## 4 All-Silicon Photodetector Structures
### TPA-Based Devices  
Despite the small value of the TPA coefficient, ranging from 0.44 cm/GW to 0.9 cm/GW at a wavelength of 1,550 nm [74], silicon optical waveguides have potential for use in TPA because of their long interaction lengths and low optical dispersion in silicon. The photocurrent generated by the TPA effect can efficiently collect embedding a p-i-n diode in the silicon waveguide. In Figure 18, the TPA-based integrated detector proposed by [PERSON] _et al._ in 2002 is reported [75]. Figure 16: Photoconductive gain _versus_ illumination power of a 1.55-\(\upmu\)m laser diode with the bias voltage as a parameter for the photodetector proposed by [PERSON] _et al._[71] in 2001. Copyright © 2001 Optical Society of America. Figure 17: Schematic cross section of the photodetector proposed by [PERSON] _et al._[72, 73]. Reprinted with permission from [PERSON]. [PERSON] _et al._ Copyright © 2010 IEEE. In Figure 18, the measured photocurrent for a bias voltage of \(-3\) V is reported and the typical non-linear behaviour of the TPA effect can be noted. [PERSON]'s device was used to perform an optical autocorrelation for measuring ultra-short laser pulses, but it was not suitable as a photodetector due to the high required optical input power value. The key to obtaining micrometer devices sensitive to low optical input is to strengthen the interaction between light and matter by tightly confining the light, _i.e._, employing high-Q microresonators. [PERSON] _et al._[76] theoretically studied the feasibility of using p-i-n diode embedded silicon micro-ring or photonic crystal resonators for ultrafast photodetection. Starting from these premises, [PERSON] _et al._[77] proposed an infra-red photodetector based on a p-i-n integrated into a high-Q width-modulated line-defect photonic crystal (PhC) nanocavity [78, 79]. The sketch of the device proposed by the Japanese authors is reported in Figure 19. The nanocavity is characterized by a lattice constant \(a=420\) nm, hole radius \(r=108\) nm, slab thickness \(t=204\) nm, \(Wi=8.72\)\(\upmu\)m and \(Ww=8.4\)\(\upmu\)m; whereas the input and output waveguides are \(1.05a\) wide and are in-line connected with the cavity through barrier line defects \(0.98a\) wide and \(11a\) long. The PhC nanocavity is characterized by an intrinsic Q factor of \(8.4\times 10^{5}\). This high Q value permits the obtention of a high generation of photocurrent into the cavity region, enabling the possibility of detecting even low input power. In particular, an external quantum responsivity of 16 mA/W at a resonance wavelength of aproximately 1,500 nm, has been measured. Furthermore, on the one hand,  
Figure 19: Schematic view of the device proposed by [PERSON] _et al._[77]. Reprinted with permission from [PERSON], _et al._ Copyright 2010, American Institute of Physics. Figure 18: Sketch **(a)** and measured photocurrent **(b)** of the TPA-based detector proposed by [PERSON] _et al._[75]. Reprinted with permission from [PERSON], _et al._, Copyright 2002, American Institute of Physics. the very small dimensions of the device allow achievement of a low dark current value (about 15 pA at room temperature for 3 V of reverse bias), and on the other hand, a small capacitance (a value of \(9.5\times 10^{-18}\) F was estimated). The resistance for the p and n regions limits the speed of the proposed device at 0.1 GHz. A silicon microdisk resonator with a laterally embedded p-i-n diode was chosen by [PERSON] _et al._[80] to enhance the TPA photocurrent. TPA is a very weak effect which is difficult to exploit for the realization of bulk all-silicon photodetectors with appreciable efficiency. For this reason, as shown in the literature, TPA exploitation in bulk silicon devices at 1,550 nm is aimed at improving the sensitivity of two-photon absorption autocorrelators, utilizing, as the two-photon absorber, a silicon avalanche photodiode (APD) [81-83].