Numerical analysis and simulation of semiconductor devices

M. R. is one of the authors of HFIELDS, a general-purpose simulation tool for silicon devices using the box-integration method and the Scharfetter-Gummel discretization scheme, which has been adopted in several research groups in industrial or academic environments since its first appearance in 1985 [69,126]. The code, supplemented with flexible mesh generator [77] and user interface [82], has been improved in the subsequent years by implementing the small-signal analysis [74], the transient analysis [72,79], the sensitivity analysis and device optimization [21,28,73,135], the mixed circuit-device simulation [75], the three-dimensional version [25,78,81,84,85,88], and the description of the thermal behavior of the lattice [10]. Further developments of the activity on HFIELDS were the incorporation of the amorphous and polycrystalline silicon (outlined in another point below), and the extension of the simulation capability to the case of solid-state sensors (see also below). In 1986, while visiting the IBM Thomas J. Watson Research Center at Yorktown Heights, M. R. first proposed an efficient discretization scheme for the so-called hydrodynamic model of semiconductor devices [19,20,145]. The hydrodynamic model improves over the customary drift-diffusion one because it is based on higher moments of the Boltzmann Transport Equation. Due to this, it is able to determine, apart from the electric potential and the concentration of the mobile charge carriers (electrons and holes), also the carrier temperature. In this way, the model lends itself to describing a number of non-local phenomena, like velocity overshoot and impact ionization, that are typical of modern submicron devices. The discretization scheme made it possible to easily incorporate the hydrodynamic model into existing device-analysis codes like HFIELDS [22,35,130,131]. Particular issues of the numerical analysis of semiconductor devices have also been dealt with in connection with the main stream of research, specifically: accurate methods for calculating the charge concentration [15], problems of grid optimization [16,23,26,67,68,80,129,132], solution of the semiconductor equation by an integral-equation approach [17], extension of discretization schemes to incorporate impact-ionization [34], methods improving the computational efficiency of the box-integration method solution of the semiconductor equations [70,46,136,139] and of the spherical-harmonics solution of the Boltzmann Transport equation [41,48,141].