Dynamic response of a p-i-n diode The packet of generated electrons is transported at speed vs and takes time t =dvs to cross the depleted region. or the case RL=0 shows that the current generated by the diode is the rectangular impulse shown of duration t and of intensity Since From which we conclude that, for the geometry considered and for a particular wavelength and material, we must accept a compromise between the internal quantum efficiency and the speed of response. Limitation due to the external circuit In order to produce a signal, a photodiode is inserted into a circuit whose components also contribute to limit the bandwidth of an optical detector. The most simple circuit consists of the capacitance of the junction CJ in parallel with a load resistance RL, with a negligible impedance of the source at high frequencies. The frequency response of such a resistor-capacitor network is

3dB Cut off frequency The cutoff frequencies f and fRC vary inversely with d, thus there is an optimal thickness for the depleted region which maximizes the global cutoff frequency f3dB The optimal thickness of d is obtained when f = fRC , giving: 3dB cut off corresponds approximately to half power 10*log(Po/P)=[dB], (Po/P) = 2, but (Io/I) = sqrt(2)

Response of a real p-i-n photodiode Consider a photodiode made of GaInAs/InP, designed for optical telecommunications at a wavelength of 1.3 m, taking into account the finite value of the optical absorption coefficient: = 1.3 104 cm1; the different saturation velocities for electrons and holes vn = 6 106 cm/s and vp = 4.8 106 cm/s; the inevitable parasitic capacitances of the circuit: CP = 50 fF; a parasitic inductance L, caused by the connecting wires, The illumination at the N side of the structure, and the diameter of the active region is 30 m. The load resistance was kept constant: RL = 50 . Curves 1 and 2 show behaviors limited by the transit time and by the circuit respectively. Curve 3 corresponds to a depleted region whose width is close to the optimum. curve 4 shows that its response can be further improved by parasitic induction. For a higher value of inductance (curve 5), the bandwidth is reduced, but a gain in signal is obtained.

S and GaAs detector responses (for 400 900 nm) Silicon has an indirect bandgap and its absorption coefficient slowly increases. The dark current is mostly caused by current generation in the depleted region, which is of the order 107 A/cm2 The response speed is often limited to less than 1 GHz by the transit time, in particular for components whose response has been extended into the infrared. Gallium arsenide has a direct bandgap; internal quantum efficiency close to 100%, and cutoff at short wavelengths due to absorption from the large-bandgap window layer (AlGaAs). The density of the dark current is of the order of 108 Acm2 at VB/2 (due to the bandgap larger than Si) and a product i ft of the order of 20 GHz Ge and GaInAs detector responses (for 900-1800 nm)