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In this paper a review of the research performed in recent years by the group of the authors is presented. The definition and basic properties of the Wigner function are first given. Several forms of its dynamical equation are then derived with the inclusion of potential and phonon scattering. For the case of a potential V(r) the effect of the classical force, for any form of V(r), is separated from quantum effects due to rapidly varying potentials. An elaboration of the dynamical equation is introduced that leads to Wigner paths formed by free flights and scattering events. These are especially suitable for a Monte Carlo solution of the transport equation for the Wigner function very similar to the semiclassical traditional Monte carlo simulation. The Monte Carlo simulation can be extended also to the momentum and frequency dependent Wigner function based on a two-time Green function. Several numerical results are presented throuhout the paper.

The stochastic nature of the switching mechanism of phase-change memory (PCM) arrays, which is a drawback for memory applications, can fruitfully be exploited to implement primitives for hardware security. By applying a set voltage pulse, whose amplitude corresponds to a switching probability of 50%, to a memory array initially placed in the full-reset state, half of the memory bits are statistically switched and programmed to state '1,' whereas the remainder of the bits persist in state '0.' Such a natural randomness can be exploited to create a true random number generator (TRNG), which is the building block of cryptographic applications. The feasibility of a TRNG by means of self-heating PCM cells is assessed and demonstrated through simulations based upon the random network model, i.e., a microscopic transport model previously developed and tested by the authors

The electric response of Ovonic devices to a time-dependent voltage is analysed by means of a charge-transport model previously proposed by the authors. The numerical implementation of the model shows that the features of the I(V ) characteristics depend not only upon the external bias, but also on more complex effects due to the interplay between intrinsic microscopic relaxation times and the inevitable parasitic elements of the system. Either stable or oscillating solutions are found according to the position of the load line. The model also allows for speculations on the potential of Ovonic materials in the design of selector devices for two-terminal non-volatile memories.

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INTRODUCTIONRecently the hydrodynamic model has become popular in the field of analysis and simulation of semiconductor devices*. The model has the merit of providing, along with the concentration and current density of the carriers, also their average energy and average energy flux. At the same time, its equations basically retain the same structure of the simpler drift-diffusion model; because of this, it has been possible to incorporate the hydrodynamic equations into existing deviceanalysis codes, thus exploiting a number of robust solution schemes already available there.The hydrodynamic model is derived by applying the moment technique to the Boltzmann transport equation (BTE) and truncating the series of moments at a suitable order. This yields a number of partial differential equations in the r, t space, specifically, the continuity equations for the carrier number, momentum, average energy and average energy flux. In this procedure, due to the integration over the wave vector space and to the series truncation, some of the information originally carried by the distribution function is lost. However, the information provided by the continuity equations indicated above is in most cases sufficient to describe the electrical behaviour of realistic semiconductor devices.It is worth noting that the term hydrodynamic model is not always given exactly the same meaning in the existing literature. What is meant here by this term is a model derived through the following steps: * Part of this work was carried out within ADEQUAT (JESSI BTl I, ESPRIT 8002) and DESSIS (ESPRIT 6075). E. Schöll (ed.), Theory of Transport Properties of Semiconductor Nanostructures