The low ionization rate of Mg acceptors in the p-gallium nitride (GaN) layer is a critical factor accounting for the low current density of E-mode GaN p-FETs. In this work, polarization-enhanced technology was adopted to enhance the ionization rate of the p-GaN channel. High-performance recessed-gate E-mode GaN p-FETs were fabricated to enable GaN complementary logic (CL) circuits. During fabrication, the channel thickness (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub>) is found to be a critical parameter that influences the device metrics. With a decrease in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> (i.e., larger recess depth), a more negative threshold voltage (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><roman>th</roman></sub>) is achieved; however, the trade-off is an increase in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\textit{R}_{\biosc{on}}$</tex-math></inline-formula>. The E-mode GaN p-FET with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> = 32 nm exhibits a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><roman>th</roman></sub> of -1.1 V, a high current density of 17.7 mA/mm, a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\textit{I}_{\biosc{on}}$</tex-math></inline-formula>/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\textit{I}_{\biosc{off}}$</tex-math></inline-formula> of 6.9 × 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><roman>7</roman></sup>, and a low subthreshold swing (SS) of 93 mV/dec. Furthermore, an E-mode n-channel p-GaN gate high electron mobility transistor (HEMT) was fabricated on the same epi-wafer, exhibiting a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><roman>th</roman></sub> of 1.3 V and an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\textit{R}_{\biosc{on}}$</tex-math></inline-formula> of 6 <roman xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ω⋅</roman>mm. Finally, a GaN CL inverter was fabricated and demonstrated under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><roman>DD</roman></sub> = 6 V. Rail-to-rail voltage swing and low static power consumption were both achieved. This work further validates the feasibility of GaN CL integrated circuits and power integrated circuits (PICs).