  We measured the response of the surface state spectrum of epitaxial Sb2Te3
thin films to applied gate electric fields by low temperature scanning
tunneling microscopy. The gate dependent shift of the Fermi level and the
screening effect from bulk carriers vary as a function of film thickness. We
observed a gap opening at the Dirac point for films thinner than four quintuple
layers, due to the coupling of the top and bottom surfaces. Moreover, the top
surface state band gap of the three quintuple layer films was found to be
tunable by back gate, indicating the possibility of observing a topological
phase transition in this system. Our results are well explained by an effective
model of 3D topological insulator thin films with structure inversion
asymmetry, indicating that three quintuple layer Sb2Te3 films are topologically
nontrivial and belong to the quantum spin Hall insulator class.
