  In this work we investigate spin diffusion in InAs quantum wells with the
Rashba spin-orbit coupling modulated by a gate voltage. The gate voltage
dependence of the spin diffusion under different temperatures is studied with
all the scattering explicitly included. Our result partially supports the claim
of the realization of the Datta-Das spin-injected field effect transistor by
Koo {\it et al.} [Science {\bf 325}, 1515 (2009)]. We also show that the
scattering plays an important role in spin diffusion in such a system.
