The responses of the plasmonic mode to an external voltage are also investigated. For the plasmonic mode, although most of the optical energy is localized in the thin oxide layer, there is still some remaining in the silicon core. When free carriers are injected into or extracted from the silicon core, the refractive index of silicon will be changed and thus the plasmonic mode will suffer a small variation accordingly. According to the sign and magnitude of drive voltage, three working regimes can be distinguished – accumulation regime, depletion regime, and inversion regime. Figures 3(a)-3(c) schematically show the free carrier dynamics in the silicon core for these three regimes. In response to a positive voltage, free electrons accumulate around the sidewall thin oxide layer (also under the cap oxide layer but much less) and the corresponding refractive index of silicon is reduced [
4]. The thickness of electron accumulation layer is determined by the Debye length [
7]. When a small negative voltage is applied, electrons near the oxide layer are pushed away and a depletion region forms; when the negative voltage is large, holes are then generated and accumulated near the oxide layer. The depletion and inversion layers can also change the refractive index of silicon. Figures 3(d) and 3(e) show the free carrier distribution along a lateral line for the carrier accumulation and inversion cases. The concentration of original silicon doping is set to be 5×10
17 cm
-3. Figure 3(f) shows
nre changes with the applied voltage. It can be found that a positive voltage monolithically reduces
nre, while a negative voltage first slightly increases and then decreases
nre due to the competition between electron depletion and hole accumulation. At 5-V drive voltage,
∆nre = -0.0043, which implies a about 10° phase change for a 10-μm-long plasmonic waveguide with a loss of 7.2 dB. It should be noted that resonance structures, such as microring resonators, photonic crystal cavities etc., can be employed to enhance the transmission sensitivity to the small refractive index change [
8].