The formation mechanism of Internal Transport Barriers (ITBs) in flux-driven turbulence is studied by means of the full-f gyrokinetic code GKNET. In the adiabatic electron case with a weak magnetic shear configuration, toroidal momentum injection can change the radial mean electric field E_r through the radial force balance, leading to a kind of driven ITB formation in which the ion thermal diffusivity by Ion Temperature Gradient (ITG) turbulence decreases to the neoclassical transport level. Only co-current toroidal rotation in the outer region can benefit the ITB formation, which mechanism is identified to originate from a positive feedback loop between the radial E_r shear and resultant momentum flux. On the other hand, in the kinetic electron case with a reversed magnetic shear configuration, robust co-intrinsic rotation is driven near the q_min surface in ITG turbulence and sustain the E_r shear through the radial force balance, leading to the spontaneous reduction of ion turbulent thermal diffusivity, while it is not observed in the adiabatic electron case. In the presence of electron heating, counter-intrinsic rotation by Trapped Electron Mode (TEM) turbulence is selectively driven in the negative magnetic shear region, which provides steeper E_r shear formation and resultant larger reduction of ion turbulent thermal diffusivity. It indicates that the co-existence of different modes can trigger the discontinuity near q_min and then spontaneous ITB formation.