Inverted-polarity ( n -up), high-speed, oxide-confined, polyimide-planarized, copper-plated 850-nm vertical-cavity surface-emitting lasers with various aperture sizes were fabricated and characterized. The reported devices demonstrated intrinsic, parasitic, and thermal maximum bandwidth limitations of 39.3, 24.6, and 22.9 GHz, respectively. VCSELs with 7 μm active area diameter and 4 μm of plated copper exhibited a maximum –3 dB frequency modulation bandwidth ( $f_{-3\;{\bf dB}\; {\rm max}}$ ) of 18.8 GHz and a resonance frequency of 14.8 GHz at a bias current density ( $J_{{\rm bias}}$ ) of only 8.8 kA/cm2, limited by thermal effects, with a high modulation current efficiency factor of 17.0 GHz/mA1/2 for quantum well VCSELs. The presented VCSELs also demonstrated a record high $f_{-3\;{\rm dB}\; {\rm max}}^{2}/J_{{\rm bias}}$ ratio of 40.2 GHz2/kA/cm2 which represents an 11% increase compared with the highest previously reported ratio. Rate-equation-based thermal VCSEL model and three-pole transfer function approximation were applied to extract several VCSELs’ parameters, which enabled the estimation of the VCSELs internal temperature and major bandwidth limitation. Particle swarm optimization was utilized in parameter extraction and optimization.