Massimo Rudan

A new discretization strategy of the semiconductor equations comprising momentum and energy balance

A discretization scheme is applied to the hydrodynamic model for semiconductor devices that generalizes the Scharfetter-Gummel method to both the momentum-conservation and the energy-conservation equations. The major advantages of the scheme are: (1) the discretization is carried out without neglecting any terms, thus providing a satisfactory description of such effects as velocity overshoot and carrier heating; and (2) the resulting equations lend themselves to a self-consistent solution procedure similar to those currently used to solve the simpler drift-diffusion equations. Two-dimensional steady-state simulations of an n-channel MOSFET and of an n-p-n BJT (bipolar junction transistor) have been carried out by means of an improved version of the program HFIELDS. Carrier-temperature plots have been obtained with a reasonable computational effort, demonstrating the efficiency of this technique. The results have been compared with those obtained with the standard drift-diffusion model and significant differences in the electron concentration have been found, especially at the drain end of the MOSFET channel. >

Electron and hole mobility in silicon at large operating temperatures. I. Bulk mobility

In this paper, an experimental investigation on high-temperature carrier mobility in bulk silicon is carried out with the aim of improving our qualitative and quantitative understanding of carrier transport under ESD events. Circular van der Pauw patterns, suitable for resistivity and Hall measurements, were designed and manufactured using both the n and p layers made available by the BCD-3 smart-power technology. The previous measurements were carried out using a special measurement setup that allows operating temperatures in excess of 400/spl deg/C to be reached within the polar expansions of a commercial magnet. A novel extraction methodology that allows for the determination of the Hall factor and drift mobility against impurity concentration and lattice temperature has been developed. Also, a compact mobility model suitable for implementation in device simulators is worked out and implemented in the DESSIS/spl copy/ code. Comparisons with the mobility models by G. Masetti et al. (1983) and D.B.M. Klaassen (1992) are shown in the temperature range between 25 and 400/spl deg/C.

Band-Structure Effects in Ultrascaled Silicon Nanowires

In this paper, we investigate band-structure effects on the transport properties of ultrascaled silicon nanowire FETs operating under quantum-ballistic conditions. More specifically, we expand the dispersion relationship epsiv(kappa) in a power series up to the third order in kappa2 and generate the corresponding higher order operator to be used within the single-electron Hamiltonian for the solution of the Schrodinger equation. We work out a hierarchy of nonparabolic models accounting for the following: 1) the shift of the subband edges and the change in the transport effective masses; 2) the higher order Hamiltonian operator; and 3) the splitting of the fourfold unprimed subbands in nanometer-size FETs. We then compute the device turn-on characteristics, the threshold shift versus diameter, and the subthreshold slope (SS) versus gate length. By compensating for the different threshold voltages, i.e., by reducing the turn- on characteristics to the same leakage current at zero gate bias, it turns out that the current discrepancies between the most general model and the bulk-parabolic model are contained within 20%. Finally, it turns out that the nonparabolic band structure gives an improved SS at the lowest gate lengths due to a reduced source-drain tunneling, reaching up to 30% enhancement.

Modeling electron and hole transport with full-band structure effects by means of the Spherical-Harmonics Expansion of the BTE

The Spherical-Harmonics solution of the Boltzmann Transport Equation (BTE) in silicon is generalized to the full-band case for both electrons and holes. The relevant scattering mechanisms, including impact ionization, are modeled consistently. Comparison with experimental data and Monte Carlo (MC) analysis emphasize the importance of a correct description of the band structure and impact ionization especially in the analysis of carrier transport at high energies, and the ability of the Spherical-Harmonics Expansion (SHE) scheme to efficiently incorporate the features of the transport mechanisms to a rather general extent.

Investigation of non‐local transport phenomena in small semiconductor devices

The hydrodynamic transport model based fin the generalized momentum and energy equations is used to simulate a n + -n-n + one-dimensional silicon device and the results are compared with Monte Carlo calculations. The non-local effects are shown to become important for lengths of the order of a few tenths of a micrometer at applied voltages around 1.0–1.5 V. The hydrodynamic and Monte Carlo velocity and energy are generally in good agreement. Finally, the effects of the thermal conductivity and of the convective terms, in regions where large gradients are present, are investigated.

Low-Field Electron Mobility Model for Ultrathin-Body SOI and Double-Gate MOSFETs With Extremely Small Silicon Thicknesses

A number of experiments have recently appeared in the literature that extensively investigate the silicon-thickness dependence of the low-field carrier mobility in ultrathin-body silicon-on-insulator (SOI) MOSFETs. The aim of this paper is to develop a compact model, suited for implementation in device- simulation tools, which accurately predicts the low-field mobility in SOI single- and double-gate MOSFETs with Si thicknesses down to 2.48 nm. Such a model is still missing in the literature, despite its importance to predict the performance of present and future devices based on ultrathin silicon layers.

Impact ionization within the hydrodynamic approach to semiconductor transport

Abstract We present a rigorous analytical treatment of band-band impact ionization in semiconductor high-field transport. The microscopic electron impact ionization scattering time is calculated for the general case of three different anisotropic parabolic bands (one for the initial valence electron, the other two for the two final conduction electrons) and an arbitrarily shaped band for the impact-ionizing energetic conduction electron. In this derivation the wave vector dependence of the matrix element is accounted for in contrast to previous calculations. The total impact ionization rate in both direct and indirect semiconductors and the associated energy relaxation rate in direct semiconductors are expressed analytically in a universal scaling form as a function of the electron temperature and a few band-structure parameters like effective masses, energy gap, and the distance in k-space between the band extrema (in case of an indirect semiconductor). Such expressions can be used in the hydrodynamic model as approximations for the collision terms arising in a moment expansion of the Boltzmann equation.

Analysis of conductivity degradation in gold/platinum-doped silicon

A general model is presented, describing the effects of gold/platinum doping in silicon. The steady-state case is then analyzed with reference to the conductivity degradation due to deep impurities in realistic cases of n- and p-type materials. In particular, the different influence of gold with respect to platinum in n-type material, due to the localization in energy of the two acceptor levels, is quantitatively explained and reproduced.

Design Considerations and Comparative Investigation of Ultra-Thin SOI, Double-Gate and Cylindrical Nanowire FETs

In this work we investigate the performance of fully-depleted silicon-on-insulator (SOI), double-gate (DG) and cylindrical nanowire (CNW) FETs, with the aim of establishing optimization procedures and appropriate scaling rules towards their extreme miniaturization limits. The simulation model fully accounts for quantum electrostatics; current transport is modeled by an improved quantum drift-diffusion approach supported by a new thickness-dependent mobility model which nicely fits the available measurements. The simple rule resulting from this investigation is that stringent short-channel effect constraints can be fulfilled at a constant oxide thickness of 2 nm, with Lg/t Si ap 5 for the SOI-FET, Lg/tSi ap 2 for the DG-FET, and Lg /tSi ap 1 for the CNW-FET

Numerical simulation of polycrystalline-Silicon MOSFET's

In this paper we investigate polycrystalline-silicon MOSFET operation by means of a two-dimensional device-analysis program developed at the University of Bologna. The grain-boundary model used in this study allows for both donor and acceptor states at the interface, and assumes a drift-diffusion transport mechanism, consistently with the general structure of the code. Results achieved thus far allow us to interpret the increased threshold voltage experimentally observed in polycrystalline-silicon MOSFETs and the device transconductance in strong inversion; on the other hand, the current increase occurring at negative gate voltages is not justified by the numerical model so far implemented. It is believed that field-enhanced emission rates and impact ionization are possible mechanims to interpret the above conduction increase.