Semiconductor-oxide-containing gate dielectrics can be formed on surfaces of semiconductor fins prior to formation of a disposable gate structure. A high dielectric constant (high-k) dielectric spacer can be formed to protect each semiconductor-oxide-containing gate dielectric. Formation of the high-k dielectric spacers may be performed after formation of gate cavities by removal of disposable gate structures, or prior to formation of disposable gate structures. The high-k dielectric spacers can be used as protective layers during an anisotropic etch that vertically extends the gate cavity, and can be removed after vertical extension of the gate cavities. A subset of the semiconductor-oxide-containing gate dielectrics can be removed for formation of high-k gate dielectrics for first type devices, while another subset of the semiconductor-oxide-containing gate dielectrics can be employed as gate dielectrics for second type devices. The vertical extension of the gate cavities increases channel widths in the fin field effect transistors.