Sensing or communication using the millimeter (mm)-wave band, such as mm-wave 5G systems and radar applications, is drawing increasing research interest. These systems typically employ an array of power amplifiers (PAs), with each PA operating at moderate output power. In this case, the power efficiency of the PA is crucial for better power and thermal management. Due to the high peak-to- average power ratios of spectrum-efficient modulations, the power back-off (PBO) efficiency is becoming increasingly important. The Class E/F switching PA is a favorable candidate at the mm-wave frequency band, as it can incorporate zero-voltage-switching (ZVS) and zero-derivative-voltage switching (ZdVS). Moreover, it reduces the I/V overlap from finite on-resistance by terminating different harmonics, leading to better peak efficiency. However, its efficiency roll-off still follows a typical Class B curve, resulting in relatively poor PBO efficiency. Recently, a voltage-mode subharmonic switching (SHS) digital PA architecture [1] -[3] has been demonstrated to improve PBO efficiency by togging PA cells at the subharmonic frequency for the output PBO. To optimize both peak and PBO efficiency, we propose a concurrent harmonic and subharmonic tuning Class E/F2,2/3 SHS PA for mm-wave operation that: 1) utilizes both harmonic and subharmonic tuning to reduce I/V overlap (i.e., conduction loss) for both peak and PBO operation and 2) allows the PA cells to toggle at a much lower frequency (i.e., subharmonic frequency) in PBO, which facilitates square switching waveform and reduces the loss of high-frequency clock routing. At the circuit level, we propose an on-chip concurrent harmonic and subharmonic tuning matching network that can simultaneously provide optimal load impedance of the fundamental (Fc), 2nd harmonic (2Fc), subharmonic (Fc/3), and 2nd harmonic of the subharmonic (2Fc/3) with a compact footprint without involving any tunable switches and elements. The proof-of-concept proto...