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In solid state electronics the miniaturization of integrated circuits implies that, even at moderate applied voltages, the components can be exposed to very intense electric fields. Advances in electronics push the devices to operate also under cyclostationary conditions, i.e. under large-signal and time-periodic conditions. A main consequence of this fact is that circuits exhibit a strongly nonlinear behavior. Furthermore, semiconductor based devices are always imbedded into a noisy environment that could strongly affect their performance, setting the lower limit for signal detection in electronic circuits. For this reason, to fully understand the complex scenario of the nonlinear phenomena involved in the devices response, an analysis of the electron dynamics in low-doped semiconductors far from equilibrium conditions is very important. Semiconductor spintronics offers a possible direction towards the development of hybrid devices that could perform logic operations, communication and storage, within the samematerial technology: electron spin could be used to store information, which could be transferred as attached to mobile carriers and, finally, detected. Despite these advantages, for the operability of prospective spintronic devices, the features of spin relaxation at relatively high temperatures, jointly with the influence of transport conditions, should be firstly well understood. This chapter reviews recent results obtained by using a three dimensional semiclassical multivalleysMonte Carlo code to simulate the nonlinear carrier dynamics in low-dopedGaAs bulks (Persano Adorno et al., 2009a; Persano Adorno, 2010; Spezia et al., 2010). The aim is to discuss and clarify the most relevant findings obtained by the investigation of: (a) the harmonic generation process and (b) the spectral density of the electron velocity fluctuations in the presence of intense sub-terahertz electric fields;(c) the influence of temperature and transport conditions on the electron spin relaxation. Since Monte Carlo approach includes, at a microscopic level, all the sources of the nonlinearities (hot carriers, velocity overshoot, intervalley transfer, etc.) which take place in electronic devices operating under large-signal conditions, it allows to study harmonic Monte Carlo Simulation of Electron Dynamics in Doped Semiconductors Driven by Electric Fields: Harmonic Generation, Hot-Carrier Noise and Spin Relaxation 13

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Monte Carlo Simulation of Electron Dynamics in Doped Semiconductors Driven by Electric Fields: Harmonic Generation, Hot-Carrier Noise and Spin Relaxation