An Efficient Impact Ionization Model for Silicon Monte Carlo Simulation

In modern VLSI technologies, submicron MOSFET devices are used in high speed as well as high performance circuits. Reducing the device dimensions without a corresponding reduction in the internal potential gives rise to so-called "hot-carrier effects", which are the major threat to device reliability. To fully understand these effects, Monte Carlo (MC) methods have been used intensively in recent years due to the fact that the charge carriers inside the devices are simulated directly and the complete physics can be obtained. Since the impact ionization (II) plays a major role in hot-carrier phenomenon, physically sound modeling of II is essential. But with its intensive CPU requirement, engineers still prefer to used simpler tools such as Hydrodynamic equations (HD) or Drift-Diffusion (DD) equations for devices design. To make a trade off between CPU time and physics, we use MC to develop a so-called Tail Electron Hydrodynamic Equations (TEHD) (see reference [2]), which is used to describe the transport properties specifically for tail electrons which are responsible for the II events. With good II model in MC, not only can we benefit from it by directly doing MC simulations for devices but also we can get good modeling parameters for TEHD.

In this project, we first developed the II model for the isotropic band structure using the complete II model for the full band structure of Silicon (See reference [1]). This II model we developed not only preserved the same scattering rate at each iso-energy surface in the first Brillouin zone of the electron momentum space as the full band one but also make the II model consistent with the isotropic band used. By tuning the deformation potentials of phonons, the MC can fit to several experimental data sets, such as drift velocity, II coefficient and quantum yield. Then we use this MC to study and further model the TEHD under nonhomogeneous (N+-I-N+ structure) as well as homogeneous (Silicon bar) electric fields. With proper modeling using a closed set of parameters (e.x. tail electron concentration n2, etc.), we can get the same II generation rate as MC not only in the channel region but also in the drain region where the hot electrons are embedded in the cool electron sea.

In conclusion, the II model of this work uses the results of accurate calculations based on the full band structure in the frame of a more simplified silicon isotropic band structure. This model is able to well reproduce several available experiment data. For TCAD usage, TEHD which is especially useful for hot carrier transport has been developed using this MC model. With proper modeling from MC, TEHD can describe tail electron and II phenomenon as well as MC and it makes TCAD for devices design more reliable and attractive.

References:
[1]. C.-S. Yao et al., "An Efficient Impact Ionization Model for Silicon Monte Carlo Simulation", VPAD93, pp. 42-43, 1993.

[2]. J.-G. Ahn et al., "A New Hydrodynamic Model for High Energy Tail Electrons", VPAD93, pp. 28-29, 1993.

Chiang-Sheng Yao(yao@gloworm.Stanford.EDU)
AEL 231
Integrated Circuits Laboratory
Stanford University
Stanford, CA 94305-4055