Physica Scripta. Vol. T69, 290-294, 1997 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Examination of MOS Structures by a 3D Particle Dynamics Monte-Carlo Simulator Including Electrothermal Effects' K. TarnayaVb, A. Gali", A. Poppe", T. Kocsis" and F. Massib a Technical University of Budapest, Dept. of Electron Devices, H-1521 Budapest, Hungary zyxwv b Uppsala University, Dept. of Electronics, POB 534, S-75121 Sweden zyxwvutsr Received May 15,1996; accepted June 18,1996 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Abstract The MicroMOS quasi-deterministic particle dynamics 3D Monte-Carlo program for submicron MOS transistors is now extended with electron- phonon interaction models for intervalley scatterfng and with a cmier- lattice energy exchange model. The impact ionisation and Auger recombination models are also improved. The carrier transport and lattice heat transport problems are self-consistently solved. As example the results of simulation, the spatial distribution of electrons, electron-phonon scat- tering events, impact ionisation events, Auger recombination events and the lattice temperature are presented. A new, low drain-to-source voltage breakdown effect has been observed. 1. Introduction In the past decade, considerable effort has been invested into the development of hydrodynamic models for conven- tional device simulators capable of considering the carrier energy transport. Recently, rigorous treatments have been given in [l] and [2], but it is doubtful that these algorithms are suitable for the correct electrothermal simulation of deep submicron devices because the statistical consideration of the distribution function concept fails for a very small number of carriers (several hundreds or thousands). There- fore, the carrier-lattice interactions and the energy transport should be considered on the microscopic level, applying Monte-Carlo simulation methods. A brief description of the principles of the MicroMOS 3D particle dynamics Monte-Carlo program for submicron MOS transistors was given in Ref. [3]. Using the particle dynamics method, all Coulomb scattering effects (e.g. carrier-carrier scattering, carrier-ionised impurity scattering) are inherently modeled. In this paper, outlines of a carrier-phonon scattering model and a carrier lattice energy exchange model are given. These match well the particle dynamics method applied for the modeling of the carrier charge and energy transport. The carrier transport and lattice heat transport problems are self-consistently solved. Figure 1 shows the examined deep submicron MOS tran- sistor structure. The dimensions of the structure are: 170nm channel length, 150nm width and depth. The thickness of the SiOz insulating layer is 5 nm. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA - 'The research has been sponsored by the DEC Extemal European Research Projects HG-001 and SW-003, the Hungarian Scientific Research Founds (OTKA 777 and OTKA T-16748) and the Swedish National Foundation for Reseach and Development ("EK). Physica Scripta T69 2. Electron-phonon scattering For electron-phonon scattering, two conditions must be satisfied : 1. In real space, the electron and phonon distances should be small enough for the interaction. 2. In k-space, the interaction should satisfy the energy and momentum conservation laws. The phonon propagation velocity is approximately equal to the velocity of sound vs (in the Si crystal, about 104m/s). For a structure having a characteristic length L, the phonon transition time is given by L VS zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG TZ-. (2.1) For a characteristic length L = 200nm, this time is about 20 ps. The Monte-Carlo simulation time step usually is less than 10- l4 s, therefore the phonon transition requires more than 2000 simulation steps. Consequently, it is reasonable to assume that the movement (displacement) of phonons from their initial place during the simulation is imperceptible. This means that they can be considered to befrozen in place during the simulation. 2.1. Energy considerations The simulated MOS transistor structure is divided into rec- tangular cells having dimensions Ax, Ay, Az, This mesh is used for the solution of the Laplace equation to determine the potential arising from external voltages, and for the solution of the heat conduction equation. The lattice con- stant of Si is aSi = 0.543nm, and each elementary cell (volume of a&) consists of 8 atoms. Thus, the number of Si Fig. 1. The examined MOS transistor structure.