enerated gain also implies a multiplication noise that adds to the other noise terms typical of a PIN photodiode. The excess noise is generally represented as a sort of shot noise amplification, SO that the expression for the power of the shot noise term has to be modified as follows: (5.28) where Gm is the avalanche gain FA is the excess noise factor, which is a function of the ionization ratio Vi, and can be writ- ten as [31,32] (5.29) Besides multiplication noise, when using an APD, it is to take into account that the dark current noise also is amplified by the avalanche mechanism. Technology for Telecommunications: Integrated Optics and Microelectronics In order to give a correct expression of the amplified dark current noise, one has to take into account that dark current can be divided into two components, depending on the physical phenomenon generating it. There is a bulk dark current and a surface leakage dark current; the first is really ampli- fied by the APD, and the second does not undergo amplification due to the fact that it is a surface phenomenon. Thus, indicating with Sbd and Ssd the spectral densities of the two components, the final APD dark current power in the detector bandwidth will be [32] (5.30) where Be is the electrical bandwidth of the front end immediately following the photodiode. 5.5 Optical Modulation Devices 5.5.1 Mach-Zehnder Modulators As we have been discussing the modulation performances of semiconductor lasers at 10 Gbit/s and more it is very difficult to transmit at long distance using laser direct modulation due to the limited modulation bandwidth and to intrinsic chirp associated to it. Among the external modulators those having better performances, if used in telecom- munication equipments, are based on a Mach-Zehnder architecture where the interfer- ometer arms are realized with a material exhibiting a strong electro-optic effect (such as LiNbO3 or the III-V semiconductors such as GaAs and InP) [33,34]. For telecommunication applications, the ones most used are those base