAs growth, and 3) thermal desorption of Eh is proposed to produce a more square InGaAs/GaAs QW than can be obtained by more standard MBE approaches.